TITLE

PARTICLE SHAPE QUANTITIES AND INFLUENCE ON GEOTECHNICAL

PROPERTIES ndash A REVIEW

Juan Manuel Rodriguez Zavala

Division of Mining and Geotechnical Engineering

Department of Civil Environmental and Natural Resources

Lulearing University of Technology

i

PREFACE

The work in this report has been carried out at the Division of Mining and

Geotechnical Engineering at Lulearing University of Technology

In this new journey now as a PhD student I have face new questions and

challenges that have improved myself not only as a student but also as a person It

has been not easy but the fellowship environment with professors students

technicians etc all in general friends benefits the daily discussion and the

interchange of ideas

The intention of the report is to build up a starting point from where the research

on particle shape developed by the author will take place It is also the intention to

present the general overview on particle shape research and make it understandable

for all readers Particle shape research is a wide area and the author focus the report

in Geotechnical Engineering The report has been split in chapters with the

intention to describe first how the measurements were developed in time and

according with authors follow by the techniques used to measure the particlersquos

dimensions It is also included those properties found in literature affected by the

particlersquos shape Finally findings are discussed with the proper conclusion

I appreciate the time taken by my supervisors Sven Knutsson and Tommy Edeskaumlr

to address me in the right direction the support they always gave me and they for

sure will give me in the near future I also must be grateful to my colleague Jens

Johansson who previous work experience on the image analysis and discussions

has been of great value and help

I would like to thank my family by the support they gave me this last two years in

the work and the joy they provide me during our spare time I understand it has not

been easy for them ether and I appreciate them effort

Juan Rodriguez

Lulearing 2012

ii

ABSTRACT

It has been shown in the early 20th

century that particle shape has an influence on

geotechnical properties Even if this is known there has been only minor progress

in explaining the processes behind its performance and has only partly

implemented in practical geotechnical analysis

This literature review covers different methods and techniques used to determine

the geometrical shape of the particles as well as reported effects of shape on

granular material behaviour

Particle shape could be classifying in three categories sphericity - the overall

particle shape and similitude with a sphere roundness - the description of the

particlersquos corners and roughness - the surface texture of the particle The categories

are scale dependent and the major scale is to sphericity while the minor belongs to

roughness

Empirical relations and standards had been developed to relate soil properties eg

internal friction angle minimum and maximum void ratio density permeability

strain with the particle shape The use of the relations and standards enhance the

bulk material performance eg asphalt mixtures and rail road ballast

The overview has shown that there is no agreement on the usage of the descriptors

and is not clear which descriptor is the best One problem has been in a large scale

classify shape properties Image analysis seems according to the review to be a

promising tool it has many advantages But the resolution in the processed image

needs to be considered since it influence descriptors such as eg the perimeter

iii

1 INTRODUCTION 1

2 AIM AND GOAL 3

3 DESCRIPTION OF SHAPE PROPERTIES 3

31 INTRODUCCTION 3 32 SCALE DEPENDENCE 4 33 FORM (3D) 5 34 FORM (2D) 9 35 ROUNDNESS OR ANGULARITY 11 36 ROUGHNESS OR SURFACE TEXTURE 18

4 TECHNIQUES IN ORDER TO DETERMINE PARTICLE SHAPE 20

41 HAND MEASUREMENT 20 42 SIEVE ANALYSIS 21 43 CHART COMPARISON 21 44 IMAGE ANALYSIS 23

5 EFFECT OF SHAPE ON SOIL PROPERTIES 25

51 INTRODUCTION 25 52 INFLUENCE OF SIZE AND SHAPE 28 53 VOID RATIO AND POROSITY 29 54 ANGLE OF REPOSE 32 55 SHEAR STRENGTH 33 56 SEDIMENTATION PROPERTIES 36 57 HYDRAULIC CONDUCTIVITY PERMEABILITY 37 58 LIQUEFACTION 39 59 GROUNDWATER AND SEEPAGE MODELLING 40

6 DISCUSSION 40

61 TERMS QUANTITIES AND DEFINITIONS 40 62 PROPERTIES 41 63 IMAGE ANALYSIS 42 64 APPLICATIONS 43

7 CONCLUSIONS 43

8 FURTHER WORK 44

9 ACKNOWLEDGMENT 44

10 REFERENCES 44

iv

ABBREVIATIONS Symbol Description Units

A Area of the projected particle area of the particle outline (2D) m2

A1 Area of the projected particle after ldquonrdquo dilatation-erosion cycles m2

AC Area of the smallest circumscribed circle m2

AC2 Area of circle with diameter equal to longest length of outline m2

ACON Convex area m2

AF Sukumara angularity factor -

ANGCON Angles subtending convex parts of the outline degree (ordm)

ANGPLA Angles subtending plane parts of the outline degree (ordm)

a Longest axes diameters of the particle m

B Greatest breadth perpendicular to L m

b Medium axes diameters of the particle m

C Circularity -

CR Convexity ratio -

c Shorter axes diameters of the particle m

Co Cohesion Pa

CPER Convex perimeter m

DA Diameter of a circle equal on area to that of the particle outline m

DAVG Mean average diameter m

DC Diameter of the smallest circumscribed circle in the particle outline m

DCIR Diameter of circumscribed sphere m

DI Diameter of the largest inscribed circle m

DS Diameter of circle fitting sharpest corner (two sharper corners DS1 DS2) m

DSV Diameter of a sphere of the same volume as particle m

DX Diameter of a pebble particle through the sharpest corner DS m

d Grain diameter (average) m

dN Nominal diameter diameter of a sphere of the same volume as the natural

particle

m

e Void ratio

F Angularity factor -

FR Fullness ratio -

g Gravitational acceleration ms2

I Intermediate axis m

k Hydraulic conductivity ms

L Longest axis of the outline m

N Number of corners (items counted) or number of divisions -

n Porosity -

P Perimeter of the projected particle perimeter of outline (2D) m

PC Perimeter of a circle of same area as particle outline m

PCON Sum of perimeter of all convex parts m

PCD Perimeter of circle of same area as drainage basin m

PD Perimeter of a drainage basin m

PI Particle index -

R Roundness -

RAVG Mean average radio of the pebble m

RCON Radius of curvature of the most convex part m

Re Reynolds number -

Rmax-in Radius of the maximum inscribed circle m

Rmin-cir Radius of the minimum circumscribed circle m

RO Roughness or surface texture -

Re Equivalent roughness of particle -

R1 Equation for predicting the settling velocity of sphere -

R3 Equation for predicting the ratio of the settling velocity of an angular

particle to that of a well-rounded particle

-

ri Radius of curvature of the corner ldquoirdquo m

S Actual surface area of the particle m2

v

Symbol Description Units

Se Equivalent strength of particle -

Ss Specific surface area -

SF Sukumara shape factor -

Sm Short axis ldquocrdquo in minimum projection plane m

s Surface area of a sphere of the same volume as the particle m2

sD Specific gravity of the sediment given by the relation density of

sedimentfluid

-

R2 Equation for predicting the ratio of the settling velocity of a non-spherical

well-rounded particle to be settling velocity of a sphere with the same

dimensionless nominal diameter

-

S Dimensionless fluid-sediment parameter -

V Total volume of soil m3

VCIR Volume of circumscribed sphere m3

Ve Velocity ms

VP Volume of particle m3

Vs Volume of voids m3

Vv Volume of solid m3

V10 voids in the aggregate compacted with 10 blows per layer -

V50 voids in the aggregate compacted with 50 blows per layer -

W Weight of the particle ton

WS Settling velocity ms

W Dimensionless settling velocity -

Y Constant to obtain by fitting to experimental data for certain ranges of S -

Z Constant to obtain by fitting to experimental data for certain ranges of S -

x Distance of the tip of the corner from the center of the maximum inscribed

circle

mm

α Measured angle degree (ordm)

αi Sakamura angles used to describe shape degree (ordm)

βi Sakamura angles used to describe angularity degree (ordm)

Σ Summation -

Ψ Sphericity -

ν Kinematics viscosity m2s

φb Basic friction angle degree (ordm)

φcs Friction angle critical state degree (ordm)

φmc Friction angle maximum contraction degree (ordm)

φrep Angle of repose degree (ordm)

φ Peak friction angle Pa

τ Shear strength Pa

σc Compressive strength Pa

σn Normal stress Pa Angle of internal friction degree (ordm)

μ Viscosity Pamiddots

μF Friction coefficient -

p Pressure drop -

ρ Density of water tonm3

ρp Density of the particle tonm3

υ Specific discharge ms

1

1 INTRODUCTION

Effects on soil behaviour from the constituent grain shape has been suggested since

the earliest 1900rsquos when Wadell (1932) Riley (1941) Pentland (1927) and some

other authors developed their own techniques to define the form and roundness of

particles Into the engineering field several research works conclude that particle

shape influence technical properties of soil material and unbound aggregates

(Santamarina and Cho 2004 Mora and Kwan 2000) Among documented properties

affected by the particle shape are eg void ratio (porosity) internal friction angle and

hydraulic conductivity (permeability) (Rouseacute et al 2008 Shinohara et al 2000

Witt and Brauns 1983) In geotechnical guidelines particle shape is incorporated in

eg soil classification (Eurocode 7) and in national guidelines eg for evaluation of

friction angle (Skredkommisionen 1995) This classification is based on ocular

inspection and quantitative judgement made by the individual practicing engineer

thus it can result in not repeatable data In evaluation of eg standard penetration test

Holubec and DrsquoAppolonia (1973) are suggesting the inclusion of the particle shape in

the evaluation of the data According with Folk (1955) the form error is negligible but

it is not in the second sub-quantity related with the corners (roundness) These

systems are not coherent in definitions The lack of possibility to objectively describe

the shape hinders the development of incorporating the effect of particle shape in

geotechnical analysis

The interest of particle shape was raised earlier in the field of geology compared to

geotechnical engineering Particle shape is considered to be the result of different

agentrsquos transport of the rock from its original place to deposits since the final pebble

form is hardly influenced by these agents (rigor of the transport exfoliation by

temperature changes moisture changes etc) in the diverse stages of their history

Furthermore there are considerations regarding on the particle genesis itself (rock

structure mineralogy hardness etc) (Wentworth 1922a) The combination of

transport and mineralogy factors complicates any attempt to correlate length of

transport and roundness due that soft rock result in rounded edges more rapidly than

hard rock if both are transported equal distances According to Barton amp Kjaernsli

(1981) rockfill materials could be classified based on origin into the following (1)

quarried rock (2) talus (3) moraine (4) glacifluvial deposits and (5) fluvial deposits

Each of these sources produces a characteristic roundness and surface texture

Pellegrino (1965) conclude that origin of the rock have strong influence determining

the shape

To define the particle form (morphology) in order to classify and compare grains

many measures has been taken in consideration (axis lengths perimeter surface area

volume etc) Probably when authors had developed the form descriptors realize that

they hadnrsquot provide enough information about the corners they could be angular or

rounded (roundness) thus the authors also focus on develop techniques to describe

them Furthermore the corners or the general surface can be rough or smooth (surface

texture) Nowadays some authors (Mitchell amp Soga 2005 Arasan et al 2010) are

using these three sub-quantities one and each describing the shape but a different

scale (form roundness surface texture)

2

During the historical development of shape descriptors the terminology has been used

differently among the published studies terms as roundness (because the roundness

could be apply in the different scales) or sphericity (how the particle approach to the

shape of a sphere) were strong (Wadell 1933 Wenworth 1933 Teller 1976 Barrett

1980 Hawkins 1993) and it was necessary in order to define a common language on

the particle shape field unfortunately still today there is not agreement on the use of

this terminology and sometimes it make difficult to understand the meaning of the

authors thatrsquos why it is better to comprehend the author technique in order to

misinterpret any word implication

Several attempts to introduce methodology to measure the particlersquos shape had been

developed over the years Manual measurement of the particles form is

overwhelming thus visual charts were developed early to diminish the measuring

time (Krumbein 1941 Krumbein and Sloss 1963 Ashenbrenner 1956 Pye and Pye

1943) Sieving was introduced to determine the flakinesselongation index but it is

confined only for a certain particle size due the practical considerations (Persson

1988) More recently image analysis on computer base has been applied on sieving

research (Andersson 2010 Mora and Kwan 2000 Persson 1998) bringing to the

industry new practical methods to determine the particle size with good results

(Andersson 2010) Particle shape with computer assisted methods are of great help

reducing dramatically the measuring time (Fernlund 2005 Kuo and Freeman 1998a

Kuo et al 1998b Bowman et al 2001)

In the civil industry eg Hot Asphalt mixtures (Kuo and Freeman 1998a Pan et al

2006) Concrete (Mora et al 1998 Quiroga and Fowle 2003) and Ballast

(Tutumluer et al 2006) particlersquos shape is of interest due the materialrsquos performance

thus standards had been developed (see appendix A) On asphalt mixtures limits of

flat and elongated particles or the amount of natural sands typically are incorporated

into specifications flat and elongated particles tend to cause problems with

compaction particle breakage loss of strength and segregation in pavement (Kuo and

Freeman 1998a) Rutting resistance of asphalt concrete under traffic and

environmental loads depend on the stability of aggregates structure in the asphalt mix

(Pan et al 2006) According with the American Railway Engineering and

Maintenance of Way Association (AREMA) ballast aggregate should be open graded

with hard angular shaped particles providing sharp corners and cubical fragments

with a minimum of flat and elongated pieces (Tutumluer et al 2006) The American

standard ASTM D 3398 (test method for index of aggregate particle shape and

texture) is an example of an indirect method to determine particle shape (see appendix

A) Aggregate characteristics of shape texture and grading influence workability

finishability bleeding pumpability and segregation of fresh concrete and affect

strength stiffness shrinkage creep density permeability and durability of hardened

concrete In fact flaky elongated angular and unfavorably graded particles lead to

higher voids content than cubical rounded and well-graded particles (Quiroga and

Fowle 2003)

Sieving is probably the most used method to determine the particle size distribution it

consist of plotting the cumulative weight of the weighted material retained by each

mesh (European standard EN 933-1 1992) This traditional method according to

Andersson (2010) is time consuming and expensive Investigations shows that the

traditional sieving has deviations when particle shape is involve the average volume

3

of the particles retained on any sieve varies considerably with the shape (Lees

1964b) thus the passing of the particles depend upon the shape of the particles

(Fernlund 1998) In some industries the Image analysis is taking advantage over the

traditional sieving technique regardless of the intrinsic error on image analysis due the

overlapping or partial hiding of the rock particles (Andersson 2010) In this case the

weight factor is substitute by pixels (Fernlund et al 2007) Sieving curve using

image analysis is not standardized but after good results in the practice (Andersson

2010) new methodology and soil descriptions could raise including its effects

2 AIM AND GOAL

The aim of this report is to review the state of the art on how to describe particle

shape of individual grains of geotechnical material and knowledge on the influence of

shape in geotechnical properties

The goals in this study are to

Describe discuss and compare particle shape and definitions

Review the known effect of particle shape on soil mechanics parameters

Discuss the potential of the role of particle shape in soil mechanics

Focus in this study has been on 2 dimensional shape definitions

The content of the report is based upon published and peer reviewed papers in

English

3 DESCRIPTION OF SHAPE PROPERTIES

31 INTRODUCCTION

Particle shape description can be classified as qualitative or quantitative Qualitative

describe in terms of words the shape of the particle (eg elongated spherical flaky

etc) and quantitative that relates the measured dimensions in the engineering field

the quantitative description of the particle is more important due the reproducibility

Quantitative geometrical measures on particles may be used as basis for qualitative

classification There are few qualitative measures in contrast with several quantitative

measures to describe the particle form Despite the amount of qualitative descriptions

none of them had been widely accepted but there are some standards (eg ASTM

D5821 EN 933-3 and BS 812) specifying mathematical definitions for industrial

purposes

Shape description of particles is also divided in

o 3D (3 dimensions) it could be obtained from a 3D scan or in a two

orthogonal images and

o 2D (2 dimensions) or particle projection where the particle outline is drawn

4

3D and 2D image analysis present challenges itself 3D analysis requires a

sophisticated equipment to scan the particle surface and create the 3D model or the

use of orthogonal images and combine them to represent the 3 dimensions The

orthogonal method could present new challenges as the minimum particle size or the

placing in orthogonal way of the particles (Fernlund 2005) 2D image analysis is easy

to perform due the non-sophisticated equipment required to take pictures (eg regular

camera or the use of microscope for smaller particles) In 2D image analysis the

particle is assumed to lay over its more stable axis (eg longest and intermediate axis

lie more or less parallel to the surface while the shortest axis is perpendicular) or

random some authors publish their own preferences about this issue (Wadell 1935

Riley 1941 Hawkins 1993)

32 SCALE DEPENDENCE

In order to describe the particle shape in detail there are a number of terms quantities

and definitions used in the literature Some authors (Mitchell amp Soga 2005 Arasan et

al 2010) are using three sub-quantities one and each describing the shape but at

different scales The terms are morphologyform roundness and surface texture In

figure 1 is shown how the scale terms are defined

At large scale the particlersquos diameters in different directions are considered At this

scale describing terms as spherical platy elongated etc are used An often seen

quantity for shape description at large scale is sphericity (antonym elongation)

Graphically the considered type of shape is marked with the dashed line in Figure 1

At intermediate scale it is focused on description of the presence of irregularities

Depending on at what scale an analysis is done corners and edges of different sizes

are identified By doing analysis inside circles defined along the particlersquos boundary

deviations are found and valuated The mentioned circles are shown in Figure 1 A

generally accepted quantity for this scale is roundness (antonym angularity)

Regarding the smallest scale terms like rough or smooth are used The descriptor is

considering the same kind of analysis as the one described above but is applied

Figure 1 Shape describing sub quantities (Mitchell amp Soga 2005)

5

within smaller circles ie at a smaller scale Surface texture is often used to name the

actual quantity The sub-quantities and antonyms are summarized in table 1

Table 1 Sub-quantities describing the particlersquos morphology and its antonym

Scale Quantity Antonym

Large scale Sphericity Elongation

Intermediate scale Roundness Angularity

Small scale Roughness Smoothness

33 FORM (3D)

Wentworth in 1922 (Blott and Pye 2008) was probably one of the first authors on

measure the particle dimensions this consisted on the obtaining of the length of the

tree axes perpendicular among each other (see figure 2) on the tree dimensions (where

agebgec) to obtain the sphericity (equation 1)

Krumbein (1941) develop a rapid method for shape measurement to determine the

sphericity this is done by measuring the longest (a) medium (b) and shorter (c) axes

diameters of the particle it can be seen in figure 2 (Always perpendicular among each

other) The radios ba and cb are located in the chart developed by his own where it

can be found the Intercept sphericity as he called (See figure 3) This chart is an easy

graphical way to relate the dimensions

c2

ba

Figure 2 Measurement of the 3 axes perpendicular among each other (Krumbein 1941)

Figure 3 Detailed chart to determining Krumbein intercept sphericity (Krumbein 1941)

(1)

6

Wadell (1932) defined the sphericity as the specific surface ratio (equation 2) Figure

4 is a schematic representation of the sphere surface and particle surface both particle

and sphere of the same volume

This way to obtain the sphericity is almost impossible to achieve as Hawkins (1993)

declares due the difficulty to get the surface area on irregular solids

Wadell (1934) also defined the sphericity based upon the particle and sphere volumes

as equation 3 (see figure 5)

Wadell (1934) used a new formula simple to manage using the diameters (see figure

6 and equation 4)

Zingg (Krumbein 1941) develop a classification based on the 3 axes relation in this

way it is easy to find out the main form of the particles as a disks spherical blades

S

s

3

CIR

P

V

V

CIR

SV

D

D

Figure 4 Same volume sphere surface (s) and particle surface (S) (modified after Johansson and Vall

2011)

Figure 5 Relation between the volume of the particle and the volume of the circumscribed

sphere (Johansson and Vall 2011)

Figure 6 Figure is showing the relation between the diameter of a circumscribed sphere and the

diameter of a sphere of the same volume as the particle (Johansson and Vall 2011)

(2)

(3)

(4)

7

and rod-like this is summarized on figure 7 Zinggrsquos classification is related with

Krumbein intercept sphericity and the figure 3

In figure 8 the figures 3 and 7 are combined the relation in the two classifications can

be seen it is an easy way to understand the morphology regarding on the a b and c

dimensions

Pye and Pye (1943) in the article ldquosphericity determinations of pebbles and sand

grainsrdquo compare the Wadellrsquos sphericity developed in 1934 (based on the diameter)

with ldquoPebble sphericityrdquo based on an ellipse this last equation (number 5) appears

two years early published by Krumbein (1941) Axis measurement is done as figure 1

denotes for equations 5 trough 12 with exception of equation 8 where the original

document was not possible to obtain

32a

cb

Figure 7 Zinggrsquos classification of pebble shape based on ratios ba and cb (Krumbein 1941)

Figure 8 Classification made by Zinggrsquos and chart to determine sphericity (Krumbein and Sloss 1963)

(5)

8

Sneed amp Folk in (1958) found a relation between the tree dimensional axes called

ldquoMaximum Projection Sphericityrdquo

In a similar way Ashenbrenner (1956) showed his equation at that time named

ldquoWorking Sphericityrdquo

Form or shape factor names are used by authors like Corey (shape factor eq 8) in the

paper published on 1949 Williams (shape factor eq 9) in 1965 Janke (form factor

eq 10) in 1966 and Dobkins amp Folk (oblate-prolate index eq 11) in 1970 (Blott and

Pye 2008)

Aschenbrenner (1956) develop the shape factor by using the relation of the tree axis

but the square of the middle one

3

2

ba

c

))ab((1)bc(16))ab((cb)(11

)ab()bc( 128

22

3 2

ab

c

acb when 1ac

b acb when

b

ac-1 2

22

2

3

cba

c

222

a

c

50c-a

b-a10

2b

ac

(6)

(7)

(8)

(9)

(10)

(11)

(12)

9

Table 2 General overview over different particle shape definitions for 3D sphericity has been compiled

and arranged chronologically

Aspect Name Author Year Based on

Sphericity (3D) Flatness index Wentworth 1922a 3-axes

True Sphericity Wadell 1932 Surface

Operational sphericity Wadell 1932 Volume

Sphericity Wadell 1934 Sphere diameter

Zinggrsquos clasification Zinggrsquos1

1935 3-axes

Intercept sphericity chart Krumbein 1941 3-axes

Pebble sphericity Pye and Pye 1943 3-axes

Corey shape factor Corey2

1949 3-axes

Working sphericity Ashenbrenner 1956 3-axes

shape factor Ashenbrenner 1956 3-axes

Maximum projection sphericity Sneed amp Folk 1958 3-axes

Williams shape factor Williams2

1965 3-axes

Janke form factor Janke2

1966 3-axes

Oblate-prolate index Dobkins amp Folk 1970 3-axes 1) Krumbein and Sloss 1963 2) Blott and Pye 2008

34 FORM (2D)

The technique to measure the sphericity is based in tree dimensions it can be found in

literature some ways to measure the ldquotwo dimensions sphericityrdquo which is simply the

perimeter of the particle projection some authors named ldquoparticle outlinerdquo or

ldquocircularityrdquo

Wadell in 1935 (Hawkins 1993) adopt a conversion of his 1934 3D sphericity

formula (equation 4) to a 2D outline He defined an orientation on the particles and

they were based on the maximum cross sectional area (outline of the particle

projecting the maximum area) The equations show the relation between diameters of

a circle of same area and smallest circumscribed circle

He also used the term ldquodegree of circularityrdquo as the ratio of the perimeter of a circle of

same area and the actual particle perimeter

Tickell in 1931 (Hawkins 1993) used his empirical relation The particle orientation

proposed was a random one It is described by the ratio between the area outline and

the area of smallest circumscribed circle

C

A

D

DC

P

PC C

CA

AC

(13)

(14)

(15)

10

Some other authors has been working with the ldquocircularityrdquo concept and had develop

them own equations as Pentland (1927) relating the area outline and area of a circle

with diameter equal to longest length outline and Cox (Riley 1941) with the ratio

area and perimeter time a constant equations 16 and 17 respectively Both authors did

not define any definite orientation of the grains

Riley (1941) realize the problems that an area perimeter and some other

measurements proposed by the above authors can carry as the time consuming and

tedious work (at that time were not computer all was made by hand) and thatrsquos why

he develop this equation easy to handle called ldquoinscribed circle sphericityrdquo He used

the same particle orientation proposed by Wadell and the relation of diameters of

inscribed and circumscribed circles

Horton 1932 (Hawkins 1993) use the relation of the drainage basing perimeter and

the perimeter of a circle of the same area as drainage basin

Janoo in 1998 (Blott and Pye 2008) develop his general ratio of perimeter to area

Sukumaran and Ashmawy (2001) develop his own shape factor (SF) defined as the

deviation of the global particle outline from a circle Figure 9 can be used as a

reference to determine the items used in the equation 21

N is referred to the number of sampling intervals o radial divisions

C2A

AC

2P

A4C

C

I

D

DC

CD

D

P

PC

A

PC

2

45ordm x N

Particleα

= SF

sumN

1=ii

(16)

(17)

(18)

(19)

(20)

(21)

11

Table 3 General chronological overview of the particle shape definitions for 2D sphericity

Aspect Name Author Year Based on

Circularity (2D) roundness Pentland 1927 area

roundness Cox1

1927 area-perimeter

roundness Tickell2

1931 area

Circularity Horton2

1932 drainage basin

outline circularity Wadell 1935 Circle diameter

degree of circularity Wadell 1935 Perimeter

inscribed circle sphericity Riley 1941 Circle diameter

Circularity Krumbein and Sloss 1963 chart

Janoo 1998 area-perimeter

Shape factor Sukumaran 2001 Segmentation of particle and angles

1) Riley 1941 2) Hawkins 1993

35 ROUNDNESS OR ANGULARITY

Roundness as described in section 32 is the second order shape descriptor Sphericity

lefts beside the corners and how they are this was notice by most of the authors sited

before and they suggested many ways to describe this second order particle property

Roundness is clearly understandable using the figure 10 Particle shape or form is the

overall configuration and denotes the similarities with a sphere (3D) or a circle (2D)

Roundness is concerning about the sharpness or the smoothness of the perimeter (2D)

Surface texture (Barret 1980) is describe as the third order subject (form is the first

and roundness the second) and it is superimposed in the corners and it is also a

property of particles surfaces between corners

Figure 9 Description of the Sukumaran factors to determine the shape and angularity (Sukumaran and

Ashmawy 2001)

12

Wadell (1935) describes his methodology calling it total degree or roundness to

obtain the roundness of a particle using the average radius of the corners in relation

with the inscribed circle diameter (see figure 11) on the equation

In the same study Wadell (1935) has used the equation

This two last equation shows slightly differences on the results (Wadell 1935)

Powers (1953) also published a graphic scale to illustrate the qualitative measure

(figure 12) It is important to highlight that any comparing chart to describe particle

properties has a high degree of subjectivity Folk (1955) concludes that when charts

are used for classification the risk of getting errors is negligible for sphericity but

large for roundness

N

R

r

Rinmax

r

R

NR

inmax

Figure 10 Form (shape) Roundness and Texture graphical description (Bowman et al 2001)

Figure 11 Wadellrsquos method to estimate the roundness corners radius and inscribed circle

(Hawkins 1993)

(22)

(23)

13

Some authors as Russel amp Taylor in 1937 Pettijohn in 1957 and Powers in 1953

developed a classification based on five and six classes (Hawkins 1993) each one

with its own class limits it is important to denote that the way they measure the

roundness is the developed by Wadell (1935) This classification and class limits are

showed in the table 4

Table 4 Degrees of roundness Wadell Values (Hawkins 1993) NA = no-applicable

Grade terms Russell amp Taylor (1937) Pettijohn (1957) Powers (1953)

Class

limits (R)

Arithmetic

midpoint

Class limits

(R)

Arithmetic midpoint Class

limits (R)

Arithmetic

midpoint

Very angular

NA

NA

NA

NA

012-017

014

Angular

000-015

0075

000-015

0125

017-025

021

Subangular

015-030

0225

015-025

0200

025-035

030

Subrounded

030-050

0400

025-040

0315

035-049

041

Rounded

050-070

0600

040-060

0500

049-070

059

Well rounded

070-100

0800

060-100

0800

070-100

084

Krumbein and Sloss (1963) published a graphical chart easy to determine the

sphericity and roundness parameters using comparison See figure 13 (Cho et al

2006)

Figure 12 A Roundness qualitative scale (Powers 1953)

Figure 13 Sphericity and roundness chart (Cho et al 2006) The roundness equation that appears here in

the chart is the wadellrsquos equation number 22

14

Fischer in 1933 (Hawkins 1993) used a straightforward method to quantify roundness

using a central point in the outline and dividing the outline in angles around this point

that were subtended by the straight or non curved parts of the profile were measured

This is illustrated in figure 14

To express the angularity value Fischer used the ratio of angles standing linear parts

on the outlines and concave respectively

Figure 14 left (A) and right (B) gives a similar angularity of approximately 042

using the above equations (Hawkins 1993)

Wentworth in 1922 used the maximum projection to define the position of the particle

to obtain the outline or contour (Barret 1980) The equation reflects the relation of the

diameter of a circle fitting the sharpest corner and the longest axis plus the shortest

axis c (minimum projection)

Wentworth (Hawkins 1993) expressed the roundness as the ratio of the radius of

curvature of the most convex part and the longest axis plus short axis

Actually these last two equations are the same just expressed in different terms when

the particle is in its maximum projection

Dimensions can be seen on figure 15 L and B represents the mayor axis a and

intermediate axis b The intention is to make difference between the 2 and 3

dimensions (L and B are for 2D as a b and c are for 3D)

deg360

ANG

=R

sumPLA

PLA

CON

ANG

ANGR

2)S(L

DR

M

S

B)4(L

RR CON

Figure 14 Fischerrsquos methods of angularity computation (Hawkins 1993)

A=inscribed circle B=circumscribed circle

(24)

(25)

(26)

(27)

15

Wentworth 1919 has a second way to express the roundness called Shape index

(Barrett 1980) and it relates the sharpest corner and the diameter of a pebble trough

the sharpest corner

Wentworth (1922b) used define the roundness as the ratio of the sharpest corner and

the average radius of the pebble

Cailleux (Barrett 1980) relates the radius of the most convex part and the longest

axis

Kuenen in 1956 show his roundness index (Barrett 1980) between the sharpest corner

and the breath axis

Dobkins amp Folk (1970) used a modified Wentworth roundness with the relation of

sharpest corner and inscribed circle diameters

AVG

CON

R

RR

x

s

D

DR

L2

RR CON

B

DR s

i

s

D

DR

3AVGAVG cbaDR2

Figure 15 Description of L and B axes (Hawkins 1993)

(28)

(29)

(30)

(31)

(32)

(33)

16

Swan in 1974 shows his equation (Barrett 1980) relating the sharpest (or the two

sharpest) corner(s) and inscribed circle diameter

Szadeczsky-Kardoss has his Average roundness of outline (Krumbein and Pettijohn

1938) relating the concave parts perimeter and the actual perimeter

Lees (1964a) developed an opposite definition to roundness it means that he

measures the angularity instead of the roundness and he calls it Degree of angularity

Figure 16 shows the items considered when equation 36 applies as the angles (α)

inscribed circle (Rmax-in) and the distance (x) The main formula is

In order to apply the last equation corners needs to be entered in the formula and each

individual result will add to each other to obtain the final degree of angularity

A roundness index appears on Janoo (1998) Kuo and Freeman (1998a) and Kuo et

al (1998b) it is described as

The last equation is on section 34 also because there is not a general agreement on the

definition furthermore some authors had used to define the roughness this is not the

only equation that has been used trying to define different aspects (sphericity

roundness or roughness) but it is a good example of the misuse of the quantities and

definitions

inmaxR

x)180(R

2P

A4R

i

ss

D

DDR

221

100P

PR CON

Figure 16 Degree of angularity measurement technique (Blot and Pye 2008)

(34)

(35)

(36)

(17)

17

Sukumaran and Ashmawy (2001) present an angularity factor (AF) calculated from

the number of sharpness corners Angles βi required to obtain the angularity factor are

shown in figure 9

Sukumaran and Ashmawy (2001) also suggested use not bigger sampling interval of

N=40 because it is the cut off between angularity factor and surface roughness If so

this equation could be used to describe the roughness

Table 5 General chronological overview of the particle roundness

Aspect Name Author Year Based on

Roundness shape index Wentworth 19191

diameter of sharper corner

shape index Wentworth 1922b sharpest corner and axis

roundness Wentworth 1933 convex parts

Fischer 19332

noncurved parts outline

Fischer 19332

noncurved-streigth parts outline

Average roundness of outline

Szadeczsky-Kardoss 19333

convex parts-perimeter

roundness Wadell 1935 diameter of corners

roundness Wadell 1935 diameter of corners

roundness Russel amp Taylor 19372

class limit table

roundness Krumbein 1941 chart

Cailleux 19471

convex parts

roundness Pettijohn 19494 class limit table

roundness Powers 1953 chart and class limit table

Kuenen 19561

axis-convex corner

roundness Krumbein and Sloss 1963 chart

degree of angularity Lees 1964a corners angles and inscribed circle

Dobkins amp Folk 1970 diameter of sharper corner

Swan 19741

diameter of sharper corners

Angularity factor Sukumaran and

Ashmawy 2001

Segmentation of particles and angles

1) Barret 1980 2) Hawkins 1993 3) Krumbein and Pettijohn 1938 4) Powers 1953

sum

sumsumN

1=i

2

i

2

N

1=i

2

i

2N

1=ii

)ordm180 -circleβ( - )(180ordm x 3

)ordm180-circleβ(-)ordm180 -Particleβ(

= AF (37)

18

36 ROUGHNESS OR SURFACE TEXTURE

A third property called texture appears early in the literature with the sphericity and

roundness properties since then texture property was longed described but it was in

accordance with the authors at that time not measurable

Wright in 1955 developed a method to quantify the surface texture or roughness of

concrete aggregate using studies done on 19 mm stones The test aggregates were first

embedded in a synthetic resin The stones were cut in thin sections The sections

projection was magnified 125 times The unevenness of the surface was traced and the

total length of the trace was measured The length was then compared with an uneven

line drawn as a series of chords (see figure 17) The difference between these two

lines was defined as the roughness factor (Janoo 1998)

However with the advance of technology it has become easier measure the roughness

and here is presented some researcherrsquos ideas how this property should be calculated

One technique used by Janoo (1988) to define the roughness can be seen in figure 18a

and is defined as the ratio between perimeter and convex perimeter

The convex perimeter is obtained using the Feretrsquos box (or diameter) tending a line in

between the touching points that the Feretrsquos box describes each time it is turn (figure

18b)

PER

OC

PR

Figure 17 Measurement method for characterizing the surface texture of an aggregate (Janoo 1998)

a) Convex perimeter (CPER) b) Feret measurement Figure 18 a) Convex perimeter (CPER) b) Feret measurement (modified after Janoo 1998)

(38)

a)

b)

19

Kuo and Freeman (1998a) and Kuo et al (1998b) use the roughness definition as the

ratio perimeter and average diameter

Erosion and dilatation image processing techniques are used to obtain the surface

texture Erosion is a morphological process by which boundary image pixels are

removed from an object surface which leaves the object less dense along the

perimeter or outer boundary Dilatation is the reverse process of erosion and a single

dilatation cycle increases the particle shape or image dimension by adding pixels

around its boundary (Pan etal 2006)

The ldquonrdquo erosion and dilatation cycles are not standardized

Mora and Kwan (2000) used the ldquoconvexity ratio CRrdquo (equation 41) and the ldquofullness

ratio FRrdquo (equation 42) in their investigation they are

The convex area is the area of the minimum convex boundaries circumscribing the

particle This is illustrated in the figure 19 The convex area is obtained in a similar

way as the convex perimeter but in this case the area between the original outline and

the convex perimeter is our convex area

AVG

OD

PR

100A

1AARO

CONo A

AR =

CONo A

AR =

Figure 19 Evaluation of area and convex area (Mora and Kuan 2000)

(39)

(40)

(41)

(42)

20

4 TECHNIQUES IN ORDER TO DETERMINE PARTICLE

SHAPE

41 HAND MEASUREMENT

Hand measurement technique was the first used by obvious reasons in order to

improve the accuracy special devices developed as the ldquosliding rod caliperrdquo used by

Krumbein (1941) it works placing the sample on the sliding road calliper as show

figure 20b the length in different positions can be obtain by using the scale provided

in the handle the ldquoconvexity gagerdquo that was actually used by opticians to measure the

curvature of lenses but easily applicable to the particle shape analysis (Wentworth

1922b) works measuring the movement of the central pivot as figure 20a shows (the

two adjacent pivots are invariable) as many the central pivot moves more is the

curvature or the ldquoSzadeczky-Kardossrsquos apparatusrdquo develop in 1933 that traces the

profile of the rock fragment so the outline traced is then analyzed (Krumbein and

Pettijohn 1938) figure 20c show equipment

Another helpful tool to determine the particle dimensions was the ldquocamera lucidardquo to

project the particlersquos contour over a circle scale appearing in Figure 21 thus it is

possible to measure the particlersquos diameter

a)

c) b)

Figure 20 a) convexity gage used to determine the curvature in particle corners (Wenworth 1922b)

b)sliding rod caliper device to measure the particle axis length (Krumbein 1941) and c)Szadeczky-

Kardoss (1933) apparatus it was utilized to obtain the particle outline

Figure 21 Circle scale used by Wadell (1935) to determine particlersquos diameter and roundness

21

42 SIEVE ANALYSIS

Bar sieving eg according to EN 933-31997 can be used to determine simple large

scale properties By combining mesh geometries the obtained results can be used to

quantify flakiness and elongation index ASTM D4791 (Flat and elongated particles

are defined as those coarse aggregate particles that have a ratio of length to thickness

equal to or greater than a specified value such as 51 The index represents the

percentage on weight of these particles) The method is not suitable for fine materials

This due to the difficulty to get the fine grains passed through the sieve and the great

amount of particles in relation to the area of the sieve (Persson 1998) eg EN 933-

31997 related to flakiness index The test is performed on aggregates with grain size

from 4 mm and up to 63 mm two sieving operations are necessary the first separates

on size fraction and the second use a bar sieve after the first sieving the average

maximum diameter of the particles is obtain and with the second sieving (bar sieving)

the shortest axis diameter is found finally with this two parameters the flakiness

index is determined

There are more standards related with the particle shape (see appendix A) but this

above presented are probably the most known using sieve analysis to determine

particlersquos geometrical properties

Sieve analysis is facing the computers age and image analysis sieving research is

taking place (Andersson 2010 Mora and Kwan 2000 Persson 1998) Industry is

also applying the image analysis sieving with decrees on the testing time compare

with the traditional sieving method An inconvenient of image analysis is the error

due the overlapping or hiding of the particles during the capture process but the

advantages are more compare with disadvantages (Anderson 2010)

43 CHART COMPARISON

Charts developed over the necessity of faster results because the long time consuming

required when measuring each particle

Krumbein (1941) present a comparison roundness chart for pebbles which were

measured by Wadellrsquos method because this property was the most difficult to measure

due to the second order scale that roundness represents (See figure 22)

Figure 22 Krumbein (1941) comparision chart for roundness

22

A qualitative chart by Powers (1953) try to include both (sphericity and roundness)

particlersquos characteristics it was divided on six roundness ranges (very angular

angular sub-angular sub-rounded rounded and well rounded) and two sphericity

series (high and low sphericity) This chart was prepared with photographs to enhance

the reader perspective (See figure 23)

A new chart including sphericity and roundness appear this time it was easier to

handle the two mean properties of particlersquos shape furthermore there was included

the numerical values that eliminated the subjectivity of qualitative description The

chart is based on Wadellrsquos definitions (Krumbein and Sloss 1963) (See figure 24)

Folk (1955) worried about the personrsquos error on the chartrsquos comparison studied the

determination of sphericity and angularity (he used the Powers 1953 comparison

chart) he found that the sphericity determination by chart comparison has a negligible

error while the roundness he concluded it was necessary to carry out a more wide

research due the high variability show by his study

Figure 23 Powers (1953) qualitative shpericity-roundness chart

Figure 24 Sphericity-roundness comparison chart (Krumbein and sloss 1963)

23

44 IMAGE ANALYSIS

Image analysis is a practical method to use for shape classification since it is fast and

can be automated Different techniques appear to process these images among them

are

o Feret Diameter the Feret diameter is the longitude between two parallel lines

this lines can rotate around one particle or outline to define dimensions as it

is shown in figure 25 these method is not a fine descriptor but as it was say

above it is a helpful tool to determine diameters (Janoo 1988)

o Fourier Mathematical Technique It produces mathematical relations that

characterize the profile of individual particles This method favours the

analysis of roughness and textural features for granular soils The problem in

the methodology remains in the re-entrant angles in order to complete the

revolution (Bowman et al 2001) see figure 26

o Fractal Dimension Irregular line at any level of scrutiny is by definition

fractal (Hyslip and Vallejo 1997) Figure 27 shows fractal analysis by the

dividing method The length of the fractal line can be defined as

N

1n

nn0 )nsinbncosa(a)(R

RD1n)(P

Figure 25 Feret measurement technique is defined by two parallel lines turning

around the particle to define the shortest and longest Feret diameter (Janoo 1988)

Figure 26 Fourier technique with two radiuses at one angle (Bowman et al 2001)

(43)

(44)

24

o Orthogonal image analysis This technique is basically the use of two images

orthogonal between them to acquire the three particle dimensions (Fernlund

2005) any of the above techniques can be used in this orthogonal way

o Laser Scanning Technique this kind of laser scanning 3D is one of the most

advanced techniques In figures 28a) we have the laser head scanning the rock

particles the particles have control points in order to keep a reference point

when move them to scan the lower part in figure 28b) we can see the laser

path followed (Lanaro and Tolppanen 2002)

Another technique is the Laser-Aided Tomography (LAT) in this case a laser sheet is

used to obtain the particles surveying (see figure 29) This technique is different and

has special requirements as to use liquid with same refractive index as the particles

particles must let the laser or certain percent of light go through (Matsushima et al

2003)

a) b)

Figure 27 Fractal analysis by the dividing method at different scrutiny scale (Hyslip and Vallejo 1997)

Figure 28 a) Scanning head b) scanning path (Lanaro and Tolppanen 2002)

Figure 30 3D scan completed ready to

use for any further measure

(Matsushima et al 2003)

Figure 29 LAT scaning particles

(Matsushima et al 2003)

25

Both 3D techniques obtain the particle shape that is later used to achieve measures as

we can see in figure 30

All these previous techniques are easily written in codes or scripts to be interpreted in

a digital way obtaining the desired measurement but there are some interesting points

in the image analysis regarding on the errors involve among them are image

resolution and orientation of the particles orientation is not relevant when it is

random and large number of particles are involve resolution have an influence on the

accuracy (Zeidan et al 2007)

When resolution is increase more accuracy is obtain and the object representation

match better with the real form in the other hand more resolution means more

spending on memory and time thus resolution needs to be according with the goal

and precision needed in any work (Schaumlfer 2002)

Schaumlfer (2002) conclude that attributes like length when measuring digital images

present relative high errors It can be vanish or at least diminish using high resolution

just for diameter but not for perimeter that keep the error as big as initially Johansson

and Vall (2011) obtain similar results when 3 different resolutions were used in the

same particle obtaining an unstable output for those termsquantities that involve the

perimeter Thus all quantities relating the perimeter should be treated with care

5 EFFECT OF SHAPE ON SOIL PROPERTIES

51 INTRODUCTION

In laboratory test on the effect on particle size on basic properties has been

investigated in several studies this relation has been discussed and various

mechanisms had been proposed to explain the behaviour of the soil in dependency

also with the shape Basically there are two mechanisms proposed The arrangement

of particles and the inter-particle contact (Santamarina and Cho 2004) and

subsequence breakage

The arrangement of particles

Arrangement of the particles can be presented in three different forms loose dense

and critical this arrangement determines the soil properties (eg density increase with

more dense arrangement) Loose and dense states are easy understandable when

figure 31 is explained while in the upper part of the figure the particles are arranged

using the minimum space needed in the lower part a span is created using the flaky

particle as a bridge this phenomena is known as ldquobridgingrdquo Bridging can produce

different geotechnical results when just the shape of the particle is changed eg void

ratio (Santamarina and Cho 2004) Particles are able to rearrange this could be done

applying pressure (energy) to the soil the pressure (energy) will create such forces

that soil particles will rotate and move (see figure 34) finishing in a more dense state

26

A loose soil will contract in volume on shearing and may not develop any peak

strength (figure 32 left) In this case the shear strength will increase gradually until

the residual shear strength is revealed once the soil has ceased contracting in volume

A dense soil may contract slightly (figure 32 right) before granular interlock prevents

further contraction (granular interlock is dependent on the shape of the grains and

their initial packing arrangement) In order to continue shearing once granular

interlock has occurred the soil must dilate (expand in volume) As additional shear

force is required to dilate the soil a peak shear strength occurs (figure 32 left) Once

this peak shear strength caused by dilation has been overcome through continued

shearing the resistance provided by the soil to the applied shear stress reduces

(termed strain softening) Strain softening will continue until no further changes in

volume of the soil occur on continued shearing Peak shear strengths are also

observed in overconsolidated clays where the natural fabric of the soil must be

destroyed prior to reaching constant volume shearing Other effects that result in peak

strengths include cementation and bonding of particles The distinctive shear strength

called the critical state is identified where the soil undergoing shear does so at a

constant volume (Schofield and Wroth 1968)

The inter-particle contact

For frictional soil ie coarse grained soil the friction between particles is the

dominating factor for strength Materials usually consisting of coarse grains (diameter

Figure 31 Bridging effect when flaky particles are combined in the bulk material (Santamarina and

Cho 2004)

Figure 32 The left part of the figure show a typical behaviour of loose and dense material over shear stress

while at the right the figures illustrate the typical volume changes

27

gt 006mm) behave as a frictional soil it means that the strength of coarse soils (silt

sand gravel etc) comes from an inter-particle mechanical friction thus ideally they

do not have traction strength In figure 33 the inter-particle contact is illustrated here

the pressure (P) is applied and two more components are found the normal load (N)

and the tangential load (T) described as the friction coefficient (μF) The forces stand

in equilibrium (Johansson and Vall 2011)

When particles equilibrium is disturbed (friction coefficient is not enough to keep

particles unmoved) the rotation is imminent and it is necessary in order to compact

the soil in figure 34 can be seen that the arrangement is a fact that inhibit or allow this

rotation and the shape in the 3 different scales are also factors because the more

spherical andor more rounded andor less roughness more easy is the rotation

(Santamarina and Cho 2004)

Breakage

Breakage is a side effect of the inter-particle contact and rotation when pressure

exceed the rock strength it can happened when the particles are tight together and

there is not enough space to rotate it is more obvious in angular particles (mesh form)

or as in figure 31 where the flaky particle ldquobridgingrdquo is not able to rotate but it can

brake by the pressure increase Yoginder et al (1985) notice that the angular particle

break during his experiments and they turn more rounded changing the original size

and form configuration at the same time there was a soil properties loosening

Figure 33 Inter-particle contact and forces acting (Axelsson 1998)

Figure 34 Rotation inhibition by the particles compaction or low void ratio (Santamarina and Cho 2004)

28

52 INFLUENCE OF SIZE AND SHAPE

Wenworth (1922a) and Pellegrino (1965) among others suggest that agent transport of

the rocks (rigor of transport temperature and moisture changes etc) determine its

shape but also the particle genesis itself (rock structure mineralogy hardness etc) It

is not possible to determine the shape of the particles based on the agent transport or

genesis but generally a shape behaviour is expected according to Mitchell and Soga

(2005) specially when the particle size is in the clay size (gt2μm) The shapes of the

most common clay minerals are platy (figure 35) with some exceptions (eg

halloysite occurs as tubes kaolinite are large thick and stiff Smectites are composed

of small very thin and filmy particles Illites are intermediate between kaolinite and

smectite and attapulgite occurs in lathlike particle shapes) Some clay minerals

photographs are presented in figure 35

Figure 35 Clay mineral shape a) hallosite b) Kaoline c) Smactites d) Illites and e) attapulgite (Modified

from Mitchell and Soga 2005)

Figure 36 Particle size range in soils Generally the particles of clay size are plate shaped (Mitchell and

Soga 2005)

a) b) c)

e) d)

29

53 VOID RATIO AND POROSITY

The void ratio (e) is the ratio of the volume of voids to the volume of solid it is

defined by the equation

Porosity (n) is the ratio of the volume of voids to the total volume of the soil it is

represented by the equation

Holubec and DrsquoAppolonia (1973) found a relation between the void ratio and

sphericity (referred in the paper as coefficient of angularity ratio of particle surface

and equivalent sphere surface) their results show that the maximum and the minimum

void ratio increases as the shpericity decreases In this study the surface was obtained

for an indirect method based on the permeability developed by Hoffman in 1959

described in the same document Rouseacute et al (2008) defined the roundness as

Wadell (1935) and he found it as an important factor controlling the minimum and

maximum void ratios Some other authors as Youd (1973) and Cho et al (2006)

conclude the same minimum and maximum void ratios increase when sphericity and

roundness decrease Another interesting result (all above authors) was the bigger

influence of the form (sphericity circularity) and roundness on the maximum void

ratio The change of the maximum void ratio is more pronounced than the change of

the minimum void ratio when the form and roundness changes (See figure 39)

Particles arrangement and interlocking are probably the factor that controls the void

ratio bridge effect permit the existence of void among the particles while interlocking

allowed the particles to form arches avoiding the possibility to rotate and stay in a

more stable configuration eg as it happens with marbles

Figures 36 37 and 38 shows proposed empirical relationships between void ratio and

shape from tables 5 and 6 (graphically the scale goes from 0 to 1 when cero mean

high angularity shpericity or circularity and one means low angularity circularity or

sphericity) Holubec and DrsquoAppolonia (1973) data was taken to obtain a power curve

and describe a tendency Santamarina and Cho (2004) show Youd equations in the

original paper Youd (1973) never presented the equation but it is easy to use the

information to draw a trend

The graphics presented in this document (figures 36 37 and 38) must be used with

certain reserves due the fact that the original data was modified in order to fit all

information in one graphic what the figures shows is just the general trend of the

behaviourrsquos material regarding on the shape If more accurate description and

information is required the author recommends consulting the reference data In the

same way equations from Holubec and DrsquoApollonia (1973) and Youd (1973) were not

presented by the authors but the use of the information was taken in order to build up

those equations on tables 6 and 7

S

V

V

V

= e

V

V

=nV

(45)

(46)

30

Table 6 Minimum void ratio equations regarding on the quantity (Ψ for sphericity C for circularity R

for roundness SF for Sukumaran shape factor and AF for Sukumaran angularity factor)

EQUATION NUMBER REFERENCE

Figure 34 (left)

4340

minΨ45490e =

47

Holubec amp DrsquoAppolonia 1973 (Ψ

was obtained using equation 2)

SF06340

mine021903180e +=

48

Sukumaran amp Ashmawy 2001 (SF

obtained using equation 21)

C05101emin

= 49

Cho etal 2006 (C obtained using

figure 12)

Figure 34 (right)

1

minR08203590e +=

50

Youd 1973 (R obtained from figure

11 and table 3)

R34080emin

= 51

Cho et al 2006 (R obtained using

figure 12)

1

minR05104330e +=

52

Rouseacute et al 2008 (R obtained by

equation 21)

AF02330

mine372004160e +=

53

Sukumaran amp Ashmawy 2001 (AF

obtained using equation 37)

Table 7 Maximum void ratio equations regarding on the quantity (Ψ for sphericity C for circularity R

for roundness SF for Sukumaran shape factor and AF for Sukumaran angularity factor)

EQUATION NUMBER REFERENCE

Figure 35 (left)

51520

max Ψ61120e = 54

Holubec and DrsquoAppolonia 1973 (Ψ

was obtained using equation 2)

SF1190

max e0016907180e += 55

Sukumaran amp Ashmawy 2001 (SF

obtained using equation 21)

C86061emax = 56

Cho etal 2006 (C obtained using

figure 12)

Figure 35 (right)

1

max R1505540e += 57

Youd 1973 (R obtained from figure

11 and table 3)

R62031emax= 58

Cho et al 2006 (R obtained using

figure 12)

1

max R107106150e += 59

Rouseacute et al 2008 (R obtained by

equation 21)

AF0530

max e12506090e += 60

Sukumaran amp Ashmawy 2001 (AF

obtained using equation 37)

Comparing figures 37 and 38 (minimum and maximum void ratio) it can be seen on

the right scheme of both figures 37 and 38 (when the factor is roundnessangularity)

that all the empirical relations has a common initial point close to 1 (it means that

particles are well rounded) while this common agreement disappear when the

roundness factor decreases (when the particles become more angular) Same figures

(37 and 38) on the left graphs (when the factor is sphericitycircularityshape) do not

present the same behaviour in fact there is more disperse initial point close to 1(when

the particles tend to be more sphericalcircular)

31

In Figure 39 the Δe (emax-emin) has been plotted to show how the maximum void ratio

and the minimum void ratio has different rate change when the particle shape

changes Maximum void ratio increases more than minimum void ratio when the

particle shape becomes less spherical andor more angular Comparing figure 39 left

and right graphics it can be seen that right present a common initial point when the

quantity (roundnessangularity) is close to one while in the left graphic the initial

point is more disperse Both ending points in both graphics (close to zero) are

dispersed

Figures 37 38 and 39 present the same behaviour right graphics (when the factor is

roundness angularity) in each figure have an initial common point while the left

graphics do not (when the factor is sphericity circularity shape)

Figure 37 Minimum void ratio based upon the relation of shape factor proposed by the authors indicated

in the figure

Figure 38 Maximum void ratio based upon the relation of shape factor proposed by the authors indicated

in the figure

04

06

08

1

12

14

16

18

2

005

015

025

035

045

055

065

075

085

095

Factor (roundness angularity)

min

imu

m v

oid

rati

o

Youd 1973 roundness

Rouse 2008 roundness

Cho 2006 roundness

Sukumaran 2001 AF

03

04

05

06

07

08

09

1

11

12

13

05

015

025

035

045

055

065

075

085

095

Factor (sphericity circularity shape)

min

imu

m v

oid

rati

oHolubec 1973 sphericity

Cho 2006 circularity

Sukumara 2001 SF

05

07

09

11

13

15

17

19

21

00

150

250

350

450

550

650

750

850

95

Factor (sphericity circularity shape)

Maxim

um

vo

id r

ati

o

Holubec 1973 sphericity

Cho 2006 circularity

Sukumara 2001 SF

05

1

15

2

25

3

35

005

015

025

035

045

055

065

075

085

095

Factor (roundness angularity)

Maxim

um

vo

id r

ati

o

Youd 1973 roundness

Rouse 2008 roundness

Cho 2006 roundness

Sukumaran 2001 AF

32

54 ANGLE OF REPOSE

The angle of repose of a granular material is the steepest angle of descent or dip of the

slope relative to the horizontal plane when material on the slope face is on the verge

of sliding as show in figure 40

According to Qazi (1975) there are five types of forces which may act between the

particles in soils

1 Force of friction between the particles

2 Force due to presence of absorbed gas andor moisture of particle

3 Mechanical forces caused by interlocking of particles of irregular shape

4 Electrostatic forces arising from friction between the particles themselves and

the surface with which they come in contact

5 Cohesion forces operating between neighbouring particles

Rouseacute et al (2008) found a decrease of angle of repose with increase roundness

based upon ASTM C1444 test (Standard Test Method for Measuring the Angle of

Repose of Free-Flowing Mold Powders) The method consist in pouring sand on a

surface cover by paper trough a funnel of specific dimensions (the nozzle diameter

depend on the sandrsquos particle size) from an altitude of 15 inches (381 mm) The sand

is release from the funnel until the peak of the cone formed by the sand stops the flow

The repose angle is obtained with the equation

H represent the 15 inches D and d represent the diameter of the cone formed by the

sand and the diameter of the funnel respectively

Figure 39 Maximum minus minimum void ratio based upon the relation of shape factor proposed by the

authors indicated in the figure

0

01

02

03

04

05

06

07

08

09

1

005

015

025

035

045

055

065

075

085

095

Factor (sphericity circularity shape)

Maxim

um

- M

inim

um

Vo

id r

ati

oHolubec 1973 sphericity

Cho 2006 circularity

Sukumara 2001 SF

0

02

04

06

08

1

12

14

16

18

005

015

025

035

045

055

065

075

085

095

Factor (roundness angularity)

Maxim

um

- M

inim

um

Vo

id r

ati

o

Youd 1973 roundness

Rouse 2008 roundness

Cho 2006 roundness

Sukumaran 2001 AF

dD

H2

tan=φ1

rep(61)

33

Rouseacute (2008) shows an empirical relation to obtain the angle of repose based on the

roundness of the particles

55 SHEAR STRENGTH

The MohrndashCoulomb failure criterion represents the linear envelope that is obtained

from a plot of the shear strength of a material versus the applied normal stress This

relation is expressed as

where τ is the shear strength σn is the normal stress co is the intercept of the failure

envelope with the τ axis and is the slope of the failure envelope The quantity c is

often called the cohesion and the angle is called the angle of internal friction

Studies show that the internal friction angle (under drained triaxial tests) increases

more rapidly on those materials having higher angularity increasing the relative

density The internal friction angle is a function of the relative density and the particle

shape (Holubec and DrsquoAppolonia 1973)

Chan and Page (1997) found in a study made with dry copper (using different shapes

and sizes ranging from 180 to 106 μm) using a direct shear test (ring share test) that

the internal friction angle increases as the angularity increases

Shinohara et al (2000) did some experiments with steel powder different shapes

using a triaxial cell in the test Shinohara never used the roundness or angularity on

the work but apply the shape factor (relation long axisshort axis) and the results were

that as this relation deviate from factor 1 the internal friction angle increases

The following empirical relations were found in the literature showing the behaviour

of the friction angle (obtained under different conditions)

)tan( noc

Figure 40 Representation of the angle of repose

(63)

(62)

34

Cho et al (2006)

(64)

(R is obtain by comparing the Krumbein chart figure 13)

Rouseacute (2008)

(65)

(66)

(R is defined using Wadell equation 22)

In figure 41 the suggested empirical relations above and lines constructed using

author data from Holubec and DrsquoAppolonia (1973) and Sukumara and Ashmawy

(2001) are plotted together to display the general trend on the particle shape and

friction angle relation Sukumaran reports two lines one based on the shape factor

(SF) and the second referring the angularity factor (AF) Sukumaran performed the

tests at constant volume

The scale used for Holubec and DrsquoAppolonia (1973) have lower and upper limits of 1

and 2 respectively (angularity form) and a scale change was applied to be able to

presented in the actual figure 41 As in the previous section (52) the author

recommend to use the original data from the references due that the figure just follows

the general trend of the behaviourrsquos particle regarding on the shape

Figure 41 The changes on the internal friction angle shows a general increase when the particle roundness

becomes angular or in the case of Sakamuran less spheric (Shape factor SF)

35

Barton and Kjaernsli (1981) suggested a model (equation 67) to predict the peak

friction angle (φrsquo) based upon numerous trixial and direct shear data tests

where

Se equivalent strength of particle

Re equivalent roughness of particle

φb basic friction angle (obtained from basic tilting test)

σn normal load

The information required for the model is (1) the uniaxial compressive strength of the

rock (2) the d50 particle size (mesh size where 50 of the particles pass through)

required to define Se (figure 42) (3) the degree of particle roundness and (4) the

porosity following compaction All data can be estimated by simple index tests

Barton and Kjaernsli (1981) suggest that particle size and sample scale has an effect

on the friction angle and includes them to obtain the equivalent strength (Se) figure 42

shows the method to obtain this value Compressive strength (σc) was chosen to be the

factor affecting the scale because micro fractures influence this property while

samples are bigger more micro fractures contain and its compressive strength reduces

The equivalent roughness is obtain using figure 43 where is required to know the

porosity (n) and the origin of the particles (a small chart is provided in the same figure

to compare the particles profile)

b

n

ee

SLogR

Figure 42 Method of estimating Equivalent Strength (Se) of rockfill based on uniaxial compressive strength

(σc ) and d50 particle size (Barton amp Kjaernsli 1981)

(67)

36

56 SEDIMENTATION PROPERTIES

A particle released in a less dense Newtonian fluid initially accelerate trough the fluid

due to the gravity Resistances to deformation of the fluid transmitted to the particle

surface drag generate forces that act to resist the particle motion The force due to the

weight (Fw) can be written as

Where ρp ρ are density of the particle and fluid (water) respectively g is the

gravitational force and Vp is the volume of the particle

And the resistance force (FD) is

Where CD is the dimensionless drag coefficient W is the weight of the particle and A

is the cross section area

Particlersquos shape has been assumed to be spherical when equations are applied on the

settling velocity Correlation deviates when particle shape departs from spherical form

Figure 43 Method of estimating Equivalent Roughness (Roe) based on porosity of rockfill

origin material degree of roundedness and smoothness of particle (Barton amp Kjaernsli 1981)

PPW ρ)gV(ρF

A2

WρCF

2

DD

(68)

(69)

37

(Dietrich 1982) and it is known that natural particles depart from spherical form

thus it is evident that this departure would have consequences

The below equation is proposed to account the shape (in this case the Corey shape

factor equation 8) in the settling velocity (Jimenez and Madsen 2003)

Jimenez and Madsen (2003) Dietrich (1982) Briggs and McCulloch (1962) and

others were working in the hydraulic shape of particles to solve problems as sediment

transport It is obvious that the equation presented and the researcherrsquos investigation

works under certain conditions (eg grain size between 0063-1 mm)

Dietrich (1982) suggests an empirical relation that accounts settling velocity size

density shape and roundness of a particle

R1 R2 and R3 are fitted equations for size and density shape and roundness

respectively

57 HYDRAULIC CONDUCTIVITY PERMEABILITY

Darcyrsquos Law Permeability is one component of Darcyrsquos law Darcys law is a simple

proportional relationship between the instantaneous discharge rate through a porous

medium the viscosity of the fluid and the pressure drop

The total velocity Ve is equal to the product of the permeability of the medium

(porous media) k the pressure drop ∆p all divided by the viscosity μ (Muskat

1937)

Darcys law is only valid for slow viscous flow most groundwater flow cases fall in

this category Typically Darcyrsquos law is valid at any flow with laminar flow (see figure

44)

Reynoldrsquos number (Laminar and turbulent Flow) Typically any laminar flow is

considered to have a Reynoldrsquos number less than one and it would be valid to apply

Darcys law Experimental tests have shown that flow regimes with Reynolds numbers

1

ND

S

S

ZY

gd1s

WW

NDN

gd)1s(4

dS

2R1R

3 10RW

pk

Ve

(70)

(71)

(72)

(73)

38

up to 10 may still be Darcian (laminar flow) as in the case of groundwater flow The

Reynolds number (a dimensionless parameter) for porous media flow is typically

expressed as

where ρ is the density of water (units of mass per volume) υ is the specific discharge

(with units of length per time) d is a representative average grain diameter for the

porous media (often taken as the 30 passing size from a grain size analysis using

sieves - with units of length) and μ is the viscosity of the fluid (Muskat 1937)

Shape effects Permeability as Head and Epps (2011) suggested is affected by the

shape and texture of soil grains Elongated or irregular particles create flow paths

which are more tortuous than those spherical particles Particles with a rough surface

texture provide more frictional resistance to flow Both effects tend to reduce the

water flow through the soil

Kozeny-Carman empirical relation accounts for the dependency of permeability on

void ratio in uniformly graded sands serious discrepancies are found when it is

applied to clays due the lack of uniform pores (Mitchell and Soga 2005)

There are various formulations of the Kozeny-Carman equation one published by

Head and Epps (2011) takes the void ratio e the specific surface area Ss and an

angularity factor F into account of permeability k

The angularity factor F considers the shape of the particles and ranges from 11 for

rounded grains 125 for sub rounded to 14 for angular particles The specific surface

Ss is defined as

d1 and d2 represent the maximum and minimum size particle in mm

Kane amp Sternheim (1988) suggest that the inclusion of the shape factor (F) has

probably the background on the Reynolds number due this factor is dependent

significantly on the shape of the obstacles and Reynolds number determines the

presence of laminar or turbulent flow Figure 44 show how the laminar flow has low

energy dissipation while turbulent flow (eg the roughness and path tortuosity) has

high energy dissipation

e1

e

FSs

2k

3

2

dRe

21

6

ddSs

(74)

(75)

(76)

39

According to Nearing and Parker (1994) the amount of soil detached during laminar

and turbulent flow is dependent on each soil and also greater on turbulent flow due the

greater shear strength generated during this kind of flow this could suggest the

greater erosion when turbulent flow is present

58 LIQUEFACTION

Soil liquefaction is a phenomenon in which soil loses much of its strength or stiffness

for a generally short time by earthquake shaking or other rapid loading Static and

dynamic liquefactions occur been the second one the most regular known

Liquefaction often occurs in saturated soils that is soils in which the space between

individual particles is completely filled with water This water exerts a pressure on the

soil particles that influences how tightly the particles themselves are pressed together

Shaking or other rapid loading can cause the water pressure to increase to the point

where the soil particles can readily move with respect to each other (Jefferies and

Been 2000)

Jefferies and Been (2000) state that it is clear that minor variation in intrinsic

properties of sand have major influence on the critical state These might be variations

on grain shape mineralogy grain size distribution surface roughness of grains etc

Yoginder et al (1985) found that substantial decrease on liquefaction resistance

occur with increase in confining pressure for rounded and angular sands (1600 kPa)

also rounded sands show an rapidly build up of resistance against liquefaction with

increasing density while angular tailing sand in contrast show such rapid increase

only at low confining pressures At low confining pressure angular material is more

resistant to liquefaction Probably the breakage of the corners on the angular particles

in tailings is ruling the lost in resistance at high confining pressures (sieve analysis

Figure 44 The figure show the extremes of flow behaviour First turbulent conditions where the flow is

essentially random and unpredictable and second the well defined Laminar flow conditions

40

after test identify the breakage of angular particles while on rounded particles the

sieve analysis was practically the same)

59 GROUNDWATER AND SEEPAGE MODELLING

In groundwater flow the particlersquos shape affects the soilrsquos pore size distribution

hence the flow characteristics (Sperry and Peirce 1995) Tortuosity and permeability

(also see section 57) are two significant macroscopic parameters of granular medium

that affect the passing flow (Hayati et al 2012) Current models incorporating the

effects of particle shape have failed to consider irregular particles such as those that

would prevail in a natural porous medium (Sperry and Peirce 1995)

Hayati et al (2012) suggested based on his results that tortuosity effect converge

when the porosity increases indicating that the shape have dominance at low and mid

porosity ranges

Sperry and Peirce (1995) research conclusions suggest that particle size and porosity

are more important predictors for hydraulic conductivity explaining the 69 of the

variability but particle shape appears to be the next most important This however

apparently comprises particles larger than 295-351 μm Differences for particle size

295-351 μm and smaller are not detectable Another interesting result in the research

was the interaction effect of the particle size and particle shape It suggests a different

packing configuration for particles of the same shape but different size (scale

dependent)

6 DISCUSSION

61 TERMS QUANTITIES AND DEFINITIONS

In order to describe the particle shape in detail there are a number of terms quantities

and definitions (qualitative and quantitative) used in the literature (eg Wadell 1932

1934 Krumbein 1941 Sneed amp Folk 1958) All mathematical definitions

(quantitatives) are models used to simplify the complexity of shape description Some

authors (Mitchell amp Soga 2005 Arasan et al 2010) are using three sub-quantities

one and each describing the shape but at different scales The terms are

morphologyform roundness and surface texture (figure 1) The three sub-quantities

are probably the best way to classify and describe a particle because not a single

definition can interpret the whole morphology Common language is needed when

descriptors are explained and these three scales represent an option It is evident in

the reviewed literature that many of the shape descriptors are presented with the same

name but also that there is not a clear meaning on what this descriptor defines eg

when there is no upper limit in the roundness does it means that the angularity never

ends Could they be more and more angular Probably they could be on theory but

not in reality

41

62 PROPERTIES

Trough various articlersquos review done in the present investigation it is recognized that

the particlersquos shape has an effect on the material properties among these are

1 Porosity (Tickell 1938 Fraser 1935 Kolbuszewski 1948) and void ratio

(Cho et al 2006 Shergold 1953 Rouseacute et al 2008 Santamarina and Cho

2004)

2 Permeability (Witt and Brauns 1983)

3 Internal friction angle (Shinohara et al 2000 Chan and Page 1997

Cheshomi et al 2009)

4 Density (Youd 1973 Holubec and DrsquoAppolonia 1973)

5 Drag coefficient Hydraulics (Briggs and McCulloch 1962)

In Table 5 is a short resume of the properties and shape effect found in peer review

articles trough different journals Most of the reviewed articles based its research on

uniform graded sands

Table 8 Compilation of properties influenced by particle shape

Repose

angle

Friction

angle

Porosity and

Void ratio Density Permeability

Settling velocity

Drag coefficient Deformation

Sphericity (3D)shape factor

NI x x x x x x

Circularity (2D)

NI x x x x NI NI

Roundness x x x x NI NI x

x influence

NI no information available

Shape of particles has an effect on the arrangement producing bridging or avoiding

the rotation of the particles and the resulting geotechnical property is affected eg

including flaky particles can result in a higher void ratio due the bridging effect

(Santamarina and Cho 2004) and depending on the loads even the size distribution is

changed due the breakage (Yoginder et al 1985) in similar way angular particles

produce higher void ratio due the avoided possibility of the particles to rotate and

compact

The influence of the chosen shape descriptor appears in this review to have minor

influence on the soil properties in the reviewed studies except on the void ratio and

the friction angle Influence of particle shape in some cases is hider by other factors

(eg size distribution) also the particle shape probably does not have influence when

particle size is in the clay order (eg hydraulic conductivity) the reason could be due

to forces as electrostatic or capillarity become more important at this level

Among the shape descriptors some are chosen more often in literature (eg aspect

ratio) there is no apparent scientific basis to use it (probably due to the simplicity of

the measurement it becomes one of the most use) but there are still some other

descriptors that may or may not show better correlation with the soil properties

Instead empirical relations had been developed regarding roundness or shape to

describe the soil behaviour it is clear that the mechanism behind the results is still not

completely understood

42

There is necessity to define the best(s) shape descriptor(s) to be used for particular

geotechnical properties

63 IMAGE ANALYSIS

Many image analysis techniques had been used to describe the particle shape eg

Fourier analysis fractal dimension tomography etc (Hyslip and Vallejo 1997) but

there is not agreement on the usage or conclusion to ensure the best particle descriptor

for geotechnical applications

There are several shape descriptors and also various techniques to capture the

particles profile (3-dimensions 3-dimension orthogonal and 2-dimensions) Each

technique presents advantages and disadvantages 3-dimensions is probably the

technique that provide more information about the particle shape but the precision

also lies in the resolution the equipment required to perform such capture could be

more or less sophisticated (scanning particles laying down in one position and later

move to complete the scanning or just falling down particles to scan it in one step)

3-dimensions orthogonal this technique use less sophisticated equipment (compare

with the previous technique) but its use is limited to particles over 1cm also

information between the orthogonal pictures is not capture 2-dimensions require non

sophisticated equipment but at the same time the shape information diminish compare

with the previous due the fact that it is possible to determine only the outline as the

particle measurements are performed in 2-dimensions it is presumed that they will lie

with its shortest axis perpendicular to the laying surface when they are flat but when

the particle tends to have more or less similar axis the laying could be random

Advantages on the use of image analysis are clear there is not subjectivity because it

is possible to obtain same result over the same images Electronic files do not loose

resolution and it is important when collaboration among distant work places is done

files can be send with the entire confidence and knowing that file properties has not

been changed Technology evolutions allowed to work with more information and it

also applies to the image processing area were the time consumed has been shortened

(more images processed in less time)

One important aspect in image analysis is the used resolution in the analysis due the

fact that there are measurements dependent and independent on resolution Thus

those dependent measurements should be avoided due the error included when they

are applied or avoid low resolution to increase the reliability Among these

parameters length is the principal parameter that is influences by resolution (eg

perimeter diameter axis etc) Resolution also has another aspect with two faces

quality versus capacity more resolution (quality) means more storage space a

minimum resolution to obtain reasonable and reliable data must be known but it

depend on each particular application

43

64 APPLICATIONS

Quantify changes in particles in the authorrsquos thought is one of the future applications

due the non-invasive methods of taking photographs in the surface of the damrsquos slope

rail road ballast or roads Sampling of the material and comparing with previous

results could show volume (3D analysis) or area (2D analysis) loss of the particles as

well as the form roundness and roughness This is important when it has been

suggested that a soil or rock embankment decrees their stability properties (eg

internal friction angle) with the loss of sphericity roundness or roughness

Seepage stock piling groundwater etc should try to include the particle shape while

modelling seepage requires grading material to not allow particles move due the

water pressure but in angular materials as it is known the void ratio is great than the

rounded soil it means the space and the possibilities for the small particles to move

are greater stock piling could be modelled incorporating the particle shape to

determine the binrsquos capacity when particle shape changes (void ratio changes when

particle shape changes) Modelling requires all information available and the

understanding of the principles that apply

Industry is actually using the particle shape to understand the soil behaviour and

transform processes into practical and economic image analysis has been included in

the quality control to determine particle shape and size because the advantages it

brings eg the acquisition of the sieving curve for pellets using digital images taken

from conveyor this allows to have the information in a short period of time with a

similar result at least enough from the practical point of view as the traditional

sieving

7 CONCLUSIONS

The conclusions of this literature review are

It has been shown that particle shape has influence on the soil behaviour

despite of partial knowledge of the mechanism behind Understanding of the

particle shape and its influence needs to be accomplished

A common language needs to be built up to standardize the meaning on

geotechnical field that involve the particle shape General relationships

between shape and properties should be developed

Based on this review it is not clear which is the best descriptor to use in

geotechnical engineering affecting he related shape to properties Instead of a

couple of standards there is no shape descriptor in geotechnical field fully

accepted

Image analysis tool is objective make the results repeatable obtain fast results

and work with more amount of information

44

Resolution needs to be taken in consideration when image analysis is been

carried out because the effects could be considerable Resolution must be set

according to the necessities Parameters as perimeter can be affected by

resolution

There are examples where particle shape has been incorporated in industries

related to geotechnical engineering eg in the ballast and asphalt industry for

quality control

8 FURTHER WORK

Three main issues have been identified in this review that will be further investigated

the limits of shape descriptors influence of grading and choice of descriptor for

relation to geotechnical properties

Shape descriptors have low and high limits frequently the limits are not the same and

the ability to describe the particlersquos shape is relative The sensitivity of each descriptor

should be compare to apply the most suitable descriptor in each situation

Sieving curve determine the particle size in a granular soil particle shape could differ

in each sieve size There is the necessity to describe the particle shape on each sieve

portion (due to practical issues) and included in the sieve curve Obtain an average

shape in determined sieve size is complicated (due to the possible presence of several

shapes) and to obtain the particle shape on the overall particlersquos size is challenging

how the particle shape should be included

Since several descriptors have been used to determine the shape of the particles and

the relation with the soil properties it is convenient to determine the descriptorrsquos

correlation with the soil properties

9 ACKNOWLEDGMENT

I would like to thanks to Lulearing University of Technology (LTU) the time I had spent

in its facilities and the kind environment it offers and University of Sonora

(UNISON) that has been providing me the financial support and the time to conclude

this journey

10 REFERENCES

Andersson T (2010) Estimating particle size distributions based on machine vision

Doctoral Thesis Departament of Computer Science and Electrical Engineering Lulearing

University of Technology ISSN 1402-1544 ISBN 978-91-7439-186-2

45

Arasan Seracettin Hasiloglu A Samet Akbulut Suat (2010) Shape particle of

natural and crished aggregate using image analysis International Journal of Civil and

Structural Engineering Vol 1 No 2 pp 221-233 ISSN 0970-4399

Aschenbrenner BC (1956) A new method of expressing particle sphericity Journal

of Sedimentary Petrology Vol 26 No 1 pp 15-31

Axelsson K (1998) Introduktion till jordmekaniken jaumlmte jordmateriallaumlran Skrift

984 Lulearing Avdelningen foumlr Geoteknologi Lulearing Tekniska Universitet (In Swedish)

Barton Nick amp Kjaernsli Bjorn (1981) Shear strength of rockfill Journal of the

Geotechnical Engineering Division Proceedings of the American Society of Civil

Engineers (ASCE) Vol 107 No GT7

Barrett P J (1980) The shape of rock particles a critical review Sedimentology

Vol 27 pp 291-303

Blott S J and Pye K (2008) Particle shape a review and new methods of

characterization and classification Sedimentology Vol 55 pp 31-63

Bowman E T Soga K and Drummond W (2001) Particle shape characterization

using Fourier descriptor analysis Geotechnique Vol 51 No 6 pp 545-554

Briggs L I McCulloch D S (1962) Hydraulic shape of sand particles Journal of

Sedimentary Petrology Vol 32 pp 645-656

Chan Leonard C Y and Page Neil W (1997) Particle fractal and load effects on

internal friction in powders Powder Technology Vol 90 pp 259-266

Cheshomi A Fakher A Jones C J F P (2009) A correlation between friction

angle and particle shape metrics in quaternary coarse alluvia Quarterly Journal of

Engineering Geology and Hydrogeology Vol 42 pp 145-155

Cho G Dodds J and Santamarina J C (2006) Particle shape effects on packing

density stiffness and strength Natural and crushed sands Journal of Geotechnical

and Geoenvironmental Engineering May 2006 pp 591-602

Dietrich William E (1982) Settling velocity of natural particles Water Resources

Research Vol 18 No 6 pp 1615-1626

Dobkins J E and Folk R L (1970) Shape development on Tahiti-nui Journal of

Sedimentary Petrology Vol 40 No 2 pp 1167-1203

Folk R L (1955) Student operator error in determining of roundness sphericity and

grain size Journal of Sedimentary Petrology Vol 25 pp 297-301

Fernlund J M R (1998) The effect of particle form on sieve analysis A test by

image analysis Engineering Geology Vol 50 No 1-2 pp 111-124

46

Fernlund J M R (2005) Image analysis method for determining 3-D shape of

coarse aggregate Cement and Concrete Research Vol 35 Issue 8 pp 1629-1637

Fernlund J M R Zimmerman Robert and Kragic Danica (2007) Influence of

volumemass on grain-size curves and conversion of image-analysis size to sieve size

Engineering Geology Vol 90 No 3-4 pp 124-137

Fraser H J (1935) Experimental study of the porosity and permeability of clastic

sediments The Journal of Geology Vol 43 pp 910-1010 ISSN 0022-1376

Hayati Ali Nemati Ahmadi Mohammad Mehdi and Mohammadi Soheil (2012)

American Physical Society Physical review E 85 036310 DOI

101103PhysRevE85036310

Hawkins A E (1993) The Shape of Powder-Particle Outlines Wiley New York

Head K H and Epps R J (2011) Manual of soil Laboratory testing Volum II

Permeability shear strength and compressibility test 3rd

edition Whittles Publishing

Scotland UK 3rd

edition

Holubec I and DrsquoAppolonia E (1973) Effect of particle shape on the engineering

properties of granular soils ASTM STP 523 pp 304-318

Hyslip James P Vallejo Luis E (1997) Fractal analysis of the roughness and size

distribution of granular materials Engineering Geology Vol 48 pp 231-244

Janoo Vincent C (1998) Quantification of shape angularity and surface texture of

base course materials US Army Corps of Engineers Cold Region Research and

Engineering Laboratory Special report 98-1

Jefferies Mike and Been Ken (2000) Soil liquefaction A critical state approach

Taylor amp Francis Group London and New York

Jimenez Jose A Madsen Ole S (2003) A simple formula to estimate settling

velocity of natural sediments Journal of Waterway Port Coastal and Ocean

Engineering Vol 129 No 2 pp 70-78

Johansson Jens and Vall Jakob (2011) Jordmaterials kornform Inverkan paring

Geotekniska Egenskaper Beskrivande storheter bestaumlmningsmetoder

Examensarbete Avdelningen foumlr Geoteknologi Institutionen foumlr Samhaumlllsbyggnad

och naturresurser Lulearing Tekniska Universitet Lulearing (In Swedish)

Kane Joseph W and Sternheim Morton M (1988) Physics John Wiley amp Sons Inc

Third edition

Kolbuszewski J (1948) An experimental study of the maximum and minimum

porosities of sands Proceedings of the Second International Conference on Soil

Mechanics and Foundation Engineering Rotterdam June 21 to 30 Sub-section IIb

pp 158-165

47

Krumbein W C and Pettijohn FJ (1938) Manual of sedimentary petrography

Appleton-Century Crofts Inc New York

Krumbein W C (1941) Measurement and geological significance of shape and

roundness of sedimentary particles Journal of Sedimentary Petrology Vol 11 No 2

pp 64-72

Krumbein W C and Sloss L L (1963) Stratigraphy and Sedimentation 2nd

ed

WH Freeman San Francisco

Kuo Chun-Yi and Freeman Reed B (1998a) Image analysis evaluation of

aggregates for asphalt concrete mixtures Transportation Research Record Vol 1615

pp 65-71

Kuo Chun-Yi Rollings Raymond and Lynch Larry N (1998b) Morphological

study of coarse aggregates using image analysis Journal of Materials in Civil

Engineering Vol 10 No 3 pp 135-142

Lanaro F Tolppanen P (2002) 3D characterization of coarse aggregates

Engineering Geology Vol 65 pp 17-30

Lees G (1964a) A new method for determining the angularity of particles

Sedimentology Vol 3 pp 2-21

Lees G (1964b) The measurement of particle shape and its influence in engineering

materials British Granite Whinstone Federation Vol 4 No 2 pp 17-38

Matsushima Takashi Saomoto Hidetaka Matsumoto Masaaki Toda Kengo

Yamada Yasuo (2003) Discrete element simulation of an assembly of irregular-

shaped grains Quantitative comparison with experiments 16th ASCE Engineering

Mechanics Conference University of Washington Seattle July 16-18

Mitchell James K and Soga Kenichi (2005) Fundamentals of soil behaviour Third

edition WILEY

Mora C F Kwan A K H Chan H C (1998) Particle size distribution analysis of

coarse aggregate using digital image processing Cement and Concrete Research Vol

28 pp 921-932

Mora C F and Kwan A K H (2000) Sphericity shape factor and convexity

measurement of coarse aggregate for concrete using digital image processing Cement

and Concrete Research Vol 30 No 3 pp 351-358

Muskat Morris (1937) The Flow of fluids through porous media Journal of Applied

Physics Vol 8 pp 274

Nearing M A and Parker S C (1994) Detachment of soil by flowing water under

turbulent and laminar conditions Soil Science Society of American Journal Vol 58

No 6 pp 1612-1614

48

Pan Tongyan Tutumluer Erol Carpenter Samuel H (2006) Effect of coarse

aggregate morphology on permanent deformation behavior of hot mix asphalt Journal

of Transportation Engineering Vol 132 No 7 pp 580-589

Pellegrino A (1965) Geotechnical properties of coarse-grained soils Proceedings

International Conference of Soil Mechanics and Foundation Engineering Vol 1 pp

97-91

Pentland A (1927) A method of measuring the angularity of sands MAG MN AL

Acta Eng Dom Transaction of the Royal Society of Canada Vol 21 Ser3xciii

Persson Anna-Lena (1998) Image analysis of shape and size of fine aggregates

Engineering Geology Vol 50 pp 177-186

Powers M C (1953) A new roundness scale for sedimentary particles Journal of

Sedimentary Petrology Vol 23 No 2 pp 117-119

Pye W and Pye M (1943) Sphericity determination of pebbles and grains Journal

of Sedimentary Petrology Vol 13 No 1 pp 28-34

Qazi M A (1975) Flow properties of granular masses A review on the angle of

repose The Arabian Journal for Science and Engineering Vol 1 No 2

Quiroga Pedro Nel and Fowle David W (2003) The effects of aggregate

characteristics on the performance of portland cement concrete Report ICAR 104-1F

Project number 104 International Center for Aggregates Research University of

Texas

Riley N A (1941) Projection sphericity Journal of Sedimentary Petrology Vol 11

No 2 pp 94-97

Rouseacute P C Fennin R J and Shuttle D A (2008) Influence of roundness on the

void ratio and strength of uniform sand Geotechnique Vol 58 No 3 227-231

Santamarina J C and Cho G C (2004) Soil behaviour The role of particle shape

Proceedings Skempton Conf London

Schofield and Wroth (1968) Critical state soil mechanics McGraw Hill

Shaumlfer Michael (2002) Digital optics Some remarks on the accuracy of particle

image analysis Particle amp Particle Systems Characterization Vol 19 No 3 pp 158-

168

Shergold F A (1953) The percentage of voids in compacted gravel as a measure of

its angularity Magazine of Concrete Research Vol 5 No 13 pp 3-10

Shinohara Kunio Oida Mikihiro Golman Boris (2000) Effect of particle shape on

angle of internal friction by triaxial compression test Powder Technology Vol 107

pp131-136

49

Skredcommisionen (1995) Ingenjoumlrsvetenskapsakademinen rapport 395 Linkoumlping

1995

Sneed E D and Folk R L (1958) Pebbles in the Colorado river Texas A study in

particle morphogenesis Journal of Geology Vol 66 pp 114-150

Sperry James M and Peirce J Jeffrey (1995) A model for estimating the hydraulic

conductivity of granular material based on grain shape grain size and porosity

Ground Water Vol 33 No 6 pp 892-898

Sukumaran B and Ashmawy A K (2001) Quantitative characterisation of the

geometry of discrete particles Geotechnique Vol 51 No 7 pp 619-627

Szaacutedeczy-Kardoss E Von (1933) Die bistimmung der abrollungsgrades Geologie

und palaumlontologie Vol 34B pp 389-401 (in German)

Teller J T (1976) Equantcy versus sphericity Sedimentology Vol 23 pp 427-428

Tickell F G (1938) Effect of the angularity of grain on porosity and permeability

bulletin of the American Association of Petroleum Geologist Vol 22 pp 1272-1274

Tutumluer E Huang H Hashash Y Ghaboussi J (2006) Aggregate shape effects

on ballast tamping and railroad track lateral stability AREMA 2006 Annual

Conference Louisville KY

Wadell H (1932) ldquoVolume Shape and roundness of rock particlesrdquo Journal of

Geology Vol 40 pp 443-451

Wadell H (1933) Sphericity and roundness of rock Particles Journal of Geology

Vol 41 No 3 pp 310ndash331

Wadell H (1934) Shape determination of large sedimental rock fragments

The Pan-American Geologist Vol 61 pp 187-220

Wadell H (1935) ldquoVolume shape and roundness of quartz particlesrdquo Journal of

Geology Vol 43 pp 250-279

Wentworth W C (1922a) The shape of beach pebbles Washington US Geological

Survey Bulletin Vol 131C pp 75-83

Wentworth W C (1922b) A method of measuring and plotting the shape of pebbles

Washington US Geological Survey Bulletin Vol 730C pp 91-114

Wentworth W C (1933) The shape of rock particle A discussion Journal of

Geology Vol 41 pp 306-309

Witt K J Brauns J (1983) Permeability-Anisotropy due to particle shape Journal

of Geotechnical Engineering Vol 109 No 9 pp 1181-1187

i

PREFACE

The work in this report has been carried out at the Division of Mining and

Geotechnical Engineering at Lulearing University of Technology

In this new journey now as a PhD student I have face new questions and

challenges that have improved myself not only as a student but also as a person It

has been not easy but the fellowship environment with professors students

technicians etc all in general friends benefits the daily discussion and the

interchange of ideas

The intention of the report is to build up a starting point from where the research

on particle shape developed by the author will take place It is also the intention to

present the general overview on particle shape research and make it understandable

for all readers Particle shape research is a wide area and the author focus the report

in Geotechnical Engineering The report has been split in chapters with the

intention to describe first how the measurements were developed in time and

according with authors follow by the techniques used to measure the particlersquos

dimensions It is also included those properties found in literature affected by the

particlersquos shape Finally findings are discussed with the proper conclusion

I appreciate the time taken by my supervisors Sven Knutsson and Tommy Edeskaumlr

to address me in the right direction the support they always gave me and they for

sure will give me in the near future I also must be grateful to my colleague Jens

Johansson who previous work experience on the image analysis and discussions

has been of great value and help

I would like to thank my family by the support they gave me this last two years in

the work and the joy they provide me during our spare time I understand it has not

been easy for them ether and I appreciate them effort

Juan Rodriguez

Lulearing 2012

ii

ABSTRACT

It has been shown in the early 20th

century that particle shape has an influence on

geotechnical properties Even if this is known there has been only minor progress

in explaining the processes behind its performance and has only partly

implemented in practical geotechnical analysis

This literature review covers different methods and techniques used to determine

the geometrical shape of the particles as well as reported effects of shape on

granular material behaviour

Particle shape could be classifying in three categories sphericity - the overall

particle shape and similitude with a sphere roundness - the description of the

particlersquos corners and roughness - the surface texture of the particle The categories

are scale dependent and the major scale is to sphericity while the minor belongs to

roughness

Empirical relations and standards had been developed to relate soil properties eg

internal friction angle minimum and maximum void ratio density permeability

strain with the particle shape The use of the relations and standards enhance the

bulk material performance eg asphalt mixtures and rail road ballast

The overview has shown that there is no agreement on the usage of the descriptors

and is not clear which descriptor is the best One problem has been in a large scale

classify shape properties Image analysis seems according to the review to be a

promising tool it has many advantages But the resolution in the processed image

needs to be considered since it influence descriptors such as eg the perimeter

iii

1 INTRODUCTION 1

2 AIM AND GOAL 3

3 DESCRIPTION OF SHAPE PROPERTIES 3

31 INTRODUCCTION 3 32 SCALE DEPENDENCE 4 33 FORM (3D) 5 34 FORM (2D) 9 35 ROUNDNESS OR ANGULARITY 11 36 ROUGHNESS OR SURFACE TEXTURE 18

4 TECHNIQUES IN ORDER TO DETERMINE PARTICLE SHAPE 20

41 HAND MEASUREMENT 20 42 SIEVE ANALYSIS 21 43 CHART COMPARISON 21 44 IMAGE ANALYSIS 23

5 EFFECT OF SHAPE ON SOIL PROPERTIES 25

51 INTRODUCTION 25 52 INFLUENCE OF SIZE AND SHAPE 28 53 VOID RATIO AND POROSITY 29 54 ANGLE OF REPOSE 32 55 SHEAR STRENGTH 33 56 SEDIMENTATION PROPERTIES 36 57 HYDRAULIC CONDUCTIVITY PERMEABILITY 37 58 LIQUEFACTION 39 59 GROUNDWATER AND SEEPAGE MODELLING 40

6 DISCUSSION 40

61 TERMS QUANTITIES AND DEFINITIONS 40 62 PROPERTIES 41 63 IMAGE ANALYSIS 42 64 APPLICATIONS 43

7 CONCLUSIONS 43

8 FURTHER WORK 44

9 ACKNOWLEDGMENT 44

10 REFERENCES 44

iv

ABBREVIATIONS Symbol Description Units

A Area of the projected particle area of the particle outline (2D) m2

A1 Area of the projected particle after ldquonrdquo dilatation-erosion cycles m2

AC Area of the smallest circumscribed circle m2

AC2 Area of circle with diameter equal to longest length of outline m2

ACON Convex area m2

AF Sukumara angularity factor -

ANGCON Angles subtending convex parts of the outline degree (ordm)

ANGPLA Angles subtending plane parts of the outline degree (ordm)

a Longest axes diameters of the particle m

B Greatest breadth perpendicular to L m

b Medium axes diameters of the particle m

C Circularity -

CR Convexity ratio -

c Shorter axes diameters of the particle m

Co Cohesion Pa

CPER Convex perimeter m

DA Diameter of a circle equal on area to that of the particle outline m

DAVG Mean average diameter m

DC Diameter of the smallest circumscribed circle in the particle outline m

DCIR Diameter of circumscribed sphere m

DI Diameter of the largest inscribed circle m

DS Diameter of circle fitting sharpest corner (two sharper corners DS1 DS2) m

DSV Diameter of a sphere of the same volume as particle m

DX Diameter of a pebble particle through the sharpest corner DS m

d Grain diameter (average) m

dN Nominal diameter diameter of a sphere of the same volume as the natural

particle

m

e Void ratio

F Angularity factor -

FR Fullness ratio -

g Gravitational acceleration ms2

I Intermediate axis m

k Hydraulic conductivity ms

L Longest axis of the outline m

N Number of corners (items counted) or number of divisions -

n Porosity -

P Perimeter of the projected particle perimeter of outline (2D) m

PC Perimeter of a circle of same area as particle outline m

PCON Sum of perimeter of all convex parts m

PCD Perimeter of circle of same area as drainage basin m

PD Perimeter of a drainage basin m

PI Particle index -

R Roundness -

RAVG Mean average radio of the pebble m

RCON Radius of curvature of the most convex part m

Re Reynolds number -

Rmax-in Radius of the maximum inscribed circle m

Rmin-cir Radius of the minimum circumscribed circle m

RO Roughness or surface texture -

Re Equivalent roughness of particle -

R1 Equation for predicting the settling velocity of sphere -

R3 Equation for predicting the ratio of the settling velocity of an angular

particle to that of a well-rounded particle

-

ri Radius of curvature of the corner ldquoirdquo m

S Actual surface area of the particle m2

v

Symbol Description Units

Se Equivalent strength of particle -

Ss Specific surface area -

SF Sukumara shape factor -

Sm Short axis ldquocrdquo in minimum projection plane m

s Surface area of a sphere of the same volume as the particle m2

sD Specific gravity of the sediment given by the relation density of

sedimentfluid

-

R2 Equation for predicting the ratio of the settling velocity of a non-spherical

well-rounded particle to be settling velocity of a sphere with the same

dimensionless nominal diameter

-

S Dimensionless fluid-sediment parameter -

V Total volume of soil m3

VCIR Volume of circumscribed sphere m3

Ve Velocity ms

VP Volume of particle m3

Vs Volume of voids m3

Vv Volume of solid m3

V10 voids in the aggregate compacted with 10 blows per layer -

V50 voids in the aggregate compacted with 50 blows per layer -

W Weight of the particle ton

WS Settling velocity ms

W Dimensionless settling velocity -

Y Constant to obtain by fitting to experimental data for certain ranges of S -

Z Constant to obtain by fitting to experimental data for certain ranges of S -

x Distance of the tip of the corner from the center of the maximum inscribed

circle

mm

α Measured angle degree (ordm)

αi Sakamura angles used to describe shape degree (ordm)

βi Sakamura angles used to describe angularity degree (ordm)

Σ Summation -

Ψ Sphericity -

ν Kinematics viscosity m2s

φb Basic friction angle degree (ordm)

φcs Friction angle critical state degree (ordm)

φmc Friction angle maximum contraction degree (ordm)

φrep Angle of repose degree (ordm)

φ Peak friction angle Pa

τ Shear strength Pa

σc Compressive strength Pa

σn Normal stress Pa Angle of internal friction degree (ordm)

μ Viscosity Pamiddots

μF Friction coefficient -

p Pressure drop -

ρ Density of water tonm3

ρp Density of the particle tonm3

υ Specific discharge ms

1

1 INTRODUCTION

Effects on soil behaviour from the constituent grain shape has been suggested since

the earliest 1900rsquos when Wadell (1932) Riley (1941) Pentland (1927) and some

other authors developed their own techniques to define the form and roundness of

particles Into the engineering field several research works conclude that particle

shape influence technical properties of soil material and unbound aggregates

(Santamarina and Cho 2004 Mora and Kwan 2000) Among documented properties

affected by the particle shape are eg void ratio (porosity) internal friction angle and

hydraulic conductivity (permeability) (Rouseacute et al 2008 Shinohara et al 2000

Witt and Brauns 1983) In geotechnical guidelines particle shape is incorporated in

eg soil classification (Eurocode 7) and in national guidelines eg for evaluation of

friction angle (Skredkommisionen 1995) This classification is based on ocular

inspection and quantitative judgement made by the individual practicing engineer

thus it can result in not repeatable data In evaluation of eg standard penetration test

Holubec and DrsquoAppolonia (1973) are suggesting the inclusion of the particle shape in

the evaluation of the data According with Folk (1955) the form error is negligible but

it is not in the second sub-quantity related with the corners (roundness) These

systems are not coherent in definitions The lack of possibility to objectively describe

the shape hinders the development of incorporating the effect of particle shape in

geotechnical analysis

The interest of particle shape was raised earlier in the field of geology compared to

geotechnical engineering Particle shape is considered to be the result of different

agentrsquos transport of the rock from its original place to deposits since the final pebble

form is hardly influenced by these agents (rigor of the transport exfoliation by

temperature changes moisture changes etc) in the diverse stages of their history

Furthermore there are considerations regarding on the particle genesis itself (rock

structure mineralogy hardness etc) (Wentworth 1922a) The combination of

transport and mineralogy factors complicates any attempt to correlate length of

transport and roundness due that soft rock result in rounded edges more rapidly than

hard rock if both are transported equal distances According to Barton amp Kjaernsli

(1981) rockfill materials could be classified based on origin into the following (1)

quarried rock (2) talus (3) moraine (4) glacifluvial deposits and (5) fluvial deposits

Each of these sources produces a characteristic roundness and surface texture

Pellegrino (1965) conclude that origin of the rock have strong influence determining

the shape

To define the particle form (morphology) in order to classify and compare grains

many measures has been taken in consideration (axis lengths perimeter surface area

volume etc) Probably when authors had developed the form descriptors realize that

they hadnrsquot provide enough information about the corners they could be angular or

rounded (roundness) thus the authors also focus on develop techniques to describe

them Furthermore the corners or the general surface can be rough or smooth (surface

texture) Nowadays some authors (Mitchell amp Soga 2005 Arasan et al 2010) are

using these three sub-quantities one and each describing the shape but a different

scale (form roundness surface texture)

2

During the historical development of shape descriptors the terminology has been used

differently among the published studies terms as roundness (because the roundness

could be apply in the different scales) or sphericity (how the particle approach to the

shape of a sphere) were strong (Wadell 1933 Wenworth 1933 Teller 1976 Barrett

1980 Hawkins 1993) and it was necessary in order to define a common language on

the particle shape field unfortunately still today there is not agreement on the use of

this terminology and sometimes it make difficult to understand the meaning of the

authors thatrsquos why it is better to comprehend the author technique in order to

misinterpret any word implication

Several attempts to introduce methodology to measure the particlersquos shape had been

developed over the years Manual measurement of the particles form is

overwhelming thus visual charts were developed early to diminish the measuring

time (Krumbein 1941 Krumbein and Sloss 1963 Ashenbrenner 1956 Pye and Pye

1943) Sieving was introduced to determine the flakinesselongation index but it is

confined only for a certain particle size due the practical considerations (Persson

1988) More recently image analysis on computer base has been applied on sieving

research (Andersson 2010 Mora and Kwan 2000 Persson 1998) bringing to the

industry new practical methods to determine the particle size with good results

(Andersson 2010) Particle shape with computer assisted methods are of great help

reducing dramatically the measuring time (Fernlund 2005 Kuo and Freeman 1998a

Kuo et al 1998b Bowman et al 2001)

In the civil industry eg Hot Asphalt mixtures (Kuo and Freeman 1998a Pan et al

2006) Concrete (Mora et al 1998 Quiroga and Fowle 2003) and Ballast

(Tutumluer et al 2006) particlersquos shape is of interest due the materialrsquos performance

thus standards had been developed (see appendix A) On asphalt mixtures limits of

flat and elongated particles or the amount of natural sands typically are incorporated

into specifications flat and elongated particles tend to cause problems with

compaction particle breakage loss of strength and segregation in pavement (Kuo and

Freeman 1998a) Rutting resistance of asphalt concrete under traffic and

environmental loads depend on the stability of aggregates structure in the asphalt mix

(Pan et al 2006) According with the American Railway Engineering and

Maintenance of Way Association (AREMA) ballast aggregate should be open graded

with hard angular shaped particles providing sharp corners and cubical fragments

with a minimum of flat and elongated pieces (Tutumluer et al 2006) The American

standard ASTM D 3398 (test method for index of aggregate particle shape and

texture) is an example of an indirect method to determine particle shape (see appendix

A) Aggregate characteristics of shape texture and grading influence workability

finishability bleeding pumpability and segregation of fresh concrete and affect

strength stiffness shrinkage creep density permeability and durability of hardened

concrete In fact flaky elongated angular and unfavorably graded particles lead to

higher voids content than cubical rounded and well-graded particles (Quiroga and

Fowle 2003)

Sieving is probably the most used method to determine the particle size distribution it

consist of plotting the cumulative weight of the weighted material retained by each

mesh (European standard EN 933-1 1992) This traditional method according to

Andersson (2010) is time consuming and expensive Investigations shows that the

traditional sieving has deviations when particle shape is involve the average volume

3

of the particles retained on any sieve varies considerably with the shape (Lees

1964b) thus the passing of the particles depend upon the shape of the particles

(Fernlund 1998) In some industries the Image analysis is taking advantage over the

traditional sieving technique regardless of the intrinsic error on image analysis due the

overlapping or partial hiding of the rock particles (Andersson 2010) In this case the

weight factor is substitute by pixels (Fernlund et al 2007) Sieving curve using

image analysis is not standardized but after good results in the practice (Andersson

2010) new methodology and soil descriptions could raise including its effects

2 AIM AND GOAL

The aim of this report is to review the state of the art on how to describe particle

shape of individual grains of geotechnical material and knowledge on the influence of

shape in geotechnical properties

The goals in this study are to

Describe discuss and compare particle shape and definitions

Review the known effect of particle shape on soil mechanics parameters

Discuss the potential of the role of particle shape in soil mechanics

Focus in this study has been on 2 dimensional shape definitions

The content of the report is based upon published and peer reviewed papers in

English

3 DESCRIPTION OF SHAPE PROPERTIES

31 INTRODUCCTION

Particle shape description can be classified as qualitative or quantitative Qualitative

describe in terms of words the shape of the particle (eg elongated spherical flaky

etc) and quantitative that relates the measured dimensions in the engineering field

the quantitative description of the particle is more important due the reproducibility

Quantitative geometrical measures on particles may be used as basis for qualitative

classification There are few qualitative measures in contrast with several quantitative

measures to describe the particle form Despite the amount of qualitative descriptions

none of them had been widely accepted but there are some standards (eg ASTM

D5821 EN 933-3 and BS 812) specifying mathematical definitions for industrial

purposes

Shape description of particles is also divided in

o 3D (3 dimensions) it could be obtained from a 3D scan or in a two

orthogonal images and

o 2D (2 dimensions) or particle projection where the particle outline is drawn

4

3D and 2D image analysis present challenges itself 3D analysis requires a

sophisticated equipment to scan the particle surface and create the 3D model or the

use of orthogonal images and combine them to represent the 3 dimensions The

orthogonal method could present new challenges as the minimum particle size or the

placing in orthogonal way of the particles (Fernlund 2005) 2D image analysis is easy

to perform due the non-sophisticated equipment required to take pictures (eg regular

camera or the use of microscope for smaller particles) In 2D image analysis the

particle is assumed to lay over its more stable axis (eg longest and intermediate axis

lie more or less parallel to the surface while the shortest axis is perpendicular) or

random some authors publish their own preferences about this issue (Wadell 1935

Riley 1941 Hawkins 1993)

32 SCALE DEPENDENCE

In order to describe the particle shape in detail there are a number of terms quantities

and definitions used in the literature Some authors (Mitchell amp Soga 2005 Arasan et

al 2010) are using three sub-quantities one and each describing the shape but at

different scales The terms are morphologyform roundness and surface texture In

figure 1 is shown how the scale terms are defined

At large scale the particlersquos diameters in different directions are considered At this

scale describing terms as spherical platy elongated etc are used An often seen

quantity for shape description at large scale is sphericity (antonym elongation)

Graphically the considered type of shape is marked with the dashed line in Figure 1

At intermediate scale it is focused on description of the presence of irregularities

Depending on at what scale an analysis is done corners and edges of different sizes

are identified By doing analysis inside circles defined along the particlersquos boundary

deviations are found and valuated The mentioned circles are shown in Figure 1 A

generally accepted quantity for this scale is roundness (antonym angularity)

Regarding the smallest scale terms like rough or smooth are used The descriptor is

considering the same kind of analysis as the one described above but is applied

Figure 1 Shape describing sub quantities (Mitchell amp Soga 2005)

5

within smaller circles ie at a smaller scale Surface texture is often used to name the

actual quantity The sub-quantities and antonyms are summarized in table 1

Table 1 Sub-quantities describing the particlersquos morphology and its antonym

Scale Quantity Antonym

Large scale Sphericity Elongation

Intermediate scale Roundness Angularity

Small scale Roughness Smoothness

33 FORM (3D)

Wentworth in 1922 (Blott and Pye 2008) was probably one of the first authors on

measure the particle dimensions this consisted on the obtaining of the length of the

tree axes perpendicular among each other (see figure 2) on the tree dimensions (where

agebgec) to obtain the sphericity (equation 1)

Krumbein (1941) develop a rapid method for shape measurement to determine the

sphericity this is done by measuring the longest (a) medium (b) and shorter (c) axes

diameters of the particle it can be seen in figure 2 (Always perpendicular among each

other) The radios ba and cb are located in the chart developed by his own where it

can be found the Intercept sphericity as he called (See figure 3) This chart is an easy

graphical way to relate the dimensions

c2

ba

Figure 2 Measurement of the 3 axes perpendicular among each other (Krumbein 1941)

Figure 3 Detailed chart to determining Krumbein intercept sphericity (Krumbein 1941)

(1)

6

Wadell (1932) defined the sphericity as the specific surface ratio (equation 2) Figure

4 is a schematic representation of the sphere surface and particle surface both particle

and sphere of the same volume

This way to obtain the sphericity is almost impossible to achieve as Hawkins (1993)

declares due the difficulty to get the surface area on irregular solids

Wadell (1934) also defined the sphericity based upon the particle and sphere volumes

as equation 3 (see figure 5)

Wadell (1934) used a new formula simple to manage using the diameters (see figure

6 and equation 4)

Zingg (Krumbein 1941) develop a classification based on the 3 axes relation in this

way it is easy to find out the main form of the particles as a disks spherical blades

S

s

3

CIR

P

V

V

CIR

SV

D

D

Figure 4 Same volume sphere surface (s) and particle surface (S) (modified after Johansson and Vall

2011)

Figure 5 Relation between the volume of the particle and the volume of the circumscribed

sphere (Johansson and Vall 2011)

Figure 6 Figure is showing the relation between the diameter of a circumscribed sphere and the

diameter of a sphere of the same volume as the particle (Johansson and Vall 2011)

(2)

(3)

(4)

7

and rod-like this is summarized on figure 7 Zinggrsquos classification is related with

Krumbein intercept sphericity and the figure 3

In figure 8 the figures 3 and 7 are combined the relation in the two classifications can

be seen it is an easy way to understand the morphology regarding on the a b and c

dimensions

Pye and Pye (1943) in the article ldquosphericity determinations of pebbles and sand

grainsrdquo compare the Wadellrsquos sphericity developed in 1934 (based on the diameter)

with ldquoPebble sphericityrdquo based on an ellipse this last equation (number 5) appears

two years early published by Krumbein (1941) Axis measurement is done as figure 1

denotes for equations 5 trough 12 with exception of equation 8 where the original

document was not possible to obtain

32a

cb

Figure 7 Zinggrsquos classification of pebble shape based on ratios ba and cb (Krumbein 1941)

Figure 8 Classification made by Zinggrsquos and chart to determine sphericity (Krumbein and Sloss 1963)

(5)

8

Sneed amp Folk in (1958) found a relation between the tree dimensional axes called

ldquoMaximum Projection Sphericityrdquo

In a similar way Ashenbrenner (1956) showed his equation at that time named

ldquoWorking Sphericityrdquo

Form or shape factor names are used by authors like Corey (shape factor eq 8) in the

paper published on 1949 Williams (shape factor eq 9) in 1965 Janke (form factor

eq 10) in 1966 and Dobkins amp Folk (oblate-prolate index eq 11) in 1970 (Blott and

Pye 2008)

Aschenbrenner (1956) develop the shape factor by using the relation of the tree axis

but the square of the middle one

3

2

ba

c

))ab((1)bc(16))ab((cb)(11

)ab()bc( 128

22

3 2

ab

c

acb when 1ac

b acb when

b

ac-1 2

22

2

3

cba

c

222

a

c

50c-a

b-a10

2b

ac

(6)

(7)

(8)

(9)

(10)

(11)

(12)

9

Table 2 General overview over different particle shape definitions for 3D sphericity has been compiled

and arranged chronologically

Aspect Name Author Year Based on

Sphericity (3D) Flatness index Wentworth 1922a 3-axes

True Sphericity Wadell 1932 Surface

Operational sphericity Wadell 1932 Volume

Sphericity Wadell 1934 Sphere diameter

Zinggrsquos clasification Zinggrsquos1

1935 3-axes

Intercept sphericity chart Krumbein 1941 3-axes

Pebble sphericity Pye and Pye 1943 3-axes

Corey shape factor Corey2

1949 3-axes

Working sphericity Ashenbrenner 1956 3-axes

shape factor Ashenbrenner 1956 3-axes

Maximum projection sphericity Sneed amp Folk 1958 3-axes

Williams shape factor Williams2

1965 3-axes

Janke form factor Janke2

1966 3-axes

Oblate-prolate index Dobkins amp Folk 1970 3-axes 1) Krumbein and Sloss 1963 2) Blott and Pye 2008

34 FORM (2D)

The technique to measure the sphericity is based in tree dimensions it can be found in

literature some ways to measure the ldquotwo dimensions sphericityrdquo which is simply the

perimeter of the particle projection some authors named ldquoparticle outlinerdquo or

ldquocircularityrdquo

Wadell in 1935 (Hawkins 1993) adopt a conversion of his 1934 3D sphericity

formula (equation 4) to a 2D outline He defined an orientation on the particles and

they were based on the maximum cross sectional area (outline of the particle

projecting the maximum area) The equations show the relation between diameters of

a circle of same area and smallest circumscribed circle

He also used the term ldquodegree of circularityrdquo as the ratio of the perimeter of a circle of

same area and the actual particle perimeter

Tickell in 1931 (Hawkins 1993) used his empirical relation The particle orientation

proposed was a random one It is described by the ratio between the area outline and

the area of smallest circumscribed circle

C

A

D

DC

P

PC C

CA

AC

(13)

(14)

(15)

10

Some other authors has been working with the ldquocircularityrdquo concept and had develop

them own equations as Pentland (1927) relating the area outline and area of a circle

with diameter equal to longest length outline and Cox (Riley 1941) with the ratio

area and perimeter time a constant equations 16 and 17 respectively Both authors did

not define any definite orientation of the grains

Riley (1941) realize the problems that an area perimeter and some other

measurements proposed by the above authors can carry as the time consuming and

tedious work (at that time were not computer all was made by hand) and thatrsquos why

he develop this equation easy to handle called ldquoinscribed circle sphericityrdquo He used

the same particle orientation proposed by Wadell and the relation of diameters of

inscribed and circumscribed circles

Horton 1932 (Hawkins 1993) use the relation of the drainage basing perimeter and

the perimeter of a circle of the same area as drainage basin

Janoo in 1998 (Blott and Pye 2008) develop his general ratio of perimeter to area

Sukumaran and Ashmawy (2001) develop his own shape factor (SF) defined as the

deviation of the global particle outline from a circle Figure 9 can be used as a

reference to determine the items used in the equation 21

N is referred to the number of sampling intervals o radial divisions

C2A

AC

2P

A4C

C

I

D

DC

CD

D

P

PC

A

PC

2

45ordm x N

Particleα

= SF

sumN

1=ii

(16)

(17)

(18)

(19)

(20)

(21)

11

Table 3 General chronological overview of the particle shape definitions for 2D sphericity

Aspect Name Author Year Based on

Circularity (2D) roundness Pentland 1927 area

roundness Cox1

1927 area-perimeter

roundness Tickell2

1931 area

Circularity Horton2

1932 drainage basin

outline circularity Wadell 1935 Circle diameter

degree of circularity Wadell 1935 Perimeter

inscribed circle sphericity Riley 1941 Circle diameter

Circularity Krumbein and Sloss 1963 chart

Janoo 1998 area-perimeter

Shape factor Sukumaran 2001 Segmentation of particle and angles

1) Riley 1941 2) Hawkins 1993

35 ROUNDNESS OR ANGULARITY

Roundness as described in section 32 is the second order shape descriptor Sphericity

lefts beside the corners and how they are this was notice by most of the authors sited

before and they suggested many ways to describe this second order particle property

Roundness is clearly understandable using the figure 10 Particle shape or form is the

overall configuration and denotes the similarities with a sphere (3D) or a circle (2D)

Roundness is concerning about the sharpness or the smoothness of the perimeter (2D)

Surface texture (Barret 1980) is describe as the third order subject (form is the first

and roundness the second) and it is superimposed in the corners and it is also a

property of particles surfaces between corners

Figure 9 Description of the Sukumaran factors to determine the shape and angularity (Sukumaran and

Ashmawy 2001)

12

Wadell (1935) describes his methodology calling it total degree or roundness to

obtain the roundness of a particle using the average radius of the corners in relation

with the inscribed circle diameter (see figure 11) on the equation

In the same study Wadell (1935) has used the equation

This two last equation shows slightly differences on the results (Wadell 1935)

Powers (1953) also published a graphic scale to illustrate the qualitative measure

(figure 12) It is important to highlight that any comparing chart to describe particle

properties has a high degree of subjectivity Folk (1955) concludes that when charts

are used for classification the risk of getting errors is negligible for sphericity but

large for roundness

N

R

r

Rinmax

r

R

NR

inmax

Figure 10 Form (shape) Roundness and Texture graphical description (Bowman et al 2001)

Figure 11 Wadellrsquos method to estimate the roundness corners radius and inscribed circle

(Hawkins 1993)

(22)

(23)

13

Some authors as Russel amp Taylor in 1937 Pettijohn in 1957 and Powers in 1953

developed a classification based on five and six classes (Hawkins 1993) each one

with its own class limits it is important to denote that the way they measure the

roundness is the developed by Wadell (1935) This classification and class limits are

showed in the table 4

Table 4 Degrees of roundness Wadell Values (Hawkins 1993) NA = no-applicable

Grade terms Russell amp Taylor (1937) Pettijohn (1957) Powers (1953)

Class

limits (R)

Arithmetic

midpoint

Class limits

(R)

Arithmetic midpoint Class

limits (R)

Arithmetic

midpoint

Very angular

NA

NA

NA

NA

012-017

014

Angular

000-015

0075

000-015

0125

017-025

021

Subangular

015-030

0225

015-025

0200

025-035

030

Subrounded

030-050

0400

025-040

0315

035-049

041

Rounded

050-070

0600

040-060

0500

049-070

059

Well rounded

070-100

0800

060-100

0800

070-100

084

Krumbein and Sloss (1963) published a graphical chart easy to determine the

sphericity and roundness parameters using comparison See figure 13 (Cho et al

2006)

Figure 12 A Roundness qualitative scale (Powers 1953)

Figure 13 Sphericity and roundness chart (Cho et al 2006) The roundness equation that appears here in

the chart is the wadellrsquos equation number 22

14

Fischer in 1933 (Hawkins 1993) used a straightforward method to quantify roundness

using a central point in the outline and dividing the outline in angles around this point

that were subtended by the straight or non curved parts of the profile were measured

This is illustrated in figure 14

To express the angularity value Fischer used the ratio of angles standing linear parts

on the outlines and concave respectively

Figure 14 left (A) and right (B) gives a similar angularity of approximately 042

using the above equations (Hawkins 1993)

Wentworth in 1922 used the maximum projection to define the position of the particle

to obtain the outline or contour (Barret 1980) The equation reflects the relation of the

diameter of a circle fitting the sharpest corner and the longest axis plus the shortest

axis c (minimum projection)

Wentworth (Hawkins 1993) expressed the roundness as the ratio of the radius of

curvature of the most convex part and the longest axis plus short axis

Actually these last two equations are the same just expressed in different terms when

the particle is in its maximum projection

Dimensions can be seen on figure 15 L and B represents the mayor axis a and

intermediate axis b The intention is to make difference between the 2 and 3

dimensions (L and B are for 2D as a b and c are for 3D)

deg360

ANG

=R

sumPLA

PLA

CON

ANG

ANGR

2)S(L

DR

M

S

B)4(L

RR CON

Figure 14 Fischerrsquos methods of angularity computation (Hawkins 1993)

A=inscribed circle B=circumscribed circle

(24)

(25)

(26)

(27)

15

Wentworth 1919 has a second way to express the roundness called Shape index

(Barrett 1980) and it relates the sharpest corner and the diameter of a pebble trough

the sharpest corner

Wentworth (1922b) used define the roundness as the ratio of the sharpest corner and

the average radius of the pebble

Cailleux (Barrett 1980) relates the radius of the most convex part and the longest

axis

Kuenen in 1956 show his roundness index (Barrett 1980) between the sharpest corner

and the breath axis

Dobkins amp Folk (1970) used a modified Wentworth roundness with the relation of

sharpest corner and inscribed circle diameters

AVG

CON

R

RR

x

s

D

DR

L2

RR CON

B

DR s

i

s

D

DR

3AVGAVG cbaDR2

Figure 15 Description of L and B axes (Hawkins 1993)

(28)

(29)

(30)

(31)

(32)

(33)

16

Swan in 1974 shows his equation (Barrett 1980) relating the sharpest (or the two

sharpest) corner(s) and inscribed circle diameter

Szadeczsky-Kardoss has his Average roundness of outline (Krumbein and Pettijohn

1938) relating the concave parts perimeter and the actual perimeter

Lees (1964a) developed an opposite definition to roundness it means that he

measures the angularity instead of the roundness and he calls it Degree of angularity

Figure 16 shows the items considered when equation 36 applies as the angles (α)

inscribed circle (Rmax-in) and the distance (x) The main formula is

In order to apply the last equation corners needs to be entered in the formula and each

individual result will add to each other to obtain the final degree of angularity

A roundness index appears on Janoo (1998) Kuo and Freeman (1998a) and Kuo et

al (1998b) it is described as

The last equation is on section 34 also because there is not a general agreement on the

definition furthermore some authors had used to define the roughness this is not the

only equation that has been used trying to define different aspects (sphericity

roundness or roughness) but it is a good example of the misuse of the quantities and

definitions

inmaxR

x)180(R

2P

A4R

i

ss

D

DDR

221

100P

PR CON

Figure 16 Degree of angularity measurement technique (Blot and Pye 2008)

(34)

(35)

(36)

(17)

17

Sukumaran and Ashmawy (2001) present an angularity factor (AF) calculated from

the number of sharpness corners Angles βi required to obtain the angularity factor are

shown in figure 9

Sukumaran and Ashmawy (2001) also suggested use not bigger sampling interval of

N=40 because it is the cut off between angularity factor and surface roughness If so

this equation could be used to describe the roughness

Table 5 General chronological overview of the particle roundness

Aspect Name Author Year Based on

Roundness shape index Wentworth 19191

diameter of sharper corner

shape index Wentworth 1922b sharpest corner and axis

roundness Wentworth 1933 convex parts

Fischer 19332

noncurved parts outline

Fischer 19332

noncurved-streigth parts outline

Average roundness of outline

Szadeczsky-Kardoss 19333

convex parts-perimeter

roundness Wadell 1935 diameter of corners

roundness Wadell 1935 diameter of corners

roundness Russel amp Taylor 19372

class limit table

roundness Krumbein 1941 chart

Cailleux 19471

convex parts

roundness Pettijohn 19494 class limit table

roundness Powers 1953 chart and class limit table

Kuenen 19561

axis-convex corner

roundness Krumbein and Sloss 1963 chart

degree of angularity Lees 1964a corners angles and inscribed circle

Dobkins amp Folk 1970 diameter of sharper corner

Swan 19741

diameter of sharper corners

Angularity factor Sukumaran and

Ashmawy 2001

Segmentation of particles and angles

1) Barret 1980 2) Hawkins 1993 3) Krumbein and Pettijohn 1938 4) Powers 1953

sum

sumsumN

1=i

2

i

2

N

1=i

2

i

2N

1=ii

)ordm180 -circleβ( - )(180ordm x 3

)ordm180-circleβ(-)ordm180 -Particleβ(

= AF (37)

18

36 ROUGHNESS OR SURFACE TEXTURE

A third property called texture appears early in the literature with the sphericity and

roundness properties since then texture property was longed described but it was in

accordance with the authors at that time not measurable

Wright in 1955 developed a method to quantify the surface texture or roughness of

concrete aggregate using studies done on 19 mm stones The test aggregates were first

embedded in a synthetic resin The stones were cut in thin sections The sections

projection was magnified 125 times The unevenness of the surface was traced and the

total length of the trace was measured The length was then compared with an uneven

line drawn as a series of chords (see figure 17) The difference between these two

lines was defined as the roughness factor (Janoo 1998)

However with the advance of technology it has become easier measure the roughness

and here is presented some researcherrsquos ideas how this property should be calculated

One technique used by Janoo (1988) to define the roughness can be seen in figure 18a

and is defined as the ratio between perimeter and convex perimeter

The convex perimeter is obtained using the Feretrsquos box (or diameter) tending a line in

between the touching points that the Feretrsquos box describes each time it is turn (figure

18b)

PER

OC

PR

Figure 17 Measurement method for characterizing the surface texture of an aggregate (Janoo 1998)

a) Convex perimeter (CPER) b) Feret measurement Figure 18 a) Convex perimeter (CPER) b) Feret measurement (modified after Janoo 1998)

(38)

a)

b)

19

Kuo and Freeman (1998a) and Kuo et al (1998b) use the roughness definition as the

ratio perimeter and average diameter

Erosion and dilatation image processing techniques are used to obtain the surface

texture Erosion is a morphological process by which boundary image pixels are

removed from an object surface which leaves the object less dense along the

perimeter or outer boundary Dilatation is the reverse process of erosion and a single

dilatation cycle increases the particle shape or image dimension by adding pixels

around its boundary (Pan etal 2006)

The ldquonrdquo erosion and dilatation cycles are not standardized

Mora and Kwan (2000) used the ldquoconvexity ratio CRrdquo (equation 41) and the ldquofullness

ratio FRrdquo (equation 42) in their investigation they are

The convex area is the area of the minimum convex boundaries circumscribing the

particle This is illustrated in the figure 19 The convex area is obtained in a similar

way as the convex perimeter but in this case the area between the original outline and

the convex perimeter is our convex area

AVG

OD

PR

100A

1AARO

CONo A

AR =

CONo A

AR =

Figure 19 Evaluation of area and convex area (Mora and Kuan 2000)

(39)

(40)

(41)

(42)

20

4 TECHNIQUES IN ORDER TO DETERMINE PARTICLE

SHAPE

41 HAND MEASUREMENT

Hand measurement technique was the first used by obvious reasons in order to

improve the accuracy special devices developed as the ldquosliding rod caliperrdquo used by

Krumbein (1941) it works placing the sample on the sliding road calliper as show

figure 20b the length in different positions can be obtain by using the scale provided

in the handle the ldquoconvexity gagerdquo that was actually used by opticians to measure the

curvature of lenses but easily applicable to the particle shape analysis (Wentworth

1922b) works measuring the movement of the central pivot as figure 20a shows (the

two adjacent pivots are invariable) as many the central pivot moves more is the

curvature or the ldquoSzadeczky-Kardossrsquos apparatusrdquo develop in 1933 that traces the

profile of the rock fragment so the outline traced is then analyzed (Krumbein and

Pettijohn 1938) figure 20c show equipment

Another helpful tool to determine the particle dimensions was the ldquocamera lucidardquo to

project the particlersquos contour over a circle scale appearing in Figure 21 thus it is

possible to measure the particlersquos diameter

a)

c) b)

Figure 20 a) convexity gage used to determine the curvature in particle corners (Wenworth 1922b)

b)sliding rod caliper device to measure the particle axis length (Krumbein 1941) and c)Szadeczky-

Kardoss (1933) apparatus it was utilized to obtain the particle outline

Figure 21 Circle scale used by Wadell (1935) to determine particlersquos diameter and roundness

21

42 SIEVE ANALYSIS

Bar sieving eg according to EN 933-31997 can be used to determine simple large

scale properties By combining mesh geometries the obtained results can be used to

quantify flakiness and elongation index ASTM D4791 (Flat and elongated particles

are defined as those coarse aggregate particles that have a ratio of length to thickness

equal to or greater than a specified value such as 51 The index represents the

percentage on weight of these particles) The method is not suitable for fine materials

This due to the difficulty to get the fine grains passed through the sieve and the great

amount of particles in relation to the area of the sieve (Persson 1998) eg EN 933-

31997 related to flakiness index The test is performed on aggregates with grain size

from 4 mm and up to 63 mm two sieving operations are necessary the first separates

on size fraction and the second use a bar sieve after the first sieving the average

maximum diameter of the particles is obtain and with the second sieving (bar sieving)

the shortest axis diameter is found finally with this two parameters the flakiness

index is determined

There are more standards related with the particle shape (see appendix A) but this

above presented are probably the most known using sieve analysis to determine

particlersquos geometrical properties

Sieve analysis is facing the computers age and image analysis sieving research is

taking place (Andersson 2010 Mora and Kwan 2000 Persson 1998) Industry is

also applying the image analysis sieving with decrees on the testing time compare

with the traditional sieving method An inconvenient of image analysis is the error

due the overlapping or hiding of the particles during the capture process but the

advantages are more compare with disadvantages (Anderson 2010)

43 CHART COMPARISON

Charts developed over the necessity of faster results because the long time consuming

required when measuring each particle

Krumbein (1941) present a comparison roundness chart for pebbles which were

measured by Wadellrsquos method because this property was the most difficult to measure

due to the second order scale that roundness represents (See figure 22)

Figure 22 Krumbein (1941) comparision chart for roundness

22

A qualitative chart by Powers (1953) try to include both (sphericity and roundness)

particlersquos characteristics it was divided on six roundness ranges (very angular

angular sub-angular sub-rounded rounded and well rounded) and two sphericity

series (high and low sphericity) This chart was prepared with photographs to enhance

the reader perspective (See figure 23)

A new chart including sphericity and roundness appear this time it was easier to

handle the two mean properties of particlersquos shape furthermore there was included

the numerical values that eliminated the subjectivity of qualitative description The

chart is based on Wadellrsquos definitions (Krumbein and Sloss 1963) (See figure 24)

Folk (1955) worried about the personrsquos error on the chartrsquos comparison studied the

determination of sphericity and angularity (he used the Powers 1953 comparison

chart) he found that the sphericity determination by chart comparison has a negligible

error while the roundness he concluded it was necessary to carry out a more wide

research due the high variability show by his study

Figure 23 Powers (1953) qualitative shpericity-roundness chart

Figure 24 Sphericity-roundness comparison chart (Krumbein and sloss 1963)

23

44 IMAGE ANALYSIS

Image analysis is a practical method to use for shape classification since it is fast and

can be automated Different techniques appear to process these images among them

are

o Feret Diameter the Feret diameter is the longitude between two parallel lines

this lines can rotate around one particle or outline to define dimensions as it

is shown in figure 25 these method is not a fine descriptor but as it was say

above it is a helpful tool to determine diameters (Janoo 1988)

o Fourier Mathematical Technique It produces mathematical relations that

characterize the profile of individual particles This method favours the

analysis of roughness and textural features for granular soils The problem in

the methodology remains in the re-entrant angles in order to complete the

revolution (Bowman et al 2001) see figure 26

o Fractal Dimension Irregular line at any level of scrutiny is by definition

fractal (Hyslip and Vallejo 1997) Figure 27 shows fractal analysis by the

dividing method The length of the fractal line can be defined as

N

1n

nn0 )nsinbncosa(a)(R

RD1n)(P

Figure 25 Feret measurement technique is defined by two parallel lines turning

around the particle to define the shortest and longest Feret diameter (Janoo 1988)

Figure 26 Fourier technique with two radiuses at one angle (Bowman et al 2001)

(43)

(44)

24

o Orthogonal image analysis This technique is basically the use of two images

orthogonal between them to acquire the three particle dimensions (Fernlund

2005) any of the above techniques can be used in this orthogonal way

o Laser Scanning Technique this kind of laser scanning 3D is one of the most

advanced techniques In figures 28a) we have the laser head scanning the rock

particles the particles have control points in order to keep a reference point

when move them to scan the lower part in figure 28b) we can see the laser

path followed (Lanaro and Tolppanen 2002)

Another technique is the Laser-Aided Tomography (LAT) in this case a laser sheet is

used to obtain the particles surveying (see figure 29) This technique is different and

has special requirements as to use liquid with same refractive index as the particles

particles must let the laser or certain percent of light go through (Matsushima et al

2003)

a) b)

Figure 27 Fractal analysis by the dividing method at different scrutiny scale (Hyslip and Vallejo 1997)

Figure 28 a) Scanning head b) scanning path (Lanaro and Tolppanen 2002)

Figure 30 3D scan completed ready to

use for any further measure

(Matsushima et al 2003)

Figure 29 LAT scaning particles

(Matsushima et al 2003)

25

Both 3D techniques obtain the particle shape that is later used to achieve measures as

we can see in figure 30

All these previous techniques are easily written in codes or scripts to be interpreted in

a digital way obtaining the desired measurement but there are some interesting points

in the image analysis regarding on the errors involve among them are image

resolution and orientation of the particles orientation is not relevant when it is

random and large number of particles are involve resolution have an influence on the

accuracy (Zeidan et al 2007)

When resolution is increase more accuracy is obtain and the object representation

match better with the real form in the other hand more resolution means more

spending on memory and time thus resolution needs to be according with the goal

and precision needed in any work (Schaumlfer 2002)

Schaumlfer (2002) conclude that attributes like length when measuring digital images

present relative high errors It can be vanish or at least diminish using high resolution

just for diameter but not for perimeter that keep the error as big as initially Johansson

and Vall (2011) obtain similar results when 3 different resolutions were used in the

same particle obtaining an unstable output for those termsquantities that involve the

perimeter Thus all quantities relating the perimeter should be treated with care

5 EFFECT OF SHAPE ON SOIL PROPERTIES

51 INTRODUCTION

In laboratory test on the effect on particle size on basic properties has been

investigated in several studies this relation has been discussed and various

mechanisms had been proposed to explain the behaviour of the soil in dependency

also with the shape Basically there are two mechanisms proposed The arrangement

of particles and the inter-particle contact (Santamarina and Cho 2004) and

subsequence breakage

The arrangement of particles

Arrangement of the particles can be presented in three different forms loose dense

and critical this arrangement determines the soil properties (eg density increase with

more dense arrangement) Loose and dense states are easy understandable when

figure 31 is explained while in the upper part of the figure the particles are arranged

using the minimum space needed in the lower part a span is created using the flaky

particle as a bridge this phenomena is known as ldquobridgingrdquo Bridging can produce

different geotechnical results when just the shape of the particle is changed eg void

ratio (Santamarina and Cho 2004) Particles are able to rearrange this could be done

applying pressure (energy) to the soil the pressure (energy) will create such forces

that soil particles will rotate and move (see figure 34) finishing in a more dense state

26

A loose soil will contract in volume on shearing and may not develop any peak

strength (figure 32 left) In this case the shear strength will increase gradually until

the residual shear strength is revealed once the soil has ceased contracting in volume

A dense soil may contract slightly (figure 32 right) before granular interlock prevents

further contraction (granular interlock is dependent on the shape of the grains and

their initial packing arrangement) In order to continue shearing once granular

interlock has occurred the soil must dilate (expand in volume) As additional shear

force is required to dilate the soil a peak shear strength occurs (figure 32 left) Once

this peak shear strength caused by dilation has been overcome through continued

shearing the resistance provided by the soil to the applied shear stress reduces

(termed strain softening) Strain softening will continue until no further changes in

volume of the soil occur on continued shearing Peak shear strengths are also

observed in overconsolidated clays where the natural fabric of the soil must be

destroyed prior to reaching constant volume shearing Other effects that result in peak

strengths include cementation and bonding of particles The distinctive shear strength

called the critical state is identified where the soil undergoing shear does so at a

constant volume (Schofield and Wroth 1968)

The inter-particle contact

For frictional soil ie coarse grained soil the friction between particles is the

dominating factor for strength Materials usually consisting of coarse grains (diameter

Figure 31 Bridging effect when flaky particles are combined in the bulk material (Santamarina and

Cho 2004)

Figure 32 The left part of the figure show a typical behaviour of loose and dense material over shear stress

while at the right the figures illustrate the typical volume changes

27

gt 006mm) behave as a frictional soil it means that the strength of coarse soils (silt

sand gravel etc) comes from an inter-particle mechanical friction thus ideally they

do not have traction strength In figure 33 the inter-particle contact is illustrated here

the pressure (P) is applied and two more components are found the normal load (N)

and the tangential load (T) described as the friction coefficient (μF) The forces stand

in equilibrium (Johansson and Vall 2011)

When particles equilibrium is disturbed (friction coefficient is not enough to keep

particles unmoved) the rotation is imminent and it is necessary in order to compact

the soil in figure 34 can be seen that the arrangement is a fact that inhibit or allow this

rotation and the shape in the 3 different scales are also factors because the more

spherical andor more rounded andor less roughness more easy is the rotation

(Santamarina and Cho 2004)

Breakage

Breakage is a side effect of the inter-particle contact and rotation when pressure

exceed the rock strength it can happened when the particles are tight together and

there is not enough space to rotate it is more obvious in angular particles (mesh form)

or as in figure 31 where the flaky particle ldquobridgingrdquo is not able to rotate but it can

brake by the pressure increase Yoginder et al (1985) notice that the angular particle

break during his experiments and they turn more rounded changing the original size

and form configuration at the same time there was a soil properties loosening

Figure 33 Inter-particle contact and forces acting (Axelsson 1998)

Figure 34 Rotation inhibition by the particles compaction or low void ratio (Santamarina and Cho 2004)

28

52 INFLUENCE OF SIZE AND SHAPE

Wenworth (1922a) and Pellegrino (1965) among others suggest that agent transport of

the rocks (rigor of transport temperature and moisture changes etc) determine its

shape but also the particle genesis itself (rock structure mineralogy hardness etc) It

is not possible to determine the shape of the particles based on the agent transport or

genesis but generally a shape behaviour is expected according to Mitchell and Soga

(2005) specially when the particle size is in the clay size (gt2μm) The shapes of the

most common clay minerals are platy (figure 35) with some exceptions (eg

halloysite occurs as tubes kaolinite are large thick and stiff Smectites are composed

of small very thin and filmy particles Illites are intermediate between kaolinite and

smectite and attapulgite occurs in lathlike particle shapes) Some clay minerals

photographs are presented in figure 35

Figure 35 Clay mineral shape a) hallosite b) Kaoline c) Smactites d) Illites and e) attapulgite (Modified

from Mitchell and Soga 2005)

Figure 36 Particle size range in soils Generally the particles of clay size are plate shaped (Mitchell and

Soga 2005)

a) b) c)

e) d)

29

53 VOID RATIO AND POROSITY

The void ratio (e) is the ratio of the volume of voids to the volume of solid it is

defined by the equation

Porosity (n) is the ratio of the volume of voids to the total volume of the soil it is

represented by the equation

Holubec and DrsquoAppolonia (1973) found a relation between the void ratio and

sphericity (referred in the paper as coefficient of angularity ratio of particle surface

and equivalent sphere surface) their results show that the maximum and the minimum

void ratio increases as the shpericity decreases In this study the surface was obtained

for an indirect method based on the permeability developed by Hoffman in 1959

described in the same document Rouseacute et al (2008) defined the roundness as

Wadell (1935) and he found it as an important factor controlling the minimum and

maximum void ratios Some other authors as Youd (1973) and Cho et al (2006)

conclude the same minimum and maximum void ratios increase when sphericity and

roundness decrease Another interesting result (all above authors) was the bigger

influence of the form (sphericity circularity) and roundness on the maximum void

ratio The change of the maximum void ratio is more pronounced than the change of

the minimum void ratio when the form and roundness changes (See figure 39)

Particles arrangement and interlocking are probably the factor that controls the void

ratio bridge effect permit the existence of void among the particles while interlocking

allowed the particles to form arches avoiding the possibility to rotate and stay in a

more stable configuration eg as it happens with marbles

Figures 36 37 and 38 shows proposed empirical relationships between void ratio and

shape from tables 5 and 6 (graphically the scale goes from 0 to 1 when cero mean

high angularity shpericity or circularity and one means low angularity circularity or

sphericity) Holubec and DrsquoAppolonia (1973) data was taken to obtain a power curve

and describe a tendency Santamarina and Cho (2004) show Youd equations in the

original paper Youd (1973) never presented the equation but it is easy to use the

information to draw a trend

The graphics presented in this document (figures 36 37 and 38) must be used with

certain reserves due the fact that the original data was modified in order to fit all

information in one graphic what the figures shows is just the general trend of the

behaviourrsquos material regarding on the shape If more accurate description and

information is required the author recommends consulting the reference data In the

same way equations from Holubec and DrsquoApollonia (1973) and Youd (1973) were not

presented by the authors but the use of the information was taken in order to build up

those equations on tables 6 and 7

S

V

V

V

= e

V

V

=nV

(45)

(46)

30

Table 6 Minimum void ratio equations regarding on the quantity (Ψ for sphericity C for circularity R

for roundness SF for Sukumaran shape factor and AF for Sukumaran angularity factor)

EQUATION NUMBER REFERENCE

Figure 34 (left)

4340

minΨ45490e =

47

Holubec amp DrsquoAppolonia 1973 (Ψ

was obtained using equation 2)

SF06340

mine021903180e +=

48

Sukumaran amp Ashmawy 2001 (SF

obtained using equation 21)

C05101emin

= 49

Cho etal 2006 (C obtained using

figure 12)

Figure 34 (right)

1

minR08203590e +=

50

Youd 1973 (R obtained from figure

11 and table 3)

R34080emin

= 51

Cho et al 2006 (R obtained using

figure 12)

1

minR05104330e +=

52

Rouseacute et al 2008 (R obtained by

equation 21)

AF02330

mine372004160e +=

53

Sukumaran amp Ashmawy 2001 (AF

obtained using equation 37)

Table 7 Maximum void ratio equations regarding on the quantity (Ψ for sphericity C for circularity R

for roundness SF for Sukumaran shape factor and AF for Sukumaran angularity factor)

EQUATION NUMBER REFERENCE

Figure 35 (left)

51520

max Ψ61120e = 54

Holubec and DrsquoAppolonia 1973 (Ψ

was obtained using equation 2)

SF1190

max e0016907180e += 55

Sukumaran amp Ashmawy 2001 (SF

obtained using equation 21)

C86061emax = 56

Cho etal 2006 (C obtained using

figure 12)

Figure 35 (right)

1

max R1505540e += 57

Youd 1973 (R obtained from figure

11 and table 3)

R62031emax= 58

Cho et al 2006 (R obtained using

figure 12)

1

max R107106150e += 59

Rouseacute et al 2008 (R obtained by

equation 21)

AF0530

max e12506090e += 60

Sukumaran amp Ashmawy 2001 (AF

obtained using equation 37)

Comparing figures 37 and 38 (minimum and maximum void ratio) it can be seen on

the right scheme of both figures 37 and 38 (when the factor is roundnessangularity)

that all the empirical relations has a common initial point close to 1 (it means that

particles are well rounded) while this common agreement disappear when the

roundness factor decreases (when the particles become more angular) Same figures

(37 and 38) on the left graphs (when the factor is sphericitycircularityshape) do not

present the same behaviour in fact there is more disperse initial point close to 1(when

the particles tend to be more sphericalcircular)

31

In Figure 39 the Δe (emax-emin) has been plotted to show how the maximum void ratio

and the minimum void ratio has different rate change when the particle shape

changes Maximum void ratio increases more than minimum void ratio when the

particle shape becomes less spherical andor more angular Comparing figure 39 left

and right graphics it can be seen that right present a common initial point when the

quantity (roundnessangularity) is close to one while in the left graphic the initial

point is more disperse Both ending points in both graphics (close to zero) are

dispersed

Figures 37 38 and 39 present the same behaviour right graphics (when the factor is

roundness angularity) in each figure have an initial common point while the left

graphics do not (when the factor is sphericity circularity shape)

Figure 37 Minimum void ratio based upon the relation of shape factor proposed by the authors indicated

in the figure

Figure 38 Maximum void ratio based upon the relation of shape factor proposed by the authors indicated

in the figure

04

06

08

1

12

14

16

18

2

005

015

025

035

045

055

065

075

085

095

Factor (roundness angularity)

min

imu

m v

oid

rati

o

Youd 1973 roundness

Rouse 2008 roundness

Cho 2006 roundness

Sukumaran 2001 AF

03

04

05

06

07

08

09

1

11

12

13

05

015

025

035

045

055

065

075

085

095

Factor (sphericity circularity shape)

min

imu

m v

oid

rati

oHolubec 1973 sphericity

Cho 2006 circularity

Sukumara 2001 SF

05

07

09

11

13

15

17

19

21

00

150

250

350

450

550

650

750

850

95

Factor (sphericity circularity shape)

Maxim

um

vo

id r

ati

o

Holubec 1973 sphericity

Cho 2006 circularity

Sukumara 2001 SF

05

1

15

2

25

3

35

005

015

025

035

045

055

065

075

085

095

Factor (roundness angularity)

Maxim

um

vo

id r

ati

o

Youd 1973 roundness

Rouse 2008 roundness

Cho 2006 roundness

Sukumaran 2001 AF

32

54 ANGLE OF REPOSE

The angle of repose of a granular material is the steepest angle of descent or dip of the

slope relative to the horizontal plane when material on the slope face is on the verge

of sliding as show in figure 40

According to Qazi (1975) there are five types of forces which may act between the

particles in soils

1 Force of friction between the particles

2 Force due to presence of absorbed gas andor moisture of particle

3 Mechanical forces caused by interlocking of particles of irregular shape

4 Electrostatic forces arising from friction between the particles themselves and

the surface with which they come in contact

5 Cohesion forces operating between neighbouring particles

Rouseacute et al (2008) found a decrease of angle of repose with increase roundness

based upon ASTM C1444 test (Standard Test Method for Measuring the Angle of

Repose of Free-Flowing Mold Powders) The method consist in pouring sand on a

surface cover by paper trough a funnel of specific dimensions (the nozzle diameter

depend on the sandrsquos particle size) from an altitude of 15 inches (381 mm) The sand

is release from the funnel until the peak of the cone formed by the sand stops the flow

The repose angle is obtained with the equation

H represent the 15 inches D and d represent the diameter of the cone formed by the

sand and the diameter of the funnel respectively

Figure 39 Maximum minus minimum void ratio based upon the relation of shape factor proposed by the

authors indicated in the figure

0

01

02

03

04

05

06

07

08

09

1

005

015

025

035

045

055

065

075

085

095

Factor (sphericity circularity shape)

Maxim

um

- M

inim

um

Vo

id r

ati

oHolubec 1973 sphericity

Cho 2006 circularity

Sukumara 2001 SF

0

02

04

06

08

1

12

14

16

18

005

015

025

035

045

055

065

075

085

095

Factor (roundness angularity)

Maxim

um

- M

inim

um

Vo

id r

ati

o

Youd 1973 roundness

Rouse 2008 roundness

Cho 2006 roundness

Sukumaran 2001 AF

dD

H2

tan=φ1

rep(61)

33

Rouseacute (2008) shows an empirical relation to obtain the angle of repose based on the

roundness of the particles

55 SHEAR STRENGTH

The MohrndashCoulomb failure criterion represents the linear envelope that is obtained

from a plot of the shear strength of a material versus the applied normal stress This

relation is expressed as

where τ is the shear strength σn is the normal stress co is the intercept of the failure

envelope with the τ axis and is the slope of the failure envelope The quantity c is

often called the cohesion and the angle is called the angle of internal friction

Studies show that the internal friction angle (under drained triaxial tests) increases

more rapidly on those materials having higher angularity increasing the relative

density The internal friction angle is a function of the relative density and the particle

shape (Holubec and DrsquoAppolonia 1973)

Chan and Page (1997) found in a study made with dry copper (using different shapes

and sizes ranging from 180 to 106 μm) using a direct shear test (ring share test) that

the internal friction angle increases as the angularity increases

Shinohara et al (2000) did some experiments with steel powder different shapes

using a triaxial cell in the test Shinohara never used the roundness or angularity on

the work but apply the shape factor (relation long axisshort axis) and the results were

that as this relation deviate from factor 1 the internal friction angle increases

The following empirical relations were found in the literature showing the behaviour

of the friction angle (obtained under different conditions)

)tan( noc

Figure 40 Representation of the angle of repose

(63)

(62)

34

Cho et al (2006)

(64)

(R is obtain by comparing the Krumbein chart figure 13)

Rouseacute (2008)

(65)

(66)

(R is defined using Wadell equation 22)

In figure 41 the suggested empirical relations above and lines constructed using

author data from Holubec and DrsquoAppolonia (1973) and Sukumara and Ashmawy

(2001) are plotted together to display the general trend on the particle shape and

friction angle relation Sukumaran reports two lines one based on the shape factor

(SF) and the second referring the angularity factor (AF) Sukumaran performed the

tests at constant volume

The scale used for Holubec and DrsquoAppolonia (1973) have lower and upper limits of 1

and 2 respectively (angularity form) and a scale change was applied to be able to

presented in the actual figure 41 As in the previous section (52) the author

recommend to use the original data from the references due that the figure just follows

the general trend of the behaviourrsquos particle regarding on the shape

Figure 41 The changes on the internal friction angle shows a general increase when the particle roundness

becomes angular or in the case of Sakamuran less spheric (Shape factor SF)

35

Barton and Kjaernsli (1981) suggested a model (equation 67) to predict the peak

friction angle (φrsquo) based upon numerous trixial and direct shear data tests

where

Se equivalent strength of particle

Re equivalent roughness of particle

φb basic friction angle (obtained from basic tilting test)

σn normal load

The information required for the model is (1) the uniaxial compressive strength of the

rock (2) the d50 particle size (mesh size where 50 of the particles pass through)

required to define Se (figure 42) (3) the degree of particle roundness and (4) the

porosity following compaction All data can be estimated by simple index tests

Barton and Kjaernsli (1981) suggest that particle size and sample scale has an effect

on the friction angle and includes them to obtain the equivalent strength (Se) figure 42

shows the method to obtain this value Compressive strength (σc) was chosen to be the

factor affecting the scale because micro fractures influence this property while

samples are bigger more micro fractures contain and its compressive strength reduces

The equivalent roughness is obtain using figure 43 where is required to know the

porosity (n) and the origin of the particles (a small chart is provided in the same figure

to compare the particles profile)

b

n

ee

SLogR

Figure 42 Method of estimating Equivalent Strength (Se) of rockfill based on uniaxial compressive strength

(σc ) and d50 particle size (Barton amp Kjaernsli 1981)

(67)

36

56 SEDIMENTATION PROPERTIES

A particle released in a less dense Newtonian fluid initially accelerate trough the fluid

due to the gravity Resistances to deformation of the fluid transmitted to the particle

surface drag generate forces that act to resist the particle motion The force due to the

weight (Fw) can be written as

Where ρp ρ are density of the particle and fluid (water) respectively g is the

gravitational force and Vp is the volume of the particle

And the resistance force (FD) is

Where CD is the dimensionless drag coefficient W is the weight of the particle and A

is the cross section area

Particlersquos shape has been assumed to be spherical when equations are applied on the

settling velocity Correlation deviates when particle shape departs from spherical form

Figure 43 Method of estimating Equivalent Roughness (Roe) based on porosity of rockfill

origin material degree of roundedness and smoothness of particle (Barton amp Kjaernsli 1981)

PPW ρ)gV(ρF

A2

WρCF

2

DD

(68)

(69)

37

(Dietrich 1982) and it is known that natural particles depart from spherical form

thus it is evident that this departure would have consequences

The below equation is proposed to account the shape (in this case the Corey shape

factor equation 8) in the settling velocity (Jimenez and Madsen 2003)

Jimenez and Madsen (2003) Dietrich (1982) Briggs and McCulloch (1962) and

others were working in the hydraulic shape of particles to solve problems as sediment

transport It is obvious that the equation presented and the researcherrsquos investigation

works under certain conditions (eg grain size between 0063-1 mm)

Dietrich (1982) suggests an empirical relation that accounts settling velocity size

density shape and roundness of a particle

R1 R2 and R3 are fitted equations for size and density shape and roundness

respectively

57 HYDRAULIC CONDUCTIVITY PERMEABILITY

Darcyrsquos Law Permeability is one component of Darcyrsquos law Darcys law is a simple

proportional relationship between the instantaneous discharge rate through a porous

medium the viscosity of the fluid and the pressure drop

The total velocity Ve is equal to the product of the permeability of the medium

(porous media) k the pressure drop ∆p all divided by the viscosity μ (Muskat

1937)

Darcys law is only valid for slow viscous flow most groundwater flow cases fall in

this category Typically Darcyrsquos law is valid at any flow with laminar flow (see figure

44)

Reynoldrsquos number (Laminar and turbulent Flow) Typically any laminar flow is

considered to have a Reynoldrsquos number less than one and it would be valid to apply

Darcys law Experimental tests have shown that flow regimes with Reynolds numbers

1

ND

S

S

ZY

gd1s

WW

NDN

gd)1s(4

dS

2R1R

3 10RW

pk

Ve

(70)

(71)

(72)

(73)

38

up to 10 may still be Darcian (laminar flow) as in the case of groundwater flow The

Reynolds number (a dimensionless parameter) for porous media flow is typically

expressed as

where ρ is the density of water (units of mass per volume) υ is the specific discharge

(with units of length per time) d is a representative average grain diameter for the

porous media (often taken as the 30 passing size from a grain size analysis using

sieves - with units of length) and μ is the viscosity of the fluid (Muskat 1937)

Shape effects Permeability as Head and Epps (2011) suggested is affected by the

shape and texture of soil grains Elongated or irregular particles create flow paths

which are more tortuous than those spherical particles Particles with a rough surface

texture provide more frictional resistance to flow Both effects tend to reduce the

water flow through the soil

Kozeny-Carman empirical relation accounts for the dependency of permeability on

void ratio in uniformly graded sands serious discrepancies are found when it is

applied to clays due the lack of uniform pores (Mitchell and Soga 2005)

There are various formulations of the Kozeny-Carman equation one published by

Head and Epps (2011) takes the void ratio e the specific surface area Ss and an

angularity factor F into account of permeability k

The angularity factor F considers the shape of the particles and ranges from 11 for

rounded grains 125 for sub rounded to 14 for angular particles The specific surface

Ss is defined as

d1 and d2 represent the maximum and minimum size particle in mm

Kane amp Sternheim (1988) suggest that the inclusion of the shape factor (F) has

probably the background on the Reynolds number due this factor is dependent

significantly on the shape of the obstacles and Reynolds number determines the

presence of laminar or turbulent flow Figure 44 show how the laminar flow has low

energy dissipation while turbulent flow (eg the roughness and path tortuosity) has

high energy dissipation

e1

e

FSs

2k

3

2

dRe

21

6

ddSs

(74)

(75)

(76)

39

According to Nearing and Parker (1994) the amount of soil detached during laminar

and turbulent flow is dependent on each soil and also greater on turbulent flow due the

greater shear strength generated during this kind of flow this could suggest the

greater erosion when turbulent flow is present

58 LIQUEFACTION

Soil liquefaction is a phenomenon in which soil loses much of its strength or stiffness

for a generally short time by earthquake shaking or other rapid loading Static and

dynamic liquefactions occur been the second one the most regular known

Liquefaction often occurs in saturated soils that is soils in which the space between

individual particles is completely filled with water This water exerts a pressure on the

soil particles that influences how tightly the particles themselves are pressed together

Shaking or other rapid loading can cause the water pressure to increase to the point

where the soil particles can readily move with respect to each other (Jefferies and

Been 2000)

Jefferies and Been (2000) state that it is clear that minor variation in intrinsic

properties of sand have major influence on the critical state These might be variations

on grain shape mineralogy grain size distribution surface roughness of grains etc

Yoginder et al (1985) found that substantial decrease on liquefaction resistance

occur with increase in confining pressure for rounded and angular sands (1600 kPa)

also rounded sands show an rapidly build up of resistance against liquefaction with

increasing density while angular tailing sand in contrast show such rapid increase

only at low confining pressures At low confining pressure angular material is more

resistant to liquefaction Probably the breakage of the corners on the angular particles

in tailings is ruling the lost in resistance at high confining pressures (sieve analysis

Figure 44 The figure show the extremes of flow behaviour First turbulent conditions where the flow is

essentially random and unpredictable and second the well defined Laminar flow conditions

40

after test identify the breakage of angular particles while on rounded particles the

sieve analysis was practically the same)

59 GROUNDWATER AND SEEPAGE MODELLING

In groundwater flow the particlersquos shape affects the soilrsquos pore size distribution

hence the flow characteristics (Sperry and Peirce 1995) Tortuosity and permeability

(also see section 57) are two significant macroscopic parameters of granular medium

that affect the passing flow (Hayati et al 2012) Current models incorporating the

effects of particle shape have failed to consider irregular particles such as those that

would prevail in a natural porous medium (Sperry and Peirce 1995)

Hayati et al (2012) suggested based on his results that tortuosity effect converge

when the porosity increases indicating that the shape have dominance at low and mid

porosity ranges

Sperry and Peirce (1995) research conclusions suggest that particle size and porosity

are more important predictors for hydraulic conductivity explaining the 69 of the

variability but particle shape appears to be the next most important This however

apparently comprises particles larger than 295-351 μm Differences for particle size

295-351 μm and smaller are not detectable Another interesting result in the research

was the interaction effect of the particle size and particle shape It suggests a different

packing configuration for particles of the same shape but different size (scale

dependent)

6 DISCUSSION

61 TERMS QUANTITIES AND DEFINITIONS

In order to describe the particle shape in detail there are a number of terms quantities

and definitions (qualitative and quantitative) used in the literature (eg Wadell 1932

1934 Krumbein 1941 Sneed amp Folk 1958) All mathematical definitions

(quantitatives) are models used to simplify the complexity of shape description Some

authors (Mitchell amp Soga 2005 Arasan et al 2010) are using three sub-quantities

one and each describing the shape but at different scales The terms are

morphologyform roundness and surface texture (figure 1) The three sub-quantities

are probably the best way to classify and describe a particle because not a single

definition can interpret the whole morphology Common language is needed when

descriptors are explained and these three scales represent an option It is evident in

the reviewed literature that many of the shape descriptors are presented with the same

name but also that there is not a clear meaning on what this descriptor defines eg

when there is no upper limit in the roundness does it means that the angularity never

ends Could they be more and more angular Probably they could be on theory but

not in reality

41

62 PROPERTIES

Trough various articlersquos review done in the present investigation it is recognized that

the particlersquos shape has an effect on the material properties among these are

1 Porosity (Tickell 1938 Fraser 1935 Kolbuszewski 1948) and void ratio

(Cho et al 2006 Shergold 1953 Rouseacute et al 2008 Santamarina and Cho

2004)

2 Permeability (Witt and Brauns 1983)

3 Internal friction angle (Shinohara et al 2000 Chan and Page 1997

Cheshomi et al 2009)

4 Density (Youd 1973 Holubec and DrsquoAppolonia 1973)

5 Drag coefficient Hydraulics (Briggs and McCulloch 1962)

In Table 5 is a short resume of the properties and shape effect found in peer review

articles trough different journals Most of the reviewed articles based its research on

uniform graded sands

Table 8 Compilation of properties influenced by particle shape

Repose

angle

Friction

angle

Porosity and

Void ratio Density Permeability

Settling velocity

Drag coefficient Deformation

Sphericity (3D)shape factor

NI x x x x x x

Circularity (2D)

NI x x x x NI NI

Roundness x x x x NI NI x

x influence

NI no information available

Shape of particles has an effect on the arrangement producing bridging or avoiding

the rotation of the particles and the resulting geotechnical property is affected eg

including flaky particles can result in a higher void ratio due the bridging effect

(Santamarina and Cho 2004) and depending on the loads even the size distribution is

changed due the breakage (Yoginder et al 1985) in similar way angular particles

produce higher void ratio due the avoided possibility of the particles to rotate and

compact

The influence of the chosen shape descriptor appears in this review to have minor

influence on the soil properties in the reviewed studies except on the void ratio and

the friction angle Influence of particle shape in some cases is hider by other factors

(eg size distribution) also the particle shape probably does not have influence when

particle size is in the clay order (eg hydraulic conductivity) the reason could be due

to forces as electrostatic or capillarity become more important at this level

Among the shape descriptors some are chosen more often in literature (eg aspect

ratio) there is no apparent scientific basis to use it (probably due to the simplicity of

the measurement it becomes one of the most use) but there are still some other

descriptors that may or may not show better correlation with the soil properties

Instead empirical relations had been developed regarding roundness or shape to

describe the soil behaviour it is clear that the mechanism behind the results is still not

completely understood

42

There is necessity to define the best(s) shape descriptor(s) to be used for particular

geotechnical properties

63 IMAGE ANALYSIS

Many image analysis techniques had been used to describe the particle shape eg

Fourier analysis fractal dimension tomography etc (Hyslip and Vallejo 1997) but

there is not agreement on the usage or conclusion to ensure the best particle descriptor

for geotechnical applications

There are several shape descriptors and also various techniques to capture the

particles profile (3-dimensions 3-dimension orthogonal and 2-dimensions) Each

technique presents advantages and disadvantages 3-dimensions is probably the

technique that provide more information about the particle shape but the precision

also lies in the resolution the equipment required to perform such capture could be

more or less sophisticated (scanning particles laying down in one position and later

move to complete the scanning or just falling down particles to scan it in one step)

3-dimensions orthogonal this technique use less sophisticated equipment (compare

with the previous technique) but its use is limited to particles over 1cm also

information between the orthogonal pictures is not capture 2-dimensions require non

sophisticated equipment but at the same time the shape information diminish compare

with the previous due the fact that it is possible to determine only the outline as the

particle measurements are performed in 2-dimensions it is presumed that they will lie

with its shortest axis perpendicular to the laying surface when they are flat but when

the particle tends to have more or less similar axis the laying could be random

Advantages on the use of image analysis are clear there is not subjectivity because it

is possible to obtain same result over the same images Electronic files do not loose

resolution and it is important when collaboration among distant work places is done

files can be send with the entire confidence and knowing that file properties has not

been changed Technology evolutions allowed to work with more information and it

also applies to the image processing area were the time consumed has been shortened

(more images processed in less time)

One important aspect in image analysis is the used resolution in the analysis due the

fact that there are measurements dependent and independent on resolution Thus

those dependent measurements should be avoided due the error included when they

are applied or avoid low resolution to increase the reliability Among these

parameters length is the principal parameter that is influences by resolution (eg

perimeter diameter axis etc) Resolution also has another aspect with two faces

quality versus capacity more resolution (quality) means more storage space a

minimum resolution to obtain reasonable and reliable data must be known but it

depend on each particular application

43

64 APPLICATIONS

Quantify changes in particles in the authorrsquos thought is one of the future applications

due the non-invasive methods of taking photographs in the surface of the damrsquos slope

rail road ballast or roads Sampling of the material and comparing with previous

results could show volume (3D analysis) or area (2D analysis) loss of the particles as

well as the form roundness and roughness This is important when it has been

suggested that a soil or rock embankment decrees their stability properties (eg

internal friction angle) with the loss of sphericity roundness or roughness

Seepage stock piling groundwater etc should try to include the particle shape while

modelling seepage requires grading material to not allow particles move due the

water pressure but in angular materials as it is known the void ratio is great than the

rounded soil it means the space and the possibilities for the small particles to move

are greater stock piling could be modelled incorporating the particle shape to

determine the binrsquos capacity when particle shape changes (void ratio changes when

particle shape changes) Modelling requires all information available and the

understanding of the principles that apply

Industry is actually using the particle shape to understand the soil behaviour and

transform processes into practical and economic image analysis has been included in

the quality control to determine particle shape and size because the advantages it

brings eg the acquisition of the sieving curve for pellets using digital images taken

from conveyor this allows to have the information in a short period of time with a

similar result at least enough from the practical point of view as the traditional

sieving

7 CONCLUSIONS

The conclusions of this literature review are

It has been shown that particle shape has influence on the soil behaviour

despite of partial knowledge of the mechanism behind Understanding of the

particle shape and its influence needs to be accomplished

A common language needs to be built up to standardize the meaning on

geotechnical field that involve the particle shape General relationships

between shape and properties should be developed

Based on this review it is not clear which is the best descriptor to use in

geotechnical engineering affecting he related shape to properties Instead of a

couple of standards there is no shape descriptor in geotechnical field fully

accepted

Image analysis tool is objective make the results repeatable obtain fast results

and work with more amount of information

44

Resolution needs to be taken in consideration when image analysis is been

carried out because the effects could be considerable Resolution must be set

according to the necessities Parameters as perimeter can be affected by

resolution

There are examples where particle shape has been incorporated in industries

related to geotechnical engineering eg in the ballast and asphalt industry for

quality control

8 FURTHER WORK

Three main issues have been identified in this review that will be further investigated

the limits of shape descriptors influence of grading and choice of descriptor for

relation to geotechnical properties

Shape descriptors have low and high limits frequently the limits are not the same and

the ability to describe the particlersquos shape is relative The sensitivity of each descriptor

should be compare to apply the most suitable descriptor in each situation

Sieving curve determine the particle size in a granular soil particle shape could differ

in each sieve size There is the necessity to describe the particle shape on each sieve

portion (due to practical issues) and included in the sieve curve Obtain an average

shape in determined sieve size is complicated (due to the possible presence of several

shapes) and to obtain the particle shape on the overall particlersquos size is challenging

how the particle shape should be included

Since several descriptors have been used to determine the shape of the particles and

the relation with the soil properties it is convenient to determine the descriptorrsquos

correlation with the soil properties

9 ACKNOWLEDGMENT

I would like to thanks to Lulearing University of Technology (LTU) the time I had spent

in its facilities and the kind environment it offers and University of Sonora

(UNISON) that has been providing me the financial support and the time to conclude

this journey

10 REFERENCES

Andersson T (2010) Estimating particle size distributions based on machine vision

Doctoral Thesis Departament of Computer Science and Electrical Engineering Lulearing

University of Technology ISSN 1402-1544 ISBN 978-91-7439-186-2

45

Arasan Seracettin Hasiloglu A Samet Akbulut Suat (2010) Shape particle of

natural and crished aggregate using image analysis International Journal of Civil and

Structural Engineering Vol 1 No 2 pp 221-233 ISSN 0970-4399

Aschenbrenner BC (1956) A new method of expressing particle sphericity Journal

of Sedimentary Petrology Vol 26 No 1 pp 15-31

Axelsson K (1998) Introduktion till jordmekaniken jaumlmte jordmateriallaumlran Skrift

984 Lulearing Avdelningen foumlr Geoteknologi Lulearing Tekniska Universitet (In Swedish)

Barton Nick amp Kjaernsli Bjorn (1981) Shear strength of rockfill Journal of the

Geotechnical Engineering Division Proceedings of the American Society of Civil

Engineers (ASCE) Vol 107 No GT7

Barrett P J (1980) The shape of rock particles a critical review Sedimentology

Vol 27 pp 291-303

Blott S J and Pye K (2008) Particle shape a review and new methods of

characterization and classification Sedimentology Vol 55 pp 31-63

Bowman E T Soga K and Drummond W (2001) Particle shape characterization

using Fourier descriptor analysis Geotechnique Vol 51 No 6 pp 545-554

Briggs L I McCulloch D S (1962) Hydraulic shape of sand particles Journal of

Sedimentary Petrology Vol 32 pp 645-656

Chan Leonard C Y and Page Neil W (1997) Particle fractal and load effects on

internal friction in powders Powder Technology Vol 90 pp 259-266

Cheshomi A Fakher A Jones C J F P (2009) A correlation between friction

angle and particle shape metrics in quaternary coarse alluvia Quarterly Journal of

Engineering Geology and Hydrogeology Vol 42 pp 145-155

Cho G Dodds J and Santamarina J C (2006) Particle shape effects on packing

density stiffness and strength Natural and crushed sands Journal of Geotechnical

and Geoenvironmental Engineering May 2006 pp 591-602

Dietrich William E (1982) Settling velocity of natural particles Water Resources

Research Vol 18 No 6 pp 1615-1626

Dobkins J E and Folk R L (1970) Shape development on Tahiti-nui Journal of

Sedimentary Petrology Vol 40 No 2 pp 1167-1203

Folk R L (1955) Student operator error in determining of roundness sphericity and

grain size Journal of Sedimentary Petrology Vol 25 pp 297-301

Fernlund J M R (1998) The effect of particle form on sieve analysis A test by

image analysis Engineering Geology Vol 50 No 1-2 pp 111-124

46

Fernlund J M R (2005) Image analysis method for determining 3-D shape of

coarse aggregate Cement and Concrete Research Vol 35 Issue 8 pp 1629-1637

Fernlund J M R Zimmerman Robert and Kragic Danica (2007) Influence of

volumemass on grain-size curves and conversion of image-analysis size to sieve size

Engineering Geology Vol 90 No 3-4 pp 124-137

Fraser H J (1935) Experimental study of the porosity and permeability of clastic

sediments The Journal of Geology Vol 43 pp 910-1010 ISSN 0022-1376

Hayati Ali Nemati Ahmadi Mohammad Mehdi and Mohammadi Soheil (2012)

American Physical Society Physical review E 85 036310 DOI

101103PhysRevE85036310

Hawkins A E (1993) The Shape of Powder-Particle Outlines Wiley New York

Head K H and Epps R J (2011) Manual of soil Laboratory testing Volum II

Permeability shear strength and compressibility test 3rd

edition Whittles Publishing

Scotland UK 3rd

edition

Holubec I and DrsquoAppolonia E (1973) Effect of particle shape on the engineering

properties of granular soils ASTM STP 523 pp 304-318

Hyslip James P Vallejo Luis E (1997) Fractal analysis of the roughness and size

distribution of granular materials Engineering Geology Vol 48 pp 231-244

Janoo Vincent C (1998) Quantification of shape angularity and surface texture of

base course materials US Army Corps of Engineers Cold Region Research and

Engineering Laboratory Special report 98-1

Jefferies Mike and Been Ken (2000) Soil liquefaction A critical state approach

Taylor amp Francis Group London and New York

Jimenez Jose A Madsen Ole S (2003) A simple formula to estimate settling

velocity of natural sediments Journal of Waterway Port Coastal and Ocean

Engineering Vol 129 No 2 pp 70-78

Johansson Jens and Vall Jakob (2011) Jordmaterials kornform Inverkan paring

Geotekniska Egenskaper Beskrivande storheter bestaumlmningsmetoder

Examensarbete Avdelningen foumlr Geoteknologi Institutionen foumlr Samhaumlllsbyggnad

och naturresurser Lulearing Tekniska Universitet Lulearing (In Swedish)

Kane Joseph W and Sternheim Morton M (1988) Physics John Wiley amp Sons Inc

Third edition

Kolbuszewski J (1948) An experimental study of the maximum and minimum

porosities of sands Proceedings of the Second International Conference on Soil

Mechanics and Foundation Engineering Rotterdam June 21 to 30 Sub-section IIb

pp 158-165

47

Krumbein W C and Pettijohn FJ (1938) Manual of sedimentary petrography

Appleton-Century Crofts Inc New York

Krumbein W C (1941) Measurement and geological significance of shape and

roundness of sedimentary particles Journal of Sedimentary Petrology Vol 11 No 2

pp 64-72

Krumbein W C and Sloss L L (1963) Stratigraphy and Sedimentation 2nd

ed

WH Freeman San Francisco

Kuo Chun-Yi and Freeman Reed B (1998a) Image analysis evaluation of

aggregates for asphalt concrete mixtures Transportation Research Record Vol 1615

pp 65-71

Kuo Chun-Yi Rollings Raymond and Lynch Larry N (1998b) Morphological

study of coarse aggregates using image analysis Journal of Materials in Civil

Engineering Vol 10 No 3 pp 135-142

Lanaro F Tolppanen P (2002) 3D characterization of coarse aggregates

Engineering Geology Vol 65 pp 17-30

Lees G (1964a) A new method for determining the angularity of particles

Sedimentology Vol 3 pp 2-21

Lees G (1964b) The measurement of particle shape and its influence in engineering

materials British Granite Whinstone Federation Vol 4 No 2 pp 17-38

Matsushima Takashi Saomoto Hidetaka Matsumoto Masaaki Toda Kengo

Yamada Yasuo (2003) Discrete element simulation of an assembly of irregular-

shaped grains Quantitative comparison with experiments 16th ASCE Engineering

Mechanics Conference University of Washington Seattle July 16-18

Mitchell James K and Soga Kenichi (2005) Fundamentals of soil behaviour Third

edition WILEY

Mora C F Kwan A K H Chan H C (1998) Particle size distribution analysis of

coarse aggregate using digital image processing Cement and Concrete Research Vol

28 pp 921-932

Mora C F and Kwan A K H (2000) Sphericity shape factor and convexity

measurement of coarse aggregate for concrete using digital image processing Cement

and Concrete Research Vol 30 No 3 pp 351-358

Muskat Morris (1937) The Flow of fluids through porous media Journal of Applied

Physics Vol 8 pp 274

Nearing M A and Parker S C (1994) Detachment of soil by flowing water under

turbulent and laminar conditions Soil Science Society of American Journal Vol 58

No 6 pp 1612-1614

48

Pan Tongyan Tutumluer Erol Carpenter Samuel H (2006) Effect of coarse

aggregate morphology on permanent deformation behavior of hot mix asphalt Journal

of Transportation Engineering Vol 132 No 7 pp 580-589

Pellegrino A (1965) Geotechnical properties of coarse-grained soils Proceedings

International Conference of Soil Mechanics and Foundation Engineering Vol 1 pp

97-91

Pentland A (1927) A method of measuring the angularity of sands MAG MN AL

Acta Eng Dom Transaction of the Royal Society of Canada Vol 21 Ser3xciii

Persson Anna-Lena (1998) Image analysis of shape and size of fine aggregates

Engineering Geology Vol 50 pp 177-186

Powers M C (1953) A new roundness scale for sedimentary particles Journal of

Sedimentary Petrology Vol 23 No 2 pp 117-119

Pye W and Pye M (1943) Sphericity determination of pebbles and grains Journal

of Sedimentary Petrology Vol 13 No 1 pp 28-34

Qazi M A (1975) Flow properties of granular masses A review on the angle of

repose The Arabian Journal for Science and Engineering Vol 1 No 2

Quiroga Pedro Nel and Fowle David W (2003) The effects of aggregate

characteristics on the performance of portland cement concrete Report ICAR 104-1F

Project number 104 International Center for Aggregates Research University of

Texas

Riley N A (1941) Projection sphericity Journal of Sedimentary Petrology Vol 11

No 2 pp 94-97

Rouseacute P C Fennin R J and Shuttle D A (2008) Influence of roundness on the

void ratio and strength of uniform sand Geotechnique Vol 58 No 3 227-231

Santamarina J C and Cho G C (2004) Soil behaviour The role of particle shape

Proceedings Skempton Conf London

Schofield and Wroth (1968) Critical state soil mechanics McGraw Hill

Shaumlfer Michael (2002) Digital optics Some remarks on the accuracy of particle

image analysis Particle amp Particle Systems Characterization Vol 19 No 3 pp 158-

168

Shergold F A (1953) The percentage of voids in compacted gravel as a measure of

its angularity Magazine of Concrete Research Vol 5 No 13 pp 3-10

Shinohara Kunio Oida Mikihiro Golman Boris (2000) Effect of particle shape on

angle of internal friction by triaxial compression test Powder Technology Vol 107

pp131-136

49

Skredcommisionen (1995) Ingenjoumlrsvetenskapsakademinen rapport 395 Linkoumlping

1995

Sneed E D and Folk R L (1958) Pebbles in the Colorado river Texas A study in

particle morphogenesis Journal of Geology Vol 66 pp 114-150

Sperry James M and Peirce J Jeffrey (1995) A model for estimating the hydraulic

conductivity of granular material based on grain shape grain size and porosity

Ground Water Vol 33 No 6 pp 892-898

Sukumaran B and Ashmawy A K (2001) Quantitative characterisation of the

geometry of discrete particles Geotechnique Vol 51 No 7 pp 619-627

Szaacutedeczy-Kardoss E Von (1933) Die bistimmung der abrollungsgrades Geologie

und palaumlontologie Vol 34B pp 389-401 (in German)

Teller J T (1976) Equantcy versus sphericity Sedimentology Vol 23 pp 427-428

Tickell F G (1938) Effect of the angularity of grain on porosity and permeability

bulletin of the American Association of Petroleum Geologist Vol 22 pp 1272-1274

Tutumluer E Huang H Hashash Y Ghaboussi J (2006) Aggregate shape effects

on ballast tamping and railroad track lateral stability AREMA 2006 Annual

Conference Louisville KY

Wadell H (1932) ldquoVolume Shape and roundness of rock particlesrdquo Journal of

Geology Vol 40 pp 443-451

Wadell H (1933) Sphericity and roundness of rock Particles Journal of Geology

Vol 41 No 3 pp 310ndash331

Wadell H (1934) Shape determination of large sedimental rock fragments

The Pan-American Geologist Vol 61 pp 187-220

Wadell H (1935) ldquoVolume shape and roundness of quartz particlesrdquo Journal of

Geology Vol 43 pp 250-279

Wentworth W C (1922a) The shape of beach pebbles Washington US Geological

Survey Bulletin Vol 131C pp 75-83

Wentworth W C (1922b) A method of measuring and plotting the shape of pebbles

Washington US Geological Survey Bulletin Vol 730C pp 91-114

Wentworth W C (1933) The shape of rock particle A discussion Journal of

Geology Vol 41 pp 306-309

Witt K J Brauns J (1983) Permeability-Anisotropy due to particle shape Journal

of Geotechnical Engineering Vol 109 No 9 pp 1181-1187

ii

ABSTRACT

It has been shown in the early 20th

century that particle shape has an influence on

geotechnical properties Even if this is known there has been only minor progress

in explaining the processes behind its performance and has only partly

implemented in practical geotechnical analysis

This literature review covers different methods and techniques used to determine

the geometrical shape of the particles as well as reported effects of shape on

granular material behaviour

Particle shape could be classifying in three categories sphericity - the overall

particle shape and similitude with a sphere roundness - the description of the

particlersquos corners and roughness - the surface texture of the particle The categories

are scale dependent and the major scale is to sphericity while the minor belongs to

roughness

Empirical relations and standards had been developed to relate soil properties eg

internal friction angle minimum and maximum void ratio density permeability

strain with the particle shape The use of the relations and standards enhance the

bulk material performance eg asphalt mixtures and rail road ballast

The overview has shown that there is no agreement on the usage of the descriptors

and is not clear which descriptor is the best One problem has been in a large scale

classify shape properties Image analysis seems according to the review to be a

promising tool it has many advantages But the resolution in the processed image

needs to be considered since it influence descriptors such as eg the perimeter

iii

1 INTRODUCTION 1

2 AIM AND GOAL 3

3 DESCRIPTION OF SHAPE PROPERTIES 3

31 INTRODUCCTION 3 32 SCALE DEPENDENCE 4 33 FORM (3D) 5 34 FORM (2D) 9 35 ROUNDNESS OR ANGULARITY 11 36 ROUGHNESS OR SURFACE TEXTURE 18

4 TECHNIQUES IN ORDER TO DETERMINE PARTICLE SHAPE 20

41 HAND MEASUREMENT 20 42 SIEVE ANALYSIS 21 43 CHART COMPARISON 21 44 IMAGE ANALYSIS 23

5 EFFECT OF SHAPE ON SOIL PROPERTIES 25

51 INTRODUCTION 25 52 INFLUENCE OF SIZE AND SHAPE 28 53 VOID RATIO AND POROSITY 29 54 ANGLE OF REPOSE 32 55 SHEAR STRENGTH 33 56 SEDIMENTATION PROPERTIES 36 57 HYDRAULIC CONDUCTIVITY PERMEABILITY 37 58 LIQUEFACTION 39 59 GROUNDWATER AND SEEPAGE MODELLING 40

6 DISCUSSION 40

61 TERMS QUANTITIES AND DEFINITIONS 40 62 PROPERTIES 41 63 IMAGE ANALYSIS 42 64 APPLICATIONS 43

7 CONCLUSIONS 43

8 FURTHER WORK 44

9 ACKNOWLEDGMENT 44

10 REFERENCES 44

iv

ABBREVIATIONS Symbol Description Units

A Area of the projected particle area of the particle outline (2D) m2

A1 Area of the projected particle after ldquonrdquo dilatation-erosion cycles m2

AC Area of the smallest circumscribed circle m2

AC2 Area of circle with diameter equal to longest length of outline m2

ACON Convex area m2

AF Sukumara angularity factor -

ANGCON Angles subtending convex parts of the outline degree (ordm)

ANGPLA Angles subtending plane parts of the outline degree (ordm)

a Longest axes diameters of the particle m

B Greatest breadth perpendicular to L m

b Medium axes diameters of the particle m

C Circularity -

CR Convexity ratio -

c Shorter axes diameters of the particle m

Co Cohesion Pa

CPER Convex perimeter m

DA Diameter of a circle equal on area to that of the particle outline m

DAVG Mean average diameter m

DC Diameter of the smallest circumscribed circle in the particle outline m

DCIR Diameter of circumscribed sphere m

DI Diameter of the largest inscribed circle m

DS Diameter of circle fitting sharpest corner (two sharper corners DS1 DS2) m

DSV Diameter of a sphere of the same volume as particle m

DX Diameter of a pebble particle through the sharpest corner DS m

d Grain diameter (average) m

dN Nominal diameter diameter of a sphere of the same volume as the natural

particle

m

e Void ratio

F Angularity factor -

FR Fullness ratio -

g Gravitational acceleration ms2

I Intermediate axis m

k Hydraulic conductivity ms

L Longest axis of the outline m

N Number of corners (items counted) or number of divisions -

n Porosity -

P Perimeter of the projected particle perimeter of outline (2D) m

PC Perimeter of a circle of same area as particle outline m

PCON Sum of perimeter of all convex parts m

PCD Perimeter of circle of same area as drainage basin m

PD Perimeter of a drainage basin m

PI Particle index -

R Roundness -

RAVG Mean average radio of the pebble m

RCON Radius of curvature of the most convex part m

Re Reynolds number -

Rmax-in Radius of the maximum inscribed circle m

Rmin-cir Radius of the minimum circumscribed circle m

RO Roughness or surface texture -

Re Equivalent roughness of particle -

R1 Equation for predicting the settling velocity of sphere -

R3 Equation for predicting the ratio of the settling velocity of an angular

particle to that of a well-rounded particle

-

ri Radius of curvature of the corner ldquoirdquo m

S Actual surface area of the particle m2

v

Symbol Description Units

Se Equivalent strength of particle -

Ss Specific surface area -

SF Sukumara shape factor -

Sm Short axis ldquocrdquo in minimum projection plane m

s Surface area of a sphere of the same volume as the particle m2

sD Specific gravity of the sediment given by the relation density of

sedimentfluid

-

R2 Equation for predicting the ratio of the settling velocity of a non-spherical

well-rounded particle to be settling velocity of a sphere with the same

dimensionless nominal diameter

-

S Dimensionless fluid-sediment parameter -

V Total volume of soil m3

VCIR Volume of circumscribed sphere m3

Ve Velocity ms

VP Volume of particle m3

Vs Volume of voids m3

Vv Volume of solid m3

V10 voids in the aggregate compacted with 10 blows per layer -

V50 voids in the aggregate compacted with 50 blows per layer -

W Weight of the particle ton

WS Settling velocity ms

W Dimensionless settling velocity -

Y Constant to obtain by fitting to experimental data for certain ranges of S -

Z Constant to obtain by fitting to experimental data for certain ranges of S -

x Distance of the tip of the corner from the center of the maximum inscribed

circle

mm

α Measured angle degree (ordm)

αi Sakamura angles used to describe shape degree (ordm)

βi Sakamura angles used to describe angularity degree (ordm)

Σ Summation -

Ψ Sphericity -

ν Kinematics viscosity m2s

φb Basic friction angle degree (ordm)

φcs Friction angle critical state degree (ordm)

φmc Friction angle maximum contraction degree (ordm)

φrep Angle of repose degree (ordm)

φ Peak friction angle Pa

τ Shear strength Pa

σc Compressive strength Pa

σn Normal stress Pa Angle of internal friction degree (ordm)

μ Viscosity Pamiddots

μF Friction coefficient -

p Pressure drop -

ρ Density of water tonm3

ρp Density of the particle tonm3

υ Specific discharge ms

1

1 INTRODUCTION

Effects on soil behaviour from the constituent grain shape has been suggested since

the earliest 1900rsquos when Wadell (1932) Riley (1941) Pentland (1927) and some

other authors developed their own techniques to define the form and roundness of

particles Into the engineering field several research works conclude that particle

shape influence technical properties of soil material and unbound aggregates

(Santamarina and Cho 2004 Mora and Kwan 2000) Among documented properties

affected by the particle shape are eg void ratio (porosity) internal friction angle and

hydraulic conductivity (permeability) (Rouseacute et al 2008 Shinohara et al 2000

Witt and Brauns 1983) In geotechnical guidelines particle shape is incorporated in

eg soil classification (Eurocode 7) and in national guidelines eg for evaluation of

friction angle (Skredkommisionen 1995) This classification is based on ocular

inspection and quantitative judgement made by the individual practicing engineer

thus it can result in not repeatable data In evaluation of eg standard penetration test

Holubec and DrsquoAppolonia (1973) are suggesting the inclusion of the particle shape in

the evaluation of the data According with Folk (1955) the form error is negligible but

it is not in the second sub-quantity related with the corners (roundness) These

systems are not coherent in definitions The lack of possibility to objectively describe

the shape hinders the development of incorporating the effect of particle shape in

geotechnical analysis

The interest of particle shape was raised earlier in the field of geology compared to

geotechnical engineering Particle shape is considered to be the result of different

agentrsquos transport of the rock from its original place to deposits since the final pebble

form is hardly influenced by these agents (rigor of the transport exfoliation by

temperature changes moisture changes etc) in the diverse stages of their history

Furthermore there are considerations regarding on the particle genesis itself (rock

structure mineralogy hardness etc) (Wentworth 1922a) The combination of

transport and mineralogy factors complicates any attempt to correlate length of

transport and roundness due that soft rock result in rounded edges more rapidly than

hard rock if both are transported equal distances According to Barton amp Kjaernsli

(1981) rockfill materials could be classified based on origin into the following (1)

quarried rock (2) talus (3) moraine (4) glacifluvial deposits and (5) fluvial deposits

Each of these sources produces a characteristic roundness and surface texture

Pellegrino (1965) conclude that origin of the rock have strong influence determining

the shape

To define the particle form (morphology) in order to classify and compare grains

many measures has been taken in consideration (axis lengths perimeter surface area

volume etc) Probably when authors had developed the form descriptors realize that

they hadnrsquot provide enough information about the corners they could be angular or

rounded (roundness) thus the authors also focus on develop techniques to describe

them Furthermore the corners or the general surface can be rough or smooth (surface

texture) Nowadays some authors (Mitchell amp Soga 2005 Arasan et al 2010) are

using these three sub-quantities one and each describing the shape but a different

scale (form roundness surface texture)

2

During the historical development of shape descriptors the terminology has been used

differently among the published studies terms as roundness (because the roundness

could be apply in the different scales) or sphericity (how the particle approach to the

shape of a sphere) were strong (Wadell 1933 Wenworth 1933 Teller 1976 Barrett

1980 Hawkins 1993) and it was necessary in order to define a common language on

the particle shape field unfortunately still today there is not agreement on the use of

this terminology and sometimes it make difficult to understand the meaning of the

authors thatrsquos why it is better to comprehend the author technique in order to

misinterpret any word implication

Several attempts to introduce methodology to measure the particlersquos shape had been

developed over the years Manual measurement of the particles form is

overwhelming thus visual charts were developed early to diminish the measuring

time (Krumbein 1941 Krumbein and Sloss 1963 Ashenbrenner 1956 Pye and Pye

1943) Sieving was introduced to determine the flakinesselongation index but it is

confined only for a certain particle size due the practical considerations (Persson

1988) More recently image analysis on computer base has been applied on sieving

research (Andersson 2010 Mora and Kwan 2000 Persson 1998) bringing to the

industry new practical methods to determine the particle size with good results

(Andersson 2010) Particle shape with computer assisted methods are of great help

reducing dramatically the measuring time (Fernlund 2005 Kuo and Freeman 1998a

Kuo et al 1998b Bowman et al 2001)

In the civil industry eg Hot Asphalt mixtures (Kuo and Freeman 1998a Pan et al

2006) Concrete (Mora et al 1998 Quiroga and Fowle 2003) and Ballast

(Tutumluer et al 2006) particlersquos shape is of interest due the materialrsquos performance

thus standards had been developed (see appendix A) On asphalt mixtures limits of

flat and elongated particles or the amount of natural sands typically are incorporated

into specifications flat and elongated particles tend to cause problems with

compaction particle breakage loss of strength and segregation in pavement (Kuo and

Freeman 1998a) Rutting resistance of asphalt concrete under traffic and

environmental loads depend on the stability of aggregates structure in the asphalt mix

(Pan et al 2006) According with the American Railway Engineering and

Maintenance of Way Association (AREMA) ballast aggregate should be open graded

with hard angular shaped particles providing sharp corners and cubical fragments

with a minimum of flat and elongated pieces (Tutumluer et al 2006) The American

standard ASTM D 3398 (test method for index of aggregate particle shape and

texture) is an example of an indirect method to determine particle shape (see appendix

A) Aggregate characteristics of shape texture and grading influence workability

finishability bleeding pumpability and segregation of fresh concrete and affect

strength stiffness shrinkage creep density permeability and durability of hardened

concrete In fact flaky elongated angular and unfavorably graded particles lead to

higher voids content than cubical rounded and well-graded particles (Quiroga and

Fowle 2003)

Sieving is probably the most used method to determine the particle size distribution it

consist of plotting the cumulative weight of the weighted material retained by each

mesh (European standard EN 933-1 1992) This traditional method according to

Andersson (2010) is time consuming and expensive Investigations shows that the

traditional sieving has deviations when particle shape is involve the average volume

3

of the particles retained on any sieve varies considerably with the shape (Lees

1964b) thus the passing of the particles depend upon the shape of the particles

(Fernlund 1998) In some industries the Image analysis is taking advantage over the

traditional sieving technique regardless of the intrinsic error on image analysis due the

overlapping or partial hiding of the rock particles (Andersson 2010) In this case the

weight factor is substitute by pixels (Fernlund et al 2007) Sieving curve using

image analysis is not standardized but after good results in the practice (Andersson

2010) new methodology and soil descriptions could raise including its effects

2 AIM AND GOAL

The aim of this report is to review the state of the art on how to describe particle

shape of individual grains of geotechnical material and knowledge on the influence of

shape in geotechnical properties

The goals in this study are to

Describe discuss and compare particle shape and definitions

Review the known effect of particle shape on soil mechanics parameters

Discuss the potential of the role of particle shape in soil mechanics

Focus in this study has been on 2 dimensional shape definitions

The content of the report is based upon published and peer reviewed papers in

English

3 DESCRIPTION OF SHAPE PROPERTIES

31 INTRODUCCTION

Particle shape description can be classified as qualitative or quantitative Qualitative

describe in terms of words the shape of the particle (eg elongated spherical flaky

etc) and quantitative that relates the measured dimensions in the engineering field

the quantitative description of the particle is more important due the reproducibility

Quantitative geometrical measures on particles may be used as basis for qualitative

classification There are few qualitative measures in contrast with several quantitative

measures to describe the particle form Despite the amount of qualitative descriptions

none of them had been widely accepted but there are some standards (eg ASTM

D5821 EN 933-3 and BS 812) specifying mathematical definitions for industrial

purposes

Shape description of particles is also divided in

o 3D (3 dimensions) it could be obtained from a 3D scan or in a two

orthogonal images and

o 2D (2 dimensions) or particle projection where the particle outline is drawn

4

3D and 2D image analysis present challenges itself 3D analysis requires a

sophisticated equipment to scan the particle surface and create the 3D model or the

use of orthogonal images and combine them to represent the 3 dimensions The

orthogonal method could present new challenges as the minimum particle size or the

placing in orthogonal way of the particles (Fernlund 2005) 2D image analysis is easy

to perform due the non-sophisticated equipment required to take pictures (eg regular

camera or the use of microscope for smaller particles) In 2D image analysis the

particle is assumed to lay over its more stable axis (eg longest and intermediate axis

lie more or less parallel to the surface while the shortest axis is perpendicular) or

random some authors publish their own preferences about this issue (Wadell 1935

Riley 1941 Hawkins 1993)

32 SCALE DEPENDENCE

In order to describe the particle shape in detail there are a number of terms quantities

and definitions used in the literature Some authors (Mitchell amp Soga 2005 Arasan et

al 2010) are using three sub-quantities one and each describing the shape but at

different scales The terms are morphologyform roundness and surface texture In

figure 1 is shown how the scale terms are defined

At large scale the particlersquos diameters in different directions are considered At this

scale describing terms as spherical platy elongated etc are used An often seen

quantity for shape description at large scale is sphericity (antonym elongation)

Graphically the considered type of shape is marked with the dashed line in Figure 1

At intermediate scale it is focused on description of the presence of irregularities

Depending on at what scale an analysis is done corners and edges of different sizes

are identified By doing analysis inside circles defined along the particlersquos boundary

deviations are found and valuated The mentioned circles are shown in Figure 1 A

generally accepted quantity for this scale is roundness (antonym angularity)

Regarding the smallest scale terms like rough or smooth are used The descriptor is

considering the same kind of analysis as the one described above but is applied

Figure 1 Shape describing sub quantities (Mitchell amp Soga 2005)

5

within smaller circles ie at a smaller scale Surface texture is often used to name the

actual quantity The sub-quantities and antonyms are summarized in table 1

Table 1 Sub-quantities describing the particlersquos morphology and its antonym

Scale Quantity Antonym

Large scale Sphericity Elongation

Intermediate scale Roundness Angularity

Small scale Roughness Smoothness

33 FORM (3D)

Wentworth in 1922 (Blott and Pye 2008) was probably one of the first authors on

measure the particle dimensions this consisted on the obtaining of the length of the

tree axes perpendicular among each other (see figure 2) on the tree dimensions (where

agebgec) to obtain the sphericity (equation 1)

Krumbein (1941) develop a rapid method for shape measurement to determine the

sphericity this is done by measuring the longest (a) medium (b) and shorter (c) axes

diameters of the particle it can be seen in figure 2 (Always perpendicular among each

other) The radios ba and cb are located in the chart developed by his own where it

can be found the Intercept sphericity as he called (See figure 3) This chart is an easy

graphical way to relate the dimensions

c2

ba

Figure 2 Measurement of the 3 axes perpendicular among each other (Krumbein 1941)

Figure 3 Detailed chart to determining Krumbein intercept sphericity (Krumbein 1941)

(1)

6

Wadell (1932) defined the sphericity as the specific surface ratio (equation 2) Figure

4 is a schematic representation of the sphere surface and particle surface both particle

and sphere of the same volume

This way to obtain the sphericity is almost impossible to achieve as Hawkins (1993)

declares due the difficulty to get the surface area on irregular solids

Wadell (1934) also defined the sphericity based upon the particle and sphere volumes

as equation 3 (see figure 5)

Wadell (1934) used a new formula simple to manage using the diameters (see figure

6 and equation 4)

Zingg (Krumbein 1941) develop a classification based on the 3 axes relation in this

way it is easy to find out the main form of the particles as a disks spherical blades

S

s

3

CIR

P

V

V

CIR

SV

D

D

Figure 4 Same volume sphere surface (s) and particle surface (S) (modified after Johansson and Vall

2011)

Figure 5 Relation between the volume of the particle and the volume of the circumscribed

sphere (Johansson and Vall 2011)

Figure 6 Figure is showing the relation between the diameter of a circumscribed sphere and the

diameter of a sphere of the same volume as the particle (Johansson and Vall 2011)

(2)

(3)

(4)

7

and rod-like this is summarized on figure 7 Zinggrsquos classification is related with

Krumbein intercept sphericity and the figure 3

In figure 8 the figures 3 and 7 are combined the relation in the two classifications can

be seen it is an easy way to understand the morphology regarding on the a b and c

dimensions

Pye and Pye (1943) in the article ldquosphericity determinations of pebbles and sand

grainsrdquo compare the Wadellrsquos sphericity developed in 1934 (based on the diameter)

with ldquoPebble sphericityrdquo based on an ellipse this last equation (number 5) appears

two years early published by Krumbein (1941) Axis measurement is done as figure 1

denotes for equations 5 trough 12 with exception of equation 8 where the original

document was not possible to obtain

32a

cb

Figure 7 Zinggrsquos classification of pebble shape based on ratios ba and cb (Krumbein 1941)

Figure 8 Classification made by Zinggrsquos and chart to determine sphericity (Krumbein and Sloss 1963)

(5)

8

Sneed amp Folk in (1958) found a relation between the tree dimensional axes called

ldquoMaximum Projection Sphericityrdquo

In a similar way Ashenbrenner (1956) showed his equation at that time named

ldquoWorking Sphericityrdquo

Form or shape factor names are used by authors like Corey (shape factor eq 8) in the

paper published on 1949 Williams (shape factor eq 9) in 1965 Janke (form factor

eq 10) in 1966 and Dobkins amp Folk (oblate-prolate index eq 11) in 1970 (Blott and

Pye 2008)

Aschenbrenner (1956) develop the shape factor by using the relation of the tree axis

but the square of the middle one

3

2

ba

c

))ab((1)bc(16))ab((cb)(11

)ab()bc( 128

22

3 2

ab

c

acb when 1ac

b acb when

b

ac-1 2

22

2

3

cba

c

222

a

c

50c-a

b-a10

2b

ac

(6)

(7)

(8)

(9)

(10)

(11)

(12)

9

Table 2 General overview over different particle shape definitions for 3D sphericity has been compiled

and arranged chronologically

Aspect Name Author Year Based on

Sphericity (3D) Flatness index Wentworth 1922a 3-axes

True Sphericity Wadell 1932 Surface

Operational sphericity Wadell 1932 Volume

Sphericity Wadell 1934 Sphere diameter

Zinggrsquos clasification Zinggrsquos1

1935 3-axes

Intercept sphericity chart Krumbein 1941 3-axes

Pebble sphericity Pye and Pye 1943 3-axes

Corey shape factor Corey2

1949 3-axes

Working sphericity Ashenbrenner 1956 3-axes

shape factor Ashenbrenner 1956 3-axes

Maximum projection sphericity Sneed amp Folk 1958 3-axes

Williams shape factor Williams2

1965 3-axes

Janke form factor Janke2

1966 3-axes

Oblate-prolate index Dobkins amp Folk 1970 3-axes 1) Krumbein and Sloss 1963 2) Blott and Pye 2008

34 FORM (2D)

The technique to measure the sphericity is based in tree dimensions it can be found in

literature some ways to measure the ldquotwo dimensions sphericityrdquo which is simply the

perimeter of the particle projection some authors named ldquoparticle outlinerdquo or

ldquocircularityrdquo

Wadell in 1935 (Hawkins 1993) adopt a conversion of his 1934 3D sphericity

formula (equation 4) to a 2D outline He defined an orientation on the particles and

they were based on the maximum cross sectional area (outline of the particle

projecting the maximum area) The equations show the relation between diameters of

a circle of same area and smallest circumscribed circle

He also used the term ldquodegree of circularityrdquo as the ratio of the perimeter of a circle of

same area and the actual particle perimeter

Tickell in 1931 (Hawkins 1993) used his empirical relation The particle orientation

proposed was a random one It is described by the ratio between the area outline and

the area of smallest circumscribed circle

C

A

D

DC

P

PC C

CA

AC

(13)

(14)

(15)

10

Some other authors has been working with the ldquocircularityrdquo concept and had develop

them own equations as Pentland (1927) relating the area outline and area of a circle

with diameter equal to longest length outline and Cox (Riley 1941) with the ratio

area and perimeter time a constant equations 16 and 17 respectively Both authors did

not define any definite orientation of the grains

Riley (1941) realize the problems that an area perimeter and some other

measurements proposed by the above authors can carry as the time consuming and

tedious work (at that time were not computer all was made by hand) and thatrsquos why

he develop this equation easy to handle called ldquoinscribed circle sphericityrdquo He used

the same particle orientation proposed by Wadell and the relation of diameters of

inscribed and circumscribed circles

Horton 1932 (Hawkins 1993) use the relation of the drainage basing perimeter and

the perimeter of a circle of the same area as drainage basin

Janoo in 1998 (Blott and Pye 2008) develop his general ratio of perimeter to area

Sukumaran and Ashmawy (2001) develop his own shape factor (SF) defined as the

deviation of the global particle outline from a circle Figure 9 can be used as a

reference to determine the items used in the equation 21

N is referred to the number of sampling intervals o radial divisions

C2A

AC

2P

A4C

C

I

D

DC

CD

D

P

PC

A

PC

2

45ordm x N

Particleα

= SF

sumN

1=ii

(16)

(17)

(18)

(19)

(20)

(21)

11

Table 3 General chronological overview of the particle shape definitions for 2D sphericity

Aspect Name Author Year Based on

Circularity (2D) roundness Pentland 1927 area

roundness Cox1

1927 area-perimeter

roundness Tickell2

1931 area

Circularity Horton2

1932 drainage basin

outline circularity Wadell 1935 Circle diameter

degree of circularity Wadell 1935 Perimeter

inscribed circle sphericity Riley 1941 Circle diameter

Circularity Krumbein and Sloss 1963 chart

Janoo 1998 area-perimeter

Shape factor Sukumaran 2001 Segmentation of particle and angles

1) Riley 1941 2) Hawkins 1993

35 ROUNDNESS OR ANGULARITY

Roundness as described in section 32 is the second order shape descriptor Sphericity

lefts beside the corners and how they are this was notice by most of the authors sited

before and they suggested many ways to describe this second order particle property

Roundness is clearly understandable using the figure 10 Particle shape or form is the

overall configuration and denotes the similarities with a sphere (3D) or a circle (2D)

Roundness is concerning about the sharpness or the smoothness of the perimeter (2D)

Surface texture (Barret 1980) is describe as the third order subject (form is the first

and roundness the second) and it is superimposed in the corners and it is also a

property of particles surfaces between corners

Figure 9 Description of the Sukumaran factors to determine the shape and angularity (Sukumaran and

Ashmawy 2001)

12

Wadell (1935) describes his methodology calling it total degree or roundness to

obtain the roundness of a particle using the average radius of the corners in relation

with the inscribed circle diameter (see figure 11) on the equation

In the same study Wadell (1935) has used the equation

This two last equation shows slightly differences on the results (Wadell 1935)

Powers (1953) also published a graphic scale to illustrate the qualitative measure

(figure 12) It is important to highlight that any comparing chart to describe particle

properties has a high degree of subjectivity Folk (1955) concludes that when charts

are used for classification the risk of getting errors is negligible for sphericity but

large for roundness

N

R

r

Rinmax

r

R

NR

inmax

Figure 10 Form (shape) Roundness and Texture graphical description (Bowman et al 2001)

Figure 11 Wadellrsquos method to estimate the roundness corners radius and inscribed circle

(Hawkins 1993)

(22)

(23)

13

Some authors as Russel amp Taylor in 1937 Pettijohn in 1957 and Powers in 1953

developed a classification based on five and six classes (Hawkins 1993) each one

with its own class limits it is important to denote that the way they measure the

roundness is the developed by Wadell (1935) This classification and class limits are

showed in the table 4

Table 4 Degrees of roundness Wadell Values (Hawkins 1993) NA = no-applicable

Grade terms Russell amp Taylor (1937) Pettijohn (1957) Powers (1953)

Class

limits (R)

Arithmetic

midpoint

Class limits

(R)

Arithmetic midpoint Class

limits (R)

Arithmetic

midpoint

Very angular

NA

NA

NA

NA

012-017

014

Angular

000-015

0075

000-015

0125

017-025

021

Subangular

015-030

0225

015-025

0200

025-035

030

Subrounded

030-050

0400

025-040

0315

035-049

041

Rounded

050-070

0600

040-060

0500

049-070

059

Well rounded

070-100

0800

060-100

0800

070-100

084

Krumbein and Sloss (1963) published a graphical chart easy to determine the

sphericity and roundness parameters using comparison See figure 13 (Cho et al

2006)

Figure 12 A Roundness qualitative scale (Powers 1953)

Figure 13 Sphericity and roundness chart (Cho et al 2006) The roundness equation that appears here in

the chart is the wadellrsquos equation number 22

14

Fischer in 1933 (Hawkins 1993) used a straightforward method to quantify roundness

using a central point in the outline and dividing the outline in angles around this point

that were subtended by the straight or non curved parts of the profile were measured

This is illustrated in figure 14

To express the angularity value Fischer used the ratio of angles standing linear parts

on the outlines and concave respectively

Figure 14 left (A) and right (B) gives a similar angularity of approximately 042

using the above equations (Hawkins 1993)

Wentworth in 1922 used the maximum projection to define the position of the particle

to obtain the outline or contour (Barret 1980) The equation reflects the relation of the

diameter of a circle fitting the sharpest corner and the longest axis plus the shortest

axis c (minimum projection)

Wentworth (Hawkins 1993) expressed the roundness as the ratio of the radius of

curvature of the most convex part and the longest axis plus short axis

Actually these last two equations are the same just expressed in different terms when

the particle is in its maximum projection

Dimensions can be seen on figure 15 L and B represents the mayor axis a and

intermediate axis b The intention is to make difference between the 2 and 3

dimensions (L and B are for 2D as a b and c are for 3D)

deg360

ANG

=R

sumPLA

PLA

CON

ANG

ANGR

2)S(L

DR

M

S

B)4(L

RR CON

Figure 14 Fischerrsquos methods of angularity computation (Hawkins 1993)

A=inscribed circle B=circumscribed circle

(24)

(25)

(26)

(27)

15

Wentworth 1919 has a second way to express the roundness called Shape index

(Barrett 1980) and it relates the sharpest corner and the diameter of a pebble trough

the sharpest corner

Wentworth (1922b) used define the roundness as the ratio of the sharpest corner and

the average radius of the pebble

Cailleux (Barrett 1980) relates the radius of the most convex part and the longest

axis

Kuenen in 1956 show his roundness index (Barrett 1980) between the sharpest corner

and the breath axis

Dobkins amp Folk (1970) used a modified Wentworth roundness with the relation of

sharpest corner and inscribed circle diameters

AVG

CON

R

RR

x

s

D

DR

L2

RR CON

B

DR s

i

s

D

DR

3AVGAVG cbaDR2

Figure 15 Description of L and B axes (Hawkins 1993)

(28)

(29)

(30)

(31)

(32)

(33)

16

Swan in 1974 shows his equation (Barrett 1980) relating the sharpest (or the two

sharpest) corner(s) and inscribed circle diameter

Szadeczsky-Kardoss has his Average roundness of outline (Krumbein and Pettijohn

1938) relating the concave parts perimeter and the actual perimeter

Lees (1964a) developed an opposite definition to roundness it means that he

measures the angularity instead of the roundness and he calls it Degree of angularity

Figure 16 shows the items considered when equation 36 applies as the angles (α)

inscribed circle (Rmax-in) and the distance (x) The main formula is

In order to apply the last equation corners needs to be entered in the formula and each

individual result will add to each other to obtain the final degree of angularity

A roundness index appears on Janoo (1998) Kuo and Freeman (1998a) and Kuo et

al (1998b) it is described as

The last equation is on section 34 also because there is not a general agreement on the

definition furthermore some authors had used to define the roughness this is not the

only equation that has been used trying to define different aspects (sphericity

roundness or roughness) but it is a good example of the misuse of the quantities and

definitions

inmaxR

x)180(R

2P

A4R

i

ss

D

DDR

221

100P

PR CON

Figure 16 Degree of angularity measurement technique (Blot and Pye 2008)

(34)

(35)

(36)

(17)

17

Sukumaran and Ashmawy (2001) present an angularity factor (AF) calculated from

the number of sharpness corners Angles βi required to obtain the angularity factor are

shown in figure 9

Sukumaran and Ashmawy (2001) also suggested use not bigger sampling interval of

N=40 because it is the cut off between angularity factor and surface roughness If so

this equation could be used to describe the roughness

Table 5 General chronological overview of the particle roundness

Aspect Name Author Year Based on

Roundness shape index Wentworth 19191

diameter of sharper corner

shape index Wentworth 1922b sharpest corner and axis

roundness Wentworth 1933 convex parts

Fischer 19332

noncurved parts outline

Fischer 19332

noncurved-streigth parts outline

Average roundness of outline

Szadeczsky-Kardoss 19333

convex parts-perimeter

roundness Wadell 1935 diameter of corners

roundness Wadell 1935 diameter of corners

roundness Russel amp Taylor 19372

class limit table

roundness Krumbein 1941 chart

Cailleux 19471

convex parts

roundness Pettijohn 19494 class limit table

roundness Powers 1953 chart and class limit table

Kuenen 19561

axis-convex corner

roundness Krumbein and Sloss 1963 chart

degree of angularity Lees 1964a corners angles and inscribed circle

Dobkins amp Folk 1970 diameter of sharper corner

Swan 19741

diameter of sharper corners

Angularity factor Sukumaran and

Ashmawy 2001

Segmentation of particles and angles

1) Barret 1980 2) Hawkins 1993 3) Krumbein and Pettijohn 1938 4) Powers 1953

sum

sumsumN

1=i

2

i

2

N

1=i

2

i

2N

1=ii

)ordm180 -circleβ( - )(180ordm x 3

)ordm180-circleβ(-)ordm180 -Particleβ(

= AF (37)

18

36 ROUGHNESS OR SURFACE TEXTURE

A third property called texture appears early in the literature with the sphericity and

roundness properties since then texture property was longed described but it was in

accordance with the authors at that time not measurable

Wright in 1955 developed a method to quantify the surface texture or roughness of

concrete aggregate using studies done on 19 mm stones The test aggregates were first

embedded in a synthetic resin The stones were cut in thin sections The sections

projection was magnified 125 times The unevenness of the surface was traced and the

total length of the trace was measured The length was then compared with an uneven

line drawn as a series of chords (see figure 17) The difference between these two

lines was defined as the roughness factor (Janoo 1998)

However with the advance of technology it has become easier measure the roughness

and here is presented some researcherrsquos ideas how this property should be calculated

One technique used by Janoo (1988) to define the roughness can be seen in figure 18a

and is defined as the ratio between perimeter and convex perimeter

The convex perimeter is obtained using the Feretrsquos box (or diameter) tending a line in

between the touching points that the Feretrsquos box describes each time it is turn (figure

18b)

PER

OC

PR

Figure 17 Measurement method for characterizing the surface texture of an aggregate (Janoo 1998)

a) Convex perimeter (CPER) b) Feret measurement Figure 18 a) Convex perimeter (CPER) b) Feret measurement (modified after Janoo 1998)

(38)

a)

b)

19

Kuo and Freeman (1998a) and Kuo et al (1998b) use the roughness definition as the

ratio perimeter and average diameter

Erosion and dilatation image processing techniques are used to obtain the surface

texture Erosion is a morphological process by which boundary image pixels are

removed from an object surface which leaves the object less dense along the

perimeter or outer boundary Dilatation is the reverse process of erosion and a single

dilatation cycle increases the particle shape or image dimension by adding pixels

around its boundary (Pan etal 2006)

The ldquonrdquo erosion and dilatation cycles are not standardized

Mora and Kwan (2000) used the ldquoconvexity ratio CRrdquo (equation 41) and the ldquofullness

ratio FRrdquo (equation 42) in their investigation they are

The convex area is the area of the minimum convex boundaries circumscribing the

particle This is illustrated in the figure 19 The convex area is obtained in a similar

way as the convex perimeter but in this case the area between the original outline and

the convex perimeter is our convex area

AVG

OD

PR

100A

1AARO

CONo A

AR =

CONo A

AR =

Figure 19 Evaluation of area and convex area (Mora and Kuan 2000)

(39)

(40)

(41)

(42)

20

4 TECHNIQUES IN ORDER TO DETERMINE PARTICLE

SHAPE

41 HAND MEASUREMENT

Hand measurement technique was the first used by obvious reasons in order to

improve the accuracy special devices developed as the ldquosliding rod caliperrdquo used by

Krumbein (1941) it works placing the sample on the sliding road calliper as show

figure 20b the length in different positions can be obtain by using the scale provided

in the handle the ldquoconvexity gagerdquo that was actually used by opticians to measure the

curvature of lenses but easily applicable to the particle shape analysis (Wentworth

1922b) works measuring the movement of the central pivot as figure 20a shows (the

two adjacent pivots are invariable) as many the central pivot moves more is the

curvature or the ldquoSzadeczky-Kardossrsquos apparatusrdquo develop in 1933 that traces the

profile of the rock fragment so the outline traced is then analyzed (Krumbein and

Pettijohn 1938) figure 20c show equipment

Another helpful tool to determine the particle dimensions was the ldquocamera lucidardquo to

project the particlersquos contour over a circle scale appearing in Figure 21 thus it is

possible to measure the particlersquos diameter

a)

c) b)

Figure 20 a) convexity gage used to determine the curvature in particle corners (Wenworth 1922b)

b)sliding rod caliper device to measure the particle axis length (Krumbein 1941) and c)Szadeczky-

Kardoss (1933) apparatus it was utilized to obtain the particle outline

Figure 21 Circle scale used by Wadell (1935) to determine particlersquos diameter and roundness

21

42 SIEVE ANALYSIS

Bar sieving eg according to EN 933-31997 can be used to determine simple large

scale properties By combining mesh geometries the obtained results can be used to

quantify flakiness and elongation index ASTM D4791 (Flat and elongated particles

are defined as those coarse aggregate particles that have a ratio of length to thickness

equal to or greater than a specified value such as 51 The index represents the

percentage on weight of these particles) The method is not suitable for fine materials

This due to the difficulty to get the fine grains passed through the sieve and the great

amount of particles in relation to the area of the sieve (Persson 1998) eg EN 933-

31997 related to flakiness index The test is performed on aggregates with grain size

from 4 mm and up to 63 mm two sieving operations are necessary the first separates

on size fraction and the second use a bar sieve after the first sieving the average

maximum diameter of the particles is obtain and with the second sieving (bar sieving)

the shortest axis diameter is found finally with this two parameters the flakiness

index is determined

There are more standards related with the particle shape (see appendix A) but this

above presented are probably the most known using sieve analysis to determine

particlersquos geometrical properties

Sieve analysis is facing the computers age and image analysis sieving research is

taking place (Andersson 2010 Mora and Kwan 2000 Persson 1998) Industry is

also applying the image analysis sieving with decrees on the testing time compare

with the traditional sieving method An inconvenient of image analysis is the error

due the overlapping or hiding of the particles during the capture process but the

advantages are more compare with disadvantages (Anderson 2010)

43 CHART COMPARISON

Charts developed over the necessity of faster results because the long time consuming

required when measuring each particle

Krumbein (1941) present a comparison roundness chart for pebbles which were

measured by Wadellrsquos method because this property was the most difficult to measure

due to the second order scale that roundness represents (See figure 22)

Figure 22 Krumbein (1941) comparision chart for roundness

22

A qualitative chart by Powers (1953) try to include both (sphericity and roundness)

particlersquos characteristics it was divided on six roundness ranges (very angular

angular sub-angular sub-rounded rounded and well rounded) and two sphericity

series (high and low sphericity) This chart was prepared with photographs to enhance

the reader perspective (See figure 23)

A new chart including sphericity and roundness appear this time it was easier to

handle the two mean properties of particlersquos shape furthermore there was included

the numerical values that eliminated the subjectivity of qualitative description The

chart is based on Wadellrsquos definitions (Krumbein and Sloss 1963) (See figure 24)

Folk (1955) worried about the personrsquos error on the chartrsquos comparison studied the

determination of sphericity and angularity (he used the Powers 1953 comparison

chart) he found that the sphericity determination by chart comparison has a negligible

error while the roundness he concluded it was necessary to carry out a more wide

research due the high variability show by his study

Figure 23 Powers (1953) qualitative shpericity-roundness chart

Figure 24 Sphericity-roundness comparison chart (Krumbein and sloss 1963)

23

44 IMAGE ANALYSIS

Image analysis is a practical method to use for shape classification since it is fast and

can be automated Different techniques appear to process these images among them

are

o Feret Diameter the Feret diameter is the longitude between two parallel lines

this lines can rotate around one particle or outline to define dimensions as it

is shown in figure 25 these method is not a fine descriptor but as it was say

above it is a helpful tool to determine diameters (Janoo 1988)

o Fourier Mathematical Technique It produces mathematical relations that

characterize the profile of individual particles This method favours the

analysis of roughness and textural features for granular soils The problem in

the methodology remains in the re-entrant angles in order to complete the

revolution (Bowman et al 2001) see figure 26

o Fractal Dimension Irregular line at any level of scrutiny is by definition

fractal (Hyslip and Vallejo 1997) Figure 27 shows fractal analysis by the

dividing method The length of the fractal line can be defined as

N

1n

nn0 )nsinbncosa(a)(R

RD1n)(P

Figure 25 Feret measurement technique is defined by two parallel lines turning

around the particle to define the shortest and longest Feret diameter (Janoo 1988)

Figure 26 Fourier technique with two radiuses at one angle (Bowman et al 2001)

(43)

(44)

24

o Orthogonal image analysis This technique is basically the use of two images

orthogonal between them to acquire the three particle dimensions (Fernlund

2005) any of the above techniques can be used in this orthogonal way

o Laser Scanning Technique this kind of laser scanning 3D is one of the most

advanced techniques In figures 28a) we have the laser head scanning the rock

particles the particles have control points in order to keep a reference point

when move them to scan the lower part in figure 28b) we can see the laser

path followed (Lanaro and Tolppanen 2002)

Another technique is the Laser-Aided Tomography (LAT) in this case a laser sheet is

used to obtain the particles surveying (see figure 29) This technique is different and

has special requirements as to use liquid with same refractive index as the particles

particles must let the laser or certain percent of light go through (Matsushima et al

2003)

a) b)

Figure 27 Fractal analysis by the dividing method at different scrutiny scale (Hyslip and Vallejo 1997)

Figure 28 a) Scanning head b) scanning path (Lanaro and Tolppanen 2002)

Figure 30 3D scan completed ready to

use for any further measure

(Matsushima et al 2003)

Figure 29 LAT scaning particles

(Matsushima et al 2003)

25

Both 3D techniques obtain the particle shape that is later used to achieve measures as

we can see in figure 30

All these previous techniques are easily written in codes or scripts to be interpreted in

a digital way obtaining the desired measurement but there are some interesting points

in the image analysis regarding on the errors involve among them are image

resolution and orientation of the particles orientation is not relevant when it is

random and large number of particles are involve resolution have an influence on the

accuracy (Zeidan et al 2007)

When resolution is increase more accuracy is obtain and the object representation

match better with the real form in the other hand more resolution means more

spending on memory and time thus resolution needs to be according with the goal

and precision needed in any work (Schaumlfer 2002)

Schaumlfer (2002) conclude that attributes like length when measuring digital images

present relative high errors It can be vanish or at least diminish using high resolution

just for diameter but not for perimeter that keep the error as big as initially Johansson

and Vall (2011) obtain similar results when 3 different resolutions were used in the

same particle obtaining an unstable output for those termsquantities that involve the

perimeter Thus all quantities relating the perimeter should be treated with care

5 EFFECT OF SHAPE ON SOIL PROPERTIES

51 INTRODUCTION

In laboratory test on the effect on particle size on basic properties has been

investigated in several studies this relation has been discussed and various

mechanisms had been proposed to explain the behaviour of the soil in dependency

also with the shape Basically there are two mechanisms proposed The arrangement

of particles and the inter-particle contact (Santamarina and Cho 2004) and

subsequence breakage

The arrangement of particles

Arrangement of the particles can be presented in three different forms loose dense

and critical this arrangement determines the soil properties (eg density increase with

more dense arrangement) Loose and dense states are easy understandable when

figure 31 is explained while in the upper part of the figure the particles are arranged

using the minimum space needed in the lower part a span is created using the flaky

particle as a bridge this phenomena is known as ldquobridgingrdquo Bridging can produce

different geotechnical results when just the shape of the particle is changed eg void

ratio (Santamarina and Cho 2004) Particles are able to rearrange this could be done

applying pressure (energy) to the soil the pressure (energy) will create such forces

that soil particles will rotate and move (see figure 34) finishing in a more dense state

26

A loose soil will contract in volume on shearing and may not develop any peak

strength (figure 32 left) In this case the shear strength will increase gradually until

the residual shear strength is revealed once the soil has ceased contracting in volume

A dense soil may contract slightly (figure 32 right) before granular interlock prevents

further contraction (granular interlock is dependent on the shape of the grains and

their initial packing arrangement) In order to continue shearing once granular

interlock has occurred the soil must dilate (expand in volume) As additional shear

force is required to dilate the soil a peak shear strength occurs (figure 32 left) Once

this peak shear strength caused by dilation has been overcome through continued

shearing the resistance provided by the soil to the applied shear stress reduces

(termed strain softening) Strain softening will continue until no further changes in

volume of the soil occur on continued shearing Peak shear strengths are also

observed in overconsolidated clays where the natural fabric of the soil must be

destroyed prior to reaching constant volume shearing Other effects that result in peak

strengths include cementation and bonding of particles The distinctive shear strength

called the critical state is identified where the soil undergoing shear does so at a

constant volume (Schofield and Wroth 1968)

The inter-particle contact

For frictional soil ie coarse grained soil the friction between particles is the

dominating factor for strength Materials usually consisting of coarse grains (diameter

Figure 31 Bridging effect when flaky particles are combined in the bulk material (Santamarina and

Cho 2004)

Figure 32 The left part of the figure show a typical behaviour of loose and dense material over shear stress

while at the right the figures illustrate the typical volume changes

27

gt 006mm) behave as a frictional soil it means that the strength of coarse soils (silt

sand gravel etc) comes from an inter-particle mechanical friction thus ideally they

do not have traction strength In figure 33 the inter-particle contact is illustrated here

the pressure (P) is applied and two more components are found the normal load (N)

and the tangential load (T) described as the friction coefficient (μF) The forces stand

in equilibrium (Johansson and Vall 2011)

When particles equilibrium is disturbed (friction coefficient is not enough to keep

particles unmoved) the rotation is imminent and it is necessary in order to compact

the soil in figure 34 can be seen that the arrangement is a fact that inhibit or allow this

rotation and the shape in the 3 different scales are also factors because the more

spherical andor more rounded andor less roughness more easy is the rotation

(Santamarina and Cho 2004)

Breakage

Breakage is a side effect of the inter-particle contact and rotation when pressure

exceed the rock strength it can happened when the particles are tight together and

there is not enough space to rotate it is more obvious in angular particles (mesh form)

or as in figure 31 where the flaky particle ldquobridgingrdquo is not able to rotate but it can

brake by the pressure increase Yoginder et al (1985) notice that the angular particle

break during his experiments and they turn more rounded changing the original size

and form configuration at the same time there was a soil properties loosening

Figure 33 Inter-particle contact and forces acting (Axelsson 1998)

Figure 34 Rotation inhibition by the particles compaction or low void ratio (Santamarina and Cho 2004)

28

52 INFLUENCE OF SIZE AND SHAPE

Wenworth (1922a) and Pellegrino (1965) among others suggest that agent transport of

the rocks (rigor of transport temperature and moisture changes etc) determine its

shape but also the particle genesis itself (rock structure mineralogy hardness etc) It

is not possible to determine the shape of the particles based on the agent transport or

genesis but generally a shape behaviour is expected according to Mitchell and Soga

(2005) specially when the particle size is in the clay size (gt2μm) The shapes of the

most common clay minerals are platy (figure 35) with some exceptions (eg

halloysite occurs as tubes kaolinite are large thick and stiff Smectites are composed

of small very thin and filmy particles Illites are intermediate between kaolinite and

smectite and attapulgite occurs in lathlike particle shapes) Some clay minerals

photographs are presented in figure 35

Figure 35 Clay mineral shape a) hallosite b) Kaoline c) Smactites d) Illites and e) attapulgite (Modified

from Mitchell and Soga 2005)

Figure 36 Particle size range in soils Generally the particles of clay size are plate shaped (Mitchell and

Soga 2005)

a) b) c)

e) d)

29

53 VOID RATIO AND POROSITY

The void ratio (e) is the ratio of the volume of voids to the volume of solid it is

defined by the equation

Porosity (n) is the ratio of the volume of voids to the total volume of the soil it is

represented by the equation

Holubec and DrsquoAppolonia (1973) found a relation between the void ratio and

sphericity (referred in the paper as coefficient of angularity ratio of particle surface

and equivalent sphere surface) their results show that the maximum and the minimum

void ratio increases as the shpericity decreases In this study the surface was obtained

for an indirect method based on the permeability developed by Hoffman in 1959

described in the same document Rouseacute et al (2008) defined the roundness as

Wadell (1935) and he found it as an important factor controlling the minimum and

maximum void ratios Some other authors as Youd (1973) and Cho et al (2006)

conclude the same minimum and maximum void ratios increase when sphericity and

roundness decrease Another interesting result (all above authors) was the bigger

influence of the form (sphericity circularity) and roundness on the maximum void

ratio The change of the maximum void ratio is more pronounced than the change of

the minimum void ratio when the form and roundness changes (See figure 39)

Particles arrangement and interlocking are probably the factor that controls the void

ratio bridge effect permit the existence of void among the particles while interlocking

allowed the particles to form arches avoiding the possibility to rotate and stay in a

more stable configuration eg as it happens with marbles

Figures 36 37 and 38 shows proposed empirical relationships between void ratio and

shape from tables 5 and 6 (graphically the scale goes from 0 to 1 when cero mean

high angularity shpericity or circularity and one means low angularity circularity or

sphericity) Holubec and DrsquoAppolonia (1973) data was taken to obtain a power curve

and describe a tendency Santamarina and Cho (2004) show Youd equations in the

original paper Youd (1973) never presented the equation but it is easy to use the

information to draw a trend

The graphics presented in this document (figures 36 37 and 38) must be used with

certain reserves due the fact that the original data was modified in order to fit all

information in one graphic what the figures shows is just the general trend of the

behaviourrsquos material regarding on the shape If more accurate description and

information is required the author recommends consulting the reference data In the

same way equations from Holubec and DrsquoApollonia (1973) and Youd (1973) were not

presented by the authors but the use of the information was taken in order to build up

those equations on tables 6 and 7

S

V

V

V

= e

V

V

=nV

(45)

(46)

30

Table 6 Minimum void ratio equations regarding on the quantity (Ψ for sphericity C for circularity R

for roundness SF for Sukumaran shape factor and AF for Sukumaran angularity factor)

EQUATION NUMBER REFERENCE

Figure 34 (left)

4340

minΨ45490e =

47

Holubec amp DrsquoAppolonia 1973 (Ψ

was obtained using equation 2)

SF06340

mine021903180e +=

48

Sukumaran amp Ashmawy 2001 (SF

obtained using equation 21)

C05101emin

= 49

Cho etal 2006 (C obtained using

figure 12)

Figure 34 (right)

1

minR08203590e +=

50

Youd 1973 (R obtained from figure

11 and table 3)

R34080emin

= 51

Cho et al 2006 (R obtained using

figure 12)

1

minR05104330e +=

52

Rouseacute et al 2008 (R obtained by

equation 21)

AF02330

mine372004160e +=

53

Sukumaran amp Ashmawy 2001 (AF

obtained using equation 37)

Table 7 Maximum void ratio equations regarding on the quantity (Ψ for sphericity C for circularity R

for roundness SF for Sukumaran shape factor and AF for Sukumaran angularity factor)

EQUATION NUMBER REFERENCE

Figure 35 (left)

51520

max Ψ61120e = 54

Holubec and DrsquoAppolonia 1973 (Ψ

was obtained using equation 2)

SF1190

max e0016907180e += 55

Sukumaran amp Ashmawy 2001 (SF

obtained using equation 21)

C86061emax = 56

Cho etal 2006 (C obtained using

figure 12)

Figure 35 (right)

1

max R1505540e += 57

Youd 1973 (R obtained from figure

11 and table 3)

R62031emax= 58

Cho et al 2006 (R obtained using

figure 12)

1

max R107106150e += 59

Rouseacute et al 2008 (R obtained by

equation 21)

AF0530

max e12506090e += 60

Sukumaran amp Ashmawy 2001 (AF

obtained using equation 37)

Comparing figures 37 and 38 (minimum and maximum void ratio) it can be seen on

the right scheme of both figures 37 and 38 (when the factor is roundnessangularity)

that all the empirical relations has a common initial point close to 1 (it means that

particles are well rounded) while this common agreement disappear when the

roundness factor decreases (when the particles become more angular) Same figures

(37 and 38) on the left graphs (when the factor is sphericitycircularityshape) do not

present the same behaviour in fact there is more disperse initial point close to 1(when

the particles tend to be more sphericalcircular)

31

In Figure 39 the Δe (emax-emin) has been plotted to show how the maximum void ratio

and the minimum void ratio has different rate change when the particle shape

changes Maximum void ratio increases more than minimum void ratio when the

particle shape becomes less spherical andor more angular Comparing figure 39 left

and right graphics it can be seen that right present a common initial point when the

quantity (roundnessangularity) is close to one while in the left graphic the initial

point is more disperse Both ending points in both graphics (close to zero) are

dispersed

Figures 37 38 and 39 present the same behaviour right graphics (when the factor is

roundness angularity) in each figure have an initial common point while the left

graphics do not (when the factor is sphericity circularity shape)

Figure 37 Minimum void ratio based upon the relation of shape factor proposed by the authors indicated

in the figure

Figure 38 Maximum void ratio based upon the relation of shape factor proposed by the authors indicated

in the figure

04

06

08

1

12

14

16

18

2

005

015

025

035

045

055

065

075

085

095

Factor (roundness angularity)

min

imu

m v

oid

rati

o

Youd 1973 roundness

Rouse 2008 roundness

Cho 2006 roundness

Sukumaran 2001 AF

03

04

05

06

07

08

09

1

11

12

13

05

015

025

035

045

055

065

075

085

095

Factor (sphericity circularity shape)

min

imu

m v

oid

rati

oHolubec 1973 sphericity

Cho 2006 circularity

Sukumara 2001 SF

05

07

09

11

13

15

17

19

21

00

150

250

350

450

550

650

750

850

95

Factor (sphericity circularity shape)

Maxim

um

vo

id r

ati

o

Holubec 1973 sphericity

Cho 2006 circularity

Sukumara 2001 SF

05

1

15

2

25

3

35

005

015

025

035

045

055

065

075

085

095

Factor (roundness angularity)

Maxim

um

vo

id r

ati

o

Youd 1973 roundness

Rouse 2008 roundness

Cho 2006 roundness

Sukumaran 2001 AF

32

54 ANGLE OF REPOSE

The angle of repose of a granular material is the steepest angle of descent or dip of the

slope relative to the horizontal plane when material on the slope face is on the verge

of sliding as show in figure 40

According to Qazi (1975) there are five types of forces which may act between the

particles in soils

1 Force of friction between the particles

2 Force due to presence of absorbed gas andor moisture of particle

3 Mechanical forces caused by interlocking of particles of irregular shape

4 Electrostatic forces arising from friction between the particles themselves and

the surface with which they come in contact

5 Cohesion forces operating between neighbouring particles

Rouseacute et al (2008) found a decrease of angle of repose with increase roundness

based upon ASTM C1444 test (Standard Test Method for Measuring the Angle of

Repose of Free-Flowing Mold Powders) The method consist in pouring sand on a

surface cover by paper trough a funnel of specific dimensions (the nozzle diameter

depend on the sandrsquos particle size) from an altitude of 15 inches (381 mm) The sand

is release from the funnel until the peak of the cone formed by the sand stops the flow

The repose angle is obtained with the equation

H represent the 15 inches D and d represent the diameter of the cone formed by the

sand and the diameter of the funnel respectively

Figure 39 Maximum minus minimum void ratio based upon the relation of shape factor proposed by the

authors indicated in the figure

0

01

02

03

04

05

06

07

08

09

1

005

015

025

035

045

055

065

075

085

095

Factor (sphericity circularity shape)

Maxim

um

- M

inim

um

Vo

id r

ati

oHolubec 1973 sphericity

Cho 2006 circularity

Sukumara 2001 SF

0

02

04

06

08

1

12

14

16

18

005

015

025

035

045

055

065

075

085

095

Factor (roundness angularity)

Maxim

um

- M

inim

um

Vo

id r

ati

o

Youd 1973 roundness

Rouse 2008 roundness

Cho 2006 roundness

Sukumaran 2001 AF

dD

H2

tan=φ1

rep(61)

33

Rouseacute (2008) shows an empirical relation to obtain the angle of repose based on the

roundness of the particles

55 SHEAR STRENGTH

The MohrndashCoulomb failure criterion represents the linear envelope that is obtained

from a plot of the shear strength of a material versus the applied normal stress This

relation is expressed as

where τ is the shear strength σn is the normal stress co is the intercept of the failure

envelope with the τ axis and is the slope of the failure envelope The quantity c is

often called the cohesion and the angle is called the angle of internal friction

Studies show that the internal friction angle (under drained triaxial tests) increases

more rapidly on those materials having higher angularity increasing the relative

density The internal friction angle is a function of the relative density and the particle

shape (Holubec and DrsquoAppolonia 1973)

Chan and Page (1997) found in a study made with dry copper (using different shapes

and sizes ranging from 180 to 106 μm) using a direct shear test (ring share test) that

the internal friction angle increases as the angularity increases

Shinohara et al (2000) did some experiments with steel powder different shapes

using a triaxial cell in the test Shinohara never used the roundness or angularity on

the work but apply the shape factor (relation long axisshort axis) and the results were

that as this relation deviate from factor 1 the internal friction angle increases

The following empirical relations were found in the literature showing the behaviour

of the friction angle (obtained under different conditions)

)tan( noc

Figure 40 Representation of the angle of repose

(63)

(62)

34

Cho et al (2006)

(64)

(R is obtain by comparing the Krumbein chart figure 13)

Rouseacute (2008)

(65)

(66)

(R is defined using Wadell equation 22)

In figure 41 the suggested empirical relations above and lines constructed using

author data from Holubec and DrsquoAppolonia (1973) and Sukumara and Ashmawy

(2001) are plotted together to display the general trend on the particle shape and

friction angle relation Sukumaran reports two lines one based on the shape factor

(SF) and the second referring the angularity factor (AF) Sukumaran performed the

tests at constant volume

The scale used for Holubec and DrsquoAppolonia (1973) have lower and upper limits of 1

and 2 respectively (angularity form) and a scale change was applied to be able to

presented in the actual figure 41 As in the previous section (52) the author

recommend to use the original data from the references due that the figure just follows

the general trend of the behaviourrsquos particle regarding on the shape

Figure 41 The changes on the internal friction angle shows a general increase when the particle roundness

becomes angular or in the case of Sakamuran less spheric (Shape factor SF)

35

Barton and Kjaernsli (1981) suggested a model (equation 67) to predict the peak

friction angle (φrsquo) based upon numerous trixial and direct shear data tests

where

Se equivalent strength of particle

Re equivalent roughness of particle

φb basic friction angle (obtained from basic tilting test)

σn normal load

The information required for the model is (1) the uniaxial compressive strength of the

rock (2) the d50 particle size (mesh size where 50 of the particles pass through)

required to define Se (figure 42) (3) the degree of particle roundness and (4) the

porosity following compaction All data can be estimated by simple index tests

Barton and Kjaernsli (1981) suggest that particle size and sample scale has an effect

on the friction angle and includes them to obtain the equivalent strength (Se) figure 42

shows the method to obtain this value Compressive strength (σc) was chosen to be the

factor affecting the scale because micro fractures influence this property while

samples are bigger more micro fractures contain and its compressive strength reduces

The equivalent roughness is obtain using figure 43 where is required to know the

porosity (n) and the origin of the particles (a small chart is provided in the same figure

to compare the particles profile)

b

n

ee

SLogR

Figure 42 Method of estimating Equivalent Strength (Se) of rockfill based on uniaxial compressive strength

(σc ) and d50 particle size (Barton amp Kjaernsli 1981)

(67)

36

56 SEDIMENTATION PROPERTIES

A particle released in a less dense Newtonian fluid initially accelerate trough the fluid

due to the gravity Resistances to deformation of the fluid transmitted to the particle

surface drag generate forces that act to resist the particle motion The force due to the

weight (Fw) can be written as

Where ρp ρ are density of the particle and fluid (water) respectively g is the

gravitational force and Vp is the volume of the particle

And the resistance force (FD) is

Where CD is the dimensionless drag coefficient W is the weight of the particle and A

is the cross section area

Particlersquos shape has been assumed to be spherical when equations are applied on the

settling velocity Correlation deviates when particle shape departs from spherical form

Figure 43 Method of estimating Equivalent Roughness (Roe) based on porosity of rockfill

origin material degree of roundedness and smoothness of particle (Barton amp Kjaernsli 1981)

PPW ρ)gV(ρF

A2

WρCF

2

DD

(68)

(69)

37

(Dietrich 1982) and it is known that natural particles depart from spherical form

thus it is evident that this departure would have consequences

The below equation is proposed to account the shape (in this case the Corey shape

factor equation 8) in the settling velocity (Jimenez and Madsen 2003)

Jimenez and Madsen (2003) Dietrich (1982) Briggs and McCulloch (1962) and

others were working in the hydraulic shape of particles to solve problems as sediment

transport It is obvious that the equation presented and the researcherrsquos investigation

works under certain conditions (eg grain size between 0063-1 mm)

Dietrich (1982) suggests an empirical relation that accounts settling velocity size

density shape and roundness of a particle

R1 R2 and R3 are fitted equations for size and density shape and roundness

respectively

57 HYDRAULIC CONDUCTIVITY PERMEABILITY

Darcyrsquos Law Permeability is one component of Darcyrsquos law Darcys law is a simple

proportional relationship between the instantaneous discharge rate through a porous

medium the viscosity of the fluid and the pressure drop

The total velocity Ve is equal to the product of the permeability of the medium

(porous media) k the pressure drop ∆p all divided by the viscosity μ (Muskat

1937)

Darcys law is only valid for slow viscous flow most groundwater flow cases fall in

this category Typically Darcyrsquos law is valid at any flow with laminar flow (see figure

44)

Reynoldrsquos number (Laminar and turbulent Flow) Typically any laminar flow is

considered to have a Reynoldrsquos number less than one and it would be valid to apply

Darcys law Experimental tests have shown that flow regimes with Reynolds numbers

1

ND

S

S

ZY

gd1s

WW

NDN

gd)1s(4

dS

2R1R

3 10RW

pk

Ve

(70)

(71)

(72)

(73)

38

up to 10 may still be Darcian (laminar flow) as in the case of groundwater flow The

Reynolds number (a dimensionless parameter) for porous media flow is typically

expressed as

where ρ is the density of water (units of mass per volume) υ is the specific discharge

(with units of length per time) d is a representative average grain diameter for the

porous media (often taken as the 30 passing size from a grain size analysis using

sieves - with units of length) and μ is the viscosity of the fluid (Muskat 1937)

Shape effects Permeability as Head and Epps (2011) suggested is affected by the

shape and texture of soil grains Elongated or irregular particles create flow paths

which are more tortuous than those spherical particles Particles with a rough surface

texture provide more frictional resistance to flow Both effects tend to reduce the

water flow through the soil

Kozeny-Carman empirical relation accounts for the dependency of permeability on

void ratio in uniformly graded sands serious discrepancies are found when it is

applied to clays due the lack of uniform pores (Mitchell and Soga 2005)

There are various formulations of the Kozeny-Carman equation one published by

Head and Epps (2011) takes the void ratio e the specific surface area Ss and an

angularity factor F into account of permeability k

The angularity factor F considers the shape of the particles and ranges from 11 for

rounded grains 125 for sub rounded to 14 for angular particles The specific surface

Ss is defined as

d1 and d2 represent the maximum and minimum size particle in mm

Kane amp Sternheim (1988) suggest that the inclusion of the shape factor (F) has

probably the background on the Reynolds number due this factor is dependent

significantly on the shape of the obstacles and Reynolds number determines the

presence of laminar or turbulent flow Figure 44 show how the laminar flow has low

energy dissipation while turbulent flow (eg the roughness and path tortuosity) has

high energy dissipation

e1

e

FSs

2k

3

2

dRe

21

6

ddSs

(74)

(75)

(76)

39

According to Nearing and Parker (1994) the amount of soil detached during laminar

and turbulent flow is dependent on each soil and also greater on turbulent flow due the

greater shear strength generated during this kind of flow this could suggest the

greater erosion when turbulent flow is present

58 LIQUEFACTION

Soil liquefaction is a phenomenon in which soil loses much of its strength or stiffness

for a generally short time by earthquake shaking or other rapid loading Static and

dynamic liquefactions occur been the second one the most regular known

Liquefaction often occurs in saturated soils that is soils in which the space between

individual particles is completely filled with water This water exerts a pressure on the

soil particles that influences how tightly the particles themselves are pressed together

Shaking or other rapid loading can cause the water pressure to increase to the point

where the soil particles can readily move with respect to each other (Jefferies and

Been 2000)

Jefferies and Been (2000) state that it is clear that minor variation in intrinsic

properties of sand have major influence on the critical state These might be variations

on grain shape mineralogy grain size distribution surface roughness of grains etc

Yoginder et al (1985) found that substantial decrease on liquefaction resistance

occur with increase in confining pressure for rounded and angular sands (1600 kPa)

also rounded sands show an rapidly build up of resistance against liquefaction with

increasing density while angular tailing sand in contrast show such rapid increase

only at low confining pressures At low confining pressure angular material is more

resistant to liquefaction Probably the breakage of the corners on the angular particles

in tailings is ruling the lost in resistance at high confining pressures (sieve analysis

Figure 44 The figure show the extremes of flow behaviour First turbulent conditions where the flow is

essentially random and unpredictable and second the well defined Laminar flow conditions

40

after test identify the breakage of angular particles while on rounded particles the

sieve analysis was practically the same)

59 GROUNDWATER AND SEEPAGE MODELLING

In groundwater flow the particlersquos shape affects the soilrsquos pore size distribution

hence the flow characteristics (Sperry and Peirce 1995) Tortuosity and permeability

(also see section 57) are two significant macroscopic parameters of granular medium

that affect the passing flow (Hayati et al 2012) Current models incorporating the

effects of particle shape have failed to consider irregular particles such as those that

would prevail in a natural porous medium (Sperry and Peirce 1995)

Hayati et al (2012) suggested based on his results that tortuosity effect converge

when the porosity increases indicating that the shape have dominance at low and mid

porosity ranges

Sperry and Peirce (1995) research conclusions suggest that particle size and porosity

are more important predictors for hydraulic conductivity explaining the 69 of the

variability but particle shape appears to be the next most important This however

apparently comprises particles larger than 295-351 μm Differences for particle size

295-351 μm and smaller are not detectable Another interesting result in the research

was the interaction effect of the particle size and particle shape It suggests a different

packing configuration for particles of the same shape but different size (scale

dependent)

6 DISCUSSION

61 TERMS QUANTITIES AND DEFINITIONS

In order to describe the particle shape in detail there are a number of terms quantities

and definitions (qualitative and quantitative) used in the literature (eg Wadell 1932

1934 Krumbein 1941 Sneed amp Folk 1958) All mathematical definitions

(quantitatives) are models used to simplify the complexity of shape description Some

authors (Mitchell amp Soga 2005 Arasan et al 2010) are using three sub-quantities

one and each describing the shape but at different scales The terms are

morphologyform roundness and surface texture (figure 1) The three sub-quantities

are probably the best way to classify and describe a particle because not a single

definition can interpret the whole morphology Common language is needed when

descriptors are explained and these three scales represent an option It is evident in

the reviewed literature that many of the shape descriptors are presented with the same

name but also that there is not a clear meaning on what this descriptor defines eg

when there is no upper limit in the roundness does it means that the angularity never

ends Could they be more and more angular Probably they could be on theory but

not in reality

41

62 PROPERTIES

Trough various articlersquos review done in the present investigation it is recognized that

the particlersquos shape has an effect on the material properties among these are

1 Porosity (Tickell 1938 Fraser 1935 Kolbuszewski 1948) and void ratio

(Cho et al 2006 Shergold 1953 Rouseacute et al 2008 Santamarina and Cho

2004)

2 Permeability (Witt and Brauns 1983)

3 Internal friction angle (Shinohara et al 2000 Chan and Page 1997

Cheshomi et al 2009)

4 Density (Youd 1973 Holubec and DrsquoAppolonia 1973)

5 Drag coefficient Hydraulics (Briggs and McCulloch 1962)

In Table 5 is a short resume of the properties and shape effect found in peer review

articles trough different journals Most of the reviewed articles based its research on

uniform graded sands

Table 8 Compilation of properties influenced by particle shape

Repose

angle

Friction

angle

Porosity and

Void ratio Density Permeability

Settling velocity

Drag coefficient Deformation

Sphericity (3D)shape factor

NI x x x x x x

Circularity (2D)

NI x x x x NI NI

Roundness x x x x NI NI x

x influence

NI no information available

Shape of particles has an effect on the arrangement producing bridging or avoiding

the rotation of the particles and the resulting geotechnical property is affected eg

including flaky particles can result in a higher void ratio due the bridging effect

(Santamarina and Cho 2004) and depending on the loads even the size distribution is

changed due the breakage (Yoginder et al 1985) in similar way angular particles

produce higher void ratio due the avoided possibility of the particles to rotate and

compact

The influence of the chosen shape descriptor appears in this review to have minor

influence on the soil properties in the reviewed studies except on the void ratio and

the friction angle Influence of particle shape in some cases is hider by other factors

(eg size distribution) also the particle shape probably does not have influence when

particle size is in the clay order (eg hydraulic conductivity) the reason could be due

to forces as electrostatic or capillarity become more important at this level

Among the shape descriptors some are chosen more often in literature (eg aspect

ratio) there is no apparent scientific basis to use it (probably due to the simplicity of

the measurement it becomes one of the most use) but there are still some other

descriptors that may or may not show better correlation with the soil properties

Instead empirical relations had been developed regarding roundness or shape to

describe the soil behaviour it is clear that the mechanism behind the results is still not

completely understood

42

There is necessity to define the best(s) shape descriptor(s) to be used for particular

geotechnical properties

63 IMAGE ANALYSIS

Many image analysis techniques had been used to describe the particle shape eg

Fourier analysis fractal dimension tomography etc (Hyslip and Vallejo 1997) but

there is not agreement on the usage or conclusion to ensure the best particle descriptor

for geotechnical applications

There are several shape descriptors and also various techniques to capture the

particles profile (3-dimensions 3-dimension orthogonal and 2-dimensions) Each

technique presents advantages and disadvantages 3-dimensions is probably the

technique that provide more information about the particle shape but the precision

also lies in the resolution the equipment required to perform such capture could be

more or less sophisticated (scanning particles laying down in one position and later

move to complete the scanning or just falling down particles to scan it in one step)

3-dimensions orthogonal this technique use less sophisticated equipment (compare

with the previous technique) but its use is limited to particles over 1cm also

information between the orthogonal pictures is not capture 2-dimensions require non

sophisticated equipment but at the same time the shape information diminish compare

with the previous due the fact that it is possible to determine only the outline as the

particle measurements are performed in 2-dimensions it is presumed that they will lie

with its shortest axis perpendicular to the laying surface when they are flat but when

the particle tends to have more or less similar axis the laying could be random

Advantages on the use of image analysis are clear there is not subjectivity because it

is possible to obtain same result over the same images Electronic files do not loose

resolution and it is important when collaboration among distant work places is done

files can be send with the entire confidence and knowing that file properties has not

been changed Technology evolutions allowed to work with more information and it

also applies to the image processing area were the time consumed has been shortened

(more images processed in less time)

One important aspect in image analysis is the used resolution in the analysis due the

fact that there are measurements dependent and independent on resolution Thus

those dependent measurements should be avoided due the error included when they

are applied or avoid low resolution to increase the reliability Among these

parameters length is the principal parameter that is influences by resolution (eg

perimeter diameter axis etc) Resolution also has another aspect with two faces

quality versus capacity more resolution (quality) means more storage space a

minimum resolution to obtain reasonable and reliable data must be known but it

depend on each particular application

43

64 APPLICATIONS

Quantify changes in particles in the authorrsquos thought is one of the future applications

due the non-invasive methods of taking photographs in the surface of the damrsquos slope

rail road ballast or roads Sampling of the material and comparing with previous

results could show volume (3D analysis) or area (2D analysis) loss of the particles as

well as the form roundness and roughness This is important when it has been

suggested that a soil or rock embankment decrees their stability properties (eg

internal friction angle) with the loss of sphericity roundness or roughness

Seepage stock piling groundwater etc should try to include the particle shape while

modelling seepage requires grading material to not allow particles move due the

water pressure but in angular materials as it is known the void ratio is great than the

rounded soil it means the space and the possibilities for the small particles to move

are greater stock piling could be modelled incorporating the particle shape to

determine the binrsquos capacity when particle shape changes (void ratio changes when

particle shape changes) Modelling requires all information available and the

understanding of the principles that apply

Industry is actually using the particle shape to understand the soil behaviour and

transform processes into practical and economic image analysis has been included in

the quality control to determine particle shape and size because the advantages it

brings eg the acquisition of the sieving curve for pellets using digital images taken

from conveyor this allows to have the information in a short period of time with a

similar result at least enough from the practical point of view as the traditional

sieving

7 CONCLUSIONS

The conclusions of this literature review are

It has been shown that particle shape has influence on the soil behaviour

despite of partial knowledge of the mechanism behind Understanding of the

particle shape and its influence needs to be accomplished

A common language needs to be built up to standardize the meaning on

geotechnical field that involve the particle shape General relationships

between shape and properties should be developed

Based on this review it is not clear which is the best descriptor to use in

geotechnical engineering affecting he related shape to properties Instead of a

couple of standards there is no shape descriptor in geotechnical field fully

accepted

Image analysis tool is objective make the results repeatable obtain fast results

and work with more amount of information

44

Resolution needs to be taken in consideration when image analysis is been

carried out because the effects could be considerable Resolution must be set

according to the necessities Parameters as perimeter can be affected by

resolution

There are examples where particle shape has been incorporated in industries

related to geotechnical engineering eg in the ballast and asphalt industry for

quality control

8 FURTHER WORK

Three main issues have been identified in this review that will be further investigated

the limits of shape descriptors influence of grading and choice of descriptor for

relation to geotechnical properties

Shape descriptors have low and high limits frequently the limits are not the same and

the ability to describe the particlersquos shape is relative The sensitivity of each descriptor

should be compare to apply the most suitable descriptor in each situation

Sieving curve determine the particle size in a granular soil particle shape could differ

in each sieve size There is the necessity to describe the particle shape on each sieve

portion (due to practical issues) and included in the sieve curve Obtain an average

shape in determined sieve size is complicated (due to the possible presence of several

shapes) and to obtain the particle shape on the overall particlersquos size is challenging

how the particle shape should be included

Since several descriptors have been used to determine the shape of the particles and

the relation with the soil properties it is convenient to determine the descriptorrsquos

correlation with the soil properties

9 ACKNOWLEDGMENT

I would like to thanks to Lulearing University of Technology (LTU) the time I had spent

in its facilities and the kind environment it offers and University of Sonora

(UNISON) that has been providing me the financial support and the time to conclude

this journey

10 REFERENCES

Andersson T (2010) Estimating particle size distributions based on machine vision

Doctoral Thesis Departament of Computer Science and Electrical Engineering Lulearing

University of Technology ISSN 1402-1544 ISBN 978-91-7439-186-2

45

Arasan Seracettin Hasiloglu A Samet Akbulut Suat (2010) Shape particle of

natural and crished aggregate using image analysis International Journal of Civil and

Structural Engineering Vol 1 No 2 pp 221-233 ISSN 0970-4399

Aschenbrenner BC (1956) A new method of expressing particle sphericity Journal

of Sedimentary Petrology Vol 26 No 1 pp 15-31

Axelsson K (1998) Introduktion till jordmekaniken jaumlmte jordmateriallaumlran Skrift

984 Lulearing Avdelningen foumlr Geoteknologi Lulearing Tekniska Universitet (In Swedish)

Barton Nick amp Kjaernsli Bjorn (1981) Shear strength of rockfill Journal of the

Geotechnical Engineering Division Proceedings of the American Society of Civil

Engineers (ASCE) Vol 107 No GT7

Barrett P J (1980) The shape of rock particles a critical review Sedimentology

Vol 27 pp 291-303

Blott S J and Pye K (2008) Particle shape a review and new methods of

characterization and classification Sedimentology Vol 55 pp 31-63

Bowman E T Soga K and Drummond W (2001) Particle shape characterization

using Fourier descriptor analysis Geotechnique Vol 51 No 6 pp 545-554

Briggs L I McCulloch D S (1962) Hydraulic shape of sand particles Journal of

Sedimentary Petrology Vol 32 pp 645-656

Chan Leonard C Y and Page Neil W (1997) Particle fractal and load effects on

internal friction in powders Powder Technology Vol 90 pp 259-266

Cheshomi A Fakher A Jones C J F P (2009) A correlation between friction

angle and particle shape metrics in quaternary coarse alluvia Quarterly Journal of

Engineering Geology and Hydrogeology Vol 42 pp 145-155

Cho G Dodds J and Santamarina J C (2006) Particle shape effects on packing

density stiffness and strength Natural and crushed sands Journal of Geotechnical

and Geoenvironmental Engineering May 2006 pp 591-602

Dietrich William E (1982) Settling velocity of natural particles Water Resources

Research Vol 18 No 6 pp 1615-1626

Dobkins J E and Folk R L (1970) Shape development on Tahiti-nui Journal of

Sedimentary Petrology Vol 40 No 2 pp 1167-1203

Folk R L (1955) Student operator error in determining of roundness sphericity and

grain size Journal of Sedimentary Petrology Vol 25 pp 297-301

Fernlund J M R (1998) The effect of particle form on sieve analysis A test by

image analysis Engineering Geology Vol 50 No 1-2 pp 111-124

46

Fernlund J M R (2005) Image analysis method for determining 3-D shape of

coarse aggregate Cement and Concrete Research Vol 35 Issue 8 pp 1629-1637

Fernlund J M R Zimmerman Robert and Kragic Danica (2007) Influence of

volumemass on grain-size curves and conversion of image-analysis size to sieve size

Engineering Geology Vol 90 No 3-4 pp 124-137

Fraser H J (1935) Experimental study of the porosity and permeability of clastic

sediments The Journal of Geology Vol 43 pp 910-1010 ISSN 0022-1376

Hayati Ali Nemati Ahmadi Mohammad Mehdi and Mohammadi Soheil (2012)

American Physical Society Physical review E 85 036310 DOI

101103PhysRevE85036310

Hawkins A E (1993) The Shape of Powder-Particle Outlines Wiley New York

Head K H and Epps R J (2011) Manual of soil Laboratory testing Volum II

Permeability shear strength and compressibility test 3rd

edition Whittles Publishing

Scotland UK 3rd

edition

Holubec I and DrsquoAppolonia E (1973) Effect of particle shape on the engineering

properties of granular soils ASTM STP 523 pp 304-318

Hyslip James P Vallejo Luis E (1997) Fractal analysis of the roughness and size

distribution of granular materials Engineering Geology Vol 48 pp 231-244

Janoo Vincent C (1998) Quantification of shape angularity and surface texture of

base course materials US Army Corps of Engineers Cold Region Research and

Engineering Laboratory Special report 98-1

Jefferies Mike and Been Ken (2000) Soil liquefaction A critical state approach

Taylor amp Francis Group London and New York

Jimenez Jose A Madsen Ole S (2003) A simple formula to estimate settling

velocity of natural sediments Journal of Waterway Port Coastal and Ocean

Engineering Vol 129 No 2 pp 70-78

Johansson Jens and Vall Jakob (2011) Jordmaterials kornform Inverkan paring

Geotekniska Egenskaper Beskrivande storheter bestaumlmningsmetoder

Examensarbete Avdelningen foumlr Geoteknologi Institutionen foumlr Samhaumlllsbyggnad

och naturresurser Lulearing Tekniska Universitet Lulearing (In Swedish)

Kane Joseph W and Sternheim Morton M (1988) Physics John Wiley amp Sons Inc

Third edition

Kolbuszewski J (1948) An experimental study of the maximum and minimum

porosities of sands Proceedings of the Second International Conference on Soil

Mechanics and Foundation Engineering Rotterdam June 21 to 30 Sub-section IIb

pp 158-165

47

Krumbein W C and Pettijohn FJ (1938) Manual of sedimentary petrography

Appleton-Century Crofts Inc New York

Krumbein W C (1941) Measurement and geological significance of shape and

roundness of sedimentary particles Journal of Sedimentary Petrology Vol 11 No 2

pp 64-72

Krumbein W C and Sloss L L (1963) Stratigraphy and Sedimentation 2nd

ed

WH Freeman San Francisco

Kuo Chun-Yi and Freeman Reed B (1998a) Image analysis evaluation of

aggregates for asphalt concrete mixtures Transportation Research Record Vol 1615

pp 65-71

Kuo Chun-Yi Rollings Raymond and Lynch Larry N (1998b) Morphological

study of coarse aggregates using image analysis Journal of Materials in Civil

Engineering Vol 10 No 3 pp 135-142

Lanaro F Tolppanen P (2002) 3D characterization of coarse aggregates

Engineering Geology Vol 65 pp 17-30

Lees G (1964a) A new method for determining the angularity of particles

Sedimentology Vol 3 pp 2-21

Lees G (1964b) The measurement of particle shape and its influence in engineering

materials British Granite Whinstone Federation Vol 4 No 2 pp 17-38

Matsushima Takashi Saomoto Hidetaka Matsumoto Masaaki Toda Kengo

Yamada Yasuo (2003) Discrete element simulation of an assembly of irregular-

shaped grains Quantitative comparison with experiments 16th ASCE Engineering

Mechanics Conference University of Washington Seattle July 16-18

Mitchell James K and Soga Kenichi (2005) Fundamentals of soil behaviour Third

edition WILEY

Mora C F Kwan A K H Chan H C (1998) Particle size distribution analysis of

coarse aggregate using digital image processing Cement and Concrete Research Vol

28 pp 921-932

Mora C F and Kwan A K H (2000) Sphericity shape factor and convexity

measurement of coarse aggregate for concrete using digital image processing Cement

and Concrete Research Vol 30 No 3 pp 351-358

Muskat Morris (1937) The Flow of fluids through porous media Journal of Applied

Physics Vol 8 pp 274

Nearing M A and Parker S C (1994) Detachment of soil by flowing water under

turbulent and laminar conditions Soil Science Society of American Journal Vol 58

No 6 pp 1612-1614

48

Pan Tongyan Tutumluer Erol Carpenter Samuel H (2006) Effect of coarse

aggregate morphology on permanent deformation behavior of hot mix asphalt Journal

of Transportation Engineering Vol 132 No 7 pp 580-589

Pellegrino A (1965) Geotechnical properties of coarse-grained soils Proceedings

International Conference of Soil Mechanics and Foundation Engineering Vol 1 pp

97-91

Pentland A (1927) A method of measuring the angularity of sands MAG MN AL

Acta Eng Dom Transaction of the Royal Society of Canada Vol 21 Ser3xciii

Persson Anna-Lena (1998) Image analysis of shape and size of fine aggregates

Engineering Geology Vol 50 pp 177-186

Powers M C (1953) A new roundness scale for sedimentary particles Journal of

Sedimentary Petrology Vol 23 No 2 pp 117-119

Pye W and Pye M (1943) Sphericity determination of pebbles and grains Journal

of Sedimentary Petrology Vol 13 No 1 pp 28-34

Qazi M A (1975) Flow properties of granular masses A review on the angle of

repose The Arabian Journal for Science and Engineering Vol 1 No 2

Quiroga Pedro Nel and Fowle David W (2003) The effects of aggregate

characteristics on the performance of portland cement concrete Report ICAR 104-1F

Project number 104 International Center for Aggregates Research University of

Texas

Riley N A (1941) Projection sphericity Journal of Sedimentary Petrology Vol 11

No 2 pp 94-97

Rouseacute P C Fennin R J and Shuttle D A (2008) Influence of roundness on the

void ratio and strength of uniform sand Geotechnique Vol 58 No 3 227-231

Santamarina J C and Cho G C (2004) Soil behaviour The role of particle shape

Proceedings Skempton Conf London

Schofield and Wroth (1968) Critical state soil mechanics McGraw Hill

Shaumlfer Michael (2002) Digital optics Some remarks on the accuracy of particle

image analysis Particle amp Particle Systems Characterization Vol 19 No 3 pp 158-

168

Shergold F A (1953) The percentage of voids in compacted gravel as a measure of

its angularity Magazine of Concrete Research Vol 5 No 13 pp 3-10

Shinohara Kunio Oida Mikihiro Golman Boris (2000) Effect of particle shape on

angle of internal friction by triaxial compression test Powder Technology Vol 107

pp131-136

49

Skredcommisionen (1995) Ingenjoumlrsvetenskapsakademinen rapport 395 Linkoumlping

1995

Sneed E D and Folk R L (1958) Pebbles in the Colorado river Texas A study in

particle morphogenesis Journal of Geology Vol 66 pp 114-150

Sperry James M and Peirce J Jeffrey (1995) A model for estimating the hydraulic

conductivity of granular material based on grain shape grain size and porosity

Ground Water Vol 33 No 6 pp 892-898

Sukumaran B and Ashmawy A K (2001) Quantitative characterisation of the

geometry of discrete particles Geotechnique Vol 51 No 7 pp 619-627

Szaacutedeczy-Kardoss E Von (1933) Die bistimmung der abrollungsgrades Geologie

und palaumlontologie Vol 34B pp 389-401 (in German)

Teller J T (1976) Equantcy versus sphericity Sedimentology Vol 23 pp 427-428

Tickell F G (1938) Effect of the angularity of grain on porosity and permeability

bulletin of the American Association of Petroleum Geologist Vol 22 pp 1272-1274

Tutumluer E Huang H Hashash Y Ghaboussi J (2006) Aggregate shape effects

on ballast tamping and railroad track lateral stability AREMA 2006 Annual

Conference Louisville KY

Wadell H (1932) ldquoVolume Shape and roundness of rock particlesrdquo Journal of

Geology Vol 40 pp 443-451

Wadell H (1933) Sphericity and roundness of rock Particles Journal of Geology

Vol 41 No 3 pp 310ndash331

Wadell H (1934) Shape determination of large sedimental rock fragments

The Pan-American Geologist Vol 61 pp 187-220

Wadell H (1935) ldquoVolume shape and roundness of quartz particlesrdquo Journal of

Geology Vol 43 pp 250-279

Wentworth W C (1922a) The shape of beach pebbles Washington US Geological

Survey Bulletin Vol 131C pp 75-83

Wentworth W C (1922b) A method of measuring and plotting the shape of pebbles

Washington US Geological Survey Bulletin Vol 730C pp 91-114

Wentworth W C (1933) The shape of rock particle A discussion Journal of

Geology Vol 41 pp 306-309

Witt K J Brauns J (1983) Permeability-Anisotropy due to particle shape Journal

of Geotechnical Engineering Vol 109 No 9 pp 1181-1187

iii

1 INTRODUCTION 1

2 AIM AND GOAL 3

3 DESCRIPTION OF SHAPE PROPERTIES 3

31 INTRODUCCTION 3 32 SCALE DEPENDENCE 4 33 FORM (3D) 5 34 FORM (2D) 9 35 ROUNDNESS OR ANGULARITY 11 36 ROUGHNESS OR SURFACE TEXTURE 18

4 TECHNIQUES IN ORDER TO DETERMINE PARTICLE SHAPE 20

41 HAND MEASUREMENT 20 42 SIEVE ANALYSIS 21 43 CHART COMPARISON 21 44 IMAGE ANALYSIS 23

5 EFFECT OF SHAPE ON SOIL PROPERTIES 25

51 INTRODUCTION 25 52 INFLUENCE OF SIZE AND SHAPE 28 53 VOID RATIO AND POROSITY 29 54 ANGLE OF REPOSE 32 55 SHEAR STRENGTH 33 56 SEDIMENTATION PROPERTIES 36 57 HYDRAULIC CONDUCTIVITY PERMEABILITY 37 58 LIQUEFACTION 39 59 GROUNDWATER AND SEEPAGE MODELLING 40

6 DISCUSSION 40

61 TERMS QUANTITIES AND DEFINITIONS 40 62 PROPERTIES 41 63 IMAGE ANALYSIS 42 64 APPLICATIONS 43

7 CONCLUSIONS 43

8 FURTHER WORK 44

9 ACKNOWLEDGMENT 44

10 REFERENCES 44

iv

ABBREVIATIONS Symbol Description Units

A Area of the projected particle area of the particle outline (2D) m2

A1 Area of the projected particle after ldquonrdquo dilatation-erosion cycles m2

AC Area of the smallest circumscribed circle m2

AC2 Area of circle with diameter equal to longest length of outline m2

ACON Convex area m2

AF Sukumara angularity factor -

ANGCON Angles subtending convex parts of the outline degree (ordm)

ANGPLA Angles subtending plane parts of the outline degree (ordm)

a Longest axes diameters of the particle m

B Greatest breadth perpendicular to L m

b Medium axes diameters of the particle m

C Circularity -

CR Convexity ratio -

c Shorter axes diameters of the particle m

Co Cohesion Pa

CPER Convex perimeter m

DA Diameter of a circle equal on area to that of the particle outline m

DAVG Mean average diameter m

DC Diameter of the smallest circumscribed circle in the particle outline m

DCIR Diameter of circumscribed sphere m

DI Diameter of the largest inscribed circle m

DS Diameter of circle fitting sharpest corner (two sharper corners DS1 DS2) m

DSV Diameter of a sphere of the same volume as particle m

DX Diameter of a pebble particle through the sharpest corner DS m

d Grain diameter (average) m

dN Nominal diameter diameter of a sphere of the same volume as the natural

particle

m

e Void ratio

F Angularity factor -

FR Fullness ratio -

g Gravitational acceleration ms2

I Intermediate axis m

k Hydraulic conductivity ms

L Longest axis of the outline m

N Number of corners (items counted) or number of divisions -

n Porosity -

P Perimeter of the projected particle perimeter of outline (2D) m

PC Perimeter of a circle of same area as particle outline m

PCON Sum of perimeter of all convex parts m

PCD Perimeter of circle of same area as drainage basin m

PD Perimeter of a drainage basin m

PI Particle index -

R Roundness -

RAVG Mean average radio of the pebble m

RCON Radius of curvature of the most convex part m

Re Reynolds number -

Rmax-in Radius of the maximum inscribed circle m

Rmin-cir Radius of the minimum circumscribed circle m

RO Roughness or surface texture -

Re Equivalent roughness of particle -

R1 Equation for predicting the settling velocity of sphere -

R3 Equation for predicting the ratio of the settling velocity of an angular

particle to that of a well-rounded particle

-

ri Radius of curvature of the corner ldquoirdquo m

S Actual surface area of the particle m2

v

Symbol Description Units

Se Equivalent strength of particle -

Ss Specific surface area -

SF Sukumara shape factor -

Sm Short axis ldquocrdquo in minimum projection plane m

s Surface area of a sphere of the same volume as the particle m2

sD Specific gravity of the sediment given by the relation density of

sedimentfluid

-

R2 Equation for predicting the ratio of the settling velocity of a non-spherical

well-rounded particle to be settling velocity of a sphere with the same

dimensionless nominal diameter

-

S Dimensionless fluid-sediment parameter -

V Total volume of soil m3

VCIR Volume of circumscribed sphere m3

Ve Velocity ms

VP Volume of particle m3

Vs Volume of voids m3

Vv Volume of solid m3

V10 voids in the aggregate compacted with 10 blows per layer -

V50 voids in the aggregate compacted with 50 blows per layer -

W Weight of the particle ton

WS Settling velocity ms

W Dimensionless settling velocity -

Y Constant to obtain by fitting to experimental data for certain ranges of S -

Z Constant to obtain by fitting to experimental data for certain ranges of S -

x Distance of the tip of the corner from the center of the maximum inscribed

circle

mm

α Measured angle degree (ordm)

αi Sakamura angles used to describe shape degree (ordm)

βi Sakamura angles used to describe angularity degree (ordm)

Σ Summation -

Ψ Sphericity -

ν Kinematics viscosity m2s

φb Basic friction angle degree (ordm)

φcs Friction angle critical state degree (ordm)

φmc Friction angle maximum contraction degree (ordm)

φrep Angle of repose degree (ordm)

φ Peak friction angle Pa

τ Shear strength Pa

σc Compressive strength Pa

σn Normal stress Pa Angle of internal friction degree (ordm)

μ Viscosity Pamiddots

μF Friction coefficient -

p Pressure drop -

ρ Density of water tonm3

ρp Density of the particle tonm3

υ Specific discharge ms

1

1 INTRODUCTION

Effects on soil behaviour from the constituent grain shape has been suggested since

the earliest 1900rsquos when Wadell (1932) Riley (1941) Pentland (1927) and some

other authors developed their own techniques to define the form and roundness of

particles Into the engineering field several research works conclude that particle

shape influence technical properties of soil material and unbound aggregates

(Santamarina and Cho 2004 Mora and Kwan 2000) Among documented properties

affected by the particle shape are eg void ratio (porosity) internal friction angle and

hydraulic conductivity (permeability) (Rouseacute et al 2008 Shinohara et al 2000

Witt and Brauns 1983) In geotechnical guidelines particle shape is incorporated in

eg soil classification (Eurocode 7) and in national guidelines eg for evaluation of

friction angle (Skredkommisionen 1995) This classification is based on ocular

inspection and quantitative judgement made by the individual practicing engineer

thus it can result in not repeatable data In evaluation of eg standard penetration test

Holubec and DrsquoAppolonia (1973) are suggesting the inclusion of the particle shape in

the evaluation of the data According with Folk (1955) the form error is negligible but

it is not in the second sub-quantity related with the corners (roundness) These

systems are not coherent in definitions The lack of possibility to objectively describe

the shape hinders the development of incorporating the effect of particle shape in

geotechnical analysis

The interest of particle shape was raised earlier in the field of geology compared to

geotechnical engineering Particle shape is considered to be the result of different

agentrsquos transport of the rock from its original place to deposits since the final pebble

form is hardly influenced by these agents (rigor of the transport exfoliation by

temperature changes moisture changes etc) in the diverse stages of their history

Furthermore there are considerations regarding on the particle genesis itself (rock

structure mineralogy hardness etc) (Wentworth 1922a) The combination of

transport and mineralogy factors complicates any attempt to correlate length of

transport and roundness due that soft rock result in rounded edges more rapidly than

hard rock if both are transported equal distances According to Barton amp Kjaernsli

(1981) rockfill materials could be classified based on origin into the following (1)

quarried rock (2) talus (3) moraine (4) glacifluvial deposits and (5) fluvial deposits

Each of these sources produces a characteristic roundness and surface texture

Pellegrino (1965) conclude that origin of the rock have strong influence determining

the shape

To define the particle form (morphology) in order to classify and compare grains

many measures has been taken in consideration (axis lengths perimeter surface area

volume etc) Probably when authors had developed the form descriptors realize that

they hadnrsquot provide enough information about the corners they could be angular or

rounded (roundness) thus the authors also focus on develop techniques to describe

them Furthermore the corners or the general surface can be rough or smooth (surface

texture) Nowadays some authors (Mitchell amp Soga 2005 Arasan et al 2010) are

using these three sub-quantities one and each describing the shape but a different

scale (form roundness surface texture)

2

During the historical development of shape descriptors the terminology has been used

differently among the published studies terms as roundness (because the roundness

could be apply in the different scales) or sphericity (how the particle approach to the

shape of a sphere) were strong (Wadell 1933 Wenworth 1933 Teller 1976 Barrett

1980 Hawkins 1993) and it was necessary in order to define a common language on

the particle shape field unfortunately still today there is not agreement on the use of

this terminology and sometimes it make difficult to understand the meaning of the

authors thatrsquos why it is better to comprehend the author technique in order to

misinterpret any word implication

Several attempts to introduce methodology to measure the particlersquos shape had been

developed over the years Manual measurement of the particles form is

overwhelming thus visual charts were developed early to diminish the measuring

time (Krumbein 1941 Krumbein and Sloss 1963 Ashenbrenner 1956 Pye and Pye

1943) Sieving was introduced to determine the flakinesselongation index but it is

confined only for a certain particle size due the practical considerations (Persson

1988) More recently image analysis on computer base has been applied on sieving

research (Andersson 2010 Mora and Kwan 2000 Persson 1998) bringing to the

industry new practical methods to determine the particle size with good results

(Andersson 2010) Particle shape with computer assisted methods are of great help

reducing dramatically the measuring time (Fernlund 2005 Kuo and Freeman 1998a

Kuo et al 1998b Bowman et al 2001)

In the civil industry eg Hot Asphalt mixtures (Kuo and Freeman 1998a Pan et al

2006) Concrete (Mora et al 1998 Quiroga and Fowle 2003) and Ballast

(Tutumluer et al 2006) particlersquos shape is of interest due the materialrsquos performance

thus standards had been developed (see appendix A) On asphalt mixtures limits of

flat and elongated particles or the amount of natural sands typically are incorporated

into specifications flat and elongated particles tend to cause problems with

compaction particle breakage loss of strength and segregation in pavement (Kuo and

Freeman 1998a) Rutting resistance of asphalt concrete under traffic and

environmental loads depend on the stability of aggregates structure in the asphalt mix

(Pan et al 2006) According with the American Railway Engineering and

Maintenance of Way Association (AREMA) ballast aggregate should be open graded

with hard angular shaped particles providing sharp corners and cubical fragments

with a minimum of flat and elongated pieces (Tutumluer et al 2006) The American

standard ASTM D 3398 (test method for index of aggregate particle shape and

texture) is an example of an indirect method to determine particle shape (see appendix

A) Aggregate characteristics of shape texture and grading influence workability

finishability bleeding pumpability and segregation of fresh concrete and affect

strength stiffness shrinkage creep density permeability and durability of hardened

concrete In fact flaky elongated angular and unfavorably graded particles lead to

higher voids content than cubical rounded and well-graded particles (Quiroga and

Fowle 2003)

Sieving is probably the most used method to determine the particle size distribution it

consist of plotting the cumulative weight of the weighted material retained by each

mesh (European standard EN 933-1 1992) This traditional method according to

Andersson (2010) is time consuming and expensive Investigations shows that the

traditional sieving has deviations when particle shape is involve the average volume

3

of the particles retained on any sieve varies considerably with the shape (Lees

1964b) thus the passing of the particles depend upon the shape of the particles

(Fernlund 1998) In some industries the Image analysis is taking advantage over the

traditional sieving technique regardless of the intrinsic error on image analysis due the

overlapping or partial hiding of the rock particles (Andersson 2010) In this case the

weight factor is substitute by pixels (Fernlund et al 2007) Sieving curve using

image analysis is not standardized but after good results in the practice (Andersson

2010) new methodology and soil descriptions could raise including its effects

2 AIM AND GOAL

The aim of this report is to review the state of the art on how to describe particle

shape of individual grains of geotechnical material and knowledge on the influence of

shape in geotechnical properties

The goals in this study are to

Describe discuss and compare particle shape and definitions

Review the known effect of particle shape on soil mechanics parameters

Discuss the potential of the role of particle shape in soil mechanics

Focus in this study has been on 2 dimensional shape definitions

The content of the report is based upon published and peer reviewed papers in

English

3 DESCRIPTION OF SHAPE PROPERTIES

31 INTRODUCCTION

Particle shape description can be classified as qualitative or quantitative Qualitative

describe in terms of words the shape of the particle (eg elongated spherical flaky

etc) and quantitative that relates the measured dimensions in the engineering field

the quantitative description of the particle is more important due the reproducibility

Quantitative geometrical measures on particles may be used as basis for qualitative

classification There are few qualitative measures in contrast with several quantitative

measures to describe the particle form Despite the amount of qualitative descriptions

none of them had been widely accepted but there are some standards (eg ASTM

D5821 EN 933-3 and BS 812) specifying mathematical definitions for industrial

purposes

Shape description of particles is also divided in

o 3D (3 dimensions) it could be obtained from a 3D scan or in a two

orthogonal images and

o 2D (2 dimensions) or particle projection where the particle outline is drawn

4

3D and 2D image analysis present challenges itself 3D analysis requires a

sophisticated equipment to scan the particle surface and create the 3D model or the

use of orthogonal images and combine them to represent the 3 dimensions The

orthogonal method could present new challenges as the minimum particle size or the

placing in orthogonal way of the particles (Fernlund 2005) 2D image analysis is easy

to perform due the non-sophisticated equipment required to take pictures (eg regular

camera or the use of microscope for smaller particles) In 2D image analysis the

particle is assumed to lay over its more stable axis (eg longest and intermediate axis

lie more or less parallel to the surface while the shortest axis is perpendicular) or

random some authors publish their own preferences about this issue (Wadell 1935

Riley 1941 Hawkins 1993)

32 SCALE DEPENDENCE

In order to describe the particle shape in detail there are a number of terms quantities

and definitions used in the literature Some authors (Mitchell amp Soga 2005 Arasan et

al 2010) are using three sub-quantities one and each describing the shape but at

different scales The terms are morphologyform roundness and surface texture In

figure 1 is shown how the scale terms are defined

At large scale the particlersquos diameters in different directions are considered At this

scale describing terms as spherical platy elongated etc are used An often seen

quantity for shape description at large scale is sphericity (antonym elongation)

Graphically the considered type of shape is marked with the dashed line in Figure 1

At intermediate scale it is focused on description of the presence of irregularities

Depending on at what scale an analysis is done corners and edges of different sizes

are identified By doing analysis inside circles defined along the particlersquos boundary

deviations are found and valuated The mentioned circles are shown in Figure 1 A

generally accepted quantity for this scale is roundness (antonym angularity)

Regarding the smallest scale terms like rough or smooth are used The descriptor is

considering the same kind of analysis as the one described above but is applied

Figure 1 Shape describing sub quantities (Mitchell amp Soga 2005)

5

within smaller circles ie at a smaller scale Surface texture is often used to name the

actual quantity The sub-quantities and antonyms are summarized in table 1

Table 1 Sub-quantities describing the particlersquos morphology and its antonym

Scale Quantity Antonym

Large scale Sphericity Elongation

Intermediate scale Roundness Angularity

Small scale Roughness Smoothness

33 FORM (3D)

Wentworth in 1922 (Blott and Pye 2008) was probably one of the first authors on

measure the particle dimensions this consisted on the obtaining of the length of the

tree axes perpendicular among each other (see figure 2) on the tree dimensions (where

agebgec) to obtain the sphericity (equation 1)

Krumbein (1941) develop a rapid method for shape measurement to determine the

sphericity this is done by measuring the longest (a) medium (b) and shorter (c) axes

diameters of the particle it can be seen in figure 2 (Always perpendicular among each

other) The radios ba and cb are located in the chart developed by his own where it

can be found the Intercept sphericity as he called (See figure 3) This chart is an easy

graphical way to relate the dimensions

c2

ba

Figure 2 Measurement of the 3 axes perpendicular among each other (Krumbein 1941)

Figure 3 Detailed chart to determining Krumbein intercept sphericity (Krumbein 1941)

(1)

6

Wadell (1932) defined the sphericity as the specific surface ratio (equation 2) Figure

4 is a schematic representation of the sphere surface and particle surface both particle

and sphere of the same volume

This way to obtain the sphericity is almost impossible to achieve as Hawkins (1993)

declares due the difficulty to get the surface area on irregular solids

Wadell (1934) also defined the sphericity based upon the particle and sphere volumes

as equation 3 (see figure 5)

Wadell (1934) used a new formula simple to manage using the diameters (see figure

6 and equation 4)

Zingg (Krumbein 1941) develop a classification based on the 3 axes relation in this

way it is easy to find out the main form of the particles as a disks spherical blades

S

s

3

CIR

P

V

V

CIR

SV

D

D

Figure 4 Same volume sphere surface (s) and particle surface (S) (modified after Johansson and Vall

2011)

Figure 5 Relation between the volume of the particle and the volume of the circumscribed

sphere (Johansson and Vall 2011)

Figure 6 Figure is showing the relation between the diameter of a circumscribed sphere and the

diameter of a sphere of the same volume as the particle (Johansson and Vall 2011)

(2)

(3)

(4)

7

and rod-like this is summarized on figure 7 Zinggrsquos classification is related with

Krumbein intercept sphericity and the figure 3

In figure 8 the figures 3 and 7 are combined the relation in the two classifications can

be seen it is an easy way to understand the morphology regarding on the a b and c

dimensions

Pye and Pye (1943) in the article ldquosphericity determinations of pebbles and sand

grainsrdquo compare the Wadellrsquos sphericity developed in 1934 (based on the diameter)

with ldquoPebble sphericityrdquo based on an ellipse this last equation (number 5) appears

two years early published by Krumbein (1941) Axis measurement is done as figure 1

denotes for equations 5 trough 12 with exception of equation 8 where the original

document was not possible to obtain

32a

cb

Figure 7 Zinggrsquos classification of pebble shape based on ratios ba and cb (Krumbein 1941)

Figure 8 Classification made by Zinggrsquos and chart to determine sphericity (Krumbein and Sloss 1963)

(5)

8

Sneed amp Folk in (1958) found a relation between the tree dimensional axes called

ldquoMaximum Projection Sphericityrdquo

In a similar way Ashenbrenner (1956) showed his equation at that time named

ldquoWorking Sphericityrdquo

Form or shape factor names are used by authors like Corey (shape factor eq 8) in the

paper published on 1949 Williams (shape factor eq 9) in 1965 Janke (form factor

eq 10) in 1966 and Dobkins amp Folk (oblate-prolate index eq 11) in 1970 (Blott and

Pye 2008)

Aschenbrenner (1956) develop the shape factor by using the relation of the tree axis

but the square of the middle one

3

2

ba

c

))ab((1)bc(16))ab((cb)(11

)ab()bc( 128

22

3 2

ab

c

acb when 1ac

b acb when

b

ac-1 2

22

2

3

cba

c

222

a

c

50c-a

b-a10

2b

ac

(6)

(7)

(8)

(9)

(10)

(11)

(12)

9

Table 2 General overview over different particle shape definitions for 3D sphericity has been compiled

and arranged chronologically

Aspect Name Author Year Based on

Sphericity (3D) Flatness index Wentworth 1922a 3-axes

True Sphericity Wadell 1932 Surface

Operational sphericity Wadell 1932 Volume

Sphericity Wadell 1934 Sphere diameter

Zinggrsquos clasification Zinggrsquos1

1935 3-axes

Intercept sphericity chart Krumbein 1941 3-axes

Pebble sphericity Pye and Pye 1943 3-axes

Corey shape factor Corey2

1949 3-axes

Working sphericity Ashenbrenner 1956 3-axes

shape factor Ashenbrenner 1956 3-axes

Maximum projection sphericity Sneed amp Folk 1958 3-axes

Williams shape factor Williams2

1965 3-axes

Janke form factor Janke2

1966 3-axes

Oblate-prolate index Dobkins amp Folk 1970 3-axes 1) Krumbein and Sloss 1963 2) Blott and Pye 2008

34 FORM (2D)

The technique to measure the sphericity is based in tree dimensions it can be found in

literature some ways to measure the ldquotwo dimensions sphericityrdquo which is simply the

perimeter of the particle projection some authors named ldquoparticle outlinerdquo or

ldquocircularityrdquo

Wadell in 1935 (Hawkins 1993) adopt a conversion of his 1934 3D sphericity

formula (equation 4) to a 2D outline He defined an orientation on the particles and

they were based on the maximum cross sectional area (outline of the particle

projecting the maximum area) The equations show the relation between diameters of

a circle of same area and smallest circumscribed circle

He also used the term ldquodegree of circularityrdquo as the ratio of the perimeter of a circle of

same area and the actual particle perimeter

Tickell in 1931 (Hawkins 1993) used his empirical relation The particle orientation

proposed was a random one It is described by the ratio between the area outline and

the area of smallest circumscribed circle

C

A

D

DC

P

PC C

CA

AC

(13)

(14)

(15)

10

Some other authors has been working with the ldquocircularityrdquo concept and had develop

them own equations as Pentland (1927) relating the area outline and area of a circle

with diameter equal to longest length outline and Cox (Riley 1941) with the ratio

area and perimeter time a constant equations 16 and 17 respectively Both authors did

not define any definite orientation of the grains

Riley (1941) realize the problems that an area perimeter and some other

measurements proposed by the above authors can carry as the time consuming and

tedious work (at that time were not computer all was made by hand) and thatrsquos why

he develop this equation easy to handle called ldquoinscribed circle sphericityrdquo He used

the same particle orientation proposed by Wadell and the relation of diameters of

inscribed and circumscribed circles

Horton 1932 (Hawkins 1993) use the relation of the drainage basing perimeter and

the perimeter of a circle of the same area as drainage basin

Janoo in 1998 (Blott and Pye 2008) develop his general ratio of perimeter to area

Sukumaran and Ashmawy (2001) develop his own shape factor (SF) defined as the

deviation of the global particle outline from a circle Figure 9 can be used as a

reference to determine the items used in the equation 21

N is referred to the number of sampling intervals o radial divisions

C2A

AC

2P

A4C

C

I

D

DC

CD

D

P

PC

A

PC

2

45ordm x N

Particleα

= SF

sumN

1=ii

(16)

(17)

(18)

(19)

(20)

(21)

11

Table 3 General chronological overview of the particle shape definitions for 2D sphericity

Aspect Name Author Year Based on

Circularity (2D) roundness Pentland 1927 area

roundness Cox1

1927 area-perimeter

roundness Tickell2

1931 area

Circularity Horton2

1932 drainage basin

outline circularity Wadell 1935 Circle diameter

degree of circularity Wadell 1935 Perimeter

inscribed circle sphericity Riley 1941 Circle diameter

Circularity Krumbein and Sloss 1963 chart

Janoo 1998 area-perimeter

Shape factor Sukumaran 2001 Segmentation of particle and angles

1) Riley 1941 2) Hawkins 1993

35 ROUNDNESS OR ANGULARITY

Roundness as described in section 32 is the second order shape descriptor Sphericity

lefts beside the corners and how they are this was notice by most of the authors sited

before and they suggested many ways to describe this second order particle property

Roundness is clearly understandable using the figure 10 Particle shape or form is the

overall configuration and denotes the similarities with a sphere (3D) or a circle (2D)

Roundness is concerning about the sharpness or the smoothness of the perimeter (2D)

Surface texture (Barret 1980) is describe as the third order subject (form is the first

and roundness the second) and it is superimposed in the corners and it is also a

property of particles surfaces between corners

Figure 9 Description of the Sukumaran factors to determine the shape and angularity (Sukumaran and

Ashmawy 2001)

12

Wadell (1935) describes his methodology calling it total degree or roundness to

obtain the roundness of a particle using the average radius of the corners in relation

with the inscribed circle diameter (see figure 11) on the equation

In the same study Wadell (1935) has used the equation

This two last equation shows slightly differences on the results (Wadell 1935)

Powers (1953) also published a graphic scale to illustrate the qualitative measure

(figure 12) It is important to highlight that any comparing chart to describe particle

properties has a high degree of subjectivity Folk (1955) concludes that when charts

are used for classification the risk of getting errors is negligible for sphericity but

large for roundness

N

R

r

Rinmax

r

R

NR

inmax

Figure 10 Form (shape) Roundness and Texture graphical description (Bowman et al 2001)

Figure 11 Wadellrsquos method to estimate the roundness corners radius and inscribed circle

(Hawkins 1993)

(22)

(23)

13

Some authors as Russel amp Taylor in 1937 Pettijohn in 1957 and Powers in 1953

developed a classification based on five and six classes (Hawkins 1993) each one

with its own class limits it is important to denote that the way they measure the

roundness is the developed by Wadell (1935) This classification and class limits are

showed in the table 4

Table 4 Degrees of roundness Wadell Values (Hawkins 1993) NA = no-applicable

Grade terms Russell amp Taylor (1937) Pettijohn (1957) Powers (1953)

Class

limits (R)

Arithmetic

midpoint

Class limits

(R)

Arithmetic midpoint Class

limits (R)

Arithmetic

midpoint

Very angular

NA

NA

NA

NA

012-017

014

Angular

000-015

0075

000-015

0125

017-025

021

Subangular

015-030

0225

015-025

0200

025-035

030

Subrounded

030-050

0400

025-040

0315

035-049

041

Rounded

050-070

0600

040-060

0500

049-070

059

Well rounded

070-100

0800

060-100

0800

070-100

084

Krumbein and Sloss (1963) published a graphical chart easy to determine the

sphericity and roundness parameters using comparison See figure 13 (Cho et al

2006)

Figure 12 A Roundness qualitative scale (Powers 1953)

Figure 13 Sphericity and roundness chart (Cho et al 2006) The roundness equation that appears here in

the chart is the wadellrsquos equation number 22

14

Fischer in 1933 (Hawkins 1993) used a straightforward method to quantify roundness

using a central point in the outline and dividing the outline in angles around this point

that were subtended by the straight or non curved parts of the profile were measured

This is illustrated in figure 14

To express the angularity value Fischer used the ratio of angles standing linear parts

on the outlines and concave respectively

Figure 14 left (A) and right (B) gives a similar angularity of approximately 042

using the above equations (Hawkins 1993)

Wentworth in 1922 used the maximum projection to define the position of the particle

to obtain the outline or contour (Barret 1980) The equation reflects the relation of the

diameter of a circle fitting the sharpest corner and the longest axis plus the shortest

axis c (minimum projection)

Wentworth (Hawkins 1993) expressed the roundness as the ratio of the radius of

curvature of the most convex part and the longest axis plus short axis

Actually these last two equations are the same just expressed in different terms when

the particle is in its maximum projection

Dimensions can be seen on figure 15 L and B represents the mayor axis a and

intermediate axis b The intention is to make difference between the 2 and 3

dimensions (L and B are for 2D as a b and c are for 3D)

deg360

ANG

=R

sumPLA

PLA

CON

ANG

ANGR

2)S(L

DR

M

S

B)4(L

RR CON

Figure 14 Fischerrsquos methods of angularity computation (Hawkins 1993)

A=inscribed circle B=circumscribed circle

(24)

(25)

(26)

(27)

15

Wentworth 1919 has a second way to express the roundness called Shape index

(Barrett 1980) and it relates the sharpest corner and the diameter of a pebble trough

the sharpest corner

Wentworth (1922b) used define the roundness as the ratio of the sharpest corner and

the average radius of the pebble

Cailleux (Barrett 1980) relates the radius of the most convex part and the longest

axis

Kuenen in 1956 show his roundness index (Barrett 1980) between the sharpest corner

and the breath axis

Dobkins amp Folk (1970) used a modified Wentworth roundness with the relation of

sharpest corner and inscribed circle diameters

AVG

CON

R

RR

x

s

D

DR

L2

RR CON

B

DR s

i

s

D

DR

3AVGAVG cbaDR2

Figure 15 Description of L and B axes (Hawkins 1993)

(28)

(29)

(30)

(31)

(32)

(33)

16

Swan in 1974 shows his equation (Barrett 1980) relating the sharpest (or the two

sharpest) corner(s) and inscribed circle diameter

Szadeczsky-Kardoss has his Average roundness of outline (Krumbein and Pettijohn

1938) relating the concave parts perimeter and the actual perimeter

Lees (1964a) developed an opposite definition to roundness it means that he

measures the angularity instead of the roundness and he calls it Degree of angularity

Figure 16 shows the items considered when equation 36 applies as the angles (α)

inscribed circle (Rmax-in) and the distance (x) The main formula is

In order to apply the last equation corners needs to be entered in the formula and each

individual result will add to each other to obtain the final degree of angularity

A roundness index appears on Janoo (1998) Kuo and Freeman (1998a) and Kuo et

al (1998b) it is described as

The last equation is on section 34 also because there is not a general agreement on the

definition furthermore some authors had used to define the roughness this is not the

only equation that has been used trying to define different aspects (sphericity

roundness or roughness) but it is a good example of the misuse of the quantities and

definitions

inmaxR

x)180(R

2P

A4R

i

ss

D

DDR

221

100P

PR CON

Figure 16 Degree of angularity measurement technique (Blot and Pye 2008)

(34)

(35)

(36)

(17)

17

Sukumaran and Ashmawy (2001) present an angularity factor (AF) calculated from

the number of sharpness corners Angles βi required to obtain the angularity factor are

shown in figure 9

Sukumaran and Ashmawy (2001) also suggested use not bigger sampling interval of

N=40 because it is the cut off between angularity factor and surface roughness If so

this equation could be used to describe the roughness

Table 5 General chronological overview of the particle roundness

Aspect Name Author Year Based on

Roundness shape index Wentworth 19191

diameter of sharper corner

shape index Wentworth 1922b sharpest corner and axis

roundness Wentworth 1933 convex parts

Fischer 19332

noncurved parts outline

Fischer 19332

noncurved-streigth parts outline

Average roundness of outline

Szadeczsky-Kardoss 19333

convex parts-perimeter

roundness Wadell 1935 diameter of corners

roundness Wadell 1935 diameter of corners

roundness Russel amp Taylor 19372

class limit table

roundness Krumbein 1941 chart

Cailleux 19471

convex parts

roundness Pettijohn 19494 class limit table

roundness Powers 1953 chart and class limit table

Kuenen 19561

axis-convex corner

roundness Krumbein and Sloss 1963 chart

degree of angularity Lees 1964a corners angles and inscribed circle

Dobkins amp Folk 1970 diameter of sharper corner

Swan 19741

diameter of sharper corners

Angularity factor Sukumaran and

Ashmawy 2001

Segmentation of particles and angles

1) Barret 1980 2) Hawkins 1993 3) Krumbein and Pettijohn 1938 4) Powers 1953

sum

sumsumN

1=i

2

i

2

N

1=i

2

i

2N

1=ii

)ordm180 -circleβ( - )(180ordm x 3

)ordm180-circleβ(-)ordm180 -Particleβ(

= AF (37)

18

36 ROUGHNESS OR SURFACE TEXTURE

A third property called texture appears early in the literature with the sphericity and

roundness properties since then texture property was longed described but it was in

accordance with the authors at that time not measurable

Wright in 1955 developed a method to quantify the surface texture or roughness of

concrete aggregate using studies done on 19 mm stones The test aggregates were first

embedded in a synthetic resin The stones were cut in thin sections The sections

projection was magnified 125 times The unevenness of the surface was traced and the

total length of the trace was measured The length was then compared with an uneven

line drawn as a series of chords (see figure 17) The difference between these two

lines was defined as the roughness factor (Janoo 1998)

However with the advance of technology it has become easier measure the roughness

and here is presented some researcherrsquos ideas how this property should be calculated

One technique used by Janoo (1988) to define the roughness can be seen in figure 18a

and is defined as the ratio between perimeter and convex perimeter

The convex perimeter is obtained using the Feretrsquos box (or diameter) tending a line in

between the touching points that the Feretrsquos box describes each time it is turn (figure

18b)

PER

OC

PR

Figure 17 Measurement method for characterizing the surface texture of an aggregate (Janoo 1998)

a) Convex perimeter (CPER) b) Feret measurement Figure 18 a) Convex perimeter (CPER) b) Feret measurement (modified after Janoo 1998)

(38)

a)

b)

19

Kuo and Freeman (1998a) and Kuo et al (1998b) use the roughness definition as the

ratio perimeter and average diameter

Erosion and dilatation image processing techniques are used to obtain the surface

texture Erosion is a morphological process by which boundary image pixels are

removed from an object surface which leaves the object less dense along the

perimeter or outer boundary Dilatation is the reverse process of erosion and a single

dilatation cycle increases the particle shape or image dimension by adding pixels

around its boundary (Pan etal 2006)

The ldquonrdquo erosion and dilatation cycles are not standardized

Mora and Kwan (2000) used the ldquoconvexity ratio CRrdquo (equation 41) and the ldquofullness

ratio FRrdquo (equation 42) in their investigation they are

The convex area is the area of the minimum convex boundaries circumscribing the

particle This is illustrated in the figure 19 The convex area is obtained in a similar

way as the convex perimeter but in this case the area between the original outline and

the convex perimeter is our convex area

AVG

OD

PR

100A

1AARO

CONo A

AR =

CONo A

AR =

Figure 19 Evaluation of area and convex area (Mora and Kuan 2000)

(39)

(40)

(41)

(42)

20

4 TECHNIQUES IN ORDER TO DETERMINE PARTICLE

SHAPE

41 HAND MEASUREMENT

Hand measurement technique was the first used by obvious reasons in order to

improve the accuracy special devices developed as the ldquosliding rod caliperrdquo used by

Krumbein (1941) it works placing the sample on the sliding road calliper as show

figure 20b the length in different positions can be obtain by using the scale provided

in the handle the ldquoconvexity gagerdquo that was actually used by opticians to measure the

curvature of lenses but easily applicable to the particle shape analysis (Wentworth

1922b) works measuring the movement of the central pivot as figure 20a shows (the

two adjacent pivots are invariable) as many the central pivot moves more is the

curvature or the ldquoSzadeczky-Kardossrsquos apparatusrdquo develop in 1933 that traces the

profile of the rock fragment so the outline traced is then analyzed (Krumbein and

Pettijohn 1938) figure 20c show equipment

Another helpful tool to determine the particle dimensions was the ldquocamera lucidardquo to

project the particlersquos contour over a circle scale appearing in Figure 21 thus it is

possible to measure the particlersquos diameter

a)

c) b)

Figure 20 a) convexity gage used to determine the curvature in particle corners (Wenworth 1922b)

b)sliding rod caliper device to measure the particle axis length (Krumbein 1941) and c)Szadeczky-

Kardoss (1933) apparatus it was utilized to obtain the particle outline

Figure 21 Circle scale used by Wadell (1935) to determine particlersquos diameter and roundness

21

42 SIEVE ANALYSIS

Bar sieving eg according to EN 933-31997 can be used to determine simple large

scale properties By combining mesh geometries the obtained results can be used to

quantify flakiness and elongation index ASTM D4791 (Flat and elongated particles

are defined as those coarse aggregate particles that have a ratio of length to thickness

equal to or greater than a specified value such as 51 The index represents the

percentage on weight of these particles) The method is not suitable for fine materials

This due to the difficulty to get the fine grains passed through the sieve and the great

amount of particles in relation to the area of the sieve (Persson 1998) eg EN 933-

31997 related to flakiness index The test is performed on aggregates with grain size

from 4 mm and up to 63 mm two sieving operations are necessary the first separates

on size fraction and the second use a bar sieve after the first sieving the average

maximum diameter of the particles is obtain and with the second sieving (bar sieving)

the shortest axis diameter is found finally with this two parameters the flakiness

index is determined

There are more standards related with the particle shape (see appendix A) but this

above presented are probably the most known using sieve analysis to determine

particlersquos geometrical properties

Sieve analysis is facing the computers age and image analysis sieving research is

taking place (Andersson 2010 Mora and Kwan 2000 Persson 1998) Industry is

also applying the image analysis sieving with decrees on the testing time compare

with the traditional sieving method An inconvenient of image analysis is the error

due the overlapping or hiding of the particles during the capture process but the

advantages are more compare with disadvantages (Anderson 2010)

43 CHART COMPARISON

Charts developed over the necessity of faster results because the long time consuming

required when measuring each particle

Krumbein (1941) present a comparison roundness chart for pebbles which were

measured by Wadellrsquos method because this property was the most difficult to measure

due to the second order scale that roundness represents (See figure 22)

Figure 22 Krumbein (1941) comparision chart for roundness

22

A qualitative chart by Powers (1953) try to include both (sphericity and roundness)

particlersquos characteristics it was divided on six roundness ranges (very angular

angular sub-angular sub-rounded rounded and well rounded) and two sphericity

series (high and low sphericity) This chart was prepared with photographs to enhance

the reader perspective (See figure 23)

A new chart including sphericity and roundness appear this time it was easier to

handle the two mean properties of particlersquos shape furthermore there was included

the numerical values that eliminated the subjectivity of qualitative description The

chart is based on Wadellrsquos definitions (Krumbein and Sloss 1963) (See figure 24)

Folk (1955) worried about the personrsquos error on the chartrsquos comparison studied the

determination of sphericity and angularity (he used the Powers 1953 comparison

chart) he found that the sphericity determination by chart comparison has a negligible

error while the roundness he concluded it was necessary to carry out a more wide

research due the high variability show by his study

Figure 23 Powers (1953) qualitative shpericity-roundness chart

Figure 24 Sphericity-roundness comparison chart (Krumbein and sloss 1963)

23

44 IMAGE ANALYSIS

Image analysis is a practical method to use for shape classification since it is fast and

can be automated Different techniques appear to process these images among them

are

o Feret Diameter the Feret diameter is the longitude between two parallel lines

this lines can rotate around one particle or outline to define dimensions as it

is shown in figure 25 these method is not a fine descriptor but as it was say

above it is a helpful tool to determine diameters (Janoo 1988)

o Fourier Mathematical Technique It produces mathematical relations that

characterize the profile of individual particles This method favours the

analysis of roughness and textural features for granular soils The problem in

the methodology remains in the re-entrant angles in order to complete the

revolution (Bowman et al 2001) see figure 26

o Fractal Dimension Irregular line at any level of scrutiny is by definition

fractal (Hyslip and Vallejo 1997) Figure 27 shows fractal analysis by the

dividing method The length of the fractal line can be defined as

N

1n

nn0 )nsinbncosa(a)(R

RD1n)(P

Figure 25 Feret measurement technique is defined by two parallel lines turning

around the particle to define the shortest and longest Feret diameter (Janoo 1988)

Figure 26 Fourier technique with two radiuses at one angle (Bowman et al 2001)

(43)

(44)

24

o Orthogonal image analysis This technique is basically the use of two images

orthogonal between them to acquire the three particle dimensions (Fernlund

2005) any of the above techniques can be used in this orthogonal way

o Laser Scanning Technique this kind of laser scanning 3D is one of the most

advanced techniques In figures 28a) we have the laser head scanning the rock

particles the particles have control points in order to keep a reference point

when move them to scan the lower part in figure 28b) we can see the laser

path followed (Lanaro and Tolppanen 2002)

Another technique is the Laser-Aided Tomography (LAT) in this case a laser sheet is

used to obtain the particles surveying (see figure 29) This technique is different and

has special requirements as to use liquid with same refractive index as the particles

particles must let the laser or certain percent of light go through (Matsushima et al

2003)

a) b)

Figure 27 Fractal analysis by the dividing method at different scrutiny scale (Hyslip and Vallejo 1997)

Figure 28 a) Scanning head b) scanning path (Lanaro and Tolppanen 2002)

Figure 30 3D scan completed ready to

use for any further measure

(Matsushima et al 2003)

Figure 29 LAT scaning particles

(Matsushima et al 2003)

25

Both 3D techniques obtain the particle shape that is later used to achieve measures as

we can see in figure 30

All these previous techniques are easily written in codes or scripts to be interpreted in

a digital way obtaining the desired measurement but there are some interesting points

in the image analysis regarding on the errors involve among them are image

resolution and orientation of the particles orientation is not relevant when it is

random and large number of particles are involve resolution have an influence on the

accuracy (Zeidan et al 2007)

When resolution is increase more accuracy is obtain and the object representation

match better with the real form in the other hand more resolution means more

spending on memory and time thus resolution needs to be according with the goal

and precision needed in any work (Schaumlfer 2002)

Schaumlfer (2002) conclude that attributes like length when measuring digital images

present relative high errors It can be vanish or at least diminish using high resolution

just for diameter but not for perimeter that keep the error as big as initially Johansson

and Vall (2011) obtain similar results when 3 different resolutions were used in the

same particle obtaining an unstable output for those termsquantities that involve the

perimeter Thus all quantities relating the perimeter should be treated with care

5 EFFECT OF SHAPE ON SOIL PROPERTIES

51 INTRODUCTION

In laboratory test on the effect on particle size on basic properties has been

investigated in several studies this relation has been discussed and various

mechanisms had been proposed to explain the behaviour of the soil in dependency

also with the shape Basically there are two mechanisms proposed The arrangement

of particles and the inter-particle contact (Santamarina and Cho 2004) and

subsequence breakage

The arrangement of particles

Arrangement of the particles can be presented in three different forms loose dense

and critical this arrangement determines the soil properties (eg density increase with

more dense arrangement) Loose and dense states are easy understandable when

figure 31 is explained while in the upper part of the figure the particles are arranged

using the minimum space needed in the lower part a span is created using the flaky

particle as a bridge this phenomena is known as ldquobridgingrdquo Bridging can produce

different geotechnical results when just the shape of the particle is changed eg void

ratio (Santamarina and Cho 2004) Particles are able to rearrange this could be done

applying pressure (energy) to the soil the pressure (energy) will create such forces

that soil particles will rotate and move (see figure 34) finishing in a more dense state

26

A loose soil will contract in volume on shearing and may not develop any peak

strength (figure 32 left) In this case the shear strength will increase gradually until

the residual shear strength is revealed once the soil has ceased contracting in volume

A dense soil may contract slightly (figure 32 right) before granular interlock prevents

further contraction (granular interlock is dependent on the shape of the grains and

their initial packing arrangement) In order to continue shearing once granular

interlock has occurred the soil must dilate (expand in volume) As additional shear

force is required to dilate the soil a peak shear strength occurs (figure 32 left) Once

this peak shear strength caused by dilation has been overcome through continued

shearing the resistance provided by the soil to the applied shear stress reduces

(termed strain softening) Strain softening will continue until no further changes in

volume of the soil occur on continued shearing Peak shear strengths are also

observed in overconsolidated clays where the natural fabric of the soil must be

destroyed prior to reaching constant volume shearing Other effects that result in peak

strengths include cementation and bonding of particles The distinctive shear strength

called the critical state is identified where the soil undergoing shear does so at a

constant volume (Schofield and Wroth 1968)

The inter-particle contact

For frictional soil ie coarse grained soil the friction between particles is the

dominating factor for strength Materials usually consisting of coarse grains (diameter

Figure 31 Bridging effect when flaky particles are combined in the bulk material (Santamarina and

Cho 2004)

Figure 32 The left part of the figure show a typical behaviour of loose and dense material over shear stress

while at the right the figures illustrate the typical volume changes

27

gt 006mm) behave as a frictional soil it means that the strength of coarse soils (silt

sand gravel etc) comes from an inter-particle mechanical friction thus ideally they

do not have traction strength In figure 33 the inter-particle contact is illustrated here

the pressure (P) is applied and two more components are found the normal load (N)

and the tangential load (T) described as the friction coefficient (μF) The forces stand

in equilibrium (Johansson and Vall 2011)

When particles equilibrium is disturbed (friction coefficient is not enough to keep

particles unmoved) the rotation is imminent and it is necessary in order to compact

the soil in figure 34 can be seen that the arrangement is a fact that inhibit or allow this

rotation and the shape in the 3 different scales are also factors because the more

spherical andor more rounded andor less roughness more easy is the rotation

(Santamarina and Cho 2004)

Breakage

Breakage is a side effect of the inter-particle contact and rotation when pressure

exceed the rock strength it can happened when the particles are tight together and

there is not enough space to rotate it is more obvious in angular particles (mesh form)

or as in figure 31 where the flaky particle ldquobridgingrdquo is not able to rotate but it can

brake by the pressure increase Yoginder et al (1985) notice that the angular particle

break during his experiments and they turn more rounded changing the original size

and form configuration at the same time there was a soil properties loosening

Figure 33 Inter-particle contact and forces acting (Axelsson 1998)

Figure 34 Rotation inhibition by the particles compaction or low void ratio (Santamarina and Cho 2004)

28

52 INFLUENCE OF SIZE AND SHAPE

Wenworth (1922a) and Pellegrino (1965) among others suggest that agent transport of

the rocks (rigor of transport temperature and moisture changes etc) determine its

shape but also the particle genesis itself (rock structure mineralogy hardness etc) It

is not possible to determine the shape of the particles based on the agent transport or

genesis but generally a shape behaviour is expected according to Mitchell and Soga

(2005) specially when the particle size is in the clay size (gt2μm) The shapes of the

most common clay minerals are platy (figure 35) with some exceptions (eg

halloysite occurs as tubes kaolinite are large thick and stiff Smectites are composed

of small very thin and filmy particles Illites are intermediate between kaolinite and

smectite and attapulgite occurs in lathlike particle shapes) Some clay minerals

photographs are presented in figure 35

Figure 35 Clay mineral shape a) hallosite b) Kaoline c) Smactites d) Illites and e) attapulgite (Modified

from Mitchell and Soga 2005)

Figure 36 Particle size range in soils Generally the particles of clay size are plate shaped (Mitchell and

Soga 2005)

a) b) c)

e) d)

29

53 VOID RATIO AND POROSITY

The void ratio (e) is the ratio of the volume of voids to the volume of solid it is

defined by the equation

Porosity (n) is the ratio of the volume of voids to the total volume of the soil it is

represented by the equation

Holubec and DrsquoAppolonia (1973) found a relation between the void ratio and

sphericity (referred in the paper as coefficient of angularity ratio of particle surface

and equivalent sphere surface) their results show that the maximum and the minimum

void ratio increases as the shpericity decreases In this study the surface was obtained

for an indirect method based on the permeability developed by Hoffman in 1959

described in the same document Rouseacute et al (2008) defined the roundness as

Wadell (1935) and he found it as an important factor controlling the minimum and

maximum void ratios Some other authors as Youd (1973) and Cho et al (2006)

conclude the same minimum and maximum void ratios increase when sphericity and

roundness decrease Another interesting result (all above authors) was the bigger

influence of the form (sphericity circularity) and roundness on the maximum void

ratio The change of the maximum void ratio is more pronounced than the change of

the minimum void ratio when the form and roundness changes (See figure 39)

Particles arrangement and interlocking are probably the factor that controls the void

ratio bridge effect permit the existence of void among the particles while interlocking

allowed the particles to form arches avoiding the possibility to rotate and stay in a

more stable configuration eg as it happens with marbles

Figures 36 37 and 38 shows proposed empirical relationships between void ratio and

shape from tables 5 and 6 (graphically the scale goes from 0 to 1 when cero mean

high angularity shpericity or circularity and one means low angularity circularity or

sphericity) Holubec and DrsquoAppolonia (1973) data was taken to obtain a power curve

and describe a tendency Santamarina and Cho (2004) show Youd equations in the

original paper Youd (1973) never presented the equation but it is easy to use the

information to draw a trend

The graphics presented in this document (figures 36 37 and 38) must be used with

certain reserves due the fact that the original data was modified in order to fit all

information in one graphic what the figures shows is just the general trend of the

behaviourrsquos material regarding on the shape If more accurate description and

information is required the author recommends consulting the reference data In the

same way equations from Holubec and DrsquoApollonia (1973) and Youd (1973) were not

presented by the authors but the use of the information was taken in order to build up

those equations on tables 6 and 7

S

V

V

V

= e

V

V

=nV

(45)

(46)

30

Table 6 Minimum void ratio equations regarding on the quantity (Ψ for sphericity C for circularity R

for roundness SF for Sukumaran shape factor and AF for Sukumaran angularity factor)

EQUATION NUMBER REFERENCE

Figure 34 (left)

4340

minΨ45490e =

47

Holubec amp DrsquoAppolonia 1973 (Ψ

was obtained using equation 2)

SF06340

mine021903180e +=

48

Sukumaran amp Ashmawy 2001 (SF

obtained using equation 21)

C05101emin

= 49

Cho etal 2006 (C obtained using

figure 12)

Figure 34 (right)

1

minR08203590e +=

50

Youd 1973 (R obtained from figure

11 and table 3)

R34080emin

= 51

Cho et al 2006 (R obtained using

figure 12)

1

minR05104330e +=

52

Rouseacute et al 2008 (R obtained by

equation 21)

AF02330

mine372004160e +=

53

Sukumaran amp Ashmawy 2001 (AF

obtained using equation 37)

Table 7 Maximum void ratio equations regarding on the quantity (Ψ for sphericity C for circularity R

for roundness SF for Sukumaran shape factor and AF for Sukumaran angularity factor)

EQUATION NUMBER REFERENCE

Figure 35 (left)

51520

max Ψ61120e = 54

Holubec and DrsquoAppolonia 1973 (Ψ

was obtained using equation 2)

SF1190

max e0016907180e += 55

Sukumaran amp Ashmawy 2001 (SF

obtained using equation 21)

C86061emax = 56

Cho etal 2006 (C obtained using

figure 12)

Figure 35 (right)

1

max R1505540e += 57

Youd 1973 (R obtained from figure

11 and table 3)

R62031emax= 58

Cho et al 2006 (R obtained using

figure 12)

1

max R107106150e += 59

Rouseacute et al 2008 (R obtained by

equation 21)

AF0530

max e12506090e += 60

Sukumaran amp Ashmawy 2001 (AF

obtained using equation 37)

Comparing figures 37 and 38 (minimum and maximum void ratio) it can be seen on

the right scheme of both figures 37 and 38 (when the factor is roundnessangularity)

that all the empirical relations has a common initial point close to 1 (it means that

particles are well rounded) while this common agreement disappear when the

roundness factor decreases (when the particles become more angular) Same figures

(37 and 38) on the left graphs (when the factor is sphericitycircularityshape) do not

present the same behaviour in fact there is more disperse initial point close to 1(when

the particles tend to be more sphericalcircular)

31

In Figure 39 the Δe (emax-emin) has been plotted to show how the maximum void ratio

and the minimum void ratio has different rate change when the particle shape

changes Maximum void ratio increases more than minimum void ratio when the

particle shape becomes less spherical andor more angular Comparing figure 39 left

and right graphics it can be seen that right present a common initial point when the

quantity (roundnessangularity) is close to one while in the left graphic the initial

point is more disperse Both ending points in both graphics (close to zero) are

dispersed

Figures 37 38 and 39 present the same behaviour right graphics (when the factor is

roundness angularity) in each figure have an initial common point while the left

graphics do not (when the factor is sphericity circularity shape)

Figure 37 Minimum void ratio based upon the relation of shape factor proposed by the authors indicated

in the figure

Figure 38 Maximum void ratio based upon the relation of shape factor proposed by the authors indicated

in the figure

04

06

08

1

12

14

16

18

2

005

015

025

035

045

055

065

075

085

095

Factor (roundness angularity)

min

imu

m v

oid

rati

o

Youd 1973 roundness

Rouse 2008 roundness

Cho 2006 roundness

Sukumaran 2001 AF

03

04

05

06

07

08

09

1

11

12

13

05

015

025

035

045

055

065

075

085

095

Factor (sphericity circularity shape)

min

imu

m v

oid

rati

oHolubec 1973 sphericity

Cho 2006 circularity

Sukumara 2001 SF

05

07

09

11

13

15

17

19

21

00

150

250

350

450

550

650

750

850

95

Factor (sphericity circularity shape)

Maxim

um

vo

id r

ati

o

Holubec 1973 sphericity

Cho 2006 circularity

Sukumara 2001 SF

05

1

15

2

25

3

35

005

015

025

035

045

055

065

075

085

095

Factor (roundness angularity)

Maxim

um

vo

id r

ati

o

Youd 1973 roundness

Rouse 2008 roundness

Cho 2006 roundness

Sukumaran 2001 AF

32

54 ANGLE OF REPOSE

The angle of repose of a granular material is the steepest angle of descent or dip of the

slope relative to the horizontal plane when material on the slope face is on the verge

of sliding as show in figure 40

According to Qazi (1975) there are five types of forces which may act between the

particles in soils

1 Force of friction between the particles

2 Force due to presence of absorbed gas andor moisture of particle

3 Mechanical forces caused by interlocking of particles of irregular shape

4 Electrostatic forces arising from friction between the particles themselves and

the surface with which they come in contact

5 Cohesion forces operating between neighbouring particles

Rouseacute et al (2008) found a decrease of angle of repose with increase roundness

based upon ASTM C1444 test (Standard Test Method for Measuring the Angle of

Repose of Free-Flowing Mold Powders) The method consist in pouring sand on a

surface cover by paper trough a funnel of specific dimensions (the nozzle diameter

depend on the sandrsquos particle size) from an altitude of 15 inches (381 mm) The sand

is release from the funnel until the peak of the cone formed by the sand stops the flow

The repose angle is obtained with the equation

H represent the 15 inches D and d represent the diameter of the cone formed by the

sand and the diameter of the funnel respectively

Figure 39 Maximum minus minimum void ratio based upon the relation of shape factor proposed by the

authors indicated in the figure

0

01

02

03

04

05

06

07

08

09

1

005

015

025

035

045

055

065

075

085

095

Factor (sphericity circularity shape)

Maxim

um

- M

inim

um

Vo

id r

ati

oHolubec 1973 sphericity

Cho 2006 circularity

Sukumara 2001 SF

0

02

04

06

08

1

12

14

16

18

005

015

025

035

045

055

065

075

085

095

Factor (roundness angularity)

Maxim

um

- M

inim

um

Vo

id r

ati

o

Youd 1973 roundness

Rouse 2008 roundness

Cho 2006 roundness

Sukumaran 2001 AF

dD

H2

tan=φ1

rep(61)

33

Rouseacute (2008) shows an empirical relation to obtain the angle of repose based on the

roundness of the particles

55 SHEAR STRENGTH

The MohrndashCoulomb failure criterion represents the linear envelope that is obtained

from a plot of the shear strength of a material versus the applied normal stress This

relation is expressed as

where τ is the shear strength σn is the normal stress co is the intercept of the failure

envelope with the τ axis and is the slope of the failure envelope The quantity c is

often called the cohesion and the angle is called the angle of internal friction

Studies show that the internal friction angle (under drained triaxial tests) increases

more rapidly on those materials having higher angularity increasing the relative

density The internal friction angle is a function of the relative density and the particle

shape (Holubec and DrsquoAppolonia 1973)

Chan and Page (1997) found in a study made with dry copper (using different shapes

and sizes ranging from 180 to 106 μm) using a direct shear test (ring share test) that

the internal friction angle increases as the angularity increases

Shinohara et al (2000) did some experiments with steel powder different shapes

using a triaxial cell in the test Shinohara never used the roundness or angularity on

the work but apply the shape factor (relation long axisshort axis) and the results were

that as this relation deviate from factor 1 the internal friction angle increases

The following empirical relations were found in the literature showing the behaviour

of the friction angle (obtained under different conditions)

)tan( noc

Figure 40 Representation of the angle of repose

(63)

(62)

34

Cho et al (2006)

(64)

(R is obtain by comparing the Krumbein chart figure 13)

Rouseacute (2008)

(65)

(66)

(R is defined using Wadell equation 22)

In figure 41 the suggested empirical relations above and lines constructed using

author data from Holubec and DrsquoAppolonia (1973) and Sukumara and Ashmawy

(2001) are plotted together to display the general trend on the particle shape and

friction angle relation Sukumaran reports two lines one based on the shape factor

(SF) and the second referring the angularity factor (AF) Sukumaran performed the

tests at constant volume

The scale used for Holubec and DrsquoAppolonia (1973) have lower and upper limits of 1

and 2 respectively (angularity form) and a scale change was applied to be able to

presented in the actual figure 41 As in the previous section (52) the author

recommend to use the original data from the references due that the figure just follows

the general trend of the behaviourrsquos particle regarding on the shape

Figure 41 The changes on the internal friction angle shows a general increase when the particle roundness

becomes angular or in the case of Sakamuran less spheric (Shape factor SF)

35

Barton and Kjaernsli (1981) suggested a model (equation 67) to predict the peak

friction angle (φrsquo) based upon numerous trixial and direct shear data tests

where

Se equivalent strength of particle

Re equivalent roughness of particle

φb basic friction angle (obtained from basic tilting test)

σn normal load

The information required for the model is (1) the uniaxial compressive strength of the

rock (2) the d50 particle size (mesh size where 50 of the particles pass through)

required to define Se (figure 42) (3) the degree of particle roundness and (4) the

porosity following compaction All data can be estimated by simple index tests

Barton and Kjaernsli (1981) suggest that particle size and sample scale has an effect

on the friction angle and includes them to obtain the equivalent strength (Se) figure 42

shows the method to obtain this value Compressive strength (σc) was chosen to be the

factor affecting the scale because micro fractures influence this property while

samples are bigger more micro fractures contain and its compressive strength reduces

The equivalent roughness is obtain using figure 43 where is required to know the

porosity (n) and the origin of the particles (a small chart is provided in the same figure

to compare the particles profile)

b

n

ee

SLogR

Figure 42 Method of estimating Equivalent Strength (Se) of rockfill based on uniaxial compressive strength

(σc ) and d50 particle size (Barton amp Kjaernsli 1981)

(67)

36

56 SEDIMENTATION PROPERTIES

A particle released in a less dense Newtonian fluid initially accelerate trough the fluid

due to the gravity Resistances to deformation of the fluid transmitted to the particle

surface drag generate forces that act to resist the particle motion The force due to the

weight (Fw) can be written as

Where ρp ρ are density of the particle and fluid (water) respectively g is the

gravitational force and Vp is the volume of the particle

And the resistance force (FD) is

Where CD is the dimensionless drag coefficient W is the weight of the particle and A

is the cross section area

Particlersquos shape has been assumed to be spherical when equations are applied on the

settling velocity Correlation deviates when particle shape departs from spherical form

Figure 43 Method of estimating Equivalent Roughness (Roe) based on porosity of rockfill

origin material degree of roundedness and smoothness of particle (Barton amp Kjaernsli 1981)

PPW ρ)gV(ρF

A2

WρCF

2

DD

(68)

(69)

37

(Dietrich 1982) and it is known that natural particles depart from spherical form

thus it is evident that this departure would have consequences

The below equation is proposed to account the shape (in this case the Corey shape

factor equation 8) in the settling velocity (Jimenez and Madsen 2003)

Jimenez and Madsen (2003) Dietrich (1982) Briggs and McCulloch (1962) and

others were working in the hydraulic shape of particles to solve problems as sediment

transport It is obvious that the equation presented and the researcherrsquos investigation

works under certain conditions (eg grain size between 0063-1 mm)

Dietrich (1982) suggests an empirical relation that accounts settling velocity size

density shape and roundness of a particle

R1 R2 and R3 are fitted equations for size and density shape and roundness

respectively

57 HYDRAULIC CONDUCTIVITY PERMEABILITY

Darcyrsquos Law Permeability is one component of Darcyrsquos law Darcys law is a simple

proportional relationship between the instantaneous discharge rate through a porous

medium the viscosity of the fluid and the pressure drop

The total velocity Ve is equal to the product of the permeability of the medium

(porous media) k the pressure drop ∆p all divided by the viscosity μ (Muskat

1937)

Darcys law is only valid for slow viscous flow most groundwater flow cases fall in

this category Typically Darcyrsquos law is valid at any flow with laminar flow (see figure

44)

Reynoldrsquos number (Laminar and turbulent Flow) Typically any laminar flow is

considered to have a Reynoldrsquos number less than one and it would be valid to apply

Darcys law Experimental tests have shown that flow regimes with Reynolds numbers

1

ND

S

S

ZY

gd1s

WW

NDN

gd)1s(4

dS

2R1R

3 10RW

pk

Ve

(70)

(71)

(72)

(73)

38

up to 10 may still be Darcian (laminar flow) as in the case of groundwater flow The

Reynolds number (a dimensionless parameter) for porous media flow is typically

expressed as

where ρ is the density of water (units of mass per volume) υ is the specific discharge

(with units of length per time) d is a representative average grain diameter for the

porous media (often taken as the 30 passing size from a grain size analysis using

sieves - with units of length) and μ is the viscosity of the fluid (Muskat 1937)

Shape effects Permeability as Head and Epps (2011) suggested is affected by the

shape and texture of soil grains Elongated or irregular particles create flow paths

which are more tortuous than those spherical particles Particles with a rough surface

texture provide more frictional resistance to flow Both effects tend to reduce the

water flow through the soil

Kozeny-Carman empirical relation accounts for the dependency of permeability on

void ratio in uniformly graded sands serious discrepancies are found when it is

applied to clays due the lack of uniform pores (Mitchell and Soga 2005)

There are various formulations of the Kozeny-Carman equation one published by

Head and Epps (2011) takes the void ratio e the specific surface area Ss and an

angularity factor F into account of permeability k

The angularity factor F considers the shape of the particles and ranges from 11 for

rounded grains 125 for sub rounded to 14 for angular particles The specific surface

Ss is defined as

d1 and d2 represent the maximum and minimum size particle in mm

Kane amp Sternheim (1988) suggest that the inclusion of the shape factor (F) has

probably the background on the Reynolds number due this factor is dependent

significantly on the shape of the obstacles and Reynolds number determines the

presence of laminar or turbulent flow Figure 44 show how the laminar flow has low

energy dissipation while turbulent flow (eg the roughness and path tortuosity) has

high energy dissipation

e1

e

FSs

2k

3

2

dRe

21

6

ddSs

(74)

(75)

(76)

39

According to Nearing and Parker (1994) the amount of soil detached during laminar

and turbulent flow is dependent on each soil and also greater on turbulent flow due the

greater shear strength generated during this kind of flow this could suggest the

greater erosion when turbulent flow is present

58 LIQUEFACTION

Soil liquefaction is a phenomenon in which soil loses much of its strength or stiffness

for a generally short time by earthquake shaking or other rapid loading Static and

dynamic liquefactions occur been the second one the most regular known

Liquefaction often occurs in saturated soils that is soils in which the space between

individual particles is completely filled with water This water exerts a pressure on the

soil particles that influences how tightly the particles themselves are pressed together

Shaking or other rapid loading can cause the water pressure to increase to the point

where the soil particles can readily move with respect to each other (Jefferies and

Been 2000)

Jefferies and Been (2000) state that it is clear that minor variation in intrinsic

properties of sand have major influence on the critical state These might be variations

on grain shape mineralogy grain size distribution surface roughness of grains etc

Yoginder et al (1985) found that substantial decrease on liquefaction resistance

occur with increase in confining pressure for rounded and angular sands (1600 kPa)

also rounded sands show an rapidly build up of resistance against liquefaction with

increasing density while angular tailing sand in contrast show such rapid increase

only at low confining pressures At low confining pressure angular material is more

resistant to liquefaction Probably the breakage of the corners on the angular particles

in tailings is ruling the lost in resistance at high confining pressures (sieve analysis

Figure 44 The figure show the extremes of flow behaviour First turbulent conditions where the flow is

essentially random and unpredictable and second the well defined Laminar flow conditions

40

after test identify the breakage of angular particles while on rounded particles the

sieve analysis was practically the same)

59 GROUNDWATER AND SEEPAGE MODELLING

In groundwater flow the particlersquos shape affects the soilrsquos pore size distribution

hence the flow characteristics (Sperry and Peirce 1995) Tortuosity and permeability

(also see section 57) are two significant macroscopic parameters of granular medium

that affect the passing flow (Hayati et al 2012) Current models incorporating the

effects of particle shape have failed to consider irregular particles such as those that

would prevail in a natural porous medium (Sperry and Peirce 1995)

Hayati et al (2012) suggested based on his results that tortuosity effect converge

when the porosity increases indicating that the shape have dominance at low and mid

porosity ranges

Sperry and Peirce (1995) research conclusions suggest that particle size and porosity

are more important predictors for hydraulic conductivity explaining the 69 of the

variability but particle shape appears to be the next most important This however

apparently comprises particles larger than 295-351 μm Differences for particle size

295-351 μm and smaller are not detectable Another interesting result in the research

was the interaction effect of the particle size and particle shape It suggests a different

packing configuration for particles of the same shape but different size (scale

dependent)

6 DISCUSSION

61 TERMS QUANTITIES AND DEFINITIONS

In order to describe the particle shape in detail there are a number of terms quantities

and definitions (qualitative and quantitative) used in the literature (eg Wadell 1932

1934 Krumbein 1941 Sneed amp Folk 1958) All mathematical definitions

(quantitatives) are models used to simplify the complexity of shape description Some

authors (Mitchell amp Soga 2005 Arasan et al 2010) are using three sub-quantities

one and each describing the shape but at different scales The terms are

morphologyform roundness and surface texture (figure 1) The three sub-quantities

are probably the best way to classify and describe a particle because not a single

definition can interpret the whole morphology Common language is needed when

descriptors are explained and these three scales represent an option It is evident in

the reviewed literature that many of the shape descriptors are presented with the same

name but also that there is not a clear meaning on what this descriptor defines eg

when there is no upper limit in the roundness does it means that the angularity never

ends Could they be more and more angular Probably they could be on theory but

not in reality

41

62 PROPERTIES

Trough various articlersquos review done in the present investigation it is recognized that

the particlersquos shape has an effect on the material properties among these are

1 Porosity (Tickell 1938 Fraser 1935 Kolbuszewski 1948) and void ratio

(Cho et al 2006 Shergold 1953 Rouseacute et al 2008 Santamarina and Cho

2004)

2 Permeability (Witt and Brauns 1983)

3 Internal friction angle (Shinohara et al 2000 Chan and Page 1997

Cheshomi et al 2009)

4 Density (Youd 1973 Holubec and DrsquoAppolonia 1973)

5 Drag coefficient Hydraulics (Briggs and McCulloch 1962)

In Table 5 is a short resume of the properties and shape effect found in peer review

articles trough different journals Most of the reviewed articles based its research on

uniform graded sands

Table 8 Compilation of properties influenced by particle shape

Repose

angle

Friction

angle

Porosity and

Void ratio Density Permeability

Settling velocity

Drag coefficient Deformation

Sphericity (3D)shape factor

NI x x x x x x

Circularity (2D)

NI x x x x NI NI

Roundness x x x x NI NI x

x influence

NI no information available

Shape of particles has an effect on the arrangement producing bridging or avoiding

the rotation of the particles and the resulting geotechnical property is affected eg

including flaky particles can result in a higher void ratio due the bridging effect

(Santamarina and Cho 2004) and depending on the loads even the size distribution is

changed due the breakage (Yoginder et al 1985) in similar way angular particles

produce higher void ratio due the avoided possibility of the particles to rotate and

compact

The influence of the chosen shape descriptor appears in this review to have minor

influence on the soil properties in the reviewed studies except on the void ratio and

the friction angle Influence of particle shape in some cases is hider by other factors

(eg size distribution) also the particle shape probably does not have influence when

particle size is in the clay order (eg hydraulic conductivity) the reason could be due

to forces as electrostatic or capillarity become more important at this level

Among the shape descriptors some are chosen more often in literature (eg aspect

ratio) there is no apparent scientific basis to use it (probably due to the simplicity of

the measurement it becomes one of the most use) but there are still some other

descriptors that may or may not show better correlation with the soil properties

Instead empirical relations had been developed regarding roundness or shape to

describe the soil behaviour it is clear that the mechanism behind the results is still not

completely understood

42

There is necessity to define the best(s) shape descriptor(s) to be used for particular

geotechnical properties

63 IMAGE ANALYSIS

Many image analysis techniques had been used to describe the particle shape eg

Fourier analysis fractal dimension tomography etc (Hyslip and Vallejo 1997) but

there is not agreement on the usage or conclusion to ensure the best particle descriptor

for geotechnical applications

There are several shape descriptors and also various techniques to capture the

particles profile (3-dimensions 3-dimension orthogonal and 2-dimensions) Each

technique presents advantages and disadvantages 3-dimensions is probably the

technique that provide more information about the particle shape but the precision

also lies in the resolution the equipment required to perform such capture could be

more or less sophisticated (scanning particles laying down in one position and later

move to complete the scanning or just falling down particles to scan it in one step)

3-dimensions orthogonal this technique use less sophisticated equipment (compare

with the previous technique) but its use is limited to particles over 1cm also

information between the orthogonal pictures is not capture 2-dimensions require non

sophisticated equipment but at the same time the shape information diminish compare

with the previous due the fact that it is possible to determine only the outline as the

particle measurements are performed in 2-dimensions it is presumed that they will lie

with its shortest axis perpendicular to the laying surface when they are flat but when

the particle tends to have more or less similar axis the laying could be random

Advantages on the use of image analysis are clear there is not subjectivity because it

is possible to obtain same result over the same images Electronic files do not loose

resolution and it is important when collaboration among distant work places is done

files can be send with the entire confidence and knowing that file properties has not

been changed Technology evolutions allowed to work with more information and it

also applies to the image processing area were the time consumed has been shortened

(more images processed in less time)

One important aspect in image analysis is the used resolution in the analysis due the

fact that there are measurements dependent and independent on resolution Thus

those dependent measurements should be avoided due the error included when they

are applied or avoid low resolution to increase the reliability Among these

parameters length is the principal parameter that is influences by resolution (eg

perimeter diameter axis etc) Resolution also has another aspect with two faces

quality versus capacity more resolution (quality) means more storage space a

minimum resolution to obtain reasonable and reliable data must be known but it

depend on each particular application

43

64 APPLICATIONS

Quantify changes in particles in the authorrsquos thought is one of the future applications

due the non-invasive methods of taking photographs in the surface of the damrsquos slope

rail road ballast or roads Sampling of the material and comparing with previous

results could show volume (3D analysis) or area (2D analysis) loss of the particles as

well as the form roundness and roughness This is important when it has been

suggested that a soil or rock embankment decrees their stability properties (eg

internal friction angle) with the loss of sphericity roundness or roughness

Seepage stock piling groundwater etc should try to include the particle shape while

modelling seepage requires grading material to not allow particles move due the

water pressure but in angular materials as it is known the void ratio is great than the

rounded soil it means the space and the possibilities for the small particles to move

are greater stock piling could be modelled incorporating the particle shape to

determine the binrsquos capacity when particle shape changes (void ratio changes when

particle shape changes) Modelling requires all information available and the

understanding of the principles that apply

Industry is actually using the particle shape to understand the soil behaviour and

transform processes into practical and economic image analysis has been included in

the quality control to determine particle shape and size because the advantages it

brings eg the acquisition of the sieving curve for pellets using digital images taken

from conveyor this allows to have the information in a short period of time with a

similar result at least enough from the practical point of view as the traditional

sieving

7 CONCLUSIONS

The conclusions of this literature review are

It has been shown that particle shape has influence on the soil behaviour

despite of partial knowledge of the mechanism behind Understanding of the

particle shape and its influence needs to be accomplished

A common language needs to be built up to standardize the meaning on

geotechnical field that involve the particle shape General relationships

between shape and properties should be developed

Based on this review it is not clear which is the best descriptor to use in

geotechnical engineering affecting he related shape to properties Instead of a

couple of standards there is no shape descriptor in geotechnical field fully

accepted

Image analysis tool is objective make the results repeatable obtain fast results

and work with more amount of information

44

Resolution needs to be taken in consideration when image analysis is been

carried out because the effects could be considerable Resolution must be set

according to the necessities Parameters as perimeter can be affected by

resolution

There are examples where particle shape has been incorporated in industries

related to geotechnical engineering eg in the ballast and asphalt industry for

quality control

8 FURTHER WORK

Three main issues have been identified in this review that will be further investigated

the limits of shape descriptors influence of grading and choice of descriptor for

relation to geotechnical properties

Shape descriptors have low and high limits frequently the limits are not the same and

the ability to describe the particlersquos shape is relative The sensitivity of each descriptor

should be compare to apply the most suitable descriptor in each situation

Sieving curve determine the particle size in a granular soil particle shape could differ

in each sieve size There is the necessity to describe the particle shape on each sieve

portion (due to practical issues) and included in the sieve curve Obtain an average

shape in determined sieve size is complicated (due to the possible presence of several

shapes) and to obtain the particle shape on the overall particlersquos size is challenging

how the particle shape should be included

Since several descriptors have been used to determine the shape of the particles and

the relation with the soil properties it is convenient to determine the descriptorrsquos

correlation with the soil properties

9 ACKNOWLEDGMENT

I would like to thanks to Lulearing University of Technology (LTU) the time I had spent

in its facilities and the kind environment it offers and University of Sonora

(UNISON) that has been providing me the financial support and the time to conclude

this journey

10 REFERENCES

Andersson T (2010) Estimating particle size distributions based on machine vision

Doctoral Thesis Departament of Computer Science and Electrical Engineering Lulearing

University of Technology ISSN 1402-1544 ISBN 978-91-7439-186-2

45

Arasan Seracettin Hasiloglu A Samet Akbulut Suat (2010) Shape particle of

natural and crished aggregate using image analysis International Journal of Civil and

Structural Engineering Vol 1 No 2 pp 221-233 ISSN 0970-4399

Aschenbrenner BC (1956) A new method of expressing particle sphericity Journal

of Sedimentary Petrology Vol 26 No 1 pp 15-31

Axelsson K (1998) Introduktion till jordmekaniken jaumlmte jordmateriallaumlran Skrift

984 Lulearing Avdelningen foumlr Geoteknologi Lulearing Tekniska Universitet (In Swedish)

Barton Nick amp Kjaernsli Bjorn (1981) Shear strength of rockfill Journal of the

Geotechnical Engineering Division Proceedings of the American Society of Civil

Engineers (ASCE) Vol 107 No GT7

Barrett P J (1980) The shape of rock particles a critical review Sedimentology

Vol 27 pp 291-303

Blott S J and Pye K (2008) Particle shape a review and new methods of

characterization and classification Sedimentology Vol 55 pp 31-63

Bowman E T Soga K and Drummond W (2001) Particle shape characterization

using Fourier descriptor analysis Geotechnique Vol 51 No 6 pp 545-554

Briggs L I McCulloch D S (1962) Hydraulic shape of sand particles Journal of

Sedimentary Petrology Vol 32 pp 645-656

Chan Leonard C Y and Page Neil W (1997) Particle fractal and load effects on

internal friction in powders Powder Technology Vol 90 pp 259-266

Cheshomi A Fakher A Jones C J F P (2009) A correlation between friction

angle and particle shape metrics in quaternary coarse alluvia Quarterly Journal of

Engineering Geology and Hydrogeology Vol 42 pp 145-155

Cho G Dodds J and Santamarina J C (2006) Particle shape effects on packing

density stiffness and strength Natural and crushed sands Journal of Geotechnical

and Geoenvironmental Engineering May 2006 pp 591-602

Dietrich William E (1982) Settling velocity of natural particles Water Resources

Research Vol 18 No 6 pp 1615-1626

Dobkins J E and Folk R L (1970) Shape development on Tahiti-nui Journal of

Sedimentary Petrology Vol 40 No 2 pp 1167-1203

Folk R L (1955) Student operator error in determining of roundness sphericity and

grain size Journal of Sedimentary Petrology Vol 25 pp 297-301

Fernlund J M R (1998) The effect of particle form on sieve analysis A test by

image analysis Engineering Geology Vol 50 No 1-2 pp 111-124

46

Fernlund J M R (2005) Image analysis method for determining 3-D shape of

coarse aggregate Cement and Concrete Research Vol 35 Issue 8 pp 1629-1637

Fernlund J M R Zimmerman Robert and Kragic Danica (2007) Influence of

volumemass on grain-size curves and conversion of image-analysis size to sieve size

Engineering Geology Vol 90 No 3-4 pp 124-137

Fraser H J (1935) Experimental study of the porosity and permeability of clastic

sediments The Journal of Geology Vol 43 pp 910-1010 ISSN 0022-1376

Hayati Ali Nemati Ahmadi Mohammad Mehdi and Mohammadi Soheil (2012)

American Physical Society Physical review E 85 036310 DOI

101103PhysRevE85036310

Hawkins A E (1993) The Shape of Powder-Particle Outlines Wiley New York

Head K H and Epps R J (2011) Manual of soil Laboratory testing Volum II

Permeability shear strength and compressibility test 3rd

edition Whittles Publishing

Scotland UK 3rd

edition

Holubec I and DrsquoAppolonia E (1973) Effect of particle shape on the engineering

properties of granular soils ASTM STP 523 pp 304-318

Hyslip James P Vallejo Luis E (1997) Fractal analysis of the roughness and size

distribution of granular materials Engineering Geology Vol 48 pp 231-244

Janoo Vincent C (1998) Quantification of shape angularity and surface texture of

base course materials US Army Corps of Engineers Cold Region Research and

Engineering Laboratory Special report 98-1

Jefferies Mike and Been Ken (2000) Soil liquefaction A critical state approach

Taylor amp Francis Group London and New York

Jimenez Jose A Madsen Ole S (2003) A simple formula to estimate settling

velocity of natural sediments Journal of Waterway Port Coastal and Ocean

Engineering Vol 129 No 2 pp 70-78

Johansson Jens and Vall Jakob (2011) Jordmaterials kornform Inverkan paring

Geotekniska Egenskaper Beskrivande storheter bestaumlmningsmetoder

Examensarbete Avdelningen foumlr Geoteknologi Institutionen foumlr Samhaumlllsbyggnad

och naturresurser Lulearing Tekniska Universitet Lulearing (In Swedish)

Kane Joseph W and Sternheim Morton M (1988) Physics John Wiley amp Sons Inc

Third edition

Kolbuszewski J (1948) An experimental study of the maximum and minimum

porosities of sands Proceedings of the Second International Conference on Soil

Mechanics and Foundation Engineering Rotterdam June 21 to 30 Sub-section IIb

pp 158-165

47

Krumbein W C and Pettijohn FJ (1938) Manual of sedimentary petrography

Appleton-Century Crofts Inc New York

Krumbein W C (1941) Measurement and geological significance of shape and

roundness of sedimentary particles Journal of Sedimentary Petrology Vol 11 No 2

pp 64-72

Krumbein W C and Sloss L L (1963) Stratigraphy and Sedimentation 2nd

ed

WH Freeman San Francisco

Kuo Chun-Yi and Freeman Reed B (1998a) Image analysis evaluation of

aggregates for asphalt concrete mixtures Transportation Research Record Vol 1615

pp 65-71

Kuo Chun-Yi Rollings Raymond and Lynch Larry N (1998b) Morphological

study of coarse aggregates using image analysis Journal of Materials in Civil

Engineering Vol 10 No 3 pp 135-142

Lanaro F Tolppanen P (2002) 3D characterization of coarse aggregates

Engineering Geology Vol 65 pp 17-30

Lees G (1964a) A new method for determining the angularity of particles

Sedimentology Vol 3 pp 2-21

Lees G (1964b) The measurement of particle shape and its influence in engineering

materials British Granite Whinstone Federation Vol 4 No 2 pp 17-38

Matsushima Takashi Saomoto Hidetaka Matsumoto Masaaki Toda Kengo

Yamada Yasuo (2003) Discrete element simulation of an assembly of irregular-

shaped grains Quantitative comparison with experiments 16th ASCE Engineering

Mechanics Conference University of Washington Seattle July 16-18

Mitchell James K and Soga Kenichi (2005) Fundamentals of soil behaviour Third

edition WILEY

Mora C F Kwan A K H Chan H C (1998) Particle size distribution analysis of

coarse aggregate using digital image processing Cement and Concrete Research Vol

28 pp 921-932

Mora C F and Kwan A K H (2000) Sphericity shape factor and convexity

measurement of coarse aggregate for concrete using digital image processing Cement

and Concrete Research Vol 30 No 3 pp 351-358

Muskat Morris (1937) The Flow of fluids through porous media Journal of Applied

Physics Vol 8 pp 274

Nearing M A and Parker S C (1994) Detachment of soil by flowing water under

turbulent and laminar conditions Soil Science Society of American Journal Vol 58

No 6 pp 1612-1614

48

Pan Tongyan Tutumluer Erol Carpenter Samuel H (2006) Effect of coarse

aggregate morphology on permanent deformation behavior of hot mix asphalt Journal

of Transportation Engineering Vol 132 No 7 pp 580-589

Pellegrino A (1965) Geotechnical properties of coarse-grained soils Proceedings

International Conference of Soil Mechanics and Foundation Engineering Vol 1 pp

97-91

Pentland A (1927) A method of measuring the angularity of sands MAG MN AL

Acta Eng Dom Transaction of the Royal Society of Canada Vol 21 Ser3xciii

Persson Anna-Lena (1998) Image analysis of shape and size of fine aggregates

Engineering Geology Vol 50 pp 177-186

Powers M C (1953) A new roundness scale for sedimentary particles Journal of

Sedimentary Petrology Vol 23 No 2 pp 117-119

Pye W and Pye M (1943) Sphericity determination of pebbles and grains Journal

of Sedimentary Petrology Vol 13 No 1 pp 28-34

Qazi M A (1975) Flow properties of granular masses A review on the angle of

repose The Arabian Journal for Science and Engineering Vol 1 No 2

Quiroga Pedro Nel and Fowle David W (2003) The effects of aggregate

characteristics on the performance of portland cement concrete Report ICAR 104-1F

Project number 104 International Center for Aggregates Research University of

Texas

Riley N A (1941) Projection sphericity Journal of Sedimentary Petrology Vol 11

No 2 pp 94-97

Rouseacute P C Fennin R J and Shuttle D A (2008) Influence of roundness on the

void ratio and strength of uniform sand Geotechnique Vol 58 No 3 227-231

Santamarina J C and Cho G C (2004) Soil behaviour The role of particle shape

Proceedings Skempton Conf London

Schofield and Wroth (1968) Critical state soil mechanics McGraw Hill

Shaumlfer Michael (2002) Digital optics Some remarks on the accuracy of particle

image analysis Particle amp Particle Systems Characterization Vol 19 No 3 pp 158-

168

Shergold F A (1953) The percentage of voids in compacted gravel as a measure of

its angularity Magazine of Concrete Research Vol 5 No 13 pp 3-10

Shinohara Kunio Oida Mikihiro Golman Boris (2000) Effect of particle shape on

angle of internal friction by triaxial compression test Powder Technology Vol 107

pp131-136

49

Skredcommisionen (1995) Ingenjoumlrsvetenskapsakademinen rapport 395 Linkoumlping

1995

Sneed E D and Folk R L (1958) Pebbles in the Colorado river Texas A study in

particle morphogenesis Journal of Geology Vol 66 pp 114-150

Sperry James M and Peirce J Jeffrey (1995) A model for estimating the hydraulic

conductivity of granular material based on grain shape grain size and porosity

Ground Water Vol 33 No 6 pp 892-898

Sukumaran B and Ashmawy A K (2001) Quantitative characterisation of the

geometry of discrete particles Geotechnique Vol 51 No 7 pp 619-627

Szaacutedeczy-Kardoss E Von (1933) Die bistimmung der abrollungsgrades Geologie

und palaumlontologie Vol 34B pp 389-401 (in German)

Teller J T (1976) Equantcy versus sphericity Sedimentology Vol 23 pp 427-428

Tickell F G (1938) Effect of the angularity of grain on porosity and permeability

bulletin of the American Association of Petroleum Geologist Vol 22 pp 1272-1274

Tutumluer E Huang H Hashash Y Ghaboussi J (2006) Aggregate shape effects

on ballast tamping and railroad track lateral stability AREMA 2006 Annual

Conference Louisville KY

Wadell H (1932) ldquoVolume Shape and roundness of rock particlesrdquo Journal of

Geology Vol 40 pp 443-451

Wadell H (1933) Sphericity and roundness of rock Particles Journal of Geology

Vol 41 No 3 pp 310ndash331

Wadell H (1934) Shape determination of large sedimental rock fragments

The Pan-American Geologist Vol 61 pp 187-220

Wadell H (1935) ldquoVolume shape and roundness of quartz particlesrdquo Journal of

Geology Vol 43 pp 250-279

Wentworth W C (1922a) The shape of beach pebbles Washington US Geological

Survey Bulletin Vol 131C pp 75-83

Wentworth W C (1922b) A method of measuring and plotting the shape of pebbles

Washington US Geological Survey Bulletin Vol 730C pp 91-114

Wentworth W C (1933) The shape of rock particle A discussion Journal of

Geology Vol 41 pp 306-309

Witt K J Brauns J (1983) Permeability-Anisotropy due to particle shape Journal

of Geotechnical Engineering Vol 109 No 9 pp 1181-1187

iv

ABBREVIATIONS Symbol Description Units

A Area of the projected particle area of the particle outline (2D) m2

A1 Area of the projected particle after ldquonrdquo dilatation-erosion cycles m2

AC Area of the smallest circumscribed circle m2

AC2 Area of circle with diameter equal to longest length of outline m2

ACON Convex area m2

AF Sukumara angularity factor -

ANGCON Angles subtending convex parts of the outline degree (ordm)

ANGPLA Angles subtending plane parts of the outline degree (ordm)

a Longest axes diameters of the particle m

B Greatest breadth perpendicular to L m

b Medium axes diameters of the particle m

C Circularity -

CR Convexity ratio -

c Shorter axes diameters of the particle m

Co Cohesion Pa

CPER Convex perimeter m

DA Diameter of a circle equal on area to that of the particle outline m

DAVG Mean average diameter m

DC Diameter of the smallest circumscribed circle in the particle outline m

DCIR Diameter of circumscribed sphere m

DI Diameter of the largest inscribed circle m

DS Diameter of circle fitting sharpest corner (two sharper corners DS1 DS2) m

DSV Diameter of a sphere of the same volume as particle m

DX Diameter of a pebble particle through the sharpest corner DS m

d Grain diameter (average) m

dN Nominal diameter diameter of a sphere of the same volume as the natural

particle

m

e Void ratio

F Angularity factor -

FR Fullness ratio -

g Gravitational acceleration ms2

I Intermediate axis m

k Hydraulic conductivity ms

L Longest axis of the outline m

N Number of corners (items counted) or number of divisions -

n Porosity -

P Perimeter of the projected particle perimeter of outline (2D) m

PC Perimeter of a circle of same area as particle outline m

PCON Sum of perimeter of all convex parts m

PCD Perimeter of circle of same area as drainage basin m

PD Perimeter of a drainage basin m

PI Particle index -

R Roundness -

RAVG Mean average radio of the pebble m

RCON Radius of curvature of the most convex part m

Re Reynolds number -

Rmax-in Radius of the maximum inscribed circle m

Rmin-cir Radius of the minimum circumscribed circle m

RO Roughness or surface texture -

Re Equivalent roughness of particle -

R1 Equation for predicting the settling velocity of sphere -

R3 Equation for predicting the ratio of the settling velocity of an angular

particle to that of a well-rounded particle

-

ri Radius of curvature of the corner ldquoirdquo m

S Actual surface area of the particle m2

v

Symbol Description Units

Se Equivalent strength of particle -

Ss Specific surface area -

SF Sukumara shape factor -

Sm Short axis ldquocrdquo in minimum projection plane m

s Surface area of a sphere of the same volume as the particle m2

sD Specific gravity of the sediment given by the relation density of

sedimentfluid

-

R2 Equation for predicting the ratio of the settling velocity of a non-spherical

well-rounded particle to be settling velocity of a sphere with the same

dimensionless nominal diameter

-

S Dimensionless fluid-sediment parameter -

V Total volume of soil m3

VCIR Volume of circumscribed sphere m3

Ve Velocity ms

VP Volume of particle m3

Vs Volume of voids m3

Vv Volume of solid m3

V10 voids in the aggregate compacted with 10 blows per layer -

V50 voids in the aggregate compacted with 50 blows per layer -

W Weight of the particle ton

WS Settling velocity ms

W Dimensionless settling velocity -

Y Constant to obtain by fitting to experimental data for certain ranges of S -

Z Constant to obtain by fitting to experimental data for certain ranges of S -

x Distance of the tip of the corner from the center of the maximum inscribed

circle

mm

α Measured angle degree (ordm)

αi Sakamura angles used to describe shape degree (ordm)

βi Sakamura angles used to describe angularity degree (ordm)

Σ Summation -

Ψ Sphericity -

ν Kinematics viscosity m2s

φb Basic friction angle degree (ordm)

φcs Friction angle critical state degree (ordm)

φmc Friction angle maximum contraction degree (ordm)

φrep Angle of repose degree (ordm)

φ Peak friction angle Pa

τ Shear strength Pa

σc Compressive strength Pa

σn Normal stress Pa Angle of internal friction degree (ordm)

μ Viscosity Pamiddots

μF Friction coefficient -

p Pressure drop -

ρ Density of water tonm3

ρp Density of the particle tonm3

υ Specific discharge ms

1

1 INTRODUCTION

Effects on soil behaviour from the constituent grain shape has been suggested since

the earliest 1900rsquos when Wadell (1932) Riley (1941) Pentland (1927) and some

other authors developed their own techniques to define the form and roundness of

particles Into the engineering field several research works conclude that particle

shape influence technical properties of soil material and unbound aggregates

(Santamarina and Cho 2004 Mora and Kwan 2000) Among documented properties

affected by the particle shape are eg void ratio (porosity) internal friction angle and

hydraulic conductivity (permeability) (Rouseacute et al 2008 Shinohara et al 2000

Witt and Brauns 1983) In geotechnical guidelines particle shape is incorporated in

eg soil classification (Eurocode 7) and in national guidelines eg for evaluation of

friction angle (Skredkommisionen 1995) This classification is based on ocular

inspection and quantitative judgement made by the individual practicing engineer

thus it can result in not repeatable data In evaluation of eg standard penetration test

Holubec and DrsquoAppolonia (1973) are suggesting the inclusion of the particle shape in

the evaluation of the data According with Folk (1955) the form error is negligible but

it is not in the second sub-quantity related with the corners (roundness) These

systems are not coherent in definitions The lack of possibility to objectively describe

the shape hinders the development of incorporating the effect of particle shape in

geotechnical analysis

The interest of particle shape was raised earlier in the field of geology compared to

geotechnical engineering Particle shape is considered to be the result of different

agentrsquos transport of the rock from its original place to deposits since the final pebble

form is hardly influenced by these agents (rigor of the transport exfoliation by

temperature changes moisture changes etc) in the diverse stages of their history

Furthermore there are considerations regarding on the particle genesis itself (rock

structure mineralogy hardness etc) (Wentworth 1922a) The combination of

transport and mineralogy factors complicates any attempt to correlate length of

transport and roundness due that soft rock result in rounded edges more rapidly than

hard rock if both are transported equal distances According to Barton amp Kjaernsli

(1981) rockfill materials could be classified based on origin into the following (1)

quarried rock (2) talus (3) moraine (4) glacifluvial deposits and (5) fluvial deposits

Each of these sources produces a characteristic roundness and surface texture

Pellegrino (1965) conclude that origin of the rock have strong influence determining

the shape

To define the particle form (morphology) in order to classify and compare grains

many measures has been taken in consideration (axis lengths perimeter surface area

volume etc) Probably when authors had developed the form descriptors realize that

they hadnrsquot provide enough information about the corners they could be angular or

rounded (roundness) thus the authors also focus on develop techniques to describe

them Furthermore the corners or the general surface can be rough or smooth (surface

texture) Nowadays some authors (Mitchell amp Soga 2005 Arasan et al 2010) are

using these three sub-quantities one and each describing the shape but a different

scale (form roundness surface texture)

2

During the historical development of shape descriptors the terminology has been used

differently among the published studies terms as roundness (because the roundness

could be apply in the different scales) or sphericity (how the particle approach to the

shape of a sphere) were strong (Wadell 1933 Wenworth 1933 Teller 1976 Barrett

1980 Hawkins 1993) and it was necessary in order to define a common language on

the particle shape field unfortunately still today there is not agreement on the use of

this terminology and sometimes it make difficult to understand the meaning of the

authors thatrsquos why it is better to comprehend the author technique in order to

misinterpret any word implication

Several attempts to introduce methodology to measure the particlersquos shape had been

developed over the years Manual measurement of the particles form is

overwhelming thus visual charts were developed early to diminish the measuring

time (Krumbein 1941 Krumbein and Sloss 1963 Ashenbrenner 1956 Pye and Pye

1943) Sieving was introduced to determine the flakinesselongation index but it is

confined only for a certain particle size due the practical considerations (Persson

1988) More recently image analysis on computer base has been applied on sieving

research (Andersson 2010 Mora and Kwan 2000 Persson 1998) bringing to the

industry new practical methods to determine the particle size with good results

(Andersson 2010) Particle shape with computer assisted methods are of great help

reducing dramatically the measuring time (Fernlund 2005 Kuo and Freeman 1998a

Kuo et al 1998b Bowman et al 2001)

In the civil industry eg Hot Asphalt mixtures (Kuo and Freeman 1998a Pan et al

2006) Concrete (Mora et al 1998 Quiroga and Fowle 2003) and Ballast

(Tutumluer et al 2006) particlersquos shape is of interest due the materialrsquos performance

thus standards had been developed (see appendix A) On asphalt mixtures limits of

flat and elongated particles or the amount of natural sands typically are incorporated

into specifications flat and elongated particles tend to cause problems with

compaction particle breakage loss of strength and segregation in pavement (Kuo and

Freeman 1998a) Rutting resistance of asphalt concrete under traffic and

environmental loads depend on the stability of aggregates structure in the asphalt mix

(Pan et al 2006) According with the American Railway Engineering and

Maintenance of Way Association (AREMA) ballast aggregate should be open graded

with hard angular shaped particles providing sharp corners and cubical fragments

with a minimum of flat and elongated pieces (Tutumluer et al 2006) The American

standard ASTM D 3398 (test method for index of aggregate particle shape and

texture) is an example of an indirect method to determine particle shape (see appendix

A) Aggregate characteristics of shape texture and grading influence workability

finishability bleeding pumpability and segregation of fresh concrete and affect

strength stiffness shrinkage creep density permeability and durability of hardened

concrete In fact flaky elongated angular and unfavorably graded particles lead to

higher voids content than cubical rounded and well-graded particles (Quiroga and

Fowle 2003)

Sieving is probably the most used method to determine the particle size distribution it

consist of plotting the cumulative weight of the weighted material retained by each

mesh (European standard EN 933-1 1992) This traditional method according to

Andersson (2010) is time consuming and expensive Investigations shows that the

traditional sieving has deviations when particle shape is involve the average volume

3

of the particles retained on any sieve varies considerably with the shape (Lees

1964b) thus the passing of the particles depend upon the shape of the particles

(Fernlund 1998) In some industries the Image analysis is taking advantage over the

traditional sieving technique regardless of the intrinsic error on image analysis due the

overlapping or partial hiding of the rock particles (Andersson 2010) In this case the

weight factor is substitute by pixels (Fernlund et al 2007) Sieving curve using

image analysis is not standardized but after good results in the practice (Andersson

2010) new methodology and soil descriptions could raise including its effects

2 AIM AND GOAL

The aim of this report is to review the state of the art on how to describe particle

shape of individual grains of geotechnical material and knowledge on the influence of

shape in geotechnical properties

The goals in this study are to

Describe discuss and compare particle shape and definitions

Review the known effect of particle shape on soil mechanics parameters

Discuss the potential of the role of particle shape in soil mechanics

Focus in this study has been on 2 dimensional shape definitions

The content of the report is based upon published and peer reviewed papers in

English

3 DESCRIPTION OF SHAPE PROPERTIES

31 INTRODUCCTION

Particle shape description can be classified as qualitative or quantitative Qualitative

describe in terms of words the shape of the particle (eg elongated spherical flaky

etc) and quantitative that relates the measured dimensions in the engineering field

the quantitative description of the particle is more important due the reproducibility

Quantitative geometrical measures on particles may be used as basis for qualitative

classification There are few qualitative measures in contrast with several quantitative

measures to describe the particle form Despite the amount of qualitative descriptions

none of them had been widely accepted but there are some standards (eg ASTM

D5821 EN 933-3 and BS 812) specifying mathematical definitions for industrial

purposes

Shape description of particles is also divided in

o 3D (3 dimensions) it could be obtained from a 3D scan or in a two

orthogonal images and

o 2D (2 dimensions) or particle projection where the particle outline is drawn

4

3D and 2D image analysis present challenges itself 3D analysis requires a

sophisticated equipment to scan the particle surface and create the 3D model or the

use of orthogonal images and combine them to represent the 3 dimensions The

orthogonal method could present new challenges as the minimum particle size or the

placing in orthogonal way of the particles (Fernlund 2005) 2D image analysis is easy

to perform due the non-sophisticated equipment required to take pictures (eg regular

camera or the use of microscope for smaller particles) In 2D image analysis the

particle is assumed to lay over its more stable axis (eg longest and intermediate axis

lie more or less parallel to the surface while the shortest axis is perpendicular) or

random some authors publish their own preferences about this issue (Wadell 1935

Riley 1941 Hawkins 1993)

32 SCALE DEPENDENCE

In order to describe the particle shape in detail there are a number of terms quantities

and definitions used in the literature Some authors (Mitchell amp Soga 2005 Arasan et

al 2010) are using three sub-quantities one and each describing the shape but at

different scales The terms are morphologyform roundness and surface texture In

figure 1 is shown how the scale terms are defined

At large scale the particlersquos diameters in different directions are considered At this

scale describing terms as spherical platy elongated etc are used An often seen

quantity for shape description at large scale is sphericity (antonym elongation)

Graphically the considered type of shape is marked with the dashed line in Figure 1

At intermediate scale it is focused on description of the presence of irregularities

Depending on at what scale an analysis is done corners and edges of different sizes

are identified By doing analysis inside circles defined along the particlersquos boundary

deviations are found and valuated The mentioned circles are shown in Figure 1 A

generally accepted quantity for this scale is roundness (antonym angularity)

Regarding the smallest scale terms like rough or smooth are used The descriptor is

considering the same kind of analysis as the one described above but is applied

Figure 1 Shape describing sub quantities (Mitchell amp Soga 2005)

5

within smaller circles ie at a smaller scale Surface texture is often used to name the

actual quantity The sub-quantities and antonyms are summarized in table 1

Table 1 Sub-quantities describing the particlersquos morphology and its antonym

Scale Quantity Antonym

Large scale Sphericity Elongation

Intermediate scale Roundness Angularity

Small scale Roughness Smoothness

33 FORM (3D)

Wentworth in 1922 (Blott and Pye 2008) was probably one of the first authors on

measure the particle dimensions this consisted on the obtaining of the length of the

tree axes perpendicular among each other (see figure 2) on the tree dimensions (where

agebgec) to obtain the sphericity (equation 1)

Krumbein (1941) develop a rapid method for shape measurement to determine the

sphericity this is done by measuring the longest (a) medium (b) and shorter (c) axes

diameters of the particle it can be seen in figure 2 (Always perpendicular among each

other) The radios ba and cb are located in the chart developed by his own where it

can be found the Intercept sphericity as he called (See figure 3) This chart is an easy

graphical way to relate the dimensions

c2

ba

Figure 2 Measurement of the 3 axes perpendicular among each other (Krumbein 1941)

Figure 3 Detailed chart to determining Krumbein intercept sphericity (Krumbein 1941)

(1)

6

Wadell (1932) defined the sphericity as the specific surface ratio (equation 2) Figure

4 is a schematic representation of the sphere surface and particle surface both particle

and sphere of the same volume

This way to obtain the sphericity is almost impossible to achieve as Hawkins (1993)

declares due the difficulty to get the surface area on irregular solids

Wadell (1934) also defined the sphericity based upon the particle and sphere volumes

as equation 3 (see figure 5)

Wadell (1934) used a new formula simple to manage using the diameters (see figure

6 and equation 4)

Zingg (Krumbein 1941) develop a classification based on the 3 axes relation in this

way it is easy to find out the main form of the particles as a disks spherical blades

S

s

3

CIR

P

V

V

CIR

SV

D

D

Figure 4 Same volume sphere surface (s) and particle surface (S) (modified after Johansson and Vall

2011)

Figure 5 Relation between the volume of the particle and the volume of the circumscribed

sphere (Johansson and Vall 2011)

Figure 6 Figure is showing the relation between the diameter of a circumscribed sphere and the

diameter of a sphere of the same volume as the particle (Johansson and Vall 2011)

(2)

(3)

(4)

7

and rod-like this is summarized on figure 7 Zinggrsquos classification is related with

Krumbein intercept sphericity and the figure 3

In figure 8 the figures 3 and 7 are combined the relation in the two classifications can

be seen it is an easy way to understand the morphology regarding on the a b and c

dimensions

Pye and Pye (1943) in the article ldquosphericity determinations of pebbles and sand

grainsrdquo compare the Wadellrsquos sphericity developed in 1934 (based on the diameter)

with ldquoPebble sphericityrdquo based on an ellipse this last equation (number 5) appears

two years early published by Krumbein (1941) Axis measurement is done as figure 1

denotes for equations 5 trough 12 with exception of equation 8 where the original

document was not possible to obtain

32a

cb

Figure 7 Zinggrsquos classification of pebble shape based on ratios ba and cb (Krumbein 1941)

Figure 8 Classification made by Zinggrsquos and chart to determine sphericity (Krumbein and Sloss 1963)

(5)

8

Sneed amp Folk in (1958) found a relation between the tree dimensional axes called

ldquoMaximum Projection Sphericityrdquo

In a similar way Ashenbrenner (1956) showed his equation at that time named

ldquoWorking Sphericityrdquo

Form or shape factor names are used by authors like Corey (shape factor eq 8) in the

paper published on 1949 Williams (shape factor eq 9) in 1965 Janke (form factor

eq 10) in 1966 and Dobkins amp Folk (oblate-prolate index eq 11) in 1970 (Blott and

Pye 2008)

Aschenbrenner (1956) develop the shape factor by using the relation of the tree axis

but the square of the middle one

3

2

ba

c

))ab((1)bc(16))ab((cb)(11

)ab()bc( 128

22

3 2

ab

c

acb when 1ac

b acb when

b

ac-1 2

22

2

3

cba

c

222

a

c

50c-a

b-a10

2b

ac

(6)

(7)

(8)

(9)

(10)

(11)

(12)

9

Table 2 General overview over different particle shape definitions for 3D sphericity has been compiled

and arranged chronologically

Aspect Name Author Year Based on

Sphericity (3D) Flatness index Wentworth 1922a 3-axes

True Sphericity Wadell 1932 Surface

Operational sphericity Wadell 1932 Volume

Sphericity Wadell 1934 Sphere diameter

Zinggrsquos clasification Zinggrsquos1

1935 3-axes

Intercept sphericity chart Krumbein 1941 3-axes

Pebble sphericity Pye and Pye 1943 3-axes

Corey shape factor Corey2

1949 3-axes

Working sphericity Ashenbrenner 1956 3-axes

shape factor Ashenbrenner 1956 3-axes

Maximum projection sphericity Sneed amp Folk 1958 3-axes

Williams shape factor Williams2

1965 3-axes

Janke form factor Janke2

1966 3-axes

Oblate-prolate index Dobkins amp Folk 1970 3-axes 1) Krumbein and Sloss 1963 2) Blott and Pye 2008

34 FORM (2D)

The technique to measure the sphericity is based in tree dimensions it can be found in

literature some ways to measure the ldquotwo dimensions sphericityrdquo which is simply the

perimeter of the particle projection some authors named ldquoparticle outlinerdquo or

ldquocircularityrdquo

Wadell in 1935 (Hawkins 1993) adopt a conversion of his 1934 3D sphericity

formula (equation 4) to a 2D outline He defined an orientation on the particles and

they were based on the maximum cross sectional area (outline of the particle

projecting the maximum area) The equations show the relation between diameters of

a circle of same area and smallest circumscribed circle

He also used the term ldquodegree of circularityrdquo as the ratio of the perimeter of a circle of

same area and the actual particle perimeter

Tickell in 1931 (Hawkins 1993) used his empirical relation The particle orientation

proposed was a random one It is described by the ratio between the area outline and

the area of smallest circumscribed circle

C

A

D

DC

P

PC C

CA

AC

(13)

(14)

(15)

10

Some other authors has been working with the ldquocircularityrdquo concept and had develop

them own equations as Pentland (1927) relating the area outline and area of a circle

with diameter equal to longest length outline and Cox (Riley 1941) with the ratio

area and perimeter time a constant equations 16 and 17 respectively Both authors did

not define any definite orientation of the grains

Riley (1941) realize the problems that an area perimeter and some other

measurements proposed by the above authors can carry as the time consuming and

tedious work (at that time were not computer all was made by hand) and thatrsquos why

he develop this equation easy to handle called ldquoinscribed circle sphericityrdquo He used

the same particle orientation proposed by Wadell and the relation of diameters of

inscribed and circumscribed circles

Horton 1932 (Hawkins 1993) use the relation of the drainage basing perimeter and

the perimeter of a circle of the same area as drainage basin

Janoo in 1998 (Blott and Pye 2008) develop his general ratio of perimeter to area

Sukumaran and Ashmawy (2001) develop his own shape factor (SF) defined as the

deviation of the global particle outline from a circle Figure 9 can be used as a

reference to determine the items used in the equation 21

N is referred to the number of sampling intervals o radial divisions

C2A

AC

2P

A4C

C

I

D

DC

CD

D

P

PC

A

PC

2

45ordm x N

Particleα

= SF

sumN

1=ii

(16)

(17)

(18)

(19)

(20)

(21)

11

Table 3 General chronological overview of the particle shape definitions for 2D sphericity

Aspect Name Author Year Based on

Circularity (2D) roundness Pentland 1927 area

roundness Cox1

1927 area-perimeter

roundness Tickell2

1931 area

Circularity Horton2

1932 drainage basin

outline circularity Wadell 1935 Circle diameter

degree of circularity Wadell 1935 Perimeter

inscribed circle sphericity Riley 1941 Circle diameter

Circularity Krumbein and Sloss 1963 chart

Janoo 1998 area-perimeter

Shape factor Sukumaran 2001 Segmentation of particle and angles

1) Riley 1941 2) Hawkins 1993

35 ROUNDNESS OR ANGULARITY

Roundness as described in section 32 is the second order shape descriptor Sphericity

lefts beside the corners and how they are this was notice by most of the authors sited

before and they suggested many ways to describe this second order particle property

Roundness is clearly understandable using the figure 10 Particle shape or form is the

overall configuration and denotes the similarities with a sphere (3D) or a circle (2D)

Roundness is concerning about the sharpness or the smoothness of the perimeter (2D)

Surface texture (Barret 1980) is describe as the third order subject (form is the first

and roundness the second) and it is superimposed in the corners and it is also a

property of particles surfaces between corners

Figure 9 Description of the Sukumaran factors to determine the shape and angularity (Sukumaran and

Ashmawy 2001)

12

Wadell (1935) describes his methodology calling it total degree or roundness to

obtain the roundness of a particle using the average radius of the corners in relation

with the inscribed circle diameter (see figure 11) on the equation

In the same study Wadell (1935) has used the equation

This two last equation shows slightly differences on the results (Wadell 1935)

Powers (1953) also published a graphic scale to illustrate the qualitative measure

(figure 12) It is important to highlight that any comparing chart to describe particle

properties has a high degree of subjectivity Folk (1955) concludes that when charts

are used for classification the risk of getting errors is negligible for sphericity but

large for roundness

N

R

r

Rinmax

r

R

NR

inmax

Figure 10 Form (shape) Roundness and Texture graphical description (Bowman et al 2001)

Figure 11 Wadellrsquos method to estimate the roundness corners radius and inscribed circle

(Hawkins 1993)

(22)

(23)

13

Some authors as Russel amp Taylor in 1937 Pettijohn in 1957 and Powers in 1953

developed a classification based on five and six classes (Hawkins 1993) each one

with its own class limits it is important to denote that the way they measure the

roundness is the developed by Wadell (1935) This classification and class limits are

showed in the table 4

Table 4 Degrees of roundness Wadell Values (Hawkins 1993) NA = no-applicable

Grade terms Russell amp Taylor (1937) Pettijohn (1957) Powers (1953)

Class

limits (R)

Arithmetic

midpoint

Class limits

(R)

Arithmetic midpoint Class

limits (R)

Arithmetic

midpoint

Very angular

NA

NA

NA

NA

012-017

014

Angular

000-015

0075

000-015

0125

017-025

021

Subangular

015-030

0225

015-025

0200

025-035

030

Subrounded

030-050

0400

025-040

0315

035-049

041

Rounded

050-070

0600

040-060

0500

049-070

059

Well rounded

070-100

0800

060-100

0800

070-100

084

Krumbein and Sloss (1963) published a graphical chart easy to determine the

sphericity and roundness parameters using comparison See figure 13 (Cho et al

2006)

Figure 12 A Roundness qualitative scale (Powers 1953)

Figure 13 Sphericity and roundness chart (Cho et al 2006) The roundness equation that appears here in

the chart is the wadellrsquos equation number 22

14

Fischer in 1933 (Hawkins 1993) used a straightforward method to quantify roundness

using a central point in the outline and dividing the outline in angles around this point

that were subtended by the straight or non curved parts of the profile were measured

This is illustrated in figure 14

To express the angularity value Fischer used the ratio of angles standing linear parts

on the outlines and concave respectively

Figure 14 left (A) and right (B) gives a similar angularity of approximately 042

using the above equations (Hawkins 1993)

Wentworth in 1922 used the maximum projection to define the position of the particle

to obtain the outline or contour (Barret 1980) The equation reflects the relation of the

diameter of a circle fitting the sharpest corner and the longest axis plus the shortest

axis c (minimum projection)

Wentworth (Hawkins 1993) expressed the roundness as the ratio of the radius of

curvature of the most convex part and the longest axis plus short axis

Actually these last two equations are the same just expressed in different terms when

the particle is in its maximum projection

Dimensions can be seen on figure 15 L and B represents the mayor axis a and

intermediate axis b The intention is to make difference between the 2 and 3

dimensions (L and B are for 2D as a b and c are for 3D)

deg360

ANG

=R

sumPLA

PLA

CON

ANG

ANGR

2)S(L

DR

M

S

B)4(L

RR CON

Figure 14 Fischerrsquos methods of angularity computation (Hawkins 1993)

A=inscribed circle B=circumscribed circle

(24)

(25)

(26)

(27)

15

Wentworth 1919 has a second way to express the roundness called Shape index

(Barrett 1980) and it relates the sharpest corner and the diameter of a pebble trough

the sharpest corner

Wentworth (1922b) used define the roundness as the ratio of the sharpest corner and

the average radius of the pebble

Cailleux (Barrett 1980) relates the radius of the most convex part and the longest

axis

Kuenen in 1956 show his roundness index (Barrett 1980) between the sharpest corner

and the breath axis

Dobkins amp Folk (1970) used a modified Wentworth roundness with the relation of

sharpest corner and inscribed circle diameters

AVG

CON

R

RR

x

s

D

DR

L2

RR CON

B

DR s

i

s

D

DR

3AVGAVG cbaDR2

Figure 15 Description of L and B axes (Hawkins 1993)

(28)

(29)

(30)

(31)

(32)

(33)

16

Swan in 1974 shows his equation (Barrett 1980) relating the sharpest (or the two

sharpest) corner(s) and inscribed circle diameter

Szadeczsky-Kardoss has his Average roundness of outline (Krumbein and Pettijohn

1938) relating the concave parts perimeter and the actual perimeter

Lees (1964a) developed an opposite definition to roundness it means that he

measures the angularity instead of the roundness and he calls it Degree of angularity

Figure 16 shows the items considered when equation 36 applies as the angles (α)

inscribed circle (Rmax-in) and the distance (x) The main formula is

In order to apply the last equation corners needs to be entered in the formula and each

individual result will add to each other to obtain the final degree of angularity

A roundness index appears on Janoo (1998) Kuo and Freeman (1998a) and Kuo et

al (1998b) it is described as

The last equation is on section 34 also because there is not a general agreement on the

definition furthermore some authors had used to define the roughness this is not the

only equation that has been used trying to define different aspects (sphericity

roundness or roughness) but it is a good example of the misuse of the quantities and

definitions

inmaxR

x)180(R

2P

A4R

i

ss

D

DDR

221

100P

PR CON

Figure 16 Degree of angularity measurement technique (Blot and Pye 2008)

(34)

(35)

(36)

(17)

17

Sukumaran and Ashmawy (2001) present an angularity factor (AF) calculated from

the number of sharpness corners Angles βi required to obtain the angularity factor are

shown in figure 9

Sukumaran and Ashmawy (2001) also suggested use not bigger sampling interval of

N=40 because it is the cut off between angularity factor and surface roughness If so

this equation could be used to describe the roughness

Table 5 General chronological overview of the particle roundness

Aspect Name Author Year Based on

Roundness shape index Wentworth 19191

diameter of sharper corner

shape index Wentworth 1922b sharpest corner and axis

roundness Wentworth 1933 convex parts

Fischer 19332

noncurved parts outline

Fischer 19332

noncurved-streigth parts outline

Average roundness of outline

Szadeczsky-Kardoss 19333

convex parts-perimeter

roundness Wadell 1935 diameter of corners

roundness Wadell 1935 diameter of corners

roundness Russel amp Taylor 19372

class limit table

roundness Krumbein 1941 chart

Cailleux 19471

convex parts

roundness Pettijohn 19494 class limit table

roundness Powers 1953 chart and class limit table

Kuenen 19561

axis-convex corner

roundness Krumbein and Sloss 1963 chart

degree of angularity Lees 1964a corners angles and inscribed circle

Dobkins amp Folk 1970 diameter of sharper corner

Swan 19741

diameter of sharper corners

Angularity factor Sukumaran and

Ashmawy 2001

Segmentation of particles and angles

1) Barret 1980 2) Hawkins 1993 3) Krumbein and Pettijohn 1938 4) Powers 1953

sum

sumsumN

1=i

2

i

2

N

1=i

2

i

2N

1=ii

)ordm180 -circleβ( - )(180ordm x 3

)ordm180-circleβ(-)ordm180 -Particleβ(

= AF (37)

18

36 ROUGHNESS OR SURFACE TEXTURE

A third property called texture appears early in the literature with the sphericity and

roundness properties since then texture property was longed described but it was in

accordance with the authors at that time not measurable

Wright in 1955 developed a method to quantify the surface texture or roughness of

concrete aggregate using studies done on 19 mm stones The test aggregates were first

embedded in a synthetic resin The stones were cut in thin sections The sections

projection was magnified 125 times The unevenness of the surface was traced and the

total length of the trace was measured The length was then compared with an uneven

line drawn as a series of chords (see figure 17) The difference between these two

lines was defined as the roughness factor (Janoo 1998)

However with the advance of technology it has become easier measure the roughness

and here is presented some researcherrsquos ideas how this property should be calculated

One technique used by Janoo (1988) to define the roughness can be seen in figure 18a

and is defined as the ratio between perimeter and convex perimeter

The convex perimeter is obtained using the Feretrsquos box (or diameter) tending a line in

between the touching points that the Feretrsquos box describes each time it is turn (figure

18b)

PER

OC

PR

Figure 17 Measurement method for characterizing the surface texture of an aggregate (Janoo 1998)

a) Convex perimeter (CPER) b) Feret measurement Figure 18 a) Convex perimeter (CPER) b) Feret measurement (modified after Janoo 1998)

(38)

a)

b)

19

Kuo and Freeman (1998a) and Kuo et al (1998b) use the roughness definition as the

ratio perimeter and average diameter

Erosion and dilatation image processing techniques are used to obtain the surface

texture Erosion is a morphological process by which boundary image pixels are

removed from an object surface which leaves the object less dense along the

perimeter or outer boundary Dilatation is the reverse process of erosion and a single

dilatation cycle increases the particle shape or image dimension by adding pixels

around its boundary (Pan etal 2006)

The ldquonrdquo erosion and dilatation cycles are not standardized

Mora and Kwan (2000) used the ldquoconvexity ratio CRrdquo (equation 41) and the ldquofullness

ratio FRrdquo (equation 42) in their investigation they are

The convex area is the area of the minimum convex boundaries circumscribing the

particle This is illustrated in the figure 19 The convex area is obtained in a similar

way as the convex perimeter but in this case the area between the original outline and

the convex perimeter is our convex area

AVG

OD

PR

100A

1AARO

CONo A

AR =

CONo A

AR =

Figure 19 Evaluation of area and convex area (Mora and Kuan 2000)

(39)

(40)

(41)

(42)

20

4 TECHNIQUES IN ORDER TO DETERMINE PARTICLE

SHAPE

41 HAND MEASUREMENT

Hand measurement technique was the first used by obvious reasons in order to

improve the accuracy special devices developed as the ldquosliding rod caliperrdquo used by

Krumbein (1941) it works placing the sample on the sliding road calliper as show

figure 20b the length in different positions can be obtain by using the scale provided

in the handle the ldquoconvexity gagerdquo that was actually used by opticians to measure the

curvature of lenses but easily applicable to the particle shape analysis (Wentworth

1922b) works measuring the movement of the central pivot as figure 20a shows (the

two adjacent pivots are invariable) as many the central pivot moves more is the

curvature or the ldquoSzadeczky-Kardossrsquos apparatusrdquo develop in 1933 that traces the

profile of the rock fragment so the outline traced is then analyzed (Krumbein and

Pettijohn 1938) figure 20c show equipment

Another helpful tool to determine the particle dimensions was the ldquocamera lucidardquo to

project the particlersquos contour over a circle scale appearing in Figure 21 thus it is

possible to measure the particlersquos diameter

a)

c) b)

Figure 20 a) convexity gage used to determine the curvature in particle corners (Wenworth 1922b)

b)sliding rod caliper device to measure the particle axis length (Krumbein 1941) and c)Szadeczky-

Kardoss (1933) apparatus it was utilized to obtain the particle outline

Figure 21 Circle scale used by Wadell (1935) to determine particlersquos diameter and roundness

21

42 SIEVE ANALYSIS

Bar sieving eg according to EN 933-31997 can be used to determine simple large

scale properties By combining mesh geometries the obtained results can be used to

quantify flakiness and elongation index ASTM D4791 (Flat and elongated particles

are defined as those coarse aggregate particles that have a ratio of length to thickness

equal to or greater than a specified value such as 51 The index represents the

percentage on weight of these particles) The method is not suitable for fine materials

This due to the difficulty to get the fine grains passed through the sieve and the great

amount of particles in relation to the area of the sieve (Persson 1998) eg EN 933-

31997 related to flakiness index The test is performed on aggregates with grain size

from 4 mm and up to 63 mm two sieving operations are necessary the first separates

on size fraction and the second use a bar sieve after the first sieving the average

maximum diameter of the particles is obtain and with the second sieving (bar sieving)

the shortest axis diameter is found finally with this two parameters the flakiness

index is determined

There are more standards related with the particle shape (see appendix A) but this

above presented are probably the most known using sieve analysis to determine

particlersquos geometrical properties

Sieve analysis is facing the computers age and image analysis sieving research is

taking place (Andersson 2010 Mora and Kwan 2000 Persson 1998) Industry is

also applying the image analysis sieving with decrees on the testing time compare

with the traditional sieving method An inconvenient of image analysis is the error

due the overlapping or hiding of the particles during the capture process but the

advantages are more compare with disadvantages (Anderson 2010)

43 CHART COMPARISON

Charts developed over the necessity of faster results because the long time consuming

required when measuring each particle

Krumbein (1941) present a comparison roundness chart for pebbles which were

measured by Wadellrsquos method because this property was the most difficult to measure

due to the second order scale that roundness represents (See figure 22)

Figure 22 Krumbein (1941) comparision chart for roundness

22

A qualitative chart by Powers (1953) try to include both (sphericity and roundness)

particlersquos characteristics it was divided on six roundness ranges (very angular

angular sub-angular sub-rounded rounded and well rounded) and two sphericity

series (high and low sphericity) This chart was prepared with photographs to enhance

the reader perspective (See figure 23)

A new chart including sphericity and roundness appear this time it was easier to

handle the two mean properties of particlersquos shape furthermore there was included

the numerical values that eliminated the subjectivity of qualitative description The

chart is based on Wadellrsquos definitions (Krumbein and Sloss 1963) (See figure 24)

Folk (1955) worried about the personrsquos error on the chartrsquos comparison studied the

determination of sphericity and angularity (he used the Powers 1953 comparison

chart) he found that the sphericity determination by chart comparison has a negligible

error while the roundness he concluded it was necessary to carry out a more wide

research due the high variability show by his study

Figure 23 Powers (1953) qualitative shpericity-roundness chart

Figure 24 Sphericity-roundness comparison chart (Krumbein and sloss 1963)

23

44 IMAGE ANALYSIS

Image analysis is a practical method to use for shape classification since it is fast and

can be automated Different techniques appear to process these images among them

are

o Feret Diameter the Feret diameter is the longitude between two parallel lines

this lines can rotate around one particle or outline to define dimensions as it

is shown in figure 25 these method is not a fine descriptor but as it was say

above it is a helpful tool to determine diameters (Janoo 1988)

o Fourier Mathematical Technique It produces mathematical relations that

characterize the profile of individual particles This method favours the

analysis of roughness and textural features for granular soils The problem in

the methodology remains in the re-entrant angles in order to complete the

revolution (Bowman et al 2001) see figure 26

o Fractal Dimension Irregular line at any level of scrutiny is by definition

fractal (Hyslip and Vallejo 1997) Figure 27 shows fractal analysis by the

dividing method The length of the fractal line can be defined as

N

1n

nn0 )nsinbncosa(a)(R

RD1n)(P

Figure 25 Feret measurement technique is defined by two parallel lines turning

around the particle to define the shortest and longest Feret diameter (Janoo 1988)

Figure 26 Fourier technique with two radiuses at one angle (Bowman et al 2001)

(43)

(44)

24

o Orthogonal image analysis This technique is basically the use of two images

orthogonal between them to acquire the three particle dimensions (Fernlund

2005) any of the above techniques can be used in this orthogonal way

o Laser Scanning Technique this kind of laser scanning 3D is one of the most

advanced techniques In figures 28a) we have the laser head scanning the rock

particles the particles have control points in order to keep a reference point

when move them to scan the lower part in figure 28b) we can see the laser

path followed (Lanaro and Tolppanen 2002)

Another technique is the Laser-Aided Tomography (LAT) in this case a laser sheet is

used to obtain the particles surveying (see figure 29) This technique is different and

has special requirements as to use liquid with same refractive index as the particles

particles must let the laser or certain percent of light go through (Matsushima et al

2003)

a) b)

Figure 27 Fractal analysis by the dividing method at different scrutiny scale (Hyslip and Vallejo 1997)

Figure 28 a) Scanning head b) scanning path (Lanaro and Tolppanen 2002)

Figure 30 3D scan completed ready to

use for any further measure

(Matsushima et al 2003)

Figure 29 LAT scaning particles

(Matsushima et al 2003)

25

Both 3D techniques obtain the particle shape that is later used to achieve measures as

we can see in figure 30

All these previous techniques are easily written in codes or scripts to be interpreted in

a digital way obtaining the desired measurement but there are some interesting points

in the image analysis regarding on the errors involve among them are image

resolution and orientation of the particles orientation is not relevant when it is

random and large number of particles are involve resolution have an influence on the

accuracy (Zeidan et al 2007)

When resolution is increase more accuracy is obtain and the object representation

match better with the real form in the other hand more resolution means more

spending on memory and time thus resolution needs to be according with the goal

and precision needed in any work (Schaumlfer 2002)

Schaumlfer (2002) conclude that attributes like length when measuring digital images

present relative high errors It can be vanish or at least diminish using high resolution

just for diameter but not for perimeter that keep the error as big as initially Johansson

and Vall (2011) obtain similar results when 3 different resolutions were used in the

same particle obtaining an unstable output for those termsquantities that involve the

perimeter Thus all quantities relating the perimeter should be treated with care

5 EFFECT OF SHAPE ON SOIL PROPERTIES

51 INTRODUCTION

In laboratory test on the effect on particle size on basic properties has been

investigated in several studies this relation has been discussed and various

mechanisms had been proposed to explain the behaviour of the soil in dependency

also with the shape Basically there are two mechanisms proposed The arrangement

of particles and the inter-particle contact (Santamarina and Cho 2004) and

subsequence breakage

The arrangement of particles

Arrangement of the particles can be presented in three different forms loose dense

and critical this arrangement determines the soil properties (eg density increase with

more dense arrangement) Loose and dense states are easy understandable when

figure 31 is explained while in the upper part of the figure the particles are arranged

using the minimum space needed in the lower part a span is created using the flaky

particle as a bridge this phenomena is known as ldquobridgingrdquo Bridging can produce

different geotechnical results when just the shape of the particle is changed eg void

ratio (Santamarina and Cho 2004) Particles are able to rearrange this could be done

applying pressure (energy) to the soil the pressure (energy) will create such forces

that soil particles will rotate and move (see figure 34) finishing in a more dense state

26

A loose soil will contract in volume on shearing and may not develop any peak

strength (figure 32 left) In this case the shear strength will increase gradually until

the residual shear strength is revealed once the soil has ceased contracting in volume

A dense soil may contract slightly (figure 32 right) before granular interlock prevents

further contraction (granular interlock is dependent on the shape of the grains and

their initial packing arrangement) In order to continue shearing once granular

interlock has occurred the soil must dilate (expand in volume) As additional shear

force is required to dilate the soil a peak shear strength occurs (figure 32 left) Once

this peak shear strength caused by dilation has been overcome through continued

shearing the resistance provided by the soil to the applied shear stress reduces

(termed strain softening) Strain softening will continue until no further changes in

volume of the soil occur on continued shearing Peak shear strengths are also

observed in overconsolidated clays where the natural fabric of the soil must be

destroyed prior to reaching constant volume shearing Other effects that result in peak

strengths include cementation and bonding of particles The distinctive shear strength

called the critical state is identified where the soil undergoing shear does so at a

constant volume (Schofield and Wroth 1968)

The inter-particle contact

For frictional soil ie coarse grained soil the friction between particles is the

dominating factor for strength Materials usually consisting of coarse grains (diameter

Figure 31 Bridging effect when flaky particles are combined in the bulk material (Santamarina and

Cho 2004)

Figure 32 The left part of the figure show a typical behaviour of loose and dense material over shear stress

while at the right the figures illustrate the typical volume changes

27

gt 006mm) behave as a frictional soil it means that the strength of coarse soils (silt

sand gravel etc) comes from an inter-particle mechanical friction thus ideally they

do not have traction strength In figure 33 the inter-particle contact is illustrated here

the pressure (P) is applied and two more components are found the normal load (N)

and the tangential load (T) described as the friction coefficient (μF) The forces stand

in equilibrium (Johansson and Vall 2011)

When particles equilibrium is disturbed (friction coefficient is not enough to keep

particles unmoved) the rotation is imminent and it is necessary in order to compact

the soil in figure 34 can be seen that the arrangement is a fact that inhibit or allow this

rotation and the shape in the 3 different scales are also factors because the more

spherical andor more rounded andor less roughness more easy is the rotation

(Santamarina and Cho 2004)

Breakage

Breakage is a side effect of the inter-particle contact and rotation when pressure

exceed the rock strength it can happened when the particles are tight together and

there is not enough space to rotate it is more obvious in angular particles (mesh form)

or as in figure 31 where the flaky particle ldquobridgingrdquo is not able to rotate but it can

brake by the pressure increase Yoginder et al (1985) notice that the angular particle

break during his experiments and they turn more rounded changing the original size

and form configuration at the same time there was a soil properties loosening

Figure 33 Inter-particle contact and forces acting (Axelsson 1998)

Figure 34 Rotation inhibition by the particles compaction or low void ratio (Santamarina and Cho 2004)

28

52 INFLUENCE OF SIZE AND SHAPE

Wenworth (1922a) and Pellegrino (1965) among others suggest that agent transport of

the rocks (rigor of transport temperature and moisture changes etc) determine its

shape but also the particle genesis itself (rock structure mineralogy hardness etc) It

is not possible to determine the shape of the particles based on the agent transport or

genesis but generally a shape behaviour is expected according to Mitchell and Soga

(2005) specially when the particle size is in the clay size (gt2μm) The shapes of the

most common clay minerals are platy (figure 35) with some exceptions (eg

halloysite occurs as tubes kaolinite are large thick and stiff Smectites are composed

of small very thin and filmy particles Illites are intermediate between kaolinite and

smectite and attapulgite occurs in lathlike particle shapes) Some clay minerals

photographs are presented in figure 35

Figure 35 Clay mineral shape a) hallosite b) Kaoline c) Smactites d) Illites and e) attapulgite (Modified

from Mitchell and Soga 2005)

Figure 36 Particle size range in soils Generally the particles of clay size are plate shaped (Mitchell and

Soga 2005)

a) b) c)

e) d)

29

53 VOID RATIO AND POROSITY

The void ratio (e) is the ratio of the volume of voids to the volume of solid it is

defined by the equation

Porosity (n) is the ratio of the volume of voids to the total volume of the soil it is

represented by the equation

Holubec and DrsquoAppolonia (1973) found a relation between the void ratio and

sphericity (referred in the paper as coefficient of angularity ratio of particle surface

and equivalent sphere surface) their results show that the maximum and the minimum

void ratio increases as the shpericity decreases In this study the surface was obtained

for an indirect method based on the permeability developed by Hoffman in 1959

described in the same document Rouseacute et al (2008) defined the roundness as

Wadell (1935) and he found it as an important factor controlling the minimum and

maximum void ratios Some other authors as Youd (1973) and Cho et al (2006)

conclude the same minimum and maximum void ratios increase when sphericity and

roundness decrease Another interesting result (all above authors) was the bigger

influence of the form (sphericity circularity) and roundness on the maximum void

ratio The change of the maximum void ratio is more pronounced than the change of

the minimum void ratio when the form and roundness changes (See figure 39)

Particles arrangement and interlocking are probably the factor that controls the void

ratio bridge effect permit the existence of void among the particles while interlocking

allowed the particles to form arches avoiding the possibility to rotate and stay in a

more stable configuration eg as it happens with marbles

Figures 36 37 and 38 shows proposed empirical relationships between void ratio and

shape from tables 5 and 6 (graphically the scale goes from 0 to 1 when cero mean

high angularity shpericity or circularity and one means low angularity circularity or

sphericity) Holubec and DrsquoAppolonia (1973) data was taken to obtain a power curve

and describe a tendency Santamarina and Cho (2004) show Youd equations in the

original paper Youd (1973) never presented the equation but it is easy to use the

information to draw a trend

The graphics presented in this document (figures 36 37 and 38) must be used with

certain reserves due the fact that the original data was modified in order to fit all

information in one graphic what the figures shows is just the general trend of the

behaviourrsquos material regarding on the shape If more accurate description and

information is required the author recommends consulting the reference data In the

same way equations from Holubec and DrsquoApollonia (1973) and Youd (1973) were not

presented by the authors but the use of the information was taken in order to build up

those equations on tables 6 and 7

S

V

V

V

= e

V

V

=nV

(45)

(46)

30

Table 6 Minimum void ratio equations regarding on the quantity (Ψ for sphericity C for circularity R

for roundness SF for Sukumaran shape factor and AF for Sukumaran angularity factor)

EQUATION NUMBER REFERENCE

Figure 34 (left)

4340

minΨ45490e =

47

Holubec amp DrsquoAppolonia 1973 (Ψ

was obtained using equation 2)

SF06340

mine021903180e +=

48

Sukumaran amp Ashmawy 2001 (SF

obtained using equation 21)

C05101emin

= 49

Cho etal 2006 (C obtained using

figure 12)

Figure 34 (right)

1

minR08203590e +=

50

Youd 1973 (R obtained from figure

11 and table 3)

R34080emin

= 51

Cho et al 2006 (R obtained using

figure 12)

1

minR05104330e +=

52

Rouseacute et al 2008 (R obtained by

equation 21)

AF02330

mine372004160e +=

53

Sukumaran amp Ashmawy 2001 (AF

obtained using equation 37)

Table 7 Maximum void ratio equations regarding on the quantity (Ψ for sphericity C for circularity R

for roundness SF for Sukumaran shape factor and AF for Sukumaran angularity factor)

EQUATION NUMBER REFERENCE

Figure 35 (left)

51520

max Ψ61120e = 54

Holubec and DrsquoAppolonia 1973 (Ψ

was obtained using equation 2)

SF1190

max e0016907180e += 55

Sukumaran amp Ashmawy 2001 (SF

obtained using equation 21)

C86061emax = 56

Cho etal 2006 (C obtained using

figure 12)

Figure 35 (right)

1

max R1505540e += 57

Youd 1973 (R obtained from figure

11 and table 3)

R62031emax= 58

Cho et al 2006 (R obtained using

figure 12)

1

max R107106150e += 59

Rouseacute et al 2008 (R obtained by

equation 21)

AF0530

max e12506090e += 60

Sukumaran amp Ashmawy 2001 (AF

obtained using equation 37)

Comparing figures 37 and 38 (minimum and maximum void ratio) it can be seen on

the right scheme of both figures 37 and 38 (when the factor is roundnessangularity)

that all the empirical relations has a common initial point close to 1 (it means that

particles are well rounded) while this common agreement disappear when the

roundness factor decreases (when the particles become more angular) Same figures

(37 and 38) on the left graphs (when the factor is sphericitycircularityshape) do not

present the same behaviour in fact there is more disperse initial point close to 1(when

the particles tend to be more sphericalcircular)

31

In Figure 39 the Δe (emax-emin) has been plotted to show how the maximum void ratio

and the minimum void ratio has different rate change when the particle shape

changes Maximum void ratio increases more than minimum void ratio when the

particle shape becomes less spherical andor more angular Comparing figure 39 left

and right graphics it can be seen that right present a common initial point when the

quantity (roundnessangularity) is close to one while in the left graphic the initial

point is more disperse Both ending points in both graphics (close to zero) are

dispersed

Figures 37 38 and 39 present the same behaviour right graphics (when the factor is

roundness angularity) in each figure have an initial common point while the left

graphics do not (when the factor is sphericity circularity shape)

Figure 37 Minimum void ratio based upon the relation of shape factor proposed by the authors indicated

in the figure

Figure 38 Maximum void ratio based upon the relation of shape factor proposed by the authors indicated

in the figure

04

06

08

1

12

14

16

18

2

005

015

025

035

045

055

065

075

085

095

Factor (roundness angularity)

min

imu

m v

oid

rati

o

Youd 1973 roundness

Rouse 2008 roundness

Cho 2006 roundness

Sukumaran 2001 AF

03

04

05

06

07

08

09

1

11

12

13

05

015

025

035

045

055

065

075

085

095

Factor (sphericity circularity shape)

min

imu

m v

oid

rati

oHolubec 1973 sphericity

Cho 2006 circularity

Sukumara 2001 SF

05

07

09

11

13

15

17

19

21

00

150

250

350

450

550

650

750

850

95

Factor (sphericity circularity shape)

Maxim

um

vo

id r

ati

o

Holubec 1973 sphericity

Cho 2006 circularity

Sukumara 2001 SF

05

1

15

2

25

3

35

005

015

025

035

045

055

065

075

085

095

Factor (roundness angularity)

Maxim

um

vo

id r

ati

o

Youd 1973 roundness

Rouse 2008 roundness

Cho 2006 roundness

Sukumaran 2001 AF

32

54 ANGLE OF REPOSE

The angle of repose of a granular material is the steepest angle of descent or dip of the

slope relative to the horizontal plane when material on the slope face is on the verge

of sliding as show in figure 40

According to Qazi (1975) there are five types of forces which may act between the

particles in soils

1 Force of friction between the particles

2 Force due to presence of absorbed gas andor moisture of particle

3 Mechanical forces caused by interlocking of particles of irregular shape

4 Electrostatic forces arising from friction between the particles themselves and

the surface with which they come in contact

5 Cohesion forces operating between neighbouring particles

Rouseacute et al (2008) found a decrease of angle of repose with increase roundness

based upon ASTM C1444 test (Standard Test Method for Measuring the Angle of

Repose of Free-Flowing Mold Powders) The method consist in pouring sand on a

surface cover by paper trough a funnel of specific dimensions (the nozzle diameter

depend on the sandrsquos particle size) from an altitude of 15 inches (381 mm) The sand

is release from the funnel until the peak of the cone formed by the sand stops the flow

The repose angle is obtained with the equation

H represent the 15 inches D and d represent the diameter of the cone formed by the

sand and the diameter of the funnel respectively

Figure 39 Maximum minus minimum void ratio based upon the relation of shape factor proposed by the

authors indicated in the figure

0

01

02

03

04

05

06

07

08

09

1

005

015

025

035

045

055

065

075

085

095

Factor (sphericity circularity shape)

Maxim

um

- M

inim

um

Vo

id r

ati

oHolubec 1973 sphericity

Cho 2006 circularity

Sukumara 2001 SF

0

02

04

06

08

1

12

14

16

18

005

015

025

035

045

055

065

075

085

095

Factor (roundness angularity)

Maxim

um

- M

inim

um

Vo

id r

ati

o

Youd 1973 roundness

Rouse 2008 roundness

Cho 2006 roundness

Sukumaran 2001 AF

dD

H2

tan=φ1

rep(61)

33

Rouseacute (2008) shows an empirical relation to obtain the angle of repose based on the

roundness of the particles

55 SHEAR STRENGTH

The MohrndashCoulomb failure criterion represents the linear envelope that is obtained

from a plot of the shear strength of a material versus the applied normal stress This

relation is expressed as

where τ is the shear strength σn is the normal stress co is the intercept of the failure

envelope with the τ axis and is the slope of the failure envelope The quantity c is

often called the cohesion and the angle is called the angle of internal friction

Studies show that the internal friction angle (under drained triaxial tests) increases

more rapidly on those materials having higher angularity increasing the relative

density The internal friction angle is a function of the relative density and the particle

shape (Holubec and DrsquoAppolonia 1973)

Chan and Page (1997) found in a study made with dry copper (using different shapes

and sizes ranging from 180 to 106 μm) using a direct shear test (ring share test) that

the internal friction angle increases as the angularity increases

Shinohara et al (2000) did some experiments with steel powder different shapes

using a triaxial cell in the test Shinohara never used the roundness or angularity on

the work but apply the shape factor (relation long axisshort axis) and the results were

that as this relation deviate from factor 1 the internal friction angle increases

The following empirical relations were found in the literature showing the behaviour

of the friction angle (obtained under different conditions)

)tan( noc

Figure 40 Representation of the angle of repose

(63)

(62)

34

Cho et al (2006)

(64)

(R is obtain by comparing the Krumbein chart figure 13)

Rouseacute (2008)

(65)

(66)

(R is defined using Wadell equation 22)

In figure 41 the suggested empirical relations above and lines constructed using

author data from Holubec and DrsquoAppolonia (1973) and Sukumara and Ashmawy

(2001) are plotted together to display the general trend on the particle shape and

friction angle relation Sukumaran reports two lines one based on the shape factor

(SF) and the second referring the angularity factor (AF) Sukumaran performed the

tests at constant volume

The scale used for Holubec and DrsquoAppolonia (1973) have lower and upper limits of 1

and 2 respectively (angularity form) and a scale change was applied to be able to

presented in the actual figure 41 As in the previous section (52) the author

recommend to use the original data from the references due that the figure just follows

the general trend of the behaviourrsquos particle regarding on the shape

Figure 41 The changes on the internal friction angle shows a general increase when the particle roundness

becomes angular or in the case of Sakamuran less spheric (Shape factor SF)

35

Barton and Kjaernsli (1981) suggested a model (equation 67) to predict the peak

friction angle (φrsquo) based upon numerous trixial and direct shear data tests

where

Se equivalent strength of particle

Re equivalent roughness of particle

φb basic friction angle (obtained from basic tilting test)

σn normal load

The information required for the model is (1) the uniaxial compressive strength of the

rock (2) the d50 particle size (mesh size where 50 of the particles pass through)

required to define Se (figure 42) (3) the degree of particle roundness and (4) the

porosity following compaction All data can be estimated by simple index tests

Barton and Kjaernsli (1981) suggest that particle size and sample scale has an effect

on the friction angle and includes them to obtain the equivalent strength (Se) figure 42

shows the method to obtain this value Compressive strength (σc) was chosen to be the

factor affecting the scale because micro fractures influence this property while

samples are bigger more micro fractures contain and its compressive strength reduces

The equivalent roughness is obtain using figure 43 where is required to know the

porosity (n) and the origin of the particles (a small chart is provided in the same figure

to compare the particles profile)

b

n

ee

SLogR

Figure 42 Method of estimating Equivalent Strength (Se) of rockfill based on uniaxial compressive strength

(σc ) and d50 particle size (Barton amp Kjaernsli 1981)

(67)

36

56 SEDIMENTATION PROPERTIES

A particle released in a less dense Newtonian fluid initially accelerate trough the fluid

due to the gravity Resistances to deformation of the fluid transmitted to the particle

surface drag generate forces that act to resist the particle motion The force due to the

weight (Fw) can be written as

Where ρp ρ are density of the particle and fluid (water) respectively g is the

gravitational force and Vp is the volume of the particle

And the resistance force (FD) is

Where CD is the dimensionless drag coefficient W is the weight of the particle and A

is the cross section area

Particlersquos shape has been assumed to be spherical when equations are applied on the

settling velocity Correlation deviates when particle shape departs from spherical form

Figure 43 Method of estimating Equivalent Roughness (Roe) based on porosity of rockfill

origin material degree of roundedness and smoothness of particle (Barton amp Kjaernsli 1981)

PPW ρ)gV(ρF

A2

WρCF

2

DD

(68)

(69)

37

(Dietrich 1982) and it is known that natural particles depart from spherical form

thus it is evident that this departure would have consequences

The below equation is proposed to account the shape (in this case the Corey shape

factor equation 8) in the settling velocity (Jimenez and Madsen 2003)

Jimenez and Madsen (2003) Dietrich (1982) Briggs and McCulloch (1962) and

others were working in the hydraulic shape of particles to solve problems as sediment

transport It is obvious that the equation presented and the researcherrsquos investigation

works under certain conditions (eg grain size between 0063-1 mm)

Dietrich (1982) suggests an empirical relation that accounts settling velocity size

density shape and roundness of a particle

R1 R2 and R3 are fitted equations for size and density shape and roundness

respectively

57 HYDRAULIC CONDUCTIVITY PERMEABILITY

Darcyrsquos Law Permeability is one component of Darcyrsquos law Darcys law is a simple

proportional relationship between the instantaneous discharge rate through a porous

medium the viscosity of the fluid and the pressure drop

The total velocity Ve is equal to the product of the permeability of the medium

(porous media) k the pressure drop ∆p all divided by the viscosity μ (Muskat

1937)

Darcys law is only valid for slow viscous flow most groundwater flow cases fall in

this category Typically Darcyrsquos law is valid at any flow with laminar flow (see figure

44)

Reynoldrsquos number (Laminar and turbulent Flow) Typically any laminar flow is

considered to have a Reynoldrsquos number less than one and it would be valid to apply

Darcys law Experimental tests have shown that flow regimes with Reynolds numbers

1

ND

S

S

ZY

gd1s

WW

NDN

gd)1s(4

dS

2R1R

3 10RW

pk

Ve

(70)

(71)

(72)

(73)

38

up to 10 may still be Darcian (laminar flow) as in the case of groundwater flow The

Reynolds number (a dimensionless parameter) for porous media flow is typically

expressed as

where ρ is the density of water (units of mass per volume) υ is the specific discharge

(with units of length per time) d is a representative average grain diameter for the

porous media (often taken as the 30 passing size from a grain size analysis using

sieves - with units of length) and μ is the viscosity of the fluid (Muskat 1937)

Shape effects Permeability as Head and Epps (2011) suggested is affected by the

shape and texture of soil grains Elongated or irregular particles create flow paths

which are more tortuous than those spherical particles Particles with a rough surface

texture provide more frictional resistance to flow Both effects tend to reduce the

water flow through the soil

Kozeny-Carman empirical relation accounts for the dependency of permeability on

void ratio in uniformly graded sands serious discrepancies are found when it is

applied to clays due the lack of uniform pores (Mitchell and Soga 2005)

There are various formulations of the Kozeny-Carman equation one published by

Head and Epps (2011) takes the void ratio e the specific surface area Ss and an

angularity factor F into account of permeability k

The angularity factor F considers the shape of the particles and ranges from 11 for

rounded grains 125 for sub rounded to 14 for angular particles The specific surface

Ss is defined as

d1 and d2 represent the maximum and minimum size particle in mm

Kane amp Sternheim (1988) suggest that the inclusion of the shape factor (F) has

probably the background on the Reynolds number due this factor is dependent

significantly on the shape of the obstacles and Reynolds number determines the

presence of laminar or turbulent flow Figure 44 show how the laminar flow has low

energy dissipation while turbulent flow (eg the roughness and path tortuosity) has

high energy dissipation

e1

e

FSs

2k

3

2

dRe

21

6

ddSs

(74)

(75)

(76)

39

According to Nearing and Parker (1994) the amount of soil detached during laminar

and turbulent flow is dependent on each soil and also greater on turbulent flow due the

greater shear strength generated during this kind of flow this could suggest the

greater erosion when turbulent flow is present

58 LIQUEFACTION

Soil liquefaction is a phenomenon in which soil loses much of its strength or stiffness

for a generally short time by earthquake shaking or other rapid loading Static and

dynamic liquefactions occur been the second one the most regular known

Liquefaction often occurs in saturated soils that is soils in which the space between

individual particles is completely filled with water This water exerts a pressure on the

soil particles that influences how tightly the particles themselves are pressed together

Shaking or other rapid loading can cause the water pressure to increase to the point

where the soil particles can readily move with respect to each other (Jefferies and

Been 2000)

Jefferies and Been (2000) state that it is clear that minor variation in intrinsic

properties of sand have major influence on the critical state These might be variations

on grain shape mineralogy grain size distribution surface roughness of grains etc

Yoginder et al (1985) found that substantial decrease on liquefaction resistance

occur with increase in confining pressure for rounded and angular sands (1600 kPa)

also rounded sands show an rapidly build up of resistance against liquefaction with

increasing density while angular tailing sand in contrast show such rapid increase

only at low confining pressures At low confining pressure angular material is more

resistant to liquefaction Probably the breakage of the corners on the angular particles

in tailings is ruling the lost in resistance at high confining pressures (sieve analysis

Figure 44 The figure show the extremes of flow behaviour First turbulent conditions where the flow is

essentially random and unpredictable and second the well defined Laminar flow conditions

40

after test identify the breakage of angular particles while on rounded particles the

sieve analysis was practically the same)

59 GROUNDWATER AND SEEPAGE MODELLING

In groundwater flow the particlersquos shape affects the soilrsquos pore size distribution

hence the flow characteristics (Sperry and Peirce 1995) Tortuosity and permeability

(also see section 57) are two significant macroscopic parameters of granular medium

that affect the passing flow (Hayati et al 2012) Current models incorporating the

effects of particle shape have failed to consider irregular particles such as those that

would prevail in a natural porous medium (Sperry and Peirce 1995)

Hayati et al (2012) suggested based on his results that tortuosity effect converge

when the porosity increases indicating that the shape have dominance at low and mid

porosity ranges

Sperry and Peirce (1995) research conclusions suggest that particle size and porosity

are more important predictors for hydraulic conductivity explaining the 69 of the

variability but particle shape appears to be the next most important This however

apparently comprises particles larger than 295-351 μm Differences for particle size

295-351 μm and smaller are not detectable Another interesting result in the research

was the interaction effect of the particle size and particle shape It suggests a different

packing configuration for particles of the same shape but different size (scale

dependent)

6 DISCUSSION

61 TERMS QUANTITIES AND DEFINITIONS

In order to describe the particle shape in detail there are a number of terms quantities

and definitions (qualitative and quantitative) used in the literature (eg Wadell 1932

1934 Krumbein 1941 Sneed amp Folk 1958) All mathematical definitions

(quantitatives) are models used to simplify the complexity of shape description Some

authors (Mitchell amp Soga 2005 Arasan et al 2010) are using three sub-quantities

one and each describing the shape but at different scales The terms are

morphologyform roundness and surface texture (figure 1) The three sub-quantities

are probably the best way to classify and describe a particle because not a single

definition can interpret the whole morphology Common language is needed when

descriptors are explained and these three scales represent an option It is evident in

the reviewed literature that many of the shape descriptors are presented with the same

name but also that there is not a clear meaning on what this descriptor defines eg

when there is no upper limit in the roundness does it means that the angularity never

ends Could they be more and more angular Probably they could be on theory but

not in reality

41

62 PROPERTIES

Trough various articlersquos review done in the present investigation it is recognized that

the particlersquos shape has an effect on the material properties among these are

1 Porosity (Tickell 1938 Fraser 1935 Kolbuszewski 1948) and void ratio

(Cho et al 2006 Shergold 1953 Rouseacute et al 2008 Santamarina and Cho

2004)

2 Permeability (Witt and Brauns 1983)

3 Internal friction angle (Shinohara et al 2000 Chan and Page 1997

Cheshomi et al 2009)

4 Density (Youd 1973 Holubec and DrsquoAppolonia 1973)

5 Drag coefficient Hydraulics (Briggs and McCulloch 1962)

In Table 5 is a short resume of the properties and shape effect found in peer review

articles trough different journals Most of the reviewed articles based its research on

uniform graded sands

Table 8 Compilation of properties influenced by particle shape

Repose

angle

Friction

angle

Porosity and

Void ratio Density Permeability

Settling velocity

Drag coefficient Deformation

Sphericity (3D)shape factor

NI x x x x x x

Circularity (2D)

NI x x x x NI NI

Roundness x x x x NI NI x

x influence

NI no information available

Shape of particles has an effect on the arrangement producing bridging or avoiding

the rotation of the particles and the resulting geotechnical property is affected eg

including flaky particles can result in a higher void ratio due the bridging effect

(Santamarina and Cho 2004) and depending on the loads even the size distribution is

changed due the breakage (Yoginder et al 1985) in similar way angular particles

produce higher void ratio due the avoided possibility of the particles to rotate and

compact

The influence of the chosen shape descriptor appears in this review to have minor

influence on the soil properties in the reviewed studies except on the void ratio and

the friction angle Influence of particle shape in some cases is hider by other factors

(eg size distribution) also the particle shape probably does not have influence when

particle size is in the clay order (eg hydraulic conductivity) the reason could be due

to forces as electrostatic or capillarity become more important at this level

Among the shape descriptors some are chosen more often in literature (eg aspect

ratio) there is no apparent scientific basis to use it (probably due to the simplicity of

the measurement it becomes one of the most use) but there are still some other

descriptors that may or may not show better correlation with the soil properties

Instead empirical relations had been developed regarding roundness or shape to

describe the soil behaviour it is clear that the mechanism behind the results is still not

completely understood

42

There is necessity to define the best(s) shape descriptor(s) to be used for particular

geotechnical properties

63 IMAGE ANALYSIS

Many image analysis techniques had been used to describe the particle shape eg

Fourier analysis fractal dimension tomography etc (Hyslip and Vallejo 1997) but

there is not agreement on the usage or conclusion to ensure the best particle descriptor

for geotechnical applications

There are several shape descriptors and also various techniques to capture the

particles profile (3-dimensions 3-dimension orthogonal and 2-dimensions) Each

technique presents advantages and disadvantages 3-dimensions is probably the

technique that provide more information about the particle shape but the precision

also lies in the resolution the equipment required to perform such capture could be

more or less sophisticated (scanning particles laying down in one position and later

move to complete the scanning or just falling down particles to scan it in one step)

3-dimensions orthogonal this technique use less sophisticated equipment (compare

with the previous technique) but its use is limited to particles over 1cm also

information between the orthogonal pictures is not capture 2-dimensions require non

sophisticated equipment but at the same time the shape information diminish compare

with the previous due the fact that it is possible to determine only the outline as the

particle measurements are performed in 2-dimensions it is presumed that they will lie

with its shortest axis perpendicular to the laying surface when they are flat but when

the particle tends to have more or less similar axis the laying could be random

Advantages on the use of image analysis are clear there is not subjectivity because it

is possible to obtain same result over the same images Electronic files do not loose

resolution and it is important when collaboration among distant work places is done

files can be send with the entire confidence and knowing that file properties has not

been changed Technology evolutions allowed to work with more information and it

also applies to the image processing area were the time consumed has been shortened

(more images processed in less time)

One important aspect in image analysis is the used resolution in the analysis due the

fact that there are measurements dependent and independent on resolution Thus

those dependent measurements should be avoided due the error included when they

are applied or avoid low resolution to increase the reliability Among these

parameters length is the principal parameter that is influences by resolution (eg

perimeter diameter axis etc) Resolution also has another aspect with two faces

quality versus capacity more resolution (quality) means more storage space a

minimum resolution to obtain reasonable and reliable data must be known but it

depend on each particular application

43

64 APPLICATIONS

Quantify changes in particles in the authorrsquos thought is one of the future applications

due the non-invasive methods of taking photographs in the surface of the damrsquos slope

rail road ballast or roads Sampling of the material and comparing with previous

results could show volume (3D analysis) or area (2D analysis) loss of the particles as

well as the form roundness and roughness This is important when it has been

suggested that a soil or rock embankment decrees their stability properties (eg

internal friction angle) with the loss of sphericity roundness or roughness

Seepage stock piling groundwater etc should try to include the particle shape while

modelling seepage requires grading material to not allow particles move due the

water pressure but in angular materials as it is known the void ratio is great than the

rounded soil it means the space and the possibilities for the small particles to move

are greater stock piling could be modelled incorporating the particle shape to

determine the binrsquos capacity when particle shape changes (void ratio changes when

particle shape changes) Modelling requires all information available and the

understanding of the principles that apply

Industry is actually using the particle shape to understand the soil behaviour and

transform processes into practical and economic image analysis has been included in

the quality control to determine particle shape and size because the advantages it

brings eg the acquisition of the sieving curve for pellets using digital images taken

from conveyor this allows to have the information in a short period of time with a

similar result at least enough from the practical point of view as the traditional

sieving

7 CONCLUSIONS

The conclusions of this literature review are

It has been shown that particle shape has influence on the soil behaviour

despite of partial knowledge of the mechanism behind Understanding of the

particle shape and its influence needs to be accomplished

A common language needs to be built up to standardize the meaning on

geotechnical field that involve the particle shape General relationships

between shape and properties should be developed

Based on this review it is not clear which is the best descriptor to use in

geotechnical engineering affecting he related shape to properties Instead of a

couple of standards there is no shape descriptor in geotechnical field fully

accepted

Image analysis tool is objective make the results repeatable obtain fast results

and work with more amount of information

44

Resolution needs to be taken in consideration when image analysis is been

carried out because the effects could be considerable Resolution must be set

according to the necessities Parameters as perimeter can be affected by

resolution

There are examples where particle shape has been incorporated in industries

related to geotechnical engineering eg in the ballast and asphalt industry for

quality control

8 FURTHER WORK

Three main issues have been identified in this review that will be further investigated

the limits of shape descriptors influence of grading and choice of descriptor for

relation to geotechnical properties

Shape descriptors have low and high limits frequently the limits are not the same and

the ability to describe the particlersquos shape is relative The sensitivity of each descriptor

should be compare to apply the most suitable descriptor in each situation

Sieving curve determine the particle size in a granular soil particle shape could differ

in each sieve size There is the necessity to describe the particle shape on each sieve

portion (due to practical issues) and included in the sieve curve Obtain an average

shape in determined sieve size is complicated (due to the possible presence of several

shapes) and to obtain the particle shape on the overall particlersquos size is challenging

how the particle shape should be included

Since several descriptors have been used to determine the shape of the particles and

the relation with the soil properties it is convenient to determine the descriptorrsquos

correlation with the soil properties

9 ACKNOWLEDGMENT

I would like to thanks to Lulearing University of Technology (LTU) the time I had spent

in its facilities and the kind environment it offers and University of Sonora

(UNISON) that has been providing me the financial support and the time to conclude

this journey

10 REFERENCES

Andersson T (2010) Estimating particle size distributions based on machine vision

Doctoral Thesis Departament of Computer Science and Electrical Engineering Lulearing

University of Technology ISSN 1402-1544 ISBN 978-91-7439-186-2

45

Arasan Seracettin Hasiloglu A Samet Akbulut Suat (2010) Shape particle of

natural and crished aggregate using image analysis International Journal of Civil and

Structural Engineering Vol 1 No 2 pp 221-233 ISSN 0970-4399

Aschenbrenner BC (1956) A new method of expressing particle sphericity Journal

of Sedimentary Petrology Vol 26 No 1 pp 15-31

Axelsson K (1998) Introduktion till jordmekaniken jaumlmte jordmateriallaumlran Skrift

984 Lulearing Avdelningen foumlr Geoteknologi Lulearing Tekniska Universitet (In Swedish)

Barton Nick amp Kjaernsli Bjorn (1981) Shear strength of rockfill Journal of the

Geotechnical Engineering Division Proceedings of the American Society of Civil

Engineers (ASCE) Vol 107 No GT7

Barrett P J (1980) The shape of rock particles a critical review Sedimentology

Vol 27 pp 291-303

Blott S J and Pye K (2008) Particle shape a review and new methods of

characterization and classification Sedimentology Vol 55 pp 31-63

Bowman E T Soga K and Drummond W (2001) Particle shape characterization

using Fourier descriptor analysis Geotechnique Vol 51 No 6 pp 545-554

Briggs L I McCulloch D S (1962) Hydraulic shape of sand particles Journal of

Sedimentary Petrology Vol 32 pp 645-656

Chan Leonard C Y and Page Neil W (1997) Particle fractal and load effects on

internal friction in powders Powder Technology Vol 90 pp 259-266

Cheshomi A Fakher A Jones C J F P (2009) A correlation between friction

angle and particle shape metrics in quaternary coarse alluvia Quarterly Journal of

Engineering Geology and Hydrogeology Vol 42 pp 145-155

Cho G Dodds J and Santamarina J C (2006) Particle shape effects on packing

density stiffness and strength Natural and crushed sands Journal of Geotechnical

and Geoenvironmental Engineering May 2006 pp 591-602

Dietrich William E (1982) Settling velocity of natural particles Water Resources

Research Vol 18 No 6 pp 1615-1626

Dobkins J E and Folk R L (1970) Shape development on Tahiti-nui Journal of

Sedimentary Petrology Vol 40 No 2 pp 1167-1203

Folk R L (1955) Student operator error in determining of roundness sphericity and

grain size Journal of Sedimentary Petrology Vol 25 pp 297-301

Fernlund J M R (1998) The effect of particle form on sieve analysis A test by

image analysis Engineering Geology Vol 50 No 1-2 pp 111-124

46

Fernlund J M R (2005) Image analysis method for determining 3-D shape of

coarse aggregate Cement and Concrete Research Vol 35 Issue 8 pp 1629-1637

Fernlund J M R Zimmerman Robert and Kragic Danica (2007) Influence of

volumemass on grain-size curves and conversion of image-analysis size to sieve size

Engineering Geology Vol 90 No 3-4 pp 124-137

Fraser H J (1935) Experimental study of the porosity and permeability of clastic

sediments The Journal of Geology Vol 43 pp 910-1010 ISSN 0022-1376

Hayati Ali Nemati Ahmadi Mohammad Mehdi and Mohammadi Soheil (2012)

American Physical Society Physical review E 85 036310 DOI

101103PhysRevE85036310

Hawkins A E (1993) The Shape of Powder-Particle Outlines Wiley New York

Head K H and Epps R J (2011) Manual of soil Laboratory testing Volum II

Permeability shear strength and compressibility test 3rd

edition Whittles Publishing

Scotland UK 3rd

edition

Holubec I and DrsquoAppolonia E (1973) Effect of particle shape on the engineering

properties of granular soils ASTM STP 523 pp 304-318

Hyslip James P Vallejo Luis E (1997) Fractal analysis of the roughness and size

distribution of granular materials Engineering Geology Vol 48 pp 231-244

Janoo Vincent C (1998) Quantification of shape angularity and surface texture of

base course materials US Army Corps of Engineers Cold Region Research and

Engineering Laboratory Special report 98-1

Jefferies Mike and Been Ken (2000) Soil liquefaction A critical state approach

Taylor amp Francis Group London and New York

Jimenez Jose A Madsen Ole S (2003) A simple formula to estimate settling

velocity of natural sediments Journal of Waterway Port Coastal and Ocean

Engineering Vol 129 No 2 pp 70-78

Johansson Jens and Vall Jakob (2011) Jordmaterials kornform Inverkan paring

Geotekniska Egenskaper Beskrivande storheter bestaumlmningsmetoder

Examensarbete Avdelningen foumlr Geoteknologi Institutionen foumlr Samhaumlllsbyggnad

och naturresurser Lulearing Tekniska Universitet Lulearing (In Swedish)

Kane Joseph W and Sternheim Morton M (1988) Physics John Wiley amp Sons Inc

Third edition

Kolbuszewski J (1948) An experimental study of the maximum and minimum

porosities of sands Proceedings of the Second International Conference on Soil

Mechanics and Foundation Engineering Rotterdam June 21 to 30 Sub-section IIb

pp 158-165

47

Krumbein W C and Pettijohn FJ (1938) Manual of sedimentary petrography

Appleton-Century Crofts Inc New York

Krumbein W C (1941) Measurement and geological significance of shape and

roundness of sedimentary particles Journal of Sedimentary Petrology Vol 11 No 2

pp 64-72

Krumbein W C and Sloss L L (1963) Stratigraphy and Sedimentation 2nd

ed

WH Freeman San Francisco

Kuo Chun-Yi and Freeman Reed B (1998a) Image analysis evaluation of

aggregates for asphalt concrete mixtures Transportation Research Record Vol 1615

pp 65-71

Kuo Chun-Yi Rollings Raymond and Lynch Larry N (1998b) Morphological

study of coarse aggregates using image analysis Journal of Materials in Civil

Engineering Vol 10 No 3 pp 135-142

Lanaro F Tolppanen P (2002) 3D characterization of coarse aggregates

Engineering Geology Vol 65 pp 17-30

Lees G (1964a) A new method for determining the angularity of particles

Sedimentology Vol 3 pp 2-21

Lees G (1964b) The measurement of particle shape and its influence in engineering

materials British Granite Whinstone Federation Vol 4 No 2 pp 17-38

Matsushima Takashi Saomoto Hidetaka Matsumoto Masaaki Toda Kengo

Yamada Yasuo (2003) Discrete element simulation of an assembly of irregular-

shaped grains Quantitative comparison with experiments 16th ASCE Engineering

Mechanics Conference University of Washington Seattle July 16-18

Mitchell James K and Soga Kenichi (2005) Fundamentals of soil behaviour Third

edition WILEY

Mora C F Kwan A K H Chan H C (1998) Particle size distribution analysis of

coarse aggregate using digital image processing Cement and Concrete Research Vol

28 pp 921-932

Mora C F and Kwan A K H (2000) Sphericity shape factor and convexity

measurement of coarse aggregate for concrete using digital image processing Cement

and Concrete Research Vol 30 No 3 pp 351-358

Muskat Morris (1937) The Flow of fluids through porous media Journal of Applied

Physics Vol 8 pp 274

Nearing M A and Parker S C (1994) Detachment of soil by flowing water under

turbulent and laminar conditions Soil Science Society of American Journal Vol 58

No 6 pp 1612-1614

48

Pan Tongyan Tutumluer Erol Carpenter Samuel H (2006) Effect of coarse

aggregate morphology on permanent deformation behavior of hot mix asphalt Journal

of Transportation Engineering Vol 132 No 7 pp 580-589

Pellegrino A (1965) Geotechnical properties of coarse-grained soils Proceedings

International Conference of Soil Mechanics and Foundation Engineering Vol 1 pp

97-91

Pentland A (1927) A method of measuring the angularity of sands MAG MN AL

Acta Eng Dom Transaction of the Royal Society of Canada Vol 21 Ser3xciii

Persson Anna-Lena (1998) Image analysis of shape and size of fine aggregates

Engineering Geology Vol 50 pp 177-186

Powers M C (1953) A new roundness scale for sedimentary particles Journal of

Sedimentary Petrology Vol 23 No 2 pp 117-119

Pye W and Pye M (1943) Sphericity determination of pebbles and grains Journal

of Sedimentary Petrology Vol 13 No 1 pp 28-34

Qazi M A (1975) Flow properties of granular masses A review on the angle of

repose The Arabian Journal for Science and Engineering Vol 1 No 2

Quiroga Pedro Nel and Fowle David W (2003) The effects of aggregate

characteristics on the performance of portland cement concrete Report ICAR 104-1F

Project number 104 International Center for Aggregates Research University of

Texas

Riley N A (1941) Projection sphericity Journal of Sedimentary Petrology Vol 11

No 2 pp 94-97

Rouseacute P C Fennin R J and Shuttle D A (2008) Influence of roundness on the

void ratio and strength of uniform sand Geotechnique Vol 58 No 3 227-231

Santamarina J C and Cho G C (2004) Soil behaviour The role of particle shape

Proceedings Skempton Conf London

Schofield and Wroth (1968) Critical state soil mechanics McGraw Hill

Shaumlfer Michael (2002) Digital optics Some remarks on the accuracy of particle

image analysis Particle amp Particle Systems Characterization Vol 19 No 3 pp 158-

168

Shergold F A (1953) The percentage of voids in compacted gravel as a measure of

its angularity Magazine of Concrete Research Vol 5 No 13 pp 3-10

Shinohara Kunio Oida Mikihiro Golman Boris (2000) Effect of particle shape on

angle of internal friction by triaxial compression test Powder Technology Vol 107

pp131-136

49

Skredcommisionen (1995) Ingenjoumlrsvetenskapsakademinen rapport 395 Linkoumlping

1995

Sneed E D and Folk R L (1958) Pebbles in the Colorado river Texas A study in

particle morphogenesis Journal of Geology Vol 66 pp 114-150

Sperry James M and Peirce J Jeffrey (1995) A model for estimating the hydraulic

conductivity of granular material based on grain shape grain size and porosity

Ground Water Vol 33 No 6 pp 892-898

Sukumaran B and Ashmawy A K (2001) Quantitative characterisation of the

geometry of discrete particles Geotechnique Vol 51 No 7 pp 619-627

Szaacutedeczy-Kardoss E Von (1933) Die bistimmung der abrollungsgrades Geologie

und palaumlontologie Vol 34B pp 389-401 (in German)

Teller J T (1976) Equantcy versus sphericity Sedimentology Vol 23 pp 427-428

Tickell F G (1938) Effect of the angularity of grain on porosity and permeability

bulletin of the American Association of Petroleum Geologist Vol 22 pp 1272-1274

Tutumluer E Huang H Hashash Y Ghaboussi J (2006) Aggregate shape effects

on ballast tamping and railroad track lateral stability AREMA 2006 Annual

Conference Louisville KY

Wadell H (1932) ldquoVolume Shape and roundness of rock particlesrdquo Journal of

Geology Vol 40 pp 443-451

Wadell H (1933) Sphericity and roundness of rock Particles Journal of Geology

Vol 41 No 3 pp 310ndash331

Wadell H (1934) Shape determination of large sedimental rock fragments

The Pan-American Geologist Vol 61 pp 187-220

Wadell H (1935) ldquoVolume shape and roundness of quartz particlesrdquo Journal of

Geology Vol 43 pp 250-279

Wentworth W C (1922a) The shape of beach pebbles Washington US Geological

Survey Bulletin Vol 131C pp 75-83

Wentworth W C (1922b) A method of measuring and plotting the shape of pebbles

Washington US Geological Survey Bulletin Vol 730C pp 91-114

Wentworth W C (1933) The shape of rock particle A discussion Journal of

Geology Vol 41 pp 306-309

Witt K J Brauns J (1983) Permeability-Anisotropy due to particle shape Journal

of Geotechnical Engineering Vol 109 No 9 pp 1181-1187

v

Symbol Description Units

Se Equivalent strength of particle -

Ss Specific surface area -

SF Sukumara shape factor -

Sm Short axis ldquocrdquo in minimum projection plane m

s Surface area of a sphere of the same volume as the particle m2

sD Specific gravity of the sediment given by the relation density of

sedimentfluid

-

R2 Equation for predicting the ratio of the settling velocity of a non-spherical

well-rounded particle to be settling velocity of a sphere with the same

dimensionless nominal diameter

-

S Dimensionless fluid-sediment parameter -

V Total volume of soil m3

VCIR Volume of circumscribed sphere m3

Ve Velocity ms

VP Volume of particle m3

Vs Volume of voids m3

Vv Volume of solid m3

V10 voids in the aggregate compacted with 10 blows per layer -

V50 voids in the aggregate compacted with 50 blows per layer -

W Weight of the particle ton

WS Settling velocity ms

W Dimensionless settling velocity -

Y Constant to obtain by fitting to experimental data for certain ranges of S -

Z Constant to obtain by fitting to experimental data for certain ranges of S -

x Distance of the tip of the corner from the center of the maximum inscribed

circle

mm

α Measured angle degree (ordm)

αi Sakamura angles used to describe shape degree (ordm)

βi Sakamura angles used to describe angularity degree (ordm)

Σ Summation -

Ψ Sphericity -

ν Kinematics viscosity m2s

φb Basic friction angle degree (ordm)

φcs Friction angle critical state degree (ordm)

φmc Friction angle maximum contraction degree (ordm)

φrep Angle of repose degree (ordm)

φ Peak friction angle Pa

τ Shear strength Pa

σc Compressive strength Pa

σn Normal stress Pa Angle of internal friction degree (ordm)

μ Viscosity Pamiddots

μF Friction coefficient -

p Pressure drop -

ρ Density of water tonm3

ρp Density of the particle tonm3

υ Specific discharge ms

1

1 INTRODUCTION

Effects on soil behaviour from the constituent grain shape has been suggested since

the earliest 1900rsquos when Wadell (1932) Riley (1941) Pentland (1927) and some

other authors developed their own techniques to define the form and roundness of

particles Into the engineering field several research works conclude that particle

shape influence technical properties of soil material and unbound aggregates

(Santamarina and Cho 2004 Mora and Kwan 2000) Among documented properties

affected by the particle shape are eg void ratio (porosity) internal friction angle and

hydraulic conductivity (permeability) (Rouseacute et al 2008 Shinohara et al 2000

Witt and Brauns 1983) In geotechnical guidelines particle shape is incorporated in

eg soil classification (Eurocode 7) and in national guidelines eg for evaluation of

friction angle (Skredkommisionen 1995) This classification is based on ocular

inspection and quantitative judgement made by the individual practicing engineer

thus it can result in not repeatable data In evaluation of eg standard penetration test

Holubec and DrsquoAppolonia (1973) are suggesting the inclusion of the particle shape in

the evaluation of the data According with Folk (1955) the form error is negligible but

it is not in the second sub-quantity related with the corners (roundness) These

systems are not coherent in definitions The lack of possibility to objectively describe

the shape hinders the development of incorporating the effect of particle shape in

geotechnical analysis

The interest of particle shape was raised earlier in the field of geology compared to

geotechnical engineering Particle shape is considered to be the result of different

agentrsquos transport of the rock from its original place to deposits since the final pebble

form is hardly influenced by these agents (rigor of the transport exfoliation by

temperature changes moisture changes etc) in the diverse stages of their history

Furthermore there are considerations regarding on the particle genesis itself (rock

structure mineralogy hardness etc) (Wentworth 1922a) The combination of

transport and mineralogy factors complicates any attempt to correlate length of

transport and roundness due that soft rock result in rounded edges more rapidly than

hard rock if both are transported equal distances According to Barton amp Kjaernsli

(1981) rockfill materials could be classified based on origin into the following (1)

quarried rock (2) talus (3) moraine (4) glacifluvial deposits and (5) fluvial deposits

Each of these sources produces a characteristic roundness and surface texture

Pellegrino (1965) conclude that origin of the rock have strong influence determining

the shape

To define the particle form (morphology) in order to classify and compare grains

many measures has been taken in consideration (axis lengths perimeter surface area

volume etc) Probably when authors had developed the form descriptors realize that

they hadnrsquot provide enough information about the corners they could be angular or

rounded (roundness) thus the authors also focus on develop techniques to describe

them Furthermore the corners or the general surface can be rough or smooth (surface

texture) Nowadays some authors (Mitchell amp Soga 2005 Arasan et al 2010) are

using these three sub-quantities one and each describing the shape but a different

scale (form roundness surface texture)

2

During the historical development of shape descriptors the terminology has been used

differently among the published studies terms as roundness (because the roundness

could be apply in the different scales) or sphericity (how the particle approach to the

shape of a sphere) were strong (Wadell 1933 Wenworth 1933 Teller 1976 Barrett

1980 Hawkins 1993) and it was necessary in order to define a common language on

the particle shape field unfortunately still today there is not agreement on the use of

this terminology and sometimes it make difficult to understand the meaning of the

authors thatrsquos why it is better to comprehend the author technique in order to

misinterpret any word implication

Several attempts to introduce methodology to measure the particlersquos shape had been

developed over the years Manual measurement of the particles form is

overwhelming thus visual charts were developed early to diminish the measuring

time (Krumbein 1941 Krumbein and Sloss 1963 Ashenbrenner 1956 Pye and Pye

1943) Sieving was introduced to determine the flakinesselongation index but it is

confined only for a certain particle size due the practical considerations (Persson

1988) More recently image analysis on computer base has been applied on sieving

research (Andersson 2010 Mora and Kwan 2000 Persson 1998) bringing to the

industry new practical methods to determine the particle size with good results

(Andersson 2010) Particle shape with computer assisted methods are of great help

reducing dramatically the measuring time (Fernlund 2005 Kuo and Freeman 1998a

Kuo et al 1998b Bowman et al 2001)

In the civil industry eg Hot Asphalt mixtures (Kuo and Freeman 1998a Pan et al

2006) Concrete (Mora et al 1998 Quiroga and Fowle 2003) and Ballast

(Tutumluer et al 2006) particlersquos shape is of interest due the materialrsquos performance

thus standards had been developed (see appendix A) On asphalt mixtures limits of

flat and elongated particles or the amount of natural sands typically are incorporated

into specifications flat and elongated particles tend to cause problems with

compaction particle breakage loss of strength and segregation in pavement (Kuo and

Freeman 1998a) Rutting resistance of asphalt concrete under traffic and

environmental loads depend on the stability of aggregates structure in the asphalt mix

(Pan et al 2006) According with the American Railway Engineering and

Maintenance of Way Association (AREMA) ballast aggregate should be open graded

with hard angular shaped particles providing sharp corners and cubical fragments

with a minimum of flat and elongated pieces (Tutumluer et al 2006) The American

standard ASTM D 3398 (test method for index of aggregate particle shape and

texture) is an example of an indirect method to determine particle shape (see appendix

A) Aggregate characteristics of shape texture and grading influence workability

finishability bleeding pumpability and segregation of fresh concrete and affect

strength stiffness shrinkage creep density permeability and durability of hardened

concrete In fact flaky elongated angular and unfavorably graded particles lead to

higher voids content than cubical rounded and well-graded particles (Quiroga and

Fowle 2003)

Sieving is probably the most used method to determine the particle size distribution it

consist of plotting the cumulative weight of the weighted material retained by each

mesh (European standard EN 933-1 1992) This traditional method according to

Andersson (2010) is time consuming and expensive Investigations shows that the

traditional sieving has deviations when particle shape is involve the average volume

3

of the particles retained on any sieve varies considerably with the shape (Lees

1964b) thus the passing of the particles depend upon the shape of the particles

(Fernlund 1998) In some industries the Image analysis is taking advantage over the

traditional sieving technique regardless of the intrinsic error on image analysis due the

overlapping or partial hiding of the rock particles (Andersson 2010) In this case the

weight factor is substitute by pixels (Fernlund et al 2007) Sieving curve using

image analysis is not standardized but after good results in the practice (Andersson

2010) new methodology and soil descriptions could raise including its effects

2 AIM AND GOAL

The aim of this report is to review the state of the art on how to describe particle

shape of individual grains of geotechnical material and knowledge on the influence of

shape in geotechnical properties

The goals in this study are to

Describe discuss and compare particle shape and definitions

Review the known effect of particle shape on soil mechanics parameters

Discuss the potential of the role of particle shape in soil mechanics

Focus in this study has been on 2 dimensional shape definitions

The content of the report is based upon published and peer reviewed papers in

English

3 DESCRIPTION OF SHAPE PROPERTIES

31 INTRODUCCTION

Particle shape description can be classified as qualitative or quantitative Qualitative

describe in terms of words the shape of the particle (eg elongated spherical flaky

etc) and quantitative that relates the measured dimensions in the engineering field

the quantitative description of the particle is more important due the reproducibility

Quantitative geometrical measures on particles may be used as basis for qualitative

classification There are few qualitative measures in contrast with several quantitative

measures to describe the particle form Despite the amount of qualitative descriptions

none of them had been widely accepted but there are some standards (eg ASTM

D5821 EN 933-3 and BS 812) specifying mathematical definitions for industrial

purposes

Shape description of particles is also divided in

o 3D (3 dimensions) it could be obtained from a 3D scan or in a two

orthogonal images and

o 2D (2 dimensions) or particle projection where the particle outline is drawn

4

3D and 2D image analysis present challenges itself 3D analysis requires a

sophisticated equipment to scan the particle surface and create the 3D model or the

use of orthogonal images and combine them to represent the 3 dimensions The

orthogonal method could present new challenges as the minimum particle size or the

placing in orthogonal way of the particles (Fernlund 2005) 2D image analysis is easy

to perform due the non-sophisticated equipment required to take pictures (eg regular

camera or the use of microscope for smaller particles) In 2D image analysis the

particle is assumed to lay over its more stable axis (eg longest and intermediate axis

lie more or less parallel to the surface while the shortest axis is perpendicular) or

random some authors publish their own preferences about this issue (Wadell 1935

Riley 1941 Hawkins 1993)

32 SCALE DEPENDENCE

In order to describe the particle shape in detail there are a number of terms quantities

and definitions used in the literature Some authors (Mitchell amp Soga 2005 Arasan et

al 2010) are using three sub-quantities one and each describing the shape but at

different scales The terms are morphologyform roundness and surface texture In

figure 1 is shown how the scale terms are defined

At large scale the particlersquos diameters in different directions are considered At this

scale describing terms as spherical platy elongated etc are used An often seen

quantity for shape description at large scale is sphericity (antonym elongation)

Graphically the considered type of shape is marked with the dashed line in Figure 1

At intermediate scale it is focused on description of the presence of irregularities

Depending on at what scale an analysis is done corners and edges of different sizes

are identified By doing analysis inside circles defined along the particlersquos boundary

deviations are found and valuated The mentioned circles are shown in Figure 1 A

generally accepted quantity for this scale is roundness (antonym angularity)

Regarding the smallest scale terms like rough or smooth are used The descriptor is

considering the same kind of analysis as the one described above but is applied

Figure 1 Shape describing sub quantities (Mitchell amp Soga 2005)

5

within smaller circles ie at a smaller scale Surface texture is often used to name the

actual quantity The sub-quantities and antonyms are summarized in table 1

Table 1 Sub-quantities describing the particlersquos morphology and its antonym

Scale Quantity Antonym

Large scale Sphericity Elongation

Intermediate scale Roundness Angularity

Small scale Roughness Smoothness

33 FORM (3D)

Wentworth in 1922 (Blott and Pye 2008) was probably one of the first authors on

measure the particle dimensions this consisted on the obtaining of the length of the

tree axes perpendicular among each other (see figure 2) on the tree dimensions (where

agebgec) to obtain the sphericity (equation 1)

Krumbein (1941) develop a rapid method for shape measurement to determine the

sphericity this is done by measuring the longest (a) medium (b) and shorter (c) axes

diameters of the particle it can be seen in figure 2 (Always perpendicular among each

other) The radios ba and cb are located in the chart developed by his own where it

can be found the Intercept sphericity as he called (See figure 3) This chart is an easy

graphical way to relate the dimensions

c2

ba

Figure 2 Measurement of the 3 axes perpendicular among each other (Krumbein 1941)

Figure 3 Detailed chart to determining Krumbein intercept sphericity (Krumbein 1941)

(1)

6

Wadell (1932) defined the sphericity as the specific surface ratio (equation 2) Figure

4 is a schematic representation of the sphere surface and particle surface both particle

and sphere of the same volume

This way to obtain the sphericity is almost impossible to achieve as Hawkins (1993)

declares due the difficulty to get the surface area on irregular solids

Wadell (1934) also defined the sphericity based upon the particle and sphere volumes

as equation 3 (see figure 5)

Wadell (1934) used a new formula simple to manage using the diameters (see figure

6 and equation 4)

Zingg (Krumbein 1941) develop a classification based on the 3 axes relation in this

way it is easy to find out the main form of the particles as a disks spherical blades

S

s

3

CIR

P

V

V

CIR

SV

D

D

Figure 4 Same volume sphere surface (s) and particle surface (S) (modified after Johansson and Vall

2011)

Figure 5 Relation between the volume of the particle and the volume of the circumscribed

sphere (Johansson and Vall 2011)

Figure 6 Figure is showing the relation between the diameter of a circumscribed sphere and the

diameter of a sphere of the same volume as the particle (Johansson and Vall 2011)

(2)

(3)

(4)

7

and rod-like this is summarized on figure 7 Zinggrsquos classification is related with

Krumbein intercept sphericity and the figure 3

In figure 8 the figures 3 and 7 are combined the relation in the two classifications can

be seen it is an easy way to understand the morphology regarding on the a b and c

dimensions

Pye and Pye (1943) in the article ldquosphericity determinations of pebbles and sand

grainsrdquo compare the Wadellrsquos sphericity developed in 1934 (based on the diameter)

with ldquoPebble sphericityrdquo based on an ellipse this last equation (number 5) appears

two years early published by Krumbein (1941) Axis measurement is done as figure 1

denotes for equations 5 trough 12 with exception of equation 8 where the original

document was not possible to obtain

32a

cb

Figure 7 Zinggrsquos classification of pebble shape based on ratios ba and cb (Krumbein 1941)

Figure 8 Classification made by Zinggrsquos and chart to determine sphericity (Krumbein and Sloss 1963)

(5)

8

Sneed amp Folk in (1958) found a relation between the tree dimensional axes called

ldquoMaximum Projection Sphericityrdquo

In a similar way Ashenbrenner (1956) showed his equation at that time named

ldquoWorking Sphericityrdquo

Form or shape factor names are used by authors like Corey (shape factor eq 8) in the

paper published on 1949 Williams (shape factor eq 9) in 1965 Janke (form factor

eq 10) in 1966 and Dobkins amp Folk (oblate-prolate index eq 11) in 1970 (Blott and

Pye 2008)

Aschenbrenner (1956) develop the shape factor by using the relation of the tree axis

but the square of the middle one

3

2

ba

c

))ab((1)bc(16))ab((cb)(11

)ab()bc( 128

22

3 2

ab

c

acb when 1ac

b acb when

b

ac-1 2

22

2

3

cba

c

222

a

c

50c-a

b-a10

2b

ac

(6)

(7)

(8)

(9)

(10)

(11)

(12)

9

Table 2 General overview over different particle shape definitions for 3D sphericity has been compiled

and arranged chronologically

Aspect Name Author Year Based on

Sphericity (3D) Flatness index Wentworth 1922a 3-axes

True Sphericity Wadell 1932 Surface

Operational sphericity Wadell 1932 Volume

Sphericity Wadell 1934 Sphere diameter

Zinggrsquos clasification Zinggrsquos1

1935 3-axes

Intercept sphericity chart Krumbein 1941 3-axes

Pebble sphericity Pye and Pye 1943 3-axes

Corey shape factor Corey2

1949 3-axes

Working sphericity Ashenbrenner 1956 3-axes

shape factor Ashenbrenner 1956 3-axes

Maximum projection sphericity Sneed amp Folk 1958 3-axes

Williams shape factor Williams2

1965 3-axes

Janke form factor Janke2

1966 3-axes

Oblate-prolate index Dobkins amp Folk 1970 3-axes 1) Krumbein and Sloss 1963 2) Blott and Pye 2008

34 FORM (2D)

The technique to measure the sphericity is based in tree dimensions it can be found in

literature some ways to measure the ldquotwo dimensions sphericityrdquo which is simply the

perimeter of the particle projection some authors named ldquoparticle outlinerdquo or

ldquocircularityrdquo

Wadell in 1935 (Hawkins 1993) adopt a conversion of his 1934 3D sphericity

formula (equation 4) to a 2D outline He defined an orientation on the particles and

they were based on the maximum cross sectional area (outline of the particle

projecting the maximum area) The equations show the relation between diameters of

a circle of same area and smallest circumscribed circle

He also used the term ldquodegree of circularityrdquo as the ratio of the perimeter of a circle of

same area and the actual particle perimeter

Tickell in 1931 (Hawkins 1993) used his empirical relation The particle orientation

proposed was a random one It is described by the ratio between the area outline and

the area of smallest circumscribed circle

C

A

D

DC

P

PC C

CA

AC

(13)

(14)

(15)

10

Some other authors has been working with the ldquocircularityrdquo concept and had develop

them own equations as Pentland (1927) relating the area outline and area of a circle

with diameter equal to longest length outline and Cox (Riley 1941) with the ratio

area and perimeter time a constant equations 16 and 17 respectively Both authors did

not define any definite orientation of the grains

Riley (1941) realize the problems that an area perimeter and some other

measurements proposed by the above authors can carry as the time consuming and

tedious work (at that time were not computer all was made by hand) and thatrsquos why

he develop this equation easy to handle called ldquoinscribed circle sphericityrdquo He used

the same particle orientation proposed by Wadell and the relation of diameters of

inscribed and circumscribed circles

Horton 1932 (Hawkins 1993) use the relation of the drainage basing perimeter and

the perimeter of a circle of the same area as drainage basin

Janoo in 1998 (Blott and Pye 2008) develop his general ratio of perimeter to area

Sukumaran and Ashmawy (2001) develop his own shape factor (SF) defined as the

deviation of the global particle outline from a circle Figure 9 can be used as a

reference to determine the items used in the equation 21

N is referred to the number of sampling intervals o radial divisions

C2A

AC

2P

A4C

C

I

D

DC

CD

D

P

PC

A

PC

2

45ordm x N

Particleα

= SF

sumN

1=ii

(16)

(17)

(18)

(19)

(20)

(21)

11

Table 3 General chronological overview of the particle shape definitions for 2D sphericity

Aspect Name Author Year Based on

Circularity (2D) roundness Pentland 1927 area

roundness Cox1

1927 area-perimeter

roundness Tickell2

1931 area

Circularity Horton2

1932 drainage basin

outline circularity Wadell 1935 Circle diameter

degree of circularity Wadell 1935 Perimeter

inscribed circle sphericity Riley 1941 Circle diameter

Circularity Krumbein and Sloss 1963 chart

Janoo 1998 area-perimeter

Shape factor Sukumaran 2001 Segmentation of particle and angles

1) Riley 1941 2) Hawkins 1993

35 ROUNDNESS OR ANGULARITY

Roundness as described in section 32 is the second order shape descriptor Sphericity

lefts beside the corners and how they are this was notice by most of the authors sited

before and they suggested many ways to describe this second order particle property

Roundness is clearly understandable using the figure 10 Particle shape or form is the

overall configuration and denotes the similarities with a sphere (3D) or a circle (2D)

Roundness is concerning about the sharpness or the smoothness of the perimeter (2D)

Surface texture (Barret 1980) is describe as the third order subject (form is the first

and roundness the second) and it is superimposed in the corners and it is also a

property of particles surfaces between corners

Figure 9 Description of the Sukumaran factors to determine the shape and angularity (Sukumaran and

Ashmawy 2001)

12

Wadell (1935) describes his methodology calling it total degree or roundness to

obtain the roundness of a particle using the average radius of the corners in relation

with the inscribed circle diameter (see figure 11) on the equation

In the same study Wadell (1935) has used the equation

This two last equation shows slightly differences on the results (Wadell 1935)

Powers (1953) also published a graphic scale to illustrate the qualitative measure

(figure 12) It is important to highlight that any comparing chart to describe particle

properties has a high degree of subjectivity Folk (1955) concludes that when charts

are used for classification the risk of getting errors is negligible for sphericity but

large for roundness

N

R

r

Rinmax

r

R

NR

inmax

Figure 10 Form (shape) Roundness and Texture graphical description (Bowman et al 2001)

Figure 11 Wadellrsquos method to estimate the roundness corners radius and inscribed circle

(Hawkins 1993)

(22)

(23)

13

Some authors as Russel amp Taylor in 1937 Pettijohn in 1957 and Powers in 1953

developed a classification based on five and six classes (Hawkins 1993) each one

with its own class limits it is important to denote that the way they measure the

roundness is the developed by Wadell (1935) This classification and class limits are

showed in the table 4

Table 4 Degrees of roundness Wadell Values (Hawkins 1993) NA = no-applicable

Grade terms Russell amp Taylor (1937) Pettijohn (1957) Powers (1953)

Class

limits (R)

Arithmetic

midpoint

Class limits

(R)

Arithmetic midpoint Class

limits (R)

Arithmetic

midpoint

Very angular

NA

NA

NA

NA

012-017

014

Angular

000-015

0075

000-015

0125

017-025

021

Subangular

015-030

0225

015-025

0200

025-035

030

Subrounded

030-050

0400

025-040

0315

035-049

041

Rounded

050-070

0600

040-060

0500

049-070

059

Well rounded

070-100

0800

060-100

0800

070-100

084

Krumbein and Sloss (1963) published a graphical chart easy to determine the

sphericity and roundness parameters using comparison See figure 13 (Cho et al

2006)

Figure 12 A Roundness qualitative scale (Powers 1953)

Figure 13 Sphericity and roundness chart (Cho et al 2006) The roundness equation that appears here in

the chart is the wadellrsquos equation number 22

14

Fischer in 1933 (Hawkins 1993) used a straightforward method to quantify roundness

using a central point in the outline and dividing the outline in angles around this point

that were subtended by the straight or non curved parts of the profile were measured

This is illustrated in figure 14

To express the angularity value Fischer used the ratio of angles standing linear parts

on the outlines and concave respectively

Figure 14 left (A) and right (B) gives a similar angularity of approximately 042

using the above equations (Hawkins 1993)

Wentworth in 1922 used the maximum projection to define the position of the particle

to obtain the outline or contour (Barret 1980) The equation reflects the relation of the

diameter of a circle fitting the sharpest corner and the longest axis plus the shortest

axis c (minimum projection)

Wentworth (Hawkins 1993) expressed the roundness as the ratio of the radius of

curvature of the most convex part and the longest axis plus short axis

Actually these last two equations are the same just expressed in different terms when

the particle is in its maximum projection

Dimensions can be seen on figure 15 L and B represents the mayor axis a and

intermediate axis b The intention is to make difference between the 2 and 3

dimensions (L and B are for 2D as a b and c are for 3D)

deg360

ANG

=R

sumPLA

PLA

CON

ANG

ANGR

2)S(L

DR

M

S

B)4(L

RR CON

Figure 14 Fischerrsquos methods of angularity computation (Hawkins 1993)

A=inscribed circle B=circumscribed circle

(24)

(25)

(26)

(27)

15

Wentworth 1919 has a second way to express the roundness called Shape index

(Barrett 1980) and it relates the sharpest corner and the diameter of a pebble trough

the sharpest corner

Wentworth (1922b) used define the roundness as the ratio of the sharpest corner and

the average radius of the pebble

Cailleux (Barrett 1980) relates the radius of the most convex part and the longest

axis

Kuenen in 1956 show his roundness index (Barrett 1980) between the sharpest corner

and the breath axis

Dobkins amp Folk (1970) used a modified Wentworth roundness with the relation of

sharpest corner and inscribed circle diameters

AVG

CON

R

RR

x

s

D

DR

L2

RR CON

B

DR s

i

s

D

DR

3AVGAVG cbaDR2

Figure 15 Description of L and B axes (Hawkins 1993)

(28)

(29)

(30)

(31)

(32)

(33)

16

Swan in 1974 shows his equation (Barrett 1980) relating the sharpest (or the two

sharpest) corner(s) and inscribed circle diameter

Szadeczsky-Kardoss has his Average roundness of outline (Krumbein and Pettijohn

1938) relating the concave parts perimeter and the actual perimeter

Lees (1964a) developed an opposite definition to roundness it means that he

measures the angularity instead of the roundness and he calls it Degree of angularity

Figure 16 shows the items considered when equation 36 applies as the angles (α)

inscribed circle (Rmax-in) and the distance (x) The main formula is

In order to apply the last equation corners needs to be entered in the formula and each

individual result will add to each other to obtain the final degree of angularity

A roundness index appears on Janoo (1998) Kuo and Freeman (1998a) and Kuo et

al (1998b) it is described as

The last equation is on section 34 also because there is not a general agreement on the

definition furthermore some authors had used to define the roughness this is not the

only equation that has been used trying to define different aspects (sphericity

roundness or roughness) but it is a good example of the misuse of the quantities and

definitions

inmaxR

x)180(R

2P

A4R

i

ss

D

DDR

221

100P

PR CON

Figure 16 Degree of angularity measurement technique (Blot and Pye 2008)

(34)

(35)

(36)

(17)

17

Sukumaran and Ashmawy (2001) present an angularity factor (AF) calculated from

the number of sharpness corners Angles βi required to obtain the angularity factor are

shown in figure 9

Sukumaran and Ashmawy (2001) also suggested use not bigger sampling interval of

N=40 because it is the cut off between angularity factor and surface roughness If so

this equation could be used to describe the roughness

Table 5 General chronological overview of the particle roundness

Aspect Name Author Year Based on

Roundness shape index Wentworth 19191

diameter of sharper corner

shape index Wentworth 1922b sharpest corner and axis

roundness Wentworth 1933 convex parts

Fischer 19332

noncurved parts outline

Fischer 19332

noncurved-streigth parts outline

Average roundness of outline

Szadeczsky-Kardoss 19333

convex parts-perimeter

roundness Wadell 1935 diameter of corners

roundness Wadell 1935 diameter of corners

roundness Russel amp Taylor 19372

class limit table

roundness Krumbein 1941 chart

Cailleux 19471

convex parts

roundness Pettijohn 19494 class limit table

roundness Powers 1953 chart and class limit table

Kuenen 19561

axis-convex corner

roundness Krumbein and Sloss 1963 chart

degree of angularity Lees 1964a corners angles and inscribed circle

Dobkins amp Folk 1970 diameter of sharper corner

Swan 19741

diameter of sharper corners

Angularity factor Sukumaran and

Ashmawy 2001

Segmentation of particles and angles

1) Barret 1980 2) Hawkins 1993 3) Krumbein and Pettijohn 1938 4) Powers 1953

sum

sumsumN

1=i

2

i

2

N

1=i

2

i

2N

1=ii

)ordm180 -circleβ( - )(180ordm x 3

)ordm180-circleβ(-)ordm180 -Particleβ(

= AF (37)

18

36 ROUGHNESS OR SURFACE TEXTURE

A third property called texture appears early in the literature with the sphericity and

roundness properties since then texture property was longed described but it was in

accordance with the authors at that time not measurable

Wright in 1955 developed a method to quantify the surface texture or roughness of

concrete aggregate using studies done on 19 mm stones The test aggregates were first

embedded in a synthetic resin The stones were cut in thin sections The sections

projection was magnified 125 times The unevenness of the surface was traced and the

total length of the trace was measured The length was then compared with an uneven

line drawn as a series of chords (see figure 17) The difference between these two

lines was defined as the roughness factor (Janoo 1998)

However with the advance of technology it has become easier measure the roughness

and here is presented some researcherrsquos ideas how this property should be calculated

One technique used by Janoo (1988) to define the roughness can be seen in figure 18a

and is defined as the ratio between perimeter and convex perimeter

The convex perimeter is obtained using the Feretrsquos box (or diameter) tending a line in

between the touching points that the Feretrsquos box describes each time it is turn (figure

18b)

PER

OC

PR

Figure 17 Measurement method for characterizing the surface texture of an aggregate (Janoo 1998)

a) Convex perimeter (CPER) b) Feret measurement Figure 18 a) Convex perimeter (CPER) b) Feret measurement (modified after Janoo 1998)

(38)

a)

b)

19

Kuo and Freeman (1998a) and Kuo et al (1998b) use the roughness definition as the

ratio perimeter and average diameter

Erosion and dilatation image processing techniques are used to obtain the surface

texture Erosion is a morphological process by which boundary image pixels are

removed from an object surface which leaves the object less dense along the

perimeter or outer boundary Dilatation is the reverse process of erosion and a single

dilatation cycle increases the particle shape or image dimension by adding pixels

around its boundary (Pan etal 2006)

The ldquonrdquo erosion and dilatation cycles are not standardized

Mora and Kwan (2000) used the ldquoconvexity ratio CRrdquo (equation 41) and the ldquofullness

ratio FRrdquo (equation 42) in their investigation they are

The convex area is the area of the minimum convex boundaries circumscribing the

particle This is illustrated in the figure 19 The convex area is obtained in a similar

way as the convex perimeter but in this case the area between the original outline and

the convex perimeter is our convex area

AVG

OD

PR

100A

1AARO

CONo A

AR =

CONo A

AR =

Figure 19 Evaluation of area and convex area (Mora and Kuan 2000)

(39)

(40)

(41)

(42)

20

4 TECHNIQUES IN ORDER TO DETERMINE PARTICLE

SHAPE

41 HAND MEASUREMENT

Hand measurement technique was the first used by obvious reasons in order to

improve the accuracy special devices developed as the ldquosliding rod caliperrdquo used by

Krumbein (1941) it works placing the sample on the sliding road calliper as show

figure 20b the length in different positions can be obtain by using the scale provided

in the handle the ldquoconvexity gagerdquo that was actually used by opticians to measure the

curvature of lenses but easily applicable to the particle shape analysis (Wentworth

1922b) works measuring the movement of the central pivot as figure 20a shows (the

two adjacent pivots are invariable) as many the central pivot moves more is the

curvature or the ldquoSzadeczky-Kardossrsquos apparatusrdquo develop in 1933 that traces the

profile of the rock fragment so the outline traced is then analyzed (Krumbein and

Pettijohn 1938) figure 20c show equipment

Another helpful tool to determine the particle dimensions was the ldquocamera lucidardquo to

project the particlersquos contour over a circle scale appearing in Figure 21 thus it is

possible to measure the particlersquos diameter

a)

c) b)

Figure 20 a) convexity gage used to determine the curvature in particle corners (Wenworth 1922b)

b)sliding rod caliper device to measure the particle axis length (Krumbein 1941) and c)Szadeczky-

Kardoss (1933) apparatus it was utilized to obtain the particle outline

Figure 21 Circle scale used by Wadell (1935) to determine particlersquos diameter and roundness

21

42 SIEVE ANALYSIS

Bar sieving eg according to EN 933-31997 can be used to determine simple large

scale properties By combining mesh geometries the obtained results can be used to

quantify flakiness and elongation index ASTM D4791 (Flat and elongated particles

are defined as those coarse aggregate particles that have a ratio of length to thickness

equal to or greater than a specified value such as 51 The index represents the

percentage on weight of these particles) The method is not suitable for fine materials

This due to the difficulty to get the fine grains passed through the sieve and the great

amount of particles in relation to the area of the sieve (Persson 1998) eg EN 933-

31997 related to flakiness index The test is performed on aggregates with grain size

from 4 mm and up to 63 mm two sieving operations are necessary the first separates

on size fraction and the second use a bar sieve after the first sieving the average

maximum diameter of the particles is obtain and with the second sieving (bar sieving)

the shortest axis diameter is found finally with this two parameters the flakiness

index is determined

There are more standards related with the particle shape (see appendix A) but this

above presented are probably the most known using sieve analysis to determine

particlersquos geometrical properties

Sieve analysis is facing the computers age and image analysis sieving research is

taking place (Andersson 2010 Mora and Kwan 2000 Persson 1998) Industry is

also applying the image analysis sieving with decrees on the testing time compare

with the traditional sieving method An inconvenient of image analysis is the error

due the overlapping or hiding of the particles during the capture process but the

advantages are more compare with disadvantages (Anderson 2010)

43 CHART COMPARISON

Charts developed over the necessity of faster results because the long time consuming

required when measuring each particle

Krumbein (1941) present a comparison roundness chart for pebbles which were

measured by Wadellrsquos method because this property was the most difficult to measure

due to the second order scale that roundness represents (See figure 22)

Figure 22 Krumbein (1941) comparision chart for roundness

22

A qualitative chart by Powers (1953) try to include both (sphericity and roundness)

particlersquos characteristics it was divided on six roundness ranges (very angular

angular sub-angular sub-rounded rounded and well rounded) and two sphericity

series (high and low sphericity) This chart was prepared with photographs to enhance

the reader perspective (See figure 23)

A new chart including sphericity and roundness appear this time it was easier to

handle the two mean properties of particlersquos shape furthermore there was included

the numerical values that eliminated the subjectivity of qualitative description The

chart is based on Wadellrsquos definitions (Krumbein and Sloss 1963) (See figure 24)

Folk (1955) worried about the personrsquos error on the chartrsquos comparison studied the

determination of sphericity and angularity (he used the Powers 1953 comparison

chart) he found that the sphericity determination by chart comparison has a negligible

error while the roundness he concluded it was necessary to carry out a more wide

research due the high variability show by his study

Figure 23 Powers (1953) qualitative shpericity-roundness chart

Figure 24 Sphericity-roundness comparison chart (Krumbein and sloss 1963)

23

44 IMAGE ANALYSIS

Image analysis is a practical method to use for shape classification since it is fast and

can be automated Different techniques appear to process these images among them

are

o Feret Diameter the Feret diameter is the longitude between two parallel lines

this lines can rotate around one particle or outline to define dimensions as it

is shown in figure 25 these method is not a fine descriptor but as it was say

above it is a helpful tool to determine diameters (Janoo 1988)

o Fourier Mathematical Technique It produces mathematical relations that

characterize the profile of individual particles This method favours the

analysis of roughness and textural features for granular soils The problem in

the methodology remains in the re-entrant angles in order to complete the

revolution (Bowman et al 2001) see figure 26

o Fractal Dimension Irregular line at any level of scrutiny is by definition

fractal (Hyslip and Vallejo 1997) Figure 27 shows fractal analysis by the

dividing method The length of the fractal line can be defined as

N

1n

nn0 )nsinbncosa(a)(R

RD1n)(P

Figure 25 Feret measurement technique is defined by two parallel lines turning

around the particle to define the shortest and longest Feret diameter (Janoo 1988)

Figure 26 Fourier technique with two radiuses at one angle (Bowman et al 2001)

(43)

(44)

24

o Orthogonal image analysis This technique is basically the use of two images

orthogonal between them to acquire the three particle dimensions (Fernlund

2005) any of the above techniques can be used in this orthogonal way

o Laser Scanning Technique this kind of laser scanning 3D is one of the most

advanced techniques In figures 28a) we have the laser head scanning the rock

particles the particles have control points in order to keep a reference point

when move them to scan the lower part in figure 28b) we can see the laser

path followed (Lanaro and Tolppanen 2002)

Another technique is the Laser-Aided Tomography (LAT) in this case a laser sheet is

used to obtain the particles surveying (see figure 29) This technique is different and

has special requirements as to use liquid with same refractive index as the particles

particles must let the laser or certain percent of light go through (Matsushima et al

2003)

a) b)

Figure 27 Fractal analysis by the dividing method at different scrutiny scale (Hyslip and Vallejo 1997)

Figure 28 a) Scanning head b) scanning path (Lanaro and Tolppanen 2002)

Figure 30 3D scan completed ready to

use for any further measure

(Matsushima et al 2003)

Figure 29 LAT scaning particles

(Matsushima et al 2003)

25

Both 3D techniques obtain the particle shape that is later used to achieve measures as

we can see in figure 30

All these previous techniques are easily written in codes or scripts to be interpreted in

a digital way obtaining the desired measurement but there are some interesting points

in the image analysis regarding on the errors involve among them are image

resolution and orientation of the particles orientation is not relevant when it is

random and large number of particles are involve resolution have an influence on the

accuracy (Zeidan et al 2007)

When resolution is increase more accuracy is obtain and the object representation

match better with the real form in the other hand more resolution means more

spending on memory and time thus resolution needs to be according with the goal

and precision needed in any work (Schaumlfer 2002)

Schaumlfer (2002) conclude that attributes like length when measuring digital images

present relative high errors It can be vanish or at least diminish using high resolution

just for diameter but not for perimeter that keep the error as big as initially Johansson

and Vall (2011) obtain similar results when 3 different resolutions were used in the

same particle obtaining an unstable output for those termsquantities that involve the

perimeter Thus all quantities relating the perimeter should be treated with care

5 EFFECT OF SHAPE ON SOIL PROPERTIES

51 INTRODUCTION

In laboratory test on the effect on particle size on basic properties has been

investigated in several studies this relation has been discussed and various

mechanisms had been proposed to explain the behaviour of the soil in dependency

also with the shape Basically there are two mechanisms proposed The arrangement

of particles and the inter-particle contact (Santamarina and Cho 2004) and

subsequence breakage

The arrangement of particles

Arrangement of the particles can be presented in three different forms loose dense

and critical this arrangement determines the soil properties (eg density increase with

more dense arrangement) Loose and dense states are easy understandable when

figure 31 is explained while in the upper part of the figure the particles are arranged

using the minimum space needed in the lower part a span is created using the flaky

particle as a bridge this phenomena is known as ldquobridgingrdquo Bridging can produce

different geotechnical results when just the shape of the particle is changed eg void

ratio (Santamarina and Cho 2004) Particles are able to rearrange this could be done

applying pressure (energy) to the soil the pressure (energy) will create such forces

that soil particles will rotate and move (see figure 34) finishing in a more dense state

26

A loose soil will contract in volume on shearing and may not develop any peak

strength (figure 32 left) In this case the shear strength will increase gradually until

the residual shear strength is revealed once the soil has ceased contracting in volume

A dense soil may contract slightly (figure 32 right) before granular interlock prevents

further contraction (granular interlock is dependent on the shape of the grains and

their initial packing arrangement) In order to continue shearing once granular

interlock has occurred the soil must dilate (expand in volume) As additional shear

force is required to dilate the soil a peak shear strength occurs (figure 32 left) Once

this peak shear strength caused by dilation has been overcome through continued

shearing the resistance provided by the soil to the applied shear stress reduces

(termed strain softening) Strain softening will continue until no further changes in

volume of the soil occur on continued shearing Peak shear strengths are also

observed in overconsolidated clays where the natural fabric of the soil must be

destroyed prior to reaching constant volume shearing Other effects that result in peak

strengths include cementation and bonding of particles The distinctive shear strength

called the critical state is identified where the soil undergoing shear does so at a

constant volume (Schofield and Wroth 1968)

The inter-particle contact

For frictional soil ie coarse grained soil the friction between particles is the

dominating factor for strength Materials usually consisting of coarse grains (diameter

Figure 31 Bridging effect when flaky particles are combined in the bulk material (Santamarina and

Cho 2004)

Figure 32 The left part of the figure show a typical behaviour of loose and dense material over shear stress

while at the right the figures illustrate the typical volume changes

27

gt 006mm) behave as a frictional soil it means that the strength of coarse soils (silt

sand gravel etc) comes from an inter-particle mechanical friction thus ideally they

do not have traction strength In figure 33 the inter-particle contact is illustrated here

the pressure (P) is applied and two more components are found the normal load (N)

and the tangential load (T) described as the friction coefficient (μF) The forces stand

in equilibrium (Johansson and Vall 2011)

When particles equilibrium is disturbed (friction coefficient is not enough to keep

particles unmoved) the rotation is imminent and it is necessary in order to compact

the soil in figure 34 can be seen that the arrangement is a fact that inhibit or allow this

rotation and the shape in the 3 different scales are also factors because the more

spherical andor more rounded andor less roughness more easy is the rotation

(Santamarina and Cho 2004)

Breakage

Breakage is a side effect of the inter-particle contact and rotation when pressure

exceed the rock strength it can happened when the particles are tight together and

there is not enough space to rotate it is more obvious in angular particles (mesh form)

or as in figure 31 where the flaky particle ldquobridgingrdquo is not able to rotate but it can

brake by the pressure increase Yoginder et al (1985) notice that the angular particle

break during his experiments and they turn more rounded changing the original size

and form configuration at the same time there was a soil properties loosening

Figure 33 Inter-particle contact and forces acting (Axelsson 1998)

Figure 34 Rotation inhibition by the particles compaction or low void ratio (Santamarina and Cho 2004)

28

52 INFLUENCE OF SIZE AND SHAPE

Wenworth (1922a) and Pellegrino (1965) among others suggest that agent transport of

the rocks (rigor of transport temperature and moisture changes etc) determine its

shape but also the particle genesis itself (rock structure mineralogy hardness etc) It

is not possible to determine the shape of the particles based on the agent transport or

genesis but generally a shape behaviour is expected according to Mitchell and Soga

(2005) specially when the particle size is in the clay size (gt2μm) The shapes of the

most common clay minerals are platy (figure 35) with some exceptions (eg

halloysite occurs as tubes kaolinite are large thick and stiff Smectites are composed

of small very thin and filmy particles Illites are intermediate between kaolinite and

smectite and attapulgite occurs in lathlike particle shapes) Some clay minerals

photographs are presented in figure 35

Figure 35 Clay mineral shape a) hallosite b) Kaoline c) Smactites d) Illites and e) attapulgite (Modified

from Mitchell and Soga 2005)

Figure 36 Particle size range in soils Generally the particles of clay size are plate shaped (Mitchell and

Soga 2005)

a) b) c)

e) d)

29

53 VOID RATIO AND POROSITY

The void ratio (e) is the ratio of the volume of voids to the volume of solid it is

defined by the equation

Porosity (n) is the ratio of the volume of voids to the total volume of the soil it is

represented by the equation

Holubec and DrsquoAppolonia (1973) found a relation between the void ratio and

sphericity (referred in the paper as coefficient of angularity ratio of particle surface

and equivalent sphere surface) their results show that the maximum and the minimum

void ratio increases as the shpericity decreases In this study the surface was obtained

for an indirect method based on the permeability developed by Hoffman in 1959

described in the same document Rouseacute et al (2008) defined the roundness as

Wadell (1935) and he found it as an important factor controlling the minimum and

maximum void ratios Some other authors as Youd (1973) and Cho et al (2006)

conclude the same minimum and maximum void ratios increase when sphericity and

roundness decrease Another interesting result (all above authors) was the bigger

influence of the form (sphericity circularity) and roundness on the maximum void

ratio The change of the maximum void ratio is more pronounced than the change of

the minimum void ratio when the form and roundness changes (See figure 39)

Particles arrangement and interlocking are probably the factor that controls the void

ratio bridge effect permit the existence of void among the particles while interlocking

allowed the particles to form arches avoiding the possibility to rotate and stay in a

more stable configuration eg as it happens with marbles

Figures 36 37 and 38 shows proposed empirical relationships between void ratio and

shape from tables 5 and 6 (graphically the scale goes from 0 to 1 when cero mean

high angularity shpericity or circularity and one means low angularity circularity or

sphericity) Holubec and DrsquoAppolonia (1973) data was taken to obtain a power curve

and describe a tendency Santamarina and Cho (2004) show Youd equations in the

original paper Youd (1973) never presented the equation but it is easy to use the

information to draw a trend

The graphics presented in this document (figures 36 37 and 38) must be used with

certain reserves due the fact that the original data was modified in order to fit all

information in one graphic what the figures shows is just the general trend of the

behaviourrsquos material regarding on the shape If more accurate description and

information is required the author recommends consulting the reference data In the

same way equations from Holubec and DrsquoApollonia (1973) and Youd (1973) were not

presented by the authors but the use of the information was taken in order to build up

those equations on tables 6 and 7

S

V

V

V

= e

V

V

=nV

(45)

(46)

30

Table 6 Minimum void ratio equations regarding on the quantity (Ψ for sphericity C for circularity R

for roundness SF for Sukumaran shape factor and AF for Sukumaran angularity factor)

EQUATION NUMBER REFERENCE

Figure 34 (left)

4340

minΨ45490e =

47

Holubec amp DrsquoAppolonia 1973 (Ψ

was obtained using equation 2)

SF06340

mine021903180e +=

48

Sukumaran amp Ashmawy 2001 (SF

obtained using equation 21)

C05101emin

= 49

Cho etal 2006 (C obtained using

figure 12)

Figure 34 (right)

1

minR08203590e +=

50

Youd 1973 (R obtained from figure

11 and table 3)

R34080emin

= 51

Cho et al 2006 (R obtained using

figure 12)

1

minR05104330e +=

52

Rouseacute et al 2008 (R obtained by

equation 21)

AF02330

mine372004160e +=

53

Sukumaran amp Ashmawy 2001 (AF

obtained using equation 37)

Table 7 Maximum void ratio equations regarding on the quantity (Ψ for sphericity C for circularity R

for roundness SF for Sukumaran shape factor and AF for Sukumaran angularity factor)

EQUATION NUMBER REFERENCE

Figure 35 (left)

51520

max Ψ61120e = 54

Holubec and DrsquoAppolonia 1973 (Ψ

was obtained using equation 2)

SF1190

max e0016907180e += 55

Sukumaran amp Ashmawy 2001 (SF

obtained using equation 21)

C86061emax = 56

Cho etal 2006 (C obtained using

figure 12)

Figure 35 (right)

1

max R1505540e += 57

Youd 1973 (R obtained from figure

11 and table 3)

R62031emax= 58

Cho et al 2006 (R obtained using

figure 12)

1

max R107106150e += 59

Rouseacute et al 2008 (R obtained by

equation 21)

AF0530

max e12506090e += 60

Sukumaran amp Ashmawy 2001 (AF

obtained using equation 37)

Comparing figures 37 and 38 (minimum and maximum void ratio) it can be seen on

the right scheme of both figures 37 and 38 (when the factor is roundnessangularity)

that all the empirical relations has a common initial point close to 1 (it means that

particles are well rounded) while this common agreement disappear when the

roundness factor decreases (when the particles become more angular) Same figures

(37 and 38) on the left graphs (when the factor is sphericitycircularityshape) do not

present the same behaviour in fact there is more disperse initial point close to 1(when

the particles tend to be more sphericalcircular)

31

In Figure 39 the Δe (emax-emin) has been plotted to show how the maximum void ratio

and the minimum void ratio has different rate change when the particle shape

changes Maximum void ratio increases more than minimum void ratio when the

particle shape becomes less spherical andor more angular Comparing figure 39 left

and right graphics it can be seen that right present a common initial point when the

quantity (roundnessangularity) is close to one while in the left graphic the initial

point is more disperse Both ending points in both graphics (close to zero) are

dispersed

Figures 37 38 and 39 present the same behaviour right graphics (when the factor is

roundness angularity) in each figure have an initial common point while the left

graphics do not (when the factor is sphericity circularity shape)

Figure 37 Minimum void ratio based upon the relation of shape factor proposed by the authors indicated

in the figure

Figure 38 Maximum void ratio based upon the relation of shape factor proposed by the authors indicated

in the figure

04

06

08

1

12

14

16

18

2

005

015

025

035

045

055

065

075

085

095

Factor (roundness angularity)

min

imu

m v

oid

rati

o

Youd 1973 roundness

Rouse 2008 roundness

Cho 2006 roundness

Sukumaran 2001 AF

03

04

05

06

07

08

09

1

11

12

13

05

015

025

035

045

055

065

075

085

095

Factor (sphericity circularity shape)

min

imu

m v

oid

rati

oHolubec 1973 sphericity

Cho 2006 circularity

Sukumara 2001 SF

05

07

09

11

13

15

17

19

21

00

150

250

350

450

550

650

750

850

95

Factor (sphericity circularity shape)

Maxim

um

vo

id r

ati

o

Holubec 1973 sphericity

Cho 2006 circularity

Sukumara 2001 SF

05

1

15

2

25

3

35

005

015

025

035

045

055

065

075

085

095

Factor (roundness angularity)

Maxim

um

vo

id r

ati

o

Youd 1973 roundness

Rouse 2008 roundness

Cho 2006 roundness

Sukumaran 2001 AF

32

54 ANGLE OF REPOSE

The angle of repose of a granular material is the steepest angle of descent or dip of the

slope relative to the horizontal plane when material on the slope face is on the verge

of sliding as show in figure 40

According to Qazi (1975) there are five types of forces which may act between the

particles in soils

1 Force of friction between the particles

2 Force due to presence of absorbed gas andor moisture of particle

3 Mechanical forces caused by interlocking of particles of irregular shape

4 Electrostatic forces arising from friction between the particles themselves and

the surface with which they come in contact

5 Cohesion forces operating between neighbouring particles

Rouseacute et al (2008) found a decrease of angle of repose with increase roundness

based upon ASTM C1444 test (Standard Test Method for Measuring the Angle of

Repose of Free-Flowing Mold Powders) The method consist in pouring sand on a

surface cover by paper trough a funnel of specific dimensions (the nozzle diameter

depend on the sandrsquos particle size) from an altitude of 15 inches (381 mm) The sand

is release from the funnel until the peak of the cone formed by the sand stops the flow

The repose angle is obtained with the equation

H represent the 15 inches D and d represent the diameter of the cone formed by the

sand and the diameter of the funnel respectively

Figure 39 Maximum minus minimum void ratio based upon the relation of shape factor proposed by the

authors indicated in the figure

0

01

02

03

04

05

06

07

08

09

1

005

015

025

035

045

055

065

075

085

095

Factor (sphericity circularity shape)

Maxim

um

- M

inim

um

Vo

id r

ati

oHolubec 1973 sphericity

Cho 2006 circularity

Sukumara 2001 SF

0

02

04

06

08

1

12

14

16

18

005

015

025

035

045

055

065

075

085

095

Factor (roundness angularity)

Maxim

um

- M

inim

um

Vo

id r

ati

o

Youd 1973 roundness

Rouse 2008 roundness

Cho 2006 roundness

Sukumaran 2001 AF

dD

H2

tan=φ1

rep(61)

33

Rouseacute (2008) shows an empirical relation to obtain the angle of repose based on the

roundness of the particles

55 SHEAR STRENGTH

The MohrndashCoulomb failure criterion represents the linear envelope that is obtained

from a plot of the shear strength of a material versus the applied normal stress This

relation is expressed as

where τ is the shear strength σn is the normal stress co is the intercept of the failure

envelope with the τ axis and is the slope of the failure envelope The quantity c is

often called the cohesion and the angle is called the angle of internal friction

Studies show that the internal friction angle (under drained triaxial tests) increases

more rapidly on those materials having higher angularity increasing the relative

density The internal friction angle is a function of the relative density and the particle

shape (Holubec and DrsquoAppolonia 1973)

Chan and Page (1997) found in a study made with dry copper (using different shapes

and sizes ranging from 180 to 106 μm) using a direct shear test (ring share test) that

the internal friction angle increases as the angularity increases

Shinohara et al (2000) did some experiments with steel powder different shapes

using a triaxial cell in the test Shinohara never used the roundness or angularity on

the work but apply the shape factor (relation long axisshort axis) and the results were

that as this relation deviate from factor 1 the internal friction angle increases

The following empirical relations were found in the literature showing the behaviour

of the friction angle (obtained under different conditions)

)tan( noc

Figure 40 Representation of the angle of repose

(63)

(62)

34

Cho et al (2006)

(64)

(R is obtain by comparing the Krumbein chart figure 13)

Rouseacute (2008)

(65)

(66)

(R is defined using Wadell equation 22)

In figure 41 the suggested empirical relations above and lines constructed using

author data from Holubec and DrsquoAppolonia (1973) and Sukumara and Ashmawy

(2001) are plotted together to display the general trend on the particle shape and

friction angle relation Sukumaran reports two lines one based on the shape factor

(SF) and the second referring the angularity factor (AF) Sukumaran performed the

tests at constant volume

The scale used for Holubec and DrsquoAppolonia (1973) have lower and upper limits of 1

and 2 respectively (angularity form) and a scale change was applied to be able to

presented in the actual figure 41 As in the previous section (52) the author

recommend to use the original data from the references due that the figure just follows

the general trend of the behaviourrsquos particle regarding on the shape

Figure 41 The changes on the internal friction angle shows a general increase when the particle roundness

becomes angular or in the case of Sakamuran less spheric (Shape factor SF)

35

Barton and Kjaernsli (1981) suggested a model (equation 67) to predict the peak

friction angle (φrsquo) based upon numerous trixial and direct shear data tests

where

Se equivalent strength of particle

Re equivalent roughness of particle

φb basic friction angle (obtained from basic tilting test)

σn normal load

The information required for the model is (1) the uniaxial compressive strength of the

rock (2) the d50 particle size (mesh size where 50 of the particles pass through)

required to define Se (figure 42) (3) the degree of particle roundness and (4) the

porosity following compaction All data can be estimated by simple index tests

Barton and Kjaernsli (1981) suggest that particle size and sample scale has an effect

on the friction angle and includes them to obtain the equivalent strength (Se) figure 42

shows the method to obtain this value Compressive strength (σc) was chosen to be the

factor affecting the scale because micro fractures influence this property while

samples are bigger more micro fractures contain and its compressive strength reduces

The equivalent roughness is obtain using figure 43 where is required to know the

porosity (n) and the origin of the particles (a small chart is provided in the same figure

to compare the particles profile)

b

n

ee

SLogR

Figure 42 Method of estimating Equivalent Strength (Se) of rockfill based on uniaxial compressive strength

(σc ) and d50 particle size (Barton amp Kjaernsli 1981)

(67)

36

56 SEDIMENTATION PROPERTIES

A particle released in a less dense Newtonian fluid initially accelerate trough the fluid

due to the gravity Resistances to deformation of the fluid transmitted to the particle

surface drag generate forces that act to resist the particle motion The force due to the

weight (Fw) can be written as

Where ρp ρ are density of the particle and fluid (water) respectively g is the

gravitational force and Vp is the volume of the particle

And the resistance force (FD) is

Where CD is the dimensionless drag coefficient W is the weight of the particle and A

is the cross section area

Particlersquos shape has been assumed to be spherical when equations are applied on the

settling velocity Correlation deviates when particle shape departs from spherical form

Figure 43 Method of estimating Equivalent Roughness (Roe) based on porosity of rockfill

origin material degree of roundedness and smoothness of particle (Barton amp Kjaernsli 1981)

PPW ρ)gV(ρF

A2

WρCF

2

DD

(68)

(69)

37

(Dietrich 1982) and it is known that natural particles depart from spherical form

thus it is evident that this departure would have consequences

The below equation is proposed to account the shape (in this case the Corey shape

factor equation 8) in the settling velocity (Jimenez and Madsen 2003)

Jimenez and Madsen (2003) Dietrich (1982) Briggs and McCulloch (1962) and

others were working in the hydraulic shape of particles to solve problems as sediment

transport It is obvious that the equation presented and the researcherrsquos investigation

works under certain conditions (eg grain size between 0063-1 mm)

Dietrich (1982) suggests an empirical relation that accounts settling velocity size

density shape and roundness of a particle

R1 R2 and R3 are fitted equations for size and density shape and roundness

respectively

57 HYDRAULIC CONDUCTIVITY PERMEABILITY

Darcyrsquos Law Permeability is one component of Darcyrsquos law Darcys law is a simple

proportional relationship between the instantaneous discharge rate through a porous

medium the viscosity of the fluid and the pressure drop

The total velocity Ve is equal to the product of the permeability of the medium

(porous media) k the pressure drop ∆p all divided by the viscosity μ (Muskat

1937)

Darcys law is only valid for slow viscous flow most groundwater flow cases fall in

this category Typically Darcyrsquos law is valid at any flow with laminar flow (see figure

44)

Reynoldrsquos number (Laminar and turbulent Flow) Typically any laminar flow is

considered to have a Reynoldrsquos number less than one and it would be valid to apply

Darcys law Experimental tests have shown that flow regimes with Reynolds numbers

1

ND

S

S

ZY

gd1s

WW

NDN

gd)1s(4

dS

2R1R

3 10RW

pk

Ve

(70)

(71)

(72)

(73)

38

up to 10 may still be Darcian (laminar flow) as in the case of groundwater flow The

Reynolds number (a dimensionless parameter) for porous media flow is typically

expressed as

where ρ is the density of water (units of mass per volume) υ is the specific discharge

(with units of length per time) d is a representative average grain diameter for the

porous media (often taken as the 30 passing size from a grain size analysis using

sieves - with units of length) and μ is the viscosity of the fluid (Muskat 1937)

Shape effects Permeability as Head and Epps (2011) suggested is affected by the

shape and texture of soil grains Elongated or irregular particles create flow paths

which are more tortuous than those spherical particles Particles with a rough surface

texture provide more frictional resistance to flow Both effects tend to reduce the

water flow through the soil

Kozeny-Carman empirical relation accounts for the dependency of permeability on

void ratio in uniformly graded sands serious discrepancies are found when it is

applied to clays due the lack of uniform pores (Mitchell and Soga 2005)

There are various formulations of the Kozeny-Carman equation one published by

Head and Epps (2011) takes the void ratio e the specific surface area Ss and an

angularity factor F into account of permeability k

The angularity factor F considers the shape of the particles and ranges from 11 for

rounded grains 125 for sub rounded to 14 for angular particles The specific surface

Ss is defined as

d1 and d2 represent the maximum and minimum size particle in mm

Kane amp Sternheim (1988) suggest that the inclusion of the shape factor (F) has

probably the background on the Reynolds number due this factor is dependent

significantly on the shape of the obstacles and Reynolds number determines the

presence of laminar or turbulent flow Figure 44 show how the laminar flow has low

energy dissipation while turbulent flow (eg the roughness and path tortuosity) has

high energy dissipation

e1

e

FSs

2k

3

2

dRe

21

6

ddSs

(74)

(75)

(76)

39

According to Nearing and Parker (1994) the amount of soil detached during laminar

and turbulent flow is dependent on each soil and also greater on turbulent flow due the

greater shear strength generated during this kind of flow this could suggest the

greater erosion when turbulent flow is present

58 LIQUEFACTION

Soil liquefaction is a phenomenon in which soil loses much of its strength or stiffness

for a generally short time by earthquake shaking or other rapid loading Static and

dynamic liquefactions occur been the second one the most regular known

Liquefaction often occurs in saturated soils that is soils in which the space between

individual particles is completely filled with water This water exerts a pressure on the

soil particles that influences how tightly the particles themselves are pressed together

Shaking or other rapid loading can cause the water pressure to increase to the point

where the soil particles can readily move with respect to each other (Jefferies and

Been 2000)

Jefferies and Been (2000) state that it is clear that minor variation in intrinsic

properties of sand have major influence on the critical state These might be variations

on grain shape mineralogy grain size distribution surface roughness of grains etc

Yoginder et al (1985) found that substantial decrease on liquefaction resistance

occur with increase in confining pressure for rounded and angular sands (1600 kPa)

also rounded sands show an rapidly build up of resistance against liquefaction with

increasing density while angular tailing sand in contrast show such rapid increase

only at low confining pressures At low confining pressure angular material is more

resistant to liquefaction Probably the breakage of the corners on the angular particles

in tailings is ruling the lost in resistance at high confining pressures (sieve analysis

Figure 44 The figure show the extremes of flow behaviour First turbulent conditions where the flow is

essentially random and unpredictable and second the well defined Laminar flow conditions

40

after test identify the breakage of angular particles while on rounded particles the

sieve analysis was practically the same)

59 GROUNDWATER AND SEEPAGE MODELLING

In groundwater flow the particlersquos shape affects the soilrsquos pore size distribution

hence the flow characteristics (Sperry and Peirce 1995) Tortuosity and permeability

(also see section 57) are two significant macroscopic parameters of granular medium

that affect the passing flow (Hayati et al 2012) Current models incorporating the

effects of particle shape have failed to consider irregular particles such as those that

would prevail in a natural porous medium (Sperry and Peirce 1995)

Hayati et al (2012) suggested based on his results that tortuosity effect converge

when the porosity increases indicating that the shape have dominance at low and mid

porosity ranges

Sperry and Peirce (1995) research conclusions suggest that particle size and porosity

are more important predictors for hydraulic conductivity explaining the 69 of the

variability but particle shape appears to be the next most important This however

apparently comprises particles larger than 295-351 μm Differences for particle size

295-351 μm and smaller are not detectable Another interesting result in the research

was the interaction effect of the particle size and particle shape It suggests a different

packing configuration for particles of the same shape but different size (scale

dependent)

6 DISCUSSION

61 TERMS QUANTITIES AND DEFINITIONS

In order to describe the particle shape in detail there are a number of terms quantities

and definitions (qualitative and quantitative) used in the literature (eg Wadell 1932

1934 Krumbein 1941 Sneed amp Folk 1958) All mathematical definitions

(quantitatives) are models used to simplify the complexity of shape description Some

authors (Mitchell amp Soga 2005 Arasan et al 2010) are using three sub-quantities

one and each describing the shape but at different scales The terms are

morphologyform roundness and surface texture (figure 1) The three sub-quantities

are probably the best way to classify and describe a particle because not a single

definition can interpret the whole morphology Common language is needed when

descriptors are explained and these three scales represent an option It is evident in

the reviewed literature that many of the shape descriptors are presented with the same

name but also that there is not a clear meaning on what this descriptor defines eg

when there is no upper limit in the roundness does it means that the angularity never

ends Could they be more and more angular Probably they could be on theory but

not in reality

41

62 PROPERTIES

Trough various articlersquos review done in the present investigation it is recognized that

the particlersquos shape has an effect on the material properties among these are

1 Porosity (Tickell 1938 Fraser 1935 Kolbuszewski 1948) and void ratio

(Cho et al 2006 Shergold 1953 Rouseacute et al 2008 Santamarina and Cho

2004)

2 Permeability (Witt and Brauns 1983)

3 Internal friction angle (Shinohara et al 2000 Chan and Page 1997

Cheshomi et al 2009)

4 Density (Youd 1973 Holubec and DrsquoAppolonia 1973)

5 Drag coefficient Hydraulics (Briggs and McCulloch 1962)

In Table 5 is a short resume of the properties and shape effect found in peer review

articles trough different journals Most of the reviewed articles based its research on

uniform graded sands

Table 8 Compilation of properties influenced by particle shape

Repose

angle

Friction

angle

Porosity and

Void ratio Density Permeability

Settling velocity

Drag coefficient Deformation

Sphericity (3D)shape factor

NI x x x x x x

Circularity (2D)

NI x x x x NI NI

Roundness x x x x NI NI x

x influence

NI no information available

Shape of particles has an effect on the arrangement producing bridging or avoiding

the rotation of the particles and the resulting geotechnical property is affected eg

including flaky particles can result in a higher void ratio due the bridging effect

(Santamarina and Cho 2004) and depending on the loads even the size distribution is

changed due the breakage (Yoginder et al 1985) in similar way angular particles

produce higher void ratio due the avoided possibility of the particles to rotate and

compact

The influence of the chosen shape descriptor appears in this review to have minor

influence on the soil properties in the reviewed studies except on the void ratio and

the friction angle Influence of particle shape in some cases is hider by other factors

(eg size distribution) also the particle shape probably does not have influence when

particle size is in the clay order (eg hydraulic conductivity) the reason could be due

to forces as electrostatic or capillarity become more important at this level

Among the shape descriptors some are chosen more often in literature (eg aspect

ratio) there is no apparent scientific basis to use it (probably due to the simplicity of

the measurement it becomes one of the most use) but there are still some other

descriptors that may or may not show better correlation with the soil properties

Instead empirical relations had been developed regarding roundness or shape to

describe the soil behaviour it is clear that the mechanism behind the results is still not

completely understood

42

There is necessity to define the best(s) shape descriptor(s) to be used for particular

geotechnical properties

63 IMAGE ANALYSIS

Many image analysis techniques had been used to describe the particle shape eg

Fourier analysis fractal dimension tomography etc (Hyslip and Vallejo 1997) but

there is not agreement on the usage or conclusion to ensure the best particle descriptor

for geotechnical applications

There are several shape descriptors and also various techniques to capture the

particles profile (3-dimensions 3-dimension orthogonal and 2-dimensions) Each

technique presents advantages and disadvantages 3-dimensions is probably the

technique that provide more information about the particle shape but the precision

also lies in the resolution the equipment required to perform such capture could be

more or less sophisticated (scanning particles laying down in one position and later

move to complete the scanning or just falling down particles to scan it in one step)

3-dimensions orthogonal this technique use less sophisticated equipment (compare

with the previous technique) but its use is limited to particles over 1cm also

information between the orthogonal pictures is not capture 2-dimensions require non

sophisticated equipment but at the same time the shape information diminish compare

with the previous due the fact that it is possible to determine only the outline as the

particle measurements are performed in 2-dimensions it is presumed that they will lie

with its shortest axis perpendicular to the laying surface when they are flat but when

the particle tends to have more or less similar axis the laying could be random

Advantages on the use of image analysis are clear there is not subjectivity because it

is possible to obtain same result over the same images Electronic files do not loose

resolution and it is important when collaboration among distant work places is done

files can be send with the entire confidence and knowing that file properties has not

been changed Technology evolutions allowed to work with more information and it

also applies to the image processing area were the time consumed has been shortened

(more images processed in less time)

One important aspect in image analysis is the used resolution in the analysis due the

fact that there are measurements dependent and independent on resolution Thus

those dependent measurements should be avoided due the error included when they

are applied or avoid low resolution to increase the reliability Among these

parameters length is the principal parameter that is influences by resolution (eg

perimeter diameter axis etc) Resolution also has another aspect with two faces

quality versus capacity more resolution (quality) means more storage space a

minimum resolution to obtain reasonable and reliable data must be known but it

depend on each particular application

43

64 APPLICATIONS

Quantify changes in particles in the authorrsquos thought is one of the future applications

due the non-invasive methods of taking photographs in the surface of the damrsquos slope

rail road ballast or roads Sampling of the material and comparing with previous

results could show volume (3D analysis) or area (2D analysis) loss of the particles as

well as the form roundness and roughness This is important when it has been

suggested that a soil or rock embankment decrees their stability properties (eg

internal friction angle) with the loss of sphericity roundness or roughness

Seepage stock piling groundwater etc should try to include the particle shape while

modelling seepage requires grading material to not allow particles move due the

water pressure but in angular materials as it is known the void ratio is great than the

rounded soil it means the space and the possibilities for the small particles to move

are greater stock piling could be modelled incorporating the particle shape to

determine the binrsquos capacity when particle shape changes (void ratio changes when

particle shape changes) Modelling requires all information available and the

understanding of the principles that apply

Industry is actually using the particle shape to understand the soil behaviour and

transform processes into practical and economic image analysis has been included in

the quality control to determine particle shape and size because the advantages it

brings eg the acquisition of the sieving curve for pellets using digital images taken

from conveyor this allows to have the information in a short period of time with a

similar result at least enough from the practical point of view as the traditional

sieving

7 CONCLUSIONS

The conclusions of this literature review are

It has been shown that particle shape has influence on the soil behaviour

despite of partial knowledge of the mechanism behind Understanding of the

particle shape and its influence needs to be accomplished

A common language needs to be built up to standardize the meaning on

geotechnical field that involve the particle shape General relationships

between shape and properties should be developed

Based on this review it is not clear which is the best descriptor to use in

geotechnical engineering affecting he related shape to properties Instead of a

couple of standards there is no shape descriptor in geotechnical field fully

accepted

Image analysis tool is objective make the results repeatable obtain fast results

and work with more amount of information

44

Resolution needs to be taken in consideration when image analysis is been

carried out because the effects could be considerable Resolution must be set

according to the necessities Parameters as perimeter can be affected by

resolution

There are examples where particle shape has been incorporated in industries

related to geotechnical engineering eg in the ballast and asphalt industry for

quality control

8 FURTHER WORK

Three main issues have been identified in this review that will be further investigated

the limits of shape descriptors influence of grading and choice of descriptor for

relation to geotechnical properties

Shape descriptors have low and high limits frequently the limits are not the same and

the ability to describe the particlersquos shape is relative The sensitivity of each descriptor

should be compare to apply the most suitable descriptor in each situation

Sieving curve determine the particle size in a granular soil particle shape could differ

in each sieve size There is the necessity to describe the particle shape on each sieve

portion (due to practical issues) and included in the sieve curve Obtain an average

shape in determined sieve size is complicated (due to the possible presence of several

shapes) and to obtain the particle shape on the overall particlersquos size is challenging

how the particle shape should be included

Since several descriptors have been used to determine the shape of the particles and

the relation with the soil properties it is convenient to determine the descriptorrsquos

correlation with the soil properties

9 ACKNOWLEDGMENT

I would like to thanks to Lulearing University of Technology (LTU) the time I had spent

in its facilities and the kind environment it offers and University of Sonora

(UNISON) that has been providing me the financial support and the time to conclude

this journey

10 REFERENCES

Andersson T (2010) Estimating particle size distributions based on machine vision

Doctoral Thesis Departament of Computer Science and Electrical Engineering Lulearing

University of Technology ISSN 1402-1544 ISBN 978-91-7439-186-2

45

Arasan Seracettin Hasiloglu A Samet Akbulut Suat (2010) Shape particle of

natural and crished aggregate using image analysis International Journal of Civil and

Structural Engineering Vol 1 No 2 pp 221-233 ISSN 0970-4399

Aschenbrenner BC (1956) A new method of expressing particle sphericity Journal

of Sedimentary Petrology Vol 26 No 1 pp 15-31

Axelsson K (1998) Introduktion till jordmekaniken jaumlmte jordmateriallaumlran Skrift

984 Lulearing Avdelningen foumlr Geoteknologi Lulearing Tekniska Universitet (In Swedish)

Barton Nick amp Kjaernsli Bjorn (1981) Shear strength of rockfill Journal of the

Geotechnical Engineering Division Proceedings of the American Society of Civil

Engineers (ASCE) Vol 107 No GT7

Barrett P J (1980) The shape of rock particles a critical review Sedimentology

Vol 27 pp 291-303

Blott S J and Pye K (2008) Particle shape a review and new methods of

characterization and classification Sedimentology Vol 55 pp 31-63

Bowman E T Soga K and Drummond W (2001) Particle shape characterization

using Fourier descriptor analysis Geotechnique Vol 51 No 6 pp 545-554

Briggs L I McCulloch D S (1962) Hydraulic shape of sand particles Journal of

Sedimentary Petrology Vol 32 pp 645-656

Chan Leonard C Y and Page Neil W (1997) Particle fractal and load effects on

internal friction in powders Powder Technology Vol 90 pp 259-266

Cheshomi A Fakher A Jones C J F P (2009) A correlation between friction

angle and particle shape metrics in quaternary coarse alluvia Quarterly Journal of

Engineering Geology and Hydrogeology Vol 42 pp 145-155

Cho G Dodds J and Santamarina J C (2006) Particle shape effects on packing

density stiffness and strength Natural and crushed sands Journal of Geotechnical

and Geoenvironmental Engineering May 2006 pp 591-602

Dietrich William E (1982) Settling velocity of natural particles Water Resources

Research Vol 18 No 6 pp 1615-1626

Dobkins J E and Folk R L (1970) Shape development on Tahiti-nui Journal of

Sedimentary Petrology Vol 40 No 2 pp 1167-1203

Folk R L (1955) Student operator error in determining of roundness sphericity and

grain size Journal of Sedimentary Petrology Vol 25 pp 297-301

Fernlund J M R (1998) The effect of particle form on sieve analysis A test by

image analysis Engineering Geology Vol 50 No 1-2 pp 111-124

46

Fernlund J M R (2005) Image analysis method for determining 3-D shape of

coarse aggregate Cement and Concrete Research Vol 35 Issue 8 pp 1629-1637

Fernlund J M R Zimmerman Robert and Kragic Danica (2007) Influence of

volumemass on grain-size curves and conversion of image-analysis size to sieve size

Engineering Geology Vol 90 No 3-4 pp 124-137

Fraser H J (1935) Experimental study of the porosity and permeability of clastic

sediments The Journal of Geology Vol 43 pp 910-1010 ISSN 0022-1376

Hayati Ali Nemati Ahmadi Mohammad Mehdi and Mohammadi Soheil (2012)

American Physical Society Physical review E 85 036310 DOI

101103PhysRevE85036310

Hawkins A E (1993) The Shape of Powder-Particle Outlines Wiley New York

Head K H and Epps R J (2011) Manual of soil Laboratory testing Volum II

Permeability shear strength and compressibility test 3rd

edition Whittles Publishing

Scotland UK 3rd

edition

Holubec I and DrsquoAppolonia E (1973) Effect of particle shape on the engineering

properties of granular soils ASTM STP 523 pp 304-318

Hyslip James P Vallejo Luis E (1997) Fractal analysis of the roughness and size

distribution of granular materials Engineering Geology Vol 48 pp 231-244

Janoo Vincent C (1998) Quantification of shape angularity and surface texture of

base course materials US Army Corps of Engineers Cold Region Research and

Engineering Laboratory Special report 98-1

Jefferies Mike and Been Ken (2000) Soil liquefaction A critical state approach

Taylor amp Francis Group London and New York

Jimenez Jose A Madsen Ole S (2003) A simple formula to estimate settling

velocity of natural sediments Journal of Waterway Port Coastal and Ocean

Engineering Vol 129 No 2 pp 70-78

Johansson Jens and Vall Jakob (2011) Jordmaterials kornform Inverkan paring

Geotekniska Egenskaper Beskrivande storheter bestaumlmningsmetoder

Examensarbete Avdelningen foumlr Geoteknologi Institutionen foumlr Samhaumlllsbyggnad

och naturresurser Lulearing Tekniska Universitet Lulearing (In Swedish)

Kane Joseph W and Sternheim Morton M (1988) Physics John Wiley amp Sons Inc

Third edition

Kolbuszewski J (1948) An experimental study of the maximum and minimum

porosities of sands Proceedings of the Second International Conference on Soil

Mechanics and Foundation Engineering Rotterdam June 21 to 30 Sub-section IIb

pp 158-165

47

Krumbein W C and Pettijohn FJ (1938) Manual of sedimentary petrography

Appleton-Century Crofts Inc New York

Krumbein W C (1941) Measurement and geological significance of shape and

roundness of sedimentary particles Journal of Sedimentary Petrology Vol 11 No 2

pp 64-72

Krumbein W C and Sloss L L (1963) Stratigraphy and Sedimentation 2nd

ed

WH Freeman San Francisco

Kuo Chun-Yi and Freeman Reed B (1998a) Image analysis evaluation of

aggregates for asphalt concrete mixtures Transportation Research Record Vol 1615

pp 65-71

Kuo Chun-Yi Rollings Raymond and Lynch Larry N (1998b) Morphological

study of coarse aggregates using image analysis Journal of Materials in Civil

Engineering Vol 10 No 3 pp 135-142

Lanaro F Tolppanen P (2002) 3D characterization of coarse aggregates

Engineering Geology Vol 65 pp 17-30

Lees G (1964a) A new method for determining the angularity of particles

Sedimentology Vol 3 pp 2-21

Lees G (1964b) The measurement of particle shape and its influence in engineering

materials British Granite Whinstone Federation Vol 4 No 2 pp 17-38

Matsushima Takashi Saomoto Hidetaka Matsumoto Masaaki Toda Kengo

Yamada Yasuo (2003) Discrete element simulation of an assembly of irregular-

shaped grains Quantitative comparison with experiments 16th ASCE Engineering

Mechanics Conference University of Washington Seattle July 16-18

Mitchell James K and Soga Kenichi (2005) Fundamentals of soil behaviour Third

edition WILEY

Mora C F Kwan A K H Chan H C (1998) Particle size distribution analysis of

coarse aggregate using digital image processing Cement and Concrete Research Vol

28 pp 921-932

Mora C F and Kwan A K H (2000) Sphericity shape factor and convexity

measurement of coarse aggregate for concrete using digital image processing Cement

and Concrete Research Vol 30 No 3 pp 351-358

Muskat Morris (1937) The Flow of fluids through porous media Journal of Applied

Physics Vol 8 pp 274

Nearing M A and Parker S C (1994) Detachment of soil by flowing water under

turbulent and laminar conditions Soil Science Society of American Journal Vol 58

No 6 pp 1612-1614

48

Pan Tongyan Tutumluer Erol Carpenter Samuel H (2006) Effect of coarse

aggregate morphology on permanent deformation behavior of hot mix asphalt Journal

of Transportation Engineering Vol 132 No 7 pp 580-589

Pellegrino A (1965) Geotechnical properties of coarse-grained soils Proceedings

International Conference of Soil Mechanics and Foundation Engineering Vol 1 pp

97-91

Pentland A (1927) A method of measuring the angularity of sands MAG MN AL

Acta Eng Dom Transaction of the Royal Society of Canada Vol 21 Ser3xciii

Persson Anna-Lena (1998) Image analysis of shape and size of fine aggregates

Engineering Geology Vol 50 pp 177-186

Powers M C (1953) A new roundness scale for sedimentary particles Journal of

Sedimentary Petrology Vol 23 No 2 pp 117-119

Pye W and Pye M (1943) Sphericity determination of pebbles and grains Journal

of Sedimentary Petrology Vol 13 No 1 pp 28-34

Qazi M A (1975) Flow properties of granular masses A review on the angle of

repose The Arabian Journal for Science and Engineering Vol 1 No 2

Quiroga Pedro Nel and Fowle David W (2003) The effects of aggregate

characteristics on the performance of portland cement concrete Report ICAR 104-1F

Project number 104 International Center for Aggregates Research University of

Texas

Riley N A (1941) Projection sphericity Journal of Sedimentary Petrology Vol 11

No 2 pp 94-97

Rouseacute P C Fennin R J and Shuttle D A (2008) Influence of roundness on the

void ratio and strength of uniform sand Geotechnique Vol 58 No 3 227-231

Santamarina J C and Cho G C (2004) Soil behaviour The role of particle shape

Proceedings Skempton Conf London

Schofield and Wroth (1968) Critical state soil mechanics McGraw Hill

Shaumlfer Michael (2002) Digital optics Some remarks on the accuracy of particle

image analysis Particle amp Particle Systems Characterization Vol 19 No 3 pp 158-

168

Shergold F A (1953) The percentage of voids in compacted gravel as a measure of

its angularity Magazine of Concrete Research Vol 5 No 13 pp 3-10

Shinohara Kunio Oida Mikihiro Golman Boris (2000) Effect of particle shape on

angle of internal friction by triaxial compression test Powder Technology Vol 107

pp131-136

49

Skredcommisionen (1995) Ingenjoumlrsvetenskapsakademinen rapport 395 Linkoumlping

1995

Sneed E D and Folk R L (1958) Pebbles in the Colorado river Texas A study in

particle morphogenesis Journal of Geology Vol 66 pp 114-150

Sperry James M and Peirce J Jeffrey (1995) A model for estimating the hydraulic

conductivity of granular material based on grain shape grain size and porosity

Ground Water Vol 33 No 6 pp 892-898

Sukumaran B and Ashmawy A K (2001) Quantitative characterisation of the

geometry of discrete particles Geotechnique Vol 51 No 7 pp 619-627

Szaacutedeczy-Kardoss E Von (1933) Die bistimmung der abrollungsgrades Geologie

und palaumlontologie Vol 34B pp 389-401 (in German)

Teller J T (1976) Equantcy versus sphericity Sedimentology Vol 23 pp 427-428

Tickell F G (1938) Effect of the angularity of grain on porosity and permeability

bulletin of the American Association of Petroleum Geologist Vol 22 pp 1272-1274

Tutumluer E Huang H Hashash Y Ghaboussi J (2006) Aggregate shape effects

on ballast tamping and railroad track lateral stability AREMA 2006 Annual

Conference Louisville KY

Wadell H (1932) ldquoVolume Shape and roundness of rock particlesrdquo Journal of

Geology Vol 40 pp 443-451

Wadell H (1933) Sphericity and roundness of rock Particles Journal of Geology

Vol 41 No 3 pp 310ndash331

Wadell H (1934) Shape determination of large sedimental rock fragments

The Pan-American Geologist Vol 61 pp 187-220

Wadell H (1935) ldquoVolume shape and roundness of quartz particlesrdquo Journal of

Geology Vol 43 pp 250-279

Wentworth W C (1922a) The shape of beach pebbles Washington US Geological

Survey Bulletin Vol 131C pp 75-83

Wentworth W C (1922b) A method of measuring and plotting the shape of pebbles

Washington US Geological Survey Bulletin Vol 730C pp 91-114

Wentworth W C (1933) The shape of rock particle A discussion Journal of

Geology Vol 41 pp 306-309

Witt K J Brauns J (1983) Permeability-Anisotropy due to particle shape Journal

of Geotechnical Engineering Vol 109 No 9 pp 1181-1187

1

1 INTRODUCTION

Effects on soil behaviour from the constituent grain shape has been suggested since

the earliest 1900rsquos when Wadell (1932) Riley (1941) Pentland (1927) and some

other authors developed their own techniques to define the form and roundness of

particles Into the engineering field several research works conclude that particle

shape influence technical properties of soil material and unbound aggregates

(Santamarina and Cho 2004 Mora and Kwan 2000) Among documented properties

affected by the particle shape are eg void ratio (porosity) internal friction angle and

hydraulic conductivity (permeability) (Rouseacute et al 2008 Shinohara et al 2000

Witt and Brauns 1983) In geotechnical guidelines particle shape is incorporated in

eg soil classification (Eurocode 7) and in national guidelines eg for evaluation of

friction angle (Skredkommisionen 1995) This classification is based on ocular

inspection and quantitative judgement made by the individual practicing engineer

thus it can result in not repeatable data In evaluation of eg standard penetration test

Holubec and DrsquoAppolonia (1973) are suggesting the inclusion of the particle shape in

the evaluation of the data According with Folk (1955) the form error is negligible but

it is not in the second sub-quantity related with the corners (roundness) These

systems are not coherent in definitions The lack of possibility to objectively describe

the shape hinders the development of incorporating the effect of particle shape in

geotechnical analysis

The interest of particle shape was raised earlier in the field of geology compared to

geotechnical engineering Particle shape is considered to be the result of different

agentrsquos transport of the rock from its original place to deposits since the final pebble

form is hardly influenced by these agents (rigor of the transport exfoliation by

temperature changes moisture changes etc) in the diverse stages of their history

Furthermore there are considerations regarding on the particle genesis itself (rock

structure mineralogy hardness etc) (Wentworth 1922a) The combination of

transport and mineralogy factors complicates any attempt to correlate length of

transport and roundness due that soft rock result in rounded edges more rapidly than

hard rock if both are transported equal distances According to Barton amp Kjaernsli

(1981) rockfill materials could be classified based on origin into the following (1)

quarried rock (2) talus (3) moraine (4) glacifluvial deposits and (5) fluvial deposits

Each of these sources produces a characteristic roundness and surface texture

Pellegrino (1965) conclude that origin of the rock have strong influence determining

the shape

To define the particle form (morphology) in order to classify and compare grains

many measures has been taken in consideration (axis lengths perimeter surface area

volume etc) Probably when authors had developed the form descriptors realize that

they hadnrsquot provide enough information about the corners they could be angular or

rounded (roundness) thus the authors also focus on develop techniques to describe

them Furthermore the corners or the general surface can be rough or smooth (surface

texture) Nowadays some authors (Mitchell amp Soga 2005 Arasan et al 2010) are

using these three sub-quantities one and each describing the shape but a different

scale (form roundness surface texture)

2

During the historical development of shape descriptors the terminology has been used

differently among the published studies terms as roundness (because the roundness

could be apply in the different scales) or sphericity (how the particle approach to the

shape of a sphere) were strong (Wadell 1933 Wenworth 1933 Teller 1976 Barrett

1980 Hawkins 1993) and it was necessary in order to define a common language on

the particle shape field unfortunately still today there is not agreement on the use of

this terminology and sometimes it make difficult to understand the meaning of the

authors thatrsquos why it is better to comprehend the author technique in order to

misinterpret any word implication

Several attempts to introduce methodology to measure the particlersquos shape had been

developed over the years Manual measurement of the particles form is

overwhelming thus visual charts were developed early to diminish the measuring

time (Krumbein 1941 Krumbein and Sloss 1963 Ashenbrenner 1956 Pye and Pye

1943) Sieving was introduced to determine the flakinesselongation index but it is

confined only for a certain particle size due the practical considerations (Persson

1988) More recently image analysis on computer base has been applied on sieving

research (Andersson 2010 Mora and Kwan 2000 Persson 1998) bringing to the

industry new practical methods to determine the particle size with good results

(Andersson 2010) Particle shape with computer assisted methods are of great help

reducing dramatically the measuring time (Fernlund 2005 Kuo and Freeman 1998a

Kuo et al 1998b Bowman et al 2001)

In the civil industry eg Hot Asphalt mixtures (Kuo and Freeman 1998a Pan et al

2006) Concrete (Mora et al 1998 Quiroga and Fowle 2003) and Ballast

(Tutumluer et al 2006) particlersquos shape is of interest due the materialrsquos performance

thus standards had been developed (see appendix A) On asphalt mixtures limits of

flat and elongated particles or the amount of natural sands typically are incorporated

into specifications flat and elongated particles tend to cause problems with

compaction particle breakage loss of strength and segregation in pavement (Kuo and

Freeman 1998a) Rutting resistance of asphalt concrete under traffic and

environmental loads depend on the stability of aggregates structure in the asphalt mix

(Pan et al 2006) According with the American Railway Engineering and

Maintenance of Way Association (AREMA) ballast aggregate should be open graded

with hard angular shaped particles providing sharp corners and cubical fragments

with a minimum of flat and elongated pieces (Tutumluer et al 2006) The American

standard ASTM D 3398 (test method for index of aggregate particle shape and

texture) is an example of an indirect method to determine particle shape (see appendix

A) Aggregate characteristics of shape texture and grading influence workability

finishability bleeding pumpability and segregation of fresh concrete and affect

strength stiffness shrinkage creep density permeability and durability of hardened

concrete In fact flaky elongated angular and unfavorably graded particles lead to

higher voids content than cubical rounded and well-graded particles (Quiroga and

Fowle 2003)

Sieving is probably the most used method to determine the particle size distribution it

consist of plotting the cumulative weight of the weighted material retained by each

mesh (European standard EN 933-1 1992) This traditional method according to

Andersson (2010) is time consuming and expensive Investigations shows that the

traditional sieving has deviations when particle shape is involve the average volume

3

of the particles retained on any sieve varies considerably with the shape (Lees

1964b) thus the passing of the particles depend upon the shape of the particles

(Fernlund 1998) In some industries the Image analysis is taking advantage over the

traditional sieving technique regardless of the intrinsic error on image analysis due the

overlapping or partial hiding of the rock particles (Andersson 2010) In this case the

weight factor is substitute by pixels (Fernlund et al 2007) Sieving curve using

image analysis is not standardized but after good results in the practice (Andersson

2010) new methodology and soil descriptions could raise including its effects

2 AIM AND GOAL

The aim of this report is to review the state of the art on how to describe particle

shape of individual grains of geotechnical material and knowledge on the influence of

shape in geotechnical properties

The goals in this study are to

Describe discuss and compare particle shape and definitions

Review the known effect of particle shape on soil mechanics parameters

Discuss the potential of the role of particle shape in soil mechanics

Focus in this study has been on 2 dimensional shape definitions

The content of the report is based upon published and peer reviewed papers in

English

3 DESCRIPTION OF SHAPE PROPERTIES

31 INTRODUCCTION

Particle shape description can be classified as qualitative or quantitative Qualitative

describe in terms of words the shape of the particle (eg elongated spherical flaky

etc) and quantitative that relates the measured dimensions in the engineering field

the quantitative description of the particle is more important due the reproducibility

Quantitative geometrical measures on particles may be used as basis for qualitative

classification There are few qualitative measures in contrast with several quantitative

measures to describe the particle form Despite the amount of qualitative descriptions

none of them had been widely accepted but there are some standards (eg ASTM

D5821 EN 933-3 and BS 812) specifying mathematical definitions for industrial

purposes

Shape description of particles is also divided in

o 3D (3 dimensions) it could be obtained from a 3D scan or in a two

orthogonal images and

o 2D (2 dimensions) or particle projection where the particle outline is drawn

4

3D and 2D image analysis present challenges itself 3D analysis requires a

sophisticated equipment to scan the particle surface and create the 3D model or the

use of orthogonal images and combine them to represent the 3 dimensions The

orthogonal method could present new challenges as the minimum particle size or the

placing in orthogonal way of the particles (Fernlund 2005) 2D image analysis is easy

to perform due the non-sophisticated equipment required to take pictures (eg regular

camera or the use of microscope for smaller particles) In 2D image analysis the

particle is assumed to lay over its more stable axis (eg longest and intermediate axis

lie more or less parallel to the surface while the shortest axis is perpendicular) or

random some authors publish their own preferences about this issue (Wadell 1935

Riley 1941 Hawkins 1993)

32 SCALE DEPENDENCE

In order to describe the particle shape in detail there are a number of terms quantities

and definitions used in the literature Some authors (Mitchell amp Soga 2005 Arasan et

al 2010) are using three sub-quantities one and each describing the shape but at

different scales The terms are morphologyform roundness and surface texture In

figure 1 is shown how the scale terms are defined

At large scale the particlersquos diameters in different directions are considered At this

scale describing terms as spherical platy elongated etc are used An often seen

quantity for shape description at large scale is sphericity (antonym elongation)

Graphically the considered type of shape is marked with the dashed line in Figure 1

At intermediate scale it is focused on description of the presence of irregularities

Depending on at what scale an analysis is done corners and edges of different sizes

are identified By doing analysis inside circles defined along the particlersquos boundary

deviations are found and valuated The mentioned circles are shown in Figure 1 A

generally accepted quantity for this scale is roundness (antonym angularity)

Regarding the smallest scale terms like rough or smooth are used The descriptor is

considering the same kind of analysis as the one described above but is applied

Figure 1 Shape describing sub quantities (Mitchell amp Soga 2005)

5

within smaller circles ie at a smaller scale Surface texture is often used to name the

actual quantity The sub-quantities and antonyms are summarized in table 1

Table 1 Sub-quantities describing the particlersquos morphology and its antonym

Scale Quantity Antonym

Large scale Sphericity Elongation

Intermediate scale Roundness Angularity

Small scale Roughness Smoothness

33 FORM (3D)

Wentworth in 1922 (Blott and Pye 2008) was probably one of the first authors on

measure the particle dimensions this consisted on the obtaining of the length of the

tree axes perpendicular among each other (see figure 2) on the tree dimensions (where

agebgec) to obtain the sphericity (equation 1)

Krumbein (1941) develop a rapid method for shape measurement to determine the

sphericity this is done by measuring the longest (a) medium (b) and shorter (c) axes

diameters of the particle it can be seen in figure 2 (Always perpendicular among each

other) The radios ba and cb are located in the chart developed by his own where it

can be found the Intercept sphericity as he called (See figure 3) This chart is an easy

graphical way to relate the dimensions

c2

ba

Figure 2 Measurement of the 3 axes perpendicular among each other (Krumbein 1941)

Figure 3 Detailed chart to determining Krumbein intercept sphericity (Krumbein 1941)

(1)

6

Wadell (1932) defined the sphericity as the specific surface ratio (equation 2) Figure

4 is a schematic representation of the sphere surface and particle surface both particle

and sphere of the same volume

This way to obtain the sphericity is almost impossible to achieve as Hawkins (1993)

declares due the difficulty to get the surface area on irregular solids

Wadell (1934) also defined the sphericity based upon the particle and sphere volumes

as equation 3 (see figure 5)

Wadell (1934) used a new formula simple to manage using the diameters (see figure

6 and equation 4)

Zingg (Krumbein 1941) develop a classification based on the 3 axes relation in this

way it is easy to find out the main form of the particles as a disks spherical blades

S

s

3

CIR

P

V

V

CIR

SV

D

D

Figure 4 Same volume sphere surface (s) and particle surface (S) (modified after Johansson and Vall

2011)

Figure 5 Relation between the volume of the particle and the volume of the circumscribed

sphere (Johansson and Vall 2011)

Figure 6 Figure is showing the relation between the diameter of a circumscribed sphere and the

diameter of a sphere of the same volume as the particle (Johansson and Vall 2011)

(2)

(3)

(4)

7

and rod-like this is summarized on figure 7 Zinggrsquos classification is related with

Krumbein intercept sphericity and the figure 3

In figure 8 the figures 3 and 7 are combined the relation in the two classifications can

be seen it is an easy way to understand the morphology regarding on the a b and c

dimensions

Pye and Pye (1943) in the article ldquosphericity determinations of pebbles and sand

grainsrdquo compare the Wadellrsquos sphericity developed in 1934 (based on the diameter)

with ldquoPebble sphericityrdquo based on an ellipse this last equation (number 5) appears

two years early published by Krumbein (1941) Axis measurement is done as figure 1

denotes for equations 5 trough 12 with exception of equation 8 where the original

document was not possible to obtain

32a

cb

Figure 7 Zinggrsquos classification of pebble shape based on ratios ba and cb (Krumbein 1941)

Figure 8 Classification made by Zinggrsquos and chart to determine sphericity (Krumbein and Sloss 1963)

(5)

8

Sneed amp Folk in (1958) found a relation between the tree dimensional axes called

ldquoMaximum Projection Sphericityrdquo

In a similar way Ashenbrenner (1956) showed his equation at that time named

ldquoWorking Sphericityrdquo

Form or shape factor names are used by authors like Corey (shape factor eq 8) in the

paper published on 1949 Williams (shape factor eq 9) in 1965 Janke (form factor

eq 10) in 1966 and Dobkins amp Folk (oblate-prolate index eq 11) in 1970 (Blott and

Pye 2008)

Aschenbrenner (1956) develop the shape factor by using the relation of the tree axis

but the square of the middle one

3

2

ba

c

))ab((1)bc(16))ab((cb)(11

)ab()bc( 128

22

3 2

ab

c

acb when 1ac

b acb when

b

ac-1 2

22

2

3

cba

c

222

a

c

50c-a

b-a10

2b

ac

(6)

(7)

(8)

(9)

(10)

(11)

(12)

9

Table 2 General overview over different particle shape definitions for 3D sphericity has been compiled

and arranged chronologically

Aspect Name Author Year Based on

Sphericity (3D) Flatness index Wentworth 1922a 3-axes

True Sphericity Wadell 1932 Surface

Operational sphericity Wadell 1932 Volume

Sphericity Wadell 1934 Sphere diameter

Zinggrsquos clasification Zinggrsquos1

1935 3-axes

Intercept sphericity chart Krumbein 1941 3-axes

Pebble sphericity Pye and Pye 1943 3-axes

Corey shape factor Corey2

1949 3-axes

Working sphericity Ashenbrenner 1956 3-axes

shape factor Ashenbrenner 1956 3-axes

Maximum projection sphericity Sneed amp Folk 1958 3-axes

Williams shape factor Williams2

1965 3-axes

Janke form factor Janke2

1966 3-axes

Oblate-prolate index Dobkins amp Folk 1970 3-axes 1) Krumbein and Sloss 1963 2) Blott and Pye 2008

34 FORM (2D)

The technique to measure the sphericity is based in tree dimensions it can be found in

literature some ways to measure the ldquotwo dimensions sphericityrdquo which is simply the

perimeter of the particle projection some authors named ldquoparticle outlinerdquo or

ldquocircularityrdquo

Wadell in 1935 (Hawkins 1993) adopt a conversion of his 1934 3D sphericity

formula (equation 4) to a 2D outline He defined an orientation on the particles and

they were based on the maximum cross sectional area (outline of the particle

projecting the maximum area) The equations show the relation between diameters of

a circle of same area and smallest circumscribed circle

He also used the term ldquodegree of circularityrdquo as the ratio of the perimeter of a circle of

same area and the actual particle perimeter

Tickell in 1931 (Hawkins 1993) used his empirical relation The particle orientation

proposed was a random one It is described by the ratio between the area outline and

the area of smallest circumscribed circle

C

A

D

DC

P

PC C

CA

AC

(13)

(14)

(15)

10

Some other authors has been working with the ldquocircularityrdquo concept and had develop

them own equations as Pentland (1927) relating the area outline and area of a circle

with diameter equal to longest length outline and Cox (Riley 1941) with the ratio

area and perimeter time a constant equations 16 and 17 respectively Both authors did

not define any definite orientation of the grains

Riley (1941) realize the problems that an area perimeter and some other

measurements proposed by the above authors can carry as the time consuming and

tedious work (at that time were not computer all was made by hand) and thatrsquos why

he develop this equation easy to handle called ldquoinscribed circle sphericityrdquo He used

the same particle orientation proposed by Wadell and the relation of diameters of

inscribed and circumscribed circles

Horton 1932 (Hawkins 1993) use the relation of the drainage basing perimeter and

the perimeter of a circle of the same area as drainage basin

Janoo in 1998 (Blott and Pye 2008) develop his general ratio of perimeter to area

Sukumaran and Ashmawy (2001) develop his own shape factor (SF) defined as the

deviation of the global particle outline from a circle Figure 9 can be used as a

reference to determine the items used in the equation 21

N is referred to the number of sampling intervals o radial divisions

C2A

AC

2P

A4C

C

I

D

DC

CD

D

P

PC

A

PC

2

45ordm x N

Particleα

= SF

sumN

1=ii

(16)

(17)

(18)

(19)

(20)

(21)

11

Table 3 General chronological overview of the particle shape definitions for 2D sphericity

Aspect Name Author Year Based on

Circularity (2D) roundness Pentland 1927 area

roundness Cox1

1927 area-perimeter

roundness Tickell2

1931 area

Circularity Horton2

1932 drainage basin

outline circularity Wadell 1935 Circle diameter

degree of circularity Wadell 1935 Perimeter

inscribed circle sphericity Riley 1941 Circle diameter

Circularity Krumbein and Sloss 1963 chart

Janoo 1998 area-perimeter

Shape factor Sukumaran 2001 Segmentation of particle and angles

1) Riley 1941 2) Hawkins 1993

35 ROUNDNESS OR ANGULARITY

Roundness as described in section 32 is the second order shape descriptor Sphericity

lefts beside the corners and how they are this was notice by most of the authors sited

before and they suggested many ways to describe this second order particle property

Roundness is clearly understandable using the figure 10 Particle shape or form is the

overall configuration and denotes the similarities with a sphere (3D) or a circle (2D)

Roundness is concerning about the sharpness or the smoothness of the perimeter (2D)

Surface texture (Barret 1980) is describe as the third order subject (form is the first

and roundness the second) and it is superimposed in the corners and it is also a

property of particles surfaces between corners

Figure 9 Description of the Sukumaran factors to determine the shape and angularity (Sukumaran and

Ashmawy 2001)

12

Wadell (1935) describes his methodology calling it total degree or roundness to

obtain the roundness of a particle using the average radius of the corners in relation

with the inscribed circle diameter (see figure 11) on the equation

In the same study Wadell (1935) has used the equation

This two last equation shows slightly differences on the results (Wadell 1935)

Powers (1953) also published a graphic scale to illustrate the qualitative measure

(figure 12) It is important to highlight that any comparing chart to describe particle

properties has a high degree of subjectivity Folk (1955) concludes that when charts

are used for classification the risk of getting errors is negligible for sphericity but

large for roundness

N

R

r

Rinmax

r

R

NR

inmax

Figure 10 Form (shape) Roundness and Texture graphical description (Bowman et al 2001)

Figure 11 Wadellrsquos method to estimate the roundness corners radius and inscribed circle

(Hawkins 1993)

(22)

(23)

13

Some authors as Russel amp Taylor in 1937 Pettijohn in 1957 and Powers in 1953

developed a classification based on five and six classes (Hawkins 1993) each one

with its own class limits it is important to denote that the way they measure the

roundness is the developed by Wadell (1935) This classification and class limits are

showed in the table 4

Table 4 Degrees of roundness Wadell Values (Hawkins 1993) NA = no-applicable

Grade terms Russell amp Taylor (1937) Pettijohn (1957) Powers (1953)

Class

limits (R)

Arithmetic

midpoint

Class limits

(R)

Arithmetic midpoint Class

limits (R)

Arithmetic

midpoint

Very angular

NA

NA

NA

NA

012-017

014

Angular

000-015

0075

000-015

0125

017-025

021

Subangular

015-030

0225

015-025

0200

025-035

030

Subrounded

030-050

0400

025-040

0315

035-049

041

Rounded

050-070

0600

040-060

0500

049-070

059

Well rounded

070-100

0800

060-100

0800

070-100

084

Krumbein and Sloss (1963) published a graphical chart easy to determine the

sphericity and roundness parameters using comparison See figure 13 (Cho et al

2006)

Figure 12 A Roundness qualitative scale (Powers 1953)

Figure 13 Sphericity and roundness chart (Cho et al 2006) The roundness equation that appears here in

the chart is the wadellrsquos equation number 22

14

Fischer in 1933 (Hawkins 1993) used a straightforward method to quantify roundness

using a central point in the outline and dividing the outline in angles around this point

that were subtended by the straight or non curved parts of the profile were measured

This is illustrated in figure 14

To express the angularity value Fischer used the ratio of angles standing linear parts

on the outlines and concave respectively

Figure 14 left (A) and right (B) gives a similar angularity of approximately 042

using the above equations (Hawkins 1993)

Wentworth in 1922 used the maximum projection to define the position of the particle

to obtain the outline or contour (Barret 1980) The equation reflects the relation of the

diameter of a circle fitting the sharpest corner and the longest axis plus the shortest

axis c (minimum projection)

Wentworth (Hawkins 1993) expressed the roundness as the ratio of the radius of

curvature of the most convex part and the longest axis plus short axis

Actually these last two equations are the same just expressed in different terms when

the particle is in its maximum projection

Dimensions can be seen on figure 15 L and B represents the mayor axis a and

intermediate axis b The intention is to make difference between the 2 and 3

dimensions (L and B are for 2D as a b and c are for 3D)

deg360

ANG

=R

sumPLA

PLA

CON

ANG

ANGR

2)S(L

DR

M

S

B)4(L

RR CON

Figure 14 Fischerrsquos methods of angularity computation (Hawkins 1993)

A=inscribed circle B=circumscribed circle

(24)

(25)

(26)

(27)

15

Wentworth 1919 has a second way to express the roundness called Shape index

(Barrett 1980) and it relates the sharpest corner and the diameter of a pebble trough

the sharpest corner

Wentworth (1922b) used define the roundness as the ratio of the sharpest corner and

the average radius of the pebble

Cailleux (Barrett 1980) relates the radius of the most convex part and the longest

axis

Kuenen in 1956 show his roundness index (Barrett 1980) between the sharpest corner

and the breath axis

Dobkins amp Folk (1970) used a modified Wentworth roundness with the relation of

sharpest corner and inscribed circle diameters

AVG

CON

R

RR

x

s

D

DR

L2

RR CON

B

DR s

i

s

D

DR

3AVGAVG cbaDR2

Figure 15 Description of L and B axes (Hawkins 1993)

(28)

(29)

(30)

(31)

(32)

(33)

16

Swan in 1974 shows his equation (Barrett 1980) relating the sharpest (or the two

sharpest) corner(s) and inscribed circle diameter

Szadeczsky-Kardoss has his Average roundness of outline (Krumbein and Pettijohn

1938) relating the concave parts perimeter and the actual perimeter

Lees (1964a) developed an opposite definition to roundness it means that he

measures the angularity instead of the roundness and he calls it Degree of angularity

Figure 16 shows the items considered when equation 36 applies as the angles (α)

inscribed circle (Rmax-in) and the distance (x) The main formula is

In order to apply the last equation corners needs to be entered in the formula and each

individual result will add to each other to obtain the final degree of angularity

A roundness index appears on Janoo (1998) Kuo and Freeman (1998a) and Kuo et

al (1998b) it is described as

The last equation is on section 34 also because there is not a general agreement on the

definition furthermore some authors had used to define the roughness this is not the

only equation that has been used trying to define different aspects (sphericity

roundness or roughness) but it is a good example of the misuse of the quantities and

definitions

inmaxR

x)180(R

2P

A4R

i

ss

D

DDR

221

100P

PR CON

Figure 16 Degree of angularity measurement technique (Blot and Pye 2008)

(34)

(35)

(36)

(17)

17

Sukumaran and Ashmawy (2001) present an angularity factor (AF) calculated from

the number of sharpness corners Angles βi required to obtain the angularity factor are

shown in figure 9

Sukumaran and Ashmawy (2001) also suggested use not bigger sampling interval of

N=40 because it is the cut off between angularity factor and surface roughness If so

this equation could be used to describe the roughness

Table 5 General chronological overview of the particle roundness

Aspect Name Author Year Based on

Roundness shape index Wentworth 19191

diameter of sharper corner

shape index Wentworth 1922b sharpest corner and axis

roundness Wentworth 1933 convex parts

Fischer 19332

noncurved parts outline

Fischer 19332

noncurved-streigth parts outline

Average roundness of outline

Szadeczsky-Kardoss 19333

convex parts-perimeter

roundness Wadell 1935 diameter of corners

roundness Wadell 1935 diameter of corners

roundness Russel amp Taylor 19372

class limit table

roundness Krumbein 1941 chart

Cailleux 19471

convex parts

roundness Pettijohn 19494 class limit table

roundness Powers 1953 chart and class limit table

Kuenen 19561

axis-convex corner

roundness Krumbein and Sloss 1963 chart

degree of angularity Lees 1964a corners angles and inscribed circle

Dobkins amp Folk 1970 diameter of sharper corner

Swan 19741

diameter of sharper corners

Angularity factor Sukumaran and

Ashmawy 2001

Segmentation of particles and angles

1) Barret 1980 2) Hawkins 1993 3) Krumbein and Pettijohn 1938 4) Powers 1953

sum

sumsumN

1=i

2

i

2

N

1=i

2

i

2N

1=ii

)ordm180 -circleβ( - )(180ordm x 3

)ordm180-circleβ(-)ordm180 -Particleβ(

= AF (37)

18

36 ROUGHNESS OR SURFACE TEXTURE

A third property called texture appears early in the literature with the sphericity and

roundness properties since then texture property was longed described but it was in

accordance with the authors at that time not measurable

Wright in 1955 developed a method to quantify the surface texture or roughness of

concrete aggregate using studies done on 19 mm stones The test aggregates were first

embedded in a synthetic resin The stones were cut in thin sections The sections

projection was magnified 125 times The unevenness of the surface was traced and the

total length of the trace was measured The length was then compared with an uneven

line drawn as a series of chords (see figure 17) The difference between these two

lines was defined as the roughness factor (Janoo 1998)

However with the advance of technology it has become easier measure the roughness

and here is presented some researcherrsquos ideas how this property should be calculated

One technique used by Janoo (1988) to define the roughness can be seen in figure 18a

and is defined as the ratio between perimeter and convex perimeter

The convex perimeter is obtained using the Feretrsquos box (or diameter) tending a line in

between the touching points that the Feretrsquos box describes each time it is turn (figure

18b)

PER

OC

PR

Figure 17 Measurement method for characterizing the surface texture of an aggregate (Janoo 1998)

a) Convex perimeter (CPER) b) Feret measurement Figure 18 a) Convex perimeter (CPER) b) Feret measurement (modified after Janoo 1998)

(38)

a)

b)

19

Kuo and Freeman (1998a) and Kuo et al (1998b) use the roughness definition as the

ratio perimeter and average diameter

Erosion and dilatation image processing techniques are used to obtain the surface

texture Erosion is a morphological process by which boundary image pixels are

removed from an object surface which leaves the object less dense along the

perimeter or outer boundary Dilatation is the reverse process of erosion and a single

dilatation cycle increases the particle shape or image dimension by adding pixels

around its boundary (Pan etal 2006)

The ldquonrdquo erosion and dilatation cycles are not standardized

Mora and Kwan (2000) used the ldquoconvexity ratio CRrdquo (equation 41) and the ldquofullness

ratio FRrdquo (equation 42) in their investigation they are

The convex area is the area of the minimum convex boundaries circumscribing the

particle This is illustrated in the figure 19 The convex area is obtained in a similar

way as the convex perimeter but in this case the area between the original outline and

the convex perimeter is our convex area

AVG

OD

PR

100A

1AARO

CONo A

AR =

CONo A

AR =

Figure 19 Evaluation of area and convex area (Mora and Kuan 2000)

(39)

(40)

(41)

(42)

20

4 TECHNIQUES IN ORDER TO DETERMINE PARTICLE

SHAPE

41 HAND MEASUREMENT

Hand measurement technique was the first used by obvious reasons in order to

improve the accuracy special devices developed as the ldquosliding rod caliperrdquo used by

Krumbein (1941) it works placing the sample on the sliding road calliper as show

figure 20b the length in different positions can be obtain by using the scale provided

in the handle the ldquoconvexity gagerdquo that was actually used by opticians to measure the

curvature of lenses but easily applicable to the particle shape analysis (Wentworth

1922b) works measuring the movement of the central pivot as figure 20a shows (the

two adjacent pivots are invariable) as many the central pivot moves more is the

curvature or the ldquoSzadeczky-Kardossrsquos apparatusrdquo develop in 1933 that traces the

profile of the rock fragment so the outline traced is then analyzed (Krumbein and

Pettijohn 1938) figure 20c show equipment

Another helpful tool to determine the particle dimensions was the ldquocamera lucidardquo to

project the particlersquos contour over a circle scale appearing in Figure 21 thus it is

possible to measure the particlersquos diameter

a)

c) b)

Figure 20 a) convexity gage used to determine the curvature in particle corners (Wenworth 1922b)

b)sliding rod caliper device to measure the particle axis length (Krumbein 1941) and c)Szadeczky-

Kardoss (1933) apparatus it was utilized to obtain the particle outline

Figure 21 Circle scale used by Wadell (1935) to determine particlersquos diameter and roundness

21

42 SIEVE ANALYSIS

Bar sieving eg according to EN 933-31997 can be used to determine simple large

scale properties By combining mesh geometries the obtained results can be used to

quantify flakiness and elongation index ASTM D4791 (Flat and elongated particles

are defined as those coarse aggregate particles that have a ratio of length to thickness

equal to or greater than a specified value such as 51 The index represents the

percentage on weight of these particles) The method is not suitable for fine materials

This due to the difficulty to get the fine grains passed through the sieve and the great

amount of particles in relation to the area of the sieve (Persson 1998) eg EN 933-

31997 related to flakiness index The test is performed on aggregates with grain size

from 4 mm and up to 63 mm two sieving operations are necessary the first separates

on size fraction and the second use a bar sieve after the first sieving the average

maximum diameter of the particles is obtain and with the second sieving (bar sieving)

the shortest axis diameter is found finally with this two parameters the flakiness

index is determined

There are more standards related with the particle shape (see appendix A) but this

above presented are probably the most known using sieve analysis to determine

particlersquos geometrical properties

Sieve analysis is facing the computers age and image analysis sieving research is

taking place (Andersson 2010 Mora and Kwan 2000 Persson 1998) Industry is

also applying the image analysis sieving with decrees on the testing time compare

with the traditional sieving method An inconvenient of image analysis is the error

due the overlapping or hiding of the particles during the capture process but the

advantages are more compare with disadvantages (Anderson 2010)

43 CHART COMPARISON

Charts developed over the necessity of faster results because the long time consuming

required when measuring each particle

Krumbein (1941) present a comparison roundness chart for pebbles which were

measured by Wadellrsquos method because this property was the most difficult to measure

due to the second order scale that roundness represents (See figure 22)

Figure 22 Krumbein (1941) comparision chart for roundness

22

A qualitative chart by Powers (1953) try to include both (sphericity and roundness)

particlersquos characteristics it was divided on six roundness ranges (very angular

angular sub-angular sub-rounded rounded and well rounded) and two sphericity

series (high and low sphericity) This chart was prepared with photographs to enhance

the reader perspective (See figure 23)

A new chart including sphericity and roundness appear this time it was easier to

handle the two mean properties of particlersquos shape furthermore there was included

the numerical values that eliminated the subjectivity of qualitative description The

chart is based on Wadellrsquos definitions (Krumbein and Sloss 1963) (See figure 24)

Folk (1955) worried about the personrsquos error on the chartrsquos comparison studied the

determination of sphericity and angularity (he used the Powers 1953 comparison

chart) he found that the sphericity determination by chart comparison has a negligible

error while the roundness he concluded it was necessary to carry out a more wide

research due the high variability show by his study

Figure 23 Powers (1953) qualitative shpericity-roundness chart

Figure 24 Sphericity-roundness comparison chart (Krumbein and sloss 1963)

23

44 IMAGE ANALYSIS

Image analysis is a practical method to use for shape classification since it is fast and

can be automated Different techniques appear to process these images among them

are

o Feret Diameter the Feret diameter is the longitude between two parallel lines

this lines can rotate around one particle or outline to define dimensions as it

is shown in figure 25 these method is not a fine descriptor but as it was say

above it is a helpful tool to determine diameters (Janoo 1988)

o Fourier Mathematical Technique It produces mathematical relations that

characterize the profile of individual particles This method favours the

analysis of roughness and textural features for granular soils The problem in

the methodology remains in the re-entrant angles in order to complete the

revolution (Bowman et al 2001) see figure 26

o Fractal Dimension Irregular line at any level of scrutiny is by definition

fractal (Hyslip and Vallejo 1997) Figure 27 shows fractal analysis by the

dividing method The length of the fractal line can be defined as

N

1n

nn0 )nsinbncosa(a)(R

RD1n)(P

Figure 25 Feret measurement technique is defined by two parallel lines turning

around the particle to define the shortest and longest Feret diameter (Janoo 1988)

Figure 26 Fourier technique with two radiuses at one angle (Bowman et al 2001)

(43)

(44)

24

o Orthogonal image analysis This technique is basically the use of two images

orthogonal between them to acquire the three particle dimensions (Fernlund

2005) any of the above techniques can be used in this orthogonal way

o Laser Scanning Technique this kind of laser scanning 3D is one of the most

advanced techniques In figures 28a) we have the laser head scanning the rock

particles the particles have control points in order to keep a reference point

when move them to scan the lower part in figure 28b) we can see the laser

path followed (Lanaro and Tolppanen 2002)

Another technique is the Laser-Aided Tomography (LAT) in this case a laser sheet is

used to obtain the particles surveying (see figure 29) This technique is different and

has special requirements as to use liquid with same refractive index as the particles

particles must let the laser or certain percent of light go through (Matsushima et al

2003)

a) b)

Figure 27 Fractal analysis by the dividing method at different scrutiny scale (Hyslip and Vallejo 1997)

Figure 28 a) Scanning head b) scanning path (Lanaro and Tolppanen 2002)

Figure 30 3D scan completed ready to

use for any further measure

(Matsushima et al 2003)

Figure 29 LAT scaning particles

(Matsushima et al 2003)

25

Both 3D techniques obtain the particle shape that is later used to achieve measures as

we can see in figure 30

All these previous techniques are easily written in codes or scripts to be interpreted in

a digital way obtaining the desired measurement but there are some interesting points

in the image analysis regarding on the errors involve among them are image

resolution and orientation of the particles orientation is not relevant when it is

random and large number of particles are involve resolution have an influence on the

accuracy (Zeidan et al 2007)

When resolution is increase more accuracy is obtain and the object representation

match better with the real form in the other hand more resolution means more

spending on memory and time thus resolution needs to be according with the goal

and precision needed in any work (Schaumlfer 2002)

Schaumlfer (2002) conclude that attributes like length when measuring digital images

present relative high errors It can be vanish or at least diminish using high resolution

just for diameter but not for perimeter that keep the error as big as initially Johansson

and Vall (2011) obtain similar results when 3 different resolutions were used in the

same particle obtaining an unstable output for those termsquantities that involve the

perimeter Thus all quantities relating the perimeter should be treated with care

5 EFFECT OF SHAPE ON SOIL PROPERTIES

51 INTRODUCTION

In laboratory test on the effect on particle size on basic properties has been

investigated in several studies this relation has been discussed and various

mechanisms had been proposed to explain the behaviour of the soil in dependency

also with the shape Basically there are two mechanisms proposed The arrangement

of particles and the inter-particle contact (Santamarina and Cho 2004) and

subsequence breakage

The arrangement of particles

Arrangement of the particles can be presented in three different forms loose dense

and critical this arrangement determines the soil properties (eg density increase with

more dense arrangement) Loose and dense states are easy understandable when

figure 31 is explained while in the upper part of the figure the particles are arranged

using the minimum space needed in the lower part a span is created using the flaky

particle as a bridge this phenomena is known as ldquobridgingrdquo Bridging can produce

different geotechnical results when just the shape of the particle is changed eg void

ratio (Santamarina and Cho 2004) Particles are able to rearrange this could be done

applying pressure (energy) to the soil the pressure (energy) will create such forces

that soil particles will rotate and move (see figure 34) finishing in a more dense state

26

A loose soil will contract in volume on shearing and may not develop any peak

strength (figure 32 left) In this case the shear strength will increase gradually until

the residual shear strength is revealed once the soil has ceased contracting in volume

A dense soil may contract slightly (figure 32 right) before granular interlock prevents

further contraction (granular interlock is dependent on the shape of the grains and

their initial packing arrangement) In order to continue shearing once granular

interlock has occurred the soil must dilate (expand in volume) As additional shear

force is required to dilate the soil a peak shear strength occurs (figure 32 left) Once

this peak shear strength caused by dilation has been overcome through continued

shearing the resistance provided by the soil to the applied shear stress reduces

(termed strain softening) Strain softening will continue until no further changes in

volume of the soil occur on continued shearing Peak shear strengths are also

observed in overconsolidated clays where the natural fabric of the soil must be

destroyed prior to reaching constant volume shearing Other effects that result in peak

strengths include cementation and bonding of particles The distinctive shear strength

called the critical state is identified where the soil undergoing shear does so at a

constant volume (Schofield and Wroth 1968)

The inter-particle contact

For frictional soil ie coarse grained soil the friction between particles is the

dominating factor for strength Materials usually consisting of coarse grains (diameter

Figure 31 Bridging effect when flaky particles are combined in the bulk material (Santamarina and

Cho 2004)

Figure 32 The left part of the figure show a typical behaviour of loose and dense material over shear stress

while at the right the figures illustrate the typical volume changes

27

gt 006mm) behave as a frictional soil it means that the strength of coarse soils (silt

sand gravel etc) comes from an inter-particle mechanical friction thus ideally they

do not have traction strength In figure 33 the inter-particle contact is illustrated here

the pressure (P) is applied and two more components are found the normal load (N)

and the tangential load (T) described as the friction coefficient (μF) The forces stand

in equilibrium (Johansson and Vall 2011)

When particles equilibrium is disturbed (friction coefficient is not enough to keep

particles unmoved) the rotation is imminent and it is necessary in order to compact

the soil in figure 34 can be seen that the arrangement is a fact that inhibit or allow this

rotation and the shape in the 3 different scales are also factors because the more

spherical andor more rounded andor less roughness more easy is the rotation

(Santamarina and Cho 2004)

Breakage

Breakage is a side effect of the inter-particle contact and rotation when pressure

exceed the rock strength it can happened when the particles are tight together and

there is not enough space to rotate it is more obvious in angular particles (mesh form)

or as in figure 31 where the flaky particle ldquobridgingrdquo is not able to rotate but it can

brake by the pressure increase Yoginder et al (1985) notice that the angular particle

break during his experiments and they turn more rounded changing the original size

and form configuration at the same time there was a soil properties loosening

Figure 33 Inter-particle contact and forces acting (Axelsson 1998)

Figure 34 Rotation inhibition by the particles compaction or low void ratio (Santamarina and Cho 2004)

28

52 INFLUENCE OF SIZE AND SHAPE

Wenworth (1922a) and Pellegrino (1965) among others suggest that agent transport of

the rocks (rigor of transport temperature and moisture changes etc) determine its

shape but also the particle genesis itself (rock structure mineralogy hardness etc) It

is not possible to determine the shape of the particles based on the agent transport or

genesis but generally a shape behaviour is expected according to Mitchell and Soga

(2005) specially when the particle size is in the clay size (gt2μm) The shapes of the

most common clay minerals are platy (figure 35) with some exceptions (eg

halloysite occurs as tubes kaolinite are large thick and stiff Smectites are composed

of small very thin and filmy particles Illites are intermediate between kaolinite and

smectite and attapulgite occurs in lathlike particle shapes) Some clay minerals

photographs are presented in figure 35

Figure 35 Clay mineral shape a) hallosite b) Kaoline c) Smactites d) Illites and e) attapulgite (Modified

from Mitchell and Soga 2005)

Figure 36 Particle size range in soils Generally the particles of clay size are plate shaped (Mitchell and

Soga 2005)

a) b) c)

e) d)

29

53 VOID RATIO AND POROSITY

The void ratio (e) is the ratio of the volume of voids to the volume of solid it is

defined by the equation

Porosity (n) is the ratio of the volume of voids to the total volume of the soil it is

represented by the equation

Holubec and DrsquoAppolonia (1973) found a relation between the void ratio and

sphericity (referred in the paper as coefficient of angularity ratio of particle surface

and equivalent sphere surface) their results show that the maximum and the minimum

void ratio increases as the shpericity decreases In this study the surface was obtained

for an indirect method based on the permeability developed by Hoffman in 1959

described in the same document Rouseacute et al (2008) defined the roundness as

Wadell (1935) and he found it as an important factor controlling the minimum and

maximum void ratios Some other authors as Youd (1973) and Cho et al (2006)

conclude the same minimum and maximum void ratios increase when sphericity and

roundness decrease Another interesting result (all above authors) was the bigger

influence of the form (sphericity circularity) and roundness on the maximum void

ratio The change of the maximum void ratio is more pronounced than the change of

the minimum void ratio when the form and roundness changes (See figure 39)

Particles arrangement and interlocking are probably the factor that controls the void

ratio bridge effect permit the existence of void among the particles while interlocking

allowed the particles to form arches avoiding the possibility to rotate and stay in a

more stable configuration eg as it happens with marbles

Figures 36 37 and 38 shows proposed empirical relationships between void ratio and

shape from tables 5 and 6 (graphically the scale goes from 0 to 1 when cero mean

high angularity shpericity or circularity and one means low angularity circularity or

sphericity) Holubec and DrsquoAppolonia (1973) data was taken to obtain a power curve

and describe a tendency Santamarina and Cho (2004) show Youd equations in the

original paper Youd (1973) never presented the equation but it is easy to use the

information to draw a trend

The graphics presented in this document (figures 36 37 and 38) must be used with

certain reserves due the fact that the original data was modified in order to fit all

information in one graphic what the figures shows is just the general trend of the

behaviourrsquos material regarding on the shape If more accurate description and

information is required the author recommends consulting the reference data In the

same way equations from Holubec and DrsquoApollonia (1973) and Youd (1973) were not

presented by the authors but the use of the information was taken in order to build up

those equations on tables 6 and 7

S

V

V

V

= e

V

V

=nV

(45)

(46)

30

Table 6 Minimum void ratio equations regarding on the quantity (Ψ for sphericity C for circularity R

for roundness SF for Sukumaran shape factor and AF for Sukumaran angularity factor)

EQUATION NUMBER REFERENCE

Figure 34 (left)

4340

minΨ45490e =

47

Holubec amp DrsquoAppolonia 1973 (Ψ

was obtained using equation 2)

SF06340

mine021903180e +=

48

Sukumaran amp Ashmawy 2001 (SF

obtained using equation 21)

C05101emin

= 49

Cho etal 2006 (C obtained using

figure 12)

Figure 34 (right)

1

minR08203590e +=

50

Youd 1973 (R obtained from figure

11 and table 3)

R34080emin

= 51

Cho et al 2006 (R obtained using

figure 12)

1

minR05104330e +=

52

Rouseacute et al 2008 (R obtained by

equation 21)

AF02330

mine372004160e +=

53

Sukumaran amp Ashmawy 2001 (AF

obtained using equation 37)

Table 7 Maximum void ratio equations regarding on the quantity (Ψ for sphericity C for circularity R

for roundness SF for Sukumaran shape factor and AF for Sukumaran angularity factor)

EQUATION NUMBER REFERENCE

Figure 35 (left)

51520

max Ψ61120e = 54

Holubec and DrsquoAppolonia 1973 (Ψ

was obtained using equation 2)

SF1190

max e0016907180e += 55

Sukumaran amp Ashmawy 2001 (SF

obtained using equation 21)

C86061emax = 56

Cho etal 2006 (C obtained using

figure 12)

Figure 35 (right)

1

max R1505540e += 57

Youd 1973 (R obtained from figure

11 and table 3)

R62031emax= 58

Cho et al 2006 (R obtained using

figure 12)

1

max R107106150e += 59

Rouseacute et al 2008 (R obtained by

equation 21)

AF0530

max e12506090e += 60

Sukumaran amp Ashmawy 2001 (AF

obtained using equation 37)

Comparing figures 37 and 38 (minimum and maximum void ratio) it can be seen on

the right scheme of both figures 37 and 38 (when the factor is roundnessangularity)

that all the empirical relations has a common initial point close to 1 (it means that

particles are well rounded) while this common agreement disappear when the

roundness factor decreases (when the particles become more angular) Same figures

(37 and 38) on the left graphs (when the factor is sphericitycircularityshape) do not

present the same behaviour in fact there is more disperse initial point close to 1(when

the particles tend to be more sphericalcircular)

31

In Figure 39 the Δe (emax-emin) has been plotted to show how the maximum void ratio

and the minimum void ratio has different rate change when the particle shape

changes Maximum void ratio increases more than minimum void ratio when the

particle shape becomes less spherical andor more angular Comparing figure 39 left

and right graphics it can be seen that right present a common initial point when the

quantity (roundnessangularity) is close to one while in the left graphic the initial

point is more disperse Both ending points in both graphics (close to zero) are

dispersed

Figures 37 38 and 39 present the same behaviour right graphics (when the factor is

roundness angularity) in each figure have an initial common point while the left

graphics do not (when the factor is sphericity circularity shape)

Figure 37 Minimum void ratio based upon the relation of shape factor proposed by the authors indicated

in the figure

Figure 38 Maximum void ratio based upon the relation of shape factor proposed by the authors indicated

in the figure

04

06

08

1

12

14

16

18

2

005

015

025

035

045

055

065

075

085

095

Factor (roundness angularity)

min

imu

m v

oid

rati

o

Youd 1973 roundness

Rouse 2008 roundness

Cho 2006 roundness

Sukumaran 2001 AF

03

04

05

06

07

08

09

1

11

12

13

05

015

025

035

045

055

065

075

085

095

Factor (sphericity circularity shape)

min

imu

m v

oid

rati

oHolubec 1973 sphericity

Cho 2006 circularity

Sukumara 2001 SF

05

07

09

11

13

15

17

19

21

00

150

250

350

450

550

650

750

850

95

Factor (sphericity circularity shape)

Maxim

um

vo

id r

ati

o

Holubec 1973 sphericity

Cho 2006 circularity

Sukumara 2001 SF

05

1

15

2

25

3

35

005

015

025

035

045

055

065

075

085

095

Factor (roundness angularity)

Maxim

um

vo

id r

ati

o

Youd 1973 roundness

Rouse 2008 roundness

Cho 2006 roundness

Sukumaran 2001 AF

32

54 ANGLE OF REPOSE

The angle of repose of a granular material is the steepest angle of descent or dip of the

slope relative to the horizontal plane when material on the slope face is on the verge

of sliding as show in figure 40

According to Qazi (1975) there are five types of forces which may act between the

particles in soils

1 Force of friction between the particles

2 Force due to presence of absorbed gas andor moisture of particle

3 Mechanical forces caused by interlocking of particles of irregular shape

4 Electrostatic forces arising from friction between the particles themselves and

the surface with which they come in contact

5 Cohesion forces operating between neighbouring particles

Rouseacute et al (2008) found a decrease of angle of repose with increase roundness

based upon ASTM C1444 test (Standard Test Method for Measuring the Angle of

Repose of Free-Flowing Mold Powders) The method consist in pouring sand on a

surface cover by paper trough a funnel of specific dimensions (the nozzle diameter

depend on the sandrsquos particle size) from an altitude of 15 inches (381 mm) The sand

is release from the funnel until the peak of the cone formed by the sand stops the flow

The repose angle is obtained with the equation

H represent the 15 inches D and d represent the diameter of the cone formed by the

sand and the diameter of the funnel respectively

Figure 39 Maximum minus minimum void ratio based upon the relation of shape factor proposed by the

authors indicated in the figure

0

01

02

03

04

05

06

07

08

09

1

005

015

025

035

045

055

065

075

085

095

Factor (sphericity circularity shape)

Maxim

um

- M

inim

um

Vo

id r

ati

oHolubec 1973 sphericity

Cho 2006 circularity

Sukumara 2001 SF

0

02

04

06

08

1

12

14

16

18

005

015

025

035

045

055

065

075

085

095

Factor (roundness angularity)

Maxim

um

- M

inim

um

Vo

id r

ati

o

Youd 1973 roundness

Rouse 2008 roundness

Cho 2006 roundness

Sukumaran 2001 AF

dD

H2

tan=φ1

rep(61)

33

Rouseacute (2008) shows an empirical relation to obtain the angle of repose based on the

roundness of the particles

55 SHEAR STRENGTH

The MohrndashCoulomb failure criterion represents the linear envelope that is obtained

from a plot of the shear strength of a material versus the applied normal stress This

relation is expressed as

where τ is the shear strength σn is the normal stress co is the intercept of the failure

envelope with the τ axis and is the slope of the failure envelope The quantity c is

often called the cohesion and the angle is called the angle of internal friction

Studies show that the internal friction angle (under drained triaxial tests) increases

more rapidly on those materials having higher angularity increasing the relative

density The internal friction angle is a function of the relative density and the particle

shape (Holubec and DrsquoAppolonia 1973)

Chan and Page (1997) found in a study made with dry copper (using different shapes

and sizes ranging from 180 to 106 μm) using a direct shear test (ring share test) that

the internal friction angle increases as the angularity increases

Shinohara et al (2000) did some experiments with steel powder different shapes

using a triaxial cell in the test Shinohara never used the roundness or angularity on

the work but apply the shape factor (relation long axisshort axis) and the results were

that as this relation deviate from factor 1 the internal friction angle increases

The following empirical relations were found in the literature showing the behaviour

of the friction angle (obtained under different conditions)

)tan( noc

Figure 40 Representation of the angle of repose

(63)

(62)

34

Cho et al (2006)

(64)

(R is obtain by comparing the Krumbein chart figure 13)

Rouseacute (2008)

(65)

(66)

(R is defined using Wadell equation 22)

In figure 41 the suggested empirical relations above and lines constructed using

author data from Holubec and DrsquoAppolonia (1973) and Sukumara and Ashmawy

(2001) are plotted together to display the general trend on the particle shape and

friction angle relation Sukumaran reports two lines one based on the shape factor

(SF) and the second referring the angularity factor (AF) Sukumaran performed the

tests at constant volume

The scale used for Holubec and DrsquoAppolonia (1973) have lower and upper limits of 1

and 2 respectively (angularity form) and a scale change was applied to be able to

presented in the actual figure 41 As in the previous section (52) the author

recommend to use the original data from the references due that the figure just follows

the general trend of the behaviourrsquos particle regarding on the shape

Figure 41 The changes on the internal friction angle shows a general increase when the particle roundness

becomes angular or in the case of Sakamuran less spheric (Shape factor SF)

35

Barton and Kjaernsli (1981) suggested a model (equation 67) to predict the peak

friction angle (φrsquo) based upon numerous trixial and direct shear data tests

where

Se equivalent strength of particle

Re equivalent roughness of particle

φb basic friction angle (obtained from basic tilting test)

σn normal load

The information required for the model is (1) the uniaxial compressive strength of the

rock (2) the d50 particle size (mesh size where 50 of the particles pass through)

required to define Se (figure 42) (3) the degree of particle roundness and (4) the

porosity following compaction All data can be estimated by simple index tests

Barton and Kjaernsli (1981) suggest that particle size and sample scale has an effect

on the friction angle and includes them to obtain the equivalent strength (Se) figure 42

shows the method to obtain this value Compressive strength (σc) was chosen to be the

factor affecting the scale because micro fractures influence this property while

samples are bigger more micro fractures contain and its compressive strength reduces

The equivalent roughness is obtain using figure 43 where is required to know the

porosity (n) and the origin of the particles (a small chart is provided in the same figure

to compare the particles profile)

b

n

ee

SLogR

Figure 42 Method of estimating Equivalent Strength (Se) of rockfill based on uniaxial compressive strength

(σc ) and d50 particle size (Barton amp Kjaernsli 1981)

(67)

36

56 SEDIMENTATION PROPERTIES

A particle released in a less dense Newtonian fluid initially accelerate trough the fluid

due to the gravity Resistances to deformation of the fluid transmitted to the particle

surface drag generate forces that act to resist the particle motion The force due to the

weight (Fw) can be written as

Where ρp ρ are density of the particle and fluid (water) respectively g is the

gravitational force and Vp is the volume of the particle

And the resistance force (FD) is

Where CD is the dimensionless drag coefficient W is the weight of the particle and A

is the cross section area

Particlersquos shape has been assumed to be spherical when equations are applied on the

settling velocity Correlation deviates when particle shape departs from spherical form

Figure 43 Method of estimating Equivalent Roughness (Roe) based on porosity of rockfill

origin material degree of roundedness and smoothness of particle (Barton amp Kjaernsli 1981)

PPW ρ)gV(ρF

A2

WρCF

2

DD

(68)

(69)

37

(Dietrich 1982) and it is known that natural particles depart from spherical form

thus it is evident that this departure would have consequences

The below equation is proposed to account the shape (in this case the Corey shape

factor equation 8) in the settling velocity (Jimenez and Madsen 2003)

Jimenez and Madsen (2003) Dietrich (1982) Briggs and McCulloch (1962) and

others were working in the hydraulic shape of particles to solve problems as sediment

transport It is obvious that the equation presented and the researcherrsquos investigation

works under certain conditions (eg grain size between 0063-1 mm)

Dietrich (1982) suggests an empirical relation that accounts settling velocity size

density shape and roundness of a particle

R1 R2 and R3 are fitted equations for size and density shape and roundness

respectively

57 HYDRAULIC CONDUCTIVITY PERMEABILITY

Darcyrsquos Law Permeability is one component of Darcyrsquos law Darcys law is a simple

proportional relationship between the instantaneous discharge rate through a porous

medium the viscosity of the fluid and the pressure drop

The total velocity Ve is equal to the product of the permeability of the medium

(porous media) k the pressure drop ∆p all divided by the viscosity μ (Muskat

1937)

Darcys law is only valid for slow viscous flow most groundwater flow cases fall in

this category Typically Darcyrsquos law is valid at any flow with laminar flow (see figure

44)

Reynoldrsquos number (Laminar and turbulent Flow) Typically any laminar flow is

considered to have a Reynoldrsquos number less than one and it would be valid to apply

Darcys law Experimental tests have shown that flow regimes with Reynolds numbers

1

ND

S

S

ZY

gd1s

WW

NDN

gd)1s(4

dS

2R1R

3 10RW

pk

Ve

(70)

(71)

(72)

(73)

38

up to 10 may still be Darcian (laminar flow) as in the case of groundwater flow The

Reynolds number (a dimensionless parameter) for porous media flow is typically

expressed as

where ρ is the density of water (units of mass per volume) υ is the specific discharge

(with units of length per time) d is a representative average grain diameter for the

porous media (often taken as the 30 passing size from a grain size analysis using

sieves - with units of length) and μ is the viscosity of the fluid (Muskat 1937)

Shape effects Permeability as Head and Epps (2011) suggested is affected by the

shape and texture of soil grains Elongated or irregular particles create flow paths

which are more tortuous than those spherical particles Particles with a rough surface

texture provide more frictional resistance to flow Both effects tend to reduce the

water flow through the soil

Kozeny-Carman empirical relation accounts for the dependency of permeability on

void ratio in uniformly graded sands serious discrepancies are found when it is

applied to clays due the lack of uniform pores (Mitchell and Soga 2005)

There are various formulations of the Kozeny-Carman equation one published by

Head and Epps (2011) takes the void ratio e the specific surface area Ss and an

angularity factor F into account of permeability k

The angularity factor F considers the shape of the particles and ranges from 11 for

rounded grains 125 for sub rounded to 14 for angular particles The specific surface

Ss is defined as

d1 and d2 represent the maximum and minimum size particle in mm

Kane amp Sternheim (1988) suggest that the inclusion of the shape factor (F) has

probably the background on the Reynolds number due this factor is dependent

significantly on the shape of the obstacles and Reynolds number determines the

presence of laminar or turbulent flow Figure 44 show how the laminar flow has low

energy dissipation while turbulent flow (eg the roughness and path tortuosity) has

high energy dissipation

e1

e

FSs

2k

3

2

dRe

21

6

ddSs

(74)

(75)

(76)

39

According to Nearing and Parker (1994) the amount of soil detached during laminar

and turbulent flow is dependent on each soil and also greater on turbulent flow due the

greater shear strength generated during this kind of flow this could suggest the

greater erosion when turbulent flow is present

58 LIQUEFACTION

Soil liquefaction is a phenomenon in which soil loses much of its strength or stiffness

for a generally short time by earthquake shaking or other rapid loading Static and

dynamic liquefactions occur been the second one the most regular known

Liquefaction often occurs in saturated soils that is soils in which the space between

individual particles is completely filled with water This water exerts a pressure on the

soil particles that influences how tightly the particles themselves are pressed together

Shaking or other rapid loading can cause the water pressure to increase to the point

where the soil particles can readily move with respect to each other (Jefferies and

Been 2000)

Jefferies and Been (2000) state that it is clear that minor variation in intrinsic

properties of sand have major influence on the critical state These might be variations

on grain shape mineralogy grain size distribution surface roughness of grains etc

Yoginder et al (1985) found that substantial decrease on liquefaction resistance

occur with increase in confining pressure for rounded and angular sands (1600 kPa)

also rounded sands show an rapidly build up of resistance against liquefaction with

increasing density while angular tailing sand in contrast show such rapid increase

only at low confining pressures At low confining pressure angular material is more

resistant to liquefaction Probably the breakage of the corners on the angular particles

in tailings is ruling the lost in resistance at high confining pressures (sieve analysis

Figure 44 The figure show the extremes of flow behaviour First turbulent conditions where the flow is

essentially random and unpredictable and second the well defined Laminar flow conditions

40

after test identify the breakage of angular particles while on rounded particles the

sieve analysis was practically the same)

59 GROUNDWATER AND SEEPAGE MODELLING

In groundwater flow the particlersquos shape affects the soilrsquos pore size distribution

hence the flow characteristics (Sperry and Peirce 1995) Tortuosity and permeability

(also see section 57) are two significant macroscopic parameters of granular medium

that affect the passing flow (Hayati et al 2012) Current models incorporating the

effects of particle shape have failed to consider irregular particles such as those that

would prevail in a natural porous medium (Sperry and Peirce 1995)

Hayati et al (2012) suggested based on his results that tortuosity effect converge

when the porosity increases indicating that the shape have dominance at low and mid

porosity ranges

Sperry and Peirce (1995) research conclusions suggest that particle size and porosity

are more important predictors for hydraulic conductivity explaining the 69 of the

variability but particle shape appears to be the next most important This however

apparently comprises particles larger than 295-351 μm Differences for particle size

295-351 μm and smaller are not detectable Another interesting result in the research

was the interaction effect of the particle size and particle shape It suggests a different

packing configuration for particles of the same shape but different size (scale

dependent)

6 DISCUSSION

61 TERMS QUANTITIES AND DEFINITIONS

In order to describe the particle shape in detail there are a number of terms quantities

and definitions (qualitative and quantitative) used in the literature (eg Wadell 1932

1934 Krumbein 1941 Sneed amp Folk 1958) All mathematical definitions

(quantitatives) are models used to simplify the complexity of shape description Some

authors (Mitchell amp Soga 2005 Arasan et al 2010) are using three sub-quantities

one and each describing the shape but at different scales The terms are

morphologyform roundness and surface texture (figure 1) The three sub-quantities

are probably the best way to classify and describe a particle because not a single

definition can interpret the whole morphology Common language is needed when

descriptors are explained and these three scales represent an option It is evident in

the reviewed literature that many of the shape descriptors are presented with the same

name but also that there is not a clear meaning on what this descriptor defines eg

when there is no upper limit in the roundness does it means that the angularity never

ends Could they be more and more angular Probably they could be on theory but

not in reality

41

62 PROPERTIES

Trough various articlersquos review done in the present investigation it is recognized that

the particlersquos shape has an effect on the material properties among these are

1 Porosity (Tickell 1938 Fraser 1935 Kolbuszewski 1948) and void ratio

(Cho et al 2006 Shergold 1953 Rouseacute et al 2008 Santamarina and Cho

2004)

2 Permeability (Witt and Brauns 1983)

3 Internal friction angle (Shinohara et al 2000 Chan and Page 1997

Cheshomi et al 2009)

4 Density (Youd 1973 Holubec and DrsquoAppolonia 1973)

5 Drag coefficient Hydraulics (Briggs and McCulloch 1962)

In Table 5 is a short resume of the properties and shape effect found in peer review

articles trough different journals Most of the reviewed articles based its research on

uniform graded sands

Table 8 Compilation of properties influenced by particle shape

Repose

angle

Friction

angle

Porosity and

Void ratio Density Permeability

Settling velocity

Drag coefficient Deformation

Sphericity (3D)shape factor

NI x x x x x x

Circularity (2D)

NI x x x x NI NI

Roundness x x x x NI NI x

x influence

NI no information available

Shape of particles has an effect on the arrangement producing bridging or avoiding

the rotation of the particles and the resulting geotechnical property is affected eg

including flaky particles can result in a higher void ratio due the bridging effect

(Santamarina and Cho 2004) and depending on the loads even the size distribution is

changed due the breakage (Yoginder et al 1985) in similar way angular particles

produce higher void ratio due the avoided possibility of the particles to rotate and

compact

The influence of the chosen shape descriptor appears in this review to have minor

influence on the soil properties in the reviewed studies except on the void ratio and

the friction angle Influence of particle shape in some cases is hider by other factors

(eg size distribution) also the particle shape probably does not have influence when

particle size is in the clay order (eg hydraulic conductivity) the reason could be due

to forces as electrostatic or capillarity become more important at this level

Among the shape descriptors some are chosen more often in literature (eg aspect

ratio) there is no apparent scientific basis to use it (probably due to the simplicity of

the measurement it becomes one of the most use) but there are still some other

descriptors that may or may not show better correlation with the soil properties

Instead empirical relations had been developed regarding roundness or shape to

describe the soil behaviour it is clear that the mechanism behind the results is still not

completely understood

42

There is necessity to define the best(s) shape descriptor(s) to be used for particular

geotechnical properties

63 IMAGE ANALYSIS

Many image analysis techniques had been used to describe the particle shape eg

Fourier analysis fractal dimension tomography etc (Hyslip and Vallejo 1997) but

there is not agreement on the usage or conclusion to ensure the best particle descriptor

for geotechnical applications

There are several shape descriptors and also various techniques to capture the

particles profile (3-dimensions 3-dimension orthogonal and 2-dimensions) Each

technique presents advantages and disadvantages 3-dimensions is probably the

technique that provide more information about the particle shape but the precision

also lies in the resolution the equipment required to perform such capture could be

more or less sophisticated (scanning particles laying down in one position and later

move to complete the scanning or just falling down particles to scan it in one step)

3-dimensions orthogonal this technique use less sophisticated equipment (compare

with the previous technique) but its use is limited to particles over 1cm also

information between the orthogonal pictures is not capture 2-dimensions require non

sophisticated equipment but at the same time the shape information diminish compare

with the previous due the fact that it is possible to determine only the outline as the

particle measurements are performed in 2-dimensions it is presumed that they will lie

with its shortest axis perpendicular to the laying surface when they are flat but when

the particle tends to have more or less similar axis the laying could be random

Advantages on the use of image analysis are clear there is not subjectivity because it

is possible to obtain same result over the same images Electronic files do not loose

resolution and it is important when collaboration among distant work places is done

files can be send with the entire confidence and knowing that file properties has not

been changed Technology evolutions allowed to work with more information and it

also applies to the image processing area were the time consumed has been shortened

(more images processed in less time)

One important aspect in image analysis is the used resolution in the analysis due the

fact that there are measurements dependent and independent on resolution Thus

those dependent measurements should be avoided due the error included when they

are applied or avoid low resolution to increase the reliability Among these

parameters length is the principal parameter that is influences by resolution (eg

perimeter diameter axis etc) Resolution also has another aspect with two faces

quality versus capacity more resolution (quality) means more storage space a

minimum resolution to obtain reasonable and reliable data must be known but it

depend on each particular application

43

64 APPLICATIONS

Quantify changes in particles in the authorrsquos thought is one of the future applications

due the non-invasive methods of taking photographs in the surface of the damrsquos slope

rail road ballast or roads Sampling of the material and comparing with previous

results could show volume (3D analysis) or area (2D analysis) loss of the particles as

well as the form roundness and roughness This is important when it has been

suggested that a soil or rock embankment decrees their stability properties (eg

internal friction angle) with the loss of sphericity roundness or roughness

Seepage stock piling groundwater etc should try to include the particle shape while

modelling seepage requires grading material to not allow particles move due the

water pressure but in angular materials as it is known the void ratio is great than the

rounded soil it means the space and the possibilities for the small particles to move

are greater stock piling could be modelled incorporating the particle shape to

determine the binrsquos capacity when particle shape changes (void ratio changes when

particle shape changes) Modelling requires all information available and the

understanding of the principles that apply

Industry is actually using the particle shape to understand the soil behaviour and

transform processes into practical and economic image analysis has been included in

the quality control to determine particle shape and size because the advantages it

brings eg the acquisition of the sieving curve for pellets using digital images taken

from conveyor this allows to have the information in a short period of time with a

similar result at least enough from the practical point of view as the traditional

sieving

7 CONCLUSIONS

The conclusions of this literature review are

It has been shown that particle shape has influence on the soil behaviour

despite of partial knowledge of the mechanism behind Understanding of the

particle shape and its influence needs to be accomplished

A common language needs to be built up to standardize the meaning on

geotechnical field that involve the particle shape General relationships

between shape and properties should be developed

Based on this review it is not clear which is the best descriptor to use in

geotechnical engineering affecting he related shape to properties Instead of a

couple of standards there is no shape descriptor in geotechnical field fully

accepted

Image analysis tool is objective make the results repeatable obtain fast results

and work with more amount of information

44

Resolution needs to be taken in consideration when image analysis is been

carried out because the effects could be considerable Resolution must be set

according to the necessities Parameters as perimeter can be affected by

resolution

There are examples where particle shape has been incorporated in industries

related to geotechnical engineering eg in the ballast and asphalt industry for

quality control

8 FURTHER WORK

Three main issues have been identified in this review that will be further investigated

the limits of shape descriptors influence of grading and choice of descriptor for

relation to geotechnical properties

Shape descriptors have low and high limits frequently the limits are not the same and

the ability to describe the particlersquos shape is relative The sensitivity of each descriptor

should be compare to apply the most suitable descriptor in each situation

Sieving curve determine the particle size in a granular soil particle shape could differ

in each sieve size There is the necessity to describe the particle shape on each sieve

portion (due to practical issues) and included in the sieve curve Obtain an average

shape in determined sieve size is complicated (due to the possible presence of several

shapes) and to obtain the particle shape on the overall particlersquos size is challenging

how the particle shape should be included

Since several descriptors have been used to determine the shape of the particles and

the relation with the soil properties it is convenient to determine the descriptorrsquos

correlation with the soil properties

9 ACKNOWLEDGMENT

I would like to thanks to Lulearing University of Technology (LTU) the time I had spent

in its facilities and the kind environment it offers and University of Sonora

(UNISON) that has been providing me the financial support and the time to conclude

this journey

10 REFERENCES

Andersson T (2010) Estimating particle size distributions based on machine vision

Doctoral Thesis Departament of Computer Science and Electrical Engineering Lulearing

University of Technology ISSN 1402-1544 ISBN 978-91-7439-186-2

45

Arasan Seracettin Hasiloglu A Samet Akbulut Suat (2010) Shape particle of

natural and crished aggregate using image analysis International Journal of Civil and

Structural Engineering Vol 1 No 2 pp 221-233 ISSN 0970-4399

Aschenbrenner BC (1956) A new method of expressing particle sphericity Journal

of Sedimentary Petrology Vol 26 No 1 pp 15-31

Axelsson K (1998) Introduktion till jordmekaniken jaumlmte jordmateriallaumlran Skrift

984 Lulearing Avdelningen foumlr Geoteknologi Lulearing Tekniska Universitet (In Swedish)

Barton Nick amp Kjaernsli Bjorn (1981) Shear strength of rockfill Journal of the

Geotechnical Engineering Division Proceedings of the American Society of Civil

Engineers (ASCE) Vol 107 No GT7

Barrett P J (1980) The shape of rock particles a critical review Sedimentology

Vol 27 pp 291-303

Blott S J and Pye K (2008) Particle shape a review and new methods of

characterization and classification Sedimentology Vol 55 pp 31-63

Bowman E T Soga K and Drummond W (2001) Particle shape characterization

using Fourier descriptor analysis Geotechnique Vol 51 No 6 pp 545-554

Briggs L I McCulloch D S (1962) Hydraulic shape of sand particles Journal of

Sedimentary Petrology Vol 32 pp 645-656

Chan Leonard C Y and Page Neil W (1997) Particle fractal and load effects on

internal friction in powders Powder Technology Vol 90 pp 259-266

Cheshomi A Fakher A Jones C J F P (2009) A correlation between friction

angle and particle shape metrics in quaternary coarse alluvia Quarterly Journal of

Engineering Geology and Hydrogeology Vol 42 pp 145-155

Cho G Dodds J and Santamarina J C (2006) Particle shape effects on packing

density stiffness and strength Natural and crushed sands Journal of Geotechnical

and Geoenvironmental Engineering May 2006 pp 591-602

Dietrich William E (1982) Settling velocity of natural particles Water Resources

Research Vol 18 No 6 pp 1615-1626

Dobkins J E and Folk R L (1970) Shape development on Tahiti-nui Journal of

Sedimentary Petrology Vol 40 No 2 pp 1167-1203

Folk R L (1955) Student operator error in determining of roundness sphericity and

grain size Journal of Sedimentary Petrology Vol 25 pp 297-301

Fernlund J M R (1998) The effect of particle form on sieve analysis A test by

image analysis Engineering Geology Vol 50 No 1-2 pp 111-124

46

Fernlund J M R (2005) Image analysis method for determining 3-D shape of

coarse aggregate Cement and Concrete Research Vol 35 Issue 8 pp 1629-1637

Fernlund J M R Zimmerman Robert and Kragic Danica (2007) Influence of

volumemass on grain-size curves and conversion of image-analysis size to sieve size

Engineering Geology Vol 90 No 3-4 pp 124-137

Fraser H J (1935) Experimental study of the porosity and permeability of clastic

sediments The Journal of Geology Vol 43 pp 910-1010 ISSN 0022-1376

Hayati Ali Nemati Ahmadi Mohammad Mehdi and Mohammadi Soheil (2012)

American Physical Society Physical review E 85 036310 DOI

101103PhysRevE85036310

Hawkins A E (1993) The Shape of Powder-Particle Outlines Wiley New York

Head K H and Epps R J (2011) Manual of soil Laboratory testing Volum II

Permeability shear strength and compressibility test 3rd

edition Whittles Publishing

Scotland UK 3rd

edition

Holubec I and DrsquoAppolonia E (1973) Effect of particle shape on the engineering

properties of granular soils ASTM STP 523 pp 304-318

Hyslip James P Vallejo Luis E (1997) Fractal analysis of the roughness and size

distribution of granular materials Engineering Geology Vol 48 pp 231-244

Janoo Vincent C (1998) Quantification of shape angularity and surface texture of

base course materials US Army Corps of Engineers Cold Region Research and

Engineering Laboratory Special report 98-1

Jefferies Mike and Been Ken (2000) Soil liquefaction A critical state approach

Taylor amp Francis Group London and New York

Jimenez Jose A Madsen Ole S (2003) A simple formula to estimate settling

velocity of natural sediments Journal of Waterway Port Coastal and Ocean

Engineering Vol 129 No 2 pp 70-78

Johansson Jens and Vall Jakob (2011) Jordmaterials kornform Inverkan paring

Geotekniska Egenskaper Beskrivande storheter bestaumlmningsmetoder

Examensarbete Avdelningen foumlr Geoteknologi Institutionen foumlr Samhaumlllsbyggnad

och naturresurser Lulearing Tekniska Universitet Lulearing (In Swedish)

Kane Joseph W and Sternheim Morton M (1988) Physics John Wiley amp Sons Inc

Third edition

Kolbuszewski J (1948) An experimental study of the maximum and minimum

porosities of sands Proceedings of the Second International Conference on Soil

Mechanics and Foundation Engineering Rotterdam June 21 to 30 Sub-section IIb

pp 158-165

47

Krumbein W C and Pettijohn FJ (1938) Manual of sedimentary petrography

Appleton-Century Crofts Inc New York

Krumbein W C (1941) Measurement and geological significance of shape and

roundness of sedimentary particles Journal of Sedimentary Petrology Vol 11 No 2

pp 64-72

Krumbein W C and Sloss L L (1963) Stratigraphy and Sedimentation 2nd

ed

WH Freeman San Francisco

Kuo Chun-Yi and Freeman Reed B (1998a) Image analysis evaluation of

aggregates for asphalt concrete mixtures Transportation Research Record Vol 1615

pp 65-71

Kuo Chun-Yi Rollings Raymond and Lynch Larry N (1998b) Morphological

study of coarse aggregates using image analysis Journal of Materials in Civil

Engineering Vol 10 No 3 pp 135-142

Lanaro F Tolppanen P (2002) 3D characterization of coarse aggregates

Engineering Geology Vol 65 pp 17-30

Lees G (1964a) A new method for determining the angularity of particles

Sedimentology Vol 3 pp 2-21

Lees G (1964b) The measurement of particle shape and its influence in engineering

materials British Granite Whinstone Federation Vol 4 No 2 pp 17-38

Matsushima Takashi Saomoto Hidetaka Matsumoto Masaaki Toda Kengo

Yamada Yasuo (2003) Discrete element simulation of an assembly of irregular-

shaped grains Quantitative comparison with experiments 16th ASCE Engineering

Mechanics Conference University of Washington Seattle July 16-18

Mitchell James K and Soga Kenichi (2005) Fundamentals of soil behaviour Third

edition WILEY

Mora C F Kwan A K H Chan H C (1998) Particle size distribution analysis of

coarse aggregate using digital image processing Cement and Concrete Research Vol

28 pp 921-932

Mora C F and Kwan A K H (2000) Sphericity shape factor and convexity

measurement of coarse aggregate for concrete using digital image processing Cement

and Concrete Research Vol 30 No 3 pp 351-358

Muskat Morris (1937) The Flow of fluids through porous media Journal of Applied

Physics Vol 8 pp 274

Nearing M A and Parker S C (1994) Detachment of soil by flowing water under

turbulent and laminar conditions Soil Science Society of American Journal Vol 58

No 6 pp 1612-1614

48

Pan Tongyan Tutumluer Erol Carpenter Samuel H (2006) Effect of coarse

aggregate morphology on permanent deformation behavior of hot mix asphalt Journal

of Transportation Engineering Vol 132 No 7 pp 580-589

Pellegrino A (1965) Geotechnical properties of coarse-grained soils Proceedings

International Conference of Soil Mechanics and Foundation Engineering Vol 1 pp

97-91

Pentland A (1927) A method of measuring the angularity of sands MAG MN AL

Acta Eng Dom Transaction of the Royal Society of Canada Vol 21 Ser3xciii

Persson Anna-Lena (1998) Image analysis of shape and size of fine aggregates

Engineering Geology Vol 50 pp 177-186

Powers M C (1953) A new roundness scale for sedimentary particles Journal of

Sedimentary Petrology Vol 23 No 2 pp 117-119

Pye W and Pye M (1943) Sphericity determination of pebbles and grains Journal

of Sedimentary Petrology Vol 13 No 1 pp 28-34

Qazi M A (1975) Flow properties of granular masses A review on the angle of

repose The Arabian Journal for Science and Engineering Vol 1 No 2

Quiroga Pedro Nel and Fowle David W (2003) The effects of aggregate

characteristics on the performance of portland cement concrete Report ICAR 104-1F

Project number 104 International Center for Aggregates Research University of

Texas

Riley N A (1941) Projection sphericity Journal of Sedimentary Petrology Vol 11

No 2 pp 94-97

Rouseacute P C Fennin R J and Shuttle D A (2008) Influence of roundness on the

void ratio and strength of uniform sand Geotechnique Vol 58 No 3 227-231

Santamarina J C and Cho G C (2004) Soil behaviour The role of particle shape

Proceedings Skempton Conf London

Schofield and Wroth (1968) Critical state soil mechanics McGraw Hill

Shaumlfer Michael (2002) Digital optics Some remarks on the accuracy of particle

image analysis Particle amp Particle Systems Characterization Vol 19 No 3 pp 158-

168

Shergold F A (1953) The percentage of voids in compacted gravel as a measure of

its angularity Magazine of Concrete Research Vol 5 No 13 pp 3-10

Shinohara Kunio Oida Mikihiro Golman Boris (2000) Effect of particle shape on

angle of internal friction by triaxial compression test Powder Technology Vol 107

pp131-136

49

Skredcommisionen (1995) Ingenjoumlrsvetenskapsakademinen rapport 395 Linkoumlping

1995

Sneed E D and Folk R L (1958) Pebbles in the Colorado river Texas A study in

particle morphogenesis Journal of Geology Vol 66 pp 114-150

Sperry James M and Peirce J Jeffrey (1995) A model for estimating the hydraulic

conductivity of granular material based on grain shape grain size and porosity

Ground Water Vol 33 No 6 pp 892-898

Sukumaran B and Ashmawy A K (2001) Quantitative characterisation of the

geometry of discrete particles Geotechnique Vol 51 No 7 pp 619-627

Szaacutedeczy-Kardoss E Von (1933) Die bistimmung der abrollungsgrades Geologie

und palaumlontologie Vol 34B pp 389-401 (in German)

Teller J T (1976) Equantcy versus sphericity Sedimentology Vol 23 pp 427-428

Tickell F G (1938) Effect of the angularity of grain on porosity and permeability

bulletin of the American Association of Petroleum Geologist Vol 22 pp 1272-1274

Tutumluer E Huang H Hashash Y Ghaboussi J (2006) Aggregate shape effects

on ballast tamping and railroad track lateral stability AREMA 2006 Annual

Conference Louisville KY

Wadell H (1932) ldquoVolume Shape and roundness of rock particlesrdquo Journal of

Geology Vol 40 pp 443-451

Wadell H (1933) Sphericity and roundness of rock Particles Journal of Geology

Vol 41 No 3 pp 310ndash331

Wadell H (1934) Shape determination of large sedimental rock fragments

The Pan-American Geologist Vol 61 pp 187-220

Wadell H (1935) ldquoVolume shape and roundness of quartz particlesrdquo Journal of

Geology Vol 43 pp 250-279

Wentworth W C (1922a) The shape of beach pebbles Washington US Geological

Survey Bulletin Vol 131C pp 75-83

Wentworth W C (1922b) A method of measuring and plotting the shape of pebbles

Washington US Geological Survey Bulletin Vol 730C pp 91-114

Wentworth W C (1933) The shape of rock particle A discussion Journal of

Geology Vol 41 pp 306-309

Witt K J Brauns J (1983) Permeability-Anisotropy due to particle shape Journal

of Geotechnical Engineering Vol 109 No 9 pp 1181-1187

2

During the historical development of shape descriptors the terminology has been used

differently among the published studies terms as roundness (because the roundness

could be apply in the different scales) or sphericity (how the particle approach to the

shape of a sphere) were strong (Wadell 1933 Wenworth 1933 Teller 1976 Barrett

1980 Hawkins 1993) and it was necessary in order to define a common language on

the particle shape field unfortunately still today there is not agreement on the use of

this terminology and sometimes it make difficult to understand the meaning of the

authors thatrsquos why it is better to comprehend the author technique in order to

misinterpret any word implication

Several attempts to introduce methodology to measure the particlersquos shape had been

developed over the years Manual measurement of the particles form is

overwhelming thus visual charts were developed early to diminish the measuring

time (Krumbein 1941 Krumbein and Sloss 1963 Ashenbrenner 1956 Pye and Pye

1943) Sieving was introduced to determine the flakinesselongation index but it is

confined only for a certain particle size due the practical considerations (Persson

1988) More recently image analysis on computer base has been applied on sieving

research (Andersson 2010 Mora and Kwan 2000 Persson 1998) bringing to the

industry new practical methods to determine the particle size with good results

(Andersson 2010) Particle shape with computer assisted methods are of great help

reducing dramatically the measuring time (Fernlund 2005 Kuo and Freeman 1998a

Kuo et al 1998b Bowman et al 2001)

In the civil industry eg Hot Asphalt mixtures (Kuo and Freeman 1998a Pan et al

2006) Concrete (Mora et al 1998 Quiroga and Fowle 2003) and Ballast

(Tutumluer et al 2006) particlersquos shape is of interest due the materialrsquos performance

thus standards had been developed (see appendix A) On asphalt mixtures limits of

flat and elongated particles or the amount of natural sands typically are incorporated

into specifications flat and elongated particles tend to cause problems with

compaction particle breakage loss of strength and segregation in pavement (Kuo and

Freeman 1998a) Rutting resistance of asphalt concrete under traffic and

environmental loads depend on the stability of aggregates structure in the asphalt mix

(Pan et al 2006) According with the American Railway Engineering and

Maintenance of Way Association (AREMA) ballast aggregate should be open graded

with hard angular shaped particles providing sharp corners and cubical fragments

with a minimum of flat and elongated pieces (Tutumluer et al 2006) The American

standard ASTM D 3398 (test method for index of aggregate particle shape and

texture) is an example of an indirect method to determine particle shape (see appendix

A) Aggregate characteristics of shape texture and grading influence workability

finishability bleeding pumpability and segregation of fresh concrete and affect

strength stiffness shrinkage creep density permeability and durability of hardened

concrete In fact flaky elongated angular and unfavorably graded particles lead to

higher voids content than cubical rounded and well-graded particles (Quiroga and

Fowle 2003)

Sieving is probably the most used method to determine the particle size distribution it

consist of plotting the cumulative weight of the weighted material retained by each

mesh (European standard EN 933-1 1992) This traditional method according to

Andersson (2010) is time consuming and expensive Investigations shows that the

traditional sieving has deviations when particle shape is involve the average volume

3

of the particles retained on any sieve varies considerably with the shape (Lees

1964b) thus the passing of the particles depend upon the shape of the particles

(Fernlund 1998) In some industries the Image analysis is taking advantage over the

traditional sieving technique regardless of the intrinsic error on image analysis due the

overlapping or partial hiding of the rock particles (Andersson 2010) In this case the

weight factor is substitute by pixels (Fernlund et al 2007) Sieving curve using

image analysis is not standardized but after good results in the practice (Andersson

2010) new methodology and soil descriptions could raise including its effects

2 AIM AND GOAL

The aim of this report is to review the state of the art on how to describe particle

shape of individual grains of geotechnical material and knowledge on the influence of

shape in geotechnical properties

The goals in this study are to

Describe discuss and compare particle shape and definitions

Review the known effect of particle shape on soil mechanics parameters

Discuss the potential of the role of particle shape in soil mechanics

Focus in this study has been on 2 dimensional shape definitions

The content of the report is based upon published and peer reviewed papers in

English

3 DESCRIPTION OF SHAPE PROPERTIES

31 INTRODUCCTION

Particle shape description can be classified as qualitative or quantitative Qualitative

describe in terms of words the shape of the particle (eg elongated spherical flaky

etc) and quantitative that relates the measured dimensions in the engineering field

the quantitative description of the particle is more important due the reproducibility

Quantitative geometrical measures on particles may be used as basis for qualitative

classification There are few qualitative measures in contrast with several quantitative

measures to describe the particle form Despite the amount of qualitative descriptions

none of them had been widely accepted but there are some standards (eg ASTM

D5821 EN 933-3 and BS 812) specifying mathematical definitions for industrial

purposes

Shape description of particles is also divided in

o 3D (3 dimensions) it could be obtained from a 3D scan or in a two

orthogonal images and

o 2D (2 dimensions) or particle projection where the particle outline is drawn

4

3D and 2D image analysis present challenges itself 3D analysis requires a

sophisticated equipment to scan the particle surface and create the 3D model or the

use of orthogonal images and combine them to represent the 3 dimensions The

orthogonal method could present new challenges as the minimum particle size or the

placing in orthogonal way of the particles (Fernlund 2005) 2D image analysis is easy

to perform due the non-sophisticated equipment required to take pictures (eg regular

camera or the use of microscope for smaller particles) In 2D image analysis the

particle is assumed to lay over its more stable axis (eg longest and intermediate axis

lie more or less parallel to the surface while the shortest axis is perpendicular) or

random some authors publish their own preferences about this issue (Wadell 1935

Riley 1941 Hawkins 1993)

32 SCALE DEPENDENCE

In order to describe the particle shape in detail there are a number of terms quantities

and definitions used in the literature Some authors (Mitchell amp Soga 2005 Arasan et

al 2010) are using three sub-quantities one and each describing the shape but at

different scales The terms are morphologyform roundness and surface texture In

figure 1 is shown how the scale terms are defined

At large scale the particlersquos diameters in different directions are considered At this

scale describing terms as spherical platy elongated etc are used An often seen

quantity for shape description at large scale is sphericity (antonym elongation)

Graphically the considered type of shape is marked with the dashed line in Figure 1

At intermediate scale it is focused on description of the presence of irregularities

Depending on at what scale an analysis is done corners and edges of different sizes

are identified By doing analysis inside circles defined along the particlersquos boundary

deviations are found and valuated The mentioned circles are shown in Figure 1 A

generally accepted quantity for this scale is roundness (antonym angularity)

Regarding the smallest scale terms like rough or smooth are used The descriptor is

considering the same kind of analysis as the one described above but is applied

Figure 1 Shape describing sub quantities (Mitchell amp Soga 2005)

5

within smaller circles ie at a smaller scale Surface texture is often used to name the

actual quantity The sub-quantities and antonyms are summarized in table 1

Table 1 Sub-quantities describing the particlersquos morphology and its antonym

Scale Quantity Antonym

Large scale Sphericity Elongation

Intermediate scale Roundness Angularity

Small scale Roughness Smoothness

33 FORM (3D)

Wentworth in 1922 (Blott and Pye 2008) was probably one of the first authors on

measure the particle dimensions this consisted on the obtaining of the length of the

tree axes perpendicular among each other (see figure 2) on the tree dimensions (where

agebgec) to obtain the sphericity (equation 1)

Krumbein (1941) develop a rapid method for shape measurement to determine the

sphericity this is done by measuring the longest (a) medium (b) and shorter (c) axes

diameters of the particle it can be seen in figure 2 (Always perpendicular among each

other) The radios ba and cb are located in the chart developed by his own where it

can be found the Intercept sphericity as he called (See figure 3) This chart is an easy

graphical way to relate the dimensions

c2

ba

Figure 2 Measurement of the 3 axes perpendicular among each other (Krumbein 1941)

Figure 3 Detailed chart to determining Krumbein intercept sphericity (Krumbein 1941)

(1)

6

Wadell (1932) defined the sphericity as the specific surface ratio (equation 2) Figure

4 is a schematic representation of the sphere surface and particle surface both particle

and sphere of the same volume

This way to obtain the sphericity is almost impossible to achieve as Hawkins (1993)

declares due the difficulty to get the surface area on irregular solids

Wadell (1934) also defined the sphericity based upon the particle and sphere volumes

as equation 3 (see figure 5)

Wadell (1934) used a new formula simple to manage using the diameters (see figure

6 and equation 4)

Zingg (Krumbein 1941) develop a classification based on the 3 axes relation in this

way it is easy to find out the main form of the particles as a disks spherical blades

S

s

3

CIR

P

V

V

CIR

SV

D

D

Figure 4 Same volume sphere surface (s) and particle surface (S) (modified after Johansson and Vall

2011)

Figure 5 Relation between the volume of the particle and the volume of the circumscribed

sphere (Johansson and Vall 2011)

Figure 6 Figure is showing the relation between the diameter of a circumscribed sphere and the

diameter of a sphere of the same volume as the particle (Johansson and Vall 2011)

(2)

(3)

(4)

7

and rod-like this is summarized on figure 7 Zinggrsquos classification is related with

Krumbein intercept sphericity and the figure 3

In figure 8 the figures 3 and 7 are combined the relation in the two classifications can

be seen it is an easy way to understand the morphology regarding on the a b and c

dimensions

Pye and Pye (1943) in the article ldquosphericity determinations of pebbles and sand

grainsrdquo compare the Wadellrsquos sphericity developed in 1934 (based on the diameter)

with ldquoPebble sphericityrdquo based on an ellipse this last equation (number 5) appears

two years early published by Krumbein (1941) Axis measurement is done as figure 1

denotes for equations 5 trough 12 with exception of equation 8 where the original

document was not possible to obtain

32a

cb

Figure 7 Zinggrsquos classification of pebble shape based on ratios ba and cb (Krumbein 1941)

Figure 8 Classification made by Zinggrsquos and chart to determine sphericity (Krumbein and Sloss 1963)

(5)

8

Sneed amp Folk in (1958) found a relation between the tree dimensional axes called

ldquoMaximum Projection Sphericityrdquo

In a similar way Ashenbrenner (1956) showed his equation at that time named

ldquoWorking Sphericityrdquo

Form or shape factor names are used by authors like Corey (shape factor eq 8) in the

paper published on 1949 Williams (shape factor eq 9) in 1965 Janke (form factor

eq 10) in 1966 and Dobkins amp Folk (oblate-prolate index eq 11) in 1970 (Blott and

Pye 2008)

Aschenbrenner (1956) develop the shape factor by using the relation of the tree axis

but the square of the middle one

3

2

ba

c

))ab((1)bc(16))ab((cb)(11

)ab()bc( 128

22

3 2

ab

c

acb when 1ac

b acb when

b

ac-1 2

22

2

3

cba

c

222

a

c

50c-a

b-a10

2b

ac

(6)

(7)

(8)

(9)

(10)

(11)

(12)

9

Table 2 General overview over different particle shape definitions for 3D sphericity has been compiled

and arranged chronologically

Aspect Name Author Year Based on

Sphericity (3D) Flatness index Wentworth 1922a 3-axes

True Sphericity Wadell 1932 Surface

Operational sphericity Wadell 1932 Volume

Sphericity Wadell 1934 Sphere diameter

Zinggrsquos clasification Zinggrsquos1

1935 3-axes

Intercept sphericity chart Krumbein 1941 3-axes

Pebble sphericity Pye and Pye 1943 3-axes

Corey shape factor Corey2

1949 3-axes

Working sphericity Ashenbrenner 1956 3-axes

shape factor Ashenbrenner 1956 3-axes

Maximum projection sphericity Sneed amp Folk 1958 3-axes

Williams shape factor Williams2

1965 3-axes

Janke form factor Janke2

1966 3-axes

Oblate-prolate index Dobkins amp Folk 1970 3-axes 1) Krumbein and Sloss 1963 2) Blott and Pye 2008

34 FORM (2D)

The technique to measure the sphericity is based in tree dimensions it can be found in

literature some ways to measure the ldquotwo dimensions sphericityrdquo which is simply the

perimeter of the particle projection some authors named ldquoparticle outlinerdquo or

ldquocircularityrdquo

Wadell in 1935 (Hawkins 1993) adopt a conversion of his 1934 3D sphericity

formula (equation 4) to a 2D outline He defined an orientation on the particles and

they were based on the maximum cross sectional area (outline of the particle

projecting the maximum area) The equations show the relation between diameters of

a circle of same area and smallest circumscribed circle

He also used the term ldquodegree of circularityrdquo as the ratio of the perimeter of a circle of

same area and the actual particle perimeter

Tickell in 1931 (Hawkins 1993) used his empirical relation The particle orientation

proposed was a random one It is described by the ratio between the area outline and

the area of smallest circumscribed circle

C

A

D

DC

P

PC C

CA

AC

(13)

(14)

(15)

10

Some other authors has been working with the ldquocircularityrdquo concept and had develop

them own equations as Pentland (1927) relating the area outline and area of a circle

with diameter equal to longest length outline and Cox (Riley 1941) with the ratio

area and perimeter time a constant equations 16 and 17 respectively Both authors did

not define any definite orientation of the grains

Riley (1941) realize the problems that an area perimeter and some other

measurements proposed by the above authors can carry as the time consuming and

tedious work (at that time were not computer all was made by hand) and thatrsquos why

he develop this equation easy to handle called ldquoinscribed circle sphericityrdquo He used

the same particle orientation proposed by Wadell and the relation of diameters of

inscribed and circumscribed circles

Horton 1932 (Hawkins 1993) use the relation of the drainage basing perimeter and

the perimeter of a circle of the same area as drainage basin

Janoo in 1998 (Blott and Pye 2008) develop his general ratio of perimeter to area

Sukumaran and Ashmawy (2001) develop his own shape factor (SF) defined as the

deviation of the global particle outline from a circle Figure 9 can be used as a

reference to determine the items used in the equation 21

N is referred to the number of sampling intervals o radial divisions

C2A

AC

2P

A4C

C

I

D

DC

CD

D

P

PC

A

PC

2

45ordm x N

Particleα

= SF

sumN

1=ii

(16)

(17)

(18)

(19)

(20)

(21)

11

Table 3 General chronological overview of the particle shape definitions for 2D sphericity

Aspect Name Author Year Based on

Circularity (2D) roundness Pentland 1927 area

roundness Cox1

1927 area-perimeter

roundness Tickell2

1931 area

Circularity Horton2

1932 drainage basin

outline circularity Wadell 1935 Circle diameter

degree of circularity Wadell 1935 Perimeter

inscribed circle sphericity Riley 1941 Circle diameter

Circularity Krumbein and Sloss 1963 chart

Janoo 1998 area-perimeter

Shape factor Sukumaran 2001 Segmentation of particle and angles

1) Riley 1941 2) Hawkins 1993

35 ROUNDNESS OR ANGULARITY

Roundness as described in section 32 is the second order shape descriptor Sphericity

lefts beside the corners and how they are this was notice by most of the authors sited

before and they suggested many ways to describe this second order particle property

Roundness is clearly understandable using the figure 10 Particle shape or form is the

overall configuration and denotes the similarities with a sphere (3D) or a circle (2D)

Roundness is concerning about the sharpness or the smoothness of the perimeter (2D)

Surface texture (Barret 1980) is describe as the third order subject (form is the first

and roundness the second) and it is superimposed in the corners and it is also a

property of particles surfaces between corners

Figure 9 Description of the Sukumaran factors to determine the shape and angularity (Sukumaran and

Ashmawy 2001)

12

Wadell (1935) describes his methodology calling it total degree or roundness to

obtain the roundness of a particle using the average radius of the corners in relation

with the inscribed circle diameter (see figure 11) on the equation

In the same study Wadell (1935) has used the equation

This two last equation shows slightly differences on the results (Wadell 1935)

Powers (1953) also published a graphic scale to illustrate the qualitative measure

(figure 12) It is important to highlight that any comparing chart to describe particle

properties has a high degree of subjectivity Folk (1955) concludes that when charts

are used for classification the risk of getting errors is negligible for sphericity but

large for roundness

N

R

r

Rinmax

r

R

NR

inmax

Figure 10 Form (shape) Roundness and Texture graphical description (Bowman et al 2001)

Figure 11 Wadellrsquos method to estimate the roundness corners radius and inscribed circle

(Hawkins 1993)

(22)

(23)

13

Some authors as Russel amp Taylor in 1937 Pettijohn in 1957 and Powers in 1953

developed a classification based on five and six classes (Hawkins 1993) each one

with its own class limits it is important to denote that the way they measure the

roundness is the developed by Wadell (1935) This classification and class limits are

showed in the table 4

Table 4 Degrees of roundness Wadell Values (Hawkins 1993) NA = no-applicable

Grade terms Russell amp Taylor (1937) Pettijohn (1957) Powers (1953)

Class

limits (R)

Arithmetic

midpoint

Class limits

(R)

Arithmetic midpoint Class

limits (R)

Arithmetic

midpoint

Very angular

NA

NA

NA

NA

012-017

014

Angular

000-015

0075

000-015

0125

017-025

021

Subangular

015-030

0225

015-025

0200

025-035

030

Subrounded

030-050

0400

025-040

0315

035-049

041

Rounded

050-070

0600

040-060

0500

049-070

059

Well rounded

070-100

0800

060-100

0800

070-100

084

Krumbein and Sloss (1963) published a graphical chart easy to determine the

sphericity and roundness parameters using comparison See figure 13 (Cho et al

2006)

Figure 12 A Roundness qualitative scale (Powers 1953)

Figure 13 Sphericity and roundness chart (Cho et al 2006) The roundness equation that appears here in

the chart is the wadellrsquos equation number 22

14

Fischer in 1933 (Hawkins 1993) used a straightforward method to quantify roundness

using a central point in the outline and dividing the outline in angles around this point

that were subtended by the straight or non curved parts of the profile were measured

This is illustrated in figure 14

To express the angularity value Fischer used the ratio of angles standing linear parts

on the outlines and concave respectively

Figure 14 left (A) and right (B) gives a similar angularity of approximately 042

using the above equations (Hawkins 1993)

Wentworth in 1922 used the maximum projection to define the position of the particle

to obtain the outline or contour (Barret 1980) The equation reflects the relation of the

diameter of a circle fitting the sharpest corner and the longest axis plus the shortest

axis c (minimum projection)

Wentworth (Hawkins 1993) expressed the roundness as the ratio of the radius of

curvature of the most convex part and the longest axis plus short axis

Actually these last two equations are the same just expressed in different terms when

the particle is in its maximum projection

Dimensions can be seen on figure 15 L and B represents the mayor axis a and

intermediate axis b The intention is to make difference between the 2 and 3

dimensions (L and B are for 2D as a b and c are for 3D)

deg360

ANG

=R

sumPLA

PLA

CON

ANG

ANGR

2)S(L

DR

M

S

B)4(L

RR CON

Figure 14 Fischerrsquos methods of angularity computation (Hawkins 1993)

A=inscribed circle B=circumscribed circle

(24)

(25)

(26)

(27)

15

Wentworth 1919 has a second way to express the roundness called Shape index

(Barrett 1980) and it relates the sharpest corner and the diameter of a pebble trough

the sharpest corner

Wentworth (1922b) used define the roundness as the ratio of the sharpest corner and

the average radius of the pebble

Cailleux (Barrett 1980) relates the radius of the most convex part and the longest

axis

Kuenen in 1956 show his roundness index (Barrett 1980) between the sharpest corner

and the breath axis

Dobkins amp Folk (1970) used a modified Wentworth roundness with the relation of

sharpest corner and inscribed circle diameters

AVG

CON

R

RR

x

s

D

DR

L2

RR CON

B

DR s

i

s

D

DR

3AVGAVG cbaDR2

Figure 15 Description of L and B axes (Hawkins 1993)

(28)

(29)

(30)

(31)

(32)

(33)

16

Swan in 1974 shows his equation (Barrett 1980) relating the sharpest (or the two

sharpest) corner(s) and inscribed circle diameter

Szadeczsky-Kardoss has his Average roundness of outline (Krumbein and Pettijohn

1938) relating the concave parts perimeter and the actual perimeter

Lees (1964a) developed an opposite definition to roundness it means that he

measures the angularity instead of the roundness and he calls it Degree of angularity

Figure 16 shows the items considered when equation 36 applies as the angles (α)

inscribed circle (Rmax-in) and the distance (x) The main formula is

In order to apply the last equation corners needs to be entered in the formula and each

individual result will add to each other to obtain the final degree of angularity

A roundness index appears on Janoo (1998) Kuo and Freeman (1998a) and Kuo et

al (1998b) it is described as

The last equation is on section 34 also because there is not a general agreement on the

definition furthermore some authors had used to define the roughness this is not the

only equation that has been used trying to define different aspects (sphericity

roundness or roughness) but it is a good example of the misuse of the quantities and

definitions

inmaxR

x)180(R

2P

A4R

i

ss

D

DDR

221

100P

PR CON

Figure 16 Degree of angularity measurement technique (Blot and Pye 2008)

(34)

(35)

(36)

(17)

17

Sukumaran and Ashmawy (2001) present an angularity factor (AF) calculated from

the number of sharpness corners Angles βi required to obtain the angularity factor are

shown in figure 9

Sukumaran and Ashmawy (2001) also suggested use not bigger sampling interval of

N=40 because it is the cut off between angularity factor and surface roughness If so

this equation could be used to describe the roughness

Table 5 General chronological overview of the particle roundness

Aspect Name Author Year Based on

Roundness shape index Wentworth 19191

diameter of sharper corner

shape index Wentworth 1922b sharpest corner and axis

roundness Wentworth 1933 convex parts

Fischer 19332

noncurved parts outline

Fischer 19332

noncurved-streigth parts outline

Average roundness of outline

Szadeczsky-Kardoss 19333

convex parts-perimeter

roundness Wadell 1935 diameter of corners

roundness Wadell 1935 diameter of corners

roundness Russel amp Taylor 19372

class limit table

roundness Krumbein 1941 chart

Cailleux 19471

convex parts

roundness Pettijohn 19494 class limit table

roundness Powers 1953 chart and class limit table

Kuenen 19561

axis-convex corner

roundness Krumbein and Sloss 1963 chart

degree of angularity Lees 1964a corners angles and inscribed circle

Dobkins amp Folk 1970 diameter of sharper corner

Swan 19741

diameter of sharper corners

Angularity factor Sukumaran and

Ashmawy 2001

Segmentation of particles and angles

1) Barret 1980 2) Hawkins 1993 3) Krumbein and Pettijohn 1938 4) Powers 1953

sum

sumsumN

1=i

2

i

2

N

1=i

2

i

2N

1=ii

)ordm180 -circleβ( - )(180ordm x 3

)ordm180-circleβ(-)ordm180 -Particleβ(

= AF (37)

18

36 ROUGHNESS OR SURFACE TEXTURE

A third property called texture appears early in the literature with the sphericity and

roundness properties since then texture property was longed described but it was in

accordance with the authors at that time not measurable

Wright in 1955 developed a method to quantify the surface texture or roughness of

concrete aggregate using studies done on 19 mm stones The test aggregates were first

embedded in a synthetic resin The stones were cut in thin sections The sections

projection was magnified 125 times The unevenness of the surface was traced and the

total length of the trace was measured The length was then compared with an uneven

line drawn as a series of chords (see figure 17) The difference between these two

lines was defined as the roughness factor (Janoo 1998)

However with the advance of technology it has become easier measure the roughness

and here is presented some researcherrsquos ideas how this property should be calculated

One technique used by Janoo (1988) to define the roughness can be seen in figure 18a

and is defined as the ratio between perimeter and convex perimeter

The convex perimeter is obtained using the Feretrsquos box (or diameter) tending a line in

between the touching points that the Feretrsquos box describes each time it is turn (figure

18b)

PER

OC

PR

Figure 17 Measurement method for characterizing the surface texture of an aggregate (Janoo 1998)

a) Convex perimeter (CPER) b) Feret measurement Figure 18 a) Convex perimeter (CPER) b) Feret measurement (modified after Janoo 1998)

(38)

a)

b)

19

Kuo and Freeman (1998a) and Kuo et al (1998b) use the roughness definition as the

ratio perimeter and average diameter

Erosion and dilatation image processing techniques are used to obtain the surface

texture Erosion is a morphological process by which boundary image pixels are

removed from an object surface which leaves the object less dense along the

perimeter or outer boundary Dilatation is the reverse process of erosion and a single

dilatation cycle increases the particle shape or image dimension by adding pixels

around its boundary (Pan etal 2006)

The ldquonrdquo erosion and dilatation cycles are not standardized

Mora and Kwan (2000) used the ldquoconvexity ratio CRrdquo (equation 41) and the ldquofullness

ratio FRrdquo (equation 42) in their investigation they are

The convex area is the area of the minimum convex boundaries circumscribing the

particle This is illustrated in the figure 19 The convex area is obtained in a similar

way as the convex perimeter but in this case the area between the original outline and

the convex perimeter is our convex area

AVG

OD

PR

100A

1AARO

CONo A

AR =

CONo A

AR =

Figure 19 Evaluation of area and convex area (Mora and Kuan 2000)

(39)

(40)

(41)

(42)

20

4 TECHNIQUES IN ORDER TO DETERMINE PARTICLE

SHAPE

41 HAND MEASUREMENT

Hand measurement technique was the first used by obvious reasons in order to

improve the accuracy special devices developed as the ldquosliding rod caliperrdquo used by

Krumbein (1941) it works placing the sample on the sliding road calliper as show

figure 20b the length in different positions can be obtain by using the scale provided

in the handle the ldquoconvexity gagerdquo that was actually used by opticians to measure the

curvature of lenses but easily applicable to the particle shape analysis (Wentworth

1922b) works measuring the movement of the central pivot as figure 20a shows (the

two adjacent pivots are invariable) as many the central pivot moves more is the

curvature or the ldquoSzadeczky-Kardossrsquos apparatusrdquo develop in 1933 that traces the

profile of the rock fragment so the outline traced is then analyzed (Krumbein and

Pettijohn 1938) figure 20c show equipment

Another helpful tool to determine the particle dimensions was the ldquocamera lucidardquo to

project the particlersquos contour over a circle scale appearing in Figure 21 thus it is

possible to measure the particlersquos diameter

a)

c) b)

Figure 20 a) convexity gage used to determine the curvature in particle corners (Wenworth 1922b)

b)sliding rod caliper device to measure the particle axis length (Krumbein 1941) and c)Szadeczky-

Kardoss (1933) apparatus it was utilized to obtain the particle outline

Figure 21 Circle scale used by Wadell (1935) to determine particlersquos diameter and roundness

21

42 SIEVE ANALYSIS

Bar sieving eg according to EN 933-31997 can be used to determine simple large

scale properties By combining mesh geometries the obtained results can be used to

quantify flakiness and elongation index ASTM D4791 (Flat and elongated particles

are defined as those coarse aggregate particles that have a ratio of length to thickness

equal to or greater than a specified value such as 51 The index represents the

percentage on weight of these particles) The method is not suitable for fine materials

This due to the difficulty to get the fine grains passed through the sieve and the great

amount of particles in relation to the area of the sieve (Persson 1998) eg EN 933-

31997 related to flakiness index The test is performed on aggregates with grain size

from 4 mm and up to 63 mm two sieving operations are necessary the first separates

on size fraction and the second use a bar sieve after the first sieving the average

maximum diameter of the particles is obtain and with the second sieving (bar sieving)

the shortest axis diameter is found finally with this two parameters the flakiness

index is determined

There are more standards related with the particle shape (see appendix A) but this

above presented are probably the most known using sieve analysis to determine

particlersquos geometrical properties

Sieve analysis is facing the computers age and image analysis sieving research is

taking place (Andersson 2010 Mora and Kwan 2000 Persson 1998) Industry is

also applying the image analysis sieving with decrees on the testing time compare

with the traditional sieving method An inconvenient of image analysis is the error

due the overlapping or hiding of the particles during the capture process but the

advantages are more compare with disadvantages (Anderson 2010)

43 CHART COMPARISON

Charts developed over the necessity of faster results because the long time consuming

required when measuring each particle

Krumbein (1941) present a comparison roundness chart for pebbles which were

measured by Wadellrsquos method because this property was the most difficult to measure

due to the second order scale that roundness represents (See figure 22)

Figure 22 Krumbein (1941) comparision chart for roundness

22

A qualitative chart by Powers (1953) try to include both (sphericity and roundness)

particlersquos characteristics it was divided on six roundness ranges (very angular

angular sub-angular sub-rounded rounded and well rounded) and two sphericity

series (high and low sphericity) This chart was prepared with photographs to enhance

the reader perspective (See figure 23)

A new chart including sphericity and roundness appear this time it was easier to

handle the two mean properties of particlersquos shape furthermore there was included

the numerical values that eliminated the subjectivity of qualitative description The

chart is based on Wadellrsquos definitions (Krumbein and Sloss 1963) (See figure 24)

Folk (1955) worried about the personrsquos error on the chartrsquos comparison studied the

determination of sphericity and angularity (he used the Powers 1953 comparison

chart) he found that the sphericity determination by chart comparison has a negligible

error while the roundness he concluded it was necessary to carry out a more wide

research due the high variability show by his study

Figure 23 Powers (1953) qualitative shpericity-roundness chart

Figure 24 Sphericity-roundness comparison chart (Krumbein and sloss 1963)

23

44 IMAGE ANALYSIS

Image analysis is a practical method to use for shape classification since it is fast and

can be automated Different techniques appear to process these images among them

are

o Feret Diameter the Feret diameter is the longitude between two parallel lines

this lines can rotate around one particle or outline to define dimensions as it

is shown in figure 25 these method is not a fine descriptor but as it was say

above it is a helpful tool to determine diameters (Janoo 1988)

o Fourier Mathematical Technique It produces mathematical relations that

characterize the profile of individual particles This method favours the

analysis of roughness and textural features for granular soils The problem in

the methodology remains in the re-entrant angles in order to complete the

revolution (Bowman et al 2001) see figure 26

o Fractal Dimension Irregular line at any level of scrutiny is by definition

fractal (Hyslip and Vallejo 1997) Figure 27 shows fractal analysis by the

dividing method The length of the fractal line can be defined as

N

1n

nn0 )nsinbncosa(a)(R

RD1n)(P

Figure 25 Feret measurement technique is defined by two parallel lines turning

around the particle to define the shortest and longest Feret diameter (Janoo 1988)

Figure 26 Fourier technique with two radiuses at one angle (Bowman et al 2001)

(43)

(44)

24

o Orthogonal image analysis This technique is basically the use of two images

orthogonal between them to acquire the three particle dimensions (Fernlund

2005) any of the above techniques can be used in this orthogonal way

o Laser Scanning Technique this kind of laser scanning 3D is one of the most

advanced techniques In figures 28a) we have the laser head scanning the rock

particles the particles have control points in order to keep a reference point

when move them to scan the lower part in figure 28b) we can see the laser

path followed (Lanaro and Tolppanen 2002)

Another technique is the Laser-Aided Tomography (LAT) in this case a laser sheet is

used to obtain the particles surveying (see figure 29) This technique is different and

has special requirements as to use liquid with same refractive index as the particles

particles must let the laser or certain percent of light go through (Matsushima et al

2003)

a) b)

Figure 27 Fractal analysis by the dividing method at different scrutiny scale (Hyslip and Vallejo 1997)

Figure 28 a) Scanning head b) scanning path (Lanaro and Tolppanen 2002)

Figure 30 3D scan completed ready to

use for any further measure

(Matsushima et al 2003)

Figure 29 LAT scaning particles

(Matsushima et al 2003)

25

Both 3D techniques obtain the particle shape that is later used to achieve measures as

we can see in figure 30

All these previous techniques are easily written in codes or scripts to be interpreted in

a digital way obtaining the desired measurement but there are some interesting points

in the image analysis regarding on the errors involve among them are image

resolution and orientation of the particles orientation is not relevant when it is

random and large number of particles are involve resolution have an influence on the

accuracy (Zeidan et al 2007)

When resolution is increase more accuracy is obtain and the object representation

match better with the real form in the other hand more resolution means more

spending on memory and time thus resolution needs to be according with the goal

and precision needed in any work (Schaumlfer 2002)

Schaumlfer (2002) conclude that attributes like length when measuring digital images

present relative high errors It can be vanish or at least diminish using high resolution

just for diameter but not for perimeter that keep the error as big as initially Johansson

and Vall (2011) obtain similar results when 3 different resolutions were used in the

same particle obtaining an unstable output for those termsquantities that involve the

perimeter Thus all quantities relating the perimeter should be treated with care

5 EFFECT OF SHAPE ON SOIL PROPERTIES

51 INTRODUCTION

In laboratory test on the effect on particle size on basic properties has been

investigated in several studies this relation has been discussed and various

mechanisms had been proposed to explain the behaviour of the soil in dependency

also with the shape Basically there are two mechanisms proposed The arrangement

of particles and the inter-particle contact (Santamarina and Cho 2004) and

subsequence breakage

The arrangement of particles

Arrangement of the particles can be presented in three different forms loose dense

and critical this arrangement determines the soil properties (eg density increase with

more dense arrangement) Loose and dense states are easy understandable when

figure 31 is explained while in the upper part of the figure the particles are arranged

using the minimum space needed in the lower part a span is created using the flaky

particle as a bridge this phenomena is known as ldquobridgingrdquo Bridging can produce

different geotechnical results when just the shape of the particle is changed eg void

ratio (Santamarina and Cho 2004) Particles are able to rearrange this could be done

applying pressure (energy) to the soil the pressure (energy) will create such forces

that soil particles will rotate and move (see figure 34) finishing in a more dense state

26

A loose soil will contract in volume on shearing and may not develop any peak

strength (figure 32 left) In this case the shear strength will increase gradually until

the residual shear strength is revealed once the soil has ceased contracting in volume

A dense soil may contract slightly (figure 32 right) before granular interlock prevents

further contraction (granular interlock is dependent on the shape of the grains and

their initial packing arrangement) In order to continue shearing once granular

interlock has occurred the soil must dilate (expand in volume) As additional shear

force is required to dilate the soil a peak shear strength occurs (figure 32 left) Once

this peak shear strength caused by dilation has been overcome through continued

shearing the resistance provided by the soil to the applied shear stress reduces

(termed strain softening) Strain softening will continue until no further changes in

volume of the soil occur on continued shearing Peak shear strengths are also

observed in overconsolidated clays where the natural fabric of the soil must be

destroyed prior to reaching constant volume shearing Other effects that result in peak

strengths include cementation and bonding of particles The distinctive shear strength

called the critical state is identified where the soil undergoing shear does so at a

constant volume (Schofield and Wroth 1968)

The inter-particle contact

For frictional soil ie coarse grained soil the friction between particles is the

dominating factor for strength Materials usually consisting of coarse grains (diameter

Figure 31 Bridging effect when flaky particles are combined in the bulk material (Santamarina and

Cho 2004)

Figure 32 The left part of the figure show a typical behaviour of loose and dense material over shear stress

while at the right the figures illustrate the typical volume changes

27

gt 006mm) behave as a frictional soil it means that the strength of coarse soils (silt

sand gravel etc) comes from an inter-particle mechanical friction thus ideally they

do not have traction strength In figure 33 the inter-particle contact is illustrated here

the pressure (P) is applied and two more components are found the normal load (N)

and the tangential load (T) described as the friction coefficient (μF) The forces stand

in equilibrium (Johansson and Vall 2011)

When particles equilibrium is disturbed (friction coefficient is not enough to keep

particles unmoved) the rotation is imminent and it is necessary in order to compact

the soil in figure 34 can be seen that the arrangement is a fact that inhibit or allow this

rotation and the shape in the 3 different scales are also factors because the more

spherical andor more rounded andor less roughness more easy is the rotation

(Santamarina and Cho 2004)

Breakage

Breakage is a side effect of the inter-particle contact and rotation when pressure

exceed the rock strength it can happened when the particles are tight together and

there is not enough space to rotate it is more obvious in angular particles (mesh form)

or as in figure 31 where the flaky particle ldquobridgingrdquo is not able to rotate but it can

brake by the pressure increase Yoginder et al (1985) notice that the angular particle

break during his experiments and they turn more rounded changing the original size

and form configuration at the same time there was a soil properties loosening

Figure 33 Inter-particle contact and forces acting (Axelsson 1998)

Figure 34 Rotation inhibition by the particles compaction or low void ratio (Santamarina and Cho 2004)

28

52 INFLUENCE OF SIZE AND SHAPE

Wenworth (1922a) and Pellegrino (1965) among others suggest that agent transport of

the rocks (rigor of transport temperature and moisture changes etc) determine its

shape but also the particle genesis itself (rock structure mineralogy hardness etc) It

is not possible to determine the shape of the particles based on the agent transport or

genesis but generally a shape behaviour is expected according to Mitchell and Soga

(2005) specially when the particle size is in the clay size (gt2μm) The shapes of the

most common clay minerals are platy (figure 35) with some exceptions (eg

halloysite occurs as tubes kaolinite are large thick and stiff Smectites are composed

of small very thin and filmy particles Illites are intermediate between kaolinite and

smectite and attapulgite occurs in lathlike particle shapes) Some clay minerals

photographs are presented in figure 35

Figure 35 Clay mineral shape a) hallosite b) Kaoline c) Smactites d) Illites and e) attapulgite (Modified

from Mitchell and Soga 2005)

Figure 36 Particle size range in soils Generally the particles of clay size are plate shaped (Mitchell and

Soga 2005)

a) b) c)

e) d)

29

53 VOID RATIO AND POROSITY

The void ratio (e) is the ratio of the volume of voids to the volume of solid it is

defined by the equation

Porosity (n) is the ratio of the volume of voids to the total volume of the soil it is

represented by the equation

Holubec and DrsquoAppolonia (1973) found a relation between the void ratio and

sphericity (referred in the paper as coefficient of angularity ratio of particle surface

and equivalent sphere surface) their results show that the maximum and the minimum

void ratio increases as the shpericity decreases In this study the surface was obtained

for an indirect method based on the permeability developed by Hoffman in 1959

described in the same document Rouseacute et al (2008) defined the roundness as

Wadell (1935) and he found it as an important factor controlling the minimum and

maximum void ratios Some other authors as Youd (1973) and Cho et al (2006)

conclude the same minimum and maximum void ratios increase when sphericity and

roundness decrease Another interesting result (all above authors) was the bigger

influence of the form (sphericity circularity) and roundness on the maximum void

ratio The change of the maximum void ratio is more pronounced than the change of

the minimum void ratio when the form and roundness changes (See figure 39)

Particles arrangement and interlocking are probably the factor that controls the void

ratio bridge effect permit the existence of void among the particles while interlocking

allowed the particles to form arches avoiding the possibility to rotate and stay in a

more stable configuration eg as it happens with marbles

Figures 36 37 and 38 shows proposed empirical relationships between void ratio and

shape from tables 5 and 6 (graphically the scale goes from 0 to 1 when cero mean

high angularity shpericity or circularity and one means low angularity circularity or

sphericity) Holubec and DrsquoAppolonia (1973) data was taken to obtain a power curve

and describe a tendency Santamarina and Cho (2004) show Youd equations in the

original paper Youd (1973) never presented the equation but it is easy to use the

information to draw a trend

The graphics presented in this document (figures 36 37 and 38) must be used with

certain reserves due the fact that the original data was modified in order to fit all

information in one graphic what the figures shows is just the general trend of the

behaviourrsquos material regarding on the shape If more accurate description and

information is required the author recommends consulting the reference data In the

same way equations from Holubec and DrsquoApollonia (1973) and Youd (1973) were not

presented by the authors but the use of the information was taken in order to build up

those equations on tables 6 and 7

S

V

V

V

= e

V

V

=nV

(45)

(46)

30

Table 6 Minimum void ratio equations regarding on the quantity (Ψ for sphericity C for circularity R

for roundness SF for Sukumaran shape factor and AF for Sukumaran angularity factor)

EQUATION NUMBER REFERENCE

Figure 34 (left)

4340

minΨ45490e =

47

Holubec amp DrsquoAppolonia 1973 (Ψ

was obtained using equation 2)

SF06340

mine021903180e +=

48

Sukumaran amp Ashmawy 2001 (SF

obtained using equation 21)

C05101emin

= 49

Cho etal 2006 (C obtained using

figure 12)

Figure 34 (right)

1

minR08203590e +=

50

Youd 1973 (R obtained from figure

11 and table 3)

R34080emin

= 51

Cho et al 2006 (R obtained using

figure 12)

1

minR05104330e +=

52

Rouseacute et al 2008 (R obtained by

equation 21)

AF02330

mine372004160e +=

53

Sukumaran amp Ashmawy 2001 (AF

obtained using equation 37)

Table 7 Maximum void ratio equations regarding on the quantity (Ψ for sphericity C for circularity R

for roundness SF for Sukumaran shape factor and AF for Sukumaran angularity factor)

EQUATION NUMBER REFERENCE

Figure 35 (left)

51520

max Ψ61120e = 54

Holubec and DrsquoAppolonia 1973 (Ψ

was obtained using equation 2)

SF1190

max e0016907180e += 55

Sukumaran amp Ashmawy 2001 (SF

obtained using equation 21)

C86061emax = 56

Cho etal 2006 (C obtained using

figure 12)

Figure 35 (right)

1

max R1505540e += 57

Youd 1973 (R obtained from figure

11 and table 3)

R62031emax= 58

Cho et al 2006 (R obtained using

figure 12)

1

max R107106150e += 59

Rouseacute et al 2008 (R obtained by

equation 21)

AF0530

max e12506090e += 60

Sukumaran amp Ashmawy 2001 (AF

obtained using equation 37)

Comparing figures 37 and 38 (minimum and maximum void ratio) it can be seen on

the right scheme of both figures 37 and 38 (when the factor is roundnessangularity)

that all the empirical relations has a common initial point close to 1 (it means that

particles are well rounded) while this common agreement disappear when the

roundness factor decreases (when the particles become more angular) Same figures

(37 and 38) on the left graphs (when the factor is sphericitycircularityshape) do not

present the same behaviour in fact there is more disperse initial point close to 1(when

the particles tend to be more sphericalcircular)

31

In Figure 39 the Δe (emax-emin) has been plotted to show how the maximum void ratio

and the minimum void ratio has different rate change when the particle shape

changes Maximum void ratio increases more than minimum void ratio when the

particle shape becomes less spherical andor more angular Comparing figure 39 left

and right graphics it can be seen that right present a common initial point when the

quantity (roundnessangularity) is close to one while in the left graphic the initial

point is more disperse Both ending points in both graphics (close to zero) are

dispersed

Figures 37 38 and 39 present the same behaviour right graphics (when the factor is

roundness angularity) in each figure have an initial common point while the left

graphics do not (when the factor is sphericity circularity shape)

Figure 37 Minimum void ratio based upon the relation of shape factor proposed by the authors indicated

in the figure

Figure 38 Maximum void ratio based upon the relation of shape factor proposed by the authors indicated

in the figure

04

06

08

1

12

14

16

18

2

005

015

025

035

045

055

065

075

085

095

Factor (roundness angularity)

min

imu

m v

oid

rati

o

Youd 1973 roundness

Rouse 2008 roundness

Cho 2006 roundness

Sukumaran 2001 AF

03

04

05

06

07

08

09

1

11

12

13

05

015

025

035

045

055

065

075

085

095

Factor (sphericity circularity shape)

min

imu

m v

oid

rati

oHolubec 1973 sphericity

Cho 2006 circularity

Sukumara 2001 SF

05

07

09

11

13

15

17

19

21

00

150

250

350

450

550

650

750

850

95

Factor (sphericity circularity shape)

Maxim

um

vo

id r

ati

o

Holubec 1973 sphericity

Cho 2006 circularity

Sukumara 2001 SF

05

1

15

2

25

3

35

005

015

025

035

045

055

065

075

085

095

Factor (roundness angularity)

Maxim

um

vo

id r

ati

o

Youd 1973 roundness

Rouse 2008 roundness

Cho 2006 roundness

Sukumaran 2001 AF

32

54 ANGLE OF REPOSE

The angle of repose of a granular material is the steepest angle of descent or dip of the

slope relative to the horizontal plane when material on the slope face is on the verge

of sliding as show in figure 40

According to Qazi (1975) there are five types of forces which may act between the

particles in soils

1 Force of friction between the particles

2 Force due to presence of absorbed gas andor moisture of particle

3 Mechanical forces caused by interlocking of particles of irregular shape

4 Electrostatic forces arising from friction between the particles themselves and

the surface with which they come in contact

5 Cohesion forces operating between neighbouring particles

Rouseacute et al (2008) found a decrease of angle of repose with increase roundness

based upon ASTM C1444 test (Standard Test Method for Measuring the Angle of

Repose of Free-Flowing Mold Powders) The method consist in pouring sand on a

surface cover by paper trough a funnel of specific dimensions (the nozzle diameter

depend on the sandrsquos particle size) from an altitude of 15 inches (381 mm) The sand

is release from the funnel until the peak of the cone formed by the sand stops the flow

The repose angle is obtained with the equation

H represent the 15 inches D and d represent the diameter of the cone formed by the

sand and the diameter of the funnel respectively

Figure 39 Maximum minus minimum void ratio based upon the relation of shape factor proposed by the

authors indicated in the figure

0

01

02

03

04

05

06

07

08

09

1

005

015

025

035

045

055

065

075

085

095

Factor (sphericity circularity shape)

Maxim

um

- M

inim

um

Vo

id r

ati

oHolubec 1973 sphericity

Cho 2006 circularity

Sukumara 2001 SF

0

02

04

06

08

1

12

14

16

18

005

015

025

035

045

055

065

075

085

095

Factor (roundness angularity)

Maxim

um

- M

inim

um

Vo

id r

ati

o

Youd 1973 roundness

Rouse 2008 roundness

Cho 2006 roundness

Sukumaran 2001 AF

dD

H2

tan=φ1

rep(61)

33

Rouseacute (2008) shows an empirical relation to obtain the angle of repose based on the

roundness of the particles

55 SHEAR STRENGTH

The MohrndashCoulomb failure criterion represents the linear envelope that is obtained

from a plot of the shear strength of a material versus the applied normal stress This

relation is expressed as

where τ is the shear strength σn is the normal stress co is the intercept of the failure

envelope with the τ axis and is the slope of the failure envelope The quantity c is

often called the cohesion and the angle is called the angle of internal friction

Studies show that the internal friction angle (under drained triaxial tests) increases

more rapidly on those materials having higher angularity increasing the relative

density The internal friction angle is a function of the relative density and the particle

shape (Holubec and DrsquoAppolonia 1973)

Chan and Page (1997) found in a study made with dry copper (using different shapes

and sizes ranging from 180 to 106 μm) using a direct shear test (ring share test) that

the internal friction angle increases as the angularity increases

Shinohara et al (2000) did some experiments with steel powder different shapes

using a triaxial cell in the test Shinohara never used the roundness or angularity on

the work but apply the shape factor (relation long axisshort axis) and the results were

that as this relation deviate from factor 1 the internal friction angle increases

The following empirical relations were found in the literature showing the behaviour

of the friction angle (obtained under different conditions)

)tan( noc

Figure 40 Representation of the angle of repose

(63)

(62)

34

Cho et al (2006)

(64)

(R is obtain by comparing the Krumbein chart figure 13)

Rouseacute (2008)

(65)

(66)

(R is defined using Wadell equation 22)

In figure 41 the suggested empirical relations above and lines constructed using

author data from Holubec and DrsquoAppolonia (1973) and Sukumara and Ashmawy

(2001) are plotted together to display the general trend on the particle shape and

friction angle relation Sukumaran reports two lines one based on the shape factor

(SF) and the second referring the angularity factor (AF) Sukumaran performed the

tests at constant volume

The scale used for Holubec and DrsquoAppolonia (1973) have lower and upper limits of 1

and 2 respectively (angularity form) and a scale change was applied to be able to

presented in the actual figure 41 As in the previous section (52) the author

recommend to use the original data from the references due that the figure just follows

the general trend of the behaviourrsquos particle regarding on the shape

Figure 41 The changes on the internal friction angle shows a general increase when the particle roundness

becomes angular or in the case of Sakamuran less spheric (Shape factor SF)

35

Barton and Kjaernsli (1981) suggested a model (equation 67) to predict the peak

friction angle (φrsquo) based upon numerous trixial and direct shear data tests

where

Se equivalent strength of particle

Re equivalent roughness of particle

φb basic friction angle (obtained from basic tilting test)

σn normal load

The information required for the model is (1) the uniaxial compressive strength of the

rock (2) the d50 particle size (mesh size where 50 of the particles pass through)

required to define Se (figure 42) (3) the degree of particle roundness and (4) the

porosity following compaction All data can be estimated by simple index tests

Barton and Kjaernsli (1981) suggest that particle size and sample scale has an effect

on the friction angle and includes them to obtain the equivalent strength (Se) figure 42

shows the method to obtain this value Compressive strength (σc) was chosen to be the

factor affecting the scale because micro fractures influence this property while

samples are bigger more micro fractures contain and its compressive strength reduces

The equivalent roughness is obtain using figure 43 where is required to know the

porosity (n) and the origin of the particles (a small chart is provided in the same figure

to compare the particles profile)

b

n

ee

SLogR

Figure 42 Method of estimating Equivalent Strength (Se) of rockfill based on uniaxial compressive strength

(σc ) and d50 particle size (Barton amp Kjaernsli 1981)

(67)

36

56 SEDIMENTATION PROPERTIES

A particle released in a less dense Newtonian fluid initially accelerate trough the fluid

due to the gravity Resistances to deformation of the fluid transmitted to the particle

surface drag generate forces that act to resist the particle motion The force due to the

weight (Fw) can be written as

Where ρp ρ are density of the particle and fluid (water) respectively g is the

gravitational force and Vp is the volume of the particle

And the resistance force (FD) is

Where CD is the dimensionless drag coefficient W is the weight of the particle and A

is the cross section area

Particlersquos shape has been assumed to be spherical when equations are applied on the

settling velocity Correlation deviates when particle shape departs from spherical form

Figure 43 Method of estimating Equivalent Roughness (Roe) based on porosity of rockfill

origin material degree of roundedness and smoothness of particle (Barton amp Kjaernsli 1981)

PPW ρ)gV(ρF

A2

WρCF

2

DD

(68)

(69)

37

(Dietrich 1982) and it is known that natural particles depart from spherical form

thus it is evident that this departure would have consequences

The below equation is proposed to account the shape (in this case the Corey shape

factor equation 8) in the settling velocity (Jimenez and Madsen 2003)

Jimenez and Madsen (2003) Dietrich (1982) Briggs and McCulloch (1962) and

others were working in the hydraulic shape of particles to solve problems as sediment

transport It is obvious that the equation presented and the researcherrsquos investigation

works under certain conditions (eg grain size between 0063-1 mm)

Dietrich (1982) suggests an empirical relation that accounts settling velocity size

density shape and roundness of a particle

R1 R2 and R3 are fitted equations for size and density shape and roundness

respectively

57 HYDRAULIC CONDUCTIVITY PERMEABILITY

Darcyrsquos Law Permeability is one component of Darcyrsquos law Darcys law is a simple

proportional relationship between the instantaneous discharge rate through a porous

medium the viscosity of the fluid and the pressure drop

The total velocity Ve is equal to the product of the permeability of the medium

(porous media) k the pressure drop ∆p all divided by the viscosity μ (Muskat

1937)

Darcys law is only valid for slow viscous flow most groundwater flow cases fall in

this category Typically Darcyrsquos law is valid at any flow with laminar flow (see figure

44)

Reynoldrsquos number (Laminar and turbulent Flow) Typically any laminar flow is

considered to have a Reynoldrsquos number less than one and it would be valid to apply

Darcys law Experimental tests have shown that flow regimes with Reynolds numbers

1

ND

S

S

ZY

gd1s

WW

NDN

gd)1s(4

dS

2R1R

3 10RW

pk

Ve

(70)

(71)

(72)

(73)

38

up to 10 may still be Darcian (laminar flow) as in the case of groundwater flow The

Reynolds number (a dimensionless parameter) for porous media flow is typically

expressed as

where ρ is the density of water (units of mass per volume) υ is the specific discharge

(with units of length per time) d is a representative average grain diameter for the

porous media (often taken as the 30 passing size from a grain size analysis using

sieves - with units of length) and μ is the viscosity of the fluid (Muskat 1937)

Shape effects Permeability as Head and Epps (2011) suggested is affected by the

shape and texture of soil grains Elongated or irregular particles create flow paths

which are more tortuous than those spherical particles Particles with a rough surface

texture provide more frictional resistance to flow Both effects tend to reduce the

water flow through the soil

Kozeny-Carman empirical relation accounts for the dependency of permeability on

void ratio in uniformly graded sands serious discrepancies are found when it is

applied to clays due the lack of uniform pores (Mitchell and Soga 2005)

There are various formulations of the Kozeny-Carman equation one published by

Head and Epps (2011) takes the void ratio e the specific surface area Ss and an

angularity factor F into account of permeability k

The angularity factor F considers the shape of the particles and ranges from 11 for

rounded grains 125 for sub rounded to 14 for angular particles The specific surface

Ss is defined as

d1 and d2 represent the maximum and minimum size particle in mm

Kane amp Sternheim (1988) suggest that the inclusion of the shape factor (F) has

probably the background on the Reynolds number due this factor is dependent

significantly on the shape of the obstacles and Reynolds number determines the

presence of laminar or turbulent flow Figure 44 show how the laminar flow has low

energy dissipation while turbulent flow (eg the roughness and path tortuosity) has

high energy dissipation

e1

e

FSs

2k

3

2

dRe

21

6

ddSs

(74)

(75)

(76)

39

According to Nearing and Parker (1994) the amount of soil detached during laminar

and turbulent flow is dependent on each soil and also greater on turbulent flow due the

greater shear strength generated during this kind of flow this could suggest the

greater erosion when turbulent flow is present

58 LIQUEFACTION

Soil liquefaction is a phenomenon in which soil loses much of its strength or stiffness

for a generally short time by earthquake shaking or other rapid loading Static and

dynamic liquefactions occur been the second one the most regular known

Liquefaction often occurs in saturated soils that is soils in which the space between

individual particles is completely filled with water This water exerts a pressure on the

soil particles that influences how tightly the particles themselves are pressed together

Shaking or other rapid loading can cause the water pressure to increase to the point

where the soil particles can readily move with respect to each other (Jefferies and

Been 2000)

Jefferies and Been (2000) state that it is clear that minor variation in intrinsic

properties of sand have major influence on the critical state These might be variations

on grain shape mineralogy grain size distribution surface roughness of grains etc

Yoginder et al (1985) found that substantial decrease on liquefaction resistance

occur with increase in confining pressure for rounded and angular sands (1600 kPa)

also rounded sands show an rapidly build up of resistance against liquefaction with

increasing density while angular tailing sand in contrast show such rapid increase

only at low confining pressures At low confining pressure angular material is more

resistant to liquefaction Probably the breakage of the corners on the angular particles

in tailings is ruling the lost in resistance at high confining pressures (sieve analysis

Figure 44 The figure show the extremes of flow behaviour First turbulent conditions where the flow is

essentially random and unpredictable and second the well defined Laminar flow conditions

40

after test identify the breakage of angular particles while on rounded particles the

sieve analysis was practically the same)

59 GROUNDWATER AND SEEPAGE MODELLING

In groundwater flow the particlersquos shape affects the soilrsquos pore size distribution

hence the flow characteristics (Sperry and Peirce 1995) Tortuosity and permeability

(also see section 57) are two significant macroscopic parameters of granular medium

that affect the passing flow (Hayati et al 2012) Current models incorporating the

effects of particle shape have failed to consider irregular particles such as those that

would prevail in a natural porous medium (Sperry and Peirce 1995)

Hayati et al (2012) suggested based on his results that tortuosity effect converge

when the porosity increases indicating that the shape have dominance at low and mid

porosity ranges

Sperry and Peirce (1995) research conclusions suggest that particle size and porosity

are more important predictors for hydraulic conductivity explaining the 69 of the

variability but particle shape appears to be the next most important This however

apparently comprises particles larger than 295-351 μm Differences for particle size

295-351 μm and smaller are not detectable Another interesting result in the research

was the interaction effect of the particle size and particle shape It suggests a different

packing configuration for particles of the same shape but different size (scale

dependent)

6 DISCUSSION

61 TERMS QUANTITIES AND DEFINITIONS

In order to describe the particle shape in detail there are a number of terms quantities

and definitions (qualitative and quantitative) used in the literature (eg Wadell 1932

1934 Krumbein 1941 Sneed amp Folk 1958) All mathematical definitions

(quantitatives) are models used to simplify the complexity of shape description Some

authors (Mitchell amp Soga 2005 Arasan et al 2010) are using three sub-quantities

one and each describing the shape but at different scales The terms are

morphologyform roundness and surface texture (figure 1) The three sub-quantities

are probably the best way to classify and describe a particle because not a single

definition can interpret the whole morphology Common language is needed when

descriptors are explained and these three scales represent an option It is evident in

the reviewed literature that many of the shape descriptors are presented with the same

name but also that there is not a clear meaning on what this descriptor defines eg

when there is no upper limit in the roundness does it means that the angularity never

ends Could they be more and more angular Probably they could be on theory but

not in reality

41

62 PROPERTIES

Trough various articlersquos review done in the present investigation it is recognized that

the particlersquos shape has an effect on the material properties among these are

1 Porosity (Tickell 1938 Fraser 1935 Kolbuszewski 1948) and void ratio

(Cho et al 2006 Shergold 1953 Rouseacute et al 2008 Santamarina and Cho

2004)

2 Permeability (Witt and Brauns 1983)

3 Internal friction angle (Shinohara et al 2000 Chan and Page 1997

Cheshomi et al 2009)

4 Density (Youd 1973 Holubec and DrsquoAppolonia 1973)

5 Drag coefficient Hydraulics (Briggs and McCulloch 1962)

In Table 5 is a short resume of the properties and shape effect found in peer review

articles trough different journals Most of the reviewed articles based its research on

uniform graded sands

Table 8 Compilation of properties influenced by particle shape

Repose

angle

Friction

angle

Porosity and

Void ratio Density Permeability

Settling velocity

Drag coefficient Deformation

Sphericity (3D)shape factor

NI x x x x x x

Circularity (2D)

NI x x x x NI NI

Roundness x x x x NI NI x

x influence

NI no information available

Shape of particles has an effect on the arrangement producing bridging or avoiding

the rotation of the particles and the resulting geotechnical property is affected eg

including flaky particles can result in a higher void ratio due the bridging effect

(Santamarina and Cho 2004) and depending on the loads even the size distribution is

changed due the breakage (Yoginder et al 1985) in similar way angular particles

produce higher void ratio due the avoided possibility of the particles to rotate and

compact

The influence of the chosen shape descriptor appears in this review to have minor

influence on the soil properties in the reviewed studies except on the void ratio and

the friction angle Influence of particle shape in some cases is hider by other factors

(eg size distribution) also the particle shape probably does not have influence when

particle size is in the clay order (eg hydraulic conductivity) the reason could be due

to forces as electrostatic or capillarity become more important at this level

Among the shape descriptors some are chosen more often in literature (eg aspect

ratio) there is no apparent scientific basis to use it (probably due to the simplicity of

the measurement it becomes one of the most use) but there are still some other

descriptors that may or may not show better correlation with the soil properties

Instead empirical relations had been developed regarding roundness or shape to

describe the soil behaviour it is clear that the mechanism behind the results is still not

completely understood

42

There is necessity to define the best(s) shape descriptor(s) to be used for particular

geotechnical properties

63 IMAGE ANALYSIS

Many image analysis techniques had been used to describe the particle shape eg

Fourier analysis fractal dimension tomography etc (Hyslip and Vallejo 1997) but

there is not agreement on the usage or conclusion to ensure the best particle descriptor

for geotechnical applications

There are several shape descriptors and also various techniques to capture the

particles profile (3-dimensions 3-dimension orthogonal and 2-dimensions) Each

technique presents advantages and disadvantages 3-dimensions is probably the

technique that provide more information about the particle shape but the precision

also lies in the resolution the equipment required to perform such capture could be

more or less sophisticated (scanning particles laying down in one position and later

move to complete the scanning or just falling down particles to scan it in one step)

3-dimensions orthogonal this technique use less sophisticated equipment (compare

with the previous technique) but its use is limited to particles over 1cm also

information between the orthogonal pictures is not capture 2-dimensions require non

sophisticated equipment but at the same time the shape information diminish compare

with the previous due the fact that it is possible to determine only the outline as the

particle measurements are performed in 2-dimensions it is presumed that they will lie

with its shortest axis perpendicular to the laying surface when they are flat but when

the particle tends to have more or less similar axis the laying could be random

Advantages on the use of image analysis are clear there is not subjectivity because it

is possible to obtain same result over the same images Electronic files do not loose

resolution and it is important when collaboration among distant work places is done

files can be send with the entire confidence and knowing that file properties has not

been changed Technology evolutions allowed to work with more information and it

also applies to the image processing area were the time consumed has been shortened

(more images processed in less time)

One important aspect in image analysis is the used resolution in the analysis due the

fact that there are measurements dependent and independent on resolution Thus

those dependent measurements should be avoided due the error included when they

are applied or avoid low resolution to increase the reliability Among these

parameters length is the principal parameter that is influences by resolution (eg

perimeter diameter axis etc) Resolution also has another aspect with two faces

quality versus capacity more resolution (quality) means more storage space a

minimum resolution to obtain reasonable and reliable data must be known but it

depend on each particular application

43

64 APPLICATIONS

Quantify changes in particles in the authorrsquos thought is one of the future applications

due the non-invasive methods of taking photographs in the surface of the damrsquos slope

rail road ballast or roads Sampling of the material and comparing with previous

results could show volume (3D analysis) or area (2D analysis) loss of the particles as

well as the form roundness and roughness This is important when it has been

suggested that a soil or rock embankment decrees their stability properties (eg

internal friction angle) with the loss of sphericity roundness or roughness

Seepage stock piling groundwater etc should try to include the particle shape while

modelling seepage requires grading material to not allow particles move due the

water pressure but in angular materials as it is known the void ratio is great than the

rounded soil it means the space and the possibilities for the small particles to move

are greater stock piling could be modelled incorporating the particle shape to

determine the binrsquos capacity when particle shape changes (void ratio changes when

particle shape changes) Modelling requires all information available and the

understanding of the principles that apply

Industry is actually using the particle shape to understand the soil behaviour and

transform processes into practical and economic image analysis has been included in

the quality control to determine particle shape and size because the advantages it

brings eg the acquisition of the sieving curve for pellets using digital images taken

from conveyor this allows to have the information in a short period of time with a

similar result at least enough from the practical point of view as the traditional

sieving

7 CONCLUSIONS

The conclusions of this literature review are

It has been shown that particle shape has influence on the soil behaviour

despite of partial knowledge of the mechanism behind Understanding of the

particle shape and its influence needs to be accomplished

A common language needs to be built up to standardize the meaning on

geotechnical field that involve the particle shape General relationships

between shape and properties should be developed

Based on this review it is not clear which is the best descriptor to use in

geotechnical engineering affecting he related shape to properties Instead of a

couple of standards there is no shape descriptor in geotechnical field fully

accepted

Image analysis tool is objective make the results repeatable obtain fast results

and work with more amount of information

44

Resolution needs to be taken in consideration when image analysis is been

carried out because the effects could be considerable Resolution must be set

according to the necessities Parameters as perimeter can be affected by

resolution

There are examples where particle shape has been incorporated in industries

related to geotechnical engineering eg in the ballast and asphalt industry for

quality control

8 FURTHER WORK

Three main issues have been identified in this review that will be further investigated

the limits of shape descriptors influence of grading and choice of descriptor for

relation to geotechnical properties

Shape descriptors have low and high limits frequently the limits are not the same and

the ability to describe the particlersquos shape is relative The sensitivity of each descriptor

should be compare to apply the most suitable descriptor in each situation

Sieving curve determine the particle size in a granular soil particle shape could differ

in each sieve size There is the necessity to describe the particle shape on each sieve

portion (due to practical issues) and included in the sieve curve Obtain an average

shape in determined sieve size is complicated (due to the possible presence of several

shapes) and to obtain the particle shape on the overall particlersquos size is challenging

how the particle shape should be included

Since several descriptors have been used to determine the shape of the particles and

the relation with the soil properties it is convenient to determine the descriptorrsquos

correlation with the soil properties

9 ACKNOWLEDGMENT

I would like to thanks to Lulearing University of Technology (LTU) the time I had spent

in its facilities and the kind environment it offers and University of Sonora

(UNISON) that has been providing me the financial support and the time to conclude

this journey

10 REFERENCES

Andersson T (2010) Estimating particle size distributions based on machine vision

Doctoral Thesis Departament of Computer Science and Electrical Engineering Lulearing

University of Technology ISSN 1402-1544 ISBN 978-91-7439-186-2

45

Arasan Seracettin Hasiloglu A Samet Akbulut Suat (2010) Shape particle of

natural and crished aggregate using image analysis International Journal of Civil and

Structural Engineering Vol 1 No 2 pp 221-233 ISSN 0970-4399

Aschenbrenner BC (1956) A new method of expressing particle sphericity Journal

of Sedimentary Petrology Vol 26 No 1 pp 15-31

Axelsson K (1998) Introduktion till jordmekaniken jaumlmte jordmateriallaumlran Skrift

984 Lulearing Avdelningen foumlr Geoteknologi Lulearing Tekniska Universitet (In Swedish)

Barton Nick amp Kjaernsli Bjorn (1981) Shear strength of rockfill Journal of the

Geotechnical Engineering Division Proceedings of the American Society of Civil

Engineers (ASCE) Vol 107 No GT7

Barrett P J (1980) The shape of rock particles a critical review Sedimentology

Vol 27 pp 291-303

Blott S J and Pye K (2008) Particle shape a review and new methods of

characterization and classification Sedimentology Vol 55 pp 31-63

Bowman E T Soga K and Drummond W (2001) Particle shape characterization

using Fourier descriptor analysis Geotechnique Vol 51 No 6 pp 545-554

Briggs L I McCulloch D S (1962) Hydraulic shape of sand particles Journal of

Sedimentary Petrology Vol 32 pp 645-656

Chan Leonard C Y and Page Neil W (1997) Particle fractal and load effects on

internal friction in powders Powder Technology Vol 90 pp 259-266

Cheshomi A Fakher A Jones C J F P (2009) A correlation between friction

angle and particle shape metrics in quaternary coarse alluvia Quarterly Journal of

Engineering Geology and Hydrogeology Vol 42 pp 145-155

Cho G Dodds J and Santamarina J C (2006) Particle shape effects on packing

density stiffness and strength Natural and crushed sands Journal of Geotechnical

and Geoenvironmental Engineering May 2006 pp 591-602

Dietrich William E (1982) Settling velocity of natural particles Water Resources

Research Vol 18 No 6 pp 1615-1626

Dobkins J E and Folk R L (1970) Shape development on Tahiti-nui Journal of

Sedimentary Petrology Vol 40 No 2 pp 1167-1203

Folk R L (1955) Student operator error in determining of roundness sphericity and

grain size Journal of Sedimentary Petrology Vol 25 pp 297-301

Fernlund J M R (1998) The effect of particle form on sieve analysis A test by

image analysis Engineering Geology Vol 50 No 1-2 pp 111-124

46

Fernlund J M R (2005) Image analysis method for determining 3-D shape of

coarse aggregate Cement and Concrete Research Vol 35 Issue 8 pp 1629-1637

Fernlund J M R Zimmerman Robert and Kragic Danica (2007) Influence of

volumemass on grain-size curves and conversion of image-analysis size to sieve size

Engineering Geology Vol 90 No 3-4 pp 124-137

Fraser H J (1935) Experimental study of the porosity and permeability of clastic

sediments The Journal of Geology Vol 43 pp 910-1010 ISSN 0022-1376

Hayati Ali Nemati Ahmadi Mohammad Mehdi and Mohammadi Soheil (2012)

American Physical Society Physical review E 85 036310 DOI

101103PhysRevE85036310

Hawkins A E (1993) The Shape of Powder-Particle Outlines Wiley New York

Head K H and Epps R J (2011) Manual of soil Laboratory testing Volum II

Permeability shear strength and compressibility test 3rd

edition Whittles Publishing

Scotland UK 3rd

edition

Holubec I and DrsquoAppolonia E (1973) Effect of particle shape on the engineering

properties of granular soils ASTM STP 523 pp 304-318

Hyslip James P Vallejo Luis E (1997) Fractal analysis of the roughness and size

distribution of granular materials Engineering Geology Vol 48 pp 231-244

Janoo Vincent C (1998) Quantification of shape angularity and surface texture of

base course materials US Army Corps of Engineers Cold Region Research and

Engineering Laboratory Special report 98-1

Jefferies Mike and Been Ken (2000) Soil liquefaction A critical state approach

Taylor amp Francis Group London and New York

Jimenez Jose A Madsen Ole S (2003) A simple formula to estimate settling

velocity of natural sediments Journal of Waterway Port Coastal and Ocean

Engineering Vol 129 No 2 pp 70-78

Johansson Jens and Vall Jakob (2011) Jordmaterials kornform Inverkan paring

Geotekniska Egenskaper Beskrivande storheter bestaumlmningsmetoder

Examensarbete Avdelningen foumlr Geoteknologi Institutionen foumlr Samhaumlllsbyggnad

och naturresurser Lulearing Tekniska Universitet Lulearing (In Swedish)

Kane Joseph W and Sternheim Morton M (1988) Physics John Wiley amp Sons Inc

Third edition

Kolbuszewski J (1948) An experimental study of the maximum and minimum

porosities of sands Proceedings of the Second International Conference on Soil

Mechanics and Foundation Engineering Rotterdam June 21 to 30 Sub-section IIb

pp 158-165

47

Krumbein W C and Pettijohn FJ (1938) Manual of sedimentary petrography

Appleton-Century Crofts Inc New York

Krumbein W C (1941) Measurement and geological significance of shape and

roundness of sedimentary particles Journal of Sedimentary Petrology Vol 11 No 2

pp 64-72

Krumbein W C and Sloss L L (1963) Stratigraphy and Sedimentation 2nd

ed

WH Freeman San Francisco

Kuo Chun-Yi and Freeman Reed B (1998a) Image analysis evaluation of

aggregates for asphalt concrete mixtures Transportation Research Record Vol 1615

pp 65-71

Kuo Chun-Yi Rollings Raymond and Lynch Larry N (1998b) Morphological

study of coarse aggregates using image analysis Journal of Materials in Civil

Engineering Vol 10 No 3 pp 135-142

Lanaro F Tolppanen P (2002) 3D characterization of coarse aggregates

Engineering Geology Vol 65 pp 17-30

Lees G (1964a) A new method for determining the angularity of particles

Sedimentology Vol 3 pp 2-21

Lees G (1964b) The measurement of particle shape and its influence in engineering

materials British Granite Whinstone Federation Vol 4 No 2 pp 17-38

Matsushima Takashi Saomoto Hidetaka Matsumoto Masaaki Toda Kengo

Yamada Yasuo (2003) Discrete element simulation of an assembly of irregular-

shaped grains Quantitative comparison with experiments 16th ASCE Engineering

Mechanics Conference University of Washington Seattle July 16-18

Mitchell James K and Soga Kenichi (2005) Fundamentals of soil behaviour Third

edition WILEY

Mora C F Kwan A K H Chan H C (1998) Particle size distribution analysis of

coarse aggregate using digital image processing Cement and Concrete Research Vol

28 pp 921-932

Mora C F and Kwan A K H (2000) Sphericity shape factor and convexity

measurement of coarse aggregate for concrete using digital image processing Cement

and Concrete Research Vol 30 No 3 pp 351-358

Muskat Morris (1937) The Flow of fluids through porous media Journal of Applied

Physics Vol 8 pp 274

Nearing M A and Parker S C (1994) Detachment of soil by flowing water under

turbulent and laminar conditions Soil Science Society of American Journal Vol 58

No 6 pp 1612-1614

48

Pan Tongyan Tutumluer Erol Carpenter Samuel H (2006) Effect of coarse

aggregate morphology on permanent deformation behavior of hot mix asphalt Journal

of Transportation Engineering Vol 132 No 7 pp 580-589

Pellegrino A (1965) Geotechnical properties of coarse-grained soils Proceedings

International Conference of Soil Mechanics and Foundation Engineering Vol 1 pp

97-91

Pentland A (1927) A method of measuring the angularity of sands MAG MN AL

Acta Eng Dom Transaction of the Royal Society of Canada Vol 21 Ser3xciii

Persson Anna-Lena (1998) Image analysis of shape and size of fine aggregates

Engineering Geology Vol 50 pp 177-186

Powers M C (1953) A new roundness scale for sedimentary particles Journal of

Sedimentary Petrology Vol 23 No 2 pp 117-119

Pye W and Pye M (1943) Sphericity determination of pebbles and grains Journal

of Sedimentary Petrology Vol 13 No 1 pp 28-34

Qazi M A (1975) Flow properties of granular masses A review on the angle of

repose The Arabian Journal for Science and Engineering Vol 1 No 2

Quiroga Pedro Nel and Fowle David W (2003) The effects of aggregate

characteristics on the performance of portland cement concrete Report ICAR 104-1F

Project number 104 International Center for Aggregates Research University of

Texas

Riley N A (1941) Projection sphericity Journal of Sedimentary Petrology Vol 11

No 2 pp 94-97

Rouseacute P C Fennin R J and Shuttle D A (2008) Influence of roundness on the

void ratio and strength of uniform sand Geotechnique Vol 58 No 3 227-231

Santamarina J C and Cho G C (2004) Soil behaviour The role of particle shape

Proceedings Skempton Conf London

Schofield and Wroth (1968) Critical state soil mechanics McGraw Hill

Shaumlfer Michael (2002) Digital optics Some remarks on the accuracy of particle

image analysis Particle amp Particle Systems Characterization Vol 19 No 3 pp 158-

168

Shergold F A (1953) The percentage of voids in compacted gravel as a measure of

its angularity Magazine of Concrete Research Vol 5 No 13 pp 3-10

Shinohara Kunio Oida Mikihiro Golman Boris (2000) Effect of particle shape on

angle of internal friction by triaxial compression test Powder Technology Vol 107

pp131-136

49

Skredcommisionen (1995) Ingenjoumlrsvetenskapsakademinen rapport 395 Linkoumlping

1995

Sneed E D and Folk R L (1958) Pebbles in the Colorado river Texas A study in

particle morphogenesis Journal of Geology Vol 66 pp 114-150

Sperry James M and Peirce J Jeffrey (1995) A model for estimating the hydraulic

conductivity of granular material based on grain shape grain size and porosity

Ground Water Vol 33 No 6 pp 892-898

Sukumaran B and Ashmawy A K (2001) Quantitative characterisation of the

geometry of discrete particles Geotechnique Vol 51 No 7 pp 619-627

Szaacutedeczy-Kardoss E Von (1933) Die bistimmung der abrollungsgrades Geologie

und palaumlontologie Vol 34B pp 389-401 (in German)

Teller J T (1976) Equantcy versus sphericity Sedimentology Vol 23 pp 427-428

Tickell F G (1938) Effect of the angularity of grain on porosity and permeability

bulletin of the American Association of Petroleum Geologist Vol 22 pp 1272-1274

Tutumluer E Huang H Hashash Y Ghaboussi J (2006) Aggregate shape effects

on ballast tamping and railroad track lateral stability AREMA 2006 Annual

Conference Louisville KY

Wadell H (1932) ldquoVolume Shape and roundness of rock particlesrdquo Journal of

Geology Vol 40 pp 443-451

Wadell H (1933) Sphericity and roundness of rock Particles Journal of Geology

Vol 41 No 3 pp 310ndash331

Wadell H (1934) Shape determination of large sedimental rock fragments

The Pan-American Geologist Vol 61 pp 187-220

Wadell H (1935) ldquoVolume shape and roundness of quartz particlesrdquo Journal of

Geology Vol 43 pp 250-279

Wentworth W C (1922a) The shape of beach pebbles Washington US Geological

Survey Bulletin Vol 131C pp 75-83

Wentworth W C (1922b) A method of measuring and plotting the shape of pebbles

Washington US Geological Survey Bulletin Vol 730C pp 91-114

Wentworth W C (1933) The shape of rock particle A discussion Journal of

Geology Vol 41 pp 306-309

Witt K J Brauns J (1983) Permeability-Anisotropy due to particle shape Journal

of Geotechnical Engineering Vol 109 No 9 pp 1181-1187

3

of the particles retained on any sieve varies considerably with the shape (Lees

1964b) thus the passing of the particles depend upon the shape of the particles

(Fernlund 1998) In some industries the Image analysis is taking advantage over the

traditional sieving technique regardless of the intrinsic error on image analysis due the

overlapping or partial hiding of the rock particles (Andersson 2010) In this case the

weight factor is substitute by pixels (Fernlund et al 2007) Sieving curve using

image analysis is not standardized but after good results in the practice (Andersson

2010) new methodology and soil descriptions could raise including its effects

2 AIM AND GOAL

The aim of this report is to review the state of the art on how to describe particle

shape of individual grains of geotechnical material and knowledge on the influence of

shape in geotechnical properties

The goals in this study are to

Describe discuss and compare particle shape and definitions

Review the known effect of particle shape on soil mechanics parameters

Discuss the potential of the role of particle shape in soil mechanics

Focus in this study has been on 2 dimensional shape definitions

The content of the report is based upon published and peer reviewed papers in

English

3 DESCRIPTION OF SHAPE PROPERTIES

31 INTRODUCCTION

Particle shape description can be classified as qualitative or quantitative Qualitative

describe in terms of words the shape of the particle (eg elongated spherical flaky

etc) and quantitative that relates the measured dimensions in the engineering field

the quantitative description of the particle is more important due the reproducibility

Quantitative geometrical measures on particles may be used as basis for qualitative

classification There are few qualitative measures in contrast with several quantitative

measures to describe the particle form Despite the amount of qualitative descriptions

none of them had been widely accepted but there are some standards (eg ASTM

D5821 EN 933-3 and BS 812) specifying mathematical definitions for industrial

purposes

Shape description of particles is also divided in

o 3D (3 dimensions) it could be obtained from a 3D scan or in a two

orthogonal images and

o 2D (2 dimensions) or particle projection where the particle outline is drawn

4

3D and 2D image analysis present challenges itself 3D analysis requires a

sophisticated equipment to scan the particle surface and create the 3D model or the

use of orthogonal images and combine them to represent the 3 dimensions The

orthogonal method could present new challenges as the minimum particle size or the

placing in orthogonal way of the particles (Fernlund 2005) 2D image analysis is easy

to perform due the non-sophisticated equipment required to take pictures (eg regular

camera or the use of microscope for smaller particles) In 2D image analysis the

particle is assumed to lay over its more stable axis (eg longest and intermediate axis

lie more or less parallel to the surface while the shortest axis is perpendicular) or

random some authors publish their own preferences about this issue (Wadell 1935

Riley 1941 Hawkins 1993)

32 SCALE DEPENDENCE

In order to describe the particle shape in detail there are a number of terms quantities

and definitions used in the literature Some authors (Mitchell amp Soga 2005 Arasan et

al 2010) are using three sub-quantities one and each describing the shape but at

different scales The terms are morphologyform roundness and surface texture In

figure 1 is shown how the scale terms are defined

At large scale the particlersquos diameters in different directions are considered At this

scale describing terms as spherical platy elongated etc are used An often seen

quantity for shape description at large scale is sphericity (antonym elongation)

Graphically the considered type of shape is marked with the dashed line in Figure 1

At intermediate scale it is focused on description of the presence of irregularities

Depending on at what scale an analysis is done corners and edges of different sizes

are identified By doing analysis inside circles defined along the particlersquos boundary

deviations are found and valuated The mentioned circles are shown in Figure 1 A

generally accepted quantity for this scale is roundness (antonym angularity)

Regarding the smallest scale terms like rough or smooth are used The descriptor is

considering the same kind of analysis as the one described above but is applied

Figure 1 Shape describing sub quantities (Mitchell amp Soga 2005)

5

within smaller circles ie at a smaller scale Surface texture is often used to name the

actual quantity The sub-quantities and antonyms are summarized in table 1

Table 1 Sub-quantities describing the particlersquos morphology and its antonym

Scale Quantity Antonym

Large scale Sphericity Elongation

Intermediate scale Roundness Angularity

Small scale Roughness Smoothness

33 FORM (3D)

Wentworth in 1922 (Blott and Pye 2008) was probably one of the first authors on

measure the particle dimensions this consisted on the obtaining of the length of the

tree axes perpendicular among each other (see figure 2) on the tree dimensions (where

agebgec) to obtain the sphericity (equation 1)

Krumbein (1941) develop a rapid method for shape measurement to determine the

sphericity this is done by measuring the longest (a) medium (b) and shorter (c) axes

diameters of the particle it can be seen in figure 2 (Always perpendicular among each

other) The radios ba and cb are located in the chart developed by his own where it

can be found the Intercept sphericity as he called (See figure 3) This chart is an easy

graphical way to relate the dimensions

c2

ba

Figure 2 Measurement of the 3 axes perpendicular among each other (Krumbein 1941)

Figure 3 Detailed chart to determining Krumbein intercept sphericity (Krumbein 1941)

(1)

6

Wadell (1932) defined the sphericity as the specific surface ratio (equation 2) Figure

4 is a schematic representation of the sphere surface and particle surface both particle

and sphere of the same volume

This way to obtain the sphericity is almost impossible to achieve as Hawkins (1993)

declares due the difficulty to get the surface area on irregular solids

Wadell (1934) also defined the sphericity based upon the particle and sphere volumes

as equation 3 (see figure 5)

Wadell (1934) used a new formula simple to manage using the diameters (see figure

6 and equation 4)

Zingg (Krumbein 1941) develop a classification based on the 3 axes relation in this

way it is easy to find out the main form of the particles as a disks spherical blades

S

s

3

CIR

P

V

V

CIR

SV

D

D

Figure 4 Same volume sphere surface (s) and particle surface (S) (modified after Johansson and Vall

2011)

Figure 5 Relation between the volume of the particle and the volume of the circumscribed

sphere (Johansson and Vall 2011)

Figure 6 Figure is showing the relation between the diameter of a circumscribed sphere and the

diameter of a sphere of the same volume as the particle (Johansson and Vall 2011)

(2)

(3)

(4)

7

and rod-like this is summarized on figure 7 Zinggrsquos classification is related with

Krumbein intercept sphericity and the figure 3

In figure 8 the figures 3 and 7 are combined the relation in the two classifications can

be seen it is an easy way to understand the morphology regarding on the a b and c

dimensions

Pye and Pye (1943) in the article ldquosphericity determinations of pebbles and sand

grainsrdquo compare the Wadellrsquos sphericity developed in 1934 (based on the diameter)

with ldquoPebble sphericityrdquo based on an ellipse this last equation (number 5) appears

two years early published by Krumbein (1941) Axis measurement is done as figure 1

denotes for equations 5 trough 12 with exception of equation 8 where the original

document was not possible to obtain

32a

cb

Figure 7 Zinggrsquos classification of pebble shape based on ratios ba and cb (Krumbein 1941)

Figure 8 Classification made by Zinggrsquos and chart to determine sphericity (Krumbein and Sloss 1963)

(5)

8

Sneed amp Folk in (1958) found a relation between the tree dimensional axes called

ldquoMaximum Projection Sphericityrdquo

In a similar way Ashenbrenner (1956) showed his equation at that time named

ldquoWorking Sphericityrdquo

Form or shape factor names are used by authors like Corey (shape factor eq 8) in the

paper published on 1949 Williams (shape factor eq 9) in 1965 Janke (form factor

eq 10) in 1966 and Dobkins amp Folk (oblate-prolate index eq 11) in 1970 (Blott and

Pye 2008)

Aschenbrenner (1956) develop the shape factor by using the relation of the tree axis

but the square of the middle one

3

2

ba

c

))ab((1)bc(16))ab((cb)(11

)ab()bc( 128

22

3 2

ab

c

acb when 1ac

b acb when

b

ac-1 2

22

2

3

cba

c

222

a

c

50c-a

b-a10

2b

ac

(6)

(7)

(8)

(9)

(10)

(11)

(12)

9

Table 2 General overview over different particle shape definitions for 3D sphericity has been compiled

and arranged chronologically

Aspect Name Author Year Based on

Sphericity (3D) Flatness index Wentworth 1922a 3-axes

True Sphericity Wadell 1932 Surface

Operational sphericity Wadell 1932 Volume

Sphericity Wadell 1934 Sphere diameter

Zinggrsquos clasification Zinggrsquos1

1935 3-axes

Intercept sphericity chart Krumbein 1941 3-axes

Pebble sphericity Pye and Pye 1943 3-axes

Corey shape factor Corey2

1949 3-axes

Working sphericity Ashenbrenner 1956 3-axes

shape factor Ashenbrenner 1956 3-axes

Maximum projection sphericity Sneed amp Folk 1958 3-axes

Williams shape factor Williams2

1965 3-axes

Janke form factor Janke2

1966 3-axes

Oblate-prolate index Dobkins amp Folk 1970 3-axes 1) Krumbein and Sloss 1963 2) Blott and Pye 2008

34 FORM (2D)

The technique to measure the sphericity is based in tree dimensions it can be found in

literature some ways to measure the ldquotwo dimensions sphericityrdquo which is simply the

perimeter of the particle projection some authors named ldquoparticle outlinerdquo or

ldquocircularityrdquo

Wadell in 1935 (Hawkins 1993) adopt a conversion of his 1934 3D sphericity

formula (equation 4) to a 2D outline He defined an orientation on the particles and

they were based on the maximum cross sectional area (outline of the particle

projecting the maximum area) The equations show the relation between diameters of

a circle of same area and smallest circumscribed circle

He also used the term ldquodegree of circularityrdquo as the ratio of the perimeter of a circle of

same area and the actual particle perimeter

Tickell in 1931 (Hawkins 1993) used his empirical relation The particle orientation

proposed was a random one It is described by the ratio between the area outline and

the area of smallest circumscribed circle

C

A

D

DC

P

PC C

CA

AC

(13)

(14)

(15)

10

Some other authors has been working with the ldquocircularityrdquo concept and had develop

them own equations as Pentland (1927) relating the area outline and area of a circle

with diameter equal to longest length outline and Cox (Riley 1941) with the ratio

area and perimeter time a constant equations 16 and 17 respectively Both authors did

not define any definite orientation of the grains

Riley (1941) realize the problems that an area perimeter and some other

measurements proposed by the above authors can carry as the time consuming and

tedious work (at that time were not computer all was made by hand) and thatrsquos why

he develop this equation easy to handle called ldquoinscribed circle sphericityrdquo He used

the same particle orientation proposed by Wadell and the relation of diameters of

inscribed and circumscribed circles

Horton 1932 (Hawkins 1993) use the relation of the drainage basing perimeter and

the perimeter of a circle of the same area as drainage basin

Janoo in 1998 (Blott and Pye 2008) develop his general ratio of perimeter to area

Sukumaran and Ashmawy (2001) develop his own shape factor (SF) defined as the

deviation of the global particle outline from a circle Figure 9 can be used as a

reference to determine the items used in the equation 21

N is referred to the number of sampling intervals o radial divisions

C2A

AC

2P

A4C

C

I

D

DC

CD

D

P

PC

A

PC

2

45ordm x N

Particleα

= SF

sumN

1=ii

(16)

(17)

(18)

(19)

(20)

(21)

11

Table 3 General chronological overview of the particle shape definitions for 2D sphericity

Aspect Name Author Year Based on

Circularity (2D) roundness Pentland 1927 area

roundness Cox1

1927 area-perimeter

roundness Tickell2

1931 area

Circularity Horton2

1932 drainage basin

outline circularity Wadell 1935 Circle diameter

degree of circularity Wadell 1935 Perimeter

inscribed circle sphericity Riley 1941 Circle diameter

Circularity Krumbein and Sloss 1963 chart

Janoo 1998 area-perimeter

Shape factor Sukumaran 2001 Segmentation of particle and angles

1) Riley 1941 2) Hawkins 1993

35 ROUNDNESS OR ANGULARITY

Roundness as described in section 32 is the second order shape descriptor Sphericity

lefts beside the corners and how they are this was notice by most of the authors sited

before and they suggested many ways to describe this second order particle property

Roundness is clearly understandable using the figure 10 Particle shape or form is the

overall configuration and denotes the similarities with a sphere (3D) or a circle (2D)

Roundness is concerning about the sharpness or the smoothness of the perimeter (2D)

Surface texture (Barret 1980) is describe as the third order subject (form is the first

and roundness the second) and it is superimposed in the corners and it is also a

property of particles surfaces between corners

Figure 9 Description of the Sukumaran factors to determine the shape and angularity (Sukumaran and

Ashmawy 2001)

12

Wadell (1935) describes his methodology calling it total degree or roundness to

obtain the roundness of a particle using the average radius of the corners in relation

with the inscribed circle diameter (see figure 11) on the equation

In the same study Wadell (1935) has used the equation

This two last equation shows slightly differences on the results (Wadell 1935)

Powers (1953) also published a graphic scale to illustrate the qualitative measure

(figure 12) It is important to highlight that any comparing chart to describe particle

properties has a high degree of subjectivity Folk (1955) concludes that when charts

are used for classification the risk of getting errors is negligible for sphericity but

large for roundness

N

R

r

Rinmax

r

R

NR

inmax

Figure 10 Form (shape) Roundness and Texture graphical description (Bowman et al 2001)

Figure 11 Wadellrsquos method to estimate the roundness corners radius and inscribed circle

(Hawkins 1993)

(22)

(23)

13

Some authors as Russel amp Taylor in 1937 Pettijohn in 1957 and Powers in 1953

developed a classification based on five and six classes (Hawkins 1993) each one

with its own class limits it is important to denote that the way they measure the

roundness is the developed by Wadell (1935) This classification and class limits are

showed in the table 4

Table 4 Degrees of roundness Wadell Values (Hawkins 1993) NA = no-applicable

Grade terms Russell amp Taylor (1937) Pettijohn (1957) Powers (1953)

Class

limits (R)

Arithmetic

midpoint

Class limits

(R)

Arithmetic midpoint Class

limits (R)

Arithmetic

midpoint

Very angular

NA

NA

NA

NA

012-017

014

Angular

000-015

0075

000-015

0125

017-025

021

Subangular

015-030

0225

015-025

0200

025-035

030

Subrounded

030-050

0400

025-040

0315

035-049

041

Rounded

050-070

0600

040-060

0500

049-070

059

Well rounded

070-100

0800

060-100

0800

070-100

084

Krumbein and Sloss (1963) published a graphical chart easy to determine the

sphericity and roundness parameters using comparison See figure 13 (Cho et al

2006)

Figure 12 A Roundness qualitative scale (Powers 1953)

Figure 13 Sphericity and roundness chart (Cho et al 2006) The roundness equation that appears here in

the chart is the wadellrsquos equation number 22

14

Fischer in 1933 (Hawkins 1993) used a straightforward method to quantify roundness

using a central point in the outline and dividing the outline in angles around this point

that were subtended by the straight or non curved parts of the profile were measured

This is illustrated in figure 14

To express the angularity value Fischer used the ratio of angles standing linear parts

on the outlines and concave respectively

Figure 14 left (A) and right (B) gives a similar angularity of approximately 042

using the above equations (Hawkins 1993)

Wentworth in 1922 used the maximum projection to define the position of the particle

to obtain the outline or contour (Barret 1980) The equation reflects the relation of the

diameter of a circle fitting the sharpest corner and the longest axis plus the shortest

axis c (minimum projection)

Wentworth (Hawkins 1993) expressed the roundness as the ratio of the radius of

curvature of the most convex part and the longest axis plus short axis

Actually these last two equations are the same just expressed in different terms when

the particle is in its maximum projection

Dimensions can be seen on figure 15 L and B represents the mayor axis a and

intermediate axis b The intention is to make difference between the 2 and 3

dimensions (L and B are for 2D as a b and c are for 3D)

deg360

ANG

=R

sumPLA

PLA

CON

ANG

ANGR

2)S(L

DR

M

S

B)4(L

RR CON

Figure 14 Fischerrsquos methods of angularity computation (Hawkins 1993)

A=inscribed circle B=circumscribed circle

(24)

(25)

(26)

(27)

15

Wentworth 1919 has a second way to express the roundness called Shape index

(Barrett 1980) and it relates the sharpest corner and the diameter of a pebble trough

the sharpest corner

Wentworth (1922b) used define the roundness as the ratio of the sharpest corner and

the average radius of the pebble

Cailleux (Barrett 1980) relates the radius of the most convex part and the longest

axis

Kuenen in 1956 show his roundness index (Barrett 1980) between the sharpest corner

and the breath axis

Dobkins amp Folk (1970) used a modified Wentworth roundness with the relation of

sharpest corner and inscribed circle diameters

AVG

CON

R

RR

x

s

D

DR

L2

RR CON

B

DR s

i

s

D

DR

3AVGAVG cbaDR2

Figure 15 Description of L and B axes (Hawkins 1993)

(28)

(29)

(30)

(31)

(32)

(33)

16

Swan in 1974 shows his equation (Barrett 1980) relating the sharpest (or the two

sharpest) corner(s) and inscribed circle diameter

Szadeczsky-Kardoss has his Average roundness of outline (Krumbein and Pettijohn

1938) relating the concave parts perimeter and the actual perimeter

Lees (1964a) developed an opposite definition to roundness it means that he

measures the angularity instead of the roundness and he calls it Degree of angularity

Figure 16 shows the items considered when equation 36 applies as the angles (α)

inscribed circle (Rmax-in) and the distance (x) The main formula is

In order to apply the last equation corners needs to be entered in the formula and each

individual result will add to each other to obtain the final degree of angularity

A roundness index appears on Janoo (1998) Kuo and Freeman (1998a) and Kuo et

al (1998b) it is described as

The last equation is on section 34 also because there is not a general agreement on the

definition furthermore some authors had used to define the roughness this is not the

only equation that has been used trying to define different aspects (sphericity

roundness or roughness) but it is a good example of the misuse of the quantities and

definitions

inmaxR

x)180(R

2P

A4R

i

ss

D

DDR

221

100P

PR CON

Figure 16 Degree of angularity measurement technique (Blot and Pye 2008)

(34)

(35)

(36)

(17)

17

Sukumaran and Ashmawy (2001) present an angularity factor (AF) calculated from

the number of sharpness corners Angles βi required to obtain the angularity factor are

shown in figure 9

Sukumaran and Ashmawy (2001) also suggested use not bigger sampling interval of

N=40 because it is the cut off between angularity factor and surface roughness If so

this equation could be used to describe the roughness

Table 5 General chronological overview of the particle roundness

Aspect Name Author Year Based on

Roundness shape index Wentworth 19191

diameter of sharper corner

shape index Wentworth 1922b sharpest corner and axis

roundness Wentworth 1933 convex parts

Fischer 19332

noncurved parts outline

Fischer 19332

noncurved-streigth parts outline

Average roundness of outline

Szadeczsky-Kardoss 19333

convex parts-perimeter

roundness Wadell 1935 diameter of corners

roundness Wadell 1935 diameter of corners

roundness Russel amp Taylor 19372

class limit table

roundness Krumbein 1941 chart

Cailleux 19471

convex parts

roundness Pettijohn 19494 class limit table

roundness Powers 1953 chart and class limit table

Kuenen 19561

axis-convex corner

roundness Krumbein and Sloss 1963 chart

degree of angularity Lees 1964a corners angles and inscribed circle

Dobkins amp Folk 1970 diameter of sharper corner

Swan 19741

diameter of sharper corners

Angularity factor Sukumaran and

Ashmawy 2001

Segmentation of particles and angles

1) Barret 1980 2) Hawkins 1993 3) Krumbein and Pettijohn 1938 4) Powers 1953

sum

sumsumN

1=i

2

i

2

N

1=i

2

i

2N

1=ii

)ordm180 -circleβ( - )(180ordm x 3

)ordm180-circleβ(-)ordm180 -Particleβ(

= AF (37)

18

36 ROUGHNESS OR SURFACE TEXTURE

A third property called texture appears early in the literature with the sphericity and

roundness properties since then texture property was longed described but it was in

accordance with the authors at that time not measurable

Wright in 1955 developed a method to quantify the surface texture or roughness of

concrete aggregate using studies done on 19 mm stones The test aggregates were first

embedded in a synthetic resin The stones were cut in thin sections The sections

projection was magnified 125 times The unevenness of the surface was traced and the

total length of the trace was measured The length was then compared with an uneven

line drawn as a series of chords (see figure 17) The difference between these two

lines was defined as the roughness factor (Janoo 1998)

However with the advance of technology it has become easier measure the roughness

and here is presented some researcherrsquos ideas how this property should be calculated

One technique used by Janoo (1988) to define the roughness can be seen in figure 18a

and is defined as the ratio between perimeter and convex perimeter

The convex perimeter is obtained using the Feretrsquos box (or diameter) tending a line in

between the touching points that the Feretrsquos box describes each time it is turn (figure

18b)

PER

OC

PR

Figure 17 Measurement method for characterizing the surface texture of an aggregate (Janoo 1998)

a) Convex perimeter (CPER) b) Feret measurement Figure 18 a) Convex perimeter (CPER) b) Feret measurement (modified after Janoo 1998)

(38)

a)

b)

19

Kuo and Freeman (1998a) and Kuo et al (1998b) use the roughness definition as the

ratio perimeter and average diameter

Erosion and dilatation image processing techniques are used to obtain the surface

texture Erosion is a morphological process by which boundary image pixels are

removed from an object surface which leaves the object less dense along the

perimeter or outer boundary Dilatation is the reverse process of erosion and a single

dilatation cycle increases the particle shape or image dimension by adding pixels

around its boundary (Pan etal 2006)

The ldquonrdquo erosion and dilatation cycles are not standardized

Mora and Kwan (2000) used the ldquoconvexity ratio CRrdquo (equation 41) and the ldquofullness

ratio FRrdquo (equation 42) in their investigation they are

The convex area is the area of the minimum convex boundaries circumscribing the

particle This is illustrated in the figure 19 The convex area is obtained in a similar

way as the convex perimeter but in this case the area between the original outline and

the convex perimeter is our convex area

AVG

OD

PR

100A

1AARO

CONo A

AR =

CONo A

AR =

Figure 19 Evaluation of area and convex area (Mora and Kuan 2000)

(39)

(40)

(41)

(42)

20

4 TECHNIQUES IN ORDER TO DETERMINE PARTICLE

SHAPE

41 HAND MEASUREMENT

Hand measurement technique was the first used by obvious reasons in order to

improve the accuracy special devices developed as the ldquosliding rod caliperrdquo used by

Krumbein (1941) it works placing the sample on the sliding road calliper as show

figure 20b the length in different positions can be obtain by using the scale provided

in the handle the ldquoconvexity gagerdquo that was actually used by opticians to measure the

curvature of lenses but easily applicable to the particle shape analysis (Wentworth

1922b) works measuring the movement of the central pivot as figure 20a shows (the

two adjacent pivots are invariable) as many the central pivot moves more is the

curvature or the ldquoSzadeczky-Kardossrsquos apparatusrdquo develop in 1933 that traces the

profile of the rock fragment so the outline traced is then analyzed (Krumbein and

Pettijohn 1938) figure 20c show equipment

Another helpful tool to determine the particle dimensions was the ldquocamera lucidardquo to

project the particlersquos contour over a circle scale appearing in Figure 21 thus it is

possible to measure the particlersquos diameter

a)

c) b)

Figure 20 a) convexity gage used to determine the curvature in particle corners (Wenworth 1922b)

b)sliding rod caliper device to measure the particle axis length (Krumbein 1941) and c)Szadeczky-

Kardoss (1933) apparatus it was utilized to obtain the particle outline

Figure 21 Circle scale used by Wadell (1935) to determine particlersquos diameter and roundness

21

42 SIEVE ANALYSIS

Bar sieving eg according to EN 933-31997 can be used to determine simple large

scale properties By combining mesh geometries the obtained results can be used to

quantify flakiness and elongation index ASTM D4791 (Flat and elongated particles

are defined as those coarse aggregate particles that have a ratio of length to thickness

equal to or greater than a specified value such as 51 The index represents the

percentage on weight of these particles) The method is not suitable for fine materials

This due to the difficulty to get the fine grains passed through the sieve and the great

amount of particles in relation to the area of the sieve (Persson 1998) eg EN 933-

31997 related to flakiness index The test is performed on aggregates with grain size

from 4 mm and up to 63 mm two sieving operations are necessary the first separates

on size fraction and the second use a bar sieve after the first sieving the average

maximum diameter of the particles is obtain and with the second sieving (bar sieving)

the shortest axis diameter is found finally with this two parameters the flakiness

index is determined

There are more standards related with the particle shape (see appendix A) but this

above presented are probably the most known using sieve analysis to determine

particlersquos geometrical properties

Sieve analysis is facing the computers age and image analysis sieving research is

taking place (Andersson 2010 Mora and Kwan 2000 Persson 1998) Industry is

also applying the image analysis sieving with decrees on the testing time compare

with the traditional sieving method An inconvenient of image analysis is the error

due the overlapping or hiding of the particles during the capture process but the

advantages are more compare with disadvantages (Anderson 2010)

43 CHART COMPARISON

Charts developed over the necessity of faster results because the long time consuming

required when measuring each particle

Krumbein (1941) present a comparison roundness chart for pebbles which were

measured by Wadellrsquos method because this property was the most difficult to measure

due to the second order scale that roundness represents (See figure 22)

Figure 22 Krumbein (1941) comparision chart for roundness

22

A qualitative chart by Powers (1953) try to include both (sphericity and roundness)

particlersquos characteristics it was divided on six roundness ranges (very angular

angular sub-angular sub-rounded rounded and well rounded) and two sphericity

series (high and low sphericity) This chart was prepared with photographs to enhance

the reader perspective (See figure 23)

A new chart including sphericity and roundness appear this time it was easier to

handle the two mean properties of particlersquos shape furthermore there was included

the numerical values that eliminated the subjectivity of qualitative description The

chart is based on Wadellrsquos definitions (Krumbein and Sloss 1963) (See figure 24)

Folk (1955) worried about the personrsquos error on the chartrsquos comparison studied the

determination of sphericity and angularity (he used the Powers 1953 comparison

chart) he found that the sphericity determination by chart comparison has a negligible

error while the roundness he concluded it was necessary to carry out a more wide

research due the high variability show by his study

Figure 23 Powers (1953) qualitative shpericity-roundness chart

Figure 24 Sphericity-roundness comparison chart (Krumbein and sloss 1963)

23

44 IMAGE ANALYSIS

Image analysis is a practical method to use for shape classification since it is fast and

can be automated Different techniques appear to process these images among them

are

o Feret Diameter the Feret diameter is the longitude between two parallel lines

this lines can rotate around one particle or outline to define dimensions as it

is shown in figure 25 these method is not a fine descriptor but as it was say

above it is a helpful tool to determine diameters (Janoo 1988)

o Fourier Mathematical Technique It produces mathematical relations that

characterize the profile of individual particles This method favours the

analysis of roughness and textural features for granular soils The problem in

the methodology remains in the re-entrant angles in order to complete the

revolution (Bowman et al 2001) see figure 26

o Fractal Dimension Irregular line at any level of scrutiny is by definition

fractal (Hyslip and Vallejo 1997) Figure 27 shows fractal analysis by the

dividing method The length of the fractal line can be defined as

N

1n

nn0 )nsinbncosa(a)(R

RD1n)(P

Figure 25 Feret measurement technique is defined by two parallel lines turning

around the particle to define the shortest and longest Feret diameter (Janoo 1988)

Figure 26 Fourier technique with two radiuses at one angle (Bowman et al 2001)

(43)

(44)

24

o Orthogonal image analysis This technique is basically the use of two images

orthogonal between them to acquire the three particle dimensions (Fernlund

2005) any of the above techniques can be used in this orthogonal way

o Laser Scanning Technique this kind of laser scanning 3D is one of the most

advanced techniques In figures 28a) we have the laser head scanning the rock

particles the particles have control points in order to keep a reference point

when move them to scan the lower part in figure 28b) we can see the laser

path followed (Lanaro and Tolppanen 2002)

Another technique is the Laser-Aided Tomography (LAT) in this case a laser sheet is

used to obtain the particles surveying (see figure 29) This technique is different and

has special requirements as to use liquid with same refractive index as the particles

particles must let the laser or certain percent of light go through (Matsushima et al

2003)

a) b)

Figure 27 Fractal analysis by the dividing method at different scrutiny scale (Hyslip and Vallejo 1997)

Figure 28 a) Scanning head b) scanning path (Lanaro and Tolppanen 2002)

Figure 30 3D scan completed ready to

use for any further measure

(Matsushima et al 2003)

Figure 29 LAT scaning particles

(Matsushima et al 2003)

25

Both 3D techniques obtain the particle shape that is later used to achieve measures as

we can see in figure 30

All these previous techniques are easily written in codes or scripts to be interpreted in

a digital way obtaining the desired measurement but there are some interesting points

in the image analysis regarding on the errors involve among them are image

resolution and orientation of the particles orientation is not relevant when it is

random and large number of particles are involve resolution have an influence on the

accuracy (Zeidan et al 2007)

When resolution is increase more accuracy is obtain and the object representation

match better with the real form in the other hand more resolution means more

spending on memory and time thus resolution needs to be according with the goal

and precision needed in any work (Schaumlfer 2002)

Schaumlfer (2002) conclude that attributes like length when measuring digital images

present relative high errors It can be vanish or at least diminish using high resolution

just for diameter but not for perimeter that keep the error as big as initially Johansson

and Vall (2011) obtain similar results when 3 different resolutions were used in the

same particle obtaining an unstable output for those termsquantities that involve the

perimeter Thus all quantities relating the perimeter should be treated with care

5 EFFECT OF SHAPE ON SOIL PROPERTIES

51 INTRODUCTION

In laboratory test on the effect on particle size on basic properties has been

investigated in several studies this relation has been discussed and various

mechanisms had been proposed to explain the behaviour of the soil in dependency

also with the shape Basically there are two mechanisms proposed The arrangement

of particles and the inter-particle contact (Santamarina and Cho 2004) and

subsequence breakage

The arrangement of particles

Arrangement of the particles can be presented in three different forms loose dense

and critical this arrangement determines the soil properties (eg density increase with

more dense arrangement) Loose and dense states are easy understandable when

figure 31 is explained while in the upper part of the figure the particles are arranged

using the minimum space needed in the lower part a span is created using the flaky

particle as a bridge this phenomena is known as ldquobridgingrdquo Bridging can produce

different geotechnical results when just the shape of the particle is changed eg void

ratio (Santamarina and Cho 2004) Particles are able to rearrange this could be done

applying pressure (energy) to the soil the pressure (energy) will create such forces

that soil particles will rotate and move (see figure 34) finishing in a more dense state

26

A loose soil will contract in volume on shearing and may not develop any peak

strength (figure 32 left) In this case the shear strength will increase gradually until

the residual shear strength is revealed once the soil has ceased contracting in volume

A dense soil may contract slightly (figure 32 right) before granular interlock prevents

further contraction (granular interlock is dependent on the shape of the grains and

their initial packing arrangement) In order to continue shearing once granular

interlock has occurred the soil must dilate (expand in volume) As additional shear

force is required to dilate the soil a peak shear strength occurs (figure 32 left) Once

this peak shear strength caused by dilation has been overcome through continued

shearing the resistance provided by the soil to the applied shear stress reduces

(termed strain softening) Strain softening will continue until no further changes in

volume of the soil occur on continued shearing Peak shear strengths are also

observed in overconsolidated clays where the natural fabric of the soil must be

destroyed prior to reaching constant volume shearing Other effects that result in peak

strengths include cementation and bonding of particles The distinctive shear strength

called the critical state is identified where the soil undergoing shear does so at a

constant volume (Schofield and Wroth 1968)

The inter-particle contact

For frictional soil ie coarse grained soil the friction between particles is the

dominating factor for strength Materials usually consisting of coarse grains (diameter

Figure 31 Bridging effect when flaky particles are combined in the bulk material (Santamarina and

Cho 2004)

Figure 32 The left part of the figure show a typical behaviour of loose and dense material over shear stress

while at the right the figures illustrate the typical volume changes

27

gt 006mm) behave as a frictional soil it means that the strength of coarse soils (silt

sand gravel etc) comes from an inter-particle mechanical friction thus ideally they

do not have traction strength In figure 33 the inter-particle contact is illustrated here

the pressure (P) is applied and two more components are found the normal load (N)

and the tangential load (T) described as the friction coefficient (μF) The forces stand

in equilibrium (Johansson and Vall 2011)

When particles equilibrium is disturbed (friction coefficient is not enough to keep

particles unmoved) the rotation is imminent and it is necessary in order to compact

the soil in figure 34 can be seen that the arrangement is a fact that inhibit or allow this

rotation and the shape in the 3 different scales are also factors because the more

spherical andor more rounded andor less roughness more easy is the rotation

(Santamarina and Cho 2004)

Breakage

Breakage is a side effect of the inter-particle contact and rotation when pressure

exceed the rock strength it can happened when the particles are tight together and

there is not enough space to rotate it is more obvious in angular particles (mesh form)

or as in figure 31 where the flaky particle ldquobridgingrdquo is not able to rotate but it can

brake by the pressure increase Yoginder et al (1985) notice that the angular particle

break during his experiments and they turn more rounded changing the original size

and form configuration at the same time there was a soil properties loosening

Figure 33 Inter-particle contact and forces acting (Axelsson 1998)

Figure 34 Rotation inhibition by the particles compaction or low void ratio (Santamarina and Cho 2004)

28

52 INFLUENCE OF SIZE AND SHAPE

Wenworth (1922a) and Pellegrino (1965) among others suggest that agent transport of

the rocks (rigor of transport temperature and moisture changes etc) determine its

shape but also the particle genesis itself (rock structure mineralogy hardness etc) It

is not possible to determine the shape of the particles based on the agent transport or

genesis but generally a shape behaviour is expected according to Mitchell and Soga

(2005) specially when the particle size is in the clay size (gt2μm) The shapes of the

most common clay minerals are platy (figure 35) with some exceptions (eg

halloysite occurs as tubes kaolinite are large thick and stiff Smectites are composed

of small very thin and filmy particles Illites are intermediate between kaolinite and

smectite and attapulgite occurs in lathlike particle shapes) Some clay minerals

photographs are presented in figure 35

Figure 35 Clay mineral shape a) hallosite b) Kaoline c) Smactites d) Illites and e) attapulgite (Modified

from Mitchell and Soga 2005)

Figure 36 Particle size range in soils Generally the particles of clay size are plate shaped (Mitchell and

Soga 2005)

a) b) c)

e) d)

29

53 VOID RATIO AND POROSITY

The void ratio (e) is the ratio of the volume of voids to the volume of solid it is

defined by the equation

Porosity (n) is the ratio of the volume of voids to the total volume of the soil it is

represented by the equation

Holubec and DrsquoAppolonia (1973) found a relation between the void ratio and

sphericity (referred in the paper as coefficient of angularity ratio of particle surface

and equivalent sphere surface) their results show that the maximum and the minimum

void ratio increases as the shpericity decreases In this study the surface was obtained

for an indirect method based on the permeability developed by Hoffman in 1959

described in the same document Rouseacute et al (2008) defined the roundness as

Wadell (1935) and he found it as an important factor controlling the minimum and

maximum void ratios Some other authors as Youd (1973) and Cho et al (2006)

conclude the same minimum and maximum void ratios increase when sphericity and

roundness decrease Another interesting result (all above authors) was the bigger

influence of the form (sphericity circularity) and roundness on the maximum void

ratio The change of the maximum void ratio is more pronounced than the change of

the minimum void ratio when the form and roundness changes (See figure 39)

Particles arrangement and interlocking are probably the factor that controls the void

ratio bridge effect permit the existence of void among the particles while interlocking

allowed the particles to form arches avoiding the possibility to rotate and stay in a

more stable configuration eg as it happens with marbles

Figures 36 37 and 38 shows proposed empirical relationships between void ratio and

shape from tables 5 and 6 (graphically the scale goes from 0 to 1 when cero mean

high angularity shpericity or circularity and one means low angularity circularity or

sphericity) Holubec and DrsquoAppolonia (1973) data was taken to obtain a power curve

and describe a tendency Santamarina and Cho (2004) show Youd equations in the

original paper Youd (1973) never presented the equation but it is easy to use the

information to draw a trend

The graphics presented in this document (figures 36 37 and 38) must be used with

certain reserves due the fact that the original data was modified in order to fit all

information in one graphic what the figures shows is just the general trend of the

behaviourrsquos material regarding on the shape If more accurate description and

information is required the author recommends consulting the reference data In the

same way equations from Holubec and DrsquoApollonia (1973) and Youd (1973) were not

presented by the authors but the use of the information was taken in order to build up

those equations on tables 6 and 7

S

V

V

V

= e

V

V

=nV

(45)

(46)

30

Table 6 Minimum void ratio equations regarding on the quantity (Ψ for sphericity C for circularity R

for roundness SF for Sukumaran shape factor and AF for Sukumaran angularity factor)

EQUATION NUMBER REFERENCE

Figure 34 (left)

4340

minΨ45490e =

47

Holubec amp DrsquoAppolonia 1973 (Ψ

was obtained using equation 2)

SF06340

mine021903180e +=

48

Sukumaran amp Ashmawy 2001 (SF

obtained using equation 21)

C05101emin

= 49

Cho etal 2006 (C obtained using

figure 12)

Figure 34 (right)

1

minR08203590e +=

50

Youd 1973 (R obtained from figure

11 and table 3)

R34080emin

= 51

Cho et al 2006 (R obtained using

figure 12)

1

minR05104330e +=

52

Rouseacute et al 2008 (R obtained by

equation 21)

AF02330

mine372004160e +=

53

Sukumaran amp Ashmawy 2001 (AF

obtained using equation 37)

Table 7 Maximum void ratio equations regarding on the quantity (Ψ for sphericity C for circularity R

for roundness SF for Sukumaran shape factor and AF for Sukumaran angularity factor)

EQUATION NUMBER REFERENCE

Figure 35 (left)

51520

max Ψ61120e = 54

Holubec and DrsquoAppolonia 1973 (Ψ

was obtained using equation 2)

SF1190

max e0016907180e += 55

Sukumaran amp Ashmawy 2001 (SF

obtained using equation 21)

C86061emax = 56

Cho etal 2006 (C obtained using

figure 12)

Figure 35 (right)

1

max R1505540e += 57

Youd 1973 (R obtained from figure

11 and table 3)

R62031emax= 58

Cho et al 2006 (R obtained using

figure 12)

1

max R107106150e += 59

Rouseacute et al 2008 (R obtained by

equation 21)

AF0530

max e12506090e += 60

Sukumaran amp Ashmawy 2001 (AF

obtained using equation 37)

Comparing figures 37 and 38 (minimum and maximum void ratio) it can be seen on

the right scheme of both figures 37 and 38 (when the factor is roundnessangularity)

that all the empirical relations has a common initial point close to 1 (it means that

particles are well rounded) while this common agreement disappear when the

roundness factor decreases (when the particles become more angular) Same figures

(37 and 38) on the left graphs (when the factor is sphericitycircularityshape) do not

present the same behaviour in fact there is more disperse initial point close to 1(when

the particles tend to be more sphericalcircular)

31

In Figure 39 the Δe (emax-emin) has been plotted to show how the maximum void ratio

and the minimum void ratio has different rate change when the particle shape

changes Maximum void ratio increases more than minimum void ratio when the

particle shape becomes less spherical andor more angular Comparing figure 39 left

and right graphics it can be seen that right present a common initial point when the

quantity (roundnessangularity) is close to one while in the left graphic the initial

point is more disperse Both ending points in both graphics (close to zero) are

dispersed

Figures 37 38 and 39 present the same behaviour right graphics (when the factor is

roundness angularity) in each figure have an initial common point while the left

graphics do not (when the factor is sphericity circularity shape)

Figure 37 Minimum void ratio based upon the relation of shape factor proposed by the authors indicated

in the figure

Figure 38 Maximum void ratio based upon the relation of shape factor proposed by the authors indicated

in the figure

04

06

08

1

12

14

16

18

2

005

015

025

035

045

055

065

075

085

095

Factor (roundness angularity)

min

imu

m v

oid

rati

o

Youd 1973 roundness

Rouse 2008 roundness

Cho 2006 roundness

Sukumaran 2001 AF

03

04

05

06

07

08

09

1

11

12

13

05

015

025

035

045

055

065

075

085

095

Factor (sphericity circularity shape)

min

imu

m v

oid

rati

oHolubec 1973 sphericity

Cho 2006 circularity

Sukumara 2001 SF

05

07

09

11

13

15

17

19

21

00

150

250

350

450

550

650

750

850

95

Factor (sphericity circularity shape)

Maxim

um

vo

id r

ati

o

Holubec 1973 sphericity

Cho 2006 circularity

Sukumara 2001 SF

05

1

15

2

25

3

35

005

015

025

035

045

055

065

075

085

095

Factor (roundness angularity)

Maxim

um

vo

id r

ati

o

Youd 1973 roundness

Rouse 2008 roundness

Cho 2006 roundness

Sukumaran 2001 AF

32

54 ANGLE OF REPOSE

The angle of repose of a granular material is the steepest angle of descent or dip of the

slope relative to the horizontal plane when material on the slope face is on the verge

of sliding as show in figure 40

According to Qazi (1975) there are five types of forces which may act between the

particles in soils

1 Force of friction between the particles

2 Force due to presence of absorbed gas andor moisture of particle

3 Mechanical forces caused by interlocking of particles of irregular shape

4 Electrostatic forces arising from friction between the particles themselves and

the surface with which they come in contact

5 Cohesion forces operating between neighbouring particles

Rouseacute et al (2008) found a decrease of angle of repose with increase roundness

based upon ASTM C1444 test (Standard Test Method for Measuring the Angle of

Repose of Free-Flowing Mold Powders) The method consist in pouring sand on a

surface cover by paper trough a funnel of specific dimensions (the nozzle diameter

depend on the sandrsquos particle size) from an altitude of 15 inches (381 mm) The sand

is release from the funnel until the peak of the cone formed by the sand stops the flow

The repose angle is obtained with the equation

H represent the 15 inches D and d represent the diameter of the cone formed by the

sand and the diameter of the funnel respectively

Figure 39 Maximum minus minimum void ratio based upon the relation of shape factor proposed by the

authors indicated in the figure

0

01

02

03

04

05

06

07

08

09

1

005

015

025

035

045

055

065

075

085

095

Factor (sphericity circularity shape)

Maxim

um

- M

inim

um

Vo

id r

ati

oHolubec 1973 sphericity

Cho 2006 circularity

Sukumara 2001 SF

0

02

04

06

08

1

12

14

16

18

005

015

025

035

045

055

065

075

085

095

Factor (roundness angularity)

Maxim

um

- M

inim

um

Vo

id r

ati

o

Youd 1973 roundness

Rouse 2008 roundness

Cho 2006 roundness

Sukumaran 2001 AF

dD

H2

tan=φ1

rep(61)

33

Rouseacute (2008) shows an empirical relation to obtain the angle of repose based on the

roundness of the particles

55 SHEAR STRENGTH

The MohrndashCoulomb failure criterion represents the linear envelope that is obtained

from a plot of the shear strength of a material versus the applied normal stress This

relation is expressed as

where τ is the shear strength σn is the normal stress co is the intercept of the failure

envelope with the τ axis and is the slope of the failure envelope The quantity c is

often called the cohesion and the angle is called the angle of internal friction

Studies show that the internal friction angle (under drained triaxial tests) increases

more rapidly on those materials having higher angularity increasing the relative

density The internal friction angle is a function of the relative density and the particle

shape (Holubec and DrsquoAppolonia 1973)

Chan and Page (1997) found in a study made with dry copper (using different shapes

and sizes ranging from 180 to 106 μm) using a direct shear test (ring share test) that

the internal friction angle increases as the angularity increases

Shinohara et al (2000) did some experiments with steel powder different shapes

using a triaxial cell in the test Shinohara never used the roundness or angularity on

the work but apply the shape factor (relation long axisshort axis) and the results were

that as this relation deviate from factor 1 the internal friction angle increases

The following empirical relations were found in the literature showing the behaviour

of the friction angle (obtained under different conditions)

)tan( noc

Figure 40 Representation of the angle of repose

(63)

(62)

34

Cho et al (2006)

(64)

(R is obtain by comparing the Krumbein chart figure 13)

Rouseacute (2008)

(65)

(66)

(R is defined using Wadell equation 22)

In figure 41 the suggested empirical relations above and lines constructed using

author data from Holubec and DrsquoAppolonia (1973) and Sukumara and Ashmawy

(2001) are plotted together to display the general trend on the particle shape and

friction angle relation Sukumaran reports two lines one based on the shape factor

(SF) and the second referring the angularity factor (AF) Sukumaran performed the

tests at constant volume

The scale used for Holubec and DrsquoAppolonia (1973) have lower and upper limits of 1

and 2 respectively (angularity form) and a scale change was applied to be able to

presented in the actual figure 41 As in the previous section (52) the author

recommend to use the original data from the references due that the figure just follows

the general trend of the behaviourrsquos particle regarding on the shape

Figure 41 The changes on the internal friction angle shows a general increase when the particle roundness

becomes angular or in the case of Sakamuran less spheric (Shape factor SF)

35

Barton and Kjaernsli (1981) suggested a model (equation 67) to predict the peak

friction angle (φrsquo) based upon numerous trixial and direct shear data tests

where

Se equivalent strength of particle

Re equivalent roughness of particle

φb basic friction angle (obtained from basic tilting test)

σn normal load

The information required for the model is (1) the uniaxial compressive strength of the

rock (2) the d50 particle size (mesh size where 50 of the particles pass through)

required to define Se (figure 42) (3) the degree of particle roundness and (4) the

porosity following compaction All data can be estimated by simple index tests

Barton and Kjaernsli (1981) suggest that particle size and sample scale has an effect

on the friction angle and includes them to obtain the equivalent strength (Se) figure 42

shows the method to obtain this value Compressive strength (σc) was chosen to be the

factor affecting the scale because micro fractures influence this property while

samples are bigger more micro fractures contain and its compressive strength reduces

The equivalent roughness is obtain using figure 43 where is required to know the

porosity (n) and the origin of the particles (a small chart is provided in the same figure

to compare the particles profile)

b

n

ee

SLogR

Figure 42 Method of estimating Equivalent Strength (Se) of rockfill based on uniaxial compressive strength

(σc ) and d50 particle size (Barton amp Kjaernsli 1981)

(67)

36

56 SEDIMENTATION PROPERTIES

A particle released in a less dense Newtonian fluid initially accelerate trough the fluid

due to the gravity Resistances to deformation of the fluid transmitted to the particle

surface drag generate forces that act to resist the particle motion The force due to the

weight (Fw) can be written as

Where ρp ρ are density of the particle and fluid (water) respectively g is the

gravitational force and Vp is the volume of the particle

And the resistance force (FD) is

Where CD is the dimensionless drag coefficient W is the weight of the particle and A

is the cross section area

Particlersquos shape has been assumed to be spherical when equations are applied on the

settling velocity Correlation deviates when particle shape departs from spherical form

Figure 43 Method of estimating Equivalent Roughness (Roe) based on porosity of rockfill

origin material degree of roundedness and smoothness of particle (Barton amp Kjaernsli 1981)

PPW ρ)gV(ρF

A2

WρCF

2

DD

(68)

(69)

37

(Dietrich 1982) and it is known that natural particles depart from spherical form

thus it is evident that this departure would have consequences

The below equation is proposed to account the shape (in this case the Corey shape

factor equation 8) in the settling velocity (Jimenez and Madsen 2003)

Jimenez and Madsen (2003) Dietrich (1982) Briggs and McCulloch (1962) and

others were working in the hydraulic shape of particles to solve problems as sediment

transport It is obvious that the equation presented and the researcherrsquos investigation

works under certain conditions (eg grain size between 0063-1 mm)

Dietrich (1982) suggests an empirical relation that accounts settling velocity size

density shape and roundness of a particle

R1 R2 and R3 are fitted equations for size and density shape and roundness

respectively

57 HYDRAULIC CONDUCTIVITY PERMEABILITY

Darcyrsquos Law Permeability is one component of Darcyrsquos law Darcys law is a simple

proportional relationship between the instantaneous discharge rate through a porous

medium the viscosity of the fluid and the pressure drop

The total velocity Ve is equal to the product of the permeability of the medium

(porous media) k the pressure drop ∆p all divided by the viscosity μ (Muskat

1937)

Darcys law is only valid for slow viscous flow most groundwater flow cases fall in

this category Typically Darcyrsquos law is valid at any flow with laminar flow (see figure

44)

Reynoldrsquos number (Laminar and turbulent Flow) Typically any laminar flow is

considered to have a Reynoldrsquos number less than one and it would be valid to apply

Darcys law Experimental tests have shown that flow regimes with Reynolds numbers

1

ND

S

S

ZY

gd1s

WW

NDN

gd)1s(4

dS

2R1R

3 10RW

pk

Ve

(70)

(71)

(72)

(73)

38

up to 10 may still be Darcian (laminar flow) as in the case of groundwater flow The

Reynolds number (a dimensionless parameter) for porous media flow is typically

expressed as

where ρ is the density of water (units of mass per volume) υ is the specific discharge

(with units of length per time) d is a representative average grain diameter for the

porous media (often taken as the 30 passing size from a grain size analysis using

sieves - with units of length) and μ is the viscosity of the fluid (Muskat 1937)

Shape effects Permeability as Head and Epps (2011) suggested is affected by the

shape and texture of soil grains Elongated or irregular particles create flow paths

which are more tortuous than those spherical particles Particles with a rough surface

texture provide more frictional resistance to flow Both effects tend to reduce the

water flow through the soil

Kozeny-Carman empirical relation accounts for the dependency of permeability on

void ratio in uniformly graded sands serious discrepancies are found when it is

applied to clays due the lack of uniform pores (Mitchell and Soga 2005)

There are various formulations of the Kozeny-Carman equation one published by

Head and Epps (2011) takes the void ratio e the specific surface area Ss and an

angularity factor F into account of permeability k

The angularity factor F considers the shape of the particles and ranges from 11 for

rounded grains 125 for sub rounded to 14 for angular particles The specific surface

Ss is defined as

d1 and d2 represent the maximum and minimum size particle in mm

Kane amp Sternheim (1988) suggest that the inclusion of the shape factor (F) has

probably the background on the Reynolds number due this factor is dependent

significantly on the shape of the obstacles and Reynolds number determines the

presence of laminar or turbulent flow Figure 44 show how the laminar flow has low

energy dissipation while turbulent flow (eg the roughness and path tortuosity) has

high energy dissipation

e1

e

FSs

2k

3

2

dRe

21

6

ddSs

(74)

(75)

(76)

39

According to Nearing and Parker (1994) the amount of soil detached during laminar

and turbulent flow is dependent on each soil and also greater on turbulent flow due the

greater shear strength generated during this kind of flow this could suggest the

greater erosion when turbulent flow is present

58 LIQUEFACTION

Soil liquefaction is a phenomenon in which soil loses much of its strength or stiffness

for a generally short time by earthquake shaking or other rapid loading Static and

dynamic liquefactions occur been the second one the most regular known

Liquefaction often occurs in saturated soils that is soils in which the space between

individual particles is completely filled with water This water exerts a pressure on the

soil particles that influences how tightly the particles themselves are pressed together

Shaking or other rapid loading can cause the water pressure to increase to the point

where the soil particles can readily move with respect to each other (Jefferies and

Been 2000)

Jefferies and Been (2000) state that it is clear that minor variation in intrinsic

properties of sand have major influence on the critical state These might be variations

on grain shape mineralogy grain size distribution surface roughness of grains etc

Yoginder et al (1985) found that substantial decrease on liquefaction resistance

occur with increase in confining pressure for rounded and angular sands (1600 kPa)

also rounded sands show an rapidly build up of resistance against liquefaction with

increasing density while angular tailing sand in contrast show such rapid increase

only at low confining pressures At low confining pressure angular material is more

resistant to liquefaction Probably the breakage of the corners on the angular particles

in tailings is ruling the lost in resistance at high confining pressures (sieve analysis

Figure 44 The figure show the extremes of flow behaviour First turbulent conditions where the flow is

essentially random and unpredictable and second the well defined Laminar flow conditions

40

after test identify the breakage of angular particles while on rounded particles the

sieve analysis was practically the same)

59 GROUNDWATER AND SEEPAGE MODELLING

In groundwater flow the particlersquos shape affects the soilrsquos pore size distribution

hence the flow characteristics (Sperry and Peirce 1995) Tortuosity and permeability

(also see section 57) are two significant macroscopic parameters of granular medium

that affect the passing flow (Hayati et al 2012) Current models incorporating the

effects of particle shape have failed to consider irregular particles such as those that

would prevail in a natural porous medium (Sperry and Peirce 1995)

Hayati et al (2012) suggested based on his results that tortuosity effect converge

when the porosity increases indicating that the shape have dominance at low and mid

porosity ranges

Sperry and Peirce (1995) research conclusions suggest that particle size and porosity

are more important predictors for hydraulic conductivity explaining the 69 of the

variability but particle shape appears to be the next most important This however

apparently comprises particles larger than 295-351 μm Differences for particle size

295-351 μm and smaller are not detectable Another interesting result in the research

was the interaction effect of the particle size and particle shape It suggests a different

packing configuration for particles of the same shape but different size (scale

dependent)

6 DISCUSSION

61 TERMS QUANTITIES AND DEFINITIONS

In order to describe the particle shape in detail there are a number of terms quantities

and definitions (qualitative and quantitative) used in the literature (eg Wadell 1932

1934 Krumbein 1941 Sneed amp Folk 1958) All mathematical definitions

(quantitatives) are models used to simplify the complexity of shape description Some

authors (Mitchell amp Soga 2005 Arasan et al 2010) are using three sub-quantities

one and each describing the shape but at different scales The terms are

morphologyform roundness and surface texture (figure 1) The three sub-quantities

are probably the best way to classify and describe a particle because not a single

definition can interpret the whole morphology Common language is needed when

descriptors are explained and these three scales represent an option It is evident in

the reviewed literature that many of the shape descriptors are presented with the same

name but also that there is not a clear meaning on what this descriptor defines eg

when there is no upper limit in the roundness does it means that the angularity never

ends Could they be more and more angular Probably they could be on theory but

not in reality

41

62 PROPERTIES

Trough various articlersquos review done in the present investigation it is recognized that

the particlersquos shape has an effect on the material properties among these are

1 Porosity (Tickell 1938 Fraser 1935 Kolbuszewski 1948) and void ratio

(Cho et al 2006 Shergold 1953 Rouseacute et al 2008 Santamarina and Cho

2004)

2 Permeability (Witt and Brauns 1983)

3 Internal friction angle (Shinohara et al 2000 Chan and Page 1997

Cheshomi et al 2009)

4 Density (Youd 1973 Holubec and DrsquoAppolonia 1973)

5 Drag coefficient Hydraulics (Briggs and McCulloch 1962)

In Table 5 is a short resume of the properties and shape effect found in peer review

articles trough different journals Most of the reviewed articles based its research on

uniform graded sands

Table 8 Compilation of properties influenced by particle shape

Repose

angle

Friction

angle

Porosity and

Void ratio Density Permeability

Settling velocity

Drag coefficient Deformation

Sphericity (3D)shape factor

NI x x x x x x

Circularity (2D)

NI x x x x NI NI

Roundness x x x x NI NI x

x influence

NI no information available

Shape of particles has an effect on the arrangement producing bridging or avoiding

the rotation of the particles and the resulting geotechnical property is affected eg

including flaky particles can result in a higher void ratio due the bridging effect

(Santamarina and Cho 2004) and depending on the loads even the size distribution is

changed due the breakage (Yoginder et al 1985) in similar way angular particles

produce higher void ratio due the avoided possibility of the particles to rotate and

compact

The influence of the chosen shape descriptor appears in this review to have minor

influence on the soil properties in the reviewed studies except on the void ratio and

the friction angle Influence of particle shape in some cases is hider by other factors

(eg size distribution) also the particle shape probably does not have influence when

particle size is in the clay order (eg hydraulic conductivity) the reason could be due

to forces as electrostatic or capillarity become more important at this level

Among the shape descriptors some are chosen more often in literature (eg aspect

ratio) there is no apparent scientific basis to use it (probably due to the simplicity of

the measurement it becomes one of the most use) but there are still some other

descriptors that may or may not show better correlation with the soil properties

Instead empirical relations had been developed regarding roundness or shape to

describe the soil behaviour it is clear that the mechanism behind the results is still not

completely understood

42

There is necessity to define the best(s) shape descriptor(s) to be used for particular

geotechnical properties

63 IMAGE ANALYSIS

Many image analysis techniques had been used to describe the particle shape eg

Fourier analysis fractal dimension tomography etc (Hyslip and Vallejo 1997) but

there is not agreement on the usage or conclusion to ensure the best particle descriptor

for geotechnical applications

There are several shape descriptors and also various techniques to capture the

particles profile (3-dimensions 3-dimension orthogonal and 2-dimensions) Each

technique presents advantages and disadvantages 3-dimensions is probably the

technique that provide more information about the particle shape but the precision

also lies in the resolution the equipment required to perform such capture could be

more or less sophisticated (scanning particles laying down in one position and later

move to complete the scanning or just falling down particles to scan it in one step)

3-dimensions orthogonal this technique use less sophisticated equipment (compare

with the previous technique) but its use is limited to particles over 1cm also

information between the orthogonal pictures is not capture 2-dimensions require non

sophisticated equipment but at the same time the shape information diminish compare

with the previous due the fact that it is possible to determine only the outline as the

particle measurements are performed in 2-dimensions it is presumed that they will lie

with its shortest axis perpendicular to the laying surface when they are flat but when

the particle tends to have more or less similar axis the laying could be random

Advantages on the use of image analysis are clear there is not subjectivity because it

is possible to obtain same result over the same images Electronic files do not loose

resolution and it is important when collaboration among distant work places is done

files can be send with the entire confidence and knowing that file properties has not

been changed Technology evolutions allowed to work with more information and it

also applies to the image processing area were the time consumed has been shortened

(more images processed in less time)

One important aspect in image analysis is the used resolution in the analysis due the

fact that there are measurements dependent and independent on resolution Thus

those dependent measurements should be avoided due the error included when they

are applied or avoid low resolution to increase the reliability Among these

parameters length is the principal parameter that is influences by resolution (eg

perimeter diameter axis etc) Resolution also has another aspect with two faces

quality versus capacity more resolution (quality) means more storage space a

minimum resolution to obtain reasonable and reliable data must be known but it

depend on each particular application

43

64 APPLICATIONS

Quantify changes in particles in the authorrsquos thought is one of the future applications

due the non-invasive methods of taking photographs in the surface of the damrsquos slope

rail road ballast or roads Sampling of the material and comparing with previous

results could show volume (3D analysis) or area (2D analysis) loss of the particles as

well as the form roundness and roughness This is important when it has been

suggested that a soil or rock embankment decrees their stability properties (eg

internal friction angle) with the loss of sphericity roundness or roughness

Seepage stock piling groundwater etc should try to include the particle shape while

modelling seepage requires grading material to not allow particles move due the

water pressure but in angular materials as it is known the void ratio is great than the

rounded soil it means the space and the possibilities for the small particles to move

are greater stock piling could be modelled incorporating the particle shape to

determine the binrsquos capacity when particle shape changes (void ratio changes when

particle shape changes) Modelling requires all information available and the

understanding of the principles that apply

Industry is actually using the particle shape to understand the soil behaviour and

transform processes into practical and economic image analysis has been included in

the quality control to determine particle shape and size because the advantages it

brings eg the acquisition of the sieving curve for pellets using digital images taken

from conveyor this allows to have the information in a short period of time with a

similar result at least enough from the practical point of view as the traditional

sieving

7 CONCLUSIONS

The conclusions of this literature review are

It has been shown that particle shape has influence on the soil behaviour

despite of partial knowledge of the mechanism behind Understanding of the

particle shape and its influence needs to be accomplished

A common language needs to be built up to standardize the meaning on

geotechnical field that involve the particle shape General relationships

between shape and properties should be developed

Based on this review it is not clear which is the best descriptor to use in

geotechnical engineering affecting he related shape to properties Instead of a

couple of standards there is no shape descriptor in geotechnical field fully

accepted

Image analysis tool is objective make the results repeatable obtain fast results

and work with more amount of information

44

Resolution needs to be taken in consideration when image analysis is been

carried out because the effects could be considerable Resolution must be set

according to the necessities Parameters as perimeter can be affected by

resolution

There are examples where particle shape has been incorporated in industries

related to geotechnical engineering eg in the ballast and asphalt industry for

quality control

8 FURTHER WORK

Three main issues have been identified in this review that will be further investigated

the limits of shape descriptors influence of grading and choice of descriptor for

relation to geotechnical properties

Shape descriptors have low and high limits frequently the limits are not the same and

the ability to describe the particlersquos shape is relative The sensitivity of each descriptor

should be compare to apply the most suitable descriptor in each situation

Sieving curve determine the particle size in a granular soil particle shape could differ

in each sieve size There is the necessity to describe the particle shape on each sieve

portion (due to practical issues) and included in the sieve curve Obtain an average

shape in determined sieve size is complicated (due to the possible presence of several

shapes) and to obtain the particle shape on the overall particlersquos size is challenging

how the particle shape should be included

Since several descriptors have been used to determine the shape of the particles and

the relation with the soil properties it is convenient to determine the descriptorrsquos

correlation with the soil properties

9 ACKNOWLEDGMENT

I would like to thanks to Lulearing University of Technology (LTU) the time I had spent

in its facilities and the kind environment it offers and University of Sonora

(UNISON) that has been providing me the financial support and the time to conclude

this journey

10 REFERENCES

Andersson T (2010) Estimating particle size distributions based on machine vision

Doctoral Thesis Departament of Computer Science and Electrical Engineering Lulearing

University of Technology ISSN 1402-1544 ISBN 978-91-7439-186-2

45

Arasan Seracettin Hasiloglu A Samet Akbulut Suat (2010) Shape particle of

natural and crished aggregate using image analysis International Journal of Civil and

Structural Engineering Vol 1 No 2 pp 221-233 ISSN 0970-4399

Aschenbrenner BC (1956) A new method of expressing particle sphericity Journal

of Sedimentary Petrology Vol 26 No 1 pp 15-31

Axelsson K (1998) Introduktion till jordmekaniken jaumlmte jordmateriallaumlran Skrift

984 Lulearing Avdelningen foumlr Geoteknologi Lulearing Tekniska Universitet (In Swedish)

Barton Nick amp Kjaernsli Bjorn (1981) Shear strength of rockfill Journal of the

Geotechnical Engineering Division Proceedings of the American Society of Civil

Engineers (ASCE) Vol 107 No GT7

Barrett P J (1980) The shape of rock particles a critical review Sedimentology

Vol 27 pp 291-303

Blott S J and Pye K (2008) Particle shape a review and new methods of

characterization and classification Sedimentology Vol 55 pp 31-63

Bowman E T Soga K and Drummond W (2001) Particle shape characterization

using Fourier descriptor analysis Geotechnique Vol 51 No 6 pp 545-554

Briggs L I McCulloch D S (1962) Hydraulic shape of sand particles Journal of

Sedimentary Petrology Vol 32 pp 645-656

Chan Leonard C Y and Page Neil W (1997) Particle fractal and load effects on

internal friction in powders Powder Technology Vol 90 pp 259-266

Cheshomi A Fakher A Jones C J F P (2009) A correlation between friction

angle and particle shape metrics in quaternary coarse alluvia Quarterly Journal of

Engineering Geology and Hydrogeology Vol 42 pp 145-155

Cho G Dodds J and Santamarina J C (2006) Particle shape effects on packing

density stiffness and strength Natural and crushed sands Journal of Geotechnical

and Geoenvironmental Engineering May 2006 pp 591-602

Dietrich William E (1982) Settling velocity of natural particles Water Resources

Research Vol 18 No 6 pp 1615-1626

Dobkins J E and Folk R L (1970) Shape development on Tahiti-nui Journal of

Sedimentary Petrology Vol 40 No 2 pp 1167-1203

Folk R L (1955) Student operator error in determining of roundness sphericity and

grain size Journal of Sedimentary Petrology Vol 25 pp 297-301

Fernlund J M R (1998) The effect of particle form on sieve analysis A test by

image analysis Engineering Geology Vol 50 No 1-2 pp 111-124

46

Fernlund J M R (2005) Image analysis method for determining 3-D shape of

coarse aggregate Cement and Concrete Research Vol 35 Issue 8 pp 1629-1637

Fernlund J M R Zimmerman Robert and Kragic Danica (2007) Influence of

volumemass on grain-size curves and conversion of image-analysis size to sieve size

Engineering Geology Vol 90 No 3-4 pp 124-137

Fraser H J (1935) Experimental study of the porosity and permeability of clastic

sediments The Journal of Geology Vol 43 pp 910-1010 ISSN 0022-1376

Hayati Ali Nemati Ahmadi Mohammad Mehdi and Mohammadi Soheil (2012)

American Physical Society Physical review E 85 036310 DOI

101103PhysRevE85036310

Hawkins A E (1993) The Shape of Powder-Particle Outlines Wiley New York

Head K H and Epps R J (2011) Manual of soil Laboratory testing Volum II

Permeability shear strength and compressibility test 3rd

edition Whittles Publishing

Scotland UK 3rd

edition

Holubec I and DrsquoAppolonia E (1973) Effect of particle shape on the engineering

properties of granular soils ASTM STP 523 pp 304-318

Hyslip James P Vallejo Luis E (1997) Fractal analysis of the roughness and size

distribution of granular materials Engineering Geology Vol 48 pp 231-244

Janoo Vincent C (1998) Quantification of shape angularity and surface texture of

base course materials US Army Corps of Engineers Cold Region Research and

Engineering Laboratory Special report 98-1

Jefferies Mike and Been Ken (2000) Soil liquefaction A critical state approach

Taylor amp Francis Group London and New York

Jimenez Jose A Madsen Ole S (2003) A simple formula to estimate settling

velocity of natural sediments Journal of Waterway Port Coastal and Ocean

Engineering Vol 129 No 2 pp 70-78

Johansson Jens and Vall Jakob (2011) Jordmaterials kornform Inverkan paring

Geotekniska Egenskaper Beskrivande storheter bestaumlmningsmetoder

Examensarbete Avdelningen foumlr Geoteknologi Institutionen foumlr Samhaumlllsbyggnad

och naturresurser Lulearing Tekniska Universitet Lulearing (In Swedish)

Kane Joseph W and Sternheim Morton M (1988) Physics John Wiley amp Sons Inc

Third edition

Kolbuszewski J (1948) An experimental study of the maximum and minimum

porosities of sands Proceedings of the Second International Conference on Soil

Mechanics and Foundation Engineering Rotterdam June 21 to 30 Sub-section IIb

pp 158-165

47

Krumbein W C and Pettijohn FJ (1938) Manual of sedimentary petrography

Appleton-Century Crofts Inc New York

Krumbein W C (1941) Measurement and geological significance of shape and

roundness of sedimentary particles Journal of Sedimentary Petrology Vol 11 No 2

pp 64-72

Krumbein W C and Sloss L L (1963) Stratigraphy and Sedimentation 2nd

ed

WH Freeman San Francisco

Kuo Chun-Yi and Freeman Reed B (1998a) Image analysis evaluation of

aggregates for asphalt concrete mixtures Transportation Research Record Vol 1615

pp 65-71

Kuo Chun-Yi Rollings Raymond and Lynch Larry N (1998b) Morphological

study of coarse aggregates using image analysis Journal of Materials in Civil

Engineering Vol 10 No 3 pp 135-142

Lanaro F Tolppanen P (2002) 3D characterization of coarse aggregates

Engineering Geology Vol 65 pp 17-30

Lees G (1964a) A new method for determining the angularity of particles

Sedimentology Vol 3 pp 2-21

Lees G (1964b) The measurement of particle shape and its influence in engineering

materials British Granite Whinstone Federation Vol 4 No 2 pp 17-38

Matsushima Takashi Saomoto Hidetaka Matsumoto Masaaki Toda Kengo

Yamada Yasuo (2003) Discrete element simulation of an assembly of irregular-

shaped grains Quantitative comparison with experiments 16th ASCE Engineering

Mechanics Conference University of Washington Seattle July 16-18

Mitchell James K and Soga Kenichi (2005) Fundamentals of soil behaviour Third

edition WILEY

Mora C F Kwan A K H Chan H C (1998) Particle size distribution analysis of

coarse aggregate using digital image processing Cement and Concrete Research Vol

28 pp 921-932

Mora C F and Kwan A K H (2000) Sphericity shape factor and convexity

measurement of coarse aggregate for concrete using digital image processing Cement

and Concrete Research Vol 30 No 3 pp 351-358

Muskat Morris (1937) The Flow of fluids through porous media Journal of Applied

Physics Vol 8 pp 274

Nearing M A and Parker S C (1994) Detachment of soil by flowing water under

turbulent and laminar conditions Soil Science Society of American Journal Vol 58

No 6 pp 1612-1614

48

Pan Tongyan Tutumluer Erol Carpenter Samuel H (2006) Effect of coarse

aggregate morphology on permanent deformation behavior of hot mix asphalt Journal

of Transportation Engineering Vol 132 No 7 pp 580-589

Pellegrino A (1965) Geotechnical properties of coarse-grained soils Proceedings

International Conference of Soil Mechanics and Foundation Engineering Vol 1 pp

97-91

Pentland A (1927) A method of measuring the angularity of sands MAG MN AL

Acta Eng Dom Transaction of the Royal Society of Canada Vol 21 Ser3xciii

Persson Anna-Lena (1998) Image analysis of shape and size of fine aggregates

Engineering Geology Vol 50 pp 177-186

Powers M C (1953) A new roundness scale for sedimentary particles Journal of

Sedimentary Petrology Vol 23 No 2 pp 117-119

Pye W and Pye M (1943) Sphericity determination of pebbles and grains Journal

of Sedimentary Petrology Vol 13 No 1 pp 28-34

Qazi M A (1975) Flow properties of granular masses A review on the angle of

repose The Arabian Journal for Science and Engineering Vol 1 No 2

Quiroga Pedro Nel and Fowle David W (2003) The effects of aggregate

characteristics on the performance of portland cement concrete Report ICAR 104-1F

Project number 104 International Center for Aggregates Research University of

Texas

Riley N A (1941) Projection sphericity Journal of Sedimentary Petrology Vol 11

No 2 pp 94-97

Rouseacute P C Fennin R J and Shuttle D A (2008) Influence of roundness on the

void ratio and strength of uniform sand Geotechnique Vol 58 No 3 227-231

Santamarina J C and Cho G C (2004) Soil behaviour The role of particle shape

Proceedings Skempton Conf London

Schofield and Wroth (1968) Critical state soil mechanics McGraw Hill

Shaumlfer Michael (2002) Digital optics Some remarks on the accuracy of particle

image analysis Particle amp Particle Systems Characterization Vol 19 No 3 pp 158-

168

Shergold F A (1953) The percentage of voids in compacted gravel as a measure of

its angularity Magazine of Concrete Research Vol 5 No 13 pp 3-10

Shinohara Kunio Oida Mikihiro Golman Boris (2000) Effect of particle shape on

angle of internal friction by triaxial compression test Powder Technology Vol 107

pp131-136

49

Skredcommisionen (1995) Ingenjoumlrsvetenskapsakademinen rapport 395 Linkoumlping

1995

Sneed E D and Folk R L (1958) Pebbles in the Colorado river Texas A study in

particle morphogenesis Journal of Geology Vol 66 pp 114-150

Sperry James M and Peirce J Jeffrey (1995) A model for estimating the hydraulic

conductivity of granular material based on grain shape grain size and porosity

Ground Water Vol 33 No 6 pp 892-898

Sukumaran B and Ashmawy A K (2001) Quantitative characterisation of the

geometry of discrete particles Geotechnique Vol 51 No 7 pp 619-627

Szaacutedeczy-Kardoss E Von (1933) Die bistimmung der abrollungsgrades Geologie

und palaumlontologie Vol 34B pp 389-401 (in German)

Teller J T (1976) Equantcy versus sphericity Sedimentology Vol 23 pp 427-428

Tickell F G (1938) Effect of the angularity of grain on porosity and permeability

bulletin of the American Association of Petroleum Geologist Vol 22 pp 1272-1274

Tutumluer E Huang H Hashash Y Ghaboussi J (2006) Aggregate shape effects

on ballast tamping and railroad track lateral stability AREMA 2006 Annual

Conference Louisville KY

Wadell H (1932) ldquoVolume Shape and roundness of rock particlesrdquo Journal of

Geology Vol 40 pp 443-451

Wadell H (1933) Sphericity and roundness of rock Particles Journal of Geology

Vol 41 No 3 pp 310ndash331

Wadell H (1934) Shape determination of large sedimental rock fragments

The Pan-American Geologist Vol 61 pp 187-220

Wadell H (1935) ldquoVolume shape and roundness of quartz particlesrdquo Journal of

Geology Vol 43 pp 250-279

Wentworth W C (1922a) The shape of beach pebbles Washington US Geological

Survey Bulletin Vol 131C pp 75-83

Wentworth W C (1922b) A method of measuring and plotting the shape of pebbles

Washington US Geological Survey Bulletin Vol 730C pp 91-114

Wentworth W C (1933) The shape of rock particle A discussion Journal of

Geology Vol 41 pp 306-309

Witt K J Brauns J (1983) Permeability-Anisotropy due to particle shape Journal

of Geotechnical Engineering Vol 109 No 9 pp 1181-1187

4

3D and 2D image analysis present challenges itself 3D analysis requires a

sophisticated equipment to scan the particle surface and create the 3D model or the

use of orthogonal images and combine them to represent the 3 dimensions The

orthogonal method could present new challenges as the minimum particle size or the

placing in orthogonal way of the particles (Fernlund 2005) 2D image analysis is easy

to perform due the non-sophisticated equipment required to take pictures (eg regular

camera or the use of microscope for smaller particles) In 2D image analysis the

particle is assumed to lay over its more stable axis (eg longest and intermediate axis

lie more or less parallel to the surface while the shortest axis is perpendicular) or

random some authors publish their own preferences about this issue (Wadell 1935

Riley 1941 Hawkins 1993)

32 SCALE DEPENDENCE

In order to describe the particle shape in detail there are a number of terms quantities

and definitions used in the literature Some authors (Mitchell amp Soga 2005 Arasan et

al 2010) are using three sub-quantities one and each describing the shape but at

different scales The terms are morphologyform roundness and surface texture In

figure 1 is shown how the scale terms are defined

At large scale the particlersquos diameters in different directions are considered At this

scale describing terms as spherical platy elongated etc are used An often seen

quantity for shape description at large scale is sphericity (antonym elongation)

Graphically the considered type of shape is marked with the dashed line in Figure 1

At intermediate scale it is focused on description of the presence of irregularities

Depending on at what scale an analysis is done corners and edges of different sizes

are identified By doing analysis inside circles defined along the particlersquos boundary

deviations are found and valuated The mentioned circles are shown in Figure 1 A

generally accepted quantity for this scale is roundness (antonym angularity)

Regarding the smallest scale terms like rough or smooth are used The descriptor is

considering the same kind of analysis as the one described above but is applied

Figure 1 Shape describing sub quantities (Mitchell amp Soga 2005)

5

within smaller circles ie at a smaller scale Surface texture is often used to name the

actual quantity The sub-quantities and antonyms are summarized in table 1

Table 1 Sub-quantities describing the particlersquos morphology and its antonym

Scale Quantity Antonym

Large scale Sphericity Elongation

Intermediate scale Roundness Angularity

Small scale Roughness Smoothness

33 FORM (3D)

Wentworth in 1922 (Blott and Pye 2008) was probably one of the first authors on

measure the particle dimensions this consisted on the obtaining of the length of the

tree axes perpendicular among each other (see figure 2) on the tree dimensions (where

agebgec) to obtain the sphericity (equation 1)

Krumbein (1941) develop a rapid method for shape measurement to determine the

sphericity this is done by measuring the longest (a) medium (b) and shorter (c) axes

diameters of the particle it can be seen in figure 2 (Always perpendicular among each

other) The radios ba and cb are located in the chart developed by his own where it

can be found the Intercept sphericity as he called (See figure 3) This chart is an easy

graphical way to relate the dimensions

c2

ba

Figure 2 Measurement of the 3 axes perpendicular among each other (Krumbein 1941)

Figure 3 Detailed chart to determining Krumbein intercept sphericity (Krumbein 1941)

(1)

6

Wadell (1932) defined the sphericity as the specific surface ratio (equation 2) Figure

4 is a schematic representation of the sphere surface and particle surface both particle

and sphere of the same volume

This way to obtain the sphericity is almost impossible to achieve as Hawkins (1993)

declares due the difficulty to get the surface area on irregular solids

Wadell (1934) also defined the sphericity based upon the particle and sphere volumes

as equation 3 (see figure 5)

Wadell (1934) used a new formula simple to manage using the diameters (see figure

6 and equation 4)

Zingg (Krumbein 1941) develop a classification based on the 3 axes relation in this

way it is easy to find out the main form of the particles as a disks spherical blades

S

s

3

CIR

P

V

V

CIR

SV

D

D

Figure 4 Same volume sphere surface (s) and particle surface (S) (modified after Johansson and Vall

2011)

Figure 5 Relation between the volume of the particle and the volume of the circumscribed

sphere (Johansson and Vall 2011)

Figure 6 Figure is showing the relation between the diameter of a circumscribed sphere and the

diameter of a sphere of the same volume as the particle (Johansson and Vall 2011)

(2)

(3)

(4)

7

and rod-like this is summarized on figure 7 Zinggrsquos classification is related with

Krumbein intercept sphericity and the figure 3

In figure 8 the figures 3 and 7 are combined the relation in the two classifications can

be seen it is an easy way to understand the morphology regarding on the a b and c

dimensions

Pye and Pye (1943) in the article ldquosphericity determinations of pebbles and sand

grainsrdquo compare the Wadellrsquos sphericity developed in 1934 (based on the diameter)

with ldquoPebble sphericityrdquo based on an ellipse this last equation (number 5) appears

two years early published by Krumbein (1941) Axis measurement is done as figure 1

denotes for equations 5 trough 12 with exception of equation 8 where the original

document was not possible to obtain

32a

cb

Figure 7 Zinggrsquos classification of pebble shape based on ratios ba and cb (Krumbein 1941)

Figure 8 Classification made by Zinggrsquos and chart to determine sphericity (Krumbein and Sloss 1963)

(5)

8

Sneed amp Folk in (1958) found a relation between the tree dimensional axes called

ldquoMaximum Projection Sphericityrdquo

In a similar way Ashenbrenner (1956) showed his equation at that time named

ldquoWorking Sphericityrdquo

Form or shape factor names are used by authors like Corey (shape factor eq 8) in the

paper published on 1949 Williams (shape factor eq 9) in 1965 Janke (form factor

eq 10) in 1966 and Dobkins amp Folk (oblate-prolate index eq 11) in 1970 (Blott and

Pye 2008)

Aschenbrenner (1956) develop the shape factor by using the relation of the tree axis

but the square of the middle one

3

2

ba

c

))ab((1)bc(16))ab((cb)(11

)ab()bc( 128

22

3 2

ab

c

acb when 1ac

b acb when

b

ac-1 2

22

2

3

cba

c

222

a

c

50c-a

b-a10

2b

ac

(6)

(7)

(8)

(9)

(10)

(11)

(12)

9

Table 2 General overview over different particle shape definitions for 3D sphericity has been compiled

and arranged chronologically

Aspect Name Author Year Based on

Sphericity (3D) Flatness index Wentworth 1922a 3-axes

True Sphericity Wadell 1932 Surface

Operational sphericity Wadell 1932 Volume

Sphericity Wadell 1934 Sphere diameter

Zinggrsquos clasification Zinggrsquos1

1935 3-axes

Intercept sphericity chart Krumbein 1941 3-axes

Pebble sphericity Pye and Pye 1943 3-axes

Corey shape factor Corey2

1949 3-axes

Working sphericity Ashenbrenner 1956 3-axes

shape factor Ashenbrenner 1956 3-axes

Maximum projection sphericity Sneed amp Folk 1958 3-axes

Williams shape factor Williams2

1965 3-axes

Janke form factor Janke2

1966 3-axes

Oblate-prolate index Dobkins amp Folk 1970 3-axes 1) Krumbein and Sloss 1963 2) Blott and Pye 2008

34 FORM (2D)

The technique to measure the sphericity is based in tree dimensions it can be found in

literature some ways to measure the ldquotwo dimensions sphericityrdquo which is simply the

perimeter of the particle projection some authors named ldquoparticle outlinerdquo or

ldquocircularityrdquo

Wadell in 1935 (Hawkins 1993) adopt a conversion of his 1934 3D sphericity

formula (equation 4) to a 2D outline He defined an orientation on the particles and

they were based on the maximum cross sectional area (outline of the particle

projecting the maximum area) The equations show the relation between diameters of

a circle of same area and smallest circumscribed circle

He also used the term ldquodegree of circularityrdquo as the ratio of the perimeter of a circle of

same area and the actual particle perimeter

Tickell in 1931 (Hawkins 1993) used his empirical relation The particle orientation

proposed was a random one It is described by the ratio between the area outline and

the area of smallest circumscribed circle

C

A

D

DC

P

PC C

CA

AC

(13)

(14)

(15)

10

Some other authors has been working with the ldquocircularityrdquo concept and had develop

them own equations as Pentland (1927) relating the area outline and area of a circle

with diameter equal to longest length outline and Cox (Riley 1941) with the ratio

area and perimeter time a constant equations 16 and 17 respectively Both authors did

not define any definite orientation of the grains

Riley (1941) realize the problems that an area perimeter and some other

measurements proposed by the above authors can carry as the time consuming and

tedious work (at that time were not computer all was made by hand) and thatrsquos why

he develop this equation easy to handle called ldquoinscribed circle sphericityrdquo He used

the same particle orientation proposed by Wadell and the relation of diameters of

inscribed and circumscribed circles

Horton 1932 (Hawkins 1993) use the relation of the drainage basing perimeter and

the perimeter of a circle of the same area as drainage basin

Janoo in 1998 (Blott and Pye 2008) develop his general ratio of perimeter to area

Sukumaran and Ashmawy (2001) develop his own shape factor (SF) defined as the

deviation of the global particle outline from a circle Figure 9 can be used as a

reference to determine the items used in the equation 21

N is referred to the number of sampling intervals o radial divisions

C2A

AC

2P

A4C

C

I

D

DC

CD

D

P

PC

A

PC

2

45ordm x N

Particleα

= SF

sumN

1=ii

(16)

(17)

(18)

(19)

(20)

(21)

11

Table 3 General chronological overview of the particle shape definitions for 2D sphericity

Aspect Name Author Year Based on

Circularity (2D) roundness Pentland 1927 area

roundness Cox1

1927 area-perimeter

roundness Tickell2

1931 area

Circularity Horton2

1932 drainage basin

outline circularity Wadell 1935 Circle diameter

degree of circularity Wadell 1935 Perimeter

inscribed circle sphericity Riley 1941 Circle diameter

Circularity Krumbein and Sloss 1963 chart

Janoo 1998 area-perimeter

Shape factor Sukumaran 2001 Segmentation of particle and angles

1) Riley 1941 2) Hawkins 1993

35 ROUNDNESS OR ANGULARITY

Roundness as described in section 32 is the second order shape descriptor Sphericity

lefts beside the corners and how they are this was notice by most of the authors sited

before and they suggested many ways to describe this second order particle property

Roundness is clearly understandable using the figure 10 Particle shape or form is the

overall configuration and denotes the similarities with a sphere (3D) or a circle (2D)

Roundness is concerning about the sharpness or the smoothness of the perimeter (2D)

Surface texture (Barret 1980) is describe as the third order subject (form is the first

and roundness the second) and it is superimposed in the corners and it is also a

property of particles surfaces between corners

Figure 9 Description of the Sukumaran factors to determine the shape and angularity (Sukumaran and

Ashmawy 2001)

12

Wadell (1935) describes his methodology calling it total degree or roundness to

obtain the roundness of a particle using the average radius of the corners in relation

with the inscribed circle diameter (see figure 11) on the equation

In the same study Wadell (1935) has used the equation

This two last equation shows slightly differences on the results (Wadell 1935)

Powers (1953) also published a graphic scale to illustrate the qualitative measure

(figure 12) It is important to highlight that any comparing chart to describe particle

properties has a high degree of subjectivity Folk (1955) concludes that when charts

are used for classification the risk of getting errors is negligible for sphericity but

large for roundness

N

R

r

Rinmax

r

R

NR

inmax

Figure 10 Form (shape) Roundness and Texture graphical description (Bowman et al 2001)

Figure 11 Wadellrsquos method to estimate the roundness corners radius and inscribed circle

(Hawkins 1993)

(22)

(23)

13

Some authors as Russel amp Taylor in 1937 Pettijohn in 1957 and Powers in 1953

developed a classification based on five and six classes (Hawkins 1993) each one

with its own class limits it is important to denote that the way they measure the

roundness is the developed by Wadell (1935) This classification and class limits are

showed in the table 4

Table 4 Degrees of roundness Wadell Values (Hawkins 1993) NA = no-applicable

Grade terms Russell amp Taylor (1937) Pettijohn (1957) Powers (1953)

Class

limits (R)

Arithmetic

midpoint

Class limits

(R)

Arithmetic midpoint Class

limits (R)

Arithmetic

midpoint

Very angular

NA

NA

NA

NA

012-017

014

Angular

000-015

0075

000-015

0125

017-025

021

Subangular

015-030

0225

015-025

0200

025-035

030

Subrounded

030-050

0400

025-040

0315

035-049

041

Rounded

050-070

0600

040-060

0500

049-070

059

Well rounded

070-100

0800

060-100

0800

070-100

084

Krumbein and Sloss (1963) published a graphical chart easy to determine the

sphericity and roundness parameters using comparison See figure 13 (Cho et al

2006)

Figure 12 A Roundness qualitative scale (Powers 1953)

Figure 13 Sphericity and roundness chart (Cho et al 2006) The roundness equation that appears here in

the chart is the wadellrsquos equation number 22

14

Fischer in 1933 (Hawkins 1993) used a straightforward method to quantify roundness

using a central point in the outline and dividing the outline in angles around this point

that were subtended by the straight or non curved parts of the profile were measured

This is illustrated in figure 14

To express the angularity value Fischer used the ratio of angles standing linear parts

on the outlines and concave respectively

Figure 14 left (A) and right (B) gives a similar angularity of approximately 042

using the above equations (Hawkins 1993)

Wentworth in 1922 used the maximum projection to define the position of the particle

to obtain the outline or contour (Barret 1980) The equation reflects the relation of the

diameter of a circle fitting the sharpest corner and the longest axis plus the shortest

axis c (minimum projection)

Wentworth (Hawkins 1993) expressed the roundness as the ratio of the radius of

curvature of the most convex part and the longest axis plus short axis

Actually these last two equations are the same just expressed in different terms when

the particle is in its maximum projection

Dimensions can be seen on figure 15 L and B represents the mayor axis a and

intermediate axis b The intention is to make difference between the 2 and 3

dimensions (L and B are for 2D as a b and c are for 3D)

deg360

ANG

=R

sumPLA

PLA

CON

ANG

ANGR

2)S(L

DR

M

S

B)4(L

RR CON

Figure 14 Fischerrsquos methods of angularity computation (Hawkins 1993)

A=inscribed circle B=circumscribed circle

(24)

(25)

(26)

(27)

15

Wentworth 1919 has a second way to express the roundness called Shape index

(Barrett 1980) and it relates the sharpest corner and the diameter of a pebble trough

the sharpest corner

Wentworth (1922b) used define the roundness as the ratio of the sharpest corner and

the average radius of the pebble

Cailleux (Barrett 1980) relates the radius of the most convex part and the longest

axis

Kuenen in 1956 show his roundness index (Barrett 1980) between the sharpest corner

and the breath axis

Dobkins amp Folk (1970) used a modified Wentworth roundness with the relation of

sharpest corner and inscribed circle diameters

AVG

CON

R

RR

x

s

D

DR

L2

RR CON

B

DR s

i

s

D

DR

3AVGAVG cbaDR2

Figure 15 Description of L and B axes (Hawkins 1993)

(28)

(29)

(30)

(31)

(32)

(33)

16

Swan in 1974 shows his equation (Barrett 1980) relating the sharpest (or the two

sharpest) corner(s) and inscribed circle diameter

Szadeczsky-Kardoss has his Average roundness of outline (Krumbein and Pettijohn

1938) relating the concave parts perimeter and the actual perimeter

Lees (1964a) developed an opposite definition to roundness it means that he

measures the angularity instead of the roundness and he calls it Degree of angularity

Figure 16 shows the items considered when equation 36 applies as the angles (α)

inscribed circle (Rmax-in) and the distance (x) The main formula is

In order to apply the last equation corners needs to be entered in the formula and each

individual result will add to each other to obtain the final degree of angularity

A roundness index appears on Janoo (1998) Kuo and Freeman (1998a) and Kuo et

al (1998b) it is described as

The last equation is on section 34 also because there is not a general agreement on the

definition furthermore some authors had used to define the roughness this is not the

only equation that has been used trying to define different aspects (sphericity

roundness or roughness) but it is a good example of the misuse of the quantities and

definitions

inmaxR

x)180(R

2P

A4R

i

ss

D

DDR

221

100P

PR CON

Figure 16 Degree of angularity measurement technique (Blot and Pye 2008)

(34)

(35)

(36)

(17)

17

Sukumaran and Ashmawy (2001) present an angularity factor (AF) calculated from

the number of sharpness corners Angles βi required to obtain the angularity factor are

shown in figure 9

Sukumaran and Ashmawy (2001) also suggested use not bigger sampling interval of

N=40 because it is the cut off between angularity factor and surface roughness If so

this equation could be used to describe the roughness

Table 5 General chronological overview of the particle roundness

Aspect Name Author Year Based on

Roundness shape index Wentworth 19191

diameter of sharper corner

shape index Wentworth 1922b sharpest corner and axis

roundness Wentworth 1933 convex parts

Fischer 19332

noncurved parts outline

Fischer 19332

noncurved-streigth parts outline

Average roundness of outline

Szadeczsky-Kardoss 19333

convex parts-perimeter

roundness Wadell 1935 diameter of corners

roundness Wadell 1935 diameter of corners

roundness Russel amp Taylor 19372

class limit table

roundness Krumbein 1941 chart

Cailleux 19471

convex parts

roundness Pettijohn 19494 class limit table

roundness Powers 1953 chart and class limit table

Kuenen 19561

axis-convex corner

roundness Krumbein and Sloss 1963 chart

degree of angularity Lees 1964a corners angles and inscribed circle

Dobkins amp Folk 1970 diameter of sharper corner

Swan 19741

diameter of sharper corners

Angularity factor Sukumaran and

Ashmawy 2001

Segmentation of particles and angles

1) Barret 1980 2) Hawkins 1993 3) Krumbein and Pettijohn 1938 4) Powers 1953

sum

sumsumN

1=i

2

i

2

N

1=i

2

i

2N

1=ii

)ordm180 -circleβ( - )(180ordm x 3

)ordm180-circleβ(-)ordm180 -Particleβ(

= AF (37)

18

36 ROUGHNESS OR SURFACE TEXTURE

A third property called texture appears early in the literature with the sphericity and

roundness properties since then texture property was longed described but it was in

accordance with the authors at that time not measurable

Wright in 1955 developed a method to quantify the surface texture or roughness of

concrete aggregate using studies done on 19 mm stones The test aggregates were first

embedded in a synthetic resin The stones were cut in thin sections The sections

projection was magnified 125 times The unevenness of the surface was traced and the

total length of the trace was measured The length was then compared with an uneven

line drawn as a series of chords (see figure 17) The difference between these two

lines was defined as the roughness factor (Janoo 1998)

However with the advance of technology it has become easier measure the roughness

and here is presented some researcherrsquos ideas how this property should be calculated

One technique used by Janoo (1988) to define the roughness can be seen in figure 18a

and is defined as the ratio between perimeter and convex perimeter

The convex perimeter is obtained using the Feretrsquos box (or diameter) tending a line in

between the touching points that the Feretrsquos box describes each time it is turn (figure

18b)

PER

OC

PR

Figure 17 Measurement method for characterizing the surface texture of an aggregate (Janoo 1998)

a) Convex perimeter (CPER) b) Feret measurement Figure 18 a) Convex perimeter (CPER) b) Feret measurement (modified after Janoo 1998)

(38)

a)

b)

19

Kuo and Freeman (1998a) and Kuo et al (1998b) use the roughness definition as the

ratio perimeter and average diameter

Erosion and dilatation image processing techniques are used to obtain the surface

texture Erosion is a morphological process by which boundary image pixels are

removed from an object surface which leaves the object less dense along the

perimeter or outer boundary Dilatation is the reverse process of erosion and a single

dilatation cycle increases the particle shape or image dimension by adding pixels

around its boundary (Pan etal 2006)

The ldquonrdquo erosion and dilatation cycles are not standardized

Mora and Kwan (2000) used the ldquoconvexity ratio CRrdquo (equation 41) and the ldquofullness

ratio FRrdquo (equation 42) in their investigation they are

The convex area is the area of the minimum convex boundaries circumscribing the

particle This is illustrated in the figure 19 The convex area is obtained in a similar

way as the convex perimeter but in this case the area between the original outline and

the convex perimeter is our convex area

AVG

OD

PR

100A

1AARO

CONo A

AR =

CONo A

AR =

Figure 19 Evaluation of area and convex area (Mora and Kuan 2000)

(39)

(40)

(41)

(42)

20

4 TECHNIQUES IN ORDER TO DETERMINE PARTICLE

SHAPE

41 HAND MEASUREMENT

Hand measurement technique was the first used by obvious reasons in order to

improve the accuracy special devices developed as the ldquosliding rod caliperrdquo used by

Krumbein (1941) it works placing the sample on the sliding road calliper as show

figure 20b the length in different positions can be obtain by using the scale provided

in the handle the ldquoconvexity gagerdquo that was actually used by opticians to measure the

curvature of lenses but easily applicable to the particle shape analysis (Wentworth

1922b) works measuring the movement of the central pivot as figure 20a shows (the

two adjacent pivots are invariable) as many the central pivot moves more is the

curvature or the ldquoSzadeczky-Kardossrsquos apparatusrdquo develop in 1933 that traces the

profile of the rock fragment so the outline traced is then analyzed (Krumbein and

Pettijohn 1938) figure 20c show equipment

Another helpful tool to determine the particle dimensions was the ldquocamera lucidardquo to

project the particlersquos contour over a circle scale appearing in Figure 21 thus it is

possible to measure the particlersquos diameter

a)

c) b)

Figure 20 a) convexity gage used to determine the curvature in particle corners (Wenworth 1922b)

b)sliding rod caliper device to measure the particle axis length (Krumbein 1941) and c)Szadeczky-

Kardoss (1933) apparatus it was utilized to obtain the particle outline

Figure 21 Circle scale used by Wadell (1935) to determine particlersquos diameter and roundness

21

42 SIEVE ANALYSIS

Bar sieving eg according to EN 933-31997 can be used to determine simple large

scale properties By combining mesh geometries the obtained results can be used to

quantify flakiness and elongation index ASTM D4791 (Flat and elongated particles

are defined as those coarse aggregate particles that have a ratio of length to thickness

equal to or greater than a specified value such as 51 The index represents the

percentage on weight of these particles) The method is not suitable for fine materials

This due to the difficulty to get the fine grains passed through the sieve and the great

amount of particles in relation to the area of the sieve (Persson 1998) eg EN 933-

31997 related to flakiness index The test is performed on aggregates with grain size

from 4 mm and up to 63 mm two sieving operations are necessary the first separates

on size fraction and the second use a bar sieve after the first sieving the average

maximum diameter of the particles is obtain and with the second sieving (bar sieving)

the shortest axis diameter is found finally with this two parameters the flakiness

index is determined

There are more standards related with the particle shape (see appendix A) but this

above presented are probably the most known using sieve analysis to determine

particlersquos geometrical properties

Sieve analysis is facing the computers age and image analysis sieving research is

taking place (Andersson 2010 Mora and Kwan 2000 Persson 1998) Industry is

also applying the image analysis sieving with decrees on the testing time compare

with the traditional sieving method An inconvenient of image analysis is the error

due the overlapping or hiding of the particles during the capture process but the

advantages are more compare with disadvantages (Anderson 2010)

43 CHART COMPARISON

Charts developed over the necessity of faster results because the long time consuming

required when measuring each particle

Krumbein (1941) present a comparison roundness chart for pebbles which were

measured by Wadellrsquos method because this property was the most difficult to measure

due to the second order scale that roundness represents (See figure 22)

Figure 22 Krumbein (1941) comparision chart for roundness

22

A qualitative chart by Powers (1953) try to include both (sphericity and roundness)

particlersquos characteristics it was divided on six roundness ranges (very angular

angular sub-angular sub-rounded rounded and well rounded) and two sphericity

series (high and low sphericity) This chart was prepared with photographs to enhance

the reader perspective (See figure 23)

A new chart including sphericity and roundness appear this time it was easier to

handle the two mean properties of particlersquos shape furthermore there was included

the numerical values that eliminated the subjectivity of qualitative description The

chart is based on Wadellrsquos definitions (Krumbein and Sloss 1963) (See figure 24)

Folk (1955) worried about the personrsquos error on the chartrsquos comparison studied the

determination of sphericity and angularity (he used the Powers 1953 comparison

chart) he found that the sphericity determination by chart comparison has a negligible

error while the roundness he concluded it was necessary to carry out a more wide

research due the high variability show by his study

Figure 23 Powers (1953) qualitative shpericity-roundness chart

Figure 24 Sphericity-roundness comparison chart (Krumbein and sloss 1963)

23

44 IMAGE ANALYSIS

Image analysis is a practical method to use for shape classification since it is fast and

can be automated Different techniques appear to process these images among them

are

o Feret Diameter the Feret diameter is the longitude between two parallel lines

this lines can rotate around one particle or outline to define dimensions as it

is shown in figure 25 these method is not a fine descriptor but as it was say

above it is a helpful tool to determine diameters (Janoo 1988)

o Fourier Mathematical Technique It produces mathematical relations that

characterize the profile of individual particles This method favours the

analysis of roughness and textural features for granular soils The problem in

the methodology remains in the re-entrant angles in order to complete the

revolution (Bowman et al 2001) see figure 26

o Fractal Dimension Irregular line at any level of scrutiny is by definition

fractal (Hyslip and Vallejo 1997) Figure 27 shows fractal analysis by the

dividing method The length of the fractal line can be defined as

N

1n

nn0 )nsinbncosa(a)(R

RD1n)(P

Figure 25 Feret measurement technique is defined by two parallel lines turning

around the particle to define the shortest and longest Feret diameter (Janoo 1988)

Figure 26 Fourier technique with two radiuses at one angle (Bowman et al 2001)

(43)

(44)

24

o Orthogonal image analysis This technique is basically the use of two images

orthogonal between them to acquire the three particle dimensions (Fernlund

2005) any of the above techniques can be used in this orthogonal way

o Laser Scanning Technique this kind of laser scanning 3D is one of the most

advanced techniques In figures 28a) we have the laser head scanning the rock

particles the particles have control points in order to keep a reference point

when move them to scan the lower part in figure 28b) we can see the laser

path followed (Lanaro and Tolppanen 2002)

Another technique is the Laser-Aided Tomography (LAT) in this case a laser sheet is

used to obtain the particles surveying (see figure 29) This technique is different and

has special requirements as to use liquid with same refractive index as the particles

particles must let the laser or certain percent of light go through (Matsushima et al

2003)

a) b)

Figure 27 Fractal analysis by the dividing method at different scrutiny scale (Hyslip and Vallejo 1997)

Figure 28 a) Scanning head b) scanning path (Lanaro and Tolppanen 2002)

Figure 30 3D scan completed ready to

use for any further measure

(Matsushima et al 2003)

Figure 29 LAT scaning particles

(Matsushima et al 2003)

25

Both 3D techniques obtain the particle shape that is later used to achieve measures as

we can see in figure 30

All these previous techniques are easily written in codes or scripts to be interpreted in

a digital way obtaining the desired measurement but there are some interesting points

in the image analysis regarding on the errors involve among them are image

resolution and orientation of the particles orientation is not relevant when it is

random and large number of particles are involve resolution have an influence on the

accuracy (Zeidan et al 2007)

When resolution is increase more accuracy is obtain and the object representation

match better with the real form in the other hand more resolution means more

spending on memory and time thus resolution needs to be according with the goal

and precision needed in any work (Schaumlfer 2002)

Schaumlfer (2002) conclude that attributes like length when measuring digital images

present relative high errors It can be vanish or at least diminish using high resolution

just for diameter but not for perimeter that keep the error as big as initially Johansson

and Vall (2011) obtain similar results when 3 different resolutions were used in the

same particle obtaining an unstable output for those termsquantities that involve the

perimeter Thus all quantities relating the perimeter should be treated with care

5 EFFECT OF SHAPE ON SOIL PROPERTIES

51 INTRODUCTION

In laboratory test on the effect on particle size on basic properties has been

investigated in several studies this relation has been discussed and various

mechanisms had been proposed to explain the behaviour of the soil in dependency

also with the shape Basically there are two mechanisms proposed The arrangement

of particles and the inter-particle contact (Santamarina and Cho 2004) and

subsequence breakage

The arrangement of particles

Arrangement of the particles can be presented in three different forms loose dense

and critical this arrangement determines the soil properties (eg density increase with

more dense arrangement) Loose and dense states are easy understandable when

figure 31 is explained while in the upper part of the figure the particles are arranged

using the minimum space needed in the lower part a span is created using the flaky

particle as a bridge this phenomena is known as ldquobridgingrdquo Bridging can produce

different geotechnical results when just the shape of the particle is changed eg void

ratio (Santamarina and Cho 2004) Particles are able to rearrange this could be done

applying pressure (energy) to the soil the pressure (energy) will create such forces

that soil particles will rotate and move (see figure 34) finishing in a more dense state

26

A loose soil will contract in volume on shearing and may not develop any peak

strength (figure 32 left) In this case the shear strength will increase gradually until

the residual shear strength is revealed once the soil has ceased contracting in volume

A dense soil may contract slightly (figure 32 right) before granular interlock prevents

further contraction (granular interlock is dependent on the shape of the grains and

their initial packing arrangement) In order to continue shearing once granular

interlock has occurred the soil must dilate (expand in volume) As additional shear

force is required to dilate the soil a peak shear strength occurs (figure 32 left) Once

this peak shear strength caused by dilation has been overcome through continued

shearing the resistance provided by the soil to the applied shear stress reduces

(termed strain softening) Strain softening will continue until no further changes in

volume of the soil occur on continued shearing Peak shear strengths are also

observed in overconsolidated clays where the natural fabric of the soil must be

destroyed prior to reaching constant volume shearing Other effects that result in peak

strengths include cementation and bonding of particles The distinctive shear strength

called the critical state is identified where the soil undergoing shear does so at a

constant volume (Schofield and Wroth 1968)

The inter-particle contact

For frictional soil ie coarse grained soil the friction between particles is the

dominating factor for strength Materials usually consisting of coarse grains (diameter

Figure 31 Bridging effect when flaky particles are combined in the bulk material (Santamarina and

Cho 2004)

Figure 32 The left part of the figure show a typical behaviour of loose and dense material over shear stress

while at the right the figures illustrate the typical volume changes

27

gt 006mm) behave as a frictional soil it means that the strength of coarse soils (silt

sand gravel etc) comes from an inter-particle mechanical friction thus ideally they

do not have traction strength In figure 33 the inter-particle contact is illustrated here

the pressure (P) is applied and two more components are found the normal load (N)

and the tangential load (T) described as the friction coefficient (μF) The forces stand

in equilibrium (Johansson and Vall 2011)

When particles equilibrium is disturbed (friction coefficient is not enough to keep

particles unmoved) the rotation is imminent and it is necessary in order to compact

the soil in figure 34 can be seen that the arrangement is a fact that inhibit or allow this

rotation and the shape in the 3 different scales are also factors because the more

spherical andor more rounded andor less roughness more easy is the rotation

(Santamarina and Cho 2004)

Breakage

Breakage is a side effect of the inter-particle contact and rotation when pressure

exceed the rock strength it can happened when the particles are tight together and

there is not enough space to rotate it is more obvious in angular particles (mesh form)

or as in figure 31 where the flaky particle ldquobridgingrdquo is not able to rotate but it can

brake by the pressure increase Yoginder et al (1985) notice that the angular particle

break during his experiments and they turn more rounded changing the original size

and form configuration at the same time there was a soil properties loosening

Figure 33 Inter-particle contact and forces acting (Axelsson 1998)

Figure 34 Rotation inhibition by the particles compaction or low void ratio (Santamarina and Cho 2004)

28

52 INFLUENCE OF SIZE AND SHAPE

Wenworth (1922a) and Pellegrino (1965) among others suggest that agent transport of

the rocks (rigor of transport temperature and moisture changes etc) determine its

shape but also the particle genesis itself (rock structure mineralogy hardness etc) It

is not possible to determine the shape of the particles based on the agent transport or

genesis but generally a shape behaviour is expected according to Mitchell and Soga

(2005) specially when the particle size is in the clay size (gt2μm) The shapes of the

most common clay minerals are platy (figure 35) with some exceptions (eg

halloysite occurs as tubes kaolinite are large thick and stiff Smectites are composed

of small very thin and filmy particles Illites are intermediate between kaolinite and

smectite and attapulgite occurs in lathlike particle shapes) Some clay minerals

photographs are presented in figure 35

Figure 35 Clay mineral shape a) hallosite b) Kaoline c) Smactites d) Illites and e) attapulgite (Modified

from Mitchell and Soga 2005)

Figure 36 Particle size range in soils Generally the particles of clay size are plate shaped (Mitchell and

Soga 2005)

a) b) c)

e) d)

29

53 VOID RATIO AND POROSITY

The void ratio (e) is the ratio of the volume of voids to the volume of solid it is

defined by the equation

Porosity (n) is the ratio of the volume of voids to the total volume of the soil it is

represented by the equation

Holubec and DrsquoAppolonia (1973) found a relation between the void ratio and

sphericity (referred in the paper as coefficient of angularity ratio of particle surface

and equivalent sphere surface) their results show that the maximum and the minimum

void ratio increases as the shpericity decreases In this study the surface was obtained

for an indirect method based on the permeability developed by Hoffman in 1959

described in the same document Rouseacute et al (2008) defined the roundness as

Wadell (1935) and he found it as an important factor controlling the minimum and

maximum void ratios Some other authors as Youd (1973) and Cho et al (2006)

conclude the same minimum and maximum void ratios increase when sphericity and

roundness decrease Another interesting result (all above authors) was the bigger

influence of the form (sphericity circularity) and roundness on the maximum void

ratio The change of the maximum void ratio is more pronounced than the change of

the minimum void ratio when the form and roundness changes (See figure 39)

Particles arrangement and interlocking are probably the factor that controls the void

ratio bridge effect permit the existence of void among the particles while interlocking

allowed the particles to form arches avoiding the possibility to rotate and stay in a

more stable configuration eg as it happens with marbles

Figures 36 37 and 38 shows proposed empirical relationships between void ratio and

shape from tables 5 and 6 (graphically the scale goes from 0 to 1 when cero mean

high angularity shpericity or circularity and one means low angularity circularity or

sphericity) Holubec and DrsquoAppolonia (1973) data was taken to obtain a power curve

and describe a tendency Santamarina and Cho (2004) show Youd equations in the

original paper Youd (1973) never presented the equation but it is easy to use the

information to draw a trend

The graphics presented in this document (figures 36 37 and 38) must be used with

certain reserves due the fact that the original data was modified in order to fit all

information in one graphic what the figures shows is just the general trend of the

behaviourrsquos material regarding on the shape If more accurate description and

information is required the author recommends consulting the reference data In the

same way equations from Holubec and DrsquoApollonia (1973) and Youd (1973) were not

presented by the authors but the use of the information was taken in order to build up

those equations on tables 6 and 7

S

V

V

V

= e

V

V

=nV

(45)

(46)

30

Table 6 Minimum void ratio equations regarding on the quantity (Ψ for sphericity C for circularity R

for roundness SF for Sukumaran shape factor and AF for Sukumaran angularity factor)

EQUATION NUMBER REFERENCE

Figure 34 (left)

4340

minΨ45490e =

47

Holubec amp DrsquoAppolonia 1973 (Ψ

was obtained using equation 2)

SF06340

mine021903180e +=

48

Sukumaran amp Ashmawy 2001 (SF

obtained using equation 21)

C05101emin

= 49

Cho etal 2006 (C obtained using

figure 12)

Figure 34 (right)

1

minR08203590e +=

50

Youd 1973 (R obtained from figure

11 and table 3)

R34080emin

= 51

Cho et al 2006 (R obtained using

figure 12)

1

minR05104330e +=

52

Rouseacute et al 2008 (R obtained by

equation 21)

AF02330

mine372004160e +=

53

Sukumaran amp Ashmawy 2001 (AF

obtained using equation 37)

Table 7 Maximum void ratio equations regarding on the quantity (Ψ for sphericity C for circularity R

for roundness SF for Sukumaran shape factor and AF for Sukumaran angularity factor)

EQUATION NUMBER REFERENCE

Figure 35 (left)

51520

max Ψ61120e = 54

Holubec and DrsquoAppolonia 1973 (Ψ

was obtained using equation 2)

SF1190

max e0016907180e += 55

Sukumaran amp Ashmawy 2001 (SF

obtained using equation 21)

C86061emax = 56

Cho etal 2006 (C obtained using

figure 12)

Figure 35 (right)

1

max R1505540e += 57

Youd 1973 (R obtained from figure

11 and table 3)

R62031emax= 58

Cho et al 2006 (R obtained using

figure 12)

1

max R107106150e += 59

Rouseacute et al 2008 (R obtained by

equation 21)

AF0530

max e12506090e += 60

Sukumaran amp Ashmawy 2001 (AF

obtained using equation 37)

Comparing figures 37 and 38 (minimum and maximum void ratio) it can be seen on

the right scheme of both figures 37 and 38 (when the factor is roundnessangularity)

that all the empirical relations has a common initial point close to 1 (it means that

particles are well rounded) while this common agreement disappear when the

roundness factor decreases (when the particles become more angular) Same figures

(37 and 38) on the left graphs (when the factor is sphericitycircularityshape) do not

present the same behaviour in fact there is more disperse initial point close to 1(when

the particles tend to be more sphericalcircular)

31

In Figure 39 the Δe (emax-emin) has been plotted to show how the maximum void ratio

and the minimum void ratio has different rate change when the particle shape

changes Maximum void ratio increases more than minimum void ratio when the

particle shape becomes less spherical andor more angular Comparing figure 39 left

and right graphics it can be seen that right present a common initial point when the

quantity (roundnessangularity) is close to one while in the left graphic the initial

point is more disperse Both ending points in both graphics (close to zero) are

dispersed

Figures 37 38 and 39 present the same behaviour right graphics (when the factor is

roundness angularity) in each figure have an initial common point while the left

graphics do not (when the factor is sphericity circularity shape)

Figure 37 Minimum void ratio based upon the relation of shape factor proposed by the authors indicated

in the figure

Figure 38 Maximum void ratio based upon the relation of shape factor proposed by the authors indicated

in the figure

04

06

08

1

12

14

16

18

2

005

015

025

035

045

055

065

075

085

095

Factor (roundness angularity)

min

imu

m v

oid

rati

o

Youd 1973 roundness

Rouse 2008 roundness

Cho 2006 roundness

Sukumaran 2001 AF

03

04

05

06

07

08

09

1

11

12

13

05

015

025

035

045

055

065

075

085

095

Factor (sphericity circularity shape)

min

imu

m v

oid

rati

oHolubec 1973 sphericity

Cho 2006 circularity

Sukumara 2001 SF

05

07

09

11

13

15

17

19

21

00

150

250

350

450

550

650

750

850

95

Factor (sphericity circularity shape)

Maxim

um

vo

id r

ati

o

Holubec 1973 sphericity

Cho 2006 circularity

Sukumara 2001 SF

05

1

15

2

25

3

35

005

015

025

035

045

055

065

075

085

095

Factor (roundness angularity)

Maxim

um

vo

id r

ati

o

Youd 1973 roundness

Rouse 2008 roundness

Cho 2006 roundness

Sukumaran 2001 AF

32

54 ANGLE OF REPOSE

The angle of repose of a granular material is the steepest angle of descent or dip of the

slope relative to the horizontal plane when material on the slope face is on the verge

of sliding as show in figure 40

According to Qazi (1975) there are five types of forces which may act between the

particles in soils

1 Force of friction between the particles

2 Force due to presence of absorbed gas andor moisture of particle

3 Mechanical forces caused by interlocking of particles of irregular shape

4 Electrostatic forces arising from friction between the particles themselves and

the surface with which they come in contact

5 Cohesion forces operating between neighbouring particles

Rouseacute et al (2008) found a decrease of angle of repose with increase roundness

based upon ASTM C1444 test (Standard Test Method for Measuring the Angle of

Repose of Free-Flowing Mold Powders) The method consist in pouring sand on a

surface cover by paper trough a funnel of specific dimensions (the nozzle diameter

depend on the sandrsquos particle size) from an altitude of 15 inches (381 mm) The sand

is release from the funnel until the peak of the cone formed by the sand stops the flow

The repose angle is obtained with the equation

H represent the 15 inches D and d represent the diameter of the cone formed by the

sand and the diameter of the funnel respectively

Figure 39 Maximum minus minimum void ratio based upon the relation of shape factor proposed by the

authors indicated in the figure

0

01

02

03

04

05

06

07

08

09

1

005

015

025

035

045

055

065

075

085

095

Factor (sphericity circularity shape)

Maxim

um

- M

inim

um

Vo

id r

ati

oHolubec 1973 sphericity

Cho 2006 circularity

Sukumara 2001 SF

0

02

04

06

08

1

12

14

16

18

005

015

025

035

045

055

065

075

085

095

Factor (roundness angularity)

Maxim

um

- M

inim

um

Vo

id r

ati

o

Youd 1973 roundness

Rouse 2008 roundness

Cho 2006 roundness

Sukumaran 2001 AF

dD

H2

tan=φ1

rep(61)

33

Rouseacute (2008) shows an empirical relation to obtain the angle of repose based on the

roundness of the particles

55 SHEAR STRENGTH

The MohrndashCoulomb failure criterion represents the linear envelope that is obtained

from a plot of the shear strength of a material versus the applied normal stress This

relation is expressed as

where τ is the shear strength σn is the normal stress co is the intercept of the failure

envelope with the τ axis and is the slope of the failure envelope The quantity c is

often called the cohesion and the angle is called the angle of internal friction

Studies show that the internal friction angle (under drained triaxial tests) increases

more rapidly on those materials having higher angularity increasing the relative

density The internal friction angle is a function of the relative density and the particle

shape (Holubec and DrsquoAppolonia 1973)

Chan and Page (1997) found in a study made with dry copper (using different shapes

and sizes ranging from 180 to 106 μm) using a direct shear test (ring share test) that

the internal friction angle increases as the angularity increases

Shinohara et al (2000) did some experiments with steel powder different shapes

using a triaxial cell in the test Shinohara never used the roundness or angularity on

the work but apply the shape factor (relation long axisshort axis) and the results were

that as this relation deviate from factor 1 the internal friction angle increases

The following empirical relations were found in the literature showing the behaviour

of the friction angle (obtained under different conditions)

)tan( noc

Figure 40 Representation of the angle of repose

(63)

(62)

34

Cho et al (2006)

(64)

(R is obtain by comparing the Krumbein chart figure 13)

Rouseacute (2008)

(65)

(66)

(R is defined using Wadell equation 22)

In figure 41 the suggested empirical relations above and lines constructed using

author data from Holubec and DrsquoAppolonia (1973) and Sukumara and Ashmawy

(2001) are plotted together to display the general trend on the particle shape and

friction angle relation Sukumaran reports two lines one based on the shape factor

(SF) and the second referring the angularity factor (AF) Sukumaran performed the

tests at constant volume

The scale used for Holubec and DrsquoAppolonia (1973) have lower and upper limits of 1

and 2 respectively (angularity form) and a scale change was applied to be able to

presented in the actual figure 41 As in the previous section (52) the author

recommend to use the original data from the references due that the figure just follows

the general trend of the behaviourrsquos particle regarding on the shape

Figure 41 The changes on the internal friction angle shows a general increase when the particle roundness

becomes angular or in the case of Sakamuran less spheric (Shape factor SF)

35

Barton and Kjaernsli (1981) suggested a model (equation 67) to predict the peak

friction angle (φrsquo) based upon numerous trixial and direct shear data tests

where

Se equivalent strength of particle

Re equivalent roughness of particle

φb basic friction angle (obtained from basic tilting test)

σn normal load

The information required for the model is (1) the uniaxial compressive strength of the

rock (2) the d50 particle size (mesh size where 50 of the particles pass through)

required to define Se (figure 42) (3) the degree of particle roundness and (4) the

porosity following compaction All data can be estimated by simple index tests

Barton and Kjaernsli (1981) suggest that particle size and sample scale has an effect

on the friction angle and includes them to obtain the equivalent strength (Se) figure 42

shows the method to obtain this value Compressive strength (σc) was chosen to be the

factor affecting the scale because micro fractures influence this property while

samples are bigger more micro fractures contain and its compressive strength reduces

The equivalent roughness is obtain using figure 43 where is required to know the

porosity (n) and the origin of the particles (a small chart is provided in the same figure

to compare the particles profile)

b

n

ee

SLogR

Figure 42 Method of estimating Equivalent Strength (Se) of rockfill based on uniaxial compressive strength

(σc ) and d50 particle size (Barton amp Kjaernsli 1981)

(67)

36

56 SEDIMENTATION PROPERTIES

A particle released in a less dense Newtonian fluid initially accelerate trough the fluid

due to the gravity Resistances to deformation of the fluid transmitted to the particle

surface drag generate forces that act to resist the particle motion The force due to the

weight (Fw) can be written as

Where ρp ρ are density of the particle and fluid (water) respectively g is the

gravitational force and Vp is the volume of the particle

And the resistance force (FD) is

Where CD is the dimensionless drag coefficient W is the weight of the particle and A

is the cross section area

Particlersquos shape has been assumed to be spherical when equations are applied on the

settling velocity Correlation deviates when particle shape departs from spherical form

Figure 43 Method of estimating Equivalent Roughness (Roe) based on porosity of rockfill

origin material degree of roundedness and smoothness of particle (Barton amp Kjaernsli 1981)

PPW ρ)gV(ρF

A2

WρCF

2

DD

(68)

(69)

37

(Dietrich 1982) and it is known that natural particles depart from spherical form

thus it is evident that this departure would have consequences

The below equation is proposed to account the shape (in this case the Corey shape

factor equation 8) in the settling velocity (Jimenez and Madsen 2003)

Jimenez and Madsen (2003) Dietrich (1982) Briggs and McCulloch (1962) and

others were working in the hydraulic shape of particles to solve problems as sediment

transport It is obvious that the equation presented and the researcherrsquos investigation

works under certain conditions (eg grain size between 0063-1 mm)

Dietrich (1982) suggests an empirical relation that accounts settling velocity size

density shape and roundness of a particle

R1 R2 and R3 are fitted equations for size and density shape and roundness

respectively

57 HYDRAULIC CONDUCTIVITY PERMEABILITY

Darcyrsquos Law Permeability is one component of Darcyrsquos law Darcys law is a simple

proportional relationship between the instantaneous discharge rate through a porous

medium the viscosity of the fluid and the pressure drop

The total velocity Ve is equal to the product of the permeability of the medium

(porous media) k the pressure drop ∆p all divided by the viscosity μ (Muskat

1937)

Darcys law is only valid for slow viscous flow most groundwater flow cases fall in

this category Typically Darcyrsquos law is valid at any flow with laminar flow (see figure

44)

Reynoldrsquos number (Laminar and turbulent Flow) Typically any laminar flow is

considered to have a Reynoldrsquos number less than one and it would be valid to apply

Darcys law Experimental tests have shown that flow regimes with Reynolds numbers

1

ND

S

S

ZY

gd1s

WW

NDN

gd)1s(4

dS

2R1R

3 10RW

pk

Ve

(70)

(71)

(72)

(73)

38

up to 10 may still be Darcian (laminar flow) as in the case of groundwater flow The

Reynolds number (a dimensionless parameter) for porous media flow is typically

expressed as

where ρ is the density of water (units of mass per volume) υ is the specific discharge

(with units of length per time) d is a representative average grain diameter for the

porous media (often taken as the 30 passing size from a grain size analysis using

sieves - with units of length) and μ is the viscosity of the fluid (Muskat 1937)

Shape effects Permeability as Head and Epps (2011) suggested is affected by the

shape and texture of soil grains Elongated or irregular particles create flow paths

which are more tortuous than those spherical particles Particles with a rough surface

texture provide more frictional resistance to flow Both effects tend to reduce the

water flow through the soil

Kozeny-Carman empirical relation accounts for the dependency of permeability on

void ratio in uniformly graded sands serious discrepancies are found when it is

applied to clays due the lack of uniform pores (Mitchell and Soga 2005)

There are various formulations of the Kozeny-Carman equation one published by

Head and Epps (2011) takes the void ratio e the specific surface area Ss and an

angularity factor F into account of permeability k

The angularity factor F considers the shape of the particles and ranges from 11 for

rounded grains 125 for sub rounded to 14 for angular particles The specific surface

Ss is defined as

d1 and d2 represent the maximum and minimum size particle in mm

Kane amp Sternheim (1988) suggest that the inclusion of the shape factor (F) has

probably the background on the Reynolds number due this factor is dependent

significantly on the shape of the obstacles and Reynolds number determines the

presence of laminar or turbulent flow Figure 44 show how the laminar flow has low

energy dissipation while turbulent flow (eg the roughness and path tortuosity) has

high energy dissipation

e1

e

FSs

2k

3

2

dRe

21

6

ddSs

(74)

(75)

(76)

39

According to Nearing and Parker (1994) the amount of soil detached during laminar

and turbulent flow is dependent on each soil and also greater on turbulent flow due the

greater shear strength generated during this kind of flow this could suggest the

greater erosion when turbulent flow is present

58 LIQUEFACTION

Soil liquefaction is a phenomenon in which soil loses much of its strength or stiffness

for a generally short time by earthquake shaking or other rapid loading Static and

dynamic liquefactions occur been the second one the most regular known

Liquefaction often occurs in saturated soils that is soils in which the space between

individual particles is completely filled with water This water exerts a pressure on the

soil particles that influences how tightly the particles themselves are pressed together

Shaking or other rapid loading can cause the water pressure to increase to the point

where the soil particles can readily move with respect to each other (Jefferies and

Been 2000)

Jefferies and Been (2000) state that it is clear that minor variation in intrinsic

properties of sand have major influence on the critical state These might be variations

on grain shape mineralogy grain size distribution surface roughness of grains etc

Yoginder et al (1985) found that substantial decrease on liquefaction resistance

occur with increase in confining pressure for rounded and angular sands (1600 kPa)

also rounded sands show an rapidly build up of resistance against liquefaction with

increasing density while angular tailing sand in contrast show such rapid increase

only at low confining pressures At low confining pressure angular material is more

resistant to liquefaction Probably the breakage of the corners on the angular particles

in tailings is ruling the lost in resistance at high confining pressures (sieve analysis

Figure 44 The figure show the extremes of flow behaviour First turbulent conditions where the flow is

essentially random and unpredictable and second the well defined Laminar flow conditions

40

after test identify the breakage of angular particles while on rounded particles the

sieve analysis was practically the same)

59 GROUNDWATER AND SEEPAGE MODELLING

In groundwater flow the particlersquos shape affects the soilrsquos pore size distribution

hence the flow characteristics (Sperry and Peirce 1995) Tortuosity and permeability

(also see section 57) are two significant macroscopic parameters of granular medium

that affect the passing flow (Hayati et al 2012) Current models incorporating the

effects of particle shape have failed to consider irregular particles such as those that

would prevail in a natural porous medium (Sperry and Peirce 1995)

Hayati et al (2012) suggested based on his results that tortuosity effect converge

when the porosity increases indicating that the shape have dominance at low and mid

porosity ranges

Sperry and Peirce (1995) research conclusions suggest that particle size and porosity

are more important predictors for hydraulic conductivity explaining the 69 of the

variability but particle shape appears to be the next most important This however

apparently comprises particles larger than 295-351 μm Differences for particle size

295-351 μm and smaller are not detectable Another interesting result in the research

was the interaction effect of the particle size and particle shape It suggests a different

packing configuration for particles of the same shape but different size (scale

dependent)

6 DISCUSSION

61 TERMS QUANTITIES AND DEFINITIONS

In order to describe the particle shape in detail there are a number of terms quantities

and definitions (qualitative and quantitative) used in the literature (eg Wadell 1932

1934 Krumbein 1941 Sneed amp Folk 1958) All mathematical definitions

(quantitatives) are models used to simplify the complexity of shape description Some

authors (Mitchell amp Soga 2005 Arasan et al 2010) are using three sub-quantities

one and each describing the shape but at different scales The terms are

morphologyform roundness and surface texture (figure 1) The three sub-quantities

are probably the best way to classify and describe a particle because not a single

definition can interpret the whole morphology Common language is needed when

descriptors are explained and these three scales represent an option It is evident in

the reviewed literature that many of the shape descriptors are presented with the same

name but also that there is not a clear meaning on what this descriptor defines eg

when there is no upper limit in the roundness does it means that the angularity never

ends Could they be more and more angular Probably they could be on theory but

not in reality

41

62 PROPERTIES

Trough various articlersquos review done in the present investigation it is recognized that

the particlersquos shape has an effect on the material properties among these are

1 Porosity (Tickell 1938 Fraser 1935 Kolbuszewski 1948) and void ratio

(Cho et al 2006 Shergold 1953 Rouseacute et al 2008 Santamarina and Cho

2004)

2 Permeability (Witt and Brauns 1983)

3 Internal friction angle (Shinohara et al 2000 Chan and Page 1997

Cheshomi et al 2009)

4 Density (Youd 1973 Holubec and DrsquoAppolonia 1973)

5 Drag coefficient Hydraulics (Briggs and McCulloch 1962)

In Table 5 is a short resume of the properties and shape effect found in peer review

articles trough different journals Most of the reviewed articles based its research on

uniform graded sands

Table 8 Compilation of properties influenced by particle shape

Repose

angle

Friction

angle

Porosity and

Void ratio Density Permeability

Settling velocity

Drag coefficient Deformation

Sphericity (3D)shape factor

NI x x x x x x

Circularity (2D)

NI x x x x NI NI

Roundness x x x x NI NI x

x influence

NI no information available

Shape of particles has an effect on the arrangement producing bridging or avoiding

the rotation of the particles and the resulting geotechnical property is affected eg

including flaky particles can result in a higher void ratio due the bridging effect

(Santamarina and Cho 2004) and depending on the loads even the size distribution is

changed due the breakage (Yoginder et al 1985) in similar way angular particles

produce higher void ratio due the avoided possibility of the particles to rotate and

compact

The influence of the chosen shape descriptor appears in this review to have minor

influence on the soil properties in the reviewed studies except on the void ratio and

the friction angle Influence of particle shape in some cases is hider by other factors

(eg size distribution) also the particle shape probably does not have influence when

particle size is in the clay order (eg hydraulic conductivity) the reason could be due

to forces as electrostatic or capillarity become more important at this level

Among the shape descriptors some are chosen more often in literature (eg aspect

ratio) there is no apparent scientific basis to use it (probably due to the simplicity of

the measurement it becomes one of the most use) but there are still some other

descriptors that may or may not show better correlation with the soil properties

Instead empirical relations had been developed regarding roundness or shape to

describe the soil behaviour it is clear that the mechanism behind the results is still not

completely understood

42

There is necessity to define the best(s) shape descriptor(s) to be used for particular

geotechnical properties

63 IMAGE ANALYSIS

Many image analysis techniques had been used to describe the particle shape eg

Fourier analysis fractal dimension tomography etc (Hyslip and Vallejo 1997) but

there is not agreement on the usage or conclusion to ensure the best particle descriptor

for geotechnical applications

There are several shape descriptors and also various techniques to capture the

particles profile (3-dimensions 3-dimension orthogonal and 2-dimensions) Each

technique presents advantages and disadvantages 3-dimensions is probably the

technique that provide more information about the particle shape but the precision

also lies in the resolution the equipment required to perform such capture could be

more or less sophisticated (scanning particles laying down in one position and later

move to complete the scanning or just falling down particles to scan it in one step)

3-dimensions orthogonal this technique use less sophisticated equipment (compare

with the previous technique) but its use is limited to particles over 1cm also

information between the orthogonal pictures is not capture 2-dimensions require non

sophisticated equipment but at the same time the shape information diminish compare

with the previous due the fact that it is possible to determine only the outline as the

particle measurements are performed in 2-dimensions it is presumed that they will lie

with its shortest axis perpendicular to the laying surface when they are flat but when

the particle tends to have more or less similar axis the laying could be random

Advantages on the use of image analysis are clear there is not subjectivity because it

is possible to obtain same result over the same images Electronic files do not loose

resolution and it is important when collaboration among distant work places is done

files can be send with the entire confidence and knowing that file properties has not

been changed Technology evolutions allowed to work with more information and it

also applies to the image processing area were the time consumed has been shortened

(more images processed in less time)

One important aspect in image analysis is the used resolution in the analysis due the

fact that there are measurements dependent and independent on resolution Thus

those dependent measurements should be avoided due the error included when they

are applied or avoid low resolution to increase the reliability Among these

parameters length is the principal parameter that is influences by resolution (eg

perimeter diameter axis etc) Resolution also has another aspect with two faces

quality versus capacity more resolution (quality) means more storage space a

minimum resolution to obtain reasonable and reliable data must be known but it

depend on each particular application

43

64 APPLICATIONS

Quantify changes in particles in the authorrsquos thought is one of the future applications

due the non-invasive methods of taking photographs in the surface of the damrsquos slope

rail road ballast or roads Sampling of the material and comparing with previous

results could show volume (3D analysis) or area (2D analysis) loss of the particles as

well as the form roundness and roughness This is important when it has been

suggested that a soil or rock embankment decrees their stability properties (eg

internal friction angle) with the loss of sphericity roundness or roughness

Seepage stock piling groundwater etc should try to include the particle shape while

modelling seepage requires grading material to not allow particles move due the

water pressure but in angular materials as it is known the void ratio is great than the

rounded soil it means the space and the possibilities for the small particles to move

are greater stock piling could be modelled incorporating the particle shape to

determine the binrsquos capacity when particle shape changes (void ratio changes when

particle shape changes) Modelling requires all information available and the

understanding of the principles that apply

Industry is actually using the particle shape to understand the soil behaviour and

transform processes into practical and economic image analysis has been included in

the quality control to determine particle shape and size because the advantages it

brings eg the acquisition of the sieving curve for pellets using digital images taken

from conveyor this allows to have the information in a short period of time with a

similar result at least enough from the practical point of view as the traditional

sieving

7 CONCLUSIONS

The conclusions of this literature review are

It has been shown that particle shape has influence on the soil behaviour

despite of partial knowledge of the mechanism behind Understanding of the

particle shape and its influence needs to be accomplished

A common language needs to be built up to standardize the meaning on

geotechnical field that involve the particle shape General relationships

between shape and properties should be developed

Based on this review it is not clear which is the best descriptor to use in

geotechnical engineering affecting he related shape to properties Instead of a

couple of standards there is no shape descriptor in geotechnical field fully

accepted

Image analysis tool is objective make the results repeatable obtain fast results

and work with more amount of information

44

Resolution needs to be taken in consideration when image analysis is been

carried out because the effects could be considerable Resolution must be set

according to the necessities Parameters as perimeter can be affected by

resolution

There are examples where particle shape has been incorporated in industries

related to geotechnical engineering eg in the ballast and asphalt industry for

quality control

8 FURTHER WORK

Three main issues have been identified in this review that will be further investigated

the limits of shape descriptors influence of grading and choice of descriptor for

relation to geotechnical properties

Shape descriptors have low and high limits frequently the limits are not the same and

the ability to describe the particlersquos shape is relative The sensitivity of each descriptor

should be compare to apply the most suitable descriptor in each situation

Sieving curve determine the particle size in a granular soil particle shape could differ

in each sieve size There is the necessity to describe the particle shape on each sieve

portion (due to practical issues) and included in the sieve curve Obtain an average

shape in determined sieve size is complicated (due to the possible presence of several

shapes) and to obtain the particle shape on the overall particlersquos size is challenging

how the particle shape should be included

Since several descriptors have been used to determine the shape of the particles and

the relation with the soil properties it is convenient to determine the descriptorrsquos

correlation with the soil properties

9 ACKNOWLEDGMENT

I would like to thanks to Lulearing University of Technology (LTU) the time I had spent

in its facilities and the kind environment it offers and University of Sonora

(UNISON) that has been providing me the financial support and the time to conclude

this journey

10 REFERENCES

Andersson T (2010) Estimating particle size distributions based on machine vision

Doctoral Thesis Departament of Computer Science and Electrical Engineering Lulearing

University of Technology ISSN 1402-1544 ISBN 978-91-7439-186-2

45

Arasan Seracettin Hasiloglu A Samet Akbulut Suat (2010) Shape particle of

natural and crished aggregate using image analysis International Journal of Civil and

Structural Engineering Vol 1 No 2 pp 221-233 ISSN 0970-4399

Aschenbrenner BC (1956) A new method of expressing particle sphericity Journal

of Sedimentary Petrology Vol 26 No 1 pp 15-31

Axelsson K (1998) Introduktion till jordmekaniken jaumlmte jordmateriallaumlran Skrift

984 Lulearing Avdelningen foumlr Geoteknologi Lulearing Tekniska Universitet (In Swedish)

Barton Nick amp Kjaernsli Bjorn (1981) Shear strength of rockfill Journal of the

Geotechnical Engineering Division Proceedings of the American Society of Civil

Engineers (ASCE) Vol 107 No GT7

Barrett P J (1980) The shape of rock particles a critical review Sedimentology

Vol 27 pp 291-303

Blott S J and Pye K (2008) Particle shape a review and new methods of

characterization and classification Sedimentology Vol 55 pp 31-63

Bowman E T Soga K and Drummond W (2001) Particle shape characterization

using Fourier descriptor analysis Geotechnique Vol 51 No 6 pp 545-554

Briggs L I McCulloch D S (1962) Hydraulic shape of sand particles Journal of

Sedimentary Petrology Vol 32 pp 645-656

Chan Leonard C Y and Page Neil W (1997) Particle fractal and load effects on

internal friction in powders Powder Technology Vol 90 pp 259-266

Cheshomi A Fakher A Jones C J F P (2009) A correlation between friction

angle and particle shape metrics in quaternary coarse alluvia Quarterly Journal of

Engineering Geology and Hydrogeology Vol 42 pp 145-155

Cho G Dodds J and Santamarina J C (2006) Particle shape effects on packing

density stiffness and strength Natural and crushed sands Journal of Geotechnical

and Geoenvironmental Engineering May 2006 pp 591-602

Dietrich William E (1982) Settling velocity of natural particles Water Resources

Research Vol 18 No 6 pp 1615-1626

Dobkins J E and Folk R L (1970) Shape development on Tahiti-nui Journal of

Sedimentary Petrology Vol 40 No 2 pp 1167-1203

Folk R L (1955) Student operator error in determining of roundness sphericity and

grain size Journal of Sedimentary Petrology Vol 25 pp 297-301

Fernlund J M R (1998) The effect of particle form on sieve analysis A test by

image analysis Engineering Geology Vol 50 No 1-2 pp 111-124

46

Fernlund J M R (2005) Image analysis method for determining 3-D shape of

coarse aggregate Cement and Concrete Research Vol 35 Issue 8 pp 1629-1637

Fernlund J M R Zimmerman Robert and Kragic Danica (2007) Influence of

volumemass on grain-size curves and conversion of image-analysis size to sieve size

Engineering Geology Vol 90 No 3-4 pp 124-137

Fraser H J (1935) Experimental study of the porosity and permeability of clastic

sediments The Journal of Geology Vol 43 pp 910-1010 ISSN 0022-1376

Hayati Ali Nemati Ahmadi Mohammad Mehdi and Mohammadi Soheil (2012)

American Physical Society Physical review E 85 036310 DOI

101103PhysRevE85036310

Hawkins A E (1993) The Shape of Powder-Particle Outlines Wiley New York

Head K H and Epps R J (2011) Manual of soil Laboratory testing Volum II

Permeability shear strength and compressibility test 3rd

edition Whittles Publishing

Scotland UK 3rd

edition

Holubec I and DrsquoAppolonia E (1973) Effect of particle shape on the engineering

properties of granular soils ASTM STP 523 pp 304-318

Hyslip James P Vallejo Luis E (1997) Fractal analysis of the roughness and size

distribution of granular materials Engineering Geology Vol 48 pp 231-244

Janoo Vincent C (1998) Quantification of shape angularity and surface texture of

base course materials US Army Corps of Engineers Cold Region Research and

Engineering Laboratory Special report 98-1

Jefferies Mike and Been Ken (2000) Soil liquefaction A critical state approach

Taylor amp Francis Group London and New York

Jimenez Jose A Madsen Ole S (2003) A simple formula to estimate settling

velocity of natural sediments Journal of Waterway Port Coastal and Ocean

Engineering Vol 129 No 2 pp 70-78

Johansson Jens and Vall Jakob (2011) Jordmaterials kornform Inverkan paring

Geotekniska Egenskaper Beskrivande storheter bestaumlmningsmetoder

Examensarbete Avdelningen foumlr Geoteknologi Institutionen foumlr Samhaumlllsbyggnad

och naturresurser Lulearing Tekniska Universitet Lulearing (In Swedish)

Kane Joseph W and Sternheim Morton M (1988) Physics John Wiley amp Sons Inc

Third edition

Kolbuszewski J (1948) An experimental study of the maximum and minimum

porosities of sands Proceedings of the Second International Conference on Soil

Mechanics and Foundation Engineering Rotterdam June 21 to 30 Sub-section IIb

pp 158-165

47

Krumbein W C and Pettijohn FJ (1938) Manual of sedimentary petrography

Appleton-Century Crofts Inc New York

Krumbein W C (1941) Measurement and geological significance of shape and

roundness of sedimentary particles Journal of Sedimentary Petrology Vol 11 No 2

pp 64-72

Krumbein W C and Sloss L L (1963) Stratigraphy and Sedimentation 2nd

ed

WH Freeman San Francisco

Kuo Chun-Yi and Freeman Reed B (1998a) Image analysis evaluation of

aggregates for asphalt concrete mixtures Transportation Research Record Vol 1615

pp 65-71

Kuo Chun-Yi Rollings Raymond and Lynch Larry N (1998b) Morphological

study of coarse aggregates using image analysis Journal of Materials in Civil

Engineering Vol 10 No 3 pp 135-142

Lanaro F Tolppanen P (2002) 3D characterization of coarse aggregates

Engineering Geology Vol 65 pp 17-30

Lees G (1964a) A new method for determining the angularity of particles

Sedimentology Vol 3 pp 2-21

Lees G (1964b) The measurement of particle shape and its influence in engineering

materials British Granite Whinstone Federation Vol 4 No 2 pp 17-38

Matsushima Takashi Saomoto Hidetaka Matsumoto Masaaki Toda Kengo

Yamada Yasuo (2003) Discrete element simulation of an assembly of irregular-

shaped grains Quantitative comparison with experiments 16th ASCE Engineering

Mechanics Conference University of Washington Seattle July 16-18

Mitchell James K and Soga Kenichi (2005) Fundamentals of soil behaviour Third

edition WILEY

Mora C F Kwan A K H Chan H C (1998) Particle size distribution analysis of

coarse aggregate using digital image processing Cement and Concrete Research Vol

28 pp 921-932

Mora C F and Kwan A K H (2000) Sphericity shape factor and convexity

measurement of coarse aggregate for concrete using digital image processing Cement

and Concrete Research Vol 30 No 3 pp 351-358

Muskat Morris (1937) The Flow of fluids through porous media Journal of Applied

Physics Vol 8 pp 274

Nearing M A and Parker S C (1994) Detachment of soil by flowing water under

turbulent and laminar conditions Soil Science Society of American Journal Vol 58

No 6 pp 1612-1614

48

Pan Tongyan Tutumluer Erol Carpenter Samuel H (2006) Effect of coarse

aggregate morphology on permanent deformation behavior of hot mix asphalt Journal

of Transportation Engineering Vol 132 No 7 pp 580-589

Pellegrino A (1965) Geotechnical properties of coarse-grained soils Proceedings

International Conference of Soil Mechanics and Foundation Engineering Vol 1 pp

97-91

Pentland A (1927) A method of measuring the angularity of sands MAG MN AL

Acta Eng Dom Transaction of the Royal Society of Canada Vol 21 Ser3xciii

Persson Anna-Lena (1998) Image analysis of shape and size of fine aggregates

Engineering Geology Vol 50 pp 177-186

Powers M C (1953) A new roundness scale for sedimentary particles Journal of

Sedimentary Petrology Vol 23 No 2 pp 117-119

Pye W and Pye M (1943) Sphericity determination of pebbles and grains Journal

of Sedimentary Petrology Vol 13 No 1 pp 28-34

Qazi M A (1975) Flow properties of granular masses A review on the angle of

repose The Arabian Journal for Science and Engineering Vol 1 No 2

Quiroga Pedro Nel and Fowle David W (2003) The effects of aggregate

characteristics on the performance of portland cement concrete Report ICAR 104-1F

Project number 104 International Center for Aggregates Research University of

Texas

Riley N A (1941) Projection sphericity Journal of Sedimentary Petrology Vol 11

No 2 pp 94-97

Rouseacute P C Fennin R J and Shuttle D A (2008) Influence of roundness on the

void ratio and strength of uniform sand Geotechnique Vol 58 No 3 227-231

Santamarina J C and Cho G C (2004) Soil behaviour The role of particle shape

Proceedings Skempton Conf London

Schofield and Wroth (1968) Critical state soil mechanics McGraw Hill

Shaumlfer Michael (2002) Digital optics Some remarks on the accuracy of particle

image analysis Particle amp Particle Systems Characterization Vol 19 No 3 pp 158-

168

Shergold F A (1953) The percentage of voids in compacted gravel as a measure of

its angularity Magazine of Concrete Research Vol 5 No 13 pp 3-10

Shinohara Kunio Oida Mikihiro Golman Boris (2000) Effect of particle shape on

angle of internal friction by triaxial compression test Powder Technology Vol 107

pp131-136

49

Skredcommisionen (1995) Ingenjoumlrsvetenskapsakademinen rapport 395 Linkoumlping

1995

Sneed E D and Folk R L (1958) Pebbles in the Colorado river Texas A study in

particle morphogenesis Journal of Geology Vol 66 pp 114-150

Sperry James M and Peirce J Jeffrey (1995) A model for estimating the hydraulic

conductivity of granular material based on grain shape grain size and porosity

Ground Water Vol 33 No 6 pp 892-898

Sukumaran B and Ashmawy A K (2001) Quantitative characterisation of the

geometry of discrete particles Geotechnique Vol 51 No 7 pp 619-627

Szaacutedeczy-Kardoss E Von (1933) Die bistimmung der abrollungsgrades Geologie

und palaumlontologie Vol 34B pp 389-401 (in German)

Teller J T (1976) Equantcy versus sphericity Sedimentology Vol 23 pp 427-428

Tickell F G (1938) Effect of the angularity of grain on porosity and permeability

bulletin of the American Association of Petroleum Geologist Vol 22 pp 1272-1274

Tutumluer E Huang H Hashash Y Ghaboussi J (2006) Aggregate shape effects

on ballast tamping and railroad track lateral stability AREMA 2006 Annual

Conference Louisville KY

Wadell H (1932) ldquoVolume Shape and roundness of rock particlesrdquo Journal of

Geology Vol 40 pp 443-451

Wadell H (1933) Sphericity and roundness of rock Particles Journal of Geology

Vol 41 No 3 pp 310ndash331

Wadell H (1934) Shape determination of large sedimental rock fragments

The Pan-American Geologist Vol 61 pp 187-220

Wadell H (1935) ldquoVolume shape and roundness of quartz particlesrdquo Journal of

Geology Vol 43 pp 250-279

Wentworth W C (1922a) The shape of beach pebbles Washington US Geological

Survey Bulletin Vol 131C pp 75-83

Wentworth W C (1922b) A method of measuring and plotting the shape of pebbles

Washington US Geological Survey Bulletin Vol 730C pp 91-114

Wentworth W C (1933) The shape of rock particle A discussion Journal of

Geology Vol 41 pp 306-309

Witt K J Brauns J (1983) Permeability-Anisotropy due to particle shape Journal

of Geotechnical Engineering Vol 109 No 9 pp 1181-1187

5

within smaller circles ie at a smaller scale Surface texture is often used to name the

actual quantity The sub-quantities and antonyms are summarized in table 1

Table 1 Sub-quantities describing the particlersquos morphology and its antonym

Scale Quantity Antonym

Large scale Sphericity Elongation

Intermediate scale Roundness Angularity

Small scale Roughness Smoothness

33 FORM (3D)

Wentworth in 1922 (Blott and Pye 2008) was probably one of the first authors on

measure the particle dimensions this consisted on the obtaining of the length of the

tree axes perpendicular among each other (see figure 2) on the tree dimensions (where

agebgec) to obtain the sphericity (equation 1)

Krumbein (1941) develop a rapid method for shape measurement to determine the

sphericity this is done by measuring the longest (a) medium (b) and shorter (c) axes

diameters of the particle it can be seen in figure 2 (Always perpendicular among each

other) The radios ba and cb are located in the chart developed by his own where it

can be found the Intercept sphericity as he called (See figure 3) This chart is an easy

graphical way to relate the dimensions

c2

ba

Figure 2 Measurement of the 3 axes perpendicular among each other (Krumbein 1941)

Figure 3 Detailed chart to determining Krumbein intercept sphericity (Krumbein 1941)

(1)

6

Wadell (1932) defined the sphericity as the specific surface ratio (equation 2) Figure

4 is a schematic representation of the sphere surface and particle surface both particle

and sphere of the same volume

This way to obtain the sphericity is almost impossible to achieve as Hawkins (1993)

declares due the difficulty to get the surface area on irregular solids

Wadell (1934) also defined the sphericity based upon the particle and sphere volumes

as equation 3 (see figure 5)

Wadell (1934) used a new formula simple to manage using the diameters (see figure

6 and equation 4)

Zingg (Krumbein 1941) develop a classification based on the 3 axes relation in this

way it is easy to find out the main form of the particles as a disks spherical blades

S

s

3

CIR

P

V

V

CIR

SV

D

D

Figure 4 Same volume sphere surface (s) and particle surface (S) (modified after Johansson and Vall

2011)

Figure 5 Relation between the volume of the particle and the volume of the circumscribed

sphere (Johansson and Vall 2011)

Figure 6 Figure is showing the relation between the diameter of a circumscribed sphere and the

diameter of a sphere of the same volume as the particle (Johansson and Vall 2011)

(2)

(3)

(4)

7

and rod-like this is summarized on figure 7 Zinggrsquos classification is related with

Krumbein intercept sphericity and the figure 3

In figure 8 the figures 3 and 7 are combined the relation in the two classifications can

be seen it is an easy way to understand the morphology regarding on the a b and c

dimensions

Pye and Pye (1943) in the article ldquosphericity determinations of pebbles and sand

grainsrdquo compare the Wadellrsquos sphericity developed in 1934 (based on the diameter)

with ldquoPebble sphericityrdquo based on an ellipse this last equation (number 5) appears

two years early published by Krumbein (1941) Axis measurement is done as figure 1

denotes for equations 5 trough 12 with exception of equation 8 where the original

document was not possible to obtain

32a

cb

Figure 7 Zinggrsquos classification of pebble shape based on ratios ba and cb (Krumbein 1941)

Figure 8 Classification made by Zinggrsquos and chart to determine sphericity (Krumbein and Sloss 1963)

(5)

8

Sneed amp Folk in (1958) found a relation between the tree dimensional axes called

ldquoMaximum Projection Sphericityrdquo

In a similar way Ashenbrenner (1956) showed his equation at that time named

ldquoWorking Sphericityrdquo

Form or shape factor names are used by authors like Corey (shape factor eq 8) in the

paper published on 1949 Williams (shape factor eq 9) in 1965 Janke (form factor

eq 10) in 1966 and Dobkins amp Folk (oblate-prolate index eq 11) in 1970 (Blott and

Pye 2008)

Aschenbrenner (1956) develop the shape factor by using the relation of the tree axis

but the square of the middle one

3

2

ba

c

))ab((1)bc(16))ab((cb)(11

)ab()bc( 128

22

3 2

ab

c

acb when 1ac

b acb when

b

ac-1 2

22

2

3

cba

c

222

a

c

50c-a

b-a10

2b

ac

(6)

(7)

(8)

(9)

(10)

(11)

(12)

9

Table 2 General overview over different particle shape definitions for 3D sphericity has been compiled

and arranged chronologically

Aspect Name Author Year Based on

Sphericity (3D) Flatness index Wentworth 1922a 3-axes

True Sphericity Wadell 1932 Surface

Operational sphericity Wadell 1932 Volume

Sphericity Wadell 1934 Sphere diameter

Zinggrsquos clasification Zinggrsquos1

1935 3-axes

Intercept sphericity chart Krumbein 1941 3-axes

Pebble sphericity Pye and Pye 1943 3-axes

Corey shape factor Corey2

1949 3-axes

Working sphericity Ashenbrenner 1956 3-axes

shape factor Ashenbrenner 1956 3-axes

Maximum projection sphericity Sneed amp Folk 1958 3-axes

Williams shape factor Williams2

1965 3-axes

Janke form factor Janke2

1966 3-axes

Oblate-prolate index Dobkins amp Folk 1970 3-axes 1) Krumbein and Sloss 1963 2) Blott and Pye 2008

34 FORM (2D)

The technique to measure the sphericity is based in tree dimensions it can be found in

literature some ways to measure the ldquotwo dimensions sphericityrdquo which is simply the

perimeter of the particle projection some authors named ldquoparticle outlinerdquo or

ldquocircularityrdquo

Wadell in 1935 (Hawkins 1993) adopt a conversion of his 1934 3D sphericity

formula (equation 4) to a 2D outline He defined an orientation on the particles and

they were based on the maximum cross sectional area (outline of the particle

projecting the maximum area) The equations show the relation between diameters of

a circle of same area and smallest circumscribed circle

He also used the term ldquodegree of circularityrdquo as the ratio of the perimeter of a circle of

same area and the actual particle perimeter

Tickell in 1931 (Hawkins 1993) used his empirical relation The particle orientation

proposed was a random one It is described by the ratio between the area outline and

the area of smallest circumscribed circle

C

A

D

DC

P

PC C

CA

AC

(13)

(14)

(15)

10

Some other authors has been working with the ldquocircularityrdquo concept and had develop

them own equations as Pentland (1927) relating the area outline and area of a circle

with diameter equal to longest length outline and Cox (Riley 1941) with the ratio

area and perimeter time a constant equations 16 and 17 respectively Both authors did

not define any definite orientation of the grains

Riley (1941) realize the problems that an area perimeter and some other

measurements proposed by the above authors can carry as the time consuming and

tedious work (at that time were not computer all was made by hand) and thatrsquos why

he develop this equation easy to handle called ldquoinscribed circle sphericityrdquo He used

the same particle orientation proposed by Wadell and the relation of diameters of

inscribed and circumscribed circles

Horton 1932 (Hawkins 1993) use the relation of the drainage basing perimeter and

the perimeter of a circle of the same area as drainage basin

Janoo in 1998 (Blott and Pye 2008) develop his general ratio of perimeter to area

Sukumaran and Ashmawy (2001) develop his own shape factor (SF) defined as the

deviation of the global particle outline from a circle Figure 9 can be used as a

reference to determine the items used in the equation 21

N is referred to the number of sampling intervals o radial divisions

C2A

AC

2P

A4C

C

I

D

DC

CD

D

P

PC

A

PC

2

45ordm x N

Particleα

= SF

sumN

1=ii

(16)

(17)

(18)

(19)

(20)

(21)

11

Table 3 General chronological overview of the particle shape definitions for 2D sphericity

Aspect Name Author Year Based on

Circularity (2D) roundness Pentland 1927 area

roundness Cox1

1927 area-perimeter

roundness Tickell2

1931 area

Circularity Horton2

1932 drainage basin

outline circularity Wadell 1935 Circle diameter

degree of circularity Wadell 1935 Perimeter

inscribed circle sphericity Riley 1941 Circle diameter

Circularity Krumbein and Sloss 1963 chart

Janoo 1998 area-perimeter

Shape factor Sukumaran 2001 Segmentation of particle and angles

1) Riley 1941 2) Hawkins 1993

35 ROUNDNESS OR ANGULARITY

Roundness as described in section 32 is the second order shape descriptor Sphericity

lefts beside the corners and how they are this was notice by most of the authors sited

before and they suggested many ways to describe this second order particle property

Roundness is clearly understandable using the figure 10 Particle shape or form is the

overall configuration and denotes the similarities with a sphere (3D) or a circle (2D)

Roundness is concerning about the sharpness or the smoothness of the perimeter (2D)

Surface texture (Barret 1980) is describe as the third order subject (form is the first

and roundness the second) and it is superimposed in the corners and it is also a

property of particles surfaces between corners

Figure 9 Description of the Sukumaran factors to determine the shape and angularity (Sukumaran and

Ashmawy 2001)

12

Wadell (1935) describes his methodology calling it total degree or roundness to

obtain the roundness of a particle using the average radius of the corners in relation

with the inscribed circle diameter (see figure 11) on the equation

In the same study Wadell (1935) has used the equation

This two last equation shows slightly differences on the results (Wadell 1935)

Powers (1953) also published a graphic scale to illustrate the qualitative measure

(figure 12) It is important to highlight that any comparing chart to describe particle

properties has a high degree of subjectivity Folk (1955) concludes that when charts

are used for classification the risk of getting errors is negligible for sphericity but

large for roundness

N

R

r

Rinmax

r

R

NR

inmax

Figure 10 Form (shape) Roundness and Texture graphical description (Bowman et al 2001)

Figure 11 Wadellrsquos method to estimate the roundness corners radius and inscribed circle

(Hawkins 1993)

(22)

(23)

13

Some authors as Russel amp Taylor in 1937 Pettijohn in 1957 and Powers in 1953

developed a classification based on five and six classes (Hawkins 1993) each one

with its own class limits it is important to denote that the way they measure the

roundness is the developed by Wadell (1935) This classification and class limits are

showed in the table 4

Table 4 Degrees of roundness Wadell Values (Hawkins 1993) NA = no-applicable

Grade terms Russell amp Taylor (1937) Pettijohn (1957) Powers (1953)

Class

limits (R)

Arithmetic

midpoint

Class limits

(R)

Arithmetic midpoint Class

limits (R)

Arithmetic

midpoint

Very angular

NA

NA

NA

NA

012-017

014

Angular

000-015

0075

000-015

0125

017-025

021

Subangular

015-030

0225

015-025

0200

025-035

030

Subrounded

030-050

0400

025-040

0315

035-049

041

Rounded

050-070

0600

040-060

0500

049-070

059

Well rounded

070-100

0800

060-100

0800

070-100

084

Krumbein and Sloss (1963) published a graphical chart easy to determine the

sphericity and roundness parameters using comparison See figure 13 (Cho et al

2006)

Figure 12 A Roundness qualitative scale (Powers 1953)

Figure 13 Sphericity and roundness chart (Cho et al 2006) The roundness equation that appears here in

the chart is the wadellrsquos equation number 22

14

Fischer in 1933 (Hawkins 1993) used a straightforward method to quantify roundness

using a central point in the outline and dividing the outline in angles around this point

that were subtended by the straight or non curved parts of the profile were measured

This is illustrated in figure 14

To express the angularity value Fischer used the ratio of angles standing linear parts

on the outlines and concave respectively

Figure 14 left (A) and right (B) gives a similar angularity of approximately 042

using the above equations (Hawkins 1993)

Wentworth in 1922 used the maximum projection to define the position of the particle

to obtain the outline or contour (Barret 1980) The equation reflects the relation of the

diameter of a circle fitting the sharpest corner and the longest axis plus the shortest

axis c (minimum projection)

Wentworth (Hawkins 1993) expressed the roundness as the ratio of the radius of

curvature of the most convex part and the longest axis plus short axis

Actually these last two equations are the same just expressed in different terms when

the particle is in its maximum projection

Dimensions can be seen on figure 15 L and B represents the mayor axis a and

intermediate axis b The intention is to make difference between the 2 and 3

dimensions (L and B are for 2D as a b and c are for 3D)

deg360

ANG

=R

sumPLA

PLA

CON

ANG

ANGR

2)S(L

DR

M

S

B)4(L

RR CON

Figure 14 Fischerrsquos methods of angularity computation (Hawkins 1993)

A=inscribed circle B=circumscribed circle

(24)

(25)

(26)

(27)

15

Wentworth 1919 has a second way to express the roundness called Shape index

(Barrett 1980) and it relates the sharpest corner and the diameter of a pebble trough

the sharpest corner

Wentworth (1922b) used define the roundness as the ratio of the sharpest corner and

the average radius of the pebble

Cailleux (Barrett 1980) relates the radius of the most convex part and the longest

axis

Kuenen in 1956 show his roundness index (Barrett 1980) between the sharpest corner

and the breath axis

Dobkins amp Folk (1970) used a modified Wentworth roundness with the relation of

sharpest corner and inscribed circle diameters

AVG

CON

R

RR

x

s

D

DR

L2

RR CON

B

DR s

i

s

D

DR

3AVGAVG cbaDR2

Figure 15 Description of L and B axes (Hawkins 1993)

(28)

(29)

(30)

(31)

(32)

(33)

16

Swan in 1974 shows his equation (Barrett 1980) relating the sharpest (or the two

sharpest) corner(s) and inscribed circle diameter

Szadeczsky-Kardoss has his Average roundness of outline (Krumbein and Pettijohn

1938) relating the concave parts perimeter and the actual perimeter

Lees (1964a) developed an opposite definition to roundness it means that he

measures the angularity instead of the roundness and he calls it Degree of angularity

Figure 16 shows the items considered when equation 36 applies as the angles (α)

inscribed circle (Rmax-in) and the distance (x) The main formula is

In order to apply the last equation corners needs to be entered in the formula and each

individual result will add to each other to obtain the final degree of angularity

A roundness index appears on Janoo (1998) Kuo and Freeman (1998a) and Kuo et

al (1998b) it is described as

The last equation is on section 34 also because there is not a general agreement on the

definition furthermore some authors had used to define the roughness this is not the

only equation that has been used trying to define different aspects (sphericity

roundness or roughness) but it is a good example of the misuse of the quantities and

definitions

inmaxR

x)180(R

2P

A4R

i

ss

D

DDR

221

100P

PR CON

Figure 16 Degree of angularity measurement technique (Blot and Pye 2008)

(34)

(35)

(36)

(17)

17

Sukumaran and Ashmawy (2001) present an angularity factor (AF) calculated from

the number of sharpness corners Angles βi required to obtain the angularity factor are

shown in figure 9

Sukumaran and Ashmawy (2001) also suggested use not bigger sampling interval of

N=40 because it is the cut off between angularity factor and surface roughness If so

this equation could be used to describe the roughness

Table 5 General chronological overview of the particle roundness

Aspect Name Author Year Based on

Roundness shape index Wentworth 19191

diameter of sharper corner

shape index Wentworth 1922b sharpest corner and axis

roundness Wentworth 1933 convex parts

Fischer 19332

noncurved parts outline

Fischer 19332

noncurved-streigth parts outline

Average roundness of outline

Szadeczsky-Kardoss 19333

convex parts-perimeter

roundness Wadell 1935 diameter of corners

roundness Wadell 1935 diameter of corners

roundness Russel amp Taylor 19372

class limit table

roundness Krumbein 1941 chart

Cailleux 19471

convex parts

roundness Pettijohn 19494 class limit table

roundness Powers 1953 chart and class limit table

Kuenen 19561

axis-convex corner

roundness Krumbein and Sloss 1963 chart

degree of angularity Lees 1964a corners angles and inscribed circle

Dobkins amp Folk 1970 diameter of sharper corner

Swan 19741

diameter of sharper corners

Angularity factor Sukumaran and

Ashmawy 2001

Segmentation of particles and angles

1) Barret 1980 2) Hawkins 1993 3) Krumbein and Pettijohn 1938 4) Powers 1953

sum

sumsumN

1=i

2

i

2

N

1=i

2

i

2N

1=ii

)ordm180 -circleβ( - )(180ordm x 3

)ordm180-circleβ(-)ordm180 -Particleβ(

= AF (37)

18

36 ROUGHNESS OR SURFACE TEXTURE

A third property called texture appears early in the literature with the sphericity and

roundness properties since then texture property was longed described but it was in

accordance with the authors at that time not measurable

Wright in 1955 developed a method to quantify the surface texture or roughness of

concrete aggregate using studies done on 19 mm stones The test aggregates were first

embedded in a synthetic resin The stones were cut in thin sections The sections

projection was magnified 125 times The unevenness of the surface was traced and the

total length of the trace was measured The length was then compared with an uneven

line drawn as a series of chords (see figure 17) The difference between these two

lines was defined as the roughness factor (Janoo 1998)

However with the advance of technology it has become easier measure the roughness

and here is presented some researcherrsquos ideas how this property should be calculated

One technique used by Janoo (1988) to define the roughness can be seen in figure 18a

and is defined as the ratio between perimeter and convex perimeter

The convex perimeter is obtained using the Feretrsquos box (or diameter) tending a line in

between the touching points that the Feretrsquos box describes each time it is turn (figure

18b)

PER

OC

PR

Figure 17 Measurement method for characterizing the surface texture of an aggregate (Janoo 1998)

a) Convex perimeter (CPER) b) Feret measurement Figure 18 a) Convex perimeter (CPER) b) Feret measurement (modified after Janoo 1998)

(38)

a)

b)

19

Kuo and Freeman (1998a) and Kuo et al (1998b) use the roughness definition as the

ratio perimeter and average diameter

Erosion and dilatation image processing techniques are used to obtain the surface

texture Erosion is a morphological process by which boundary image pixels are

removed from an object surface which leaves the object less dense along the

perimeter or outer boundary Dilatation is the reverse process of erosion and a single

dilatation cycle increases the particle shape or image dimension by adding pixels

around its boundary (Pan etal 2006)

The ldquonrdquo erosion and dilatation cycles are not standardized

Mora and Kwan (2000) used the ldquoconvexity ratio CRrdquo (equation 41) and the ldquofullness

ratio FRrdquo (equation 42) in their investigation they are

The convex area is the area of the minimum convex boundaries circumscribing the

particle This is illustrated in the figure 19 The convex area is obtained in a similar

way as the convex perimeter but in this case the area between the original outline and

the convex perimeter is our convex area

AVG

OD

PR

100A

1AARO

CONo A

AR =

CONo A

AR =

Figure 19 Evaluation of area and convex area (Mora and Kuan 2000)

(39)

(40)

(41)

(42)

20

4 TECHNIQUES IN ORDER TO DETERMINE PARTICLE

SHAPE

41 HAND MEASUREMENT

Hand measurement technique was the first used by obvious reasons in order to

improve the accuracy special devices developed as the ldquosliding rod caliperrdquo used by

Krumbein (1941) it works placing the sample on the sliding road calliper as show

figure 20b the length in different positions can be obtain by using the scale provided

in the handle the ldquoconvexity gagerdquo that was actually used by opticians to measure the

curvature of lenses but easily applicable to the particle shape analysis (Wentworth

1922b) works measuring the movement of the central pivot as figure 20a shows (the

two adjacent pivots are invariable) as many the central pivot moves more is the

curvature or the ldquoSzadeczky-Kardossrsquos apparatusrdquo develop in 1933 that traces the

profile of the rock fragment so the outline traced is then analyzed (Krumbein and

Pettijohn 1938) figure 20c show equipment

Another helpful tool to determine the particle dimensions was the ldquocamera lucidardquo to

project the particlersquos contour over a circle scale appearing in Figure 21 thus it is

possible to measure the particlersquos diameter

a)

c) b)

Figure 20 a) convexity gage used to determine the curvature in particle corners (Wenworth 1922b)

b)sliding rod caliper device to measure the particle axis length (Krumbein 1941) and c)Szadeczky-

Kardoss (1933) apparatus it was utilized to obtain the particle outline

Figure 21 Circle scale used by Wadell (1935) to determine particlersquos diameter and roundness

21

42 SIEVE ANALYSIS

Bar sieving eg according to EN 933-31997 can be used to determine simple large

scale properties By combining mesh geometries the obtained results can be used to

quantify flakiness and elongation index ASTM D4791 (Flat and elongated particles

are defined as those coarse aggregate particles that have a ratio of length to thickness

equal to or greater than a specified value such as 51 The index represents the

percentage on weight of these particles) The method is not suitable for fine materials

This due to the difficulty to get the fine grains passed through the sieve and the great

amount of particles in relation to the area of the sieve (Persson 1998) eg EN 933-

31997 related to flakiness index The test is performed on aggregates with grain size

from 4 mm and up to 63 mm two sieving operations are necessary the first separates

on size fraction and the second use a bar sieve after the first sieving the average

maximum diameter of the particles is obtain and with the second sieving (bar sieving)

the shortest axis diameter is found finally with this two parameters the flakiness

index is determined

There are more standards related with the particle shape (see appendix A) but this

above presented are probably the most known using sieve analysis to determine

particlersquos geometrical properties

Sieve analysis is facing the computers age and image analysis sieving research is

taking place (Andersson 2010 Mora and Kwan 2000 Persson 1998) Industry is

also applying the image analysis sieving with decrees on the testing time compare

with the traditional sieving method An inconvenient of image analysis is the error

due the overlapping or hiding of the particles during the capture process but the

advantages are more compare with disadvantages (Anderson 2010)

43 CHART COMPARISON

Charts developed over the necessity of faster results because the long time consuming

required when measuring each particle

Krumbein (1941) present a comparison roundness chart for pebbles which were

measured by Wadellrsquos method because this property was the most difficult to measure

due to the second order scale that roundness represents (See figure 22)

Figure 22 Krumbein (1941) comparision chart for roundness

22

A qualitative chart by Powers (1953) try to include both (sphericity and roundness)

particlersquos characteristics it was divided on six roundness ranges (very angular

angular sub-angular sub-rounded rounded and well rounded) and two sphericity

series (high and low sphericity) This chart was prepared with photographs to enhance

the reader perspective (See figure 23)

A new chart including sphericity and roundness appear this time it was easier to

handle the two mean properties of particlersquos shape furthermore there was included

the numerical values that eliminated the subjectivity of qualitative description The

chart is based on Wadellrsquos definitions (Krumbein and Sloss 1963) (See figure 24)

Folk (1955) worried about the personrsquos error on the chartrsquos comparison studied the

determination of sphericity and angularity (he used the Powers 1953 comparison

chart) he found that the sphericity determination by chart comparison has a negligible

error while the roundness he concluded it was necessary to carry out a more wide

research due the high variability show by his study

Figure 23 Powers (1953) qualitative shpericity-roundness chart

Figure 24 Sphericity-roundness comparison chart (Krumbein and sloss 1963)

23

44 IMAGE ANALYSIS

Image analysis is a practical method to use for shape classification since it is fast and

can be automated Different techniques appear to process these images among them

are

o Feret Diameter the Feret diameter is the longitude between two parallel lines

this lines can rotate around one particle or outline to define dimensions as it

is shown in figure 25 these method is not a fine descriptor but as it was say

above it is a helpful tool to determine diameters (Janoo 1988)

o Fourier Mathematical Technique It produces mathematical relations that

characterize the profile of individual particles This method favours the

analysis of roughness and textural features for granular soils The problem in

the methodology remains in the re-entrant angles in order to complete the

revolution (Bowman et al 2001) see figure 26

o Fractal Dimension Irregular line at any level of scrutiny is by definition

fractal (Hyslip and Vallejo 1997) Figure 27 shows fractal analysis by the

dividing method The length of the fractal line can be defined as

N

1n

nn0 )nsinbncosa(a)(R

RD1n)(P

Figure 25 Feret measurement technique is defined by two parallel lines turning

around the particle to define the shortest and longest Feret diameter (Janoo 1988)

Figure 26 Fourier technique with two radiuses at one angle (Bowman et al 2001)

(43)

(44)

24

o Orthogonal image analysis This technique is basically the use of two images

orthogonal between them to acquire the three particle dimensions (Fernlund

2005) any of the above techniques can be used in this orthogonal way

o Laser Scanning Technique this kind of laser scanning 3D is one of the most

advanced techniques In figures 28a) we have the laser head scanning the rock

particles the particles have control points in order to keep a reference point

when move them to scan the lower part in figure 28b) we can see the laser

path followed (Lanaro and Tolppanen 2002)

Another technique is the Laser-Aided Tomography (LAT) in this case a laser sheet is

used to obtain the particles surveying (see figure 29) This technique is different and

has special requirements as to use liquid with same refractive index as the particles

particles must let the laser or certain percent of light go through (Matsushima et al

2003)

a) b)

Figure 27 Fractal analysis by the dividing method at different scrutiny scale (Hyslip and Vallejo 1997)

Figure 28 a) Scanning head b) scanning path (Lanaro and Tolppanen 2002)

Figure 30 3D scan completed ready to

use for any further measure

(Matsushima et al 2003)

Figure 29 LAT scaning particles

(Matsushima et al 2003)

25

Both 3D techniques obtain the particle shape that is later used to achieve measures as

we can see in figure 30

All these previous techniques are easily written in codes or scripts to be interpreted in

a digital way obtaining the desired measurement but there are some interesting points

in the image analysis regarding on the errors involve among them are image

resolution and orientation of the particles orientation is not relevant when it is

random and large number of particles are involve resolution have an influence on the

accuracy (Zeidan et al 2007)

When resolution is increase more accuracy is obtain and the object representation

match better with the real form in the other hand more resolution means more

spending on memory and time thus resolution needs to be according with the goal

and precision needed in any work (Schaumlfer 2002)

Schaumlfer (2002) conclude that attributes like length when measuring digital images

present relative high errors It can be vanish or at least diminish using high resolution

just for diameter but not for perimeter that keep the error as big as initially Johansson

and Vall (2011) obtain similar results when 3 different resolutions were used in the

same particle obtaining an unstable output for those termsquantities that involve the

perimeter Thus all quantities relating the perimeter should be treated with care

5 EFFECT OF SHAPE ON SOIL PROPERTIES

51 INTRODUCTION

In laboratory test on the effect on particle size on basic properties has been

investigated in several studies this relation has been discussed and various

mechanisms had been proposed to explain the behaviour of the soil in dependency

also with the shape Basically there are two mechanisms proposed The arrangement

of particles and the inter-particle contact (Santamarina and Cho 2004) and

subsequence breakage

The arrangement of particles

Arrangement of the particles can be presented in three different forms loose dense

and critical this arrangement determines the soil properties (eg density increase with

more dense arrangement) Loose and dense states are easy understandable when

figure 31 is explained while in the upper part of the figure the particles are arranged

using the minimum space needed in the lower part a span is created using the flaky

particle as a bridge this phenomena is known as ldquobridgingrdquo Bridging can produce

different geotechnical results when just the shape of the particle is changed eg void

ratio (Santamarina and Cho 2004) Particles are able to rearrange this could be done

applying pressure (energy) to the soil the pressure (energy) will create such forces

that soil particles will rotate and move (see figure 34) finishing in a more dense state

26

A loose soil will contract in volume on shearing and may not develop any peak

strength (figure 32 left) In this case the shear strength will increase gradually until

the residual shear strength is revealed once the soil has ceased contracting in volume

A dense soil may contract slightly (figure 32 right) before granular interlock prevents

further contraction (granular interlock is dependent on the shape of the grains and

their initial packing arrangement) In order to continue shearing once granular

interlock has occurred the soil must dilate (expand in volume) As additional shear

force is required to dilate the soil a peak shear strength occurs (figure 32 left) Once

this peak shear strength caused by dilation has been overcome through continued

shearing the resistance provided by the soil to the applied shear stress reduces

(termed strain softening) Strain softening will continue until no further changes in

volume of the soil occur on continued shearing Peak shear strengths are also

observed in overconsolidated clays where the natural fabric of the soil must be

destroyed prior to reaching constant volume shearing Other effects that result in peak

strengths include cementation and bonding of particles The distinctive shear strength

called the critical state is identified where the soil undergoing shear does so at a

constant volume (Schofield and Wroth 1968)

The inter-particle contact

For frictional soil ie coarse grained soil the friction between particles is the

dominating factor for strength Materials usually consisting of coarse grains (diameter

Figure 31 Bridging effect when flaky particles are combined in the bulk material (Santamarina and

Cho 2004)

Figure 32 The left part of the figure show a typical behaviour of loose and dense material over shear stress

while at the right the figures illustrate the typical volume changes

27

gt 006mm) behave as a frictional soil it means that the strength of coarse soils (silt

sand gravel etc) comes from an inter-particle mechanical friction thus ideally they

do not have traction strength In figure 33 the inter-particle contact is illustrated here

the pressure (P) is applied and two more components are found the normal load (N)

and the tangential load (T) described as the friction coefficient (μF) The forces stand

in equilibrium (Johansson and Vall 2011)

When particles equilibrium is disturbed (friction coefficient is not enough to keep

particles unmoved) the rotation is imminent and it is necessary in order to compact

the soil in figure 34 can be seen that the arrangement is a fact that inhibit or allow this

rotation and the shape in the 3 different scales are also factors because the more

spherical andor more rounded andor less roughness more easy is the rotation

(Santamarina and Cho 2004)

Breakage

Breakage is a side effect of the inter-particle contact and rotation when pressure

exceed the rock strength it can happened when the particles are tight together and

there is not enough space to rotate it is more obvious in angular particles (mesh form)

or as in figure 31 where the flaky particle ldquobridgingrdquo is not able to rotate but it can

brake by the pressure increase Yoginder et al (1985) notice that the angular particle

break during his experiments and they turn more rounded changing the original size

and form configuration at the same time there was a soil properties loosening

Figure 33 Inter-particle contact and forces acting (Axelsson 1998)

Figure 34 Rotation inhibition by the particles compaction or low void ratio (Santamarina and Cho 2004)

28

52 INFLUENCE OF SIZE AND SHAPE

Wenworth (1922a) and Pellegrino (1965) among others suggest that agent transport of

the rocks (rigor of transport temperature and moisture changes etc) determine its

shape but also the particle genesis itself (rock structure mineralogy hardness etc) It

is not possible to determine the shape of the particles based on the agent transport or

genesis but generally a shape behaviour is expected according to Mitchell and Soga

(2005) specially when the particle size is in the clay size (gt2μm) The shapes of the

most common clay minerals are platy (figure 35) with some exceptions (eg

halloysite occurs as tubes kaolinite are large thick and stiff Smectites are composed

of small very thin and filmy particles Illites are intermediate between kaolinite and

smectite and attapulgite occurs in lathlike particle shapes) Some clay minerals

photographs are presented in figure 35

Figure 35 Clay mineral shape a) hallosite b) Kaoline c) Smactites d) Illites and e) attapulgite (Modified

from Mitchell and Soga 2005)

Figure 36 Particle size range in soils Generally the particles of clay size are plate shaped (Mitchell and

Soga 2005)

a) b) c)

e) d)

29

53 VOID RATIO AND POROSITY

The void ratio (e) is the ratio of the volume of voids to the volume of solid it is

defined by the equation

Porosity (n) is the ratio of the volume of voids to the total volume of the soil it is

represented by the equation

Holubec and DrsquoAppolonia (1973) found a relation between the void ratio and

sphericity (referred in the paper as coefficient of angularity ratio of particle surface

and equivalent sphere surface) their results show that the maximum and the minimum

void ratio increases as the shpericity decreases In this study the surface was obtained

for an indirect method based on the permeability developed by Hoffman in 1959

described in the same document Rouseacute et al (2008) defined the roundness as

Wadell (1935) and he found it as an important factor controlling the minimum and

maximum void ratios Some other authors as Youd (1973) and Cho et al (2006)

conclude the same minimum and maximum void ratios increase when sphericity and

roundness decrease Another interesting result (all above authors) was the bigger

influence of the form (sphericity circularity) and roundness on the maximum void

ratio The change of the maximum void ratio is more pronounced than the change of

the minimum void ratio when the form and roundness changes (See figure 39)

Particles arrangement and interlocking are probably the factor that controls the void

ratio bridge effect permit the existence of void among the particles while interlocking

allowed the particles to form arches avoiding the possibility to rotate and stay in a

more stable configuration eg as it happens with marbles

Figures 36 37 and 38 shows proposed empirical relationships between void ratio and

shape from tables 5 and 6 (graphically the scale goes from 0 to 1 when cero mean

high angularity shpericity or circularity and one means low angularity circularity or

sphericity) Holubec and DrsquoAppolonia (1973) data was taken to obtain a power curve

and describe a tendency Santamarina and Cho (2004) show Youd equations in the

original paper Youd (1973) never presented the equation but it is easy to use the

information to draw a trend

The graphics presented in this document (figures 36 37 and 38) must be used with

certain reserves due the fact that the original data was modified in order to fit all

information in one graphic what the figures shows is just the general trend of the

behaviourrsquos material regarding on the shape If more accurate description and

information is required the author recommends consulting the reference data In the

same way equations from Holubec and DrsquoApollonia (1973) and Youd (1973) were not

presented by the authors but the use of the information was taken in order to build up

those equations on tables 6 and 7

S

V

V

V

= e

V

V

=nV

(45)

(46)

30

Table 6 Minimum void ratio equations regarding on the quantity (Ψ for sphericity C for circularity R

for roundness SF for Sukumaran shape factor and AF for Sukumaran angularity factor)

EQUATION NUMBER REFERENCE

Figure 34 (left)

4340

minΨ45490e =

47

Holubec amp DrsquoAppolonia 1973 (Ψ

was obtained using equation 2)

SF06340

mine021903180e +=

48

Sukumaran amp Ashmawy 2001 (SF

obtained using equation 21)

C05101emin

= 49

Cho etal 2006 (C obtained using

figure 12)

Figure 34 (right)

1

minR08203590e +=

50

Youd 1973 (R obtained from figure

11 and table 3)

R34080emin

= 51

Cho et al 2006 (R obtained using

figure 12)

1

minR05104330e +=

52

Rouseacute et al 2008 (R obtained by

equation 21)

AF02330

mine372004160e +=

53

Sukumaran amp Ashmawy 2001 (AF

obtained using equation 37)

Table 7 Maximum void ratio equations regarding on the quantity (Ψ for sphericity C for circularity R

for roundness SF for Sukumaran shape factor and AF for Sukumaran angularity factor)

EQUATION NUMBER REFERENCE

Figure 35 (left)

51520

max Ψ61120e = 54

Holubec and DrsquoAppolonia 1973 (Ψ

was obtained using equation 2)

SF1190

max e0016907180e += 55

Sukumaran amp Ashmawy 2001 (SF

obtained using equation 21)

C86061emax = 56

Cho etal 2006 (C obtained using

figure 12)

Figure 35 (right)

1

max R1505540e += 57

Youd 1973 (R obtained from figure

11 and table 3)

R62031emax= 58

Cho et al 2006 (R obtained using

figure 12)

1

max R107106150e += 59

Rouseacute et al 2008 (R obtained by

equation 21)

AF0530

max e12506090e += 60

Sukumaran amp Ashmawy 2001 (AF

obtained using equation 37)

Comparing figures 37 and 38 (minimum and maximum void ratio) it can be seen on

the right scheme of both figures 37 and 38 (when the factor is roundnessangularity)

that all the empirical relations has a common initial point close to 1 (it means that

particles are well rounded) while this common agreement disappear when the

roundness factor decreases (when the particles become more angular) Same figures

(37 and 38) on the left graphs (when the factor is sphericitycircularityshape) do not

present the same behaviour in fact there is more disperse initial point close to 1(when

the particles tend to be more sphericalcircular)

31

In Figure 39 the Δe (emax-emin) has been plotted to show how the maximum void ratio

and the minimum void ratio has different rate change when the particle shape

changes Maximum void ratio increases more than minimum void ratio when the

particle shape becomes less spherical andor more angular Comparing figure 39 left

and right graphics it can be seen that right present a common initial point when the

quantity (roundnessangularity) is close to one while in the left graphic the initial

point is more disperse Both ending points in both graphics (close to zero) are

dispersed

Figures 37 38 and 39 present the same behaviour right graphics (when the factor is

roundness angularity) in each figure have an initial common point while the left

graphics do not (when the factor is sphericity circularity shape)

Figure 37 Minimum void ratio based upon the relation of shape factor proposed by the authors indicated

in the figure

Figure 38 Maximum void ratio based upon the relation of shape factor proposed by the authors indicated

in the figure

04

06

08

1

12

14

16

18

2

005

015

025

035

045

055

065

075

085

095

Factor (roundness angularity)

min

imu

m v

oid

rati

o

Youd 1973 roundness

Rouse 2008 roundness

Cho 2006 roundness

Sukumaran 2001 AF

03

04

05

06

07

08

09

1

11

12

13

05

015

025

035

045

055

065

075

085

095

Factor (sphericity circularity shape)

min

imu

m v

oid

rati

oHolubec 1973 sphericity

Cho 2006 circularity

Sukumara 2001 SF

05

07

09

11

13

15

17

19

21

00

150

250

350

450

550

650

750

850

95

Factor (sphericity circularity shape)

Maxim

um

vo

id r

ati

o

Holubec 1973 sphericity

Cho 2006 circularity

Sukumara 2001 SF

05

1

15

2

25

3

35

005

015

025

035

045

055

065

075

085

095

Factor (roundness angularity)

Maxim

um

vo

id r

ati

o

Youd 1973 roundness

Rouse 2008 roundness

Cho 2006 roundness

Sukumaran 2001 AF

32

54 ANGLE OF REPOSE

The angle of repose of a granular material is the steepest angle of descent or dip of the

slope relative to the horizontal plane when material on the slope face is on the verge

of sliding as show in figure 40

According to Qazi (1975) there are five types of forces which may act between the

particles in soils

1 Force of friction between the particles

2 Force due to presence of absorbed gas andor moisture of particle

3 Mechanical forces caused by interlocking of particles of irregular shape

4 Electrostatic forces arising from friction between the particles themselves and

the surface with which they come in contact

5 Cohesion forces operating between neighbouring particles

Rouseacute et al (2008) found a decrease of angle of repose with increase roundness

based upon ASTM C1444 test (Standard Test Method for Measuring the Angle of

Repose of Free-Flowing Mold Powders) The method consist in pouring sand on a

surface cover by paper trough a funnel of specific dimensions (the nozzle diameter

depend on the sandrsquos particle size) from an altitude of 15 inches (381 mm) The sand

is release from the funnel until the peak of the cone formed by the sand stops the flow

The repose angle is obtained with the equation

H represent the 15 inches D and d represent the diameter of the cone formed by the

sand and the diameter of the funnel respectively

Figure 39 Maximum minus minimum void ratio based upon the relation of shape factor proposed by the

authors indicated in the figure

0

01

02

03

04

05

06

07

08

09

1

005

015

025

035

045

055

065

075

085

095

Factor (sphericity circularity shape)

Maxim

um

- M

inim

um

Vo

id r

ati

oHolubec 1973 sphericity

Cho 2006 circularity

Sukumara 2001 SF

0

02

04

06

08

1

12

14

16

18

005

015

025

035

045

055

065

075

085

095

Factor (roundness angularity)

Maxim

um

- M

inim

um

Vo

id r

ati

o

Youd 1973 roundness

Rouse 2008 roundness

Cho 2006 roundness

Sukumaran 2001 AF

dD

H2

tan=φ1

rep(61)

33

Rouseacute (2008) shows an empirical relation to obtain the angle of repose based on the

roundness of the particles

55 SHEAR STRENGTH

The MohrndashCoulomb failure criterion represents the linear envelope that is obtained

from a plot of the shear strength of a material versus the applied normal stress This

relation is expressed as

where τ is the shear strength σn is the normal stress co is the intercept of the failure

envelope with the τ axis and is the slope of the failure envelope The quantity c is

often called the cohesion and the angle is called the angle of internal friction

Studies show that the internal friction angle (under drained triaxial tests) increases

more rapidly on those materials having higher angularity increasing the relative

density The internal friction angle is a function of the relative density and the particle

shape (Holubec and DrsquoAppolonia 1973)

Chan and Page (1997) found in a study made with dry copper (using different shapes

and sizes ranging from 180 to 106 μm) using a direct shear test (ring share test) that

the internal friction angle increases as the angularity increases

Shinohara et al (2000) did some experiments with steel powder different shapes

using a triaxial cell in the test Shinohara never used the roundness or angularity on

the work but apply the shape factor (relation long axisshort axis) and the results were

that as this relation deviate from factor 1 the internal friction angle increases

The following empirical relations were found in the literature showing the behaviour

of the friction angle (obtained under different conditions)

)tan( noc

Figure 40 Representation of the angle of repose

(63)

(62)

34

Cho et al (2006)

(64)

(R is obtain by comparing the Krumbein chart figure 13)

Rouseacute (2008)

(65)

(66)

(R is defined using Wadell equation 22)

In figure 41 the suggested empirical relations above and lines constructed using

author data from Holubec and DrsquoAppolonia (1973) and Sukumara and Ashmawy

(2001) are plotted together to display the general trend on the particle shape and

friction angle relation Sukumaran reports two lines one based on the shape factor

(SF) and the second referring the angularity factor (AF) Sukumaran performed the

tests at constant volume

The scale used for Holubec and DrsquoAppolonia (1973) have lower and upper limits of 1

and 2 respectively (angularity form) and a scale change was applied to be able to

presented in the actual figure 41 As in the previous section (52) the author

recommend to use the original data from the references due that the figure just follows

the general trend of the behaviourrsquos particle regarding on the shape

Figure 41 The changes on the internal friction angle shows a general increase when the particle roundness

becomes angular or in the case of Sakamuran less spheric (Shape factor SF)

35

Barton and Kjaernsli (1981) suggested a model (equation 67) to predict the peak

friction angle (φrsquo) based upon numerous trixial and direct shear data tests

where

Se equivalent strength of particle

Re equivalent roughness of particle

φb basic friction angle (obtained from basic tilting test)

σn normal load

The information required for the model is (1) the uniaxial compressive strength of the

rock (2) the d50 particle size (mesh size where 50 of the particles pass through)

required to define Se (figure 42) (3) the degree of particle roundness and (4) the

porosity following compaction All data can be estimated by simple index tests

Barton and Kjaernsli (1981) suggest that particle size and sample scale has an effect

on the friction angle and includes them to obtain the equivalent strength (Se) figure 42

shows the method to obtain this value Compressive strength (σc) was chosen to be the

factor affecting the scale because micro fractures influence this property while

samples are bigger more micro fractures contain and its compressive strength reduces

The equivalent roughness is obtain using figure 43 where is required to know the

porosity (n) and the origin of the particles (a small chart is provided in the same figure

to compare the particles profile)

b

n

ee

SLogR

Figure 42 Method of estimating Equivalent Strength (Se) of rockfill based on uniaxial compressive strength

(σc ) and d50 particle size (Barton amp Kjaernsli 1981)

(67)

36

56 SEDIMENTATION PROPERTIES

A particle released in a less dense Newtonian fluid initially accelerate trough the fluid

due to the gravity Resistances to deformation of the fluid transmitted to the particle

surface drag generate forces that act to resist the particle motion The force due to the

weight (Fw) can be written as

Where ρp ρ are density of the particle and fluid (water) respectively g is the

gravitational force and Vp is the volume of the particle

And the resistance force (FD) is

Where CD is the dimensionless drag coefficient W is the weight of the particle and A

is the cross section area

Particlersquos shape has been assumed to be spherical when equations are applied on the

settling velocity Correlation deviates when particle shape departs from spherical form

Figure 43 Method of estimating Equivalent Roughness (Roe) based on porosity of rockfill

origin material degree of roundedness and smoothness of particle (Barton amp Kjaernsli 1981)

PPW ρ)gV(ρF

A2

WρCF

2

DD

(68)

(69)

37

(Dietrich 1982) and it is known that natural particles depart from spherical form

thus it is evident that this departure would have consequences

The below equation is proposed to account the shape (in this case the Corey shape

factor equation 8) in the settling velocity (Jimenez and Madsen 2003)

Jimenez and Madsen (2003) Dietrich (1982) Briggs and McCulloch (1962) and

others were working in the hydraulic shape of particles to solve problems as sediment

transport It is obvious that the equation presented and the researcherrsquos investigation

works under certain conditions (eg grain size between 0063-1 mm)

Dietrich (1982) suggests an empirical relation that accounts settling velocity size

density shape and roundness of a particle

R1 R2 and R3 are fitted equations for size and density shape and roundness

respectively

57 HYDRAULIC CONDUCTIVITY PERMEABILITY

Darcyrsquos Law Permeability is one component of Darcyrsquos law Darcys law is a simple

proportional relationship between the instantaneous discharge rate through a porous

medium the viscosity of the fluid and the pressure drop

The total velocity Ve is equal to the product of the permeability of the medium

(porous media) k the pressure drop ∆p all divided by the viscosity μ (Muskat

1937)

Darcys law is only valid for slow viscous flow most groundwater flow cases fall in

this category Typically Darcyrsquos law is valid at any flow with laminar flow (see figure

44)

Reynoldrsquos number (Laminar and turbulent Flow) Typically any laminar flow is

considered to have a Reynoldrsquos number less than one and it would be valid to apply

Darcys law Experimental tests have shown that flow regimes with Reynolds numbers

1

ND

S

S

ZY

gd1s

WW

NDN

gd)1s(4

dS

2R1R

3 10RW

pk

Ve

(70)

(71)

(72)

(73)

38

up to 10 may still be Darcian (laminar flow) as in the case of groundwater flow The

Reynolds number (a dimensionless parameter) for porous media flow is typically

expressed as

where ρ is the density of water (units of mass per volume) υ is the specific discharge

(with units of length per time) d is a representative average grain diameter for the

porous media (often taken as the 30 passing size from a grain size analysis using

sieves - with units of length) and μ is the viscosity of the fluid (Muskat 1937)

Shape effects Permeability as Head and Epps (2011) suggested is affected by the

shape and texture of soil grains Elongated or irregular particles create flow paths

which are more tortuous than those spherical particles Particles with a rough surface

texture provide more frictional resistance to flow Both effects tend to reduce the

water flow through the soil

Kozeny-Carman empirical relation accounts for the dependency of permeability on

void ratio in uniformly graded sands serious discrepancies are found when it is

applied to clays due the lack of uniform pores (Mitchell and Soga 2005)

There are various formulations of the Kozeny-Carman equation one published by

Head and Epps (2011) takes the void ratio e the specific surface area Ss and an

angularity factor F into account of permeability k

The angularity factor F considers the shape of the particles and ranges from 11 for

rounded grains 125 for sub rounded to 14 for angular particles The specific surface

Ss is defined as

d1 and d2 represent the maximum and minimum size particle in mm

Kane amp Sternheim (1988) suggest that the inclusion of the shape factor (F) has

probably the background on the Reynolds number due this factor is dependent

significantly on the shape of the obstacles and Reynolds number determines the

presence of laminar or turbulent flow Figure 44 show how the laminar flow has low

energy dissipation while turbulent flow (eg the roughness and path tortuosity) has

high energy dissipation

e1

e

FSs

2k

3

2

dRe

21

6

ddSs

(74)

(75)

(76)

39

According to Nearing and Parker (1994) the amount of soil detached during laminar

and turbulent flow is dependent on each soil and also greater on turbulent flow due the

greater shear strength generated during this kind of flow this could suggest the

greater erosion when turbulent flow is present

58 LIQUEFACTION

Soil liquefaction is a phenomenon in which soil loses much of its strength or stiffness

for a generally short time by earthquake shaking or other rapid loading Static and

dynamic liquefactions occur been the second one the most regular known

Liquefaction often occurs in saturated soils that is soils in which the space between

individual particles is completely filled with water This water exerts a pressure on the

soil particles that influences how tightly the particles themselves are pressed together

Shaking or other rapid loading can cause the water pressure to increase to the point

where the soil particles can readily move with respect to each other (Jefferies and

Been 2000)

Jefferies and Been (2000) state that it is clear that minor variation in intrinsic

properties of sand have major influence on the critical state These might be variations

on grain shape mineralogy grain size distribution surface roughness of grains etc

Yoginder et al (1985) found that substantial decrease on liquefaction resistance

occur with increase in confining pressure for rounded and angular sands (1600 kPa)

also rounded sands show an rapidly build up of resistance against liquefaction with

increasing density while angular tailing sand in contrast show such rapid increase

only at low confining pressures At low confining pressure angular material is more

resistant to liquefaction Probably the breakage of the corners on the angular particles

in tailings is ruling the lost in resistance at high confining pressures (sieve analysis

Figure 44 The figure show the extremes of flow behaviour First turbulent conditions where the flow is

essentially random and unpredictable and second the well defined Laminar flow conditions

40

after test identify the breakage of angular particles while on rounded particles the

sieve analysis was practically the same)

59 GROUNDWATER AND SEEPAGE MODELLING

In groundwater flow the particlersquos shape affects the soilrsquos pore size distribution

hence the flow characteristics (Sperry and Peirce 1995) Tortuosity and permeability

(also see section 57) are two significant macroscopic parameters of granular medium

that affect the passing flow (Hayati et al 2012) Current models incorporating the

effects of particle shape have failed to consider irregular particles such as those that

would prevail in a natural porous medium (Sperry and Peirce 1995)

Hayati et al (2012) suggested based on his results that tortuosity effect converge

when the porosity increases indicating that the shape have dominance at low and mid

porosity ranges

Sperry and Peirce (1995) research conclusions suggest that particle size and porosity

are more important predictors for hydraulic conductivity explaining the 69 of the

variability but particle shape appears to be the next most important This however

apparently comprises particles larger than 295-351 μm Differences for particle size

295-351 μm and smaller are not detectable Another interesting result in the research

was the interaction effect of the particle size and particle shape It suggests a different

packing configuration for particles of the same shape but different size (scale

dependent)

6 DISCUSSION

61 TERMS QUANTITIES AND DEFINITIONS

In order to describe the particle shape in detail there are a number of terms quantities

and definitions (qualitative and quantitative) used in the literature (eg Wadell 1932

1934 Krumbein 1941 Sneed amp Folk 1958) All mathematical definitions

(quantitatives) are models used to simplify the complexity of shape description Some

authors (Mitchell amp Soga 2005 Arasan et al 2010) are using three sub-quantities

one and each describing the shape but at different scales The terms are

morphologyform roundness and surface texture (figure 1) The three sub-quantities

are probably the best way to classify and describe a particle because not a single

definition can interpret the whole morphology Common language is needed when

descriptors are explained and these three scales represent an option It is evident in

the reviewed literature that many of the shape descriptors are presented with the same

name but also that there is not a clear meaning on what this descriptor defines eg

when there is no upper limit in the roundness does it means that the angularity never

ends Could they be more and more angular Probably they could be on theory but

not in reality

41

62 PROPERTIES

Trough various articlersquos review done in the present investigation it is recognized that

the particlersquos shape has an effect on the material properties among these are

1 Porosity (Tickell 1938 Fraser 1935 Kolbuszewski 1948) and void ratio

(Cho et al 2006 Shergold 1953 Rouseacute et al 2008 Santamarina and Cho

2004)

2 Permeability (Witt and Brauns 1983)

3 Internal friction angle (Shinohara et al 2000 Chan and Page 1997

Cheshomi et al 2009)

4 Density (Youd 1973 Holubec and DrsquoAppolonia 1973)

5 Drag coefficient Hydraulics (Briggs and McCulloch 1962)

In Table 5 is a short resume of the properties and shape effect found in peer review

articles trough different journals Most of the reviewed articles based its research on

uniform graded sands

Table 8 Compilation of properties influenced by particle shape

Repose

angle

Friction

angle

Porosity and

Void ratio Density Permeability

Settling velocity

Drag coefficient Deformation

Sphericity (3D)shape factor

NI x x x x x x

Circularity (2D)

NI x x x x NI NI

Roundness x x x x NI NI x

x influence

NI no information available

Shape of particles has an effect on the arrangement producing bridging or avoiding

the rotation of the particles and the resulting geotechnical property is affected eg

including flaky particles can result in a higher void ratio due the bridging effect

(Santamarina and Cho 2004) and depending on the loads even the size distribution is

changed due the breakage (Yoginder et al 1985) in similar way angular particles

produce higher void ratio due the avoided possibility of the particles to rotate and

compact

The influence of the chosen shape descriptor appears in this review to have minor

influence on the soil properties in the reviewed studies except on the void ratio and

the friction angle Influence of particle shape in some cases is hider by other factors

(eg size distribution) also the particle shape probably does not have influence when

particle size is in the clay order (eg hydraulic conductivity) the reason could be due

to forces as electrostatic or capillarity become more important at this level

Among the shape descriptors some are chosen more often in literature (eg aspect

ratio) there is no apparent scientific basis to use it (probably due to the simplicity of

the measurement it becomes one of the most use) but there are still some other

descriptors that may or may not show better correlation with the soil properties

Instead empirical relations had been developed regarding roundness or shape to

describe the soil behaviour it is clear that the mechanism behind the results is still not

completely understood

42

There is necessity to define the best(s) shape descriptor(s) to be used for particular

geotechnical properties

63 IMAGE ANALYSIS

Many image analysis techniques had been used to describe the particle shape eg

Fourier analysis fractal dimension tomography etc (Hyslip and Vallejo 1997) but

there is not agreement on the usage or conclusion to ensure the best particle descriptor

for geotechnical applications

There are several shape descriptors and also various techniques to capture the

particles profile (3-dimensions 3-dimension orthogonal and 2-dimensions) Each

technique presents advantages and disadvantages 3-dimensions is probably the

technique that provide more information about the particle shape but the precision

also lies in the resolution the equipment required to perform such capture could be

more or less sophisticated (scanning particles laying down in one position and later

move to complete the scanning or just falling down particles to scan it in one step)

3-dimensions orthogonal this technique use less sophisticated equipment (compare

with the previous technique) but its use is limited to particles over 1cm also

information between the orthogonal pictures is not capture 2-dimensions require non

sophisticated equipment but at the same time the shape information diminish compare

with the previous due the fact that it is possible to determine only the outline as the

particle measurements are performed in 2-dimensions it is presumed that they will lie

with its shortest axis perpendicular to the laying surface when they are flat but when

the particle tends to have more or less similar axis the laying could be random

Advantages on the use of image analysis are clear there is not subjectivity because it

is possible to obtain same result over the same images Electronic files do not loose

resolution and it is important when collaboration among distant work places is done

files can be send with the entire confidence and knowing that file properties has not

been changed Technology evolutions allowed to work with more information and it

also applies to the image processing area were the time consumed has been shortened

(more images processed in less time)

One important aspect in image analysis is the used resolution in the analysis due the

fact that there are measurements dependent and independent on resolution Thus

those dependent measurements should be avoided due the error included when they

are applied or avoid low resolution to increase the reliability Among these

parameters length is the principal parameter that is influences by resolution (eg

perimeter diameter axis etc) Resolution also has another aspect with two faces

quality versus capacity more resolution (quality) means more storage space a

minimum resolution to obtain reasonable and reliable data must be known but it

depend on each particular application

43

64 APPLICATIONS

Quantify changes in particles in the authorrsquos thought is one of the future applications

due the non-invasive methods of taking photographs in the surface of the damrsquos slope

rail road ballast or roads Sampling of the material and comparing with previous

results could show volume (3D analysis) or area (2D analysis) loss of the particles as

well as the form roundness and roughness This is important when it has been

suggested that a soil or rock embankment decrees their stability properties (eg

internal friction angle) with the loss of sphericity roundness or roughness

Seepage stock piling groundwater etc should try to include the particle shape while

modelling seepage requires grading material to not allow particles move due the

water pressure but in angular materials as it is known the void ratio is great than the

rounded soil it means the space and the possibilities for the small particles to move

are greater stock piling could be modelled incorporating the particle shape to

determine the binrsquos capacity when particle shape changes (void ratio changes when

particle shape changes) Modelling requires all information available and the

understanding of the principles that apply

Industry is actually using the particle shape to understand the soil behaviour and

transform processes into practical and economic image analysis has been included in

the quality control to determine particle shape and size because the advantages it

brings eg the acquisition of the sieving curve for pellets using digital images taken

from conveyor this allows to have the information in a short period of time with a

similar result at least enough from the practical point of view as the traditional

sieving

7 CONCLUSIONS

The conclusions of this literature review are

It has been shown that particle shape has influence on the soil behaviour

despite of partial knowledge of the mechanism behind Understanding of the

particle shape and its influence needs to be accomplished

A common language needs to be built up to standardize the meaning on

geotechnical field that involve the particle shape General relationships

between shape and properties should be developed

Based on this review it is not clear which is the best descriptor to use in

geotechnical engineering affecting he related shape to properties Instead of a

couple of standards there is no shape descriptor in geotechnical field fully

accepted

Image analysis tool is objective make the results repeatable obtain fast results

and work with more amount of information

44

Resolution needs to be taken in consideration when image analysis is been

carried out because the effects could be considerable Resolution must be set

according to the necessities Parameters as perimeter can be affected by

resolution

There are examples where particle shape has been incorporated in industries

related to geotechnical engineering eg in the ballast and asphalt industry for

quality control

8 FURTHER WORK

Three main issues have been identified in this review that will be further investigated

the limits of shape descriptors influence of grading and choice of descriptor for

relation to geotechnical properties

Shape descriptors have low and high limits frequently the limits are not the same and

the ability to describe the particlersquos shape is relative The sensitivity of each descriptor

should be compare to apply the most suitable descriptor in each situation

Sieving curve determine the particle size in a granular soil particle shape could differ

in each sieve size There is the necessity to describe the particle shape on each sieve

portion (due to practical issues) and included in the sieve curve Obtain an average

shape in determined sieve size is complicated (due to the possible presence of several

shapes) and to obtain the particle shape on the overall particlersquos size is challenging

how the particle shape should be included

Since several descriptors have been used to determine the shape of the particles and

the relation with the soil properties it is convenient to determine the descriptorrsquos

correlation with the soil properties

9 ACKNOWLEDGMENT

I would like to thanks to Lulearing University of Technology (LTU) the time I had spent

in its facilities and the kind environment it offers and University of Sonora

(UNISON) that has been providing me the financial support and the time to conclude

this journey

10 REFERENCES

Andersson T (2010) Estimating particle size distributions based on machine vision

Doctoral Thesis Departament of Computer Science and Electrical Engineering Lulearing

University of Technology ISSN 1402-1544 ISBN 978-91-7439-186-2

45

Arasan Seracettin Hasiloglu A Samet Akbulut Suat (2010) Shape particle of

natural and crished aggregate using image analysis International Journal of Civil and

Structural Engineering Vol 1 No 2 pp 221-233 ISSN 0970-4399

Aschenbrenner BC (1956) A new method of expressing particle sphericity Journal

of Sedimentary Petrology Vol 26 No 1 pp 15-31

Axelsson K (1998) Introduktion till jordmekaniken jaumlmte jordmateriallaumlran Skrift

984 Lulearing Avdelningen foumlr Geoteknologi Lulearing Tekniska Universitet (In Swedish)

Barton Nick amp Kjaernsli Bjorn (1981) Shear strength of rockfill Journal of the

Geotechnical Engineering Division Proceedings of the American Society of Civil

Engineers (ASCE) Vol 107 No GT7

Barrett P J (1980) The shape of rock particles a critical review Sedimentology

Vol 27 pp 291-303

Blott S J and Pye K (2008) Particle shape a review and new methods of

characterization and classification Sedimentology Vol 55 pp 31-63

Bowman E T Soga K and Drummond W (2001) Particle shape characterization

using Fourier descriptor analysis Geotechnique Vol 51 No 6 pp 545-554

Briggs L I McCulloch D S (1962) Hydraulic shape of sand particles Journal of

Sedimentary Petrology Vol 32 pp 645-656

Chan Leonard C Y and Page Neil W (1997) Particle fractal and load effects on

internal friction in powders Powder Technology Vol 90 pp 259-266

Cheshomi A Fakher A Jones C J F P (2009) A correlation between friction

angle and particle shape metrics in quaternary coarse alluvia Quarterly Journal of

Engineering Geology and Hydrogeology Vol 42 pp 145-155

Cho G Dodds J and Santamarina J C (2006) Particle shape effects on packing

density stiffness and strength Natural and crushed sands Journal of Geotechnical

and Geoenvironmental Engineering May 2006 pp 591-602

Dietrich William E (1982) Settling velocity of natural particles Water Resources

Research Vol 18 No 6 pp 1615-1626

Dobkins J E and Folk R L (1970) Shape development on Tahiti-nui Journal of

Sedimentary Petrology Vol 40 No 2 pp 1167-1203

Folk R L (1955) Student operator error in determining of roundness sphericity and

grain size Journal of Sedimentary Petrology Vol 25 pp 297-301

Fernlund J M R (1998) The effect of particle form on sieve analysis A test by

image analysis Engineering Geology Vol 50 No 1-2 pp 111-124

46

Fernlund J M R (2005) Image analysis method for determining 3-D shape of

coarse aggregate Cement and Concrete Research Vol 35 Issue 8 pp 1629-1637

Fernlund J M R Zimmerman Robert and Kragic Danica (2007) Influence of

volumemass on grain-size curves and conversion of image-analysis size to sieve size

Engineering Geology Vol 90 No 3-4 pp 124-137

Fraser H J (1935) Experimental study of the porosity and permeability of clastic

sediments The Journal of Geology Vol 43 pp 910-1010 ISSN 0022-1376

Hayati Ali Nemati Ahmadi Mohammad Mehdi and Mohammadi Soheil (2012)

American Physical Society Physical review E 85 036310 DOI

101103PhysRevE85036310

Hawkins A E (1993) The Shape of Powder-Particle Outlines Wiley New York

Head K H and Epps R J (2011) Manual of soil Laboratory testing Volum II

Permeability shear strength and compressibility test 3rd

edition Whittles Publishing

Scotland UK 3rd

edition

Holubec I and DrsquoAppolonia E (1973) Effect of particle shape on the engineering

properties of granular soils ASTM STP 523 pp 304-318

Hyslip James P Vallejo Luis E (1997) Fractal analysis of the roughness and size

distribution of granular materials Engineering Geology Vol 48 pp 231-244

Janoo Vincent C (1998) Quantification of shape angularity and surface texture of

base course materials US Army Corps of Engineers Cold Region Research and

Engineering Laboratory Special report 98-1

Jefferies Mike and Been Ken (2000) Soil liquefaction A critical state approach

Taylor amp Francis Group London and New York

Jimenez Jose A Madsen Ole S (2003) A simple formula to estimate settling

velocity of natural sediments Journal of Waterway Port Coastal and Ocean

Engineering Vol 129 No 2 pp 70-78

Johansson Jens and Vall Jakob (2011) Jordmaterials kornform Inverkan paring

Geotekniska Egenskaper Beskrivande storheter bestaumlmningsmetoder

Examensarbete Avdelningen foumlr Geoteknologi Institutionen foumlr Samhaumlllsbyggnad

och naturresurser Lulearing Tekniska Universitet Lulearing (In Swedish)

Kane Joseph W and Sternheim Morton M (1988) Physics John Wiley amp Sons Inc

Third edition

Kolbuszewski J (1948) An experimental study of the maximum and minimum

porosities of sands Proceedings of the Second International Conference on Soil

Mechanics and Foundation Engineering Rotterdam June 21 to 30 Sub-section IIb

pp 158-165

47

Krumbein W C and Pettijohn FJ (1938) Manual of sedimentary petrography

Appleton-Century Crofts Inc New York

Krumbein W C (1941) Measurement and geological significance of shape and

roundness of sedimentary particles Journal of Sedimentary Petrology Vol 11 No 2

pp 64-72

Krumbein W C and Sloss L L (1963) Stratigraphy and Sedimentation 2nd

ed

WH Freeman San Francisco

Kuo Chun-Yi and Freeman Reed B (1998a) Image analysis evaluation of

aggregates for asphalt concrete mixtures Transportation Research Record Vol 1615

pp 65-71

Kuo Chun-Yi Rollings Raymond and Lynch Larry N (1998b) Morphological

study of coarse aggregates using image analysis Journal of Materials in Civil

Engineering Vol 10 No 3 pp 135-142

Lanaro F Tolppanen P (2002) 3D characterization of coarse aggregates

Engineering Geology Vol 65 pp 17-30

Lees G (1964a) A new method for determining the angularity of particles

Sedimentology Vol 3 pp 2-21

Lees G (1964b) The measurement of particle shape and its influence in engineering

materials British Granite Whinstone Federation Vol 4 No 2 pp 17-38

Matsushima Takashi Saomoto Hidetaka Matsumoto Masaaki Toda Kengo

Yamada Yasuo (2003) Discrete element simulation of an assembly of irregular-

shaped grains Quantitative comparison with experiments 16th ASCE Engineering

Mechanics Conference University of Washington Seattle July 16-18

Mitchell James K and Soga Kenichi (2005) Fundamentals of soil behaviour Third

edition WILEY

Mora C F Kwan A K H Chan H C (1998) Particle size distribution analysis of

coarse aggregate using digital image processing Cement and Concrete Research Vol

28 pp 921-932

Mora C F and Kwan A K H (2000) Sphericity shape factor and convexity

measurement of coarse aggregate for concrete using digital image processing Cement

and Concrete Research Vol 30 No 3 pp 351-358

Muskat Morris (1937) The Flow of fluids through porous media Journal of Applied

Physics Vol 8 pp 274

Nearing M A and Parker S C (1994) Detachment of soil by flowing water under

turbulent and laminar conditions Soil Science Society of American Journal Vol 58

No 6 pp 1612-1614

48

Pan Tongyan Tutumluer Erol Carpenter Samuel H (2006) Effect of coarse

aggregate morphology on permanent deformation behavior of hot mix asphalt Journal

of Transportation Engineering Vol 132 No 7 pp 580-589

Pellegrino A (1965) Geotechnical properties of coarse-grained soils Proceedings

International Conference of Soil Mechanics and Foundation Engineering Vol 1 pp

97-91

Pentland A (1927) A method of measuring the angularity of sands MAG MN AL

Acta Eng Dom Transaction of the Royal Society of Canada Vol 21 Ser3xciii

Persson Anna-Lena (1998) Image analysis of shape and size of fine aggregates

Engineering Geology Vol 50 pp 177-186

Powers M C (1953) A new roundness scale for sedimentary particles Journal of

Sedimentary Petrology Vol 23 No 2 pp 117-119

Pye W and Pye M (1943) Sphericity determination of pebbles and grains Journal

of Sedimentary Petrology Vol 13 No 1 pp 28-34

Qazi M A (1975) Flow properties of granular masses A review on the angle of

repose The Arabian Journal for Science and Engineering Vol 1 No 2

Quiroga Pedro Nel and Fowle David W (2003) The effects of aggregate

characteristics on the performance of portland cement concrete Report ICAR 104-1F

Project number 104 International Center for Aggregates Research University of

Texas

Riley N A (1941) Projection sphericity Journal of Sedimentary Petrology Vol 11

No 2 pp 94-97

Rouseacute P C Fennin R J and Shuttle D A (2008) Influence of roundness on the

void ratio and strength of uniform sand Geotechnique Vol 58 No 3 227-231

Santamarina J C and Cho G C (2004) Soil behaviour The role of particle shape

Proceedings Skempton Conf London

Schofield and Wroth (1968) Critical state soil mechanics McGraw Hill

Shaumlfer Michael (2002) Digital optics Some remarks on the accuracy of particle

image analysis Particle amp Particle Systems Characterization Vol 19 No 3 pp 158-

168

Shergold F A (1953) The percentage of voids in compacted gravel as a measure of

its angularity Magazine of Concrete Research Vol 5 No 13 pp 3-10

Shinohara Kunio Oida Mikihiro Golman Boris (2000) Effect of particle shape on

angle of internal friction by triaxial compression test Powder Technology Vol 107

pp131-136

49

Skredcommisionen (1995) Ingenjoumlrsvetenskapsakademinen rapport 395 Linkoumlping

1995

Sneed E D and Folk R L (1958) Pebbles in the Colorado river Texas A study in

particle morphogenesis Journal of Geology Vol 66 pp 114-150

Sperry James M and Peirce J Jeffrey (1995) A model for estimating the hydraulic

conductivity of granular material based on grain shape grain size and porosity

Ground Water Vol 33 No 6 pp 892-898

Sukumaran B and Ashmawy A K (2001) Quantitative characterisation of the

geometry of discrete particles Geotechnique Vol 51 No 7 pp 619-627

Szaacutedeczy-Kardoss E Von (1933) Die bistimmung der abrollungsgrades Geologie

und palaumlontologie Vol 34B pp 389-401 (in German)

Teller J T (1976) Equantcy versus sphericity Sedimentology Vol 23 pp 427-428

Tickell F G (1938) Effect of the angularity of grain on porosity and permeability

bulletin of the American Association of Petroleum Geologist Vol 22 pp 1272-1274

Tutumluer E Huang H Hashash Y Ghaboussi J (2006) Aggregate shape effects

on ballast tamping and railroad track lateral stability AREMA 2006 Annual

Conference Louisville KY

Wadell H (1932) ldquoVolume Shape and roundness of rock particlesrdquo Journal of

Geology Vol 40 pp 443-451

Wadell H (1933) Sphericity and roundness of rock Particles Journal of Geology

Vol 41 No 3 pp 310ndash331

Wadell H (1934) Shape determination of large sedimental rock fragments

The Pan-American Geologist Vol 61 pp 187-220

Wadell H (1935) ldquoVolume shape and roundness of quartz particlesrdquo Journal of

Geology Vol 43 pp 250-279

Wentworth W C (1922a) The shape of beach pebbles Washington US Geological

Survey Bulletin Vol 131C pp 75-83

Wentworth W C (1922b) A method of measuring and plotting the shape of pebbles

Washington US Geological Survey Bulletin Vol 730C pp 91-114

Wentworth W C (1933) The shape of rock particle A discussion Journal of

Geology Vol 41 pp 306-309

Witt K J Brauns J (1983) Permeability-Anisotropy due to particle shape Journal

of Geotechnical Engineering Vol 109 No 9 pp 1181-1187

6

Wadell (1932) defined the sphericity as the specific surface ratio (equation 2) Figure

4 is a schematic representation of the sphere surface and particle surface both particle

and sphere of the same volume

This way to obtain the sphericity is almost impossible to achieve as Hawkins (1993)

declares due the difficulty to get the surface area on irregular solids

Wadell (1934) also defined the sphericity based upon the particle and sphere volumes

as equation 3 (see figure 5)

Wadell (1934) used a new formula simple to manage using the diameters (see figure

6 and equation 4)

Zingg (Krumbein 1941) develop a classification based on the 3 axes relation in this

way it is easy to find out the main form of the particles as a disks spherical blades

S

s

3

CIR

P

V

V

CIR

SV

D

D

Figure 4 Same volume sphere surface (s) and particle surface (S) (modified after Johansson and Vall

2011)

Figure 5 Relation between the volume of the particle and the volume of the circumscribed

sphere (Johansson and Vall 2011)

Figure 6 Figure is showing the relation between the diameter of a circumscribed sphere and the

diameter of a sphere of the same volume as the particle (Johansson and Vall 2011)

(2)

(3)

(4)

7

and rod-like this is summarized on figure 7 Zinggrsquos classification is related with

Krumbein intercept sphericity and the figure 3

In figure 8 the figures 3 and 7 are combined the relation in the two classifications can

be seen it is an easy way to understand the morphology regarding on the a b and c

dimensions

Pye and Pye (1943) in the article ldquosphericity determinations of pebbles and sand

grainsrdquo compare the Wadellrsquos sphericity developed in 1934 (based on the diameter)

with ldquoPebble sphericityrdquo based on an ellipse this last equation (number 5) appears

two years early published by Krumbein (1941) Axis measurement is done as figure 1

denotes for equations 5 trough 12 with exception of equation 8 where the original

document was not possible to obtain

32a

cb

Figure 7 Zinggrsquos classification of pebble shape based on ratios ba and cb (Krumbein 1941)

Figure 8 Classification made by Zinggrsquos and chart to determine sphericity (Krumbein and Sloss 1963)

(5)

8

Sneed amp Folk in (1958) found a relation between the tree dimensional axes called

ldquoMaximum Projection Sphericityrdquo

In a similar way Ashenbrenner (1956) showed his equation at that time named

ldquoWorking Sphericityrdquo

Form or shape factor names are used by authors like Corey (shape factor eq 8) in the

paper published on 1949 Williams (shape factor eq 9) in 1965 Janke (form factor

eq 10) in 1966 and Dobkins amp Folk (oblate-prolate index eq 11) in 1970 (Blott and

Pye 2008)

Aschenbrenner (1956) develop the shape factor by using the relation of the tree axis

but the square of the middle one

3

2

ba

c

))ab((1)bc(16))ab((cb)(11

)ab()bc( 128

22

3 2

ab

c

acb when 1ac

b acb when

b

ac-1 2

22

2

3

cba

c

222

a

c

50c-a

b-a10

2b

ac

(6)

(7)

(8)

(9)

(10)

(11)

(12)

9

Table 2 General overview over different particle shape definitions for 3D sphericity has been compiled

and arranged chronologically

Aspect Name Author Year Based on

Sphericity (3D) Flatness index Wentworth 1922a 3-axes

True Sphericity Wadell 1932 Surface

Operational sphericity Wadell 1932 Volume

Sphericity Wadell 1934 Sphere diameter

Zinggrsquos clasification Zinggrsquos1

1935 3-axes

Intercept sphericity chart Krumbein 1941 3-axes

Pebble sphericity Pye and Pye 1943 3-axes

Corey shape factor Corey2

1949 3-axes

Working sphericity Ashenbrenner 1956 3-axes

shape factor Ashenbrenner 1956 3-axes

Maximum projection sphericity Sneed amp Folk 1958 3-axes

Williams shape factor Williams2

1965 3-axes

Janke form factor Janke2

1966 3-axes

Oblate-prolate index Dobkins amp Folk 1970 3-axes 1) Krumbein and Sloss 1963 2) Blott and Pye 2008

34 FORM (2D)

The technique to measure the sphericity is based in tree dimensions it can be found in

literature some ways to measure the ldquotwo dimensions sphericityrdquo which is simply the

perimeter of the particle projection some authors named ldquoparticle outlinerdquo or

ldquocircularityrdquo

Wadell in 1935 (Hawkins 1993) adopt a conversion of his 1934 3D sphericity

formula (equation 4) to a 2D outline He defined an orientation on the particles and

they were based on the maximum cross sectional area (outline of the particle

projecting the maximum area) The equations show the relation between diameters of

a circle of same area and smallest circumscribed circle

He also used the term ldquodegree of circularityrdquo as the ratio of the perimeter of a circle of

same area and the actual particle perimeter

Tickell in 1931 (Hawkins 1993) used his empirical relation The particle orientation

proposed was a random one It is described by the ratio between the area outline and

the area of smallest circumscribed circle

C

A

D

DC

P

PC C

CA

AC

(13)

(14)

(15)

10

Some other authors has been working with the ldquocircularityrdquo concept and had develop

them own equations as Pentland (1927) relating the area outline and area of a circle

with diameter equal to longest length outline and Cox (Riley 1941) with the ratio

area and perimeter time a constant equations 16 and 17 respectively Both authors did

not define any definite orientation of the grains

Riley (1941) realize the problems that an area perimeter and some other

measurements proposed by the above authors can carry as the time consuming and

tedious work (at that time were not computer all was made by hand) and thatrsquos why

he develop this equation easy to handle called ldquoinscribed circle sphericityrdquo He used

the same particle orientation proposed by Wadell and the relation of diameters of

inscribed and circumscribed circles

Horton 1932 (Hawkins 1993) use the relation of the drainage basing perimeter and

the perimeter of a circle of the same area as drainage basin

Janoo in 1998 (Blott and Pye 2008) develop his general ratio of perimeter to area

Sukumaran and Ashmawy (2001) develop his own shape factor (SF) defined as the

deviation of the global particle outline from a circle Figure 9 can be used as a

reference to determine the items used in the equation 21

N is referred to the number of sampling intervals o radial divisions

C2A

AC

2P

A4C

C

I

D

DC

CD

D

P

PC

A

PC

2

45ordm x N

Particleα

= SF

sumN

1=ii

(16)

(17)

(18)

(19)

(20)

(21)

11

Table 3 General chronological overview of the particle shape definitions for 2D sphericity

Aspect Name Author Year Based on

Circularity (2D) roundness Pentland 1927 area

roundness Cox1

1927 area-perimeter

roundness Tickell2

1931 area

Circularity Horton2

1932 drainage basin

outline circularity Wadell 1935 Circle diameter

degree of circularity Wadell 1935 Perimeter

inscribed circle sphericity Riley 1941 Circle diameter

Circularity Krumbein and Sloss 1963 chart

Janoo 1998 area-perimeter

Shape factor Sukumaran 2001 Segmentation of particle and angles

1) Riley 1941 2) Hawkins 1993

35 ROUNDNESS OR ANGULARITY

Roundness as described in section 32 is the second order shape descriptor Sphericity

lefts beside the corners and how they are this was notice by most of the authors sited

before and they suggested many ways to describe this second order particle property

Roundness is clearly understandable using the figure 10 Particle shape or form is the

overall configuration and denotes the similarities with a sphere (3D) or a circle (2D)

Roundness is concerning about the sharpness or the smoothness of the perimeter (2D)

Surface texture (Barret 1980) is describe as the third order subject (form is the first

and roundness the second) and it is superimposed in the corners and it is also a

property of particles surfaces between corners

Figure 9 Description of the Sukumaran factors to determine the shape and angularity (Sukumaran and

Ashmawy 2001)

12

Wadell (1935) describes his methodology calling it total degree or roundness to

obtain the roundness of a particle using the average radius of the corners in relation

with the inscribed circle diameter (see figure 11) on the equation

In the same study Wadell (1935) has used the equation

This two last equation shows slightly differences on the results (Wadell 1935)

Powers (1953) also published a graphic scale to illustrate the qualitative measure

(figure 12) It is important to highlight that any comparing chart to describe particle

properties has a high degree of subjectivity Folk (1955) concludes that when charts

are used for classification the risk of getting errors is negligible for sphericity but

large for roundness

N

R

r

Rinmax

r

R

NR

inmax

Figure 10 Form (shape) Roundness and Texture graphical description (Bowman et al 2001)

Figure 11 Wadellrsquos method to estimate the roundness corners radius and inscribed circle

(Hawkins 1993)

(22)

(23)

13

Some authors as Russel amp Taylor in 1937 Pettijohn in 1957 and Powers in 1953

developed a classification based on five and six classes (Hawkins 1993) each one

with its own class limits it is important to denote that the way they measure the

roundness is the developed by Wadell (1935) This classification and class limits are

showed in the table 4

Table 4 Degrees of roundness Wadell Values (Hawkins 1993) NA = no-applicable

Grade terms Russell amp Taylor (1937) Pettijohn (1957) Powers (1953)

Class

limits (R)

Arithmetic

midpoint

Class limits

(R)

Arithmetic midpoint Class

limits (R)

Arithmetic

midpoint

Very angular

NA

NA

NA

NA

012-017

014

Angular

000-015

0075

000-015

0125

017-025

021

Subangular

015-030

0225

015-025

0200

025-035

030

Subrounded

030-050

0400

025-040

0315

035-049

041

Rounded

050-070

0600

040-060

0500

049-070

059

Well rounded

070-100

0800

060-100

0800

070-100

084

Krumbein and Sloss (1963) published a graphical chart easy to determine the

sphericity and roundness parameters using comparison See figure 13 (Cho et al

2006)

Figure 12 A Roundness qualitative scale (Powers 1953)

Figure 13 Sphericity and roundness chart (Cho et al 2006) The roundness equation that appears here in

the chart is the wadellrsquos equation number 22

14

Fischer in 1933 (Hawkins 1993) used a straightforward method to quantify roundness

using a central point in the outline and dividing the outline in angles around this point

that were subtended by the straight or non curved parts of the profile were measured

This is illustrated in figure 14

To express the angularity value Fischer used the ratio of angles standing linear parts

on the outlines and concave respectively

Figure 14 left (A) and right (B) gives a similar angularity of approximately 042

using the above equations (Hawkins 1993)

Wentworth in 1922 used the maximum projection to define the position of the particle

to obtain the outline or contour (Barret 1980) The equation reflects the relation of the

diameter of a circle fitting the sharpest corner and the longest axis plus the shortest

axis c (minimum projection)

Wentworth (Hawkins 1993) expressed the roundness as the ratio of the radius of

curvature of the most convex part and the longest axis plus short axis

Actually these last two equations are the same just expressed in different terms when

the particle is in its maximum projection

Dimensions can be seen on figure 15 L and B represents the mayor axis a and

intermediate axis b The intention is to make difference between the 2 and 3

dimensions (L and B are for 2D as a b and c are for 3D)

deg360

ANG

=R

sumPLA

PLA

CON

ANG

ANGR

2)S(L

DR

M

S

B)4(L

RR CON

Figure 14 Fischerrsquos methods of angularity computation (Hawkins 1993)

A=inscribed circle B=circumscribed circle

(24)

(25)

(26)

(27)

15

Wentworth 1919 has a second way to express the roundness called Shape index

(Barrett 1980) and it relates the sharpest corner and the diameter of a pebble trough

the sharpest corner

Wentworth (1922b) used define the roundness as the ratio of the sharpest corner and

the average radius of the pebble

Cailleux (Barrett 1980) relates the radius of the most convex part and the longest

axis

Kuenen in 1956 show his roundness index (Barrett 1980) between the sharpest corner

and the breath axis

Dobkins amp Folk (1970) used a modified Wentworth roundness with the relation of

sharpest corner and inscribed circle diameters

AVG

CON

R

RR

x

s

D

DR

L2

RR CON

B

DR s

i

s

D

DR

3AVGAVG cbaDR2

Figure 15 Description of L and B axes (Hawkins 1993)

(28)

(29)

(30)

(31)

(32)

(33)

16

Swan in 1974 shows his equation (Barrett 1980) relating the sharpest (or the two

sharpest) corner(s) and inscribed circle diameter

Szadeczsky-Kardoss has his Average roundness of outline (Krumbein and Pettijohn

1938) relating the concave parts perimeter and the actual perimeter

Lees (1964a) developed an opposite definition to roundness it means that he

measures the angularity instead of the roundness and he calls it Degree of angularity

Figure 16 shows the items considered when equation 36 applies as the angles (α)

inscribed circle (Rmax-in) and the distance (x) The main formula is

In order to apply the last equation corners needs to be entered in the formula and each

individual result will add to each other to obtain the final degree of angularity

A roundness index appears on Janoo (1998) Kuo and Freeman (1998a) and Kuo et

al (1998b) it is described as

The last equation is on section 34 also because there is not a general agreement on the

definition furthermore some authors had used to define the roughness this is not the

only equation that has been used trying to define different aspects (sphericity

roundness or roughness) but it is a good example of the misuse of the quantities and

definitions

inmaxR

x)180(R

2P

A4R

i

ss

D

DDR

221

100P

PR CON

Figure 16 Degree of angularity measurement technique (Blot and Pye 2008)

(34)

(35)

(36)

(17)

17

Sukumaran and Ashmawy (2001) present an angularity factor (AF) calculated from

the number of sharpness corners Angles βi required to obtain the angularity factor are

shown in figure 9

Sukumaran and Ashmawy (2001) also suggested use not bigger sampling interval of

N=40 because it is the cut off between angularity factor and surface roughness If so

this equation could be used to describe the roughness

Table 5 General chronological overview of the particle roundness

Aspect Name Author Year Based on

Roundness shape index Wentworth 19191

diameter of sharper corner

shape index Wentworth 1922b sharpest corner and axis

roundness Wentworth 1933 convex parts

Fischer 19332

noncurved parts outline

Fischer 19332

noncurved-streigth parts outline

Average roundness of outline

Szadeczsky-Kardoss 19333

convex parts-perimeter

roundness Wadell 1935 diameter of corners

roundness Wadell 1935 diameter of corners

roundness Russel amp Taylor 19372

class limit table

roundness Krumbein 1941 chart

Cailleux 19471

convex parts

roundness Pettijohn 19494 class limit table

roundness Powers 1953 chart and class limit table

Kuenen 19561

axis-convex corner

roundness Krumbein and Sloss 1963 chart

degree of angularity Lees 1964a corners angles and inscribed circle

Dobkins amp Folk 1970 diameter of sharper corner

Swan 19741

diameter of sharper corners

Angularity factor Sukumaran and

Ashmawy 2001

Segmentation of particles and angles

1) Barret 1980 2) Hawkins 1993 3) Krumbein and Pettijohn 1938 4) Powers 1953

sum

sumsumN

1=i

2

i

2

N

1=i

2

i

2N

1=ii

)ordm180 -circleβ( - )(180ordm x 3

)ordm180-circleβ(-)ordm180 -Particleβ(

= AF (37)

18

36 ROUGHNESS OR SURFACE TEXTURE

A third property called texture appears early in the literature with the sphericity and

roundness properties since then texture property was longed described but it was in

accordance with the authors at that time not measurable

Wright in 1955 developed a method to quantify the surface texture or roughness of

concrete aggregate using studies done on 19 mm stones The test aggregates were first

embedded in a synthetic resin The stones were cut in thin sections The sections

projection was magnified 125 times The unevenness of the surface was traced and the

total length of the trace was measured The length was then compared with an uneven

line drawn as a series of chords (see figure 17) The difference between these two

lines was defined as the roughness factor (Janoo 1998)

However with the advance of technology it has become easier measure the roughness

and here is presented some researcherrsquos ideas how this property should be calculated

One technique used by Janoo (1988) to define the roughness can be seen in figure 18a

and is defined as the ratio between perimeter and convex perimeter

The convex perimeter is obtained using the Feretrsquos box (or diameter) tending a line in

between the touching points that the Feretrsquos box describes each time it is turn (figure

18b)

PER

OC

PR

Figure 17 Measurement method for characterizing the surface texture of an aggregate (Janoo 1998)

a) Convex perimeter (CPER) b) Feret measurement Figure 18 a) Convex perimeter (CPER) b) Feret measurement (modified after Janoo 1998)

(38)

a)

b)

19

Kuo and Freeman (1998a) and Kuo et al (1998b) use the roughness definition as the

ratio perimeter and average diameter

Erosion and dilatation image processing techniques are used to obtain the surface

texture Erosion is a morphological process by which boundary image pixels are

removed from an object surface which leaves the object less dense along the

perimeter or outer boundary Dilatation is the reverse process of erosion and a single

dilatation cycle increases the particle shape or image dimension by adding pixels

around its boundary (Pan etal 2006)

The ldquonrdquo erosion and dilatation cycles are not standardized

Mora and Kwan (2000) used the ldquoconvexity ratio CRrdquo (equation 41) and the ldquofullness

ratio FRrdquo (equation 42) in their investigation they are

The convex area is the area of the minimum convex boundaries circumscribing the

particle This is illustrated in the figure 19 The convex area is obtained in a similar

way as the convex perimeter but in this case the area between the original outline and

the convex perimeter is our convex area

AVG

OD

PR

100A

1AARO

CONo A

AR =

CONo A

AR =

Figure 19 Evaluation of area and convex area (Mora and Kuan 2000)

(39)

(40)

(41)

(42)

20

4 TECHNIQUES IN ORDER TO DETERMINE PARTICLE

SHAPE

41 HAND MEASUREMENT

Hand measurement technique was the first used by obvious reasons in order to

improve the accuracy special devices developed as the ldquosliding rod caliperrdquo used by

Krumbein (1941) it works placing the sample on the sliding road calliper as show

figure 20b the length in different positions can be obtain by using the scale provided

in the handle the ldquoconvexity gagerdquo that was actually used by opticians to measure the

curvature of lenses but easily applicable to the particle shape analysis (Wentworth

1922b) works measuring the movement of the central pivot as figure 20a shows (the

two adjacent pivots are invariable) as many the central pivot moves more is the

curvature or the ldquoSzadeczky-Kardossrsquos apparatusrdquo develop in 1933 that traces the

profile of the rock fragment so the outline traced is then analyzed (Krumbein and

Pettijohn 1938) figure 20c show equipment

Another helpful tool to determine the particle dimensions was the ldquocamera lucidardquo to

project the particlersquos contour over a circle scale appearing in Figure 21 thus it is

possible to measure the particlersquos diameter

a)

c) b)

Figure 20 a) convexity gage used to determine the curvature in particle corners (Wenworth 1922b)

b)sliding rod caliper device to measure the particle axis length (Krumbein 1941) and c)Szadeczky-

Kardoss (1933) apparatus it was utilized to obtain the particle outline

Figure 21 Circle scale used by Wadell (1935) to determine particlersquos diameter and roundness

21

42 SIEVE ANALYSIS

Bar sieving eg according to EN 933-31997 can be used to determine simple large

scale properties By combining mesh geometries the obtained results can be used to

quantify flakiness and elongation index ASTM D4791 (Flat and elongated particles

are defined as those coarse aggregate particles that have a ratio of length to thickness

equal to or greater than a specified value such as 51 The index represents the

percentage on weight of these particles) The method is not suitable for fine materials

This due to the difficulty to get the fine grains passed through the sieve and the great

amount of particles in relation to the area of the sieve (Persson 1998) eg EN 933-

31997 related to flakiness index The test is performed on aggregates with grain size

from 4 mm and up to 63 mm two sieving operations are necessary the first separates

on size fraction and the second use a bar sieve after the first sieving the average

maximum diameter of the particles is obtain and with the second sieving (bar sieving)

the shortest axis diameter is found finally with this two parameters the flakiness

index is determined

There are more standards related with the particle shape (see appendix A) but this

above presented are probably the most known using sieve analysis to determine

particlersquos geometrical properties

Sieve analysis is facing the computers age and image analysis sieving research is

taking place (Andersson 2010 Mora and Kwan 2000 Persson 1998) Industry is

also applying the image analysis sieving with decrees on the testing time compare

with the traditional sieving method An inconvenient of image analysis is the error

due the overlapping or hiding of the particles during the capture process but the

advantages are more compare with disadvantages (Anderson 2010)

43 CHART COMPARISON

Charts developed over the necessity of faster results because the long time consuming

required when measuring each particle

Krumbein (1941) present a comparison roundness chart for pebbles which were

measured by Wadellrsquos method because this property was the most difficult to measure

due to the second order scale that roundness represents (See figure 22)

Figure 22 Krumbein (1941) comparision chart for roundness

22

A qualitative chart by Powers (1953) try to include both (sphericity and roundness)

particlersquos characteristics it was divided on six roundness ranges (very angular

angular sub-angular sub-rounded rounded and well rounded) and two sphericity

series (high and low sphericity) This chart was prepared with photographs to enhance

the reader perspective (See figure 23)

A new chart including sphericity and roundness appear this time it was easier to

handle the two mean properties of particlersquos shape furthermore there was included

the numerical values that eliminated the subjectivity of qualitative description The

chart is based on Wadellrsquos definitions (Krumbein and Sloss 1963) (See figure 24)

Folk (1955) worried about the personrsquos error on the chartrsquos comparison studied the

determination of sphericity and angularity (he used the Powers 1953 comparison

chart) he found that the sphericity determination by chart comparison has a negligible

error while the roundness he concluded it was necessary to carry out a more wide

research due the high variability show by his study

Figure 23 Powers (1953) qualitative shpericity-roundness chart

Figure 24 Sphericity-roundness comparison chart (Krumbein and sloss 1963)

23

44 IMAGE ANALYSIS

Image analysis is a practical method to use for shape classification since it is fast and

can be automated Different techniques appear to process these images among them

are

o Feret Diameter the Feret diameter is the longitude between two parallel lines

this lines can rotate around one particle or outline to define dimensions as it

is shown in figure 25 these method is not a fine descriptor but as it was say

above it is a helpful tool to determine diameters (Janoo 1988)

o Fourier Mathematical Technique It produces mathematical relations that

characterize the profile of individual particles This method favours the

analysis of roughness and textural features for granular soils The problem in

the methodology remains in the re-entrant angles in order to complete the

revolution (Bowman et al 2001) see figure 26

o Fractal Dimension Irregular line at any level of scrutiny is by definition

fractal (Hyslip and Vallejo 1997) Figure 27 shows fractal analysis by the

dividing method The length of the fractal line can be defined as

N

1n

nn0 )nsinbncosa(a)(R

RD1n)(P

Figure 25 Feret measurement technique is defined by two parallel lines turning

around the particle to define the shortest and longest Feret diameter (Janoo 1988)

Figure 26 Fourier technique with two radiuses at one angle (Bowman et al 2001)

(43)

(44)

24

o Orthogonal image analysis This technique is basically the use of two images

orthogonal between them to acquire the three particle dimensions (Fernlund

2005) any of the above techniques can be used in this orthogonal way

o Laser Scanning Technique this kind of laser scanning 3D is one of the most

advanced techniques In figures 28a) we have the laser head scanning the rock

particles the particles have control points in order to keep a reference point

when move them to scan the lower part in figure 28b) we can see the laser

path followed (Lanaro and Tolppanen 2002)

Another technique is the Laser-Aided Tomography (LAT) in this case a laser sheet is

used to obtain the particles surveying (see figure 29) This technique is different and

has special requirements as to use liquid with same refractive index as the particles

particles must let the laser or certain percent of light go through (Matsushima et al

2003)

a) b)

Figure 27 Fractal analysis by the dividing method at different scrutiny scale (Hyslip and Vallejo 1997)

Figure 28 a) Scanning head b) scanning path (Lanaro and Tolppanen 2002)

Figure 30 3D scan completed ready to

use for any further measure

(Matsushima et al 2003)

Figure 29 LAT scaning particles

(Matsushima et al 2003)

25

Both 3D techniques obtain the particle shape that is later used to achieve measures as

we can see in figure 30

All these previous techniques are easily written in codes or scripts to be interpreted in

a digital way obtaining the desired measurement but there are some interesting points

in the image analysis regarding on the errors involve among them are image

resolution and orientation of the particles orientation is not relevant when it is

random and large number of particles are involve resolution have an influence on the

accuracy (Zeidan et al 2007)

When resolution is increase more accuracy is obtain and the object representation

match better with the real form in the other hand more resolution means more

spending on memory and time thus resolution needs to be according with the goal

and precision needed in any work (Schaumlfer 2002)

Schaumlfer (2002) conclude that attributes like length when measuring digital images

present relative high errors It can be vanish or at least diminish using high resolution

just for diameter but not for perimeter that keep the error as big as initially Johansson

and Vall (2011) obtain similar results when 3 different resolutions were used in the

same particle obtaining an unstable output for those termsquantities that involve the

perimeter Thus all quantities relating the perimeter should be treated with care

5 EFFECT OF SHAPE ON SOIL PROPERTIES

51 INTRODUCTION

In laboratory test on the effect on particle size on basic properties has been

investigated in several studies this relation has been discussed and various

mechanisms had been proposed to explain the behaviour of the soil in dependency

also with the shape Basically there are two mechanisms proposed The arrangement

of particles and the inter-particle contact (Santamarina and Cho 2004) and

subsequence breakage

The arrangement of particles

Arrangement of the particles can be presented in three different forms loose dense

and critical this arrangement determines the soil properties (eg density increase with

more dense arrangement) Loose and dense states are easy understandable when

figure 31 is explained while in the upper part of the figure the particles are arranged

using the minimum space needed in the lower part a span is created using the flaky

particle as a bridge this phenomena is known as ldquobridgingrdquo Bridging can produce

different geotechnical results when just the shape of the particle is changed eg void

ratio (Santamarina and Cho 2004) Particles are able to rearrange this could be done

applying pressure (energy) to the soil the pressure (energy) will create such forces

that soil particles will rotate and move (see figure 34) finishing in a more dense state

26

A loose soil will contract in volume on shearing and may not develop any peak

strength (figure 32 left) In this case the shear strength will increase gradually until

the residual shear strength is revealed once the soil has ceased contracting in volume

A dense soil may contract slightly (figure 32 right) before granular interlock prevents

further contraction (granular interlock is dependent on the shape of the grains and

their initial packing arrangement) In order to continue shearing once granular

interlock has occurred the soil must dilate (expand in volume) As additional shear

force is required to dilate the soil a peak shear strength occurs (figure 32 left) Once

this peak shear strength caused by dilation has been overcome through continued

shearing the resistance provided by the soil to the applied shear stress reduces

(termed strain softening) Strain softening will continue until no further changes in

volume of the soil occur on continued shearing Peak shear strengths are also

observed in overconsolidated clays where the natural fabric of the soil must be

destroyed prior to reaching constant volume shearing Other effects that result in peak

strengths include cementation and bonding of particles The distinctive shear strength

called the critical state is identified where the soil undergoing shear does so at a

constant volume (Schofield and Wroth 1968)

The inter-particle contact

For frictional soil ie coarse grained soil the friction between particles is the

dominating factor for strength Materials usually consisting of coarse grains (diameter

Figure 31 Bridging effect when flaky particles are combined in the bulk material (Santamarina and

Cho 2004)

Figure 32 The left part of the figure show a typical behaviour of loose and dense material over shear stress

while at the right the figures illustrate the typical volume changes

27

gt 006mm) behave as a frictional soil it means that the strength of coarse soils (silt

sand gravel etc) comes from an inter-particle mechanical friction thus ideally they

do not have traction strength In figure 33 the inter-particle contact is illustrated here

the pressure (P) is applied and two more components are found the normal load (N)

and the tangential load (T) described as the friction coefficient (μF) The forces stand

in equilibrium (Johansson and Vall 2011)

When particles equilibrium is disturbed (friction coefficient is not enough to keep

particles unmoved) the rotation is imminent and it is necessary in order to compact

the soil in figure 34 can be seen that the arrangement is a fact that inhibit or allow this

rotation and the shape in the 3 different scales are also factors because the more

spherical andor more rounded andor less roughness more easy is the rotation

(Santamarina and Cho 2004)

Breakage

Breakage is a side effect of the inter-particle contact and rotation when pressure

exceed the rock strength it can happened when the particles are tight together and

there is not enough space to rotate it is more obvious in angular particles (mesh form)

or as in figure 31 where the flaky particle ldquobridgingrdquo is not able to rotate but it can

brake by the pressure increase Yoginder et al (1985) notice that the angular particle

break during his experiments and they turn more rounded changing the original size

and form configuration at the same time there was a soil properties loosening

Figure 33 Inter-particle contact and forces acting (Axelsson 1998)

Figure 34 Rotation inhibition by the particles compaction or low void ratio (Santamarina and Cho 2004)

28

52 INFLUENCE OF SIZE AND SHAPE

Wenworth (1922a) and Pellegrino (1965) among others suggest that agent transport of

the rocks (rigor of transport temperature and moisture changes etc) determine its

shape but also the particle genesis itself (rock structure mineralogy hardness etc) It

is not possible to determine the shape of the particles based on the agent transport or

genesis but generally a shape behaviour is expected according to Mitchell and Soga

(2005) specially when the particle size is in the clay size (gt2μm) The shapes of the

most common clay minerals are platy (figure 35) with some exceptions (eg

halloysite occurs as tubes kaolinite are large thick and stiff Smectites are composed

of small very thin and filmy particles Illites are intermediate between kaolinite and

smectite and attapulgite occurs in lathlike particle shapes) Some clay minerals

photographs are presented in figure 35

Figure 35 Clay mineral shape a) hallosite b) Kaoline c) Smactites d) Illites and e) attapulgite (Modified

from Mitchell and Soga 2005)

Figure 36 Particle size range in soils Generally the particles of clay size are plate shaped (Mitchell and

Soga 2005)

a) b) c)

e) d)

29

53 VOID RATIO AND POROSITY

The void ratio (e) is the ratio of the volume of voids to the volume of solid it is

defined by the equation

Porosity (n) is the ratio of the volume of voids to the total volume of the soil it is

represented by the equation

Holubec and DrsquoAppolonia (1973) found a relation between the void ratio and

sphericity (referred in the paper as coefficient of angularity ratio of particle surface

and equivalent sphere surface) their results show that the maximum and the minimum

void ratio increases as the shpericity decreases In this study the surface was obtained

for an indirect method based on the permeability developed by Hoffman in 1959

described in the same document Rouseacute et al (2008) defined the roundness as

Wadell (1935) and he found it as an important factor controlling the minimum and

maximum void ratios Some other authors as Youd (1973) and Cho et al (2006)

conclude the same minimum and maximum void ratios increase when sphericity and

roundness decrease Another interesting result (all above authors) was the bigger

influence of the form (sphericity circularity) and roundness on the maximum void

ratio The change of the maximum void ratio is more pronounced than the change of

the minimum void ratio when the form and roundness changes (See figure 39)

Particles arrangement and interlocking are probably the factor that controls the void

ratio bridge effect permit the existence of void among the particles while interlocking

allowed the particles to form arches avoiding the possibility to rotate and stay in a

more stable configuration eg as it happens with marbles

Figures 36 37 and 38 shows proposed empirical relationships between void ratio and

shape from tables 5 and 6 (graphically the scale goes from 0 to 1 when cero mean

high angularity shpericity or circularity and one means low angularity circularity or

sphericity) Holubec and DrsquoAppolonia (1973) data was taken to obtain a power curve

and describe a tendency Santamarina and Cho (2004) show Youd equations in the

original paper Youd (1973) never presented the equation but it is easy to use the

information to draw a trend

The graphics presented in this document (figures 36 37 and 38) must be used with

certain reserves due the fact that the original data was modified in order to fit all

information in one graphic what the figures shows is just the general trend of the

behaviourrsquos material regarding on the shape If more accurate description and

information is required the author recommends consulting the reference data In the

same way equations from Holubec and DrsquoApollonia (1973) and Youd (1973) were not

presented by the authors but the use of the information was taken in order to build up

those equations on tables 6 and 7

S

V

V

V

= e

V

V

=nV

(45)

(46)

30

Table 6 Minimum void ratio equations regarding on the quantity (Ψ for sphericity C for circularity R

for roundness SF for Sukumaran shape factor and AF for Sukumaran angularity factor)

EQUATION NUMBER REFERENCE

Figure 34 (left)

4340

minΨ45490e =

47

Holubec amp DrsquoAppolonia 1973 (Ψ

was obtained using equation 2)

SF06340

mine021903180e +=

48

Sukumaran amp Ashmawy 2001 (SF

obtained using equation 21)

C05101emin

= 49

Cho etal 2006 (C obtained using

figure 12)

Figure 34 (right)

1

minR08203590e +=

50

Youd 1973 (R obtained from figure

11 and table 3)

R34080emin

= 51

Cho et al 2006 (R obtained using

figure 12)

1

minR05104330e +=

52

Rouseacute et al 2008 (R obtained by

equation 21)

AF02330

mine372004160e +=

53

Sukumaran amp Ashmawy 2001 (AF

obtained using equation 37)

Table 7 Maximum void ratio equations regarding on the quantity (Ψ for sphericity C for circularity R

for roundness SF for Sukumaran shape factor and AF for Sukumaran angularity factor)

EQUATION NUMBER REFERENCE

Figure 35 (left)

51520

max Ψ61120e = 54

Holubec and DrsquoAppolonia 1973 (Ψ

was obtained using equation 2)

SF1190

max e0016907180e += 55

Sukumaran amp Ashmawy 2001 (SF

obtained using equation 21)

C86061emax = 56

Cho etal 2006 (C obtained using

figure 12)

Figure 35 (right)

1

max R1505540e += 57

Youd 1973 (R obtained from figure

11 and table 3)

R62031emax= 58

Cho et al 2006 (R obtained using

figure 12)

1

max R107106150e += 59

Rouseacute et al 2008 (R obtained by

equation 21)

AF0530

max e12506090e += 60

Sukumaran amp Ashmawy 2001 (AF

obtained using equation 37)

Comparing figures 37 and 38 (minimum and maximum void ratio) it can be seen on

the right scheme of both figures 37 and 38 (when the factor is roundnessangularity)

that all the empirical relations has a common initial point close to 1 (it means that

particles are well rounded) while this common agreement disappear when the

roundness factor decreases (when the particles become more angular) Same figures

(37 and 38) on the left graphs (when the factor is sphericitycircularityshape) do not

present the same behaviour in fact there is more disperse initial point close to 1(when

the particles tend to be more sphericalcircular)

31

In Figure 39 the Δe (emax-emin) has been plotted to show how the maximum void ratio

and the minimum void ratio has different rate change when the particle shape

changes Maximum void ratio increases more than minimum void ratio when the

particle shape becomes less spherical andor more angular Comparing figure 39 left

and right graphics it can be seen that right present a common initial point when the

quantity (roundnessangularity) is close to one while in the left graphic the initial

point is more disperse Both ending points in both graphics (close to zero) are

dispersed

Figures 37 38 and 39 present the same behaviour right graphics (when the factor is

roundness angularity) in each figure have an initial common point while the left

graphics do not (when the factor is sphericity circularity shape)

Figure 37 Minimum void ratio based upon the relation of shape factor proposed by the authors indicated

in the figure

Figure 38 Maximum void ratio based upon the relation of shape factor proposed by the authors indicated

in the figure

04

06

08

1

12

14

16

18

2

005

015

025

035

045

055

065

075

085

095

Factor (roundness angularity)

min

imu

m v

oid

rati

o

Youd 1973 roundness

Rouse 2008 roundness

Cho 2006 roundness

Sukumaran 2001 AF

03

04

05

06

07

08

09

1

11

12

13

05

015

025

035

045

055

065

075

085

095

Factor (sphericity circularity shape)

min

imu

m v

oid

rati

oHolubec 1973 sphericity

Cho 2006 circularity

Sukumara 2001 SF

05

07

09

11

13

15

17

19

21

00

150

250

350

450

550

650

750

850

95

Factor (sphericity circularity shape)

Maxim

um

vo

id r

ati

o

Holubec 1973 sphericity

Cho 2006 circularity

Sukumara 2001 SF

05

1

15

2

25

3

35

005

015

025

035

045

055

065

075

085

095

Factor (roundness angularity)

Maxim

um

vo

id r

ati

o

Youd 1973 roundness

Rouse 2008 roundness

Cho 2006 roundness

Sukumaran 2001 AF

32

54 ANGLE OF REPOSE

The angle of repose of a granular material is the steepest angle of descent or dip of the

slope relative to the horizontal plane when material on the slope face is on the verge

of sliding as show in figure 40

According to Qazi (1975) there are five types of forces which may act between the

particles in soils

1 Force of friction between the particles

2 Force due to presence of absorbed gas andor moisture of particle

3 Mechanical forces caused by interlocking of particles of irregular shape

4 Electrostatic forces arising from friction between the particles themselves and

the surface with which they come in contact

5 Cohesion forces operating between neighbouring particles

Rouseacute et al (2008) found a decrease of angle of repose with increase roundness

based upon ASTM C1444 test (Standard Test Method for Measuring the Angle of

Repose of Free-Flowing Mold Powders) The method consist in pouring sand on a

surface cover by paper trough a funnel of specific dimensions (the nozzle diameter

depend on the sandrsquos particle size) from an altitude of 15 inches (381 mm) The sand

is release from the funnel until the peak of the cone formed by the sand stops the flow

The repose angle is obtained with the equation

H represent the 15 inches D and d represent the diameter of the cone formed by the

sand and the diameter of the funnel respectively

Figure 39 Maximum minus minimum void ratio based upon the relation of shape factor proposed by the

authors indicated in the figure

0

01

02

03

04

05

06

07

08

09

1

005

015

025

035

045

055

065

075

085

095

Factor (sphericity circularity shape)

Maxim

um

- M

inim

um

Vo

id r

ati

oHolubec 1973 sphericity

Cho 2006 circularity

Sukumara 2001 SF

0

02

04

06

08

1

12

14

16

18

005

015

025

035

045

055

065

075

085

095

Factor (roundness angularity)

Maxim

um

- M

inim

um

Vo

id r

ati

o

Youd 1973 roundness

Rouse 2008 roundness

Cho 2006 roundness

Sukumaran 2001 AF

dD

H2

tan=φ1

rep(61)

33

Rouseacute (2008) shows an empirical relation to obtain the angle of repose based on the

roundness of the particles

55 SHEAR STRENGTH

The MohrndashCoulomb failure criterion represents the linear envelope that is obtained

from a plot of the shear strength of a material versus the applied normal stress This

relation is expressed as

where τ is the shear strength σn is the normal stress co is the intercept of the failure

envelope with the τ axis and is the slope of the failure envelope The quantity c is

often called the cohesion and the angle is called the angle of internal friction

Studies show that the internal friction angle (under drained triaxial tests) increases

more rapidly on those materials having higher angularity increasing the relative

density The internal friction angle is a function of the relative density and the particle

shape (Holubec and DrsquoAppolonia 1973)

Chan and Page (1997) found in a study made with dry copper (using different shapes

and sizes ranging from 180 to 106 μm) using a direct shear test (ring share test) that

the internal friction angle increases as the angularity increases

Shinohara et al (2000) did some experiments with steel powder different shapes

using a triaxial cell in the test Shinohara never used the roundness or angularity on

the work but apply the shape factor (relation long axisshort axis) and the results were

that as this relation deviate from factor 1 the internal friction angle increases

The following empirical relations were found in the literature showing the behaviour

of the friction angle (obtained under different conditions)

)tan( noc

Figure 40 Representation of the angle of repose

(63)

(62)

34

Cho et al (2006)

(64)

(R is obtain by comparing the Krumbein chart figure 13)

Rouseacute (2008)

(65)

(66)

(R is defined using Wadell equation 22)

In figure 41 the suggested empirical relations above and lines constructed using

author data from Holubec and DrsquoAppolonia (1973) and Sukumara and Ashmawy

(2001) are plotted together to display the general trend on the particle shape and

friction angle relation Sukumaran reports two lines one based on the shape factor

(SF) and the second referring the angularity factor (AF) Sukumaran performed the

tests at constant volume

The scale used for Holubec and DrsquoAppolonia (1973) have lower and upper limits of 1

and 2 respectively (angularity form) and a scale change was applied to be able to

presented in the actual figure 41 As in the previous section (52) the author

recommend to use the original data from the references due that the figure just follows

the general trend of the behaviourrsquos particle regarding on the shape

Figure 41 The changes on the internal friction angle shows a general increase when the particle roundness

becomes angular or in the case of Sakamuran less spheric (Shape factor SF)

35

Barton and Kjaernsli (1981) suggested a model (equation 67) to predict the peak

friction angle (φrsquo) based upon numerous trixial and direct shear data tests

where

Se equivalent strength of particle

Re equivalent roughness of particle

φb basic friction angle (obtained from basic tilting test)

σn normal load

The information required for the model is (1) the uniaxial compressive strength of the

rock (2) the d50 particle size (mesh size where 50 of the particles pass through)

required to define Se (figure 42) (3) the degree of particle roundness and (4) the

porosity following compaction All data can be estimated by simple index tests

Barton and Kjaernsli (1981) suggest that particle size and sample scale has an effect

on the friction angle and includes them to obtain the equivalent strength (Se) figure 42

shows the method to obtain this value Compressive strength (σc) was chosen to be the

factor affecting the scale because micro fractures influence this property while

samples are bigger more micro fractures contain and its compressive strength reduces

The equivalent roughness is obtain using figure 43 where is required to know the

porosity (n) and the origin of the particles (a small chart is provided in the same figure

to compare the particles profile)

b

n

ee

SLogR

Figure 42 Method of estimating Equivalent Strength (Se) of rockfill based on uniaxial compressive strength

(σc ) and d50 particle size (Barton amp Kjaernsli 1981)

(67)

36

56 SEDIMENTATION PROPERTIES

A particle released in a less dense Newtonian fluid initially accelerate trough the fluid

due to the gravity Resistances to deformation of the fluid transmitted to the particle

surface drag generate forces that act to resist the particle motion The force due to the

weight (Fw) can be written as

Where ρp ρ are density of the particle and fluid (water) respectively g is the

gravitational force and Vp is the volume of the particle

And the resistance force (FD) is

Where CD is the dimensionless drag coefficient W is the weight of the particle and A

is the cross section area

Particlersquos shape has been assumed to be spherical when equations are applied on the

settling velocity Correlation deviates when particle shape departs from spherical form

Figure 43 Method of estimating Equivalent Roughness (Roe) based on porosity of rockfill

origin material degree of roundedness and smoothness of particle (Barton amp Kjaernsli 1981)

PPW ρ)gV(ρF

A2

WρCF

2

DD

(68)

(69)

37

(Dietrich 1982) and it is known that natural particles depart from spherical form

thus it is evident that this departure would have consequences

The below equation is proposed to account the shape (in this case the Corey shape

factor equation 8) in the settling velocity (Jimenez and Madsen 2003)

Jimenez and Madsen (2003) Dietrich (1982) Briggs and McCulloch (1962) and

others were working in the hydraulic shape of particles to solve problems as sediment

transport It is obvious that the equation presented and the researcherrsquos investigation

works under certain conditions (eg grain size between 0063-1 mm)

Dietrich (1982) suggests an empirical relation that accounts settling velocity size

density shape and roundness of a particle

R1 R2 and R3 are fitted equations for size and density shape and roundness

respectively

57 HYDRAULIC CONDUCTIVITY PERMEABILITY

Darcyrsquos Law Permeability is one component of Darcyrsquos law Darcys law is a simple

proportional relationship between the instantaneous discharge rate through a porous

medium the viscosity of the fluid and the pressure drop

The total velocity Ve is equal to the product of the permeability of the medium

(porous media) k the pressure drop ∆p all divided by the viscosity μ (Muskat

1937)

Darcys law is only valid for slow viscous flow most groundwater flow cases fall in

this category Typically Darcyrsquos law is valid at any flow with laminar flow (see figure

44)

Reynoldrsquos number (Laminar and turbulent Flow) Typically any laminar flow is

considered to have a Reynoldrsquos number less than one and it would be valid to apply

Darcys law Experimental tests have shown that flow regimes with Reynolds numbers

1

ND

S

S

ZY

gd1s

WW

NDN

gd)1s(4

dS

2R1R

3 10RW

pk

Ve

(70)

(71)

(72)

(73)

38

up to 10 may still be Darcian (laminar flow) as in the case of groundwater flow The

Reynolds number (a dimensionless parameter) for porous media flow is typically

expressed as

where ρ is the density of water (units of mass per volume) υ is the specific discharge

(with units of length per time) d is a representative average grain diameter for the

porous media (often taken as the 30 passing size from a grain size analysis using

sieves - with units of length) and μ is the viscosity of the fluid (Muskat 1937)

Shape effects Permeability as Head and Epps (2011) suggested is affected by the

shape and texture of soil grains Elongated or irregular particles create flow paths

which are more tortuous than those spherical particles Particles with a rough surface

texture provide more frictional resistance to flow Both effects tend to reduce the

water flow through the soil

Kozeny-Carman empirical relation accounts for the dependency of permeability on

void ratio in uniformly graded sands serious discrepancies are found when it is

applied to clays due the lack of uniform pores (Mitchell and Soga 2005)

There are various formulations of the Kozeny-Carman equation one published by

Head and Epps (2011) takes the void ratio e the specific surface area Ss and an

angularity factor F into account of permeability k

The angularity factor F considers the shape of the particles and ranges from 11 for

rounded grains 125 for sub rounded to 14 for angular particles The specific surface

Ss is defined as

d1 and d2 represent the maximum and minimum size particle in mm

Kane amp Sternheim (1988) suggest that the inclusion of the shape factor (F) has

probably the background on the Reynolds number due this factor is dependent

significantly on the shape of the obstacles and Reynolds number determines the

presence of laminar or turbulent flow Figure 44 show how the laminar flow has low

energy dissipation while turbulent flow (eg the roughness and path tortuosity) has

high energy dissipation

e1

e

FSs

2k

3

2

dRe

21

6

ddSs

(74)

(75)

(76)

39

According to Nearing and Parker (1994) the amount of soil detached during laminar

and turbulent flow is dependent on each soil and also greater on turbulent flow due the

greater shear strength generated during this kind of flow this could suggest the

greater erosion when turbulent flow is present

58 LIQUEFACTION

Soil liquefaction is a phenomenon in which soil loses much of its strength or stiffness

for a generally short time by earthquake shaking or other rapid loading Static and

dynamic liquefactions occur been the second one the most regular known

Liquefaction often occurs in saturated soils that is soils in which the space between

individual particles is completely filled with water This water exerts a pressure on the

soil particles that influences how tightly the particles themselves are pressed together

Shaking or other rapid loading can cause the water pressure to increase to the point

where the soil particles can readily move with respect to each other (Jefferies and

Been 2000)

Jefferies and Been (2000) state that it is clear that minor variation in intrinsic

properties of sand have major influence on the critical state These might be variations

on grain shape mineralogy grain size distribution surface roughness of grains etc

Yoginder et al (1985) found that substantial decrease on liquefaction resistance

occur with increase in confining pressure for rounded and angular sands (1600 kPa)

also rounded sands show an rapidly build up of resistance against liquefaction with

increasing density while angular tailing sand in contrast show such rapid increase

only at low confining pressures At low confining pressure angular material is more

resistant to liquefaction Probably the breakage of the corners on the angular particles

in tailings is ruling the lost in resistance at high confining pressures (sieve analysis

Figure 44 The figure show the extremes of flow behaviour First turbulent conditions where the flow is

essentially random and unpredictable and second the well defined Laminar flow conditions

40

after test identify the breakage of angular particles while on rounded particles the

sieve analysis was practically the same)

59 GROUNDWATER AND SEEPAGE MODELLING

In groundwater flow the particlersquos shape affects the soilrsquos pore size distribution

hence the flow characteristics (Sperry and Peirce 1995) Tortuosity and permeability

(also see section 57) are two significant macroscopic parameters of granular medium

that affect the passing flow (Hayati et al 2012) Current models incorporating the

effects of particle shape have failed to consider irregular particles such as those that

would prevail in a natural porous medium (Sperry and Peirce 1995)

Hayati et al (2012) suggested based on his results that tortuosity effect converge

when the porosity increases indicating that the shape have dominance at low and mid

porosity ranges

Sperry and Peirce (1995) research conclusions suggest that particle size and porosity

are more important predictors for hydraulic conductivity explaining the 69 of the

variability but particle shape appears to be the next most important This however

apparently comprises particles larger than 295-351 μm Differences for particle size

295-351 μm and smaller are not detectable Another interesting result in the research

was the interaction effect of the particle size and particle shape It suggests a different

packing configuration for particles of the same shape but different size (scale

dependent)

6 DISCUSSION

61 TERMS QUANTITIES AND DEFINITIONS

In order to describe the particle shape in detail there are a number of terms quantities

and definitions (qualitative and quantitative) used in the literature (eg Wadell 1932

1934 Krumbein 1941 Sneed amp Folk 1958) All mathematical definitions

(quantitatives) are models used to simplify the complexity of shape description Some

authors (Mitchell amp Soga 2005 Arasan et al 2010) are using three sub-quantities

one and each describing the shape but at different scales The terms are

morphologyform roundness and surface texture (figure 1) The three sub-quantities

are probably the best way to classify and describe a particle because not a single

definition can interpret the whole morphology Common language is needed when

descriptors are explained and these three scales represent an option It is evident in

the reviewed literature that many of the shape descriptors are presented with the same

name but also that there is not a clear meaning on what this descriptor defines eg

when there is no upper limit in the roundness does it means that the angularity never

ends Could they be more and more angular Probably they could be on theory but

not in reality

41

62 PROPERTIES

Trough various articlersquos review done in the present investigation it is recognized that

the particlersquos shape has an effect on the material properties among these are

1 Porosity (Tickell 1938 Fraser 1935 Kolbuszewski 1948) and void ratio

(Cho et al 2006 Shergold 1953 Rouseacute et al 2008 Santamarina and Cho

2004)

2 Permeability (Witt and Brauns 1983)

3 Internal friction angle (Shinohara et al 2000 Chan and Page 1997

Cheshomi et al 2009)

4 Density (Youd 1973 Holubec and DrsquoAppolonia 1973)

5 Drag coefficient Hydraulics (Briggs and McCulloch 1962)

In Table 5 is a short resume of the properties and shape effect found in peer review

articles trough different journals Most of the reviewed articles based its research on

uniform graded sands

Table 8 Compilation of properties influenced by particle shape

Repose

angle

Friction

angle

Porosity and

Void ratio Density Permeability

Settling velocity

Drag coefficient Deformation

Sphericity (3D)shape factor

NI x x x x x x

Circularity (2D)

NI x x x x NI NI

Roundness x x x x NI NI x

x influence

NI no information available

Shape of particles has an effect on the arrangement producing bridging or avoiding

the rotation of the particles and the resulting geotechnical property is affected eg

including flaky particles can result in a higher void ratio due the bridging effect

(Santamarina and Cho 2004) and depending on the loads even the size distribution is

changed due the breakage (Yoginder et al 1985) in similar way angular particles

produce higher void ratio due the avoided possibility of the particles to rotate and

compact

The influence of the chosen shape descriptor appears in this review to have minor

influence on the soil properties in the reviewed studies except on the void ratio and

the friction angle Influence of particle shape in some cases is hider by other factors

(eg size distribution) also the particle shape probably does not have influence when

particle size is in the clay order (eg hydraulic conductivity) the reason could be due

to forces as electrostatic or capillarity become more important at this level

Among the shape descriptors some are chosen more often in literature (eg aspect

ratio) there is no apparent scientific basis to use it (probably due to the simplicity of

the measurement it becomes one of the most use) but there are still some other

descriptors that may or may not show better correlation with the soil properties

Instead empirical relations had been developed regarding roundness or shape to

describe the soil behaviour it is clear that the mechanism behind the results is still not

completely understood

42

There is necessity to define the best(s) shape descriptor(s) to be used for particular

geotechnical properties

63 IMAGE ANALYSIS

Many image analysis techniques had been used to describe the particle shape eg

Fourier analysis fractal dimension tomography etc (Hyslip and Vallejo 1997) but

there is not agreement on the usage or conclusion to ensure the best particle descriptor

for geotechnical applications

There are several shape descriptors and also various techniques to capture the

particles profile (3-dimensions 3-dimension orthogonal and 2-dimensions) Each

technique presents advantages and disadvantages 3-dimensions is probably the

technique that provide more information about the particle shape but the precision

also lies in the resolution the equipment required to perform such capture could be

more or less sophisticated (scanning particles laying down in one position and later

move to complete the scanning or just falling down particles to scan it in one step)

3-dimensions orthogonal this technique use less sophisticated equipment (compare

with the previous technique) but its use is limited to particles over 1cm also

information between the orthogonal pictures is not capture 2-dimensions require non

sophisticated equipment but at the same time the shape information diminish compare

with the previous due the fact that it is possible to determine only the outline as the

particle measurements are performed in 2-dimensions it is presumed that they will lie

with its shortest axis perpendicular to the laying surface when they are flat but when

the particle tends to have more or less similar axis the laying could be random

Advantages on the use of image analysis are clear there is not subjectivity because it

is possible to obtain same result over the same images Electronic files do not loose

resolution and it is important when collaboration among distant work places is done

files can be send with the entire confidence and knowing that file properties has not

been changed Technology evolutions allowed to work with more information and it

also applies to the image processing area were the time consumed has been shortened

(more images processed in less time)

One important aspect in image analysis is the used resolution in the analysis due the

fact that there are measurements dependent and independent on resolution Thus

those dependent measurements should be avoided due the error included when they

are applied or avoid low resolution to increase the reliability Among these

parameters length is the principal parameter that is influences by resolution (eg

perimeter diameter axis etc) Resolution also has another aspect with two faces

quality versus capacity more resolution (quality) means more storage space a

minimum resolution to obtain reasonable and reliable data must be known but it

depend on each particular application

43

64 APPLICATIONS

Quantify changes in particles in the authorrsquos thought is one of the future applications

due the non-invasive methods of taking photographs in the surface of the damrsquos slope

rail road ballast or roads Sampling of the material and comparing with previous

results could show volume (3D analysis) or area (2D analysis) loss of the particles as

well as the form roundness and roughness This is important when it has been

suggested that a soil or rock embankment decrees their stability properties (eg

internal friction angle) with the loss of sphericity roundness or roughness

Seepage stock piling groundwater etc should try to include the particle shape while

modelling seepage requires grading material to not allow particles move due the

water pressure but in angular materials as it is known the void ratio is great than the

rounded soil it means the space and the possibilities for the small particles to move

are greater stock piling could be modelled incorporating the particle shape to

determine the binrsquos capacity when particle shape changes (void ratio changes when

particle shape changes) Modelling requires all information available and the

understanding of the principles that apply

Industry is actually using the particle shape to understand the soil behaviour and

transform processes into practical and economic image analysis has been included in

the quality control to determine particle shape and size because the advantages it

brings eg the acquisition of the sieving curve for pellets using digital images taken

from conveyor this allows to have the information in a short period of time with a

similar result at least enough from the practical point of view as the traditional

sieving

7 CONCLUSIONS

The conclusions of this literature review are

It has been shown that particle shape has influence on the soil behaviour

despite of partial knowledge of the mechanism behind Understanding of the

particle shape and its influence needs to be accomplished

A common language needs to be built up to standardize the meaning on

geotechnical field that involve the particle shape General relationships

between shape and properties should be developed

Based on this review it is not clear which is the best descriptor to use in

geotechnical engineering affecting he related shape to properties Instead of a

couple of standards there is no shape descriptor in geotechnical field fully

accepted

Image analysis tool is objective make the results repeatable obtain fast results

and work with more amount of information

44

Resolution needs to be taken in consideration when image analysis is been

carried out because the effects could be considerable Resolution must be set

according to the necessities Parameters as perimeter can be affected by

resolution

There are examples where particle shape has been incorporated in industries

related to geotechnical engineering eg in the ballast and asphalt industry for

quality control

8 FURTHER WORK

Three main issues have been identified in this review that will be further investigated

the limits of shape descriptors influence of grading and choice of descriptor for

relation to geotechnical properties

Shape descriptors have low and high limits frequently the limits are not the same and

the ability to describe the particlersquos shape is relative The sensitivity of each descriptor

should be compare to apply the most suitable descriptor in each situation

Sieving curve determine the particle size in a granular soil particle shape could differ

in each sieve size There is the necessity to describe the particle shape on each sieve

portion (due to practical issues) and included in the sieve curve Obtain an average

shape in determined sieve size is complicated (due to the possible presence of several

shapes) and to obtain the particle shape on the overall particlersquos size is challenging

how the particle shape should be included

Since several descriptors have been used to determine the shape of the particles and

the relation with the soil properties it is convenient to determine the descriptorrsquos

correlation with the soil properties

9 ACKNOWLEDGMENT

I would like to thanks to Lulearing University of Technology (LTU) the time I had spent

in its facilities and the kind environment it offers and University of Sonora

(UNISON) that has been providing me the financial support and the time to conclude

this journey

10 REFERENCES

Andersson T (2010) Estimating particle size distributions based on machine vision

Doctoral Thesis Departament of Computer Science and Electrical Engineering Lulearing

University of Technology ISSN 1402-1544 ISBN 978-91-7439-186-2

45

Arasan Seracettin Hasiloglu A Samet Akbulut Suat (2010) Shape particle of

natural and crished aggregate using image analysis International Journal of Civil and

Structural Engineering Vol 1 No 2 pp 221-233 ISSN 0970-4399

Aschenbrenner BC (1956) A new method of expressing particle sphericity Journal

of Sedimentary Petrology Vol 26 No 1 pp 15-31

Axelsson K (1998) Introduktion till jordmekaniken jaumlmte jordmateriallaumlran Skrift

984 Lulearing Avdelningen foumlr Geoteknologi Lulearing Tekniska Universitet (In Swedish)

Barton Nick amp Kjaernsli Bjorn (1981) Shear strength of rockfill Journal of the

Geotechnical Engineering Division Proceedings of the American Society of Civil

Engineers (ASCE) Vol 107 No GT7

Barrett P J (1980) The shape of rock particles a critical review Sedimentology

Vol 27 pp 291-303

Blott S J and Pye K (2008) Particle shape a review and new methods of

characterization and classification Sedimentology Vol 55 pp 31-63

Bowman E T Soga K and Drummond W (2001) Particle shape characterization

using Fourier descriptor analysis Geotechnique Vol 51 No 6 pp 545-554

Briggs L I McCulloch D S (1962) Hydraulic shape of sand particles Journal of

Sedimentary Petrology Vol 32 pp 645-656

Chan Leonard C Y and Page Neil W (1997) Particle fractal and load effects on

internal friction in powders Powder Technology Vol 90 pp 259-266

Cheshomi A Fakher A Jones C J F P (2009) A correlation between friction

angle and particle shape metrics in quaternary coarse alluvia Quarterly Journal of

Engineering Geology and Hydrogeology Vol 42 pp 145-155

Cho G Dodds J and Santamarina J C (2006) Particle shape effects on packing

density stiffness and strength Natural and crushed sands Journal of Geotechnical

and Geoenvironmental Engineering May 2006 pp 591-602

Dietrich William E (1982) Settling velocity of natural particles Water Resources

Research Vol 18 No 6 pp 1615-1626

Dobkins J E and Folk R L (1970) Shape development on Tahiti-nui Journal of

Sedimentary Petrology Vol 40 No 2 pp 1167-1203

Folk R L (1955) Student operator error in determining of roundness sphericity and

grain size Journal of Sedimentary Petrology Vol 25 pp 297-301

Fernlund J M R (1998) The effect of particle form on sieve analysis A test by

image analysis Engineering Geology Vol 50 No 1-2 pp 111-124

46

Fernlund J M R (2005) Image analysis method for determining 3-D shape of

coarse aggregate Cement and Concrete Research Vol 35 Issue 8 pp 1629-1637

Fernlund J M R Zimmerman Robert and Kragic Danica (2007) Influence of

volumemass on grain-size curves and conversion of image-analysis size to sieve size

Engineering Geology Vol 90 No 3-4 pp 124-137

Fraser H J (1935) Experimental study of the porosity and permeability of clastic

sediments The Journal of Geology Vol 43 pp 910-1010 ISSN 0022-1376

Hayati Ali Nemati Ahmadi Mohammad Mehdi and Mohammadi Soheil (2012)

American Physical Society Physical review E 85 036310 DOI

101103PhysRevE85036310

Hawkins A E (1993) The Shape of Powder-Particle Outlines Wiley New York

Head K H and Epps R J (2011) Manual of soil Laboratory testing Volum II

Permeability shear strength and compressibility test 3rd

edition Whittles Publishing

Scotland UK 3rd

edition

Holubec I and DrsquoAppolonia E (1973) Effect of particle shape on the engineering

properties of granular soils ASTM STP 523 pp 304-318

Hyslip James P Vallejo Luis E (1997) Fractal analysis of the roughness and size

distribution of granular materials Engineering Geology Vol 48 pp 231-244

Janoo Vincent C (1998) Quantification of shape angularity and surface texture of

base course materials US Army Corps of Engineers Cold Region Research and

Engineering Laboratory Special report 98-1

Jefferies Mike and Been Ken (2000) Soil liquefaction A critical state approach

Taylor amp Francis Group London and New York

Jimenez Jose A Madsen Ole S (2003) A simple formula to estimate settling

velocity of natural sediments Journal of Waterway Port Coastal and Ocean

Engineering Vol 129 No 2 pp 70-78

Johansson Jens and Vall Jakob (2011) Jordmaterials kornform Inverkan paring

Geotekniska Egenskaper Beskrivande storheter bestaumlmningsmetoder

Examensarbete Avdelningen foumlr Geoteknologi Institutionen foumlr Samhaumlllsbyggnad

och naturresurser Lulearing Tekniska Universitet Lulearing (In Swedish)

Kane Joseph W and Sternheim Morton M (1988) Physics John Wiley amp Sons Inc

Third edition

Kolbuszewski J (1948) An experimental study of the maximum and minimum

porosities of sands Proceedings of the Second International Conference on Soil

Mechanics and Foundation Engineering Rotterdam June 21 to 30 Sub-section IIb

pp 158-165

47

Krumbein W C and Pettijohn FJ (1938) Manual of sedimentary petrography

Appleton-Century Crofts Inc New York

Krumbein W C (1941) Measurement and geological significance of shape and

roundness of sedimentary particles Journal of Sedimentary Petrology Vol 11 No 2

pp 64-72

Krumbein W C and Sloss L L (1963) Stratigraphy and Sedimentation 2nd

ed

WH Freeman San Francisco

Kuo Chun-Yi and Freeman Reed B (1998a) Image analysis evaluation of

aggregates for asphalt concrete mixtures Transportation Research Record Vol 1615

pp 65-71

Kuo Chun-Yi Rollings Raymond and Lynch Larry N (1998b) Morphological

study of coarse aggregates using image analysis Journal of Materials in Civil

Engineering Vol 10 No 3 pp 135-142

Lanaro F Tolppanen P (2002) 3D characterization of coarse aggregates

Engineering Geology Vol 65 pp 17-30

Lees G (1964a) A new method for determining the angularity of particles

Sedimentology Vol 3 pp 2-21

Lees G (1964b) The measurement of particle shape and its influence in engineering

materials British Granite Whinstone Federation Vol 4 No 2 pp 17-38

Matsushima Takashi Saomoto Hidetaka Matsumoto Masaaki Toda Kengo

Yamada Yasuo (2003) Discrete element simulation of an assembly of irregular-

shaped grains Quantitative comparison with experiments 16th ASCE Engineering

Mechanics Conference University of Washington Seattle July 16-18

Mitchell James K and Soga Kenichi (2005) Fundamentals of soil behaviour Third

edition WILEY

Mora C F Kwan A K H Chan H C (1998) Particle size distribution analysis of

coarse aggregate using digital image processing Cement and Concrete Research Vol

28 pp 921-932

Mora C F and Kwan A K H (2000) Sphericity shape factor and convexity

measurement of coarse aggregate for concrete using digital image processing Cement

and Concrete Research Vol 30 No 3 pp 351-358

Muskat Morris (1937) The Flow of fluids through porous media Journal of Applied

Physics Vol 8 pp 274

Nearing M A and Parker S C (1994) Detachment of soil by flowing water under

turbulent and laminar conditions Soil Science Society of American Journal Vol 58

No 6 pp 1612-1614

48

Pan Tongyan Tutumluer Erol Carpenter Samuel H (2006) Effect of coarse

aggregate morphology on permanent deformation behavior of hot mix asphalt Journal

of Transportation Engineering Vol 132 No 7 pp 580-589

Pellegrino A (1965) Geotechnical properties of coarse-grained soils Proceedings

International Conference of Soil Mechanics and Foundation Engineering Vol 1 pp

97-91

Pentland A (1927) A method of measuring the angularity of sands MAG MN AL

Acta Eng Dom Transaction of the Royal Society of Canada Vol 21 Ser3xciii

Persson Anna-Lena (1998) Image analysis of shape and size of fine aggregates

Engineering Geology Vol 50 pp 177-186

Powers M C (1953) A new roundness scale for sedimentary particles Journal of

Sedimentary Petrology Vol 23 No 2 pp 117-119

Pye W and Pye M (1943) Sphericity determination of pebbles and grains Journal

of Sedimentary Petrology Vol 13 No 1 pp 28-34

Qazi M A (1975) Flow properties of granular masses A review on the angle of

repose The Arabian Journal for Science and Engineering Vol 1 No 2

Quiroga Pedro Nel and Fowle David W (2003) The effects of aggregate

characteristics on the performance of portland cement concrete Report ICAR 104-1F

Project number 104 International Center for Aggregates Research University of

Texas

Riley N A (1941) Projection sphericity Journal of Sedimentary Petrology Vol 11

No 2 pp 94-97

Rouseacute P C Fennin R J and Shuttle D A (2008) Influence of roundness on the

void ratio and strength of uniform sand Geotechnique Vol 58 No 3 227-231

Santamarina J C and Cho G C (2004) Soil behaviour The role of particle shape

Proceedings Skempton Conf London

Schofield and Wroth (1968) Critical state soil mechanics McGraw Hill

Shaumlfer Michael (2002) Digital optics Some remarks on the accuracy of particle

image analysis Particle amp Particle Systems Characterization Vol 19 No 3 pp 158-

168

Shergold F A (1953) The percentage of voids in compacted gravel as a measure of

its angularity Magazine of Concrete Research Vol 5 No 13 pp 3-10

Shinohara Kunio Oida Mikihiro Golman Boris (2000) Effect of particle shape on

angle of internal friction by triaxial compression test Powder Technology Vol 107

pp131-136

49

Skredcommisionen (1995) Ingenjoumlrsvetenskapsakademinen rapport 395 Linkoumlping

1995

Sneed E D and Folk R L (1958) Pebbles in the Colorado river Texas A study in

particle morphogenesis Journal of Geology Vol 66 pp 114-150

Sperry James M and Peirce J Jeffrey (1995) A model for estimating the hydraulic

conductivity of granular material based on grain shape grain size and porosity

Ground Water Vol 33 No 6 pp 892-898

Sukumaran B and Ashmawy A K (2001) Quantitative characterisation of the

geometry of discrete particles Geotechnique Vol 51 No 7 pp 619-627

Szaacutedeczy-Kardoss E Von (1933) Die bistimmung der abrollungsgrades Geologie

und palaumlontologie Vol 34B pp 389-401 (in German)

Teller J T (1976) Equantcy versus sphericity Sedimentology Vol 23 pp 427-428

Tickell F G (1938) Effect of the angularity of grain on porosity and permeability

bulletin of the American Association of Petroleum Geologist Vol 22 pp 1272-1274

Tutumluer E Huang H Hashash Y Ghaboussi J (2006) Aggregate shape effects

on ballast tamping and railroad track lateral stability AREMA 2006 Annual

Conference Louisville KY

Wadell H (1932) ldquoVolume Shape and roundness of rock particlesrdquo Journal of

Geology Vol 40 pp 443-451

Wadell H (1933) Sphericity and roundness of rock Particles Journal of Geology

Vol 41 No 3 pp 310ndash331

Wadell H (1934) Shape determination of large sedimental rock fragments

The Pan-American Geologist Vol 61 pp 187-220

Wadell H (1935) ldquoVolume shape and roundness of quartz particlesrdquo Journal of

Geology Vol 43 pp 250-279

Wentworth W C (1922a) The shape of beach pebbles Washington US Geological

Survey Bulletin Vol 131C pp 75-83

Wentworth W C (1922b) A method of measuring and plotting the shape of pebbles

Washington US Geological Survey Bulletin Vol 730C pp 91-114

Wentworth W C (1933) The shape of rock particle A discussion Journal of

Geology Vol 41 pp 306-309

Witt K J Brauns J (1983) Permeability-Anisotropy due to particle shape Journal

of Geotechnical Engineering Vol 109 No 9 pp 1181-1187

7

and rod-like this is summarized on figure 7 Zinggrsquos classification is related with

Krumbein intercept sphericity and the figure 3

In figure 8 the figures 3 and 7 are combined the relation in the two classifications can

be seen it is an easy way to understand the morphology regarding on the a b and c

dimensions

Pye and Pye (1943) in the article ldquosphericity determinations of pebbles and sand

grainsrdquo compare the Wadellrsquos sphericity developed in 1934 (based on the diameter)

with ldquoPebble sphericityrdquo based on an ellipse this last equation (number 5) appears

two years early published by Krumbein (1941) Axis measurement is done as figure 1

denotes for equations 5 trough 12 with exception of equation 8 where the original

document was not possible to obtain

32a

cb

Figure 7 Zinggrsquos classification of pebble shape based on ratios ba and cb (Krumbein 1941)

Figure 8 Classification made by Zinggrsquos and chart to determine sphericity (Krumbein and Sloss 1963)

(5)

8

Sneed amp Folk in (1958) found a relation between the tree dimensional axes called

ldquoMaximum Projection Sphericityrdquo

In a similar way Ashenbrenner (1956) showed his equation at that time named

ldquoWorking Sphericityrdquo

Form or shape factor names are used by authors like Corey (shape factor eq 8) in the

paper published on 1949 Williams (shape factor eq 9) in 1965 Janke (form factor

eq 10) in 1966 and Dobkins amp Folk (oblate-prolate index eq 11) in 1970 (Blott and

Pye 2008)

Aschenbrenner (1956) develop the shape factor by using the relation of the tree axis

but the square of the middle one

3

2

ba

c

))ab((1)bc(16))ab((cb)(11

)ab()bc( 128

22

3 2

ab

c

acb when 1ac

b acb when

b

ac-1 2

22

2

3

cba

c

222

a

c

50c-a

b-a10

2b

ac

(6)

(7)

(8)

(9)

(10)

(11)

(12)

9

Table 2 General overview over different particle shape definitions for 3D sphericity has been compiled

and arranged chronologically

Aspect Name Author Year Based on

Sphericity (3D) Flatness index Wentworth 1922a 3-axes

True Sphericity Wadell 1932 Surface

Operational sphericity Wadell 1932 Volume

Sphericity Wadell 1934 Sphere diameter

Zinggrsquos clasification Zinggrsquos1

1935 3-axes

Intercept sphericity chart Krumbein 1941 3-axes

Pebble sphericity Pye and Pye 1943 3-axes

Corey shape factor Corey2

1949 3-axes

Working sphericity Ashenbrenner 1956 3-axes

shape factor Ashenbrenner 1956 3-axes

Maximum projection sphericity Sneed amp Folk 1958 3-axes

Williams shape factor Williams2

1965 3-axes

Janke form factor Janke2

1966 3-axes

Oblate-prolate index Dobkins amp Folk 1970 3-axes 1) Krumbein and Sloss 1963 2) Blott and Pye 2008

34 FORM (2D)

The technique to measure the sphericity is based in tree dimensions it can be found in

literature some ways to measure the ldquotwo dimensions sphericityrdquo which is simply the

perimeter of the particle projection some authors named ldquoparticle outlinerdquo or

ldquocircularityrdquo

Wadell in 1935 (Hawkins 1993) adopt a conversion of his 1934 3D sphericity

formula (equation 4) to a 2D outline He defined an orientation on the particles and

they were based on the maximum cross sectional area (outline of the particle

projecting the maximum area) The equations show the relation between diameters of

a circle of same area and smallest circumscribed circle

He also used the term ldquodegree of circularityrdquo as the ratio of the perimeter of a circle of

same area and the actual particle perimeter

Tickell in 1931 (Hawkins 1993) used his empirical relation The particle orientation

proposed was a random one It is described by the ratio between the area outline and

the area of smallest circumscribed circle

C

A

D

DC

P

PC C

CA

AC

(13)

(14)

(15)

10

Some other authors has been working with the ldquocircularityrdquo concept and had develop

them own equations as Pentland (1927) relating the area outline and area of a circle

with diameter equal to longest length outline and Cox (Riley 1941) with the ratio

area and perimeter time a constant equations 16 and 17 respectively Both authors did

not define any definite orientation of the grains

Riley (1941) realize the problems that an area perimeter and some other

measurements proposed by the above authors can carry as the time consuming and

tedious work (at that time were not computer all was made by hand) and thatrsquos why

he develop this equation easy to handle called ldquoinscribed circle sphericityrdquo He used

the same particle orientation proposed by Wadell and the relation of diameters of

inscribed and circumscribed circles

Horton 1932 (Hawkins 1993) use the relation of the drainage basing perimeter and

the perimeter of a circle of the same area as drainage basin

Janoo in 1998 (Blott and Pye 2008) develop his general ratio of perimeter to area

Sukumaran and Ashmawy (2001) develop his own shape factor (SF) defined as the

deviation of the global particle outline from a circle Figure 9 can be used as a

reference to determine the items used in the equation 21

N is referred to the number of sampling intervals o radial divisions

C2A

AC

2P

A4C

C

I

D

DC

CD

D

P

PC

A

PC

2

45ordm x N

Particleα

= SF

sumN

1=ii

(16)

(17)

(18)

(19)

(20)

(21)

11

Table 3 General chronological overview of the particle shape definitions for 2D sphericity

Aspect Name Author Year Based on

Circularity (2D) roundness Pentland 1927 area

roundness Cox1

1927 area-perimeter

roundness Tickell2

1931 area

Circularity Horton2

1932 drainage basin

outline circularity Wadell 1935 Circle diameter

degree of circularity Wadell 1935 Perimeter

inscribed circle sphericity Riley 1941 Circle diameter

Circularity Krumbein and Sloss 1963 chart

Janoo 1998 area-perimeter

Shape factor Sukumaran 2001 Segmentation of particle and angles

1) Riley 1941 2) Hawkins 1993

35 ROUNDNESS OR ANGULARITY

Roundness as described in section 32 is the second order shape descriptor Sphericity

lefts beside the corners and how they are this was notice by most of the authors sited

before and they suggested many ways to describe this second order particle property

Roundness is clearly understandable using the figure 10 Particle shape or form is the

overall configuration and denotes the similarities with a sphere (3D) or a circle (2D)

Roundness is concerning about the sharpness or the smoothness of the perimeter (2D)

Surface texture (Barret 1980) is describe as the third order subject (form is the first

and roundness the second) and it is superimposed in the corners and it is also a

property of particles surfaces between corners

Figure 9 Description of the Sukumaran factors to determine the shape and angularity (Sukumaran and

Ashmawy 2001)

12

Wadell (1935) describes his methodology calling it total degree or roundness to

obtain the roundness of a particle using the average radius of the corners in relation

with the inscribed circle diameter (see figure 11) on the equation

In the same study Wadell (1935) has used the equation

This two last equation shows slightly differences on the results (Wadell 1935)

Powers (1953) also published a graphic scale to illustrate the qualitative measure

(figure 12) It is important to highlight that any comparing chart to describe particle

properties has a high degree of subjectivity Folk (1955) concludes that when charts

are used for classification the risk of getting errors is negligible for sphericity but

large for roundness

N

R

r

Rinmax

r

R

NR

inmax

Figure 10 Form (shape) Roundness and Texture graphical description (Bowman et al 2001)

Figure 11 Wadellrsquos method to estimate the roundness corners radius and inscribed circle

(Hawkins 1993)

(22)

(23)

13

Some authors as Russel amp Taylor in 1937 Pettijohn in 1957 and Powers in 1953

developed a classification based on five and six classes (Hawkins 1993) each one

with its own class limits it is important to denote that the way they measure the

roundness is the developed by Wadell (1935) This classification and class limits are

showed in the table 4

Table 4 Degrees of roundness Wadell Values (Hawkins 1993) NA = no-applicable

Grade terms Russell amp Taylor (1937) Pettijohn (1957) Powers (1953)

Class

limits (R)

Arithmetic

midpoint

Class limits

(R)

Arithmetic midpoint Class

limits (R)

Arithmetic

midpoint

Very angular

NA

NA

NA

NA

012-017

014

Angular

000-015

0075

000-015

0125

017-025

021

Subangular

015-030

0225

015-025

0200

025-035

030

Subrounded

030-050

0400

025-040

0315

035-049

041

Rounded

050-070

0600

040-060

0500

049-070

059

Well rounded

070-100

0800

060-100

0800

070-100

084

Krumbein and Sloss (1963) published a graphical chart easy to determine the

sphericity and roundness parameters using comparison See figure 13 (Cho et al

2006)

Figure 12 A Roundness qualitative scale (Powers 1953)

Figure 13 Sphericity and roundness chart (Cho et al 2006) The roundness equation that appears here in

the chart is the wadellrsquos equation number 22

14

Fischer in 1933 (Hawkins 1993) used a straightforward method to quantify roundness

using a central point in the outline and dividing the outline in angles around this point

that were subtended by the straight or non curved parts of the profile were measured

This is illustrated in figure 14

To express the angularity value Fischer used the ratio of angles standing linear parts

on the outlines and concave respectively

Figure 14 left (A) and right (B) gives a similar angularity of approximately 042

using the above equations (Hawkins 1993)

Wentworth in 1922 used the maximum projection to define the position of the particle

to obtain the outline or contour (Barret 1980) The equation reflects the relation of the

diameter of a circle fitting the sharpest corner and the longest axis plus the shortest

axis c (minimum projection)

Wentworth (Hawkins 1993) expressed the roundness as the ratio of the radius of

curvature of the most convex part and the longest axis plus short axis

Actually these last two equations are the same just expressed in different terms when

the particle is in its maximum projection

Dimensions can be seen on figure 15 L and B represents the mayor axis a and

intermediate axis b The intention is to make difference between the 2 and 3

dimensions (L and B are for 2D as a b and c are for 3D)

deg360

ANG

=R

sumPLA

PLA

CON

ANG

ANGR

2)S(L

DR

M

S

B)4(L

RR CON

Figure 14 Fischerrsquos methods of angularity computation (Hawkins 1993)

A=inscribed circle B=circumscribed circle

(24)

(25)

(26)

(27)

15

Wentworth 1919 has a second way to express the roundness called Shape index

(Barrett 1980) and it relates the sharpest corner and the diameter of a pebble trough

the sharpest corner

Wentworth (1922b) used define the roundness as the ratio of the sharpest corner and

the average radius of the pebble

Cailleux (Barrett 1980) relates the radius of the most convex part and the longest

axis

Kuenen in 1956 show his roundness index (Barrett 1980) between the sharpest corner

and the breath axis

Dobkins amp Folk (1970) used a modified Wentworth roundness with the relation of

sharpest corner and inscribed circle diameters

AVG

CON

R

RR

x

s

D

DR

L2

RR CON

B

DR s

i

s

D

DR

3AVGAVG cbaDR2

Figure 15 Description of L and B axes (Hawkins 1993)

(28)

(29)

(30)

(31)

(32)

(33)

16

Swan in 1974 shows his equation (Barrett 1980) relating the sharpest (or the two

sharpest) corner(s) and inscribed circle diameter

Szadeczsky-Kardoss has his Average roundness of outline (Krumbein and Pettijohn

1938) relating the concave parts perimeter and the actual perimeter

Lees (1964a) developed an opposite definition to roundness it means that he

measures the angularity instead of the roundness and he calls it Degree of angularity

Figure 16 shows the items considered when equation 36 applies as the angles (α)

inscribed circle (Rmax-in) and the distance (x) The main formula is

In order to apply the last equation corners needs to be entered in the formula and each

individual result will add to each other to obtain the final degree of angularity

A roundness index appears on Janoo (1998) Kuo and Freeman (1998a) and Kuo et

al (1998b) it is described as

The last equation is on section 34 also because there is not a general agreement on the

definition furthermore some authors had used to define the roughness this is not the

only equation that has been used trying to define different aspects (sphericity

roundness or roughness) but it is a good example of the misuse of the quantities and

definitions

inmaxR

x)180(R

2P

A4R

i

ss

D

DDR

221

100P

PR CON

Figure 16 Degree of angularity measurement technique (Blot and Pye 2008)

(34)

(35)

(36)

(17)

17

Sukumaran and Ashmawy (2001) present an angularity factor (AF) calculated from

the number of sharpness corners Angles βi required to obtain the angularity factor are

shown in figure 9

Sukumaran and Ashmawy (2001) also suggested use not bigger sampling interval of

N=40 because it is the cut off between angularity factor and surface roughness If so

this equation could be used to describe the roughness

Table 5 General chronological overview of the particle roundness

Aspect Name Author Year Based on

Roundness shape index Wentworth 19191

diameter of sharper corner

shape index Wentworth 1922b sharpest corner and axis

roundness Wentworth 1933 convex parts

Fischer 19332

noncurved parts outline

Fischer 19332

noncurved-streigth parts outline

Average roundness of outline

Szadeczsky-Kardoss 19333

convex parts-perimeter

roundness Wadell 1935 diameter of corners

roundness Wadell 1935 diameter of corners

roundness Russel amp Taylor 19372

class limit table

roundness Krumbein 1941 chart

Cailleux 19471

convex parts

roundness Pettijohn 19494 class limit table

roundness Powers 1953 chart and class limit table

Kuenen 19561

axis-convex corner

roundness Krumbein and Sloss 1963 chart

degree of angularity Lees 1964a corners angles and inscribed circle

Dobkins amp Folk 1970 diameter of sharper corner

Swan 19741

diameter of sharper corners

Angularity factor Sukumaran and

Ashmawy 2001

Segmentation of particles and angles

1) Barret 1980 2) Hawkins 1993 3) Krumbein and Pettijohn 1938 4) Powers 1953

sum

sumsumN

1=i

2

i

2

N

1=i

2

i

2N

1=ii

)ordm180 -circleβ( - )(180ordm x 3

)ordm180-circleβ(-)ordm180 -Particleβ(

= AF (37)

18

36 ROUGHNESS OR SURFACE TEXTURE

A third property called texture appears early in the literature with the sphericity and

roundness properties since then texture property was longed described but it was in

accordance with the authors at that time not measurable

Wright in 1955 developed a method to quantify the surface texture or roughness of

concrete aggregate using studies done on 19 mm stones The test aggregates were first

embedded in a synthetic resin The stones were cut in thin sections The sections

projection was magnified 125 times The unevenness of the surface was traced and the

total length of the trace was measured The length was then compared with an uneven

line drawn as a series of chords (see figure 17) The difference between these two

lines was defined as the roughness factor (Janoo 1998)

However with the advance of technology it has become easier measure the roughness

and here is presented some researcherrsquos ideas how this property should be calculated

One technique used by Janoo (1988) to define the roughness can be seen in figure 18a

and is defined as the ratio between perimeter and convex perimeter

The convex perimeter is obtained using the Feretrsquos box (or diameter) tending a line in

between the touching points that the Feretrsquos box describes each time it is turn (figure

18b)

PER

OC

PR

Figure 17 Measurement method for characterizing the surface texture of an aggregate (Janoo 1998)

a) Convex perimeter (CPER) b) Feret measurement Figure 18 a) Convex perimeter (CPER) b) Feret measurement (modified after Janoo 1998)

(38)

a)

b)

19

Kuo and Freeman (1998a) and Kuo et al (1998b) use the roughness definition as the

ratio perimeter and average diameter

Erosion and dilatation image processing techniques are used to obtain the surface

texture Erosion is a morphological process by which boundary image pixels are

removed from an object surface which leaves the object less dense along the

perimeter or outer boundary Dilatation is the reverse process of erosion and a single

dilatation cycle increases the particle shape or image dimension by adding pixels

around its boundary (Pan etal 2006)

The ldquonrdquo erosion and dilatation cycles are not standardized

Mora and Kwan (2000) used the ldquoconvexity ratio CRrdquo (equation 41) and the ldquofullness

ratio FRrdquo (equation 42) in their investigation they are

The convex area is the area of the minimum convex boundaries circumscribing the

particle This is illustrated in the figure 19 The convex area is obtained in a similar

way as the convex perimeter but in this case the area between the original outline and

the convex perimeter is our convex area

AVG

OD

PR

100A

1AARO

CONo A

AR =

CONo A

AR =

Figure 19 Evaluation of area and convex area (Mora and Kuan 2000)

(39)

(40)

(41)

(42)

20

4 TECHNIQUES IN ORDER TO DETERMINE PARTICLE

SHAPE

41 HAND MEASUREMENT

Hand measurement technique was the first used by obvious reasons in order to

improve the accuracy special devices developed as the ldquosliding rod caliperrdquo used by

Krumbein (1941) it works placing the sample on the sliding road calliper as show

figure 20b the length in different positions can be obtain by using the scale provided

in the handle the ldquoconvexity gagerdquo that was actually used by opticians to measure the

curvature of lenses but easily applicable to the particle shape analysis (Wentworth

1922b) works measuring the movement of the central pivot as figure 20a shows (the

two adjacent pivots are invariable) as many the central pivot moves more is the

curvature or the ldquoSzadeczky-Kardossrsquos apparatusrdquo develop in 1933 that traces the

profile of the rock fragment so the outline traced is then analyzed (Krumbein and

Pettijohn 1938) figure 20c show equipment

Another helpful tool to determine the particle dimensions was the ldquocamera lucidardquo to

project the particlersquos contour over a circle scale appearing in Figure 21 thus it is

possible to measure the particlersquos diameter

a)

c) b)

Figure 20 a) convexity gage used to determine the curvature in particle corners (Wenworth 1922b)

b)sliding rod caliper device to measure the particle axis length (Krumbein 1941) and c)Szadeczky-

Kardoss (1933) apparatus it was utilized to obtain the particle outline

Figure 21 Circle scale used by Wadell (1935) to determine particlersquos diameter and roundness

21

42 SIEVE ANALYSIS

Bar sieving eg according to EN 933-31997 can be used to determine simple large

scale properties By combining mesh geometries the obtained results can be used to

quantify flakiness and elongation index ASTM D4791 (Flat and elongated particles

are defined as those coarse aggregate particles that have a ratio of length to thickness

equal to or greater than a specified value such as 51 The index represents the

percentage on weight of these particles) The method is not suitable for fine materials

This due to the difficulty to get the fine grains passed through the sieve and the great

amount of particles in relation to the area of the sieve (Persson 1998) eg EN 933-

31997 related to flakiness index The test is performed on aggregates with grain size

from 4 mm and up to 63 mm two sieving operations are necessary the first separates

on size fraction and the second use a bar sieve after the first sieving the average

maximum diameter of the particles is obtain and with the second sieving (bar sieving)

the shortest axis diameter is found finally with this two parameters the flakiness

index is determined

There are more standards related with the particle shape (see appendix A) but this

above presented are probably the most known using sieve analysis to determine

particlersquos geometrical properties

Sieve analysis is facing the computers age and image analysis sieving research is

taking place (Andersson 2010 Mora and Kwan 2000 Persson 1998) Industry is

also applying the image analysis sieving with decrees on the testing time compare

with the traditional sieving method An inconvenient of image analysis is the error

due the overlapping or hiding of the particles during the capture process but the

advantages are more compare with disadvantages (Anderson 2010)

43 CHART COMPARISON

Charts developed over the necessity of faster results because the long time consuming

required when measuring each particle

Krumbein (1941) present a comparison roundness chart for pebbles which were

measured by Wadellrsquos method because this property was the most difficult to measure

due to the second order scale that roundness represents (See figure 22)

Figure 22 Krumbein (1941) comparision chart for roundness

22

A qualitative chart by Powers (1953) try to include both (sphericity and roundness)

particlersquos characteristics it was divided on six roundness ranges (very angular

angular sub-angular sub-rounded rounded and well rounded) and two sphericity

series (high and low sphericity) This chart was prepared with photographs to enhance

the reader perspective (See figure 23)

A new chart including sphericity and roundness appear this time it was easier to

handle the two mean properties of particlersquos shape furthermore there was included

the numerical values that eliminated the subjectivity of qualitative description The

chart is based on Wadellrsquos definitions (Krumbein and Sloss 1963) (See figure 24)

Folk (1955) worried about the personrsquos error on the chartrsquos comparison studied the

determination of sphericity and angularity (he used the Powers 1953 comparison

chart) he found that the sphericity determination by chart comparison has a negligible

error while the roundness he concluded it was necessary to carry out a more wide

research due the high variability show by his study

Figure 23 Powers (1953) qualitative shpericity-roundness chart

Figure 24 Sphericity-roundness comparison chart (Krumbein and sloss 1963)

23

44 IMAGE ANALYSIS

Image analysis is a practical method to use for shape classification since it is fast and

can be automated Different techniques appear to process these images among them

are

o Feret Diameter the Feret diameter is the longitude between two parallel lines

this lines can rotate around one particle or outline to define dimensions as it

is shown in figure 25 these method is not a fine descriptor but as it was say

above it is a helpful tool to determine diameters (Janoo 1988)

o Fourier Mathematical Technique It produces mathematical relations that

characterize the profile of individual particles This method favours the

analysis of roughness and textural features for granular soils The problem in

the methodology remains in the re-entrant angles in order to complete the

revolution (Bowman et al 2001) see figure 26

o Fractal Dimension Irregular line at any level of scrutiny is by definition

fractal (Hyslip and Vallejo 1997) Figure 27 shows fractal analysis by the

dividing method The length of the fractal line can be defined as

N

1n

nn0 )nsinbncosa(a)(R

RD1n)(P

Figure 25 Feret measurement technique is defined by two parallel lines turning

around the particle to define the shortest and longest Feret diameter (Janoo 1988)

Figure 26 Fourier technique with two radiuses at one angle (Bowman et al 2001)

(43)

(44)

24

o Orthogonal image analysis This technique is basically the use of two images

orthogonal between them to acquire the three particle dimensions (Fernlund

2005) any of the above techniques can be used in this orthogonal way

o Laser Scanning Technique this kind of laser scanning 3D is one of the most

advanced techniques In figures 28a) we have the laser head scanning the rock

particles the particles have control points in order to keep a reference point

when move them to scan the lower part in figure 28b) we can see the laser

path followed (Lanaro and Tolppanen 2002)

Another technique is the Laser-Aided Tomography (LAT) in this case a laser sheet is

used to obtain the particles surveying (see figure 29) This technique is different and

has special requirements as to use liquid with same refractive index as the particles

particles must let the laser or certain percent of light go through (Matsushima et al

2003)

a) b)

Figure 27 Fractal analysis by the dividing method at different scrutiny scale (Hyslip and Vallejo 1997)

Figure 28 a) Scanning head b) scanning path (Lanaro and Tolppanen 2002)

Figure 30 3D scan completed ready to

use for any further measure

(Matsushima et al 2003)

Figure 29 LAT scaning particles

(Matsushima et al 2003)

25

Both 3D techniques obtain the particle shape that is later used to achieve measures as

we can see in figure 30

All these previous techniques are easily written in codes or scripts to be interpreted in

a digital way obtaining the desired measurement but there are some interesting points

in the image analysis regarding on the errors involve among them are image

resolution and orientation of the particles orientation is not relevant when it is

random and large number of particles are involve resolution have an influence on the

accuracy (Zeidan et al 2007)

When resolution is increase more accuracy is obtain and the object representation

match better with the real form in the other hand more resolution means more

spending on memory and time thus resolution needs to be according with the goal

and precision needed in any work (Schaumlfer 2002)

Schaumlfer (2002) conclude that attributes like length when measuring digital images

present relative high errors It can be vanish or at least diminish using high resolution

just for diameter but not for perimeter that keep the error as big as initially Johansson

and Vall (2011) obtain similar results when 3 different resolutions were used in the

same particle obtaining an unstable output for those termsquantities that involve the

perimeter Thus all quantities relating the perimeter should be treated with care

5 EFFECT OF SHAPE ON SOIL PROPERTIES

51 INTRODUCTION

In laboratory test on the effect on particle size on basic properties has been

investigated in several studies this relation has been discussed and various

mechanisms had been proposed to explain the behaviour of the soil in dependency

also with the shape Basically there are two mechanisms proposed The arrangement

of particles and the inter-particle contact (Santamarina and Cho 2004) and

subsequence breakage

The arrangement of particles

Arrangement of the particles can be presented in three different forms loose dense

and critical this arrangement determines the soil properties (eg density increase with

more dense arrangement) Loose and dense states are easy understandable when

figure 31 is explained while in the upper part of the figure the particles are arranged

using the minimum space needed in the lower part a span is created using the flaky

particle as a bridge this phenomena is known as ldquobridgingrdquo Bridging can produce

different geotechnical results when just the shape of the particle is changed eg void

ratio (Santamarina and Cho 2004) Particles are able to rearrange this could be done

applying pressure (energy) to the soil the pressure (energy) will create such forces

that soil particles will rotate and move (see figure 34) finishing in a more dense state

26

A loose soil will contract in volume on shearing and may not develop any peak

strength (figure 32 left) In this case the shear strength will increase gradually until

the residual shear strength is revealed once the soil has ceased contracting in volume

A dense soil may contract slightly (figure 32 right) before granular interlock prevents

further contraction (granular interlock is dependent on the shape of the grains and

their initial packing arrangement) In order to continue shearing once granular

interlock has occurred the soil must dilate (expand in volume) As additional shear

force is required to dilate the soil a peak shear strength occurs (figure 32 left) Once

this peak shear strength caused by dilation has been overcome through continued

shearing the resistance provided by the soil to the applied shear stress reduces

(termed strain softening) Strain softening will continue until no further changes in

volume of the soil occur on continued shearing Peak shear strengths are also

observed in overconsolidated clays where the natural fabric of the soil must be

destroyed prior to reaching constant volume shearing Other effects that result in peak

strengths include cementation and bonding of particles The distinctive shear strength

called the critical state is identified where the soil undergoing shear does so at a

constant volume (Schofield and Wroth 1968)

The inter-particle contact

For frictional soil ie coarse grained soil the friction between particles is the

dominating factor for strength Materials usually consisting of coarse grains (diameter

Figure 31 Bridging effect when flaky particles are combined in the bulk material (Santamarina and

Cho 2004)

Figure 32 The left part of the figure show a typical behaviour of loose and dense material over shear stress

while at the right the figures illustrate the typical volume changes

27

gt 006mm) behave as a frictional soil it means that the strength of coarse soils (silt

sand gravel etc) comes from an inter-particle mechanical friction thus ideally they

do not have traction strength In figure 33 the inter-particle contact is illustrated here

the pressure (P) is applied and two more components are found the normal load (N)

and the tangential load (T) described as the friction coefficient (μF) The forces stand

in equilibrium (Johansson and Vall 2011)

When particles equilibrium is disturbed (friction coefficient is not enough to keep

particles unmoved) the rotation is imminent and it is necessary in order to compact

the soil in figure 34 can be seen that the arrangement is a fact that inhibit or allow this

rotation and the shape in the 3 different scales are also factors because the more

spherical andor more rounded andor less roughness more easy is the rotation

(Santamarina and Cho 2004)

Breakage

Breakage is a side effect of the inter-particle contact and rotation when pressure

exceed the rock strength it can happened when the particles are tight together and

there is not enough space to rotate it is more obvious in angular particles (mesh form)

or as in figure 31 where the flaky particle ldquobridgingrdquo is not able to rotate but it can

brake by the pressure increase Yoginder et al (1985) notice that the angular particle

break during his experiments and they turn more rounded changing the original size

and form configuration at the same time there was a soil properties loosening

Figure 33 Inter-particle contact and forces acting (Axelsson 1998)

Figure 34 Rotation inhibition by the particles compaction or low void ratio (Santamarina and Cho 2004)

28

52 INFLUENCE OF SIZE AND SHAPE

Wenworth (1922a) and Pellegrino (1965) among others suggest that agent transport of

the rocks (rigor of transport temperature and moisture changes etc) determine its

shape but also the particle genesis itself (rock structure mineralogy hardness etc) It

is not possible to determine the shape of the particles based on the agent transport or

genesis but generally a shape behaviour is expected according to Mitchell and Soga

(2005) specially when the particle size is in the clay size (gt2μm) The shapes of the

most common clay minerals are platy (figure 35) with some exceptions (eg

halloysite occurs as tubes kaolinite are large thick and stiff Smectites are composed

of small very thin and filmy particles Illites are intermediate between kaolinite and

smectite and attapulgite occurs in lathlike particle shapes) Some clay minerals

photographs are presented in figure 35

Figure 35 Clay mineral shape a) hallosite b) Kaoline c) Smactites d) Illites and e) attapulgite (Modified

from Mitchell and Soga 2005)

Figure 36 Particle size range in soils Generally the particles of clay size are plate shaped (Mitchell and

Soga 2005)

a) b) c)

e) d)

29

53 VOID RATIO AND POROSITY

The void ratio (e) is the ratio of the volume of voids to the volume of solid it is

defined by the equation

Porosity (n) is the ratio of the volume of voids to the total volume of the soil it is

represented by the equation

Holubec and DrsquoAppolonia (1973) found a relation between the void ratio and

sphericity (referred in the paper as coefficient of angularity ratio of particle surface

and equivalent sphere surface) their results show that the maximum and the minimum

void ratio increases as the shpericity decreases In this study the surface was obtained

for an indirect method based on the permeability developed by Hoffman in 1959

described in the same document Rouseacute et al (2008) defined the roundness as

Wadell (1935) and he found it as an important factor controlling the minimum and

maximum void ratios Some other authors as Youd (1973) and Cho et al (2006)

conclude the same minimum and maximum void ratios increase when sphericity and

roundness decrease Another interesting result (all above authors) was the bigger

influence of the form (sphericity circularity) and roundness on the maximum void

ratio The change of the maximum void ratio is more pronounced than the change of

the minimum void ratio when the form and roundness changes (See figure 39)

Particles arrangement and interlocking are probably the factor that controls the void

ratio bridge effect permit the existence of void among the particles while interlocking

allowed the particles to form arches avoiding the possibility to rotate and stay in a

more stable configuration eg as it happens with marbles

Figures 36 37 and 38 shows proposed empirical relationships between void ratio and

shape from tables 5 and 6 (graphically the scale goes from 0 to 1 when cero mean

high angularity shpericity or circularity and one means low angularity circularity or

sphericity) Holubec and DrsquoAppolonia (1973) data was taken to obtain a power curve

and describe a tendency Santamarina and Cho (2004) show Youd equations in the

original paper Youd (1973) never presented the equation but it is easy to use the

information to draw a trend

The graphics presented in this document (figures 36 37 and 38) must be used with

certain reserves due the fact that the original data was modified in order to fit all

information in one graphic what the figures shows is just the general trend of the

behaviourrsquos material regarding on the shape If more accurate description and

information is required the author recommends consulting the reference data In the

same way equations from Holubec and DrsquoApollonia (1973) and Youd (1973) were not

presented by the authors but the use of the information was taken in order to build up

those equations on tables 6 and 7

S

V

V

V

= e

V

V

=nV

(45)

(46)

30

Table 6 Minimum void ratio equations regarding on the quantity (Ψ for sphericity C for circularity R

for roundness SF for Sukumaran shape factor and AF for Sukumaran angularity factor)

EQUATION NUMBER REFERENCE

Figure 34 (left)

4340

minΨ45490e =

47

Holubec amp DrsquoAppolonia 1973 (Ψ

was obtained using equation 2)

SF06340

mine021903180e +=

48

Sukumaran amp Ashmawy 2001 (SF

obtained using equation 21)

C05101emin

= 49

Cho etal 2006 (C obtained using

figure 12)

Figure 34 (right)

1

minR08203590e +=

50

Youd 1973 (R obtained from figure

11 and table 3)

R34080emin

= 51

Cho et al 2006 (R obtained using

figure 12)

1

minR05104330e +=

52

Rouseacute et al 2008 (R obtained by

equation 21)

AF02330

mine372004160e +=

53

Sukumaran amp Ashmawy 2001 (AF

obtained using equation 37)

Table 7 Maximum void ratio equations regarding on the quantity (Ψ for sphericity C for circularity R

for roundness SF for Sukumaran shape factor and AF for Sukumaran angularity factor)

EQUATION NUMBER REFERENCE

Figure 35 (left)

51520

max Ψ61120e = 54

Holubec and DrsquoAppolonia 1973 (Ψ

was obtained using equation 2)

SF1190

max e0016907180e += 55

Sukumaran amp Ashmawy 2001 (SF

obtained using equation 21)

C86061emax = 56

Cho etal 2006 (C obtained using

figure 12)

Figure 35 (right)

1

max R1505540e += 57

Youd 1973 (R obtained from figure

11 and table 3)

R62031emax= 58

Cho et al 2006 (R obtained using

figure 12)

1

max R107106150e += 59

Rouseacute et al 2008 (R obtained by

equation 21)

AF0530

max e12506090e += 60

Sukumaran amp Ashmawy 2001 (AF

obtained using equation 37)

Comparing figures 37 and 38 (minimum and maximum void ratio) it can be seen on

the right scheme of both figures 37 and 38 (when the factor is roundnessangularity)

that all the empirical relations has a common initial point close to 1 (it means that

particles are well rounded) while this common agreement disappear when the

roundness factor decreases (when the particles become more angular) Same figures

(37 and 38) on the left graphs (when the factor is sphericitycircularityshape) do not

present the same behaviour in fact there is more disperse initial point close to 1(when

the particles tend to be more sphericalcircular)

31

In Figure 39 the Δe (emax-emin) has been plotted to show how the maximum void ratio

and the minimum void ratio has different rate change when the particle shape

changes Maximum void ratio increases more than minimum void ratio when the

particle shape becomes less spherical andor more angular Comparing figure 39 left

and right graphics it can be seen that right present a common initial point when the

quantity (roundnessangularity) is close to one while in the left graphic the initial

point is more disperse Both ending points in both graphics (close to zero) are

dispersed

Figures 37 38 and 39 present the same behaviour right graphics (when the factor is

roundness angularity) in each figure have an initial common point while the left

graphics do not (when the factor is sphericity circularity shape)

Figure 37 Minimum void ratio based upon the relation of shape factor proposed by the authors indicated

in the figure

Figure 38 Maximum void ratio based upon the relation of shape factor proposed by the authors indicated

in the figure

04

06

08

1

12

14

16

18

2

005

015

025

035

045

055

065

075

085

095

Factor (roundness angularity)

min

imu

m v

oid

rati

o

Youd 1973 roundness

Rouse 2008 roundness

Cho 2006 roundness

Sukumaran 2001 AF

03

04

05

06

07

08

09

1

11

12

13

05

015

025

035

045

055

065

075

085

095

Factor (sphericity circularity shape)

min

imu

m v

oid

rati

oHolubec 1973 sphericity

Cho 2006 circularity

Sukumara 2001 SF

05

07

09

11

13

15

17

19

21

00

150

250

350

450

550

650

750

850

95

Factor (sphericity circularity shape)

Maxim

um

vo

id r

ati

o

Holubec 1973 sphericity

Cho 2006 circularity

Sukumara 2001 SF

05

1

15

2

25

3

35

005

015

025

035

045

055

065

075

085

095

Factor (roundness angularity)

Maxim

um

vo

id r

ati

o

Youd 1973 roundness

Rouse 2008 roundness

Cho 2006 roundness

Sukumaran 2001 AF

32

54 ANGLE OF REPOSE

The angle of repose of a granular material is the steepest angle of descent or dip of the

slope relative to the horizontal plane when material on the slope face is on the verge

of sliding as show in figure 40

According to Qazi (1975) there are five types of forces which may act between the

particles in soils

1 Force of friction between the particles

2 Force due to presence of absorbed gas andor moisture of particle

3 Mechanical forces caused by interlocking of particles of irregular shape

4 Electrostatic forces arising from friction between the particles themselves and

the surface with which they come in contact

5 Cohesion forces operating between neighbouring particles

Rouseacute et al (2008) found a decrease of angle of repose with increase roundness

based upon ASTM C1444 test (Standard Test Method for Measuring the Angle of

Repose of Free-Flowing Mold Powders) The method consist in pouring sand on a

surface cover by paper trough a funnel of specific dimensions (the nozzle diameter

depend on the sandrsquos particle size) from an altitude of 15 inches (381 mm) The sand

is release from the funnel until the peak of the cone formed by the sand stops the flow

The repose angle is obtained with the equation

H represent the 15 inches D and d represent the diameter of the cone formed by the

sand and the diameter of the funnel respectively

Figure 39 Maximum minus minimum void ratio based upon the relation of shape factor proposed by the

authors indicated in the figure

0

01

02

03

04

05

06

07

08

09

1

005

015

025

035

045

055

065

075

085

095

Factor (sphericity circularity shape)

Maxim

um

- M

inim

um

Vo

id r

ati

oHolubec 1973 sphericity

Cho 2006 circularity

Sukumara 2001 SF

0

02

04

06

08

1

12

14

16

18

005

015

025

035

045

055

065

075

085

095

Factor (roundness angularity)

Maxim

um

- M

inim

um

Vo

id r

ati

o

Youd 1973 roundness

Rouse 2008 roundness

Cho 2006 roundness

Sukumaran 2001 AF

dD

H2

tan=φ1

rep(61)

33

Rouseacute (2008) shows an empirical relation to obtain the angle of repose based on the

roundness of the particles

55 SHEAR STRENGTH

The MohrndashCoulomb failure criterion represents the linear envelope that is obtained

from a plot of the shear strength of a material versus the applied normal stress This

relation is expressed as

where τ is the shear strength σn is the normal stress co is the intercept of the failure

envelope with the τ axis and is the slope of the failure envelope The quantity c is

often called the cohesion and the angle is called the angle of internal friction

Studies show that the internal friction angle (under drained triaxial tests) increases

more rapidly on those materials having higher angularity increasing the relative

density The internal friction angle is a function of the relative density and the particle

shape (Holubec and DrsquoAppolonia 1973)

Chan and Page (1997) found in a study made with dry copper (using different shapes

and sizes ranging from 180 to 106 μm) using a direct shear test (ring share test) that

the internal friction angle increases as the angularity increases

Shinohara et al (2000) did some experiments with steel powder different shapes

using a triaxial cell in the test Shinohara never used the roundness or angularity on

the work but apply the shape factor (relation long axisshort axis) and the results were

that as this relation deviate from factor 1 the internal friction angle increases

The following empirical relations were found in the literature showing the behaviour

of the friction angle (obtained under different conditions)

)tan( noc

Figure 40 Representation of the angle of repose

(63)

(62)

34

Cho et al (2006)

(64)

(R is obtain by comparing the Krumbein chart figure 13)

Rouseacute (2008)

(65)

(66)

(R is defined using Wadell equation 22)

In figure 41 the suggested empirical relations above and lines constructed using

author data from Holubec and DrsquoAppolonia (1973) and Sukumara and Ashmawy

(2001) are plotted together to display the general trend on the particle shape and

friction angle relation Sukumaran reports two lines one based on the shape factor

(SF) and the second referring the angularity factor (AF) Sukumaran performed the

tests at constant volume

The scale used for Holubec and DrsquoAppolonia (1973) have lower and upper limits of 1

and 2 respectively (angularity form) and a scale change was applied to be able to

presented in the actual figure 41 As in the previous section (52) the author

recommend to use the original data from the references due that the figure just follows

the general trend of the behaviourrsquos particle regarding on the shape

Figure 41 The changes on the internal friction angle shows a general increase when the particle roundness

becomes angular or in the case of Sakamuran less spheric (Shape factor SF)

35

Barton and Kjaernsli (1981) suggested a model (equation 67) to predict the peak

friction angle (φrsquo) based upon numerous trixial and direct shear data tests

where

Se equivalent strength of particle

Re equivalent roughness of particle

φb basic friction angle (obtained from basic tilting test)

σn normal load

The information required for the model is (1) the uniaxial compressive strength of the

rock (2) the d50 particle size (mesh size where 50 of the particles pass through)

required to define Se (figure 42) (3) the degree of particle roundness and (4) the

porosity following compaction All data can be estimated by simple index tests

Barton and Kjaernsli (1981) suggest that particle size and sample scale has an effect

on the friction angle and includes them to obtain the equivalent strength (Se) figure 42

shows the method to obtain this value Compressive strength (σc) was chosen to be the

factor affecting the scale because micro fractures influence this property while

samples are bigger more micro fractures contain and its compressive strength reduces

The equivalent roughness is obtain using figure 43 where is required to know the

porosity (n) and the origin of the particles (a small chart is provided in the same figure

to compare the particles profile)

b

n

ee

SLogR

Figure 42 Method of estimating Equivalent Strength (Se) of rockfill based on uniaxial compressive strength

(σc ) and d50 particle size (Barton amp Kjaernsli 1981)

(67)

36

56 SEDIMENTATION PROPERTIES

A particle released in a less dense Newtonian fluid initially accelerate trough the fluid

due to the gravity Resistances to deformation of the fluid transmitted to the particle

surface drag generate forces that act to resist the particle motion The force due to the

weight (Fw) can be written as

Where ρp ρ are density of the particle and fluid (water) respectively g is the

gravitational force and Vp is the volume of the particle

And the resistance force (FD) is

Where CD is the dimensionless drag coefficient W is the weight of the particle and A

is the cross section area

Particlersquos shape has been assumed to be spherical when equations are applied on the

settling velocity Correlation deviates when particle shape departs from spherical form

Figure 43 Method of estimating Equivalent Roughness (Roe) based on porosity of rockfill

origin material degree of roundedness and smoothness of particle (Barton amp Kjaernsli 1981)

PPW ρ)gV(ρF

A2

WρCF

2

DD

(68)

(69)

37

(Dietrich 1982) and it is known that natural particles depart from spherical form

thus it is evident that this departure would have consequences

The below equation is proposed to account the shape (in this case the Corey shape

factor equation 8) in the settling velocity (Jimenez and Madsen 2003)

Jimenez and Madsen (2003) Dietrich (1982) Briggs and McCulloch (1962) and

others were working in the hydraulic shape of particles to solve problems as sediment

transport It is obvious that the equation presented and the researcherrsquos investigation

works under certain conditions (eg grain size between 0063-1 mm)

Dietrich (1982) suggests an empirical relation that accounts settling velocity size

density shape and roundness of a particle

R1 R2 and R3 are fitted equations for size and density shape and roundness

respectively

57 HYDRAULIC CONDUCTIVITY PERMEABILITY

Darcyrsquos Law Permeability is one component of Darcyrsquos law Darcys law is a simple

proportional relationship between the instantaneous discharge rate through a porous

medium the viscosity of the fluid and the pressure drop

The total velocity Ve is equal to the product of the permeability of the medium

(porous media) k the pressure drop ∆p all divided by the viscosity μ (Muskat

1937)

Darcys law is only valid for slow viscous flow most groundwater flow cases fall in

this category Typically Darcyrsquos law is valid at any flow with laminar flow (see figure

44)

Reynoldrsquos number (Laminar and turbulent Flow) Typically any laminar flow is

considered to have a Reynoldrsquos number less than one and it would be valid to apply

Darcys law Experimental tests have shown that flow regimes with Reynolds numbers

1

ND

S

S

ZY

gd1s

WW

NDN

gd)1s(4

dS

2R1R

3 10RW

pk

Ve

(70)

(71)

(72)

(73)

38

up to 10 may still be Darcian (laminar flow) as in the case of groundwater flow The

Reynolds number (a dimensionless parameter) for porous media flow is typically

expressed as

where ρ is the density of water (units of mass per volume) υ is the specific discharge

(with units of length per time) d is a representative average grain diameter for the

porous media (often taken as the 30 passing size from a grain size analysis using

sieves - with units of length) and μ is the viscosity of the fluid (Muskat 1937)

Shape effects Permeability as Head and Epps (2011) suggested is affected by the

shape and texture of soil grains Elongated or irregular particles create flow paths

which are more tortuous than those spherical particles Particles with a rough surface

texture provide more frictional resistance to flow Both effects tend to reduce the

water flow through the soil

Kozeny-Carman empirical relation accounts for the dependency of permeability on

void ratio in uniformly graded sands serious discrepancies are found when it is

applied to clays due the lack of uniform pores (Mitchell and Soga 2005)

There are various formulations of the Kozeny-Carman equation one published by

Head and Epps (2011) takes the void ratio e the specific surface area Ss and an

angularity factor F into account of permeability k

The angularity factor F considers the shape of the particles and ranges from 11 for

rounded grains 125 for sub rounded to 14 for angular particles The specific surface

Ss is defined as

d1 and d2 represent the maximum and minimum size particle in mm

Kane amp Sternheim (1988) suggest that the inclusion of the shape factor (F) has

probably the background on the Reynolds number due this factor is dependent

significantly on the shape of the obstacles and Reynolds number determines the

presence of laminar or turbulent flow Figure 44 show how the laminar flow has low

energy dissipation while turbulent flow (eg the roughness and path tortuosity) has

high energy dissipation

e1

e

FSs

2k

3

2

dRe

21

6

ddSs

(74)

(75)

(76)

39

According to Nearing and Parker (1994) the amount of soil detached during laminar

and turbulent flow is dependent on each soil and also greater on turbulent flow due the

greater shear strength generated during this kind of flow this could suggest the

greater erosion when turbulent flow is present

58 LIQUEFACTION

Soil liquefaction is a phenomenon in which soil loses much of its strength or stiffness

for a generally short time by earthquake shaking or other rapid loading Static and

dynamic liquefactions occur been the second one the most regular known

Liquefaction often occurs in saturated soils that is soils in which the space between

individual particles is completely filled with water This water exerts a pressure on the

soil particles that influences how tightly the particles themselves are pressed together

Shaking or other rapid loading can cause the water pressure to increase to the point

where the soil particles can readily move with respect to each other (Jefferies and

Been 2000)

Jefferies and Been (2000) state that it is clear that minor variation in intrinsic

properties of sand have major influence on the critical state These might be variations

on grain shape mineralogy grain size distribution surface roughness of grains etc

Yoginder et al (1985) found that substantial decrease on liquefaction resistance

occur with increase in confining pressure for rounded and angular sands (1600 kPa)

also rounded sands show an rapidly build up of resistance against liquefaction with

increasing density while angular tailing sand in contrast show such rapid increase

only at low confining pressures At low confining pressure angular material is more

resistant to liquefaction Probably the breakage of the corners on the angular particles

in tailings is ruling the lost in resistance at high confining pressures (sieve analysis

Figure 44 The figure show the extremes of flow behaviour First turbulent conditions where the flow is

essentially random and unpredictable and second the well defined Laminar flow conditions

40

after test identify the breakage of angular particles while on rounded particles the

sieve analysis was practically the same)

59 GROUNDWATER AND SEEPAGE MODELLING

In groundwater flow the particlersquos shape affects the soilrsquos pore size distribution

hence the flow characteristics (Sperry and Peirce 1995) Tortuosity and permeability

(also see section 57) are two significant macroscopic parameters of granular medium

that affect the passing flow (Hayati et al 2012) Current models incorporating the

effects of particle shape have failed to consider irregular particles such as those that

would prevail in a natural porous medium (Sperry and Peirce 1995)

Hayati et al (2012) suggested based on his results that tortuosity effect converge

when the porosity increases indicating that the shape have dominance at low and mid

porosity ranges

Sperry and Peirce (1995) research conclusions suggest that particle size and porosity

are more important predictors for hydraulic conductivity explaining the 69 of the

variability but particle shape appears to be the next most important This however

apparently comprises particles larger than 295-351 μm Differences for particle size

295-351 μm and smaller are not detectable Another interesting result in the research

was the interaction effect of the particle size and particle shape It suggests a different

packing configuration for particles of the same shape but different size (scale

dependent)

6 DISCUSSION

61 TERMS QUANTITIES AND DEFINITIONS

In order to describe the particle shape in detail there are a number of terms quantities

and definitions (qualitative and quantitative) used in the literature (eg Wadell 1932

1934 Krumbein 1941 Sneed amp Folk 1958) All mathematical definitions

(quantitatives) are models used to simplify the complexity of shape description Some

authors (Mitchell amp Soga 2005 Arasan et al 2010) are using three sub-quantities

one and each describing the shape but at different scales The terms are

morphologyform roundness and surface texture (figure 1) The three sub-quantities

are probably the best way to classify and describe a particle because not a single

definition can interpret the whole morphology Common language is needed when

descriptors are explained and these three scales represent an option It is evident in

the reviewed literature that many of the shape descriptors are presented with the same

name but also that there is not a clear meaning on what this descriptor defines eg

when there is no upper limit in the roundness does it means that the angularity never

ends Could they be more and more angular Probably they could be on theory but

not in reality

41

62 PROPERTIES

Trough various articlersquos review done in the present investigation it is recognized that

the particlersquos shape has an effect on the material properties among these are

1 Porosity (Tickell 1938 Fraser 1935 Kolbuszewski 1948) and void ratio

(Cho et al 2006 Shergold 1953 Rouseacute et al 2008 Santamarina and Cho

2004)

2 Permeability (Witt and Brauns 1983)

3 Internal friction angle (Shinohara et al 2000 Chan and Page 1997

Cheshomi et al 2009)

4 Density (Youd 1973 Holubec and DrsquoAppolonia 1973)

5 Drag coefficient Hydraulics (Briggs and McCulloch 1962)

In Table 5 is a short resume of the properties and shape effect found in peer review

articles trough different journals Most of the reviewed articles based its research on

uniform graded sands

Table 8 Compilation of properties influenced by particle shape

Repose

angle

Friction

angle

Porosity and

Void ratio Density Permeability

Settling velocity

Drag coefficient Deformation

Sphericity (3D)shape factor

NI x x x x x x

Circularity (2D)

NI x x x x NI NI

Roundness x x x x NI NI x

x influence

NI no information available

Shape of particles has an effect on the arrangement producing bridging or avoiding

the rotation of the particles and the resulting geotechnical property is affected eg

including flaky particles can result in a higher void ratio due the bridging effect

(Santamarina and Cho 2004) and depending on the loads even the size distribution is

changed due the breakage (Yoginder et al 1985) in similar way angular particles

produce higher void ratio due the avoided possibility of the particles to rotate and

compact

The influence of the chosen shape descriptor appears in this review to have minor

influence on the soil properties in the reviewed studies except on the void ratio and

the friction angle Influence of particle shape in some cases is hider by other factors

(eg size distribution) also the particle shape probably does not have influence when

particle size is in the clay order (eg hydraulic conductivity) the reason could be due

to forces as electrostatic or capillarity become more important at this level

Among the shape descriptors some are chosen more often in literature (eg aspect

ratio) there is no apparent scientific basis to use it (probably due to the simplicity of

the measurement it becomes one of the most use) but there are still some other

descriptors that may or may not show better correlation with the soil properties

Instead empirical relations had been developed regarding roundness or shape to

describe the soil behaviour it is clear that the mechanism behind the results is still not

completely understood

42

There is necessity to define the best(s) shape descriptor(s) to be used for particular

geotechnical properties

63 IMAGE ANALYSIS

Many image analysis techniques had been used to describe the particle shape eg

Fourier analysis fractal dimension tomography etc (Hyslip and Vallejo 1997) but

there is not agreement on the usage or conclusion to ensure the best particle descriptor

for geotechnical applications

There are several shape descriptors and also various techniques to capture the

particles profile (3-dimensions 3-dimension orthogonal and 2-dimensions) Each

technique presents advantages and disadvantages 3-dimensions is probably the

technique that provide more information about the particle shape but the precision

also lies in the resolution the equipment required to perform such capture could be

more or less sophisticated (scanning particles laying down in one position and later

move to complete the scanning or just falling down particles to scan it in one step)

3-dimensions orthogonal this technique use less sophisticated equipment (compare

with the previous technique) but its use is limited to particles over 1cm also

information between the orthogonal pictures is not capture 2-dimensions require non

sophisticated equipment but at the same time the shape information diminish compare

with the previous due the fact that it is possible to determine only the outline as the

particle measurements are performed in 2-dimensions it is presumed that they will lie

with its shortest axis perpendicular to the laying surface when they are flat but when

the particle tends to have more or less similar axis the laying could be random

Advantages on the use of image analysis are clear there is not subjectivity because it

is possible to obtain same result over the same images Electronic files do not loose

resolution and it is important when collaboration among distant work places is done

files can be send with the entire confidence and knowing that file properties has not

been changed Technology evolutions allowed to work with more information and it

also applies to the image processing area were the time consumed has been shortened

(more images processed in less time)

One important aspect in image analysis is the used resolution in the analysis due the

fact that there are measurements dependent and independent on resolution Thus

those dependent measurements should be avoided due the error included when they

are applied or avoid low resolution to increase the reliability Among these

parameters length is the principal parameter that is influences by resolution (eg

perimeter diameter axis etc) Resolution also has another aspect with two faces

quality versus capacity more resolution (quality) means more storage space a

minimum resolution to obtain reasonable and reliable data must be known but it

depend on each particular application

43

64 APPLICATIONS

Quantify changes in particles in the authorrsquos thought is one of the future applications

due the non-invasive methods of taking photographs in the surface of the damrsquos slope

rail road ballast or roads Sampling of the material and comparing with previous

results could show volume (3D analysis) or area (2D analysis) loss of the particles as

well as the form roundness and roughness This is important when it has been

suggested that a soil or rock embankment decrees their stability properties (eg

internal friction angle) with the loss of sphericity roundness or roughness

Seepage stock piling groundwater etc should try to include the particle shape while

modelling seepage requires grading material to not allow particles move due the

water pressure but in angular materials as it is known the void ratio is great than the

rounded soil it means the space and the possibilities for the small particles to move

are greater stock piling could be modelled incorporating the particle shape to

determine the binrsquos capacity when particle shape changes (void ratio changes when

particle shape changes) Modelling requires all information available and the

understanding of the principles that apply

Industry is actually using the particle shape to understand the soil behaviour and

transform processes into practical and economic image analysis has been included in

the quality control to determine particle shape and size because the advantages it

brings eg the acquisition of the sieving curve for pellets using digital images taken

from conveyor this allows to have the information in a short period of time with a

similar result at least enough from the practical point of view as the traditional

sieving

7 CONCLUSIONS

The conclusions of this literature review are

It has been shown that particle shape has influence on the soil behaviour

despite of partial knowledge of the mechanism behind Understanding of the

particle shape and its influence needs to be accomplished

A common language needs to be built up to standardize the meaning on

geotechnical field that involve the particle shape General relationships

between shape and properties should be developed

Based on this review it is not clear which is the best descriptor to use in

geotechnical engineering affecting he related shape to properties Instead of a

couple of standards there is no shape descriptor in geotechnical field fully

accepted

Image analysis tool is objective make the results repeatable obtain fast results

and work with more amount of information

44

Resolution needs to be taken in consideration when image analysis is been

carried out because the effects could be considerable Resolution must be set

according to the necessities Parameters as perimeter can be affected by

resolution

There are examples where particle shape has been incorporated in industries

related to geotechnical engineering eg in the ballast and asphalt industry for

quality control

8 FURTHER WORK

Three main issues have been identified in this review that will be further investigated

the limits of shape descriptors influence of grading and choice of descriptor for

relation to geotechnical properties

Shape descriptors have low and high limits frequently the limits are not the same and

the ability to describe the particlersquos shape is relative The sensitivity of each descriptor

should be compare to apply the most suitable descriptor in each situation

Sieving curve determine the particle size in a granular soil particle shape could differ

in each sieve size There is the necessity to describe the particle shape on each sieve

portion (due to practical issues) and included in the sieve curve Obtain an average

shape in determined sieve size is complicated (due to the possible presence of several

shapes) and to obtain the particle shape on the overall particlersquos size is challenging

how the particle shape should be included

Since several descriptors have been used to determine the shape of the particles and

the relation with the soil properties it is convenient to determine the descriptorrsquos

correlation with the soil properties

9 ACKNOWLEDGMENT

I would like to thanks to Lulearing University of Technology (LTU) the time I had spent

in its facilities and the kind environment it offers and University of Sonora

(UNISON) that has been providing me the financial support and the time to conclude

this journey

10 REFERENCES

Andersson T (2010) Estimating particle size distributions based on machine vision

Doctoral Thesis Departament of Computer Science and Electrical Engineering Lulearing

University of Technology ISSN 1402-1544 ISBN 978-91-7439-186-2

45

Arasan Seracettin Hasiloglu A Samet Akbulut Suat (2010) Shape particle of

natural and crished aggregate using image analysis International Journal of Civil and

Structural Engineering Vol 1 No 2 pp 221-233 ISSN 0970-4399

Aschenbrenner BC (1956) A new method of expressing particle sphericity Journal

of Sedimentary Petrology Vol 26 No 1 pp 15-31

Axelsson K (1998) Introduktion till jordmekaniken jaumlmte jordmateriallaumlran Skrift

984 Lulearing Avdelningen foumlr Geoteknologi Lulearing Tekniska Universitet (In Swedish)

Barton Nick amp Kjaernsli Bjorn (1981) Shear strength of rockfill Journal of the

Geotechnical Engineering Division Proceedings of the American Society of Civil

Engineers (ASCE) Vol 107 No GT7

Barrett P J (1980) The shape of rock particles a critical review Sedimentology

Vol 27 pp 291-303

Blott S J and Pye K (2008) Particle shape a review and new methods of

characterization and classification Sedimentology Vol 55 pp 31-63

Bowman E T Soga K and Drummond W (2001) Particle shape characterization

using Fourier descriptor analysis Geotechnique Vol 51 No 6 pp 545-554

Briggs L I McCulloch D S (1962) Hydraulic shape of sand particles Journal of

Sedimentary Petrology Vol 32 pp 645-656

Chan Leonard C Y and Page Neil W (1997) Particle fractal and load effects on

internal friction in powders Powder Technology Vol 90 pp 259-266

Cheshomi A Fakher A Jones C J F P (2009) A correlation between friction

angle and particle shape metrics in quaternary coarse alluvia Quarterly Journal of

Engineering Geology and Hydrogeology Vol 42 pp 145-155

Cho G Dodds J and Santamarina J C (2006) Particle shape effects on packing

density stiffness and strength Natural and crushed sands Journal of Geotechnical

and Geoenvironmental Engineering May 2006 pp 591-602

Dietrich William E (1982) Settling velocity of natural particles Water Resources

Research Vol 18 No 6 pp 1615-1626

Dobkins J E and Folk R L (1970) Shape development on Tahiti-nui Journal of

Sedimentary Petrology Vol 40 No 2 pp 1167-1203

Folk R L (1955) Student operator error in determining of roundness sphericity and

grain size Journal of Sedimentary Petrology Vol 25 pp 297-301

Fernlund J M R (1998) The effect of particle form on sieve analysis A test by

image analysis Engineering Geology Vol 50 No 1-2 pp 111-124

46

Fernlund J M R (2005) Image analysis method for determining 3-D shape of

coarse aggregate Cement and Concrete Research Vol 35 Issue 8 pp 1629-1637

Fernlund J M R Zimmerman Robert and Kragic Danica (2007) Influence of

volumemass on grain-size curves and conversion of image-analysis size to sieve size

Engineering Geology Vol 90 No 3-4 pp 124-137

Fraser H J (1935) Experimental study of the porosity and permeability of clastic

sediments The Journal of Geology Vol 43 pp 910-1010 ISSN 0022-1376

Hayati Ali Nemati Ahmadi Mohammad Mehdi and Mohammadi Soheil (2012)

American Physical Society Physical review E 85 036310 DOI

101103PhysRevE85036310

Hawkins A E (1993) The Shape of Powder-Particle Outlines Wiley New York

Head K H and Epps R J (2011) Manual of soil Laboratory testing Volum II

Permeability shear strength and compressibility test 3rd

edition Whittles Publishing

Scotland UK 3rd

edition

Holubec I and DrsquoAppolonia E (1973) Effect of particle shape on the engineering

properties of granular soils ASTM STP 523 pp 304-318

Hyslip James P Vallejo Luis E (1997) Fractal analysis of the roughness and size

distribution of granular materials Engineering Geology Vol 48 pp 231-244

Janoo Vincent C (1998) Quantification of shape angularity and surface texture of

base course materials US Army Corps of Engineers Cold Region Research and

Engineering Laboratory Special report 98-1

Jefferies Mike and Been Ken (2000) Soil liquefaction A critical state approach

Taylor amp Francis Group London and New York

Jimenez Jose A Madsen Ole S (2003) A simple formula to estimate settling

velocity of natural sediments Journal of Waterway Port Coastal and Ocean

Engineering Vol 129 No 2 pp 70-78

Johansson Jens and Vall Jakob (2011) Jordmaterials kornform Inverkan paring

Geotekniska Egenskaper Beskrivande storheter bestaumlmningsmetoder

Examensarbete Avdelningen foumlr Geoteknologi Institutionen foumlr Samhaumlllsbyggnad

och naturresurser Lulearing Tekniska Universitet Lulearing (In Swedish)

Kane Joseph W and Sternheim Morton M (1988) Physics John Wiley amp Sons Inc

Third edition

Kolbuszewski J (1948) An experimental study of the maximum and minimum

porosities of sands Proceedings of the Second International Conference on Soil

Mechanics and Foundation Engineering Rotterdam June 21 to 30 Sub-section IIb

pp 158-165

47

Krumbein W C and Pettijohn FJ (1938) Manual of sedimentary petrography

Appleton-Century Crofts Inc New York

Krumbein W C (1941) Measurement and geological significance of shape and

roundness of sedimentary particles Journal of Sedimentary Petrology Vol 11 No 2

pp 64-72

Krumbein W C and Sloss L L (1963) Stratigraphy and Sedimentation 2nd

ed

WH Freeman San Francisco

Kuo Chun-Yi and Freeman Reed B (1998a) Image analysis evaluation of

aggregates for asphalt concrete mixtures Transportation Research Record Vol 1615

pp 65-71

Kuo Chun-Yi Rollings Raymond and Lynch Larry N (1998b) Morphological

study of coarse aggregates using image analysis Journal of Materials in Civil

Engineering Vol 10 No 3 pp 135-142

Lanaro F Tolppanen P (2002) 3D characterization of coarse aggregates

Engineering Geology Vol 65 pp 17-30

Lees G (1964a) A new method for determining the angularity of particles

Sedimentology Vol 3 pp 2-21

Lees G (1964b) The measurement of particle shape and its influence in engineering

materials British Granite Whinstone Federation Vol 4 No 2 pp 17-38

Matsushima Takashi Saomoto Hidetaka Matsumoto Masaaki Toda Kengo

Yamada Yasuo (2003) Discrete element simulation of an assembly of irregular-

shaped grains Quantitative comparison with experiments 16th ASCE Engineering

Mechanics Conference University of Washington Seattle July 16-18

Mitchell James K and Soga Kenichi (2005) Fundamentals of soil behaviour Third

edition WILEY

Mora C F Kwan A K H Chan H C (1998) Particle size distribution analysis of

coarse aggregate using digital image processing Cement and Concrete Research Vol

28 pp 921-932

Mora C F and Kwan A K H (2000) Sphericity shape factor and convexity

measurement of coarse aggregate for concrete using digital image processing Cement

and Concrete Research Vol 30 No 3 pp 351-358

Muskat Morris (1937) The Flow of fluids through porous media Journal of Applied

Physics Vol 8 pp 274

Nearing M A and Parker S C (1994) Detachment of soil by flowing water under

turbulent and laminar conditions Soil Science Society of American Journal Vol 58

No 6 pp 1612-1614

48

Pan Tongyan Tutumluer Erol Carpenter Samuel H (2006) Effect of coarse

aggregate morphology on permanent deformation behavior of hot mix asphalt Journal

of Transportation Engineering Vol 132 No 7 pp 580-589

Pellegrino A (1965) Geotechnical properties of coarse-grained soils Proceedings

International Conference of Soil Mechanics and Foundation Engineering Vol 1 pp

97-91

Pentland A (1927) A method of measuring the angularity of sands MAG MN AL

Acta Eng Dom Transaction of the Royal Society of Canada Vol 21 Ser3xciii

Persson Anna-Lena (1998) Image analysis of shape and size of fine aggregates

Engineering Geology Vol 50 pp 177-186

Powers M C (1953) A new roundness scale for sedimentary particles Journal of

Sedimentary Petrology Vol 23 No 2 pp 117-119

Pye W and Pye M (1943) Sphericity determination of pebbles and grains Journal

of Sedimentary Petrology Vol 13 No 1 pp 28-34

Qazi M A (1975) Flow properties of granular masses A review on the angle of

repose The Arabian Journal for Science and Engineering Vol 1 No 2

Quiroga Pedro Nel and Fowle David W (2003) The effects of aggregate

characteristics on the performance of portland cement concrete Report ICAR 104-1F

Project number 104 International Center for Aggregates Research University of

Texas

Riley N A (1941) Projection sphericity Journal of Sedimentary Petrology Vol 11

No 2 pp 94-97

Rouseacute P C Fennin R J and Shuttle D A (2008) Influence of roundness on the

void ratio and strength of uniform sand Geotechnique Vol 58 No 3 227-231

Santamarina J C and Cho G C (2004) Soil behaviour The role of particle shape

Proceedings Skempton Conf London

Schofield and Wroth (1968) Critical state soil mechanics McGraw Hill

Shaumlfer Michael (2002) Digital optics Some remarks on the accuracy of particle

image analysis Particle amp Particle Systems Characterization Vol 19 No 3 pp 158-

168

Shergold F A (1953) The percentage of voids in compacted gravel as a measure of

its angularity Magazine of Concrete Research Vol 5 No 13 pp 3-10

Shinohara Kunio Oida Mikihiro Golman Boris (2000) Effect of particle shape on

angle of internal friction by triaxial compression test Powder Technology Vol 107

pp131-136

49

Skredcommisionen (1995) Ingenjoumlrsvetenskapsakademinen rapport 395 Linkoumlping

1995

Sneed E D and Folk R L (1958) Pebbles in the Colorado river Texas A study in

particle morphogenesis Journal of Geology Vol 66 pp 114-150

Sperry James M and Peirce J Jeffrey (1995) A model for estimating the hydraulic

conductivity of granular material based on grain shape grain size and porosity

Ground Water Vol 33 No 6 pp 892-898

Sukumaran B and Ashmawy A K (2001) Quantitative characterisation of the

geometry of discrete particles Geotechnique Vol 51 No 7 pp 619-627

Szaacutedeczy-Kardoss E Von (1933) Die bistimmung der abrollungsgrades Geologie

und palaumlontologie Vol 34B pp 389-401 (in German)

Teller J T (1976) Equantcy versus sphericity Sedimentology Vol 23 pp 427-428

Tickell F G (1938) Effect of the angularity of grain on porosity and permeability

bulletin of the American Association of Petroleum Geologist Vol 22 pp 1272-1274

Tutumluer E Huang H Hashash Y Ghaboussi J (2006) Aggregate shape effects

on ballast tamping and railroad track lateral stability AREMA 2006 Annual

Conference Louisville KY

Wadell H (1932) ldquoVolume Shape and roundness of rock particlesrdquo Journal of

Geology Vol 40 pp 443-451

Wadell H (1933) Sphericity and roundness of rock Particles Journal of Geology

Vol 41 No 3 pp 310ndash331

Wadell H (1934) Shape determination of large sedimental rock fragments

The Pan-American Geologist Vol 61 pp 187-220

Wadell H (1935) ldquoVolume shape and roundness of quartz particlesrdquo Journal of

Geology Vol 43 pp 250-279

Wentworth W C (1922a) The shape of beach pebbles Washington US Geological

Survey Bulletin Vol 131C pp 75-83

Wentworth W C (1922b) A method of measuring and plotting the shape of pebbles

Washington US Geological Survey Bulletin Vol 730C pp 91-114

Wentworth W C (1933) The shape of rock particle A discussion Journal of

Geology Vol 41 pp 306-309

Witt K J Brauns J (1983) Permeability-Anisotropy due to particle shape Journal

of Geotechnical Engineering Vol 109 No 9 pp 1181-1187

8

Sneed amp Folk in (1958) found a relation between the tree dimensional axes called

ldquoMaximum Projection Sphericityrdquo

In a similar way Ashenbrenner (1956) showed his equation at that time named

ldquoWorking Sphericityrdquo

Form or shape factor names are used by authors like Corey (shape factor eq 8) in the

paper published on 1949 Williams (shape factor eq 9) in 1965 Janke (form factor

eq 10) in 1966 and Dobkins amp Folk (oblate-prolate index eq 11) in 1970 (Blott and

Pye 2008)

Aschenbrenner (1956) develop the shape factor by using the relation of the tree axis

but the square of the middle one

3

2

ba

c

))ab((1)bc(16))ab((cb)(11

)ab()bc( 128

22

3 2

ab

c

acb when 1ac

b acb when

b

ac-1 2

22

2

3

cba

c

222

a

c

50c-a

b-a10

2b

ac

(6)

(7)

(8)

(9)

(10)

(11)

(12)

9

Table 2 General overview over different particle shape definitions for 3D sphericity has been compiled

and arranged chronologically

Aspect Name Author Year Based on

Sphericity (3D) Flatness index Wentworth 1922a 3-axes

True Sphericity Wadell 1932 Surface

Operational sphericity Wadell 1932 Volume

Sphericity Wadell 1934 Sphere diameter

Zinggrsquos clasification Zinggrsquos1

1935 3-axes

Intercept sphericity chart Krumbein 1941 3-axes

Pebble sphericity Pye and Pye 1943 3-axes

Corey shape factor Corey2

1949 3-axes

Working sphericity Ashenbrenner 1956 3-axes

shape factor Ashenbrenner 1956 3-axes

Maximum projection sphericity Sneed amp Folk 1958 3-axes

Williams shape factor Williams2

1965 3-axes

Janke form factor Janke2

1966 3-axes

Oblate-prolate index Dobkins amp Folk 1970 3-axes 1) Krumbein and Sloss 1963 2) Blott and Pye 2008

34 FORM (2D)

The technique to measure the sphericity is based in tree dimensions it can be found in

literature some ways to measure the ldquotwo dimensions sphericityrdquo which is simply the

perimeter of the particle projection some authors named ldquoparticle outlinerdquo or

ldquocircularityrdquo

Wadell in 1935 (Hawkins 1993) adopt a conversion of his 1934 3D sphericity

formula (equation 4) to a 2D outline He defined an orientation on the particles and

they were based on the maximum cross sectional area (outline of the particle

projecting the maximum area) The equations show the relation between diameters of

a circle of same area and smallest circumscribed circle

He also used the term ldquodegree of circularityrdquo as the ratio of the perimeter of a circle of

same area and the actual particle perimeter

Tickell in 1931 (Hawkins 1993) used his empirical relation The particle orientation

proposed was a random one It is described by the ratio between the area outline and

the area of smallest circumscribed circle

C

A

D

DC

P

PC C

CA

AC

(13)

(14)

(15)

10

Some other authors has been working with the ldquocircularityrdquo concept and had develop

them own equations as Pentland (1927) relating the area outline and area of a circle

with diameter equal to longest length outline and Cox (Riley 1941) with the ratio

area and perimeter time a constant equations 16 and 17 respectively Both authors did

not define any definite orientation of the grains

Riley (1941) realize the problems that an area perimeter and some other

measurements proposed by the above authors can carry as the time consuming and

tedious work (at that time were not computer all was made by hand) and thatrsquos why

he develop this equation easy to handle called ldquoinscribed circle sphericityrdquo He used

the same particle orientation proposed by Wadell and the relation of diameters of

inscribed and circumscribed circles

Horton 1932 (Hawkins 1993) use the relation of the drainage basing perimeter and

the perimeter of a circle of the same area as drainage basin

Janoo in 1998 (Blott and Pye 2008) develop his general ratio of perimeter to area

Sukumaran and Ashmawy (2001) develop his own shape factor (SF) defined as the

deviation of the global particle outline from a circle Figure 9 can be used as a

reference to determine the items used in the equation 21

N is referred to the number of sampling intervals o radial divisions

C2A

AC

2P

A4C

C

I

D

DC

CD

D

P

PC

A

PC

2

45ordm x N

Particleα

= SF

sumN

1=ii

(16)

(17)

(18)

(19)

(20)

(21)

11

Table 3 General chronological overview of the particle shape definitions for 2D sphericity

Aspect Name Author Year Based on

Circularity (2D) roundness Pentland 1927 area

roundness Cox1

1927 area-perimeter

roundness Tickell2

1931 area

Circularity Horton2

1932 drainage basin

outline circularity Wadell 1935 Circle diameter

degree of circularity Wadell 1935 Perimeter

inscribed circle sphericity Riley 1941 Circle diameter

Circularity Krumbein and Sloss 1963 chart

Janoo 1998 area-perimeter

Shape factor Sukumaran 2001 Segmentation of particle and angles

1) Riley 1941 2) Hawkins 1993

35 ROUNDNESS OR ANGULARITY

Roundness as described in section 32 is the second order shape descriptor Sphericity

lefts beside the corners and how they are this was notice by most of the authors sited

before and they suggested many ways to describe this second order particle property

Roundness is clearly understandable using the figure 10 Particle shape or form is the

overall configuration and denotes the similarities with a sphere (3D) or a circle (2D)

Roundness is concerning about the sharpness or the smoothness of the perimeter (2D)

Surface texture (Barret 1980) is describe as the third order subject (form is the first

and roundness the second) and it is superimposed in the corners and it is also a

property of particles surfaces between corners

Figure 9 Description of the Sukumaran factors to determine the shape and angularity (Sukumaran and

Ashmawy 2001)

12

Wadell (1935) describes his methodology calling it total degree or roundness to

obtain the roundness of a particle using the average radius of the corners in relation

with the inscribed circle diameter (see figure 11) on the equation

In the same study Wadell (1935) has used the equation

This two last equation shows slightly differences on the results (Wadell 1935)

Powers (1953) also published a graphic scale to illustrate the qualitative measure

(figure 12) It is important to highlight that any comparing chart to describe particle

properties has a high degree of subjectivity Folk (1955) concludes that when charts

are used for classification the risk of getting errors is negligible for sphericity but

large for roundness

N

R

r

Rinmax

r

R

NR

inmax

Figure 10 Form (shape) Roundness and Texture graphical description (Bowman et al 2001)

Figure 11 Wadellrsquos method to estimate the roundness corners radius and inscribed circle

(Hawkins 1993)

(22)

(23)

13

Some authors as Russel amp Taylor in 1937 Pettijohn in 1957 and Powers in 1953

developed a classification based on five and six classes (Hawkins 1993) each one

with its own class limits it is important to denote that the way they measure the

roundness is the developed by Wadell (1935) This classification and class limits are

showed in the table 4

Table 4 Degrees of roundness Wadell Values (Hawkins 1993) NA = no-applicable

Grade terms Russell amp Taylor (1937) Pettijohn (1957) Powers (1953)

Class

limits (R)

Arithmetic

midpoint

Class limits

(R)

Arithmetic midpoint Class

limits (R)

Arithmetic

midpoint

Very angular

NA

NA

NA

NA

012-017

014

Angular

000-015

0075

000-015

0125

017-025

021

Subangular

015-030

0225

015-025

0200

025-035

030

Subrounded

030-050

0400

025-040

0315

035-049

041

Rounded

050-070

0600

040-060

0500

049-070

059

Well rounded

070-100

0800

060-100

0800

070-100

084

Krumbein and Sloss (1963) published a graphical chart easy to determine the

sphericity and roundness parameters using comparison See figure 13 (Cho et al

2006)

Figure 12 A Roundness qualitative scale (Powers 1953)

Figure 13 Sphericity and roundness chart (Cho et al 2006) The roundness equation that appears here in

the chart is the wadellrsquos equation number 22

14

Fischer in 1933 (Hawkins 1993) used a straightforward method to quantify roundness

using a central point in the outline and dividing the outline in angles around this point

that were subtended by the straight or non curved parts of the profile were measured

This is illustrated in figure 14

To express the angularity value Fischer used the ratio of angles standing linear parts

on the outlines and concave respectively

Figure 14 left (A) and right (B) gives a similar angularity of approximately 042

using the above equations (Hawkins 1993)

Wentworth in 1922 used the maximum projection to define the position of the particle

to obtain the outline or contour (Barret 1980) The equation reflects the relation of the

diameter of a circle fitting the sharpest corner and the longest axis plus the shortest

axis c (minimum projection)

Wentworth (Hawkins 1993) expressed the roundness as the ratio of the radius of

curvature of the most convex part and the longest axis plus short axis

Actually these last two equations are the same just expressed in different terms when

the particle is in its maximum projection

Dimensions can be seen on figure 15 L and B represents the mayor axis a and

intermediate axis b The intention is to make difference between the 2 and 3

dimensions (L and B are for 2D as a b and c are for 3D)

deg360

ANG

=R

sumPLA

PLA

CON

ANG

ANGR

2)S(L

DR

M

S

B)4(L

RR CON

Figure 14 Fischerrsquos methods of angularity computation (Hawkins 1993)

A=inscribed circle B=circumscribed circle

(24)

(25)

(26)

(27)

15

Wentworth 1919 has a second way to express the roundness called Shape index

(Barrett 1980) and it relates the sharpest corner and the diameter of a pebble trough

the sharpest corner

Wentworth (1922b) used define the roundness as the ratio of the sharpest corner and

the average radius of the pebble

Cailleux (Barrett 1980) relates the radius of the most convex part and the longest

axis

Kuenen in 1956 show his roundness index (Barrett 1980) between the sharpest corner

and the breath axis

Dobkins amp Folk (1970) used a modified Wentworth roundness with the relation of

sharpest corner and inscribed circle diameters

AVG

CON

R

RR

x

s

D

DR

L2

RR CON

B

DR s

i

s

D

DR

3AVGAVG cbaDR2

Figure 15 Description of L and B axes (Hawkins 1993)

(28)

(29)

(30)

(31)

(32)

(33)

16

Swan in 1974 shows his equation (Barrett 1980) relating the sharpest (or the two

sharpest) corner(s) and inscribed circle diameter

Szadeczsky-Kardoss has his Average roundness of outline (Krumbein and Pettijohn

1938) relating the concave parts perimeter and the actual perimeter

Lees (1964a) developed an opposite definition to roundness it means that he

measures the angularity instead of the roundness and he calls it Degree of angularity

Figure 16 shows the items considered when equation 36 applies as the angles (α)

inscribed circle (Rmax-in) and the distance (x) The main formula is

In order to apply the last equation corners needs to be entered in the formula and each

individual result will add to each other to obtain the final degree of angularity

A roundness index appears on Janoo (1998) Kuo and Freeman (1998a) and Kuo et

al (1998b) it is described as

The last equation is on section 34 also because there is not a general agreement on the

definition furthermore some authors had used to define the roughness this is not the

only equation that has been used trying to define different aspects (sphericity

roundness or roughness) but it is a good example of the misuse of the quantities and

definitions

inmaxR

x)180(R

2P

A4R

i

ss

D

DDR

221

100P

PR CON

Figure 16 Degree of angularity measurement technique (Blot and Pye 2008)

(34)

(35)

(36)

(17)

17

Sukumaran and Ashmawy (2001) present an angularity factor (AF) calculated from

the number of sharpness corners Angles βi required to obtain the angularity factor are

shown in figure 9

Sukumaran and Ashmawy (2001) also suggested use not bigger sampling interval of

N=40 because it is the cut off between angularity factor and surface roughness If so

this equation could be used to describe the roughness

Table 5 General chronological overview of the particle roundness

Aspect Name Author Year Based on

Roundness shape index Wentworth 19191

diameter of sharper corner

shape index Wentworth 1922b sharpest corner and axis

roundness Wentworth 1933 convex parts

Fischer 19332

noncurved parts outline

Fischer 19332

noncurved-streigth parts outline

Average roundness of outline

Szadeczsky-Kardoss 19333

convex parts-perimeter

roundness Wadell 1935 diameter of corners

roundness Wadell 1935 diameter of corners

roundness Russel amp Taylor 19372

class limit table

roundness Krumbein 1941 chart

Cailleux 19471

convex parts

roundness Pettijohn 19494 class limit table

roundness Powers 1953 chart and class limit table

Kuenen 19561

axis-convex corner

roundness Krumbein and Sloss 1963 chart

degree of angularity Lees 1964a corners angles and inscribed circle

Dobkins amp Folk 1970 diameter of sharper corner

Swan 19741

diameter of sharper corners

Angularity factor Sukumaran and

Ashmawy 2001

Segmentation of particles and angles

1) Barret 1980 2) Hawkins 1993 3) Krumbein and Pettijohn 1938 4) Powers 1953

sum

sumsumN

1=i

2

i

2

N

1=i

2

i

2N

1=ii

)ordm180 -circleβ( - )(180ordm x 3

)ordm180-circleβ(-)ordm180 -Particleβ(

= AF (37)

18

36 ROUGHNESS OR SURFACE TEXTURE

A third property called texture appears early in the literature with the sphericity and

roundness properties since then texture property was longed described but it was in

accordance with the authors at that time not measurable

Wright in 1955 developed a method to quantify the surface texture or roughness of

concrete aggregate using studies done on 19 mm stones The test aggregates were first

embedded in a synthetic resin The stones were cut in thin sections The sections

projection was magnified 125 times The unevenness of the surface was traced and the

total length of the trace was measured The length was then compared with an uneven

line drawn as a series of chords (see figure 17) The difference between these two

lines was defined as the roughness factor (Janoo 1998)

However with the advance of technology it has become easier measure the roughness

and here is presented some researcherrsquos ideas how this property should be calculated

One technique used by Janoo (1988) to define the roughness can be seen in figure 18a

and is defined as the ratio between perimeter and convex perimeter

The convex perimeter is obtained using the Feretrsquos box (or diameter) tending a line in

between the touching points that the Feretrsquos box describes each time it is turn (figure

18b)

PER

OC

PR

Figure 17 Measurement method for characterizing the surface texture of an aggregate (Janoo 1998)

a) Convex perimeter (CPER) b) Feret measurement Figure 18 a) Convex perimeter (CPER) b) Feret measurement (modified after Janoo 1998)

(38)

a)

b)

19

Kuo and Freeman (1998a) and Kuo et al (1998b) use the roughness definition as the

ratio perimeter and average diameter

Erosion and dilatation image processing techniques are used to obtain the surface

texture Erosion is a morphological process by which boundary image pixels are

removed from an object surface which leaves the object less dense along the

perimeter or outer boundary Dilatation is the reverse process of erosion and a single

dilatation cycle increases the particle shape or image dimension by adding pixels

around its boundary (Pan etal 2006)

The ldquonrdquo erosion and dilatation cycles are not standardized

Mora and Kwan (2000) used the ldquoconvexity ratio CRrdquo (equation 41) and the ldquofullness

ratio FRrdquo (equation 42) in their investigation they are

The convex area is the area of the minimum convex boundaries circumscribing the

particle This is illustrated in the figure 19 The convex area is obtained in a similar

way as the convex perimeter but in this case the area between the original outline and

the convex perimeter is our convex area

AVG

OD

PR

100A

1AARO

CONo A

AR =

CONo A

AR =

Figure 19 Evaluation of area and convex area (Mora and Kuan 2000)

(39)

(40)

(41)

(42)

20

4 TECHNIQUES IN ORDER TO DETERMINE PARTICLE

SHAPE

41 HAND MEASUREMENT

Hand measurement technique was the first used by obvious reasons in order to

improve the accuracy special devices developed as the ldquosliding rod caliperrdquo used by

Krumbein (1941) it works placing the sample on the sliding road calliper as show

figure 20b the length in different positions can be obtain by using the scale provided

in the handle the ldquoconvexity gagerdquo that was actually used by opticians to measure the

curvature of lenses but easily applicable to the particle shape analysis (Wentworth

1922b) works measuring the movement of the central pivot as figure 20a shows (the

two adjacent pivots are invariable) as many the central pivot moves more is the

curvature or the ldquoSzadeczky-Kardossrsquos apparatusrdquo develop in 1933 that traces the

profile of the rock fragment so the outline traced is then analyzed (Krumbein and

Pettijohn 1938) figure 20c show equipment

Another helpful tool to determine the particle dimensions was the ldquocamera lucidardquo to

project the particlersquos contour over a circle scale appearing in Figure 21 thus it is

possible to measure the particlersquos diameter

a)

c) b)

Figure 20 a) convexity gage used to determine the curvature in particle corners (Wenworth 1922b)

b)sliding rod caliper device to measure the particle axis length (Krumbein 1941) and c)Szadeczky-

Kardoss (1933) apparatus it was utilized to obtain the particle outline

Figure 21 Circle scale used by Wadell (1935) to determine particlersquos diameter and roundness

21

42 SIEVE ANALYSIS

Bar sieving eg according to EN 933-31997 can be used to determine simple large

scale properties By combining mesh geometries the obtained results can be used to

quantify flakiness and elongation index ASTM D4791 (Flat and elongated particles

are defined as those coarse aggregate particles that have a ratio of length to thickness

equal to or greater than a specified value such as 51 The index represents the

percentage on weight of these particles) The method is not suitable for fine materials

This due to the difficulty to get the fine grains passed through the sieve and the great

amount of particles in relation to the area of the sieve (Persson 1998) eg EN 933-

31997 related to flakiness index The test is performed on aggregates with grain size

from 4 mm and up to 63 mm two sieving operations are necessary the first separates

on size fraction and the second use a bar sieve after the first sieving the average

maximum diameter of the particles is obtain and with the second sieving (bar sieving)

the shortest axis diameter is found finally with this two parameters the flakiness

index is determined

There are more standards related with the particle shape (see appendix A) but this

above presented are probably the most known using sieve analysis to determine

particlersquos geometrical properties

Sieve analysis is facing the computers age and image analysis sieving research is

taking place (Andersson 2010 Mora and Kwan 2000 Persson 1998) Industry is

also applying the image analysis sieving with decrees on the testing time compare

with the traditional sieving method An inconvenient of image analysis is the error

due the overlapping or hiding of the particles during the capture process but the

advantages are more compare with disadvantages (Anderson 2010)

43 CHART COMPARISON

Charts developed over the necessity of faster results because the long time consuming

required when measuring each particle

Krumbein (1941) present a comparison roundness chart for pebbles which were

measured by Wadellrsquos method because this property was the most difficult to measure

due to the second order scale that roundness represents (See figure 22)

Figure 22 Krumbein (1941) comparision chart for roundness

22

A qualitative chart by Powers (1953) try to include both (sphericity and roundness)

particlersquos characteristics it was divided on six roundness ranges (very angular

angular sub-angular sub-rounded rounded and well rounded) and two sphericity

series (high and low sphericity) This chart was prepared with photographs to enhance

the reader perspective (See figure 23)

A new chart including sphericity and roundness appear this time it was easier to

handle the two mean properties of particlersquos shape furthermore there was included

the numerical values that eliminated the subjectivity of qualitative description The

chart is based on Wadellrsquos definitions (Krumbein and Sloss 1963) (See figure 24)

Folk (1955) worried about the personrsquos error on the chartrsquos comparison studied the

determination of sphericity and angularity (he used the Powers 1953 comparison

chart) he found that the sphericity determination by chart comparison has a negligible

error while the roundness he concluded it was necessary to carry out a more wide

research due the high variability show by his study

Figure 23 Powers (1953) qualitative shpericity-roundness chart

Figure 24 Sphericity-roundness comparison chart (Krumbein and sloss 1963)

23

44 IMAGE ANALYSIS

Image analysis is a practical method to use for shape classification since it is fast and

can be automated Different techniques appear to process these images among them

are

o Feret Diameter the Feret diameter is the longitude between two parallel lines

this lines can rotate around one particle or outline to define dimensions as it

is shown in figure 25 these method is not a fine descriptor but as it was say

above it is a helpful tool to determine diameters (Janoo 1988)

o Fourier Mathematical Technique It produces mathematical relations that

characterize the profile of individual particles This method favours the

analysis of roughness and textural features for granular soils The problem in

the methodology remains in the re-entrant angles in order to complete the

revolution (Bowman et al 2001) see figure 26

o Fractal Dimension Irregular line at any level of scrutiny is by definition

fractal (Hyslip and Vallejo 1997) Figure 27 shows fractal analysis by the

dividing method The length of the fractal line can be defined as

N

1n

nn0 )nsinbncosa(a)(R

RD1n)(P

Figure 25 Feret measurement technique is defined by two parallel lines turning

around the particle to define the shortest and longest Feret diameter (Janoo 1988)

Figure 26 Fourier technique with two radiuses at one angle (Bowman et al 2001)

(43)

(44)

24

o Orthogonal image analysis This technique is basically the use of two images

orthogonal between them to acquire the three particle dimensions (Fernlund

2005) any of the above techniques can be used in this orthogonal way

o Laser Scanning Technique this kind of laser scanning 3D is one of the most

advanced techniques In figures 28a) we have the laser head scanning the rock

particles the particles have control points in order to keep a reference point

when move them to scan the lower part in figure 28b) we can see the laser

path followed (Lanaro and Tolppanen 2002)

Another technique is the Laser-Aided Tomography (LAT) in this case a laser sheet is

used to obtain the particles surveying (see figure 29) This technique is different and

has special requirements as to use liquid with same refractive index as the particles

particles must let the laser or certain percent of light go through (Matsushima et al

2003)

a) b)

Figure 27 Fractal analysis by the dividing method at different scrutiny scale (Hyslip and Vallejo 1997)

Figure 28 a) Scanning head b) scanning path (Lanaro and Tolppanen 2002)

Figure 30 3D scan completed ready to

use for any further measure

(Matsushima et al 2003)

Figure 29 LAT scaning particles

(Matsushima et al 2003)

25

Both 3D techniques obtain the particle shape that is later used to achieve measures as

we can see in figure 30

All these previous techniques are easily written in codes or scripts to be interpreted in

a digital way obtaining the desired measurement but there are some interesting points

in the image analysis regarding on the errors involve among them are image

resolution and orientation of the particles orientation is not relevant when it is

random and large number of particles are involve resolution have an influence on the

accuracy (Zeidan et al 2007)

When resolution is increase more accuracy is obtain and the object representation

match better with the real form in the other hand more resolution means more

spending on memory and time thus resolution needs to be according with the goal

and precision needed in any work (Schaumlfer 2002)

Schaumlfer (2002) conclude that attributes like length when measuring digital images

present relative high errors It can be vanish or at least diminish using high resolution

just for diameter but not for perimeter that keep the error as big as initially Johansson

and Vall (2011) obtain similar results when 3 different resolutions were used in the

same particle obtaining an unstable output for those termsquantities that involve the

perimeter Thus all quantities relating the perimeter should be treated with care

5 EFFECT OF SHAPE ON SOIL PROPERTIES

51 INTRODUCTION

In laboratory test on the effect on particle size on basic properties has been

investigated in several studies this relation has been discussed and various

mechanisms had been proposed to explain the behaviour of the soil in dependency

also with the shape Basically there are two mechanisms proposed The arrangement

of particles and the inter-particle contact (Santamarina and Cho 2004) and

subsequence breakage

The arrangement of particles

Arrangement of the particles can be presented in three different forms loose dense

and critical this arrangement determines the soil properties (eg density increase with

more dense arrangement) Loose and dense states are easy understandable when

figure 31 is explained while in the upper part of the figure the particles are arranged

using the minimum space needed in the lower part a span is created using the flaky

particle as a bridge this phenomena is known as ldquobridgingrdquo Bridging can produce

different geotechnical results when just the shape of the particle is changed eg void

ratio (Santamarina and Cho 2004) Particles are able to rearrange this could be done

applying pressure (energy) to the soil the pressure (energy) will create such forces

that soil particles will rotate and move (see figure 34) finishing in a more dense state

26

A loose soil will contract in volume on shearing and may not develop any peak

strength (figure 32 left) In this case the shear strength will increase gradually until

the residual shear strength is revealed once the soil has ceased contracting in volume

A dense soil may contract slightly (figure 32 right) before granular interlock prevents

further contraction (granular interlock is dependent on the shape of the grains and

their initial packing arrangement) In order to continue shearing once granular

interlock has occurred the soil must dilate (expand in volume) As additional shear

force is required to dilate the soil a peak shear strength occurs (figure 32 left) Once

this peak shear strength caused by dilation has been overcome through continued

shearing the resistance provided by the soil to the applied shear stress reduces

(termed strain softening) Strain softening will continue until no further changes in

volume of the soil occur on continued shearing Peak shear strengths are also

observed in overconsolidated clays where the natural fabric of the soil must be

destroyed prior to reaching constant volume shearing Other effects that result in peak

strengths include cementation and bonding of particles The distinctive shear strength

called the critical state is identified where the soil undergoing shear does so at a

constant volume (Schofield and Wroth 1968)

The inter-particle contact

For frictional soil ie coarse grained soil the friction between particles is the

dominating factor for strength Materials usually consisting of coarse grains (diameter

Figure 31 Bridging effect when flaky particles are combined in the bulk material (Santamarina and

Cho 2004)

Figure 32 The left part of the figure show a typical behaviour of loose and dense material over shear stress

while at the right the figures illustrate the typical volume changes

27

gt 006mm) behave as a frictional soil it means that the strength of coarse soils (silt

sand gravel etc) comes from an inter-particle mechanical friction thus ideally they

do not have traction strength In figure 33 the inter-particle contact is illustrated here

the pressure (P) is applied and two more components are found the normal load (N)

and the tangential load (T) described as the friction coefficient (μF) The forces stand

in equilibrium (Johansson and Vall 2011)

When particles equilibrium is disturbed (friction coefficient is not enough to keep

particles unmoved) the rotation is imminent and it is necessary in order to compact

the soil in figure 34 can be seen that the arrangement is a fact that inhibit or allow this

rotation and the shape in the 3 different scales are also factors because the more

spherical andor more rounded andor less roughness more easy is the rotation

(Santamarina and Cho 2004)

Breakage

Breakage is a side effect of the inter-particle contact and rotation when pressure

exceed the rock strength it can happened when the particles are tight together and

there is not enough space to rotate it is more obvious in angular particles (mesh form)

or as in figure 31 where the flaky particle ldquobridgingrdquo is not able to rotate but it can

brake by the pressure increase Yoginder et al (1985) notice that the angular particle

break during his experiments and they turn more rounded changing the original size

and form configuration at the same time there was a soil properties loosening

Figure 33 Inter-particle contact and forces acting (Axelsson 1998)

Figure 34 Rotation inhibition by the particles compaction or low void ratio (Santamarina and Cho 2004)

28

52 INFLUENCE OF SIZE AND SHAPE

Wenworth (1922a) and Pellegrino (1965) among others suggest that agent transport of

the rocks (rigor of transport temperature and moisture changes etc) determine its

shape but also the particle genesis itself (rock structure mineralogy hardness etc) It

is not possible to determine the shape of the particles based on the agent transport or

genesis but generally a shape behaviour is expected according to Mitchell and Soga

(2005) specially when the particle size is in the clay size (gt2μm) The shapes of the

most common clay minerals are platy (figure 35) with some exceptions (eg

halloysite occurs as tubes kaolinite are large thick and stiff Smectites are composed

of small very thin and filmy particles Illites are intermediate between kaolinite and

smectite and attapulgite occurs in lathlike particle shapes) Some clay minerals

photographs are presented in figure 35

Figure 35 Clay mineral shape a) hallosite b) Kaoline c) Smactites d) Illites and e) attapulgite (Modified

from Mitchell and Soga 2005)

Figure 36 Particle size range in soils Generally the particles of clay size are plate shaped (Mitchell and

Soga 2005)

a) b) c)

e) d)

29

53 VOID RATIO AND POROSITY

The void ratio (e) is the ratio of the volume of voids to the volume of solid it is

defined by the equation

Porosity (n) is the ratio of the volume of voids to the total volume of the soil it is

represented by the equation

Holubec and DrsquoAppolonia (1973) found a relation between the void ratio and

sphericity (referred in the paper as coefficient of angularity ratio of particle surface

and equivalent sphere surface) their results show that the maximum and the minimum

void ratio increases as the shpericity decreases In this study the surface was obtained

for an indirect method based on the permeability developed by Hoffman in 1959

described in the same document Rouseacute et al (2008) defined the roundness as

Wadell (1935) and he found it as an important factor controlling the minimum and

maximum void ratios Some other authors as Youd (1973) and Cho et al (2006)

conclude the same minimum and maximum void ratios increase when sphericity and

roundness decrease Another interesting result (all above authors) was the bigger

influence of the form (sphericity circularity) and roundness on the maximum void

ratio The change of the maximum void ratio is more pronounced than the change of

the minimum void ratio when the form and roundness changes (See figure 39)

Particles arrangement and interlocking are probably the factor that controls the void

ratio bridge effect permit the existence of void among the particles while interlocking

allowed the particles to form arches avoiding the possibility to rotate and stay in a

more stable configuration eg as it happens with marbles

Figures 36 37 and 38 shows proposed empirical relationships between void ratio and

shape from tables 5 and 6 (graphically the scale goes from 0 to 1 when cero mean

high angularity shpericity or circularity and one means low angularity circularity or

sphericity) Holubec and DrsquoAppolonia (1973) data was taken to obtain a power curve

and describe a tendency Santamarina and Cho (2004) show Youd equations in the

original paper Youd (1973) never presented the equation but it is easy to use the

information to draw a trend

The graphics presented in this document (figures 36 37 and 38) must be used with

certain reserves due the fact that the original data was modified in order to fit all

information in one graphic what the figures shows is just the general trend of the

behaviourrsquos material regarding on the shape If more accurate description and

information is required the author recommends consulting the reference data In the

same way equations from Holubec and DrsquoApollonia (1973) and Youd (1973) were not

presented by the authors but the use of the information was taken in order to build up

those equations on tables 6 and 7

S

V

V

V

= e

V

V

=nV

(45)

(46)

30

Table 6 Minimum void ratio equations regarding on the quantity (Ψ for sphericity C for circularity R

for roundness SF for Sukumaran shape factor and AF for Sukumaran angularity factor)

EQUATION NUMBER REFERENCE

Figure 34 (left)

4340

minΨ45490e =

47

Holubec amp DrsquoAppolonia 1973 (Ψ

was obtained using equation 2)

SF06340

mine021903180e +=

48

Sukumaran amp Ashmawy 2001 (SF

obtained using equation 21)

C05101emin

= 49

Cho etal 2006 (C obtained using

figure 12)

Figure 34 (right)

1

minR08203590e +=

50

Youd 1973 (R obtained from figure

11 and table 3)

R34080emin

= 51

Cho et al 2006 (R obtained using

figure 12)

1

minR05104330e +=

52

Rouseacute et al 2008 (R obtained by

equation 21)

AF02330

mine372004160e +=

53

Sukumaran amp Ashmawy 2001 (AF

obtained using equation 37)

Table 7 Maximum void ratio equations regarding on the quantity (Ψ for sphericity C for circularity R

for roundness SF for Sukumaran shape factor and AF for Sukumaran angularity factor)

EQUATION NUMBER REFERENCE

Figure 35 (left)

51520

max Ψ61120e = 54

Holubec and DrsquoAppolonia 1973 (Ψ

was obtained using equation 2)

SF1190

max e0016907180e += 55

Sukumaran amp Ashmawy 2001 (SF

obtained using equation 21)

C86061emax = 56

Cho etal 2006 (C obtained using

figure 12)

Figure 35 (right)

1

max R1505540e += 57

Youd 1973 (R obtained from figure

11 and table 3)

R62031emax= 58

Cho et al 2006 (R obtained using

figure 12)

1

max R107106150e += 59

Rouseacute et al 2008 (R obtained by

equation 21)

AF0530

max e12506090e += 60

Sukumaran amp Ashmawy 2001 (AF

obtained using equation 37)

Comparing figures 37 and 38 (minimum and maximum void ratio) it can be seen on

the right scheme of both figures 37 and 38 (when the factor is roundnessangularity)

that all the empirical relations has a common initial point close to 1 (it means that

particles are well rounded) while this common agreement disappear when the

roundness factor decreases (when the particles become more angular) Same figures

(37 and 38) on the left graphs (when the factor is sphericitycircularityshape) do not

present the same behaviour in fact there is more disperse initial point close to 1(when

the particles tend to be more sphericalcircular)

31

In Figure 39 the Δe (emax-emin) has been plotted to show how the maximum void ratio

and the minimum void ratio has different rate change when the particle shape

changes Maximum void ratio increases more than minimum void ratio when the

particle shape becomes less spherical andor more angular Comparing figure 39 left

and right graphics it can be seen that right present a common initial point when the

quantity (roundnessangularity) is close to one while in the left graphic the initial

point is more disperse Both ending points in both graphics (close to zero) are

dispersed

Figures 37 38 and 39 present the same behaviour right graphics (when the factor is

roundness angularity) in each figure have an initial common point while the left

graphics do not (when the factor is sphericity circularity shape)

Figure 37 Minimum void ratio based upon the relation of shape factor proposed by the authors indicated

in the figure

Figure 38 Maximum void ratio based upon the relation of shape factor proposed by the authors indicated

in the figure

04

06

08

1

12

14

16

18

2

005

015

025

035

045

055

065

075

085

095

Factor (roundness angularity)

min

imu

m v

oid

rati

o

Youd 1973 roundness

Rouse 2008 roundness

Cho 2006 roundness

Sukumaran 2001 AF

03

04

05

06

07

08

09

1

11

12

13

05

015

025

035

045

055

065

075

085

095

Factor (sphericity circularity shape)

min

imu

m v

oid

rati

oHolubec 1973 sphericity

Cho 2006 circularity

Sukumara 2001 SF

05

07

09

11

13

15

17

19

21

00

150

250

350

450

550

650

750

850

95

Factor (sphericity circularity shape)

Maxim

um

vo

id r

ati

o

Holubec 1973 sphericity

Cho 2006 circularity

Sukumara 2001 SF

05

1

15

2

25

3

35

005

015

025

035

045

055

065

075

085

095

Factor (roundness angularity)

Maxim

um

vo

id r

ati

o

Youd 1973 roundness

Rouse 2008 roundness

Cho 2006 roundness

Sukumaran 2001 AF

32

54 ANGLE OF REPOSE

The angle of repose of a granular material is the steepest angle of descent or dip of the

slope relative to the horizontal plane when material on the slope face is on the verge

of sliding as show in figure 40

According to Qazi (1975) there are five types of forces which may act between the

particles in soils

1 Force of friction between the particles

2 Force due to presence of absorbed gas andor moisture of particle

3 Mechanical forces caused by interlocking of particles of irregular shape

4 Electrostatic forces arising from friction between the particles themselves and

the surface with which they come in contact

5 Cohesion forces operating between neighbouring particles

Rouseacute et al (2008) found a decrease of angle of repose with increase roundness

based upon ASTM C1444 test (Standard Test Method for Measuring the Angle of

Repose of Free-Flowing Mold Powders) The method consist in pouring sand on a

surface cover by paper trough a funnel of specific dimensions (the nozzle diameter

depend on the sandrsquos particle size) from an altitude of 15 inches (381 mm) The sand

is release from the funnel until the peak of the cone formed by the sand stops the flow

The repose angle is obtained with the equation

H represent the 15 inches D and d represent the diameter of the cone formed by the

sand and the diameter of the funnel respectively

Figure 39 Maximum minus minimum void ratio based upon the relation of shape factor proposed by the

authors indicated in the figure

0

01

02

03

04

05

06

07

08

09

1

005

015

025

035

045

055

065

075

085

095

Factor (sphericity circularity shape)

Maxim

um

- M

inim

um

Vo

id r

ati

oHolubec 1973 sphericity

Cho 2006 circularity

Sukumara 2001 SF

0

02

04

06

08

1

12

14

16

18

005

015

025

035

045

055

065

075

085

095

Factor (roundness angularity)

Maxim

um

- M

inim

um

Vo

id r

ati

o

Youd 1973 roundness

Rouse 2008 roundness

Cho 2006 roundness

Sukumaran 2001 AF

dD

H2

tan=φ1

rep(61)

33

Rouseacute (2008) shows an empirical relation to obtain the angle of repose based on the

roundness of the particles

55 SHEAR STRENGTH

The MohrndashCoulomb failure criterion represents the linear envelope that is obtained

from a plot of the shear strength of a material versus the applied normal stress This

relation is expressed as

where τ is the shear strength σn is the normal stress co is the intercept of the failure

envelope with the τ axis and is the slope of the failure envelope The quantity c is

often called the cohesion and the angle is called the angle of internal friction

Studies show that the internal friction angle (under drained triaxial tests) increases

more rapidly on those materials having higher angularity increasing the relative

density The internal friction angle is a function of the relative density and the particle

shape (Holubec and DrsquoAppolonia 1973)

Chan and Page (1997) found in a study made with dry copper (using different shapes

and sizes ranging from 180 to 106 μm) using a direct shear test (ring share test) that

the internal friction angle increases as the angularity increases

Shinohara et al (2000) did some experiments with steel powder different shapes

using a triaxial cell in the test Shinohara never used the roundness or angularity on

the work but apply the shape factor (relation long axisshort axis) and the results were

that as this relation deviate from factor 1 the internal friction angle increases

The following empirical relations were found in the literature showing the behaviour

of the friction angle (obtained under different conditions)

)tan( noc

Figure 40 Representation of the angle of repose

(63)

(62)

34

Cho et al (2006)

(64)

(R is obtain by comparing the Krumbein chart figure 13)

Rouseacute (2008)

(65)

(66)

(R is defined using Wadell equation 22)

In figure 41 the suggested empirical relations above and lines constructed using

author data from Holubec and DrsquoAppolonia (1973) and Sukumara and Ashmawy

(2001) are plotted together to display the general trend on the particle shape and

friction angle relation Sukumaran reports two lines one based on the shape factor

(SF) and the second referring the angularity factor (AF) Sukumaran performed the

tests at constant volume

The scale used for Holubec and DrsquoAppolonia (1973) have lower and upper limits of 1

and 2 respectively (angularity form) and a scale change was applied to be able to

presented in the actual figure 41 As in the previous section (52) the author

recommend to use the original data from the references due that the figure just follows

the general trend of the behaviourrsquos particle regarding on the shape

Figure 41 The changes on the internal friction angle shows a general increase when the particle roundness

becomes angular or in the case of Sakamuran less spheric (Shape factor SF)

35

Barton and Kjaernsli (1981) suggested a model (equation 67) to predict the peak

friction angle (φrsquo) based upon numerous trixial and direct shear data tests

where

Se equivalent strength of particle

Re equivalent roughness of particle

φb basic friction angle (obtained from basic tilting test)

σn normal load

The information required for the model is (1) the uniaxial compressive strength of the

rock (2) the d50 particle size (mesh size where 50 of the particles pass through)

required to define Se (figure 42) (3) the degree of particle roundness and (4) the

porosity following compaction All data can be estimated by simple index tests

Barton and Kjaernsli (1981) suggest that particle size and sample scale has an effect

on the friction angle and includes them to obtain the equivalent strength (Se) figure 42

shows the method to obtain this value Compressive strength (σc) was chosen to be the

factor affecting the scale because micro fractures influence this property while

samples are bigger more micro fractures contain and its compressive strength reduces

The equivalent roughness is obtain using figure 43 where is required to know the

porosity (n) and the origin of the particles (a small chart is provided in the same figure

to compare the particles profile)

b

n

ee

SLogR

Figure 42 Method of estimating Equivalent Strength (Se) of rockfill based on uniaxial compressive strength

(σc ) and d50 particle size (Barton amp Kjaernsli 1981)

(67)

36

56 SEDIMENTATION PROPERTIES

A particle released in a less dense Newtonian fluid initially accelerate trough the fluid

due to the gravity Resistances to deformation of the fluid transmitted to the particle

surface drag generate forces that act to resist the particle motion The force due to the

weight (Fw) can be written as

Where ρp ρ are density of the particle and fluid (water) respectively g is the

gravitational force and Vp is the volume of the particle

And the resistance force (FD) is

Where CD is the dimensionless drag coefficient W is the weight of the particle and A

is the cross section area

Particlersquos shape has been assumed to be spherical when equations are applied on the

settling velocity Correlation deviates when particle shape departs from spherical form

Figure 43 Method of estimating Equivalent Roughness (Roe) based on porosity of rockfill

origin material degree of roundedness and smoothness of particle (Barton amp Kjaernsli 1981)

PPW ρ)gV(ρF

A2

WρCF

2

DD

(68)

(69)

37

(Dietrich 1982) and it is known that natural particles depart from spherical form

thus it is evident that this departure would have consequences

The below equation is proposed to account the shape (in this case the Corey shape

factor equation 8) in the settling velocity (Jimenez and Madsen 2003)

Jimenez and Madsen (2003) Dietrich (1982) Briggs and McCulloch (1962) and

others were working in the hydraulic shape of particles to solve problems as sediment

transport It is obvious that the equation presented and the researcherrsquos investigation

works under certain conditions (eg grain size between 0063-1 mm)

Dietrich (1982) suggests an empirical relation that accounts settling velocity size

density shape and roundness of a particle

R1 R2 and R3 are fitted equations for size and density shape and roundness

respectively

57 HYDRAULIC CONDUCTIVITY PERMEABILITY

Darcyrsquos Law Permeability is one component of Darcyrsquos law Darcys law is a simple

proportional relationship between the instantaneous discharge rate through a porous

medium the viscosity of the fluid and the pressure drop

The total velocity Ve is equal to the product of the permeability of the medium

(porous media) k the pressure drop ∆p all divided by the viscosity μ (Muskat

1937)

Darcys law is only valid for slow viscous flow most groundwater flow cases fall in

this category Typically Darcyrsquos law is valid at any flow with laminar flow (see figure

44)

Reynoldrsquos number (Laminar and turbulent Flow) Typically any laminar flow is

considered to have a Reynoldrsquos number less than one and it would be valid to apply

Darcys law Experimental tests have shown that flow regimes with Reynolds numbers

1

ND

S

S

ZY

gd1s

WW

NDN

gd)1s(4

dS

2R1R

3 10RW

pk

Ve

(70)

(71)

(72)

(73)

38

up to 10 may still be Darcian (laminar flow) as in the case of groundwater flow The

Reynolds number (a dimensionless parameter) for porous media flow is typically

expressed as

where ρ is the density of water (units of mass per volume) υ is the specific discharge

(with units of length per time) d is a representative average grain diameter for the

porous media (often taken as the 30 passing size from a grain size analysis using

sieves - with units of length) and μ is the viscosity of the fluid (Muskat 1937)

Shape effects Permeability as Head and Epps (2011) suggested is affected by the

shape and texture of soil grains Elongated or irregular particles create flow paths

which are more tortuous than those spherical particles Particles with a rough surface

texture provide more frictional resistance to flow Both effects tend to reduce the

water flow through the soil

Kozeny-Carman empirical relation accounts for the dependency of permeability on

void ratio in uniformly graded sands serious discrepancies are found when it is

applied to clays due the lack of uniform pores (Mitchell and Soga 2005)

There are various formulations of the Kozeny-Carman equation one published by

Head and Epps (2011) takes the void ratio e the specific surface area Ss and an

angularity factor F into account of permeability k

The angularity factor F considers the shape of the particles and ranges from 11 for

rounded grains 125 for sub rounded to 14 for angular particles The specific surface

Ss is defined as

d1 and d2 represent the maximum and minimum size particle in mm

Kane amp Sternheim (1988) suggest that the inclusion of the shape factor (F) has

probably the background on the Reynolds number due this factor is dependent

significantly on the shape of the obstacles and Reynolds number determines the

presence of laminar or turbulent flow Figure 44 show how the laminar flow has low

energy dissipation while turbulent flow (eg the roughness and path tortuosity) has

high energy dissipation

e1

e

FSs

2k

3

2

dRe

21

6

ddSs

(74)

(75)

(76)

39

According to Nearing and Parker (1994) the amount of soil detached during laminar

and turbulent flow is dependent on each soil and also greater on turbulent flow due the

greater shear strength generated during this kind of flow this could suggest the

greater erosion when turbulent flow is present

58 LIQUEFACTION

Soil liquefaction is a phenomenon in which soil loses much of its strength or stiffness

for a generally short time by earthquake shaking or other rapid loading Static and

dynamic liquefactions occur been the second one the most regular known

Liquefaction often occurs in saturated soils that is soils in which the space between

individual particles is completely filled with water This water exerts a pressure on the

soil particles that influences how tightly the particles themselves are pressed together

Shaking or other rapid loading can cause the water pressure to increase to the point

where the soil particles can readily move with respect to each other (Jefferies and

Been 2000)

Jefferies and Been (2000) state that it is clear that minor variation in intrinsic

properties of sand have major influence on the critical state These might be variations

on grain shape mineralogy grain size distribution surface roughness of grains etc

Yoginder et al (1985) found that substantial decrease on liquefaction resistance

occur with increase in confining pressure for rounded and angular sands (1600 kPa)

also rounded sands show an rapidly build up of resistance against liquefaction with

increasing density while angular tailing sand in contrast show such rapid increase

only at low confining pressures At low confining pressure angular material is more

resistant to liquefaction Probably the breakage of the corners on the angular particles

in tailings is ruling the lost in resistance at high confining pressures (sieve analysis

Figure 44 The figure show the extremes of flow behaviour First turbulent conditions where the flow is

essentially random and unpredictable and second the well defined Laminar flow conditions

40

after test identify the breakage of angular particles while on rounded particles the

sieve analysis was practically the same)

59 GROUNDWATER AND SEEPAGE MODELLING

In groundwater flow the particlersquos shape affects the soilrsquos pore size distribution

hence the flow characteristics (Sperry and Peirce 1995) Tortuosity and permeability

(also see section 57) are two significant macroscopic parameters of granular medium

that affect the passing flow (Hayati et al 2012) Current models incorporating the

effects of particle shape have failed to consider irregular particles such as those that

would prevail in a natural porous medium (Sperry and Peirce 1995)

Hayati et al (2012) suggested based on his results that tortuosity effect converge

when the porosity increases indicating that the shape have dominance at low and mid

porosity ranges

Sperry and Peirce (1995) research conclusions suggest that particle size and porosity

are more important predictors for hydraulic conductivity explaining the 69 of the

variability but particle shape appears to be the next most important This however

apparently comprises particles larger than 295-351 μm Differences for particle size

295-351 μm and smaller are not detectable Another interesting result in the research

was the interaction effect of the particle size and particle shape It suggests a different

packing configuration for particles of the same shape but different size (scale

dependent)

6 DISCUSSION

61 TERMS QUANTITIES AND DEFINITIONS

In order to describe the particle shape in detail there are a number of terms quantities

and definitions (qualitative and quantitative) used in the literature (eg Wadell 1932

1934 Krumbein 1941 Sneed amp Folk 1958) All mathematical definitions

(quantitatives) are models used to simplify the complexity of shape description Some

authors (Mitchell amp Soga 2005 Arasan et al 2010) are using three sub-quantities

one and each describing the shape but at different scales The terms are

morphologyform roundness and surface texture (figure 1) The three sub-quantities

are probably the best way to classify and describe a particle because not a single

definition can interpret the whole morphology Common language is needed when

descriptors are explained and these three scales represent an option It is evident in

the reviewed literature that many of the shape descriptors are presented with the same

name but also that there is not a clear meaning on what this descriptor defines eg

when there is no upper limit in the roundness does it means that the angularity never

ends Could they be more and more angular Probably they could be on theory but

not in reality

41

62 PROPERTIES

Trough various articlersquos review done in the present investigation it is recognized that

the particlersquos shape has an effect on the material properties among these are

1 Porosity (Tickell 1938 Fraser 1935 Kolbuszewski 1948) and void ratio

(Cho et al 2006 Shergold 1953 Rouseacute et al 2008 Santamarina and Cho

2004)

2 Permeability (Witt and Brauns 1983)

3 Internal friction angle (Shinohara et al 2000 Chan and Page 1997

Cheshomi et al 2009)

4 Density (Youd 1973 Holubec and DrsquoAppolonia 1973)

5 Drag coefficient Hydraulics (Briggs and McCulloch 1962)

In Table 5 is a short resume of the properties and shape effect found in peer review

articles trough different journals Most of the reviewed articles based its research on

uniform graded sands

Table 8 Compilation of properties influenced by particle shape

Repose

angle

Friction

angle

Porosity and

Void ratio Density Permeability

Settling velocity

Drag coefficient Deformation

Sphericity (3D)shape factor

NI x x x x x x

Circularity (2D)

NI x x x x NI NI

Roundness x x x x NI NI x

x influence

NI no information available

Shape of particles has an effect on the arrangement producing bridging or avoiding

the rotation of the particles and the resulting geotechnical property is affected eg

including flaky particles can result in a higher void ratio due the bridging effect

(Santamarina and Cho 2004) and depending on the loads even the size distribution is

changed due the breakage (Yoginder et al 1985) in similar way angular particles

produce higher void ratio due the avoided possibility of the particles to rotate and

compact

The influence of the chosen shape descriptor appears in this review to have minor

influence on the soil properties in the reviewed studies except on the void ratio and

the friction angle Influence of particle shape in some cases is hider by other factors

(eg size distribution) also the particle shape probably does not have influence when

particle size is in the clay order (eg hydraulic conductivity) the reason could be due

to forces as electrostatic or capillarity become more important at this level

Among the shape descriptors some are chosen more often in literature (eg aspect

ratio) there is no apparent scientific basis to use it (probably due to the simplicity of

the measurement it becomes one of the most use) but there are still some other

descriptors that may or may not show better correlation with the soil properties

Instead empirical relations had been developed regarding roundness or shape to

describe the soil behaviour it is clear that the mechanism behind the results is still not

completely understood

42

There is necessity to define the best(s) shape descriptor(s) to be used for particular

geotechnical properties

63 IMAGE ANALYSIS

Many image analysis techniques had been used to describe the particle shape eg

Fourier analysis fractal dimension tomography etc (Hyslip and Vallejo 1997) but

there is not agreement on the usage or conclusion to ensure the best particle descriptor

for geotechnical applications

There are several shape descriptors and also various techniques to capture the

particles profile (3-dimensions 3-dimension orthogonal and 2-dimensions) Each

technique presents advantages and disadvantages 3-dimensions is probably the

technique that provide more information about the particle shape but the precision

also lies in the resolution the equipment required to perform such capture could be

more or less sophisticated (scanning particles laying down in one position and later

move to complete the scanning or just falling down particles to scan it in one step)

3-dimensions orthogonal this technique use less sophisticated equipment (compare

with the previous technique) but its use is limited to particles over 1cm also

information between the orthogonal pictures is not capture 2-dimensions require non

sophisticated equipment but at the same time the shape information diminish compare

with the previous due the fact that it is possible to determine only the outline as the

particle measurements are performed in 2-dimensions it is presumed that they will lie

with its shortest axis perpendicular to the laying surface when they are flat but when

the particle tends to have more or less similar axis the laying could be random

Advantages on the use of image analysis are clear there is not subjectivity because it

is possible to obtain same result over the same images Electronic files do not loose

resolution and it is important when collaboration among distant work places is done

files can be send with the entire confidence and knowing that file properties has not

been changed Technology evolutions allowed to work with more information and it

also applies to the image processing area were the time consumed has been shortened

(more images processed in less time)

One important aspect in image analysis is the used resolution in the analysis due the

fact that there are measurements dependent and independent on resolution Thus

those dependent measurements should be avoided due the error included when they

are applied or avoid low resolution to increase the reliability Among these

parameters length is the principal parameter that is influences by resolution (eg

perimeter diameter axis etc) Resolution also has another aspect with two faces

quality versus capacity more resolution (quality) means more storage space a

minimum resolution to obtain reasonable and reliable data must be known but it

depend on each particular application

43

64 APPLICATIONS

Quantify changes in particles in the authorrsquos thought is one of the future applications

due the non-invasive methods of taking photographs in the surface of the damrsquos slope

rail road ballast or roads Sampling of the material and comparing with previous

results could show volume (3D analysis) or area (2D analysis) loss of the particles as

well as the form roundness and roughness This is important when it has been

suggested that a soil or rock embankment decrees their stability properties (eg

internal friction angle) with the loss of sphericity roundness or roughness

Seepage stock piling groundwater etc should try to include the particle shape while

modelling seepage requires grading material to not allow particles move due the

water pressure but in angular materials as it is known the void ratio is great than the

rounded soil it means the space and the possibilities for the small particles to move

are greater stock piling could be modelled incorporating the particle shape to

determine the binrsquos capacity when particle shape changes (void ratio changes when

particle shape changes) Modelling requires all information available and the

understanding of the principles that apply

Industry is actually using the particle shape to understand the soil behaviour and

transform processes into practical and economic image analysis has been included in

the quality control to determine particle shape and size because the advantages it

brings eg the acquisition of the sieving curve for pellets using digital images taken

from conveyor this allows to have the information in a short period of time with a

similar result at least enough from the practical point of view as the traditional

sieving

7 CONCLUSIONS

The conclusions of this literature review are

It has been shown that particle shape has influence on the soil behaviour

despite of partial knowledge of the mechanism behind Understanding of the

particle shape and its influence needs to be accomplished

A common language needs to be built up to standardize the meaning on

geotechnical field that involve the particle shape General relationships

between shape and properties should be developed

Based on this review it is not clear which is the best descriptor to use in

geotechnical engineering affecting he related shape to properties Instead of a

couple of standards there is no shape descriptor in geotechnical field fully

accepted

Image analysis tool is objective make the results repeatable obtain fast results

and work with more amount of information

44

Resolution needs to be taken in consideration when image analysis is been

carried out because the effects could be considerable Resolution must be set

according to the necessities Parameters as perimeter can be affected by

resolution

There are examples where particle shape has been incorporated in industries

related to geotechnical engineering eg in the ballast and asphalt industry for

quality control

8 FURTHER WORK

Three main issues have been identified in this review that will be further investigated

the limits of shape descriptors influence of grading and choice of descriptor for

relation to geotechnical properties

Shape descriptors have low and high limits frequently the limits are not the same and

the ability to describe the particlersquos shape is relative The sensitivity of each descriptor

should be compare to apply the most suitable descriptor in each situation

Sieving curve determine the particle size in a granular soil particle shape could differ

in each sieve size There is the necessity to describe the particle shape on each sieve

portion (due to practical issues) and included in the sieve curve Obtain an average

shape in determined sieve size is complicated (due to the possible presence of several

shapes) and to obtain the particle shape on the overall particlersquos size is challenging

how the particle shape should be included

Since several descriptors have been used to determine the shape of the particles and

the relation with the soil properties it is convenient to determine the descriptorrsquos

correlation with the soil properties

9 ACKNOWLEDGMENT

I would like to thanks to Lulearing University of Technology (LTU) the time I had spent

in its facilities and the kind environment it offers and University of Sonora

(UNISON) that has been providing me the financial support and the time to conclude

this journey

10 REFERENCES

Andersson T (2010) Estimating particle size distributions based on machine vision

Doctoral Thesis Departament of Computer Science and Electrical Engineering Lulearing

University of Technology ISSN 1402-1544 ISBN 978-91-7439-186-2

45

Arasan Seracettin Hasiloglu A Samet Akbulut Suat (2010) Shape particle of

natural and crished aggregate using image analysis International Journal of Civil and

Structural Engineering Vol 1 No 2 pp 221-233 ISSN 0970-4399

Aschenbrenner BC (1956) A new method of expressing particle sphericity Journal

of Sedimentary Petrology Vol 26 No 1 pp 15-31

Axelsson K (1998) Introduktion till jordmekaniken jaumlmte jordmateriallaumlran Skrift

984 Lulearing Avdelningen foumlr Geoteknologi Lulearing Tekniska Universitet (In Swedish)

Barton Nick amp Kjaernsli Bjorn (1981) Shear strength of rockfill Journal of the

Geotechnical Engineering Division Proceedings of the American Society of Civil

Engineers (ASCE) Vol 107 No GT7

Barrett P J (1980) The shape of rock particles a critical review Sedimentology

Vol 27 pp 291-303

Blott S J and Pye K (2008) Particle shape a review and new methods of

characterization and classification Sedimentology Vol 55 pp 31-63

Bowman E T Soga K and Drummond W (2001) Particle shape characterization

using Fourier descriptor analysis Geotechnique Vol 51 No 6 pp 545-554

Briggs L I McCulloch D S (1962) Hydraulic shape of sand particles Journal of

Sedimentary Petrology Vol 32 pp 645-656

Chan Leonard C Y and Page Neil W (1997) Particle fractal and load effects on

internal friction in powders Powder Technology Vol 90 pp 259-266

Cheshomi A Fakher A Jones C J F P (2009) A correlation between friction

angle and particle shape metrics in quaternary coarse alluvia Quarterly Journal of

Engineering Geology and Hydrogeology Vol 42 pp 145-155

Cho G Dodds J and Santamarina J C (2006) Particle shape effects on packing

density stiffness and strength Natural and crushed sands Journal of Geotechnical

and Geoenvironmental Engineering May 2006 pp 591-602

Dietrich William E (1982) Settling velocity of natural particles Water Resources

Research Vol 18 No 6 pp 1615-1626

Dobkins J E and Folk R L (1970) Shape development on Tahiti-nui Journal of

Sedimentary Petrology Vol 40 No 2 pp 1167-1203

Folk R L (1955) Student operator error in determining of roundness sphericity and

grain size Journal of Sedimentary Petrology Vol 25 pp 297-301

Fernlund J M R (1998) The effect of particle form on sieve analysis A test by

image analysis Engineering Geology Vol 50 No 1-2 pp 111-124

46

Fernlund J M R (2005) Image analysis method for determining 3-D shape of

coarse aggregate Cement and Concrete Research Vol 35 Issue 8 pp 1629-1637

Fernlund J M R Zimmerman Robert and Kragic Danica (2007) Influence of

volumemass on grain-size curves and conversion of image-analysis size to sieve size

Engineering Geology Vol 90 No 3-4 pp 124-137

Fraser H J (1935) Experimental study of the porosity and permeability of clastic

sediments The Journal of Geology Vol 43 pp 910-1010 ISSN 0022-1376

Hayati Ali Nemati Ahmadi Mohammad Mehdi and Mohammadi Soheil (2012)

American Physical Society Physical review E 85 036310 DOI

101103PhysRevE85036310

Hawkins A E (1993) The Shape of Powder-Particle Outlines Wiley New York

Head K H and Epps R J (2011) Manual of soil Laboratory testing Volum II

Permeability shear strength and compressibility test 3rd

edition Whittles Publishing

Scotland UK 3rd

edition

Holubec I and DrsquoAppolonia E (1973) Effect of particle shape on the engineering

properties of granular soils ASTM STP 523 pp 304-318

Hyslip James P Vallejo Luis E (1997) Fractal analysis of the roughness and size

distribution of granular materials Engineering Geology Vol 48 pp 231-244

Janoo Vincent C (1998) Quantification of shape angularity and surface texture of

base course materials US Army Corps of Engineers Cold Region Research and

Engineering Laboratory Special report 98-1

Jefferies Mike and Been Ken (2000) Soil liquefaction A critical state approach

Taylor amp Francis Group London and New York

Jimenez Jose A Madsen Ole S (2003) A simple formula to estimate settling

velocity of natural sediments Journal of Waterway Port Coastal and Ocean

Engineering Vol 129 No 2 pp 70-78

Johansson Jens and Vall Jakob (2011) Jordmaterials kornform Inverkan paring

Geotekniska Egenskaper Beskrivande storheter bestaumlmningsmetoder

Examensarbete Avdelningen foumlr Geoteknologi Institutionen foumlr Samhaumlllsbyggnad

och naturresurser Lulearing Tekniska Universitet Lulearing (In Swedish)

Kane Joseph W and Sternheim Morton M (1988) Physics John Wiley amp Sons Inc

Third edition

Kolbuszewski J (1948) An experimental study of the maximum and minimum

porosities of sands Proceedings of the Second International Conference on Soil

Mechanics and Foundation Engineering Rotterdam June 21 to 30 Sub-section IIb

pp 158-165

47

Krumbein W C and Pettijohn FJ (1938) Manual of sedimentary petrography

Appleton-Century Crofts Inc New York

Krumbein W C (1941) Measurement and geological significance of shape and

roundness of sedimentary particles Journal of Sedimentary Petrology Vol 11 No 2

pp 64-72

Krumbein W C and Sloss L L (1963) Stratigraphy and Sedimentation 2nd

ed

WH Freeman San Francisco

Kuo Chun-Yi and Freeman Reed B (1998a) Image analysis evaluation of

aggregates for asphalt concrete mixtures Transportation Research Record Vol 1615

pp 65-71

Kuo Chun-Yi Rollings Raymond and Lynch Larry N (1998b) Morphological

study of coarse aggregates using image analysis Journal of Materials in Civil

Engineering Vol 10 No 3 pp 135-142

Lanaro F Tolppanen P (2002) 3D characterization of coarse aggregates

Engineering Geology Vol 65 pp 17-30

Lees G (1964a) A new method for determining the angularity of particles

Sedimentology Vol 3 pp 2-21

Lees G (1964b) The measurement of particle shape and its influence in engineering

materials British Granite Whinstone Federation Vol 4 No 2 pp 17-38

Matsushima Takashi Saomoto Hidetaka Matsumoto Masaaki Toda Kengo

Yamada Yasuo (2003) Discrete element simulation of an assembly of irregular-

shaped grains Quantitative comparison with experiments 16th ASCE Engineering

Mechanics Conference University of Washington Seattle July 16-18

Mitchell James K and Soga Kenichi (2005) Fundamentals of soil behaviour Third

edition WILEY

Mora C F Kwan A K H Chan H C (1998) Particle size distribution analysis of

coarse aggregate using digital image processing Cement and Concrete Research Vol

28 pp 921-932

Mora C F and Kwan A K H (2000) Sphericity shape factor and convexity

measurement of coarse aggregate for concrete using digital image processing Cement

and Concrete Research Vol 30 No 3 pp 351-358

Muskat Morris (1937) The Flow of fluids through porous media Journal of Applied

Physics Vol 8 pp 274

Nearing M A and Parker S C (1994) Detachment of soil by flowing water under

turbulent and laminar conditions Soil Science Society of American Journal Vol 58

No 6 pp 1612-1614

48

Pan Tongyan Tutumluer Erol Carpenter Samuel H (2006) Effect of coarse

aggregate morphology on permanent deformation behavior of hot mix asphalt Journal

of Transportation Engineering Vol 132 No 7 pp 580-589

Pellegrino A (1965) Geotechnical properties of coarse-grained soils Proceedings

International Conference of Soil Mechanics and Foundation Engineering Vol 1 pp

97-91

Pentland A (1927) A method of measuring the angularity of sands MAG MN AL

Acta Eng Dom Transaction of the Royal Society of Canada Vol 21 Ser3xciii

Persson Anna-Lena (1998) Image analysis of shape and size of fine aggregates

Engineering Geology Vol 50 pp 177-186

Powers M C (1953) A new roundness scale for sedimentary particles Journal of

Sedimentary Petrology Vol 23 No 2 pp 117-119

Pye W and Pye M (1943) Sphericity determination of pebbles and grains Journal

of Sedimentary Petrology Vol 13 No 1 pp 28-34

Qazi M A (1975) Flow properties of granular masses A review on the angle of

repose The Arabian Journal for Science and Engineering Vol 1 No 2

Quiroga Pedro Nel and Fowle David W (2003) The effects of aggregate

characteristics on the performance of portland cement concrete Report ICAR 104-1F

Project number 104 International Center for Aggregates Research University of

Texas

Riley N A (1941) Projection sphericity Journal of Sedimentary Petrology Vol 11

No 2 pp 94-97

Rouseacute P C Fennin R J and Shuttle D A (2008) Influence of roundness on the

void ratio and strength of uniform sand Geotechnique Vol 58 No 3 227-231

Santamarina J C and Cho G C (2004) Soil behaviour The role of particle shape

Proceedings Skempton Conf London

Schofield and Wroth (1968) Critical state soil mechanics McGraw Hill

Shaumlfer Michael (2002) Digital optics Some remarks on the accuracy of particle

image analysis Particle amp Particle Systems Characterization Vol 19 No 3 pp 158-

168

Shergold F A (1953) The percentage of voids in compacted gravel as a measure of

its angularity Magazine of Concrete Research Vol 5 No 13 pp 3-10

Shinohara Kunio Oida Mikihiro Golman Boris (2000) Effect of particle shape on

angle of internal friction by triaxial compression test Powder Technology Vol 107

pp131-136

49

Skredcommisionen (1995) Ingenjoumlrsvetenskapsakademinen rapport 395 Linkoumlping

1995

Sneed E D and Folk R L (1958) Pebbles in the Colorado river Texas A study in

particle morphogenesis Journal of Geology Vol 66 pp 114-150

Sperry James M and Peirce J Jeffrey (1995) A model for estimating the hydraulic

conductivity of granular material based on grain shape grain size and porosity

Ground Water Vol 33 No 6 pp 892-898

Sukumaran B and Ashmawy A K (2001) Quantitative characterisation of the

geometry of discrete particles Geotechnique Vol 51 No 7 pp 619-627

Szaacutedeczy-Kardoss E Von (1933) Die bistimmung der abrollungsgrades Geologie

und palaumlontologie Vol 34B pp 389-401 (in German)

Teller J T (1976) Equantcy versus sphericity Sedimentology Vol 23 pp 427-428

Tickell F G (1938) Effect of the angularity of grain on porosity and permeability

bulletin of the American Association of Petroleum Geologist Vol 22 pp 1272-1274

Tutumluer E Huang H Hashash Y Ghaboussi J (2006) Aggregate shape effects

on ballast tamping and railroad track lateral stability AREMA 2006 Annual

Conference Louisville KY

Wadell H (1932) ldquoVolume Shape and roundness of rock particlesrdquo Journal of

Geology Vol 40 pp 443-451

Wadell H (1933) Sphericity and roundness of rock Particles Journal of Geology

Vol 41 No 3 pp 310ndash331

Wadell H (1934) Shape determination of large sedimental rock fragments

The Pan-American Geologist Vol 61 pp 187-220

Wadell H (1935) ldquoVolume shape and roundness of quartz particlesrdquo Journal of

Geology Vol 43 pp 250-279

Wentworth W C (1922a) The shape of beach pebbles Washington US Geological

Survey Bulletin Vol 131C pp 75-83

Wentworth W C (1922b) A method of measuring and plotting the shape of pebbles

Washington US Geological Survey Bulletin Vol 730C pp 91-114

Wentworth W C (1933) The shape of rock particle A discussion Journal of

Geology Vol 41 pp 306-309

Witt K J Brauns J (1983) Permeability-Anisotropy due to particle shape Journal

of Geotechnical Engineering Vol 109 No 9 pp 1181-1187

9

Table 2 General overview over different particle shape definitions for 3D sphericity has been compiled

and arranged chronologically

Aspect Name Author Year Based on

Sphericity (3D) Flatness index Wentworth 1922a 3-axes

True Sphericity Wadell 1932 Surface

Operational sphericity Wadell 1932 Volume

Sphericity Wadell 1934 Sphere diameter

Zinggrsquos clasification Zinggrsquos1

1935 3-axes

Intercept sphericity chart Krumbein 1941 3-axes

Pebble sphericity Pye and Pye 1943 3-axes

Corey shape factor Corey2

1949 3-axes

Working sphericity Ashenbrenner 1956 3-axes

shape factor Ashenbrenner 1956 3-axes

Maximum projection sphericity Sneed amp Folk 1958 3-axes

Williams shape factor Williams2

1965 3-axes

Janke form factor Janke2

1966 3-axes

Oblate-prolate index Dobkins amp Folk 1970 3-axes 1) Krumbein and Sloss 1963 2) Blott and Pye 2008

34 FORM (2D)

The technique to measure the sphericity is based in tree dimensions it can be found in

literature some ways to measure the ldquotwo dimensions sphericityrdquo which is simply the

perimeter of the particle projection some authors named ldquoparticle outlinerdquo or

ldquocircularityrdquo

Wadell in 1935 (Hawkins 1993) adopt a conversion of his 1934 3D sphericity

formula (equation 4) to a 2D outline He defined an orientation on the particles and

they were based on the maximum cross sectional area (outline of the particle

projecting the maximum area) The equations show the relation between diameters of

a circle of same area and smallest circumscribed circle

He also used the term ldquodegree of circularityrdquo as the ratio of the perimeter of a circle of

same area and the actual particle perimeter

Tickell in 1931 (Hawkins 1993) used his empirical relation The particle orientation

proposed was a random one It is described by the ratio between the area outline and

the area of smallest circumscribed circle

C

A

D

DC

P

PC C

CA

AC

(13)

(14)

(15)

10

Some other authors has been working with the ldquocircularityrdquo concept and had develop

them own equations as Pentland (1927) relating the area outline and area of a circle

with diameter equal to longest length outline and Cox (Riley 1941) with the ratio

area and perimeter time a constant equations 16 and 17 respectively Both authors did

not define any definite orientation of the grains

Riley (1941) realize the problems that an area perimeter and some other

measurements proposed by the above authors can carry as the time consuming and

tedious work (at that time were not computer all was made by hand) and thatrsquos why

he develop this equation easy to handle called ldquoinscribed circle sphericityrdquo He used

the same particle orientation proposed by Wadell and the relation of diameters of

inscribed and circumscribed circles

Horton 1932 (Hawkins 1993) use the relation of the drainage basing perimeter and

the perimeter of a circle of the same area as drainage basin

Janoo in 1998 (Blott and Pye 2008) develop his general ratio of perimeter to area

Sukumaran and Ashmawy (2001) develop his own shape factor (SF) defined as the

deviation of the global particle outline from a circle Figure 9 can be used as a

reference to determine the items used in the equation 21

N is referred to the number of sampling intervals o radial divisions

C2A

AC

2P

A4C

C

I

D

DC

CD

D

P

PC

A

PC

2

45ordm x N

Particleα

= SF

sumN

1=ii

(16)

(17)

(18)

(19)

(20)

(21)

11

Table 3 General chronological overview of the particle shape definitions for 2D sphericity

Aspect Name Author Year Based on

Circularity (2D) roundness Pentland 1927 area

roundness Cox1

1927 area-perimeter

roundness Tickell2

1931 area

Circularity Horton2

1932 drainage basin

outline circularity Wadell 1935 Circle diameter

degree of circularity Wadell 1935 Perimeter

inscribed circle sphericity Riley 1941 Circle diameter

Circularity Krumbein and Sloss 1963 chart

Janoo 1998 area-perimeter

Shape factor Sukumaran 2001 Segmentation of particle and angles

1) Riley 1941 2) Hawkins 1993

35 ROUNDNESS OR ANGULARITY

Roundness as described in section 32 is the second order shape descriptor Sphericity

lefts beside the corners and how they are this was notice by most of the authors sited

before and they suggested many ways to describe this second order particle property

Roundness is clearly understandable using the figure 10 Particle shape or form is the

overall configuration and denotes the similarities with a sphere (3D) or a circle (2D)

Roundness is concerning about the sharpness or the smoothness of the perimeter (2D)

Surface texture (Barret 1980) is describe as the third order subject (form is the first

and roundness the second) and it is superimposed in the corners and it is also a

property of particles surfaces between corners

Figure 9 Description of the Sukumaran factors to determine the shape and angularity (Sukumaran and

Ashmawy 2001)

12

Wadell (1935) describes his methodology calling it total degree or roundness to

obtain the roundness of a particle using the average radius of the corners in relation

with the inscribed circle diameter (see figure 11) on the equation

In the same study Wadell (1935) has used the equation

This two last equation shows slightly differences on the results (Wadell 1935)

Powers (1953) also published a graphic scale to illustrate the qualitative measure

(figure 12) It is important to highlight that any comparing chart to describe particle

properties has a high degree of subjectivity Folk (1955) concludes that when charts

are used for classification the risk of getting errors is negligible for sphericity but

large for roundness

N

R

r

Rinmax

r

R

NR

inmax

Figure 10 Form (shape) Roundness and Texture graphical description (Bowman et al 2001)

Figure 11 Wadellrsquos method to estimate the roundness corners radius and inscribed circle

(Hawkins 1993)

(22)

(23)

13

Some authors as Russel amp Taylor in 1937 Pettijohn in 1957 and Powers in 1953

developed a classification based on five and six classes (Hawkins 1993) each one

with its own class limits it is important to denote that the way they measure the

roundness is the developed by Wadell (1935) This classification and class limits are

showed in the table 4

Table 4 Degrees of roundness Wadell Values (Hawkins 1993) NA = no-applicable

Grade terms Russell amp Taylor (1937) Pettijohn (1957) Powers (1953)

Class

limits (R)

Arithmetic

midpoint

Class limits

(R)

Arithmetic midpoint Class

limits (R)

Arithmetic

midpoint

Very angular

NA

NA

NA

NA

012-017

014

Angular

000-015

0075

000-015

0125

017-025

021

Subangular

015-030

0225

015-025

0200

025-035

030

Subrounded

030-050

0400

025-040

0315

035-049

041

Rounded

050-070

0600

040-060

0500

049-070

059

Well rounded

070-100

0800

060-100

0800

070-100

084

Krumbein and Sloss (1963) published a graphical chart easy to determine the

sphericity and roundness parameters using comparison See figure 13 (Cho et al

2006)

Figure 12 A Roundness qualitative scale (Powers 1953)

Figure 13 Sphericity and roundness chart (Cho et al 2006) The roundness equation that appears here in

the chart is the wadellrsquos equation number 22

14

Fischer in 1933 (Hawkins 1993) used a straightforward method to quantify roundness

using a central point in the outline and dividing the outline in angles around this point

that were subtended by the straight or non curved parts of the profile were measured

This is illustrated in figure 14

To express the angularity value Fischer used the ratio of angles standing linear parts

on the outlines and concave respectively

Figure 14 left (A) and right (B) gives a similar angularity of approximately 042

using the above equations (Hawkins 1993)

Wentworth in 1922 used the maximum projection to define the position of the particle

to obtain the outline or contour (Barret 1980) The equation reflects the relation of the

diameter of a circle fitting the sharpest corner and the longest axis plus the shortest

axis c (minimum projection)

Wentworth (Hawkins 1993) expressed the roundness as the ratio of the radius of

curvature of the most convex part and the longest axis plus short axis

Actually these last two equations are the same just expressed in different terms when

the particle is in its maximum projection

Dimensions can be seen on figure 15 L and B represents the mayor axis a and

intermediate axis b The intention is to make difference between the 2 and 3

dimensions (L and B are for 2D as a b and c are for 3D)

deg360

ANG

=R

sumPLA

PLA

CON

ANG

ANGR

2)S(L

DR

M

S

B)4(L

RR CON

Figure 14 Fischerrsquos methods of angularity computation (Hawkins 1993)

A=inscribed circle B=circumscribed circle

(24)

(25)

(26)

(27)

15

Wentworth 1919 has a second way to express the roundness called Shape index

(Barrett 1980) and it relates the sharpest corner and the diameter of a pebble trough

the sharpest corner

Wentworth (1922b) used define the roundness as the ratio of the sharpest corner and

the average radius of the pebble

Cailleux (Barrett 1980) relates the radius of the most convex part and the longest

axis

Kuenen in 1956 show his roundness index (Barrett 1980) between the sharpest corner

and the breath axis

Dobkins amp Folk (1970) used a modified Wentworth roundness with the relation of

sharpest corner and inscribed circle diameters

AVG

CON

R

RR

x

s

D

DR

L2

RR CON

B

DR s

i

s

D

DR

3AVGAVG cbaDR2

Figure 15 Description of L and B axes (Hawkins 1993)

(28)

(29)

(30)

(31)

(32)

(33)

16

Swan in 1974 shows his equation (Barrett 1980) relating the sharpest (or the two

sharpest) corner(s) and inscribed circle diameter

Szadeczsky-Kardoss has his Average roundness of outline (Krumbein and Pettijohn

1938) relating the concave parts perimeter and the actual perimeter

Lees (1964a) developed an opposite definition to roundness it means that he

measures the angularity instead of the roundness and he calls it Degree of angularity

Figure 16 shows the items considered when equation 36 applies as the angles (α)

inscribed circle (Rmax-in) and the distance (x) The main formula is

In order to apply the last equation corners needs to be entered in the formula and each

individual result will add to each other to obtain the final degree of angularity

A roundness index appears on Janoo (1998) Kuo and Freeman (1998a) and Kuo et

al (1998b) it is described as

The last equation is on section 34 also because there is not a general agreement on the

definition furthermore some authors had used to define the roughness this is not the

only equation that has been used trying to define different aspects (sphericity

roundness or roughness) but it is a good example of the misuse of the quantities and

definitions

inmaxR

x)180(R

2P

A4R

i

ss

D

DDR

221

100P

PR CON

Figure 16 Degree of angularity measurement technique (Blot and Pye 2008)

(34)

(35)

(36)

(17)

17

Sukumaran and Ashmawy (2001) present an angularity factor (AF) calculated from

the number of sharpness corners Angles βi required to obtain the angularity factor are

shown in figure 9

Sukumaran and Ashmawy (2001) also suggested use not bigger sampling interval of

N=40 because it is the cut off between angularity factor and surface roughness If so

this equation could be used to describe the roughness

Table 5 General chronological overview of the particle roundness

Aspect Name Author Year Based on

Roundness shape index Wentworth 19191

diameter of sharper corner

shape index Wentworth 1922b sharpest corner and axis

roundness Wentworth 1933 convex parts

Fischer 19332

noncurved parts outline

Fischer 19332

noncurved-streigth parts outline

Average roundness of outline

Szadeczsky-Kardoss 19333

convex parts-perimeter

roundness Wadell 1935 diameter of corners

roundness Wadell 1935 diameter of corners

roundness Russel amp Taylor 19372

class limit table

roundness Krumbein 1941 chart

Cailleux 19471

convex parts

roundness Pettijohn 19494 class limit table

roundness Powers 1953 chart and class limit table

Kuenen 19561

axis-convex corner

roundness Krumbein and Sloss 1963 chart

degree of angularity Lees 1964a corners angles and inscribed circle

Dobkins amp Folk 1970 diameter of sharper corner

Swan 19741

diameter of sharper corners

Angularity factor Sukumaran and

Ashmawy 2001

Segmentation of particles and angles

1) Barret 1980 2) Hawkins 1993 3) Krumbein and Pettijohn 1938 4) Powers 1953

sum

sumsumN

1=i

2

i

2

N

1=i

2

i

2N

1=ii

)ordm180 -circleβ( - )(180ordm x 3

)ordm180-circleβ(-)ordm180 -Particleβ(

= AF (37)

18

36 ROUGHNESS OR SURFACE TEXTURE

A third property called texture appears early in the literature with the sphericity and

roundness properties since then texture property was longed described but it was in

accordance with the authors at that time not measurable

Wright in 1955 developed a method to quantify the surface texture or roughness of

concrete aggregate using studies done on 19 mm stones The test aggregates were first

embedded in a synthetic resin The stones were cut in thin sections The sections

projection was magnified 125 times The unevenness of the surface was traced and the

total length of the trace was measured The length was then compared with an uneven

line drawn as a series of chords (see figure 17) The difference between these two

lines was defined as the roughness factor (Janoo 1998)

However with the advance of technology it has become easier measure the roughness

and here is presented some researcherrsquos ideas how this property should be calculated

One technique used by Janoo (1988) to define the roughness can be seen in figure 18a

and is defined as the ratio between perimeter and convex perimeter

The convex perimeter is obtained using the Feretrsquos box (or diameter) tending a line in

between the touching points that the Feretrsquos box describes each time it is turn (figure

18b)

PER

OC

PR

Figure 17 Measurement method for characterizing the surface texture of an aggregate (Janoo 1998)

a) Convex perimeter (CPER) b) Feret measurement Figure 18 a) Convex perimeter (CPER) b) Feret measurement (modified after Janoo 1998)

(38)

a)

b)

19

Kuo and Freeman (1998a) and Kuo et al (1998b) use the roughness definition as the

ratio perimeter and average diameter

Erosion and dilatation image processing techniques are used to obtain the surface

texture Erosion is a morphological process by which boundary image pixels are

removed from an object surface which leaves the object less dense along the

perimeter or outer boundary Dilatation is the reverse process of erosion and a single

dilatation cycle increases the particle shape or image dimension by adding pixels

around its boundary (Pan etal 2006)

The ldquonrdquo erosion and dilatation cycles are not standardized

Mora and Kwan (2000) used the ldquoconvexity ratio CRrdquo (equation 41) and the ldquofullness

ratio FRrdquo (equation 42) in their investigation they are

The convex area is the area of the minimum convex boundaries circumscribing the

particle This is illustrated in the figure 19 The convex area is obtained in a similar

way as the convex perimeter but in this case the area between the original outline and

the convex perimeter is our convex area

AVG

OD

PR

100A

1AARO

CONo A

AR =

CONo A

AR =

Figure 19 Evaluation of area and convex area (Mora and Kuan 2000)

(39)

(40)

(41)

(42)

20

4 TECHNIQUES IN ORDER TO DETERMINE PARTICLE

SHAPE

41 HAND MEASUREMENT

Hand measurement technique was the first used by obvious reasons in order to

improve the accuracy special devices developed as the ldquosliding rod caliperrdquo used by

Krumbein (1941) it works placing the sample on the sliding road calliper as show

figure 20b the length in different positions can be obtain by using the scale provided

in the handle the ldquoconvexity gagerdquo that was actually used by opticians to measure the

curvature of lenses but easily applicable to the particle shape analysis (Wentworth

1922b) works measuring the movement of the central pivot as figure 20a shows (the

two adjacent pivots are invariable) as many the central pivot moves more is the

curvature or the ldquoSzadeczky-Kardossrsquos apparatusrdquo develop in 1933 that traces the

profile of the rock fragment so the outline traced is then analyzed (Krumbein and

Pettijohn 1938) figure 20c show equipment

Another helpful tool to determine the particle dimensions was the ldquocamera lucidardquo to

project the particlersquos contour over a circle scale appearing in Figure 21 thus it is

possible to measure the particlersquos diameter

a)

c) b)

Figure 20 a) convexity gage used to determine the curvature in particle corners (Wenworth 1922b)

b)sliding rod caliper device to measure the particle axis length (Krumbein 1941) and c)Szadeczky-

Kardoss (1933) apparatus it was utilized to obtain the particle outline

Figure 21 Circle scale used by Wadell (1935) to determine particlersquos diameter and roundness

21

42 SIEVE ANALYSIS

Bar sieving eg according to EN 933-31997 can be used to determine simple large

scale properties By combining mesh geometries the obtained results can be used to

quantify flakiness and elongation index ASTM D4791 (Flat and elongated particles

are defined as those coarse aggregate particles that have a ratio of length to thickness

equal to or greater than a specified value such as 51 The index represents the

percentage on weight of these particles) The method is not suitable for fine materials

This due to the difficulty to get the fine grains passed through the sieve and the great

amount of particles in relation to the area of the sieve (Persson 1998) eg EN 933-

31997 related to flakiness index The test is performed on aggregates with grain size

from 4 mm and up to 63 mm two sieving operations are necessary the first separates

on size fraction and the second use a bar sieve after the first sieving the average

maximum diameter of the particles is obtain and with the second sieving (bar sieving)

the shortest axis diameter is found finally with this two parameters the flakiness

index is determined

There are more standards related with the particle shape (see appendix A) but this

above presented are probably the most known using sieve analysis to determine

particlersquos geometrical properties

Sieve analysis is facing the computers age and image analysis sieving research is

taking place (Andersson 2010 Mora and Kwan 2000 Persson 1998) Industry is

also applying the image analysis sieving with decrees on the testing time compare

with the traditional sieving method An inconvenient of image analysis is the error

due the overlapping or hiding of the particles during the capture process but the

advantages are more compare with disadvantages (Anderson 2010)

43 CHART COMPARISON

Charts developed over the necessity of faster results because the long time consuming

required when measuring each particle

Krumbein (1941) present a comparison roundness chart for pebbles which were

measured by Wadellrsquos method because this property was the most difficult to measure

due to the second order scale that roundness represents (See figure 22)

Figure 22 Krumbein (1941) comparision chart for roundness

22

A qualitative chart by Powers (1953) try to include both (sphericity and roundness)

particlersquos characteristics it was divided on six roundness ranges (very angular

angular sub-angular sub-rounded rounded and well rounded) and two sphericity

series (high and low sphericity) This chart was prepared with photographs to enhance

the reader perspective (See figure 23)

A new chart including sphericity and roundness appear this time it was easier to

handle the two mean properties of particlersquos shape furthermore there was included

the numerical values that eliminated the subjectivity of qualitative description The

chart is based on Wadellrsquos definitions (Krumbein and Sloss 1963) (See figure 24)

Folk (1955) worried about the personrsquos error on the chartrsquos comparison studied the

determination of sphericity and angularity (he used the Powers 1953 comparison

chart) he found that the sphericity determination by chart comparison has a negligible

error while the roundness he concluded it was necessary to carry out a more wide

research due the high variability show by his study

Figure 23 Powers (1953) qualitative shpericity-roundness chart

Figure 24 Sphericity-roundness comparison chart (Krumbein and sloss 1963)

23

44 IMAGE ANALYSIS

Image analysis is a practical method to use for shape classification since it is fast and

can be automated Different techniques appear to process these images among them

are

o Feret Diameter the Feret diameter is the longitude between two parallel lines

this lines can rotate around one particle or outline to define dimensions as it

is shown in figure 25 these method is not a fine descriptor but as it was say

above it is a helpful tool to determine diameters (Janoo 1988)

o Fourier Mathematical Technique It produces mathematical relations that

characterize the profile of individual particles This method favours the

analysis of roughness and textural features for granular soils The problem in

the methodology remains in the re-entrant angles in order to complete the

revolution (Bowman et al 2001) see figure 26

o Fractal Dimension Irregular line at any level of scrutiny is by definition

fractal (Hyslip and Vallejo 1997) Figure 27 shows fractal analysis by the

dividing method The length of the fractal line can be defined as

N

1n

nn0 )nsinbncosa(a)(R

RD1n)(P

Figure 25 Feret measurement technique is defined by two parallel lines turning

around the particle to define the shortest and longest Feret diameter (Janoo 1988)

Figure 26 Fourier technique with two radiuses at one angle (Bowman et al 2001)

(43)

(44)

24

o Orthogonal image analysis This technique is basically the use of two images

orthogonal between them to acquire the three particle dimensions (Fernlund

2005) any of the above techniques can be used in this orthogonal way

o Laser Scanning Technique this kind of laser scanning 3D is one of the most

advanced techniques In figures 28a) we have the laser head scanning the rock

particles the particles have control points in order to keep a reference point

when move them to scan the lower part in figure 28b) we can see the laser

path followed (Lanaro and Tolppanen 2002)

Another technique is the Laser-Aided Tomography (LAT) in this case a laser sheet is

used to obtain the particles surveying (see figure 29) This technique is different and

has special requirements as to use liquid with same refractive index as the particles

particles must let the laser or certain percent of light go through (Matsushima et al

2003)

a) b)

Figure 27 Fractal analysis by the dividing method at different scrutiny scale (Hyslip and Vallejo 1997)

Figure 28 a) Scanning head b) scanning path (Lanaro and Tolppanen 2002)

Figure 30 3D scan completed ready to

use for any further measure

(Matsushima et al 2003)

Figure 29 LAT scaning particles

(Matsushima et al 2003)

25

Both 3D techniques obtain the particle shape that is later used to achieve measures as

we can see in figure 30

All these previous techniques are easily written in codes or scripts to be interpreted in

a digital way obtaining the desired measurement but there are some interesting points

in the image analysis regarding on the errors involve among them are image

resolution and orientation of the particles orientation is not relevant when it is

random and large number of particles are involve resolution have an influence on the

accuracy (Zeidan et al 2007)

When resolution is increase more accuracy is obtain and the object representation

match better with the real form in the other hand more resolution means more

spending on memory and time thus resolution needs to be according with the goal

and precision needed in any work (Schaumlfer 2002)

Schaumlfer (2002) conclude that attributes like length when measuring digital images

present relative high errors It can be vanish or at least diminish using high resolution

just for diameter but not for perimeter that keep the error as big as initially Johansson

and Vall (2011) obtain similar results when 3 different resolutions were used in the

same particle obtaining an unstable output for those termsquantities that involve the

perimeter Thus all quantities relating the perimeter should be treated with care

5 EFFECT OF SHAPE ON SOIL PROPERTIES

51 INTRODUCTION

In laboratory test on the effect on particle size on basic properties has been

investigated in several studies this relation has been discussed and various

mechanisms had been proposed to explain the behaviour of the soil in dependency

also with the shape Basically there are two mechanisms proposed The arrangement

of particles and the inter-particle contact (Santamarina and Cho 2004) and

subsequence breakage

The arrangement of particles

Arrangement of the particles can be presented in three different forms loose dense

and critical this arrangement determines the soil properties (eg density increase with

more dense arrangement) Loose and dense states are easy understandable when

figure 31 is explained while in the upper part of the figure the particles are arranged

using the minimum space needed in the lower part a span is created using the flaky

particle as a bridge this phenomena is known as ldquobridgingrdquo Bridging can produce

different geotechnical results when just the shape of the particle is changed eg void

ratio (Santamarina and Cho 2004) Particles are able to rearrange this could be done

applying pressure (energy) to the soil the pressure (energy) will create such forces

that soil particles will rotate and move (see figure 34) finishing in a more dense state

26

A loose soil will contract in volume on shearing and may not develop any peak

strength (figure 32 left) In this case the shear strength will increase gradually until

the residual shear strength is revealed once the soil has ceased contracting in volume

A dense soil may contract slightly (figure 32 right) before granular interlock prevents

further contraction (granular interlock is dependent on the shape of the grains and

their initial packing arrangement) In order to continue shearing once granular

interlock has occurred the soil must dilate (expand in volume) As additional shear

force is required to dilate the soil a peak shear strength occurs (figure 32 left) Once

this peak shear strength caused by dilation has been overcome through continued

shearing the resistance provided by the soil to the applied shear stress reduces

(termed strain softening) Strain softening will continue until no further changes in

volume of the soil occur on continued shearing Peak shear strengths are also

observed in overconsolidated clays where the natural fabric of the soil must be

destroyed prior to reaching constant volume shearing Other effects that result in peak

strengths include cementation and bonding of particles The distinctive shear strength

called the critical state is identified where the soil undergoing shear does so at a

constant volume (Schofield and Wroth 1968)

The inter-particle contact

For frictional soil ie coarse grained soil the friction between particles is the

dominating factor for strength Materials usually consisting of coarse grains (diameter

Figure 31 Bridging effect when flaky particles are combined in the bulk material (Santamarina and

Cho 2004)

Figure 32 The left part of the figure show a typical behaviour of loose and dense material over shear stress

while at the right the figures illustrate the typical volume changes

27

gt 006mm) behave as a frictional soil it means that the strength of coarse soils (silt

sand gravel etc) comes from an inter-particle mechanical friction thus ideally they

do not have traction strength In figure 33 the inter-particle contact is illustrated here

the pressure (P) is applied and two more components are found the normal load (N)

and the tangential load (T) described as the friction coefficient (μF) The forces stand

in equilibrium (Johansson and Vall 2011)

When particles equilibrium is disturbed (friction coefficient is not enough to keep

particles unmoved) the rotation is imminent and it is necessary in order to compact

the soil in figure 34 can be seen that the arrangement is a fact that inhibit or allow this

rotation and the shape in the 3 different scales are also factors because the more

spherical andor more rounded andor less roughness more easy is the rotation

(Santamarina and Cho 2004)

Breakage

Breakage is a side effect of the inter-particle contact and rotation when pressure

exceed the rock strength it can happened when the particles are tight together and

there is not enough space to rotate it is more obvious in angular particles (mesh form)

or as in figure 31 where the flaky particle ldquobridgingrdquo is not able to rotate but it can

brake by the pressure increase Yoginder et al (1985) notice that the angular particle

break during his experiments and they turn more rounded changing the original size

and form configuration at the same time there was a soil properties loosening

Figure 33 Inter-particle contact and forces acting (Axelsson 1998)

Figure 34 Rotation inhibition by the particles compaction or low void ratio (Santamarina and Cho 2004)

28

52 INFLUENCE OF SIZE AND SHAPE

Wenworth (1922a) and Pellegrino (1965) among others suggest that agent transport of

the rocks (rigor of transport temperature and moisture changes etc) determine its

shape but also the particle genesis itself (rock structure mineralogy hardness etc) It

is not possible to determine the shape of the particles based on the agent transport or

genesis but generally a shape behaviour is expected according to Mitchell and Soga

(2005) specially when the particle size is in the clay size (gt2μm) The shapes of the

most common clay minerals are platy (figure 35) with some exceptions (eg

halloysite occurs as tubes kaolinite are large thick and stiff Smectites are composed

of small very thin and filmy particles Illites are intermediate between kaolinite and

smectite and attapulgite occurs in lathlike particle shapes) Some clay minerals

photographs are presented in figure 35

Figure 35 Clay mineral shape a) hallosite b) Kaoline c) Smactites d) Illites and e) attapulgite (Modified

from Mitchell and Soga 2005)

Figure 36 Particle size range in soils Generally the particles of clay size are plate shaped (Mitchell and

Soga 2005)

a) b) c)

e) d)

29

53 VOID RATIO AND POROSITY

The void ratio (e) is the ratio of the volume of voids to the volume of solid it is

defined by the equation

Porosity (n) is the ratio of the volume of voids to the total volume of the soil it is

represented by the equation

Holubec and DrsquoAppolonia (1973) found a relation between the void ratio and

sphericity (referred in the paper as coefficient of angularity ratio of particle surface

and equivalent sphere surface) their results show that the maximum and the minimum

void ratio increases as the shpericity decreases In this study the surface was obtained

for an indirect method based on the permeability developed by Hoffman in 1959

described in the same document Rouseacute et al (2008) defined the roundness as

Wadell (1935) and he found it as an important factor controlling the minimum and

maximum void ratios Some other authors as Youd (1973) and Cho et al (2006)

conclude the same minimum and maximum void ratios increase when sphericity and

roundness decrease Another interesting result (all above authors) was the bigger

influence of the form (sphericity circularity) and roundness on the maximum void

ratio The change of the maximum void ratio is more pronounced than the change of

the minimum void ratio when the form and roundness changes (See figure 39)

Particles arrangement and interlocking are probably the factor that controls the void

ratio bridge effect permit the existence of void among the particles while interlocking

allowed the particles to form arches avoiding the possibility to rotate and stay in a

more stable configuration eg as it happens with marbles

Figures 36 37 and 38 shows proposed empirical relationships between void ratio and

shape from tables 5 and 6 (graphically the scale goes from 0 to 1 when cero mean

high angularity shpericity or circularity and one means low angularity circularity or

sphericity) Holubec and DrsquoAppolonia (1973) data was taken to obtain a power curve

and describe a tendency Santamarina and Cho (2004) show Youd equations in the

original paper Youd (1973) never presented the equation but it is easy to use the

information to draw a trend

The graphics presented in this document (figures 36 37 and 38) must be used with

certain reserves due the fact that the original data was modified in order to fit all

information in one graphic what the figures shows is just the general trend of the

behaviourrsquos material regarding on the shape If more accurate description and

information is required the author recommends consulting the reference data In the

same way equations from Holubec and DrsquoApollonia (1973) and Youd (1973) were not

presented by the authors but the use of the information was taken in order to build up

those equations on tables 6 and 7

S

V

V

V

= e

V

V

=nV

(45)

(46)

30

Table 6 Minimum void ratio equations regarding on the quantity (Ψ for sphericity C for circularity R

for roundness SF for Sukumaran shape factor and AF for Sukumaran angularity factor)

EQUATION NUMBER REFERENCE

Figure 34 (left)

4340

minΨ45490e =

47

Holubec amp DrsquoAppolonia 1973 (Ψ

was obtained using equation 2)

SF06340

mine021903180e +=

48

Sukumaran amp Ashmawy 2001 (SF

obtained using equation 21)

C05101emin

= 49

Cho etal 2006 (C obtained using

figure 12)

Figure 34 (right)

1

minR08203590e +=

50

Youd 1973 (R obtained from figure

11 and table 3)

R34080emin

= 51

Cho et al 2006 (R obtained using

figure 12)

1

minR05104330e +=

52

Rouseacute et al 2008 (R obtained by

equation 21)

AF02330

mine372004160e +=

53

Sukumaran amp Ashmawy 2001 (AF

obtained using equation 37)

Table 7 Maximum void ratio equations regarding on the quantity (Ψ for sphericity C for circularity R

for roundness SF for Sukumaran shape factor and AF for Sukumaran angularity factor)

EQUATION NUMBER REFERENCE

Figure 35 (left)

51520

max Ψ61120e = 54

Holubec and DrsquoAppolonia 1973 (Ψ

was obtained using equation 2)

SF1190

max e0016907180e += 55

Sukumaran amp Ashmawy 2001 (SF

obtained using equation 21)

C86061emax = 56

Cho etal 2006 (C obtained using

figure 12)

Figure 35 (right)

1

max R1505540e += 57

Youd 1973 (R obtained from figure

11 and table 3)

R62031emax= 58

Cho et al 2006 (R obtained using

figure 12)

1

max R107106150e += 59

Rouseacute et al 2008 (R obtained by

equation 21)

AF0530

max e12506090e += 60

Sukumaran amp Ashmawy 2001 (AF

obtained using equation 37)

Comparing figures 37 and 38 (minimum and maximum void ratio) it can be seen on

the right scheme of both figures 37 and 38 (when the factor is roundnessangularity)

that all the empirical relations has a common initial point close to 1 (it means that

particles are well rounded) while this common agreement disappear when the

roundness factor decreases (when the particles become more angular) Same figures

(37 and 38) on the left graphs (when the factor is sphericitycircularityshape) do not

present the same behaviour in fact there is more disperse initial point close to 1(when

the particles tend to be more sphericalcircular)

31

In Figure 39 the Δe (emax-emin) has been plotted to show how the maximum void ratio

and the minimum void ratio has different rate change when the particle shape

changes Maximum void ratio increases more than minimum void ratio when the

particle shape becomes less spherical andor more angular Comparing figure 39 left

and right graphics it can be seen that right present a common initial point when the

quantity (roundnessangularity) is close to one while in the left graphic the initial

point is more disperse Both ending points in both graphics (close to zero) are

dispersed

Figures 37 38 and 39 present the same behaviour right graphics (when the factor is

roundness angularity) in each figure have an initial common point while the left

graphics do not (when the factor is sphericity circularity shape)

Figure 37 Minimum void ratio based upon the relation of shape factor proposed by the authors indicated

in the figure

Figure 38 Maximum void ratio based upon the relation of shape factor proposed by the authors indicated

in the figure

04

06

08

1

12

14

16

18

2

005

015

025

035

045

055

065

075

085

095

Factor (roundness angularity)

min

imu

m v

oid

rati

o

Youd 1973 roundness

Rouse 2008 roundness

Cho 2006 roundness

Sukumaran 2001 AF

03

04

05

06

07

08

09

1

11

12

13

05

015

025

035

045

055

065

075

085

095

Factor (sphericity circularity shape)

min

imu

m v

oid

rati

oHolubec 1973 sphericity

Cho 2006 circularity

Sukumara 2001 SF

05

07

09

11

13

15

17

19

21

00

150

250

350

450

550

650

750

850

95

Factor (sphericity circularity shape)

Maxim

um

vo

id r

ati

o

Holubec 1973 sphericity

Cho 2006 circularity

Sukumara 2001 SF

05

1

15

2

25

3

35

005

015

025

035

045

055

065

075

085

095

Factor (roundness angularity)

Maxim

um

vo

id r

ati

o

Youd 1973 roundness

Rouse 2008 roundness

Cho 2006 roundness

Sukumaran 2001 AF

32

54 ANGLE OF REPOSE

The angle of repose of a granular material is the steepest angle of descent or dip of the

slope relative to the horizontal plane when material on the slope face is on the verge

of sliding as show in figure 40

According to Qazi (1975) there are five types of forces which may act between the

particles in soils

1 Force of friction between the particles

2 Force due to presence of absorbed gas andor moisture of particle

3 Mechanical forces caused by interlocking of particles of irregular shape

4 Electrostatic forces arising from friction between the particles themselves and

the surface with which they come in contact

5 Cohesion forces operating between neighbouring particles

Rouseacute et al (2008) found a decrease of angle of repose with increase roundness

based upon ASTM C1444 test (Standard Test Method for Measuring the Angle of

Repose of Free-Flowing Mold Powders) The method consist in pouring sand on a

surface cover by paper trough a funnel of specific dimensions (the nozzle diameter

depend on the sandrsquos particle size) from an altitude of 15 inches (381 mm) The sand

is release from the funnel until the peak of the cone formed by the sand stops the flow

The repose angle is obtained with the equation

H represent the 15 inches D and d represent the diameter of the cone formed by the

sand and the diameter of the funnel respectively

Figure 39 Maximum minus minimum void ratio based upon the relation of shape factor proposed by the

authors indicated in the figure

0

01

02

03

04

05

06

07

08

09

1

005

015

025

035

045

055

065

075

085

095

Factor (sphericity circularity shape)

Maxim

um

- M

inim

um

Vo

id r

ati

oHolubec 1973 sphericity

Cho 2006 circularity

Sukumara 2001 SF

0

02

04

06

08

1

12

14

16

18

005

015

025

035

045

055

065

075

085

095

Factor (roundness angularity)

Maxim

um

- M

inim

um

Vo

id r

ati

o

Youd 1973 roundness

Rouse 2008 roundness

Cho 2006 roundness

Sukumaran 2001 AF

dD

H2

tan=φ1

rep(61)

33

Rouseacute (2008) shows an empirical relation to obtain the angle of repose based on the

roundness of the particles

55 SHEAR STRENGTH

The MohrndashCoulomb failure criterion represents the linear envelope that is obtained

from a plot of the shear strength of a material versus the applied normal stress This

relation is expressed as

where τ is the shear strength σn is the normal stress co is the intercept of the failure

envelope with the τ axis and is the slope of the failure envelope The quantity c is

often called the cohesion and the angle is called the angle of internal friction

Studies show that the internal friction angle (under drained triaxial tests) increases

more rapidly on those materials having higher angularity increasing the relative

density The internal friction angle is a function of the relative density and the particle

shape (Holubec and DrsquoAppolonia 1973)

Chan and Page (1997) found in a study made with dry copper (using different shapes

and sizes ranging from 180 to 106 μm) using a direct shear test (ring share test) that

the internal friction angle increases as the angularity increases

Shinohara et al (2000) did some experiments with steel powder different shapes

using a triaxial cell in the test Shinohara never used the roundness or angularity on

the work but apply the shape factor (relation long axisshort axis) and the results were

that as this relation deviate from factor 1 the internal friction angle increases

The following empirical relations were found in the literature showing the behaviour

of the friction angle (obtained under different conditions)

)tan( noc

Figure 40 Representation of the angle of repose

(63)

(62)

34

Cho et al (2006)

(64)

(R is obtain by comparing the Krumbein chart figure 13)

Rouseacute (2008)

(65)

(66)

(R is defined using Wadell equation 22)

In figure 41 the suggested empirical relations above and lines constructed using

author data from Holubec and DrsquoAppolonia (1973) and Sukumara and Ashmawy

(2001) are plotted together to display the general trend on the particle shape and

friction angle relation Sukumaran reports two lines one based on the shape factor

(SF) and the second referring the angularity factor (AF) Sukumaran performed the

tests at constant volume

The scale used for Holubec and DrsquoAppolonia (1973) have lower and upper limits of 1

and 2 respectively (angularity form) and a scale change was applied to be able to

presented in the actual figure 41 As in the previous section (52) the author

recommend to use the original data from the references due that the figure just follows

the general trend of the behaviourrsquos particle regarding on the shape

Figure 41 The changes on the internal friction angle shows a general increase when the particle roundness

becomes angular or in the case of Sakamuran less spheric (Shape factor SF)

35

Barton and Kjaernsli (1981) suggested a model (equation 67) to predict the peak

friction angle (φrsquo) based upon numerous trixial and direct shear data tests

where

Se equivalent strength of particle

Re equivalent roughness of particle

φb basic friction angle (obtained from basic tilting test)

σn normal load

The information required for the model is (1) the uniaxial compressive strength of the

rock (2) the d50 particle size (mesh size where 50 of the particles pass through)

required to define Se (figure 42) (3) the degree of particle roundness and (4) the

porosity following compaction All data can be estimated by simple index tests

Barton and Kjaernsli (1981) suggest that particle size and sample scale has an effect

on the friction angle and includes them to obtain the equivalent strength (Se) figure 42

shows the method to obtain this value Compressive strength (σc) was chosen to be the

factor affecting the scale because micro fractures influence this property while

samples are bigger more micro fractures contain and its compressive strength reduces

The equivalent roughness is obtain using figure 43 where is required to know the

porosity (n) and the origin of the particles (a small chart is provided in the same figure

to compare the particles profile)

b

n

ee

SLogR

Figure 42 Method of estimating Equivalent Strength (Se) of rockfill based on uniaxial compressive strength

(σc ) and d50 particle size (Barton amp Kjaernsli 1981)

(67)

36

56 SEDIMENTATION PROPERTIES

A particle released in a less dense Newtonian fluid initially accelerate trough the fluid

due to the gravity Resistances to deformation of the fluid transmitted to the particle

surface drag generate forces that act to resist the particle motion The force due to the

weight (Fw) can be written as

Where ρp ρ are density of the particle and fluid (water) respectively g is the

gravitational force and Vp is the volume of the particle

And the resistance force (FD) is

Where CD is the dimensionless drag coefficient W is the weight of the particle and A

is the cross section area

Particlersquos shape has been assumed to be spherical when equations are applied on the

settling velocity Correlation deviates when particle shape departs from spherical form

Figure 43 Method of estimating Equivalent Roughness (Roe) based on porosity of rockfill

origin material degree of roundedness and smoothness of particle (Barton amp Kjaernsli 1981)

PPW ρ)gV(ρF

A2

WρCF

2

DD

(68)

(69)

37

(Dietrich 1982) and it is known that natural particles depart from spherical form

thus it is evident that this departure would have consequences

The below equation is proposed to account the shape (in this case the Corey shape

factor equation 8) in the settling velocity (Jimenez and Madsen 2003)

Jimenez and Madsen (2003) Dietrich (1982) Briggs and McCulloch (1962) and

others were working in the hydraulic shape of particles to solve problems as sediment

transport It is obvious that the equation presented and the researcherrsquos investigation

works under certain conditions (eg grain size between 0063-1 mm)

Dietrich (1982) suggests an empirical relation that accounts settling velocity size

density shape and roundness of a particle

R1 R2 and R3 are fitted equations for size and density shape and roundness

respectively

57 HYDRAULIC CONDUCTIVITY PERMEABILITY

Darcyrsquos Law Permeability is one component of Darcyrsquos law Darcys law is a simple

proportional relationship between the instantaneous discharge rate through a porous

medium the viscosity of the fluid and the pressure drop

The total velocity Ve is equal to the product of the permeability of the medium

(porous media) k the pressure drop ∆p all divided by the viscosity μ (Muskat

1937)

Darcys law is only valid for slow viscous flow most groundwater flow cases fall in

this category Typically Darcyrsquos law is valid at any flow with laminar flow (see figure

44)

Reynoldrsquos number (Laminar and turbulent Flow) Typically any laminar flow is

considered to have a Reynoldrsquos number less than one and it would be valid to apply

Darcys law Experimental tests have shown that flow regimes with Reynolds numbers

1

ND

S

S

ZY

gd1s

WW

NDN

gd)1s(4

dS

2R1R

3 10RW

pk

Ve

(70)

(71)

(72)

(73)

38

up to 10 may still be Darcian (laminar flow) as in the case of groundwater flow The

Reynolds number (a dimensionless parameter) for porous media flow is typically

expressed as

where ρ is the density of water (units of mass per volume) υ is the specific discharge

(with units of length per time) d is a representative average grain diameter for the

porous media (often taken as the 30 passing size from a grain size analysis using

sieves - with units of length) and μ is the viscosity of the fluid (Muskat 1937)

Shape effects Permeability as Head and Epps (2011) suggested is affected by the

shape and texture of soil grains Elongated or irregular particles create flow paths

which are more tortuous than those spherical particles Particles with a rough surface

texture provide more frictional resistance to flow Both effects tend to reduce the

water flow through the soil

Kozeny-Carman empirical relation accounts for the dependency of permeability on

void ratio in uniformly graded sands serious discrepancies are found when it is

applied to clays due the lack of uniform pores (Mitchell and Soga 2005)

There are various formulations of the Kozeny-Carman equation one published by

Head and Epps (2011) takes the void ratio e the specific surface area Ss and an

angularity factor F into account of permeability k

The angularity factor F considers the shape of the particles and ranges from 11 for

rounded grains 125 for sub rounded to 14 for angular particles The specific surface

Ss is defined as

d1 and d2 represent the maximum and minimum size particle in mm

Kane amp Sternheim (1988) suggest that the inclusion of the shape factor (F) has

probably the background on the Reynolds number due this factor is dependent

significantly on the shape of the obstacles and Reynolds number determines the

presence of laminar or turbulent flow Figure 44 show how the laminar flow has low

energy dissipation while turbulent flow (eg the roughness and path tortuosity) has

high energy dissipation

e1

e

FSs

2k

3

2

dRe

21

6

ddSs

(74)

(75)

(76)

39

According to Nearing and Parker (1994) the amount of soil detached during laminar

and turbulent flow is dependent on each soil and also greater on turbulent flow due the

greater shear strength generated during this kind of flow this could suggest the

greater erosion when turbulent flow is present

58 LIQUEFACTION

Soil liquefaction is a phenomenon in which soil loses much of its strength or stiffness

for a generally short time by earthquake shaking or other rapid loading Static and

dynamic liquefactions occur been the second one the most regular known

Liquefaction often occurs in saturated soils that is soils in which the space between

individual particles is completely filled with water This water exerts a pressure on the

soil particles that influences how tightly the particles themselves are pressed together

Shaking or other rapid loading can cause the water pressure to increase to the point

where the soil particles can readily move with respect to each other (Jefferies and

Been 2000)

Jefferies and Been (2000) state that it is clear that minor variation in intrinsic

properties of sand have major influence on the critical state These might be variations

on grain shape mineralogy grain size distribution surface roughness of grains etc

Yoginder et al (1985) found that substantial decrease on liquefaction resistance

occur with increase in confining pressure for rounded and angular sands (1600 kPa)

also rounded sands show an rapidly build up of resistance against liquefaction with

increasing density while angular tailing sand in contrast show such rapid increase

only at low confining pressures At low confining pressure angular material is more

resistant to liquefaction Probably the breakage of the corners on the angular particles

in tailings is ruling the lost in resistance at high confining pressures (sieve analysis

Figure 44 The figure show the extremes of flow behaviour First turbulent conditions where the flow is

essentially random and unpredictable and second the well defined Laminar flow conditions

40

after test identify the breakage of angular particles while on rounded particles the

sieve analysis was practically the same)

59 GROUNDWATER AND SEEPAGE MODELLING

In groundwater flow the particlersquos shape affects the soilrsquos pore size distribution

hence the flow characteristics (Sperry and Peirce 1995) Tortuosity and permeability

(also see section 57) are two significant macroscopic parameters of granular medium

that affect the passing flow (Hayati et al 2012) Current models incorporating the

effects of particle shape have failed to consider irregular particles such as those that

would prevail in a natural porous medium (Sperry and Peirce 1995)

Hayati et al (2012) suggested based on his results that tortuosity effect converge

when the porosity increases indicating that the shape have dominance at low and mid

porosity ranges

Sperry and Peirce (1995) research conclusions suggest that particle size and porosity

are more important predictors for hydraulic conductivity explaining the 69 of the

variability but particle shape appears to be the next most important This however

apparently comprises particles larger than 295-351 μm Differences for particle size

295-351 μm and smaller are not detectable Another interesting result in the research

was the interaction effect of the particle size and particle shape It suggests a different

packing configuration for particles of the same shape but different size (scale

dependent)

6 DISCUSSION

61 TERMS QUANTITIES AND DEFINITIONS

In order to describe the particle shape in detail there are a number of terms quantities

and definitions (qualitative and quantitative) used in the literature (eg Wadell 1932

1934 Krumbein 1941 Sneed amp Folk 1958) All mathematical definitions

(quantitatives) are models used to simplify the complexity of shape description Some

authors (Mitchell amp Soga 2005 Arasan et al 2010) are using three sub-quantities

one and each describing the shape but at different scales The terms are

morphologyform roundness and surface texture (figure 1) The three sub-quantities

are probably the best way to classify and describe a particle because not a single

definition can interpret the whole morphology Common language is needed when

descriptors are explained and these three scales represent an option It is evident in

the reviewed literature that many of the shape descriptors are presented with the same

name but also that there is not a clear meaning on what this descriptor defines eg

when there is no upper limit in the roundness does it means that the angularity never

ends Could they be more and more angular Probably they could be on theory but

not in reality

41

62 PROPERTIES

Trough various articlersquos review done in the present investigation it is recognized that

the particlersquos shape has an effect on the material properties among these are

1 Porosity (Tickell 1938 Fraser 1935 Kolbuszewski 1948) and void ratio

(Cho et al 2006 Shergold 1953 Rouseacute et al 2008 Santamarina and Cho

2004)

2 Permeability (Witt and Brauns 1983)

3 Internal friction angle (Shinohara et al 2000 Chan and Page 1997

Cheshomi et al 2009)

4 Density (Youd 1973 Holubec and DrsquoAppolonia 1973)

5 Drag coefficient Hydraulics (Briggs and McCulloch 1962)

In Table 5 is a short resume of the properties and shape effect found in peer review

articles trough different journals Most of the reviewed articles based its research on

uniform graded sands

Table 8 Compilation of properties influenced by particle shape

Repose

angle

Friction

angle

Porosity and

Void ratio Density Permeability

Settling velocity

Drag coefficient Deformation

Sphericity (3D)shape factor

NI x x x x x x

Circularity (2D)

NI x x x x NI NI

Roundness x x x x NI NI x

x influence

NI no information available

Shape of particles has an effect on the arrangement producing bridging or avoiding

the rotation of the particles and the resulting geotechnical property is affected eg

including flaky particles can result in a higher void ratio due the bridging effect

(Santamarina and Cho 2004) and depending on the loads even the size distribution is

changed due the breakage (Yoginder et al 1985) in similar way angular particles

produce higher void ratio due the avoided possibility of the particles to rotate and

compact

The influence of the chosen shape descriptor appears in this review to have minor

influence on the soil properties in the reviewed studies except on the void ratio and

the friction angle Influence of particle shape in some cases is hider by other factors

(eg size distribution) also the particle shape probably does not have influence when

particle size is in the clay order (eg hydraulic conductivity) the reason could be due

to forces as electrostatic or capillarity become more important at this level

Among the shape descriptors some are chosen more often in literature (eg aspect

ratio) there is no apparent scientific basis to use it (probably due to the simplicity of

the measurement it becomes one of the most use) but there are still some other

descriptors that may or may not show better correlation with the soil properties

Instead empirical relations had been developed regarding roundness or shape to

describe the soil behaviour it is clear that the mechanism behind the results is still not

completely understood

42

There is necessity to define the best(s) shape descriptor(s) to be used for particular

geotechnical properties

63 IMAGE ANALYSIS

Many image analysis techniques had been used to describe the particle shape eg

Fourier analysis fractal dimension tomography etc (Hyslip and Vallejo 1997) but

there is not agreement on the usage or conclusion to ensure the best particle descriptor

for geotechnical applications

There are several shape descriptors and also various techniques to capture the

particles profile (3-dimensions 3-dimension orthogonal and 2-dimensions) Each

technique presents advantages and disadvantages 3-dimensions is probably the

technique that provide more information about the particle shape but the precision

also lies in the resolution the equipment required to perform such capture could be

more or less sophisticated (scanning particles laying down in one position and later

move to complete the scanning or just falling down particles to scan it in one step)

3-dimensions orthogonal this technique use less sophisticated equipment (compare

with the previous technique) but its use is limited to particles over 1cm also

information between the orthogonal pictures is not capture 2-dimensions require non

sophisticated equipment but at the same time the shape information diminish compare

with the previous due the fact that it is possible to determine only the outline as the

particle measurements are performed in 2-dimensions it is presumed that they will lie

with its shortest axis perpendicular to the laying surface when they are flat but when

the particle tends to have more or less similar axis the laying could be random

Advantages on the use of image analysis are clear there is not subjectivity because it

is possible to obtain same result over the same images Electronic files do not loose

resolution and it is important when collaboration among distant work places is done

files can be send with the entire confidence and knowing that file properties has not

been changed Technology evolutions allowed to work with more information and it

also applies to the image processing area were the time consumed has been shortened

(more images processed in less time)

One important aspect in image analysis is the used resolution in the analysis due the

fact that there are measurements dependent and independent on resolution Thus

those dependent measurements should be avoided due the error included when they

are applied or avoid low resolution to increase the reliability Among these

parameters length is the principal parameter that is influences by resolution (eg

perimeter diameter axis etc) Resolution also has another aspect with two faces

quality versus capacity more resolution (quality) means more storage space a

minimum resolution to obtain reasonable and reliable data must be known but it

depend on each particular application

43

64 APPLICATIONS

Quantify changes in particles in the authorrsquos thought is one of the future applications

due the non-invasive methods of taking photographs in the surface of the damrsquos slope

rail road ballast or roads Sampling of the material and comparing with previous

results could show volume (3D analysis) or area (2D analysis) loss of the particles as

well as the form roundness and roughness This is important when it has been

suggested that a soil or rock embankment decrees their stability properties (eg

internal friction angle) with the loss of sphericity roundness or roughness

Seepage stock piling groundwater etc should try to include the particle shape while

modelling seepage requires grading material to not allow particles move due the

water pressure but in angular materials as it is known the void ratio is great than the

rounded soil it means the space and the possibilities for the small particles to move

are greater stock piling could be modelled incorporating the particle shape to

determine the binrsquos capacity when particle shape changes (void ratio changes when

particle shape changes) Modelling requires all information available and the

understanding of the principles that apply

Industry is actually using the particle shape to understand the soil behaviour and

transform processes into practical and economic image analysis has been included in

the quality control to determine particle shape and size because the advantages it

brings eg the acquisition of the sieving curve for pellets using digital images taken

from conveyor this allows to have the information in a short period of time with a

similar result at least enough from the practical point of view as the traditional

sieving

7 CONCLUSIONS

The conclusions of this literature review are

It has been shown that particle shape has influence on the soil behaviour

despite of partial knowledge of the mechanism behind Understanding of the

particle shape and its influence needs to be accomplished

A common language needs to be built up to standardize the meaning on

geotechnical field that involve the particle shape General relationships

between shape and properties should be developed

Based on this review it is not clear which is the best descriptor to use in

geotechnical engineering affecting he related shape to properties Instead of a

couple of standards there is no shape descriptor in geotechnical field fully

accepted

Image analysis tool is objective make the results repeatable obtain fast results

and work with more amount of information

44

Resolution needs to be taken in consideration when image analysis is been

carried out because the effects could be considerable Resolution must be set

according to the necessities Parameters as perimeter can be affected by

resolution

There are examples where particle shape has been incorporated in industries

related to geotechnical engineering eg in the ballast and asphalt industry for

quality control

8 FURTHER WORK

Three main issues have been identified in this review that will be further investigated

the limits of shape descriptors influence of grading and choice of descriptor for

relation to geotechnical properties

Shape descriptors have low and high limits frequently the limits are not the same and

the ability to describe the particlersquos shape is relative The sensitivity of each descriptor

should be compare to apply the most suitable descriptor in each situation

Sieving curve determine the particle size in a granular soil particle shape could differ

in each sieve size There is the necessity to describe the particle shape on each sieve

portion (due to practical issues) and included in the sieve curve Obtain an average

shape in determined sieve size is complicated (due to the possible presence of several

shapes) and to obtain the particle shape on the overall particlersquos size is challenging

how the particle shape should be included

Since several descriptors have been used to determine the shape of the particles and

the relation with the soil properties it is convenient to determine the descriptorrsquos

correlation with the soil properties

9 ACKNOWLEDGMENT

I would like to thanks to Lulearing University of Technology (LTU) the time I had spent

in its facilities and the kind environment it offers and University of Sonora

(UNISON) that has been providing me the financial support and the time to conclude

this journey

10 REFERENCES

Andersson T (2010) Estimating particle size distributions based on machine vision

Doctoral Thesis Departament of Computer Science and Electrical Engineering Lulearing

University of Technology ISSN 1402-1544 ISBN 978-91-7439-186-2

45

Arasan Seracettin Hasiloglu A Samet Akbulut Suat (2010) Shape particle of

natural and crished aggregate using image analysis International Journal of Civil and

Structural Engineering Vol 1 No 2 pp 221-233 ISSN 0970-4399

Aschenbrenner BC (1956) A new method of expressing particle sphericity Journal

of Sedimentary Petrology Vol 26 No 1 pp 15-31

Axelsson K (1998) Introduktion till jordmekaniken jaumlmte jordmateriallaumlran Skrift

984 Lulearing Avdelningen foumlr Geoteknologi Lulearing Tekniska Universitet (In Swedish)

Barton Nick amp Kjaernsli Bjorn (1981) Shear strength of rockfill Journal of the

Geotechnical Engineering Division Proceedings of the American Society of Civil

Engineers (ASCE) Vol 107 No GT7

Barrett P J (1980) The shape of rock particles a critical review Sedimentology

Vol 27 pp 291-303

Blott S J and Pye K (2008) Particle shape a review and new methods of

characterization and classification Sedimentology Vol 55 pp 31-63

Bowman E T Soga K and Drummond W (2001) Particle shape characterization

using Fourier descriptor analysis Geotechnique Vol 51 No 6 pp 545-554

Briggs L I McCulloch D S (1962) Hydraulic shape of sand particles Journal of

Sedimentary Petrology Vol 32 pp 645-656

Chan Leonard C Y and Page Neil W (1997) Particle fractal and load effects on

internal friction in powders Powder Technology Vol 90 pp 259-266

Cheshomi A Fakher A Jones C J F P (2009) A correlation between friction

angle and particle shape metrics in quaternary coarse alluvia Quarterly Journal of

Engineering Geology and Hydrogeology Vol 42 pp 145-155

Cho G Dodds J and Santamarina J C (2006) Particle shape effects on packing

density stiffness and strength Natural and crushed sands Journal of Geotechnical

and Geoenvironmental Engineering May 2006 pp 591-602

Dietrich William E (1982) Settling velocity of natural particles Water Resources

Research Vol 18 No 6 pp 1615-1626

Dobkins J E and Folk R L (1970) Shape development on Tahiti-nui Journal of

Sedimentary Petrology Vol 40 No 2 pp 1167-1203

Folk R L (1955) Student operator error in determining of roundness sphericity and

grain size Journal of Sedimentary Petrology Vol 25 pp 297-301

Fernlund J M R (1998) The effect of particle form on sieve analysis A test by

image analysis Engineering Geology Vol 50 No 1-2 pp 111-124

46

Fernlund J M R (2005) Image analysis method for determining 3-D shape of

coarse aggregate Cement and Concrete Research Vol 35 Issue 8 pp 1629-1637

Fernlund J M R Zimmerman Robert and Kragic Danica (2007) Influence of

volumemass on grain-size curves and conversion of image-analysis size to sieve size

Engineering Geology Vol 90 No 3-4 pp 124-137

Fraser H J (1935) Experimental study of the porosity and permeability of clastic

sediments The Journal of Geology Vol 43 pp 910-1010 ISSN 0022-1376

Hayati Ali Nemati Ahmadi Mohammad Mehdi and Mohammadi Soheil (2012)

American Physical Society Physical review E 85 036310 DOI

101103PhysRevE85036310

Hawkins A E (1993) The Shape of Powder-Particle Outlines Wiley New York

Head K H and Epps R J (2011) Manual of soil Laboratory testing Volum II

Permeability shear strength and compressibility test 3rd

edition Whittles Publishing

Scotland UK 3rd

edition

Holubec I and DrsquoAppolonia E (1973) Effect of particle shape on the engineering

properties of granular soils ASTM STP 523 pp 304-318

Hyslip James P Vallejo Luis E (1997) Fractal analysis of the roughness and size

distribution of granular materials Engineering Geology Vol 48 pp 231-244

Janoo Vincent C (1998) Quantification of shape angularity and surface texture of

base course materials US Army Corps of Engineers Cold Region Research and

Engineering Laboratory Special report 98-1

Jefferies Mike and Been Ken (2000) Soil liquefaction A critical state approach

Taylor amp Francis Group London and New York

Jimenez Jose A Madsen Ole S (2003) A simple formula to estimate settling

velocity of natural sediments Journal of Waterway Port Coastal and Ocean

Engineering Vol 129 No 2 pp 70-78

Johansson Jens and Vall Jakob (2011) Jordmaterials kornform Inverkan paring

Geotekniska Egenskaper Beskrivande storheter bestaumlmningsmetoder

Examensarbete Avdelningen foumlr Geoteknologi Institutionen foumlr Samhaumlllsbyggnad

och naturresurser Lulearing Tekniska Universitet Lulearing (In Swedish)

Kane Joseph W and Sternheim Morton M (1988) Physics John Wiley amp Sons Inc

Third edition

Kolbuszewski J (1948) An experimental study of the maximum and minimum

porosities of sands Proceedings of the Second International Conference on Soil

Mechanics and Foundation Engineering Rotterdam June 21 to 30 Sub-section IIb

pp 158-165

47

Krumbein W C and Pettijohn FJ (1938) Manual of sedimentary petrography

Appleton-Century Crofts Inc New York

Krumbein W C (1941) Measurement and geological significance of shape and

roundness of sedimentary particles Journal of Sedimentary Petrology Vol 11 No 2

pp 64-72

Krumbein W C and Sloss L L (1963) Stratigraphy and Sedimentation 2nd

ed

WH Freeman San Francisco

Kuo Chun-Yi and Freeman Reed B (1998a) Image analysis evaluation of

aggregates for asphalt concrete mixtures Transportation Research Record Vol 1615

pp 65-71

Kuo Chun-Yi Rollings Raymond and Lynch Larry N (1998b) Morphological

study of coarse aggregates using image analysis Journal of Materials in Civil

Engineering Vol 10 No 3 pp 135-142

Lanaro F Tolppanen P (2002) 3D characterization of coarse aggregates

Engineering Geology Vol 65 pp 17-30

Lees G (1964a) A new method for determining the angularity of particles

Sedimentology Vol 3 pp 2-21

Lees G (1964b) The measurement of particle shape and its influence in engineering

materials British Granite Whinstone Federation Vol 4 No 2 pp 17-38

Matsushima Takashi Saomoto Hidetaka Matsumoto Masaaki Toda Kengo

Yamada Yasuo (2003) Discrete element simulation of an assembly of irregular-

shaped grains Quantitative comparison with experiments 16th ASCE Engineering

Mechanics Conference University of Washington Seattle July 16-18

Mitchell James K and Soga Kenichi (2005) Fundamentals of soil behaviour Third

edition WILEY

Mora C F Kwan A K H Chan H C (1998) Particle size distribution analysis of

coarse aggregate using digital image processing Cement and Concrete Research Vol

28 pp 921-932

Mora C F and Kwan A K H (2000) Sphericity shape factor and convexity

measurement of coarse aggregate for concrete using digital image processing Cement

and Concrete Research Vol 30 No 3 pp 351-358

Muskat Morris (1937) The Flow of fluids through porous media Journal of Applied

Physics Vol 8 pp 274

Nearing M A and Parker S C (1994) Detachment of soil by flowing water under

turbulent and laminar conditions Soil Science Society of American Journal Vol 58

No 6 pp 1612-1614

48

Pan Tongyan Tutumluer Erol Carpenter Samuel H (2006) Effect of coarse

aggregate morphology on permanent deformation behavior of hot mix asphalt Journal

of Transportation Engineering Vol 132 No 7 pp 580-589

Pellegrino A (1965) Geotechnical properties of coarse-grained soils Proceedings

International Conference of Soil Mechanics and Foundation Engineering Vol 1 pp

97-91

Pentland A (1927) A method of measuring the angularity of sands MAG MN AL

Acta Eng Dom Transaction of the Royal Society of Canada Vol 21 Ser3xciii

Persson Anna-Lena (1998) Image analysis of shape and size of fine aggregates

Engineering Geology Vol 50 pp 177-186

Powers M C (1953) A new roundness scale for sedimentary particles Journal of

Sedimentary Petrology Vol 23 No 2 pp 117-119

Pye W and Pye M (1943) Sphericity determination of pebbles and grains Journal

of Sedimentary Petrology Vol 13 No 1 pp 28-34

Qazi M A (1975) Flow properties of granular masses A review on the angle of

repose The Arabian Journal for Science and Engineering Vol 1 No 2

Quiroga Pedro Nel and Fowle David W (2003) The effects of aggregate

characteristics on the performance of portland cement concrete Report ICAR 104-1F

Project number 104 International Center for Aggregates Research University of

Texas

Riley N A (1941) Projection sphericity Journal of Sedimentary Petrology Vol 11

No 2 pp 94-97

Rouseacute P C Fennin R J and Shuttle D A (2008) Influence of roundness on the

void ratio and strength of uniform sand Geotechnique Vol 58 No 3 227-231

Santamarina J C and Cho G C (2004) Soil behaviour The role of particle shape

Proceedings Skempton Conf London

Schofield and Wroth (1968) Critical state soil mechanics McGraw Hill

Shaumlfer Michael (2002) Digital optics Some remarks on the accuracy of particle

image analysis Particle amp Particle Systems Characterization Vol 19 No 3 pp 158-

168

Shergold F A (1953) The percentage of voids in compacted gravel as a measure of

its angularity Magazine of Concrete Research Vol 5 No 13 pp 3-10

Shinohara Kunio Oida Mikihiro Golman Boris (2000) Effect of particle shape on

angle of internal friction by triaxial compression test Powder Technology Vol 107

pp131-136

49

Skredcommisionen (1995) Ingenjoumlrsvetenskapsakademinen rapport 395 Linkoumlping

1995

Sneed E D and Folk R L (1958) Pebbles in the Colorado river Texas A study in

particle morphogenesis Journal of Geology Vol 66 pp 114-150

Sperry James M and Peirce J Jeffrey (1995) A model for estimating the hydraulic

conductivity of granular material based on grain shape grain size and porosity

Ground Water Vol 33 No 6 pp 892-898

Sukumaran B and Ashmawy A K (2001) Quantitative characterisation of the

geometry of discrete particles Geotechnique Vol 51 No 7 pp 619-627

Szaacutedeczy-Kardoss E Von (1933) Die bistimmung der abrollungsgrades Geologie

und palaumlontologie Vol 34B pp 389-401 (in German)

Teller J T (1976) Equantcy versus sphericity Sedimentology Vol 23 pp 427-428

Tickell F G (1938) Effect of the angularity of grain on porosity and permeability

bulletin of the American Association of Petroleum Geologist Vol 22 pp 1272-1274

Tutumluer E Huang H Hashash Y Ghaboussi J (2006) Aggregate shape effects

on ballast tamping and railroad track lateral stability AREMA 2006 Annual

Conference Louisville KY

Wadell H (1932) ldquoVolume Shape and roundness of rock particlesrdquo Journal of

Geology Vol 40 pp 443-451

Wadell H (1933) Sphericity and roundness of rock Particles Journal of Geology

Vol 41 No 3 pp 310ndash331

Wadell H (1934) Shape determination of large sedimental rock fragments

The Pan-American Geologist Vol 61 pp 187-220

Wadell H (1935) ldquoVolume shape and roundness of quartz particlesrdquo Journal of

Geology Vol 43 pp 250-279

Wentworth W C (1922a) The shape of beach pebbles Washington US Geological

Survey Bulletin Vol 131C pp 75-83

Wentworth W C (1922b) A method of measuring and plotting the shape of pebbles

Washington US Geological Survey Bulletin Vol 730C pp 91-114

Wentworth W C (1933) The shape of rock particle A discussion Journal of

Geology Vol 41 pp 306-309

Witt K J Brauns J (1983) Permeability-Anisotropy due to particle shape Journal

of Geotechnical Engineering Vol 109 No 9 pp 1181-1187

10

Some other authors has been working with the ldquocircularityrdquo concept and had develop

them own equations as Pentland (1927) relating the area outline and area of a circle

with diameter equal to longest length outline and Cox (Riley 1941) with the ratio

area and perimeter time a constant equations 16 and 17 respectively Both authors did

not define any definite orientation of the grains

Riley (1941) realize the problems that an area perimeter and some other

measurements proposed by the above authors can carry as the time consuming and

tedious work (at that time were not computer all was made by hand) and thatrsquos why

he develop this equation easy to handle called ldquoinscribed circle sphericityrdquo He used

the same particle orientation proposed by Wadell and the relation of diameters of

inscribed and circumscribed circles

Horton 1932 (Hawkins 1993) use the relation of the drainage basing perimeter and

the perimeter of a circle of the same area as drainage basin

Janoo in 1998 (Blott and Pye 2008) develop his general ratio of perimeter to area

Sukumaran and Ashmawy (2001) develop his own shape factor (SF) defined as the

deviation of the global particle outline from a circle Figure 9 can be used as a

reference to determine the items used in the equation 21

N is referred to the number of sampling intervals o radial divisions

C2A

AC

2P

A4C

C

I

D

DC

CD

D

P

PC

A

PC

2

45ordm x N

Particleα

= SF

sumN

1=ii

(16)

(17)

(18)

(19)

(20)

(21)

11

Table 3 General chronological overview of the particle shape definitions for 2D sphericity

Aspect Name Author Year Based on

Circularity (2D) roundness Pentland 1927 area

roundness Cox1

1927 area-perimeter

roundness Tickell2

1931 area

Circularity Horton2

1932 drainage basin

outline circularity Wadell 1935 Circle diameter

degree of circularity Wadell 1935 Perimeter

inscribed circle sphericity Riley 1941 Circle diameter

Circularity Krumbein and Sloss 1963 chart

Janoo 1998 area-perimeter

Shape factor Sukumaran 2001 Segmentation of particle and angles

1) Riley 1941 2) Hawkins 1993

35 ROUNDNESS OR ANGULARITY

Roundness as described in section 32 is the second order shape descriptor Sphericity

lefts beside the corners and how they are this was notice by most of the authors sited

before and they suggested many ways to describe this second order particle property

Roundness is clearly understandable using the figure 10 Particle shape or form is the

overall configuration and denotes the similarities with a sphere (3D) or a circle (2D)

Roundness is concerning about the sharpness or the smoothness of the perimeter (2D)

Surface texture (Barret 1980) is describe as the third order subject (form is the first

and roundness the second) and it is superimposed in the corners and it is also a

property of particles surfaces between corners

Figure 9 Description of the Sukumaran factors to determine the shape and angularity (Sukumaran and

Ashmawy 2001)

12

Wadell (1935) describes his methodology calling it total degree or roundness to

obtain the roundness of a particle using the average radius of the corners in relation

with the inscribed circle diameter (see figure 11) on the equation

In the same study Wadell (1935) has used the equation

This two last equation shows slightly differences on the results (Wadell 1935)

Powers (1953) also published a graphic scale to illustrate the qualitative measure

(figure 12) It is important to highlight that any comparing chart to describe particle

properties has a high degree of subjectivity Folk (1955) concludes that when charts

are used for classification the risk of getting errors is negligible for sphericity but

large for roundness

N

R

r

Rinmax

r

R

NR

inmax

Figure 10 Form (shape) Roundness and Texture graphical description (Bowman et al 2001)

Figure 11 Wadellrsquos method to estimate the roundness corners radius and inscribed circle

(Hawkins 1993)

(22)

(23)

13

Some authors as Russel amp Taylor in 1937 Pettijohn in 1957 and Powers in 1953

developed a classification based on five and six classes (Hawkins 1993) each one

with its own class limits it is important to denote that the way they measure the

roundness is the developed by Wadell (1935) This classification and class limits are

showed in the table 4

Table 4 Degrees of roundness Wadell Values (Hawkins 1993) NA = no-applicable

Grade terms Russell amp Taylor (1937) Pettijohn (1957) Powers (1953)

Class

limits (R)

Arithmetic

midpoint

Class limits

(R)

Arithmetic midpoint Class

limits (R)

Arithmetic

midpoint

Very angular

NA

NA

NA

NA

012-017

014

Angular

000-015

0075

000-015

0125

017-025

021

Subangular

015-030

0225

015-025

0200

025-035

030

Subrounded

030-050

0400

025-040

0315

035-049

041

Rounded

050-070

0600

040-060

0500

049-070

059

Well rounded

070-100

0800

060-100

0800

070-100

084

Krumbein and Sloss (1963) published a graphical chart easy to determine the

sphericity and roundness parameters using comparison See figure 13 (Cho et al

2006)

Figure 12 A Roundness qualitative scale (Powers 1953)

Figure 13 Sphericity and roundness chart (Cho et al 2006) The roundness equation that appears here in

the chart is the wadellrsquos equation number 22

14

Fischer in 1933 (Hawkins 1993) used a straightforward method to quantify roundness

using a central point in the outline and dividing the outline in angles around this point

that were subtended by the straight or non curved parts of the profile were measured

This is illustrated in figure 14

To express the angularity value Fischer used the ratio of angles standing linear parts

on the outlines and concave respectively

Figure 14 left (A) and right (B) gives a similar angularity of approximately 042

using the above equations (Hawkins 1993)

Wentworth in 1922 used the maximum projection to define the position of the particle

to obtain the outline or contour (Barret 1980) The equation reflects the relation of the

diameter of a circle fitting the sharpest corner and the longest axis plus the shortest

axis c (minimum projection)

Wentworth (Hawkins 1993) expressed the roundness as the ratio of the radius of

curvature of the most convex part and the longest axis plus short axis

Actually these last two equations are the same just expressed in different terms when

the particle is in its maximum projection

Dimensions can be seen on figure 15 L and B represents the mayor axis a and

intermediate axis b The intention is to make difference between the 2 and 3

dimensions (L and B are for 2D as a b and c are for 3D)

deg360

ANG

=R

sumPLA

PLA

CON

ANG

ANGR

2)S(L

DR

M

S

B)4(L

RR CON

Figure 14 Fischerrsquos methods of angularity computation (Hawkins 1993)

A=inscribed circle B=circumscribed circle

(24)

(25)

(26)

(27)

15

Wentworth 1919 has a second way to express the roundness called Shape index

(Barrett 1980) and it relates the sharpest corner and the diameter of a pebble trough

the sharpest corner

Wentworth (1922b) used define the roundness as the ratio of the sharpest corner and

the average radius of the pebble

Cailleux (Barrett 1980) relates the radius of the most convex part and the longest

axis

Kuenen in 1956 show his roundness index (Barrett 1980) between the sharpest corner

and the breath axis

Dobkins amp Folk (1970) used a modified Wentworth roundness with the relation of

sharpest corner and inscribed circle diameters

AVG

CON

R

RR

x

s

D

DR

L2

RR CON

B

DR s

i

s

D

DR

3AVGAVG cbaDR2

Figure 15 Description of L and B axes (Hawkins 1993)

(28)

(29)

(30)

(31)

(32)

(33)

16

Swan in 1974 shows his equation (Barrett 1980) relating the sharpest (or the two

sharpest) corner(s) and inscribed circle diameter

Szadeczsky-Kardoss has his Average roundness of outline (Krumbein and Pettijohn

1938) relating the concave parts perimeter and the actual perimeter

Lees (1964a) developed an opposite definition to roundness it means that he

measures the angularity instead of the roundness and he calls it Degree of angularity

Figure 16 shows the items considered when equation 36 applies as the angles (α)

inscribed circle (Rmax-in) and the distance (x) The main formula is

In order to apply the last equation corners needs to be entered in the formula and each

individual result will add to each other to obtain the final degree of angularity

A roundness index appears on Janoo (1998) Kuo and Freeman (1998a) and Kuo et

al (1998b) it is described as

The last equation is on section 34 also because there is not a general agreement on the

definition furthermore some authors had used to define the roughness this is not the

only equation that has been used trying to define different aspects (sphericity

roundness or roughness) but it is a good example of the misuse of the quantities and

definitions

inmaxR

x)180(R

2P

A4R

i

ss

D

DDR

221

100P

PR CON

Figure 16 Degree of angularity measurement technique (Blot and Pye 2008)

(34)

(35)

(36)

(17)

17

Sukumaran and Ashmawy (2001) present an angularity factor (AF) calculated from

the number of sharpness corners Angles βi required to obtain the angularity factor are

shown in figure 9

Sukumaran and Ashmawy (2001) also suggested use not bigger sampling interval of

N=40 because it is the cut off between angularity factor and surface roughness If so

this equation could be used to describe the roughness

Table 5 General chronological overview of the particle roundness

Aspect Name Author Year Based on

Roundness shape index Wentworth 19191

diameter of sharper corner

shape index Wentworth 1922b sharpest corner and axis

roundness Wentworth 1933 convex parts

Fischer 19332

noncurved parts outline

Fischer 19332

noncurved-streigth parts outline

Average roundness of outline

Szadeczsky-Kardoss 19333

convex parts-perimeter

roundness Wadell 1935 diameter of corners

roundness Wadell 1935 diameter of corners

roundness Russel amp Taylor 19372

class limit table

roundness Krumbein 1941 chart

Cailleux 19471

convex parts

roundness Pettijohn 19494 class limit table

roundness Powers 1953 chart and class limit table

Kuenen 19561

axis-convex corner

roundness Krumbein and Sloss 1963 chart

degree of angularity Lees 1964a corners angles and inscribed circle

Dobkins amp Folk 1970 diameter of sharper corner

Swan 19741

diameter of sharper corners

Angularity factor Sukumaran and

Ashmawy 2001

Segmentation of particles and angles

1) Barret 1980 2) Hawkins 1993 3) Krumbein and Pettijohn 1938 4) Powers 1953

sum

sumsumN

1=i

2

i

2

N

1=i

2

i

2N

1=ii

)ordm180 -circleβ( - )(180ordm x 3

)ordm180-circleβ(-)ordm180 -Particleβ(

= AF (37)

18

36 ROUGHNESS OR SURFACE TEXTURE

A third property called texture appears early in the literature with the sphericity and

roundness properties since then texture property was longed described but it was in

accordance with the authors at that time not measurable

Wright in 1955 developed a method to quantify the surface texture or roughness of

concrete aggregate using studies done on 19 mm stones The test aggregates were first

embedded in a synthetic resin The stones were cut in thin sections The sections

projection was magnified 125 times The unevenness of the surface was traced and the

total length of the trace was measured The length was then compared with an uneven

line drawn as a series of chords (see figure 17) The difference between these two

lines was defined as the roughness factor (Janoo 1998)

However with the advance of technology it has become easier measure the roughness

and here is presented some researcherrsquos ideas how this property should be calculated

One technique used by Janoo (1988) to define the roughness can be seen in figure 18a

and is defined as the ratio between perimeter and convex perimeter

The convex perimeter is obtained using the Feretrsquos box (or diameter) tending a line in

between the touching points that the Feretrsquos box describes each time it is turn (figure

18b)

PER

OC

PR

Figure 17 Measurement method for characterizing the surface texture of an aggregate (Janoo 1998)

a) Convex perimeter (CPER) b) Feret measurement Figure 18 a) Convex perimeter (CPER) b) Feret measurement (modified after Janoo 1998)

(38)

a)

b)

19

Kuo and Freeman (1998a) and Kuo et al (1998b) use the roughness definition as the

ratio perimeter and average diameter

Erosion and dilatation image processing techniques are used to obtain the surface

texture Erosion is a morphological process by which boundary image pixels are

removed from an object surface which leaves the object less dense along the

perimeter or outer boundary Dilatation is the reverse process of erosion and a single

dilatation cycle increases the particle shape or image dimension by adding pixels

around its boundary (Pan etal 2006)

The ldquonrdquo erosion and dilatation cycles are not standardized

Mora and Kwan (2000) used the ldquoconvexity ratio CRrdquo (equation 41) and the ldquofullness

ratio FRrdquo (equation 42) in their investigation they are

The convex area is the area of the minimum convex boundaries circumscribing the

particle This is illustrated in the figure 19 The convex area is obtained in a similar

way as the convex perimeter but in this case the area between the original outline and

the convex perimeter is our convex area

AVG

OD

PR

100A

1AARO

CONo A

AR =

CONo A

AR =

Figure 19 Evaluation of area and convex area (Mora and Kuan 2000)

(39)

(40)

(41)

(42)

20

4 TECHNIQUES IN ORDER TO DETERMINE PARTICLE

SHAPE

41 HAND MEASUREMENT

Hand measurement technique was the first used by obvious reasons in order to

improve the accuracy special devices developed as the ldquosliding rod caliperrdquo used by

Krumbein (1941) it works placing the sample on the sliding road calliper as show

figure 20b the length in different positions can be obtain by using the scale provided

in the handle the ldquoconvexity gagerdquo that was actually used by opticians to measure the

curvature of lenses but easily applicable to the particle shape analysis (Wentworth

1922b) works measuring the movement of the central pivot as figure 20a shows (the

two adjacent pivots are invariable) as many the central pivot moves more is the

curvature or the ldquoSzadeczky-Kardossrsquos apparatusrdquo develop in 1933 that traces the

profile of the rock fragment so the outline traced is then analyzed (Krumbein and

Pettijohn 1938) figure 20c show equipment

Another helpful tool to determine the particle dimensions was the ldquocamera lucidardquo to

project the particlersquos contour over a circle scale appearing in Figure 21 thus it is

possible to measure the particlersquos diameter

a)

c) b)

Figure 20 a) convexity gage used to determine the curvature in particle corners (Wenworth 1922b)

b)sliding rod caliper device to measure the particle axis length (Krumbein 1941) and c)Szadeczky-

Kardoss (1933) apparatus it was utilized to obtain the particle outline

Figure 21 Circle scale used by Wadell (1935) to determine particlersquos diameter and roundness

21

42 SIEVE ANALYSIS

Bar sieving eg according to EN 933-31997 can be used to determine simple large

scale properties By combining mesh geometries the obtained results can be used to

quantify flakiness and elongation index ASTM D4791 (Flat and elongated particles

are defined as those coarse aggregate particles that have a ratio of length to thickness

equal to or greater than a specified value such as 51 The index represents the

percentage on weight of these particles) The method is not suitable for fine materials

This due to the difficulty to get the fine grains passed through the sieve and the great

amount of particles in relation to the area of the sieve (Persson 1998) eg EN 933-

31997 related to flakiness index The test is performed on aggregates with grain size

from 4 mm and up to 63 mm two sieving operations are necessary the first separates

on size fraction and the second use a bar sieve after the first sieving the average

maximum diameter of the particles is obtain and with the second sieving (bar sieving)

the shortest axis diameter is found finally with this two parameters the flakiness

index is determined

There are more standards related with the particle shape (see appendix A) but this

above presented are probably the most known using sieve analysis to determine

particlersquos geometrical properties

Sieve analysis is facing the computers age and image analysis sieving research is

taking place (Andersson 2010 Mora and Kwan 2000 Persson 1998) Industry is

also applying the image analysis sieving with decrees on the testing time compare

with the traditional sieving method An inconvenient of image analysis is the error

due the overlapping or hiding of the particles during the capture process but the

advantages are more compare with disadvantages (Anderson 2010)

43 CHART COMPARISON

Charts developed over the necessity of faster results because the long time consuming

required when measuring each particle

Krumbein (1941) present a comparison roundness chart for pebbles which were

measured by Wadellrsquos method because this property was the most difficult to measure

due to the second order scale that roundness represents (See figure 22)

Figure 22 Krumbein (1941) comparision chart for roundness

22

A qualitative chart by Powers (1953) try to include both (sphericity and roundness)

particlersquos characteristics it was divided on six roundness ranges (very angular

angular sub-angular sub-rounded rounded and well rounded) and two sphericity

series (high and low sphericity) This chart was prepared with photographs to enhance

the reader perspective (See figure 23)

A new chart including sphericity and roundness appear this time it was easier to

handle the two mean properties of particlersquos shape furthermore there was included

the numerical values that eliminated the subjectivity of qualitative description The

chart is based on Wadellrsquos definitions (Krumbein and Sloss 1963) (See figure 24)

Folk (1955) worried about the personrsquos error on the chartrsquos comparison studied the

determination of sphericity and angularity (he used the Powers 1953 comparison

chart) he found that the sphericity determination by chart comparison has a negligible

error while the roundness he concluded it was necessary to carry out a more wide

research due the high variability show by his study

Figure 23 Powers (1953) qualitative shpericity-roundness chart

Figure 24 Sphericity-roundness comparison chart (Krumbein and sloss 1963)

23

44 IMAGE ANALYSIS

Image analysis is a practical method to use for shape classification since it is fast and

can be automated Different techniques appear to process these images among them

are

o Feret Diameter the Feret diameter is the longitude between two parallel lines

this lines can rotate around one particle or outline to define dimensions as it

is shown in figure 25 these method is not a fine descriptor but as it was say

above it is a helpful tool to determine diameters (Janoo 1988)

o Fourier Mathematical Technique It produces mathematical relations that

characterize the profile of individual particles This method favours the

analysis of roughness and textural features for granular soils The problem in

the methodology remains in the re-entrant angles in order to complete the

revolution (Bowman et al 2001) see figure 26

o Fractal Dimension Irregular line at any level of scrutiny is by definition

fractal (Hyslip and Vallejo 1997) Figure 27 shows fractal analysis by the

dividing method The length of the fractal line can be defined as

N

1n

nn0 )nsinbncosa(a)(R

RD1n)(P

Figure 25 Feret measurement technique is defined by two parallel lines turning

around the particle to define the shortest and longest Feret diameter (Janoo 1988)

Figure 26 Fourier technique with two radiuses at one angle (Bowman et al 2001)

(43)

(44)

24

o Orthogonal image analysis This technique is basically the use of two images

orthogonal between them to acquire the three particle dimensions (Fernlund

2005) any of the above techniques can be used in this orthogonal way

o Laser Scanning Technique this kind of laser scanning 3D is one of the most

advanced techniques In figures 28a) we have the laser head scanning the rock

particles the particles have control points in order to keep a reference point

when move them to scan the lower part in figure 28b) we can see the laser

path followed (Lanaro and Tolppanen 2002)

Another technique is the Laser-Aided Tomography (LAT) in this case a laser sheet is

used to obtain the particles surveying (see figure 29) This technique is different and

has special requirements as to use liquid with same refractive index as the particles

particles must let the laser or certain percent of light go through (Matsushima et al

2003)

a) b)

Figure 27 Fractal analysis by the dividing method at different scrutiny scale (Hyslip and Vallejo 1997)

Figure 28 a) Scanning head b) scanning path (Lanaro and Tolppanen 2002)

Figure 30 3D scan completed ready to

use for any further measure

(Matsushima et al 2003)

Figure 29 LAT scaning particles

(Matsushima et al 2003)

25

Both 3D techniques obtain the particle shape that is later used to achieve measures as

we can see in figure 30

All these previous techniques are easily written in codes or scripts to be interpreted in

a digital way obtaining the desired measurement but there are some interesting points

in the image analysis regarding on the errors involve among them are image

resolution and orientation of the particles orientation is not relevant when it is

random and large number of particles are involve resolution have an influence on the

accuracy (Zeidan et al 2007)

When resolution is increase more accuracy is obtain and the object representation

match better with the real form in the other hand more resolution means more

spending on memory and time thus resolution needs to be according with the goal

and precision needed in any work (Schaumlfer 2002)

Schaumlfer (2002) conclude that attributes like length when measuring digital images

present relative high errors It can be vanish or at least diminish using high resolution

just for diameter but not for perimeter that keep the error as big as initially Johansson

and Vall (2011) obtain similar results when 3 different resolutions were used in the

same particle obtaining an unstable output for those termsquantities that involve the

perimeter Thus all quantities relating the perimeter should be treated with care

5 EFFECT OF SHAPE ON SOIL PROPERTIES

51 INTRODUCTION

In laboratory test on the effect on particle size on basic properties has been

investigated in several studies this relation has been discussed and various

mechanisms had been proposed to explain the behaviour of the soil in dependency

also with the shape Basically there are two mechanisms proposed The arrangement

of particles and the inter-particle contact (Santamarina and Cho 2004) and

subsequence breakage

The arrangement of particles

Arrangement of the particles can be presented in three different forms loose dense

and critical this arrangement determines the soil properties (eg density increase with

more dense arrangement) Loose and dense states are easy understandable when

figure 31 is explained while in the upper part of the figure the particles are arranged

using the minimum space needed in the lower part a span is created using the flaky

particle as a bridge this phenomena is known as ldquobridgingrdquo Bridging can produce

different geotechnical results when just the shape of the particle is changed eg void

ratio (Santamarina and Cho 2004) Particles are able to rearrange this could be done

applying pressure (energy) to the soil the pressure (energy) will create such forces

that soil particles will rotate and move (see figure 34) finishing in a more dense state

26

A loose soil will contract in volume on shearing and may not develop any peak

strength (figure 32 left) In this case the shear strength will increase gradually until

the residual shear strength is revealed once the soil has ceased contracting in volume

A dense soil may contract slightly (figure 32 right) before granular interlock prevents

further contraction (granular interlock is dependent on the shape of the grains and

their initial packing arrangement) In order to continue shearing once granular

interlock has occurred the soil must dilate (expand in volume) As additional shear

force is required to dilate the soil a peak shear strength occurs (figure 32 left) Once

this peak shear strength caused by dilation has been overcome through continued

shearing the resistance provided by the soil to the applied shear stress reduces

(termed strain softening) Strain softening will continue until no further changes in

volume of the soil occur on continued shearing Peak shear strengths are also

observed in overconsolidated clays where the natural fabric of the soil must be

destroyed prior to reaching constant volume shearing Other effects that result in peak

strengths include cementation and bonding of particles The distinctive shear strength

called the critical state is identified where the soil undergoing shear does so at a

constant volume (Schofield and Wroth 1968)

The inter-particle contact

For frictional soil ie coarse grained soil the friction between particles is the

dominating factor for strength Materials usually consisting of coarse grains (diameter

Figure 31 Bridging effect when flaky particles are combined in the bulk material (Santamarina and

Cho 2004)

Figure 32 The left part of the figure show a typical behaviour of loose and dense material over shear stress

while at the right the figures illustrate the typical volume changes

27

gt 006mm) behave as a frictional soil it means that the strength of coarse soils (silt

sand gravel etc) comes from an inter-particle mechanical friction thus ideally they

do not have traction strength In figure 33 the inter-particle contact is illustrated here

the pressure (P) is applied and two more components are found the normal load (N)

and the tangential load (T) described as the friction coefficient (μF) The forces stand

in equilibrium (Johansson and Vall 2011)

When particles equilibrium is disturbed (friction coefficient is not enough to keep

particles unmoved) the rotation is imminent and it is necessary in order to compact

the soil in figure 34 can be seen that the arrangement is a fact that inhibit or allow this

rotation and the shape in the 3 different scales are also factors because the more

spherical andor more rounded andor less roughness more easy is the rotation

(Santamarina and Cho 2004)

Breakage

Breakage is a side effect of the inter-particle contact and rotation when pressure

exceed the rock strength it can happened when the particles are tight together and

there is not enough space to rotate it is more obvious in angular particles (mesh form)

or as in figure 31 where the flaky particle ldquobridgingrdquo is not able to rotate but it can

brake by the pressure increase Yoginder et al (1985) notice that the angular particle

break during his experiments and they turn more rounded changing the original size

and form configuration at the same time there was a soil properties loosening

Figure 33 Inter-particle contact and forces acting (Axelsson 1998)

Figure 34 Rotation inhibition by the particles compaction or low void ratio (Santamarina and Cho 2004)

28

52 INFLUENCE OF SIZE AND SHAPE

Wenworth (1922a) and Pellegrino (1965) among others suggest that agent transport of

the rocks (rigor of transport temperature and moisture changes etc) determine its

shape but also the particle genesis itself (rock structure mineralogy hardness etc) It

is not possible to determine the shape of the particles based on the agent transport or

genesis but generally a shape behaviour is expected according to Mitchell and Soga

(2005) specially when the particle size is in the clay size (gt2μm) The shapes of the

most common clay minerals are platy (figure 35) with some exceptions (eg

halloysite occurs as tubes kaolinite are large thick and stiff Smectites are composed

of small very thin and filmy particles Illites are intermediate between kaolinite and

smectite and attapulgite occurs in lathlike particle shapes) Some clay minerals

photographs are presented in figure 35

Figure 35 Clay mineral shape a) hallosite b) Kaoline c) Smactites d) Illites and e) attapulgite (Modified

from Mitchell and Soga 2005)

Figure 36 Particle size range in soils Generally the particles of clay size are plate shaped (Mitchell and

Soga 2005)

a) b) c)

e) d)

29

53 VOID RATIO AND POROSITY

The void ratio (e) is the ratio of the volume of voids to the volume of solid it is

defined by the equation

Porosity (n) is the ratio of the volume of voids to the total volume of the soil it is

represented by the equation

Holubec and DrsquoAppolonia (1973) found a relation between the void ratio and

sphericity (referred in the paper as coefficient of angularity ratio of particle surface

and equivalent sphere surface) their results show that the maximum and the minimum

void ratio increases as the shpericity decreases In this study the surface was obtained

for an indirect method based on the permeability developed by Hoffman in 1959

described in the same document Rouseacute et al (2008) defined the roundness as

Wadell (1935) and he found it as an important factor controlling the minimum and

maximum void ratios Some other authors as Youd (1973) and Cho et al (2006)

conclude the same minimum and maximum void ratios increase when sphericity and

roundness decrease Another interesting result (all above authors) was the bigger

influence of the form (sphericity circularity) and roundness on the maximum void

ratio The change of the maximum void ratio is more pronounced than the change of

the minimum void ratio when the form and roundness changes (See figure 39)

Particles arrangement and interlocking are probably the factor that controls the void

ratio bridge effect permit the existence of void among the particles while interlocking

allowed the particles to form arches avoiding the possibility to rotate and stay in a

more stable configuration eg as it happens with marbles

Figures 36 37 and 38 shows proposed empirical relationships between void ratio and

shape from tables 5 and 6 (graphically the scale goes from 0 to 1 when cero mean

high angularity shpericity or circularity and one means low angularity circularity or

sphericity) Holubec and DrsquoAppolonia (1973) data was taken to obtain a power curve

and describe a tendency Santamarina and Cho (2004) show Youd equations in the

original paper Youd (1973) never presented the equation but it is easy to use the

information to draw a trend

The graphics presented in this document (figures 36 37 and 38) must be used with

certain reserves due the fact that the original data was modified in order to fit all

information in one graphic what the figures shows is just the general trend of the

behaviourrsquos material regarding on the shape If more accurate description and

information is required the author recommends consulting the reference data In the

same way equations from Holubec and DrsquoApollonia (1973) and Youd (1973) were not

presented by the authors but the use of the information was taken in order to build up

those equations on tables 6 and 7

S

V

V

V

= e

V

V

=nV

(45)

(46)

30

Table 6 Minimum void ratio equations regarding on the quantity (Ψ for sphericity C for circularity R

for roundness SF for Sukumaran shape factor and AF for Sukumaran angularity factor)

EQUATION NUMBER REFERENCE

Figure 34 (left)

4340

minΨ45490e =

47

Holubec amp DrsquoAppolonia 1973 (Ψ

was obtained using equation 2)

SF06340

mine021903180e +=

48

Sukumaran amp Ashmawy 2001 (SF

obtained using equation 21)

C05101emin

= 49

Cho etal 2006 (C obtained using

figure 12)

Figure 34 (right)

1

minR08203590e +=

50

Youd 1973 (R obtained from figure

11 and table 3)

R34080emin

= 51

Cho et al 2006 (R obtained using

figure 12)

1

minR05104330e +=

52

Rouseacute et al 2008 (R obtained by

equation 21)

AF02330

mine372004160e +=

53

Sukumaran amp Ashmawy 2001 (AF

obtained using equation 37)

Table 7 Maximum void ratio equations regarding on the quantity (Ψ for sphericity C for circularity R

for roundness SF for Sukumaran shape factor and AF for Sukumaran angularity factor)

EQUATION NUMBER REFERENCE

Figure 35 (left)

51520

max Ψ61120e = 54

Holubec and DrsquoAppolonia 1973 (Ψ

was obtained using equation 2)

SF1190

max e0016907180e += 55

Sukumaran amp Ashmawy 2001 (SF

obtained using equation 21)

C86061emax = 56

Cho etal 2006 (C obtained using

figure 12)

Figure 35 (right)

1

max R1505540e += 57

Youd 1973 (R obtained from figure

11 and table 3)

R62031emax= 58

Cho et al 2006 (R obtained using

figure 12)

1

max R107106150e += 59

Rouseacute et al 2008 (R obtained by

equation 21)

AF0530

max e12506090e += 60

Sukumaran amp Ashmawy 2001 (AF

obtained using equation 37)

Comparing figures 37 and 38 (minimum and maximum void ratio) it can be seen on

the right scheme of both figures 37 and 38 (when the factor is roundnessangularity)

that all the empirical relations has a common initial point close to 1 (it means that

particles are well rounded) while this common agreement disappear when the

roundness factor decreases (when the particles become more angular) Same figures

(37 and 38) on the left graphs (when the factor is sphericitycircularityshape) do not

present the same behaviour in fact there is more disperse initial point close to 1(when

the particles tend to be more sphericalcircular)

31

In Figure 39 the Δe (emax-emin) has been plotted to show how the maximum void ratio

and the minimum void ratio has different rate change when the particle shape

changes Maximum void ratio increases more than minimum void ratio when the

particle shape becomes less spherical andor more angular Comparing figure 39 left

and right graphics it can be seen that right present a common initial point when the

quantity (roundnessangularity) is close to one while in the left graphic the initial

point is more disperse Both ending points in both graphics (close to zero) are

dispersed

Figures 37 38 and 39 present the same behaviour right graphics (when the factor is

roundness angularity) in each figure have an initial common point while the left

graphics do not (when the factor is sphericity circularity shape)

Figure 37 Minimum void ratio based upon the relation of shape factor proposed by the authors indicated

in the figure

Figure 38 Maximum void ratio based upon the relation of shape factor proposed by the authors indicated

in the figure

04

06

08

1

12

14

16

18

2

005

015

025

035

045

055

065

075

085

095

Factor (roundness angularity)

min

imu

m v

oid

rati

o

Youd 1973 roundness

Rouse 2008 roundness

Cho 2006 roundness

Sukumaran 2001 AF

03

04

05

06

07

08

09

1

11

12

13

05

015

025

035

045

055

065

075

085

095

Factor (sphericity circularity shape)

min

imu

m v

oid

rati

oHolubec 1973 sphericity

Cho 2006 circularity

Sukumara 2001 SF

05

07

09

11

13

15

17

19

21

00

150

250

350

450

550

650

750

850

95

Factor (sphericity circularity shape)

Maxim

um

vo

id r

ati

o

Holubec 1973 sphericity

Cho 2006 circularity

Sukumara 2001 SF

05

1

15

2

25

3

35

005

015

025

035

045

055

065

075

085

095

Factor (roundness angularity)

Maxim

um

vo

id r

ati

o

Youd 1973 roundness

Rouse 2008 roundness

Cho 2006 roundness

Sukumaran 2001 AF

32

54 ANGLE OF REPOSE

The angle of repose of a granular material is the steepest angle of descent or dip of the

slope relative to the horizontal plane when material on the slope face is on the verge

of sliding as show in figure 40

According to Qazi (1975) there are five types of forces which may act between the

particles in soils

1 Force of friction between the particles

2 Force due to presence of absorbed gas andor moisture of particle

3 Mechanical forces caused by interlocking of particles of irregular shape

4 Electrostatic forces arising from friction between the particles themselves and

the surface with which they come in contact

5 Cohesion forces operating between neighbouring particles

Rouseacute et al (2008) found a decrease of angle of repose with increase roundness

based upon ASTM C1444 test (Standard Test Method for Measuring the Angle of

Repose of Free-Flowing Mold Powders) The method consist in pouring sand on a

surface cover by paper trough a funnel of specific dimensions (the nozzle diameter

depend on the sandrsquos particle size) from an altitude of 15 inches (381 mm) The sand

is release from the funnel until the peak of the cone formed by the sand stops the flow

The repose angle is obtained with the equation

H represent the 15 inches D and d represent the diameter of the cone formed by the

sand and the diameter of the funnel respectively

Figure 39 Maximum minus minimum void ratio based upon the relation of shape factor proposed by the

authors indicated in the figure

0

01

02

03

04

05

06

07

08

09

1

005

015

025

035

045

055

065

075

085

095

Factor (sphericity circularity shape)

Maxim

um

- M

inim

um

Vo

id r

ati

oHolubec 1973 sphericity

Cho 2006 circularity

Sukumara 2001 SF

0

02

04

06

08

1

12

14

16

18

005

015

025

035

045

055

065

075

085

095

Factor (roundness angularity)

Maxim

um

- M

inim

um

Vo

id r

ati

o

Youd 1973 roundness

Rouse 2008 roundness

Cho 2006 roundness

Sukumaran 2001 AF

dD

H2

tan=φ1

rep(61)

33

Rouseacute (2008) shows an empirical relation to obtain the angle of repose based on the

roundness of the particles

55 SHEAR STRENGTH

The MohrndashCoulomb failure criterion represents the linear envelope that is obtained

from a plot of the shear strength of a material versus the applied normal stress This

relation is expressed as

where τ is the shear strength σn is the normal stress co is the intercept of the failure

envelope with the τ axis and is the slope of the failure envelope The quantity c is

often called the cohesion and the angle is called the angle of internal friction

Studies show that the internal friction angle (under drained triaxial tests) increases

more rapidly on those materials having higher angularity increasing the relative

density The internal friction angle is a function of the relative density and the particle

shape (Holubec and DrsquoAppolonia 1973)

Chan and Page (1997) found in a study made with dry copper (using different shapes

and sizes ranging from 180 to 106 μm) using a direct shear test (ring share test) that

the internal friction angle increases as the angularity increases

Shinohara et al (2000) did some experiments with steel powder different shapes

using a triaxial cell in the test Shinohara never used the roundness or angularity on

the work but apply the shape factor (relation long axisshort axis) and the results were

that as this relation deviate from factor 1 the internal friction angle increases

The following empirical relations were found in the literature showing the behaviour

of the friction angle (obtained under different conditions)

)tan( noc

Figure 40 Representation of the angle of repose

(63)

(62)

34

Cho et al (2006)

(64)

(R is obtain by comparing the Krumbein chart figure 13)

Rouseacute (2008)

(65)

(66)

(R is defined using Wadell equation 22)

In figure 41 the suggested empirical relations above and lines constructed using

author data from Holubec and DrsquoAppolonia (1973) and Sukumara and Ashmawy

(2001) are plotted together to display the general trend on the particle shape and

friction angle relation Sukumaran reports two lines one based on the shape factor

(SF) and the second referring the angularity factor (AF) Sukumaran performed the

tests at constant volume

The scale used for Holubec and DrsquoAppolonia (1973) have lower and upper limits of 1

and 2 respectively (angularity form) and a scale change was applied to be able to

presented in the actual figure 41 As in the previous section (52) the author

recommend to use the original data from the references due that the figure just follows

the general trend of the behaviourrsquos particle regarding on the shape

Figure 41 The changes on the internal friction angle shows a general increase when the particle roundness

becomes angular or in the case of Sakamuran less spheric (Shape factor SF)

35

Barton and Kjaernsli (1981) suggested a model (equation 67) to predict the peak

friction angle (φrsquo) based upon numerous trixial and direct shear data tests

where

Se equivalent strength of particle

Re equivalent roughness of particle

φb basic friction angle (obtained from basic tilting test)

σn normal load

The information required for the model is (1) the uniaxial compressive strength of the

rock (2) the d50 particle size (mesh size where 50 of the particles pass through)

required to define Se (figure 42) (3) the degree of particle roundness and (4) the

porosity following compaction All data can be estimated by simple index tests

Barton and Kjaernsli (1981) suggest that particle size and sample scale has an effect

on the friction angle and includes them to obtain the equivalent strength (Se) figure 42

shows the method to obtain this value Compressive strength (σc) was chosen to be the

factor affecting the scale because micro fractures influence this property while

samples are bigger more micro fractures contain and its compressive strength reduces

The equivalent roughness is obtain using figure 43 where is required to know the

porosity (n) and the origin of the particles (a small chart is provided in the same figure

to compare the particles profile)

b

n

ee

SLogR

Figure 42 Method of estimating Equivalent Strength (Se) of rockfill based on uniaxial compressive strength

(σc ) and d50 particle size (Barton amp Kjaernsli 1981)

(67)

36

56 SEDIMENTATION PROPERTIES

A particle released in a less dense Newtonian fluid initially accelerate trough the fluid

due to the gravity Resistances to deformation of the fluid transmitted to the particle

surface drag generate forces that act to resist the particle motion The force due to the

weight (Fw) can be written as

Where ρp ρ are density of the particle and fluid (water) respectively g is the

gravitational force and Vp is the volume of the particle

And the resistance force (FD) is

Where CD is the dimensionless drag coefficient W is the weight of the particle and A

is the cross section area

Particlersquos shape has been assumed to be spherical when equations are applied on the

settling velocity Correlation deviates when particle shape departs from spherical form

Figure 43 Method of estimating Equivalent Roughness (Roe) based on porosity of rockfill

origin material degree of roundedness and smoothness of particle (Barton amp Kjaernsli 1981)

PPW ρ)gV(ρF

A2

WρCF

2

DD

(68)

(69)

37

(Dietrich 1982) and it is known that natural particles depart from spherical form

thus it is evident that this departure would have consequences

The below equation is proposed to account the shape (in this case the Corey shape

factor equation 8) in the settling velocity (Jimenez and Madsen 2003)

Jimenez and Madsen (2003) Dietrich (1982) Briggs and McCulloch (1962) and

others were working in the hydraulic shape of particles to solve problems as sediment

transport It is obvious that the equation presented and the researcherrsquos investigation

works under certain conditions (eg grain size between 0063-1 mm)

Dietrich (1982) suggests an empirical relation that accounts settling velocity size

density shape and roundness of a particle

R1 R2 and R3 are fitted equations for size and density shape and roundness

respectively

57 HYDRAULIC CONDUCTIVITY PERMEABILITY

Darcyrsquos Law Permeability is one component of Darcyrsquos law Darcys law is a simple

proportional relationship between the instantaneous discharge rate through a porous

medium the viscosity of the fluid and the pressure drop

The total velocity Ve is equal to the product of the permeability of the medium

(porous media) k the pressure drop ∆p all divided by the viscosity μ (Muskat

1937)

Darcys law is only valid for slow viscous flow most groundwater flow cases fall in

this category Typically Darcyrsquos law is valid at any flow with laminar flow (see figure

44)

Reynoldrsquos number (Laminar and turbulent Flow) Typically any laminar flow is

considered to have a Reynoldrsquos number less than one and it would be valid to apply

Darcys law Experimental tests have shown that flow regimes with Reynolds numbers

1

ND

S

S

ZY

gd1s

WW

NDN

gd)1s(4

dS

2R1R

3 10RW

pk

Ve

(70)

(71)

(72)

(73)

38

up to 10 may still be Darcian (laminar flow) as in the case of groundwater flow The

Reynolds number (a dimensionless parameter) for porous media flow is typically

expressed as

where ρ is the density of water (units of mass per volume) υ is the specific discharge

(with units of length per time) d is a representative average grain diameter for the

porous media (often taken as the 30 passing size from a grain size analysis using

sieves - with units of length) and μ is the viscosity of the fluid (Muskat 1937)

Shape effects Permeability as Head and Epps (2011) suggested is affected by the

shape and texture of soil grains Elongated or irregular particles create flow paths

which are more tortuous than those spherical particles Particles with a rough surface

texture provide more frictional resistance to flow Both effects tend to reduce the

water flow through the soil

Kozeny-Carman empirical relation accounts for the dependency of permeability on

void ratio in uniformly graded sands serious discrepancies are found when it is

applied to clays due the lack of uniform pores (Mitchell and Soga 2005)

There are various formulations of the Kozeny-Carman equation one published by

Head and Epps (2011) takes the void ratio e the specific surface area Ss and an

angularity factor F into account of permeability k

The angularity factor F considers the shape of the particles and ranges from 11 for

rounded grains 125 for sub rounded to 14 for angular particles The specific surface

Ss is defined as

d1 and d2 represent the maximum and minimum size particle in mm

Kane amp Sternheim (1988) suggest that the inclusion of the shape factor (F) has

probably the background on the Reynolds number due this factor is dependent

significantly on the shape of the obstacles and Reynolds number determines the

presence of laminar or turbulent flow Figure 44 show how the laminar flow has low

energy dissipation while turbulent flow (eg the roughness and path tortuosity) has

high energy dissipation

e1

e

FSs

2k

3

2

dRe

21

6

ddSs

(74)

(75)

(76)

39

According to Nearing and Parker (1994) the amount of soil detached during laminar

and turbulent flow is dependent on each soil and also greater on turbulent flow due the

greater shear strength generated during this kind of flow this could suggest the

greater erosion when turbulent flow is present

58 LIQUEFACTION

Soil liquefaction is a phenomenon in which soil loses much of its strength or stiffness

for a generally short time by earthquake shaking or other rapid loading Static and

dynamic liquefactions occur been the second one the most regular known

Liquefaction often occurs in saturated soils that is soils in which the space between

individual particles is completely filled with water This water exerts a pressure on the

soil particles that influences how tightly the particles themselves are pressed together

Shaking or other rapid loading can cause the water pressure to increase to the point

where the soil particles can readily move with respect to each other (Jefferies and

Been 2000)

Jefferies and Been (2000) state that it is clear that minor variation in intrinsic

properties of sand have major influence on the critical state These might be variations

on grain shape mineralogy grain size distribution surface roughness of grains etc

Yoginder et al (1985) found that substantial decrease on liquefaction resistance

occur with increase in confining pressure for rounded and angular sands (1600 kPa)

also rounded sands show an rapidly build up of resistance against liquefaction with

increasing density while angular tailing sand in contrast show such rapid increase

only at low confining pressures At low confining pressure angular material is more

resistant to liquefaction Probably the breakage of the corners on the angular particles

in tailings is ruling the lost in resistance at high confining pressures (sieve analysis

Figure 44 The figure show the extremes of flow behaviour First turbulent conditions where the flow is

essentially random and unpredictable and second the well defined Laminar flow conditions

40

after test identify the breakage of angular particles while on rounded particles the

sieve analysis was practically the same)

59 GROUNDWATER AND SEEPAGE MODELLING

In groundwater flow the particlersquos shape affects the soilrsquos pore size distribution

hence the flow characteristics (Sperry and Peirce 1995) Tortuosity and permeability

(also see section 57) are two significant macroscopic parameters of granular medium

that affect the passing flow (Hayati et al 2012) Current models incorporating the

effects of particle shape have failed to consider irregular particles such as those that

would prevail in a natural porous medium (Sperry and Peirce 1995)

Hayati et al (2012) suggested based on his results that tortuosity effect converge

when the porosity increases indicating that the shape have dominance at low and mid

porosity ranges

Sperry and Peirce (1995) research conclusions suggest that particle size and porosity

are more important predictors for hydraulic conductivity explaining the 69 of the

variability but particle shape appears to be the next most important This however

apparently comprises particles larger than 295-351 μm Differences for particle size

295-351 μm and smaller are not detectable Another interesting result in the research

was the interaction effect of the particle size and particle shape It suggests a different

packing configuration for particles of the same shape but different size (scale

dependent)

6 DISCUSSION

61 TERMS QUANTITIES AND DEFINITIONS

In order to describe the particle shape in detail there are a number of terms quantities

and definitions (qualitative and quantitative) used in the literature (eg Wadell 1932

1934 Krumbein 1941 Sneed amp Folk 1958) All mathematical definitions

(quantitatives) are models used to simplify the complexity of shape description Some

authors (Mitchell amp Soga 2005 Arasan et al 2010) are using three sub-quantities

one and each describing the shape but at different scales The terms are

morphologyform roundness and surface texture (figure 1) The three sub-quantities

are probably the best way to classify and describe a particle because not a single

definition can interpret the whole morphology Common language is needed when

descriptors are explained and these three scales represent an option It is evident in

the reviewed literature that many of the shape descriptors are presented with the same

name but also that there is not a clear meaning on what this descriptor defines eg

when there is no upper limit in the roundness does it means that the angularity never

ends Could they be more and more angular Probably they could be on theory but

not in reality

41

62 PROPERTIES

Trough various articlersquos review done in the present investigation it is recognized that

the particlersquos shape has an effect on the material properties among these are

1 Porosity (Tickell 1938 Fraser 1935 Kolbuszewski 1948) and void ratio

(Cho et al 2006 Shergold 1953 Rouseacute et al 2008 Santamarina and Cho

2004)

2 Permeability (Witt and Brauns 1983)

3 Internal friction angle (Shinohara et al 2000 Chan and Page 1997

Cheshomi et al 2009)

4 Density (Youd 1973 Holubec and DrsquoAppolonia 1973)

5 Drag coefficient Hydraulics (Briggs and McCulloch 1962)

In Table 5 is a short resume of the properties and shape effect found in peer review

articles trough different journals Most of the reviewed articles based its research on

uniform graded sands

Table 8 Compilation of properties influenced by particle shape

Repose

angle

Friction

angle

Porosity and

Void ratio Density Permeability

Settling velocity

Drag coefficient Deformation

Sphericity (3D)shape factor

NI x x x x x x

Circularity (2D)

NI x x x x NI NI

Roundness x x x x NI NI x

x influence

NI no information available

Shape of particles has an effect on the arrangement producing bridging or avoiding

the rotation of the particles and the resulting geotechnical property is affected eg

including flaky particles can result in a higher void ratio due the bridging effect

(Santamarina and Cho 2004) and depending on the loads even the size distribution is

changed due the breakage (Yoginder et al 1985) in similar way angular particles

produce higher void ratio due the avoided possibility of the particles to rotate and

compact

The influence of the chosen shape descriptor appears in this review to have minor

influence on the soil properties in the reviewed studies except on the void ratio and

the friction angle Influence of particle shape in some cases is hider by other factors

(eg size distribution) also the particle shape probably does not have influence when

particle size is in the clay order (eg hydraulic conductivity) the reason could be due

to forces as electrostatic or capillarity become more important at this level

Among the shape descriptors some are chosen more often in literature (eg aspect

ratio) there is no apparent scientific basis to use it (probably due to the simplicity of

the measurement it becomes one of the most use) but there are still some other

descriptors that may or may not show better correlation with the soil properties

Instead empirical relations had been developed regarding roundness or shape to

describe the soil behaviour it is clear that the mechanism behind the results is still not

completely understood

42

There is necessity to define the best(s) shape descriptor(s) to be used for particular

geotechnical properties

63 IMAGE ANALYSIS

Many image analysis techniques had been used to describe the particle shape eg

Fourier analysis fractal dimension tomography etc (Hyslip and Vallejo 1997) but

there is not agreement on the usage or conclusion to ensure the best particle descriptor

for geotechnical applications

There are several shape descriptors and also various techniques to capture the

particles profile (3-dimensions 3-dimension orthogonal and 2-dimensions) Each

technique presents advantages and disadvantages 3-dimensions is probably the

technique that provide more information about the particle shape but the precision

also lies in the resolution the equipment required to perform such capture could be

more or less sophisticated (scanning particles laying down in one position and later

move to complete the scanning or just falling down particles to scan it in one step)

3-dimensions orthogonal this technique use less sophisticated equipment (compare

with the previous technique) but its use is limited to particles over 1cm also

information between the orthogonal pictures is not capture 2-dimensions require non

sophisticated equipment but at the same time the shape information diminish compare

with the previous due the fact that it is possible to determine only the outline as the

particle measurements are performed in 2-dimensions it is presumed that they will lie

with its shortest axis perpendicular to the laying surface when they are flat but when

the particle tends to have more or less similar axis the laying could be random

Advantages on the use of image analysis are clear there is not subjectivity because it

is possible to obtain same result over the same images Electronic files do not loose

resolution and it is important when collaboration among distant work places is done

files can be send with the entire confidence and knowing that file properties has not

been changed Technology evolutions allowed to work with more information and it

also applies to the image processing area were the time consumed has been shortened

(more images processed in less time)

One important aspect in image analysis is the used resolution in the analysis due the

fact that there are measurements dependent and independent on resolution Thus

those dependent measurements should be avoided due the error included when they

are applied or avoid low resolution to increase the reliability Among these

parameters length is the principal parameter that is influences by resolution (eg

perimeter diameter axis etc) Resolution also has another aspect with two faces

quality versus capacity more resolution (quality) means more storage space a

minimum resolution to obtain reasonable and reliable data must be known but it

depend on each particular application

43

64 APPLICATIONS

Quantify changes in particles in the authorrsquos thought is one of the future applications

due the non-invasive methods of taking photographs in the surface of the damrsquos slope

rail road ballast or roads Sampling of the material and comparing with previous

results could show volume (3D analysis) or area (2D analysis) loss of the particles as

well as the form roundness and roughness This is important when it has been

suggested that a soil or rock embankment decrees their stability properties (eg

internal friction angle) with the loss of sphericity roundness or roughness

Seepage stock piling groundwater etc should try to include the particle shape while

modelling seepage requires grading material to not allow particles move due the

water pressure but in angular materials as it is known the void ratio is great than the

rounded soil it means the space and the possibilities for the small particles to move

are greater stock piling could be modelled incorporating the particle shape to

determine the binrsquos capacity when particle shape changes (void ratio changes when

particle shape changes) Modelling requires all information available and the

understanding of the principles that apply

Industry is actually using the particle shape to understand the soil behaviour and

transform processes into practical and economic image analysis has been included in

the quality control to determine particle shape and size because the advantages it

brings eg the acquisition of the sieving curve for pellets using digital images taken

from conveyor this allows to have the information in a short period of time with a

similar result at least enough from the practical point of view as the traditional

sieving

7 CONCLUSIONS

The conclusions of this literature review are

It has been shown that particle shape has influence on the soil behaviour

despite of partial knowledge of the mechanism behind Understanding of the

particle shape and its influence needs to be accomplished

A common language needs to be built up to standardize the meaning on

geotechnical field that involve the particle shape General relationships

between shape and properties should be developed

Based on this review it is not clear which is the best descriptor to use in

geotechnical engineering affecting he related shape to properties Instead of a

couple of standards there is no shape descriptor in geotechnical field fully

accepted

Image analysis tool is objective make the results repeatable obtain fast results

and work with more amount of information

44

Resolution needs to be taken in consideration when image analysis is been

carried out because the effects could be considerable Resolution must be set

according to the necessities Parameters as perimeter can be affected by

resolution

There are examples where particle shape has been incorporated in industries

related to geotechnical engineering eg in the ballast and asphalt industry for

quality control

8 FURTHER WORK

Three main issues have been identified in this review that will be further investigated

the limits of shape descriptors influence of grading and choice of descriptor for

relation to geotechnical properties

Shape descriptors have low and high limits frequently the limits are not the same and

the ability to describe the particlersquos shape is relative The sensitivity of each descriptor

should be compare to apply the most suitable descriptor in each situation

Sieving curve determine the particle size in a granular soil particle shape could differ

in each sieve size There is the necessity to describe the particle shape on each sieve

portion (due to practical issues) and included in the sieve curve Obtain an average

shape in determined sieve size is complicated (due to the possible presence of several

shapes) and to obtain the particle shape on the overall particlersquos size is challenging

how the particle shape should be included

Since several descriptors have been used to determine the shape of the particles and

the relation with the soil properties it is convenient to determine the descriptorrsquos

correlation with the soil properties

9 ACKNOWLEDGMENT

I would like to thanks to Lulearing University of Technology (LTU) the time I had spent

in its facilities and the kind environment it offers and University of Sonora

(UNISON) that has been providing me the financial support and the time to conclude

this journey

10 REFERENCES

Andersson T (2010) Estimating particle size distributions based on machine vision

Doctoral Thesis Departament of Computer Science and Electrical Engineering Lulearing

University of Technology ISSN 1402-1544 ISBN 978-91-7439-186-2

45

Arasan Seracettin Hasiloglu A Samet Akbulut Suat (2010) Shape particle of

natural and crished aggregate using image analysis International Journal of Civil and

Structural Engineering Vol 1 No 2 pp 221-233 ISSN 0970-4399

Aschenbrenner BC (1956) A new method of expressing particle sphericity Journal

of Sedimentary Petrology Vol 26 No 1 pp 15-31

Axelsson K (1998) Introduktion till jordmekaniken jaumlmte jordmateriallaumlran Skrift

984 Lulearing Avdelningen foumlr Geoteknologi Lulearing Tekniska Universitet (In Swedish)

Barton Nick amp Kjaernsli Bjorn (1981) Shear strength of rockfill Journal of the

Geotechnical Engineering Division Proceedings of the American Society of Civil

Engineers (ASCE) Vol 107 No GT7

Barrett P J (1980) The shape of rock particles a critical review Sedimentology

Vol 27 pp 291-303

Blott S J and Pye K (2008) Particle shape a review and new methods of

characterization and classification Sedimentology Vol 55 pp 31-63

Bowman E T Soga K and Drummond W (2001) Particle shape characterization

using Fourier descriptor analysis Geotechnique Vol 51 No 6 pp 545-554

Briggs L I McCulloch D S (1962) Hydraulic shape of sand particles Journal of

Sedimentary Petrology Vol 32 pp 645-656

Chan Leonard C Y and Page Neil W (1997) Particle fractal and load effects on

internal friction in powders Powder Technology Vol 90 pp 259-266

Cheshomi A Fakher A Jones C J F P (2009) A correlation between friction

angle and particle shape metrics in quaternary coarse alluvia Quarterly Journal of

Engineering Geology and Hydrogeology Vol 42 pp 145-155

Cho G Dodds J and Santamarina J C (2006) Particle shape effects on packing

density stiffness and strength Natural and crushed sands Journal of Geotechnical

and Geoenvironmental Engineering May 2006 pp 591-602

Dietrich William E (1982) Settling velocity of natural particles Water Resources

Research Vol 18 No 6 pp 1615-1626

Dobkins J E and Folk R L (1970) Shape development on Tahiti-nui Journal of

Sedimentary Petrology Vol 40 No 2 pp 1167-1203

Folk R L (1955) Student operator error in determining of roundness sphericity and

grain size Journal of Sedimentary Petrology Vol 25 pp 297-301

Fernlund J M R (1998) The effect of particle form on sieve analysis A test by

image analysis Engineering Geology Vol 50 No 1-2 pp 111-124

46

Fernlund J M R (2005) Image analysis method for determining 3-D shape of

coarse aggregate Cement and Concrete Research Vol 35 Issue 8 pp 1629-1637

Fernlund J M R Zimmerman Robert and Kragic Danica (2007) Influence of

volumemass on grain-size curves and conversion of image-analysis size to sieve size

Engineering Geology Vol 90 No 3-4 pp 124-137

Fraser H J (1935) Experimental study of the porosity and permeability of clastic

sediments The Journal of Geology Vol 43 pp 910-1010 ISSN 0022-1376

Hayati Ali Nemati Ahmadi Mohammad Mehdi and Mohammadi Soheil (2012)

American Physical Society Physical review E 85 036310 DOI

101103PhysRevE85036310

Hawkins A E (1993) The Shape of Powder-Particle Outlines Wiley New York

Head K H and Epps R J (2011) Manual of soil Laboratory testing Volum II

Permeability shear strength and compressibility test 3rd

edition Whittles Publishing

Scotland UK 3rd

edition

Holubec I and DrsquoAppolonia E (1973) Effect of particle shape on the engineering

properties of granular soils ASTM STP 523 pp 304-318

Hyslip James P Vallejo Luis E (1997) Fractal analysis of the roughness and size

distribution of granular materials Engineering Geology Vol 48 pp 231-244

Janoo Vincent C (1998) Quantification of shape angularity and surface texture of

base course materials US Army Corps of Engineers Cold Region Research and

Engineering Laboratory Special report 98-1

Jefferies Mike and Been Ken (2000) Soil liquefaction A critical state approach

Taylor amp Francis Group London and New York

Jimenez Jose A Madsen Ole S (2003) A simple formula to estimate settling

velocity of natural sediments Journal of Waterway Port Coastal and Ocean

Engineering Vol 129 No 2 pp 70-78

Johansson Jens and Vall Jakob (2011) Jordmaterials kornform Inverkan paring

Geotekniska Egenskaper Beskrivande storheter bestaumlmningsmetoder

Examensarbete Avdelningen foumlr Geoteknologi Institutionen foumlr Samhaumlllsbyggnad

och naturresurser Lulearing Tekniska Universitet Lulearing (In Swedish)

Kane Joseph W and Sternheim Morton M (1988) Physics John Wiley amp Sons Inc

Third edition

Kolbuszewski J (1948) An experimental study of the maximum and minimum

porosities of sands Proceedings of the Second International Conference on Soil

Mechanics and Foundation Engineering Rotterdam June 21 to 30 Sub-section IIb

pp 158-165

47

Krumbein W C and Pettijohn FJ (1938) Manual of sedimentary petrography

Appleton-Century Crofts Inc New York

Krumbein W C (1941) Measurement and geological significance of shape and

roundness of sedimentary particles Journal of Sedimentary Petrology Vol 11 No 2

pp 64-72

Krumbein W C and Sloss L L (1963) Stratigraphy and Sedimentation 2nd

ed

WH Freeman San Francisco

Kuo Chun-Yi and Freeman Reed B (1998a) Image analysis evaluation of

aggregates for asphalt concrete mixtures Transportation Research Record Vol 1615

pp 65-71

Kuo Chun-Yi Rollings Raymond and Lynch Larry N (1998b) Morphological

study of coarse aggregates using image analysis Journal of Materials in Civil

Engineering Vol 10 No 3 pp 135-142

Lanaro F Tolppanen P (2002) 3D characterization of coarse aggregates

Engineering Geology Vol 65 pp 17-30

Lees G (1964a) A new method for determining the angularity of particles

Sedimentology Vol 3 pp 2-21

Lees G (1964b) The measurement of particle shape and its influence in engineering

materials British Granite Whinstone Federation Vol 4 No 2 pp 17-38

Matsushima Takashi Saomoto Hidetaka Matsumoto Masaaki Toda Kengo

Yamada Yasuo (2003) Discrete element simulation of an assembly of irregular-

shaped grains Quantitative comparison with experiments 16th ASCE Engineering

Mechanics Conference University of Washington Seattle July 16-18

Mitchell James K and Soga Kenichi (2005) Fundamentals of soil behaviour Third

edition WILEY

Mora C F Kwan A K H Chan H C (1998) Particle size distribution analysis of

coarse aggregate using digital image processing Cement and Concrete Research Vol

28 pp 921-932

Mora C F and Kwan A K H (2000) Sphericity shape factor and convexity

measurement of coarse aggregate for concrete using digital image processing Cement

and Concrete Research Vol 30 No 3 pp 351-358

Muskat Morris (1937) The Flow of fluids through porous media Journal of Applied

Physics Vol 8 pp 274

Nearing M A and Parker S C (1994) Detachment of soil by flowing water under

turbulent and laminar conditions Soil Science Society of American Journal Vol 58

No 6 pp 1612-1614

48

Pan Tongyan Tutumluer Erol Carpenter Samuel H (2006) Effect of coarse

aggregate morphology on permanent deformation behavior of hot mix asphalt Journal

of Transportation Engineering Vol 132 No 7 pp 580-589

Pellegrino A (1965) Geotechnical properties of coarse-grained soils Proceedings

International Conference of Soil Mechanics and Foundation Engineering Vol 1 pp

97-91

Pentland A (1927) A method of measuring the angularity of sands MAG MN AL

Acta Eng Dom Transaction of the Royal Society of Canada Vol 21 Ser3xciii

Persson Anna-Lena (1998) Image analysis of shape and size of fine aggregates

Engineering Geology Vol 50 pp 177-186

Powers M C (1953) A new roundness scale for sedimentary particles Journal of

Sedimentary Petrology Vol 23 No 2 pp 117-119

Pye W and Pye M (1943) Sphericity determination of pebbles and grains Journal

of Sedimentary Petrology Vol 13 No 1 pp 28-34

Qazi M A (1975) Flow properties of granular masses A review on the angle of

repose The Arabian Journal for Science and Engineering Vol 1 No 2

Quiroga Pedro Nel and Fowle David W (2003) The effects of aggregate

characteristics on the performance of portland cement concrete Report ICAR 104-1F

Project number 104 International Center for Aggregates Research University of

Texas

Riley N A (1941) Projection sphericity Journal of Sedimentary Petrology Vol 11

No 2 pp 94-97

Rouseacute P C Fennin R J and Shuttle D A (2008) Influence of roundness on the

void ratio and strength of uniform sand Geotechnique Vol 58 No 3 227-231

Santamarina J C and Cho G C (2004) Soil behaviour The role of particle shape

Proceedings Skempton Conf London

Schofield and Wroth (1968) Critical state soil mechanics McGraw Hill

Shaumlfer Michael (2002) Digital optics Some remarks on the accuracy of particle

image analysis Particle amp Particle Systems Characterization Vol 19 No 3 pp 158-

168

Shergold F A (1953) The percentage of voids in compacted gravel as a measure of

its angularity Magazine of Concrete Research Vol 5 No 13 pp 3-10

Shinohara Kunio Oida Mikihiro Golman Boris (2000) Effect of particle shape on

angle of internal friction by triaxial compression test Powder Technology Vol 107

pp131-136

49

Skredcommisionen (1995) Ingenjoumlrsvetenskapsakademinen rapport 395 Linkoumlping

1995

Sneed E D and Folk R L (1958) Pebbles in the Colorado river Texas A study in

particle morphogenesis Journal of Geology Vol 66 pp 114-150

Sperry James M and Peirce J Jeffrey (1995) A model for estimating the hydraulic

conductivity of granular material based on grain shape grain size and porosity

Ground Water Vol 33 No 6 pp 892-898

Sukumaran B and Ashmawy A K (2001) Quantitative characterisation of the

geometry of discrete particles Geotechnique Vol 51 No 7 pp 619-627

Szaacutedeczy-Kardoss E Von (1933) Die bistimmung der abrollungsgrades Geologie

und palaumlontologie Vol 34B pp 389-401 (in German)

Teller J T (1976) Equantcy versus sphericity Sedimentology Vol 23 pp 427-428

Tickell F G (1938) Effect of the angularity of grain on porosity and permeability

bulletin of the American Association of Petroleum Geologist Vol 22 pp 1272-1274

Tutumluer E Huang H Hashash Y Ghaboussi J (2006) Aggregate shape effects

on ballast tamping and railroad track lateral stability AREMA 2006 Annual

Conference Louisville KY

Wadell H (1932) ldquoVolume Shape and roundness of rock particlesrdquo Journal of

Geology Vol 40 pp 443-451

Wadell H (1933) Sphericity and roundness of rock Particles Journal of Geology

Vol 41 No 3 pp 310ndash331

Wadell H (1934) Shape determination of large sedimental rock fragments

The Pan-American Geologist Vol 61 pp 187-220

Wadell H (1935) ldquoVolume shape and roundness of quartz particlesrdquo Journal of

Geology Vol 43 pp 250-279

Wentworth W C (1922a) The shape of beach pebbles Washington US Geological

Survey Bulletin Vol 131C pp 75-83

Wentworth W C (1922b) A method of measuring and plotting the shape of pebbles

Washington US Geological Survey Bulletin Vol 730C pp 91-114

Wentworth W C (1933) The shape of rock particle A discussion Journal of

Geology Vol 41 pp 306-309

Witt K J Brauns J (1983) Permeability-Anisotropy due to particle shape Journal

of Geotechnical Engineering Vol 109 No 9 pp 1181-1187

11

Table 3 General chronological overview of the particle shape definitions for 2D sphericity

Aspect Name Author Year Based on

Circularity (2D) roundness Pentland 1927 area

roundness Cox1

1927 area-perimeter

roundness Tickell2

1931 area

Circularity Horton2

1932 drainage basin

outline circularity Wadell 1935 Circle diameter

degree of circularity Wadell 1935 Perimeter

inscribed circle sphericity Riley 1941 Circle diameter

Circularity Krumbein and Sloss 1963 chart

Janoo 1998 area-perimeter

Shape factor Sukumaran 2001 Segmentation of particle and angles

1) Riley 1941 2) Hawkins 1993

35 ROUNDNESS OR ANGULARITY

Roundness as described in section 32 is the second order shape descriptor Sphericity

lefts beside the corners and how they are this was notice by most of the authors sited

before and they suggested many ways to describe this second order particle property

Roundness is clearly understandable using the figure 10 Particle shape or form is the

overall configuration and denotes the similarities with a sphere (3D) or a circle (2D)

Roundness is concerning about the sharpness or the smoothness of the perimeter (2D)

Surface texture (Barret 1980) is describe as the third order subject (form is the first

and roundness the second) and it is superimposed in the corners and it is also a

property of particles surfaces between corners

Figure 9 Description of the Sukumaran factors to determine the shape and angularity (Sukumaran and

Ashmawy 2001)

12

Wadell (1935) describes his methodology calling it total degree or roundness to

obtain the roundness of a particle using the average radius of the corners in relation

with the inscribed circle diameter (see figure 11) on the equation

In the same study Wadell (1935) has used the equation

This two last equation shows slightly differences on the results (Wadell 1935)

Powers (1953) also published a graphic scale to illustrate the qualitative measure

(figure 12) It is important to highlight that any comparing chart to describe particle

properties has a high degree of subjectivity Folk (1955) concludes that when charts

are used for classification the risk of getting errors is negligible for sphericity but

large for roundness

N

R

r

Rinmax

r

R

NR

inmax

Figure 10 Form (shape) Roundness and Texture graphical description (Bowman et al 2001)

Figure 11 Wadellrsquos method to estimate the roundness corners radius and inscribed circle

(Hawkins 1993)

(22)

(23)

13

Some authors as Russel amp Taylor in 1937 Pettijohn in 1957 and Powers in 1953

developed a classification based on five and six classes (Hawkins 1993) each one

with its own class limits it is important to denote that the way they measure the

roundness is the developed by Wadell (1935) This classification and class limits are

showed in the table 4

Table 4 Degrees of roundness Wadell Values (Hawkins 1993) NA = no-applicable

Grade terms Russell amp Taylor (1937) Pettijohn (1957) Powers (1953)

Class

limits (R)

Arithmetic

midpoint

Class limits

(R)

Arithmetic midpoint Class

limits (R)

Arithmetic

midpoint

Very angular

NA

NA

NA

NA

012-017

014

Angular

000-015

0075

000-015

0125

017-025

021

Subangular

015-030

0225

015-025

0200

025-035

030

Subrounded

030-050

0400

025-040

0315

035-049

041

Rounded

050-070

0600

040-060

0500

049-070

059

Well rounded

070-100

0800

060-100

0800

070-100

084

Krumbein and Sloss (1963) published a graphical chart easy to determine the

sphericity and roundness parameters using comparison See figure 13 (Cho et al

2006)

Figure 12 A Roundness qualitative scale (Powers 1953)

Figure 13 Sphericity and roundness chart (Cho et al 2006) The roundness equation that appears here in

the chart is the wadellrsquos equation number 22

14

Fischer in 1933 (Hawkins 1993) used a straightforward method to quantify roundness

using a central point in the outline and dividing the outline in angles around this point

that were subtended by the straight or non curved parts of the profile were measured

This is illustrated in figure 14

To express the angularity value Fischer used the ratio of angles standing linear parts

on the outlines and concave respectively

Figure 14 left (A) and right (B) gives a similar angularity of approximately 042

using the above equations (Hawkins 1993)

Wentworth in 1922 used the maximum projection to define the position of the particle

to obtain the outline or contour (Barret 1980) The equation reflects the relation of the

diameter of a circle fitting the sharpest corner and the longest axis plus the shortest

axis c (minimum projection)

Wentworth (Hawkins 1993) expressed the roundness as the ratio of the radius of

curvature of the most convex part and the longest axis plus short axis

Actually these last two equations are the same just expressed in different terms when

the particle is in its maximum projection

Dimensions can be seen on figure 15 L and B represents the mayor axis a and

intermediate axis b The intention is to make difference between the 2 and 3

dimensions (L and B are for 2D as a b and c are for 3D)

deg360

ANG

=R

sumPLA

PLA

CON

ANG

ANGR

2)S(L

DR

M

S

B)4(L

RR CON

Figure 14 Fischerrsquos methods of angularity computation (Hawkins 1993)

A=inscribed circle B=circumscribed circle

(24)

(25)

(26)

(27)

15

Wentworth 1919 has a second way to express the roundness called Shape index

(Barrett 1980) and it relates the sharpest corner and the diameter of a pebble trough

the sharpest corner

Wentworth (1922b) used define the roundness as the ratio of the sharpest corner and

the average radius of the pebble

Cailleux (Barrett 1980) relates the radius of the most convex part and the longest

axis

Kuenen in 1956 show his roundness index (Barrett 1980) between the sharpest corner

and the breath axis

Dobkins amp Folk (1970) used a modified Wentworth roundness with the relation of

sharpest corner and inscribed circle diameters

AVG

CON

R

RR

x

s

D

DR

L2

RR CON

B

DR s

i

s

D

DR

3AVGAVG cbaDR2

Figure 15 Description of L and B axes (Hawkins 1993)

(28)

(29)

(30)

(31)

(32)

(33)

16

Swan in 1974 shows his equation (Barrett 1980) relating the sharpest (or the two

sharpest) corner(s) and inscribed circle diameter

Szadeczsky-Kardoss has his Average roundness of outline (Krumbein and Pettijohn

1938) relating the concave parts perimeter and the actual perimeter

Lees (1964a) developed an opposite definition to roundness it means that he

measures the angularity instead of the roundness and he calls it Degree of angularity

Figure 16 shows the items considered when equation 36 applies as the angles (α)

inscribed circle (Rmax-in) and the distance (x) The main formula is

In order to apply the last equation corners needs to be entered in the formula and each

individual result will add to each other to obtain the final degree of angularity

A roundness index appears on Janoo (1998) Kuo and Freeman (1998a) and Kuo et

al (1998b) it is described as

The last equation is on section 34 also because there is not a general agreement on the

definition furthermore some authors had used to define the roughness this is not the

only equation that has been used trying to define different aspects (sphericity

roundness or roughness) but it is a good example of the misuse of the quantities and

definitions

inmaxR

x)180(R

2P

A4R

i

ss

D

DDR

221

100P

PR CON

Figure 16 Degree of angularity measurement technique (Blot and Pye 2008)

(34)

(35)

(36)

(17)

17

Sukumaran and Ashmawy (2001) present an angularity factor (AF) calculated from

the number of sharpness corners Angles βi required to obtain the angularity factor are

shown in figure 9

Sukumaran and Ashmawy (2001) also suggested use not bigger sampling interval of

N=40 because it is the cut off between angularity factor and surface roughness If so

this equation could be used to describe the roughness

Table 5 General chronological overview of the particle roundness

Aspect Name Author Year Based on

Roundness shape index Wentworth 19191

diameter of sharper corner

shape index Wentworth 1922b sharpest corner and axis

roundness Wentworth 1933 convex parts

Fischer 19332

noncurved parts outline

Fischer 19332

noncurved-streigth parts outline

Average roundness of outline

Szadeczsky-Kardoss 19333

convex parts-perimeter

roundness Wadell 1935 diameter of corners

roundness Wadell 1935 diameter of corners

roundness Russel amp Taylor 19372

class limit table

roundness Krumbein 1941 chart

Cailleux 19471

convex parts

roundness Pettijohn 19494 class limit table

roundness Powers 1953 chart and class limit table

Kuenen 19561

axis-convex corner

roundness Krumbein and Sloss 1963 chart

degree of angularity Lees 1964a corners angles and inscribed circle

Dobkins amp Folk 1970 diameter of sharper corner

Swan 19741

diameter of sharper corners

Angularity factor Sukumaran and

Ashmawy 2001

Segmentation of particles and angles

1) Barret 1980 2) Hawkins 1993 3) Krumbein and Pettijohn 1938 4) Powers 1953

sum

sumsumN

1=i

2

i

2

N

1=i

2

i

2N

1=ii

)ordm180 -circleβ( - )(180ordm x 3

)ordm180-circleβ(-)ordm180 -Particleβ(

= AF (37)

18

36 ROUGHNESS OR SURFACE TEXTURE

A third property called texture appears early in the literature with the sphericity and

roundness properties since then texture property was longed described but it was in

accordance with the authors at that time not measurable

Wright in 1955 developed a method to quantify the surface texture or roughness of

concrete aggregate using studies done on 19 mm stones The test aggregates were first

embedded in a synthetic resin The stones were cut in thin sections The sections

projection was magnified 125 times The unevenness of the surface was traced and the

total length of the trace was measured The length was then compared with an uneven

line drawn as a series of chords (see figure 17) The difference between these two

lines was defined as the roughness factor (Janoo 1998)

However with the advance of technology it has become easier measure the roughness

and here is presented some researcherrsquos ideas how this property should be calculated

One technique used by Janoo (1988) to define the roughness can be seen in figure 18a

and is defined as the ratio between perimeter and convex perimeter

The convex perimeter is obtained using the Feretrsquos box (or diameter) tending a line in

between the touching points that the Feretrsquos box describes each time it is turn (figure

18b)

PER

OC

PR

Figure 17 Measurement method for characterizing the surface texture of an aggregate (Janoo 1998)

a) Convex perimeter (CPER) b) Feret measurement Figure 18 a) Convex perimeter (CPER) b) Feret measurement (modified after Janoo 1998)

(38)

a)

b)

19

Kuo and Freeman (1998a) and Kuo et al (1998b) use the roughness definition as the

ratio perimeter and average diameter

Erosion and dilatation image processing techniques are used to obtain the surface

texture Erosion is a morphological process by which boundary image pixels are

removed from an object surface which leaves the object less dense along the

perimeter or outer boundary Dilatation is the reverse process of erosion and a single

dilatation cycle increases the particle shape or image dimension by adding pixels

around its boundary (Pan etal 2006)

The ldquonrdquo erosion and dilatation cycles are not standardized

Mora and Kwan (2000) used the ldquoconvexity ratio CRrdquo (equation 41) and the ldquofullness

ratio FRrdquo (equation 42) in their investigation they are

The convex area is the area of the minimum convex boundaries circumscribing the

particle This is illustrated in the figure 19 The convex area is obtained in a similar

way as the convex perimeter but in this case the area between the original outline and

the convex perimeter is our convex area

AVG

OD

PR

100A

1AARO

CONo A

AR =

CONo A

AR =

Figure 19 Evaluation of area and convex area (Mora and Kuan 2000)

(39)

(40)

(41)

(42)

20

4 TECHNIQUES IN ORDER TO DETERMINE PARTICLE

SHAPE

41 HAND MEASUREMENT

Hand measurement technique was the first used by obvious reasons in order to

improve the accuracy special devices developed as the ldquosliding rod caliperrdquo used by

Krumbein (1941) it works placing the sample on the sliding road calliper as show

figure 20b the length in different positions can be obtain by using the scale provided

in the handle the ldquoconvexity gagerdquo that was actually used by opticians to measure the

curvature of lenses but easily applicable to the particle shape analysis (Wentworth

1922b) works measuring the movement of the central pivot as figure 20a shows (the

two adjacent pivots are invariable) as many the central pivot moves more is the

curvature or the ldquoSzadeczky-Kardossrsquos apparatusrdquo develop in 1933 that traces the

profile of the rock fragment so the outline traced is then analyzed (Krumbein and

Pettijohn 1938) figure 20c show equipment

Another helpful tool to determine the particle dimensions was the ldquocamera lucidardquo to

project the particlersquos contour over a circle scale appearing in Figure 21 thus it is

possible to measure the particlersquos diameter

a)

c) b)

Figure 20 a) convexity gage used to determine the curvature in particle corners (Wenworth 1922b)

b)sliding rod caliper device to measure the particle axis length (Krumbein 1941) and c)Szadeczky-

Kardoss (1933) apparatus it was utilized to obtain the particle outline

Figure 21 Circle scale used by Wadell (1935) to determine particlersquos diameter and roundness

21

42 SIEVE ANALYSIS

Bar sieving eg according to EN 933-31997 can be used to determine simple large

scale properties By combining mesh geometries the obtained results can be used to

quantify flakiness and elongation index ASTM D4791 (Flat and elongated particles

are defined as those coarse aggregate particles that have a ratio of length to thickness

equal to or greater than a specified value such as 51 The index represents the

percentage on weight of these particles) The method is not suitable for fine materials

This due to the difficulty to get the fine grains passed through the sieve and the great

amount of particles in relation to the area of the sieve (Persson 1998) eg EN 933-

31997 related to flakiness index The test is performed on aggregates with grain size

from 4 mm and up to 63 mm two sieving operations are necessary the first separates

on size fraction and the second use a bar sieve after the first sieving the average

maximum diameter of the particles is obtain and with the second sieving (bar sieving)

the shortest axis diameter is found finally with this two parameters the flakiness

index is determined

There are more standards related with the particle shape (see appendix A) but this

above presented are probably the most known using sieve analysis to determine

particlersquos geometrical properties

Sieve analysis is facing the computers age and image analysis sieving research is

taking place (Andersson 2010 Mora and Kwan 2000 Persson 1998) Industry is

also applying the image analysis sieving with decrees on the testing time compare

with the traditional sieving method An inconvenient of image analysis is the error

due the overlapping or hiding of the particles during the capture process but the

advantages are more compare with disadvantages (Anderson 2010)

43 CHART COMPARISON

Charts developed over the necessity of faster results because the long time consuming

required when measuring each particle

Krumbein (1941) present a comparison roundness chart for pebbles which were

measured by Wadellrsquos method because this property was the most difficult to measure

due to the second order scale that roundness represents (See figure 22)

Figure 22 Krumbein (1941) comparision chart for roundness

22

A qualitative chart by Powers (1953) try to include both (sphericity and roundness)

particlersquos characteristics it was divided on six roundness ranges (very angular

angular sub-angular sub-rounded rounded and well rounded) and two sphericity

series (high and low sphericity) This chart was prepared with photographs to enhance

the reader perspective (See figure 23)

A new chart including sphericity and roundness appear this time it was easier to

handle the two mean properties of particlersquos shape furthermore there was included

the numerical values that eliminated the subjectivity of qualitative description The

chart is based on Wadellrsquos definitions (Krumbein and Sloss 1963) (See figure 24)

Folk (1955) worried about the personrsquos error on the chartrsquos comparison studied the

determination of sphericity and angularity (he used the Powers 1953 comparison

chart) he found that the sphericity determination by chart comparison has a negligible

error while the roundness he concluded it was necessary to carry out a more wide

research due the high variability show by his study

Figure 23 Powers (1953) qualitative shpericity-roundness chart

Figure 24 Sphericity-roundness comparison chart (Krumbein and sloss 1963)

23

44 IMAGE ANALYSIS

Image analysis is a practical method to use for shape classification since it is fast and

can be automated Different techniques appear to process these images among them

are

o Feret Diameter the Feret diameter is the longitude between two parallel lines

this lines can rotate around one particle or outline to define dimensions as it

is shown in figure 25 these method is not a fine descriptor but as it was say

above it is a helpful tool to determine diameters (Janoo 1988)

o Fourier Mathematical Technique It produces mathematical relations that

characterize the profile of individual particles This method favours the

analysis of roughness and textural features for granular soils The problem in

the methodology remains in the re-entrant angles in order to complete the

revolution (Bowman et al 2001) see figure 26

o Fractal Dimension Irregular line at any level of scrutiny is by definition

fractal (Hyslip and Vallejo 1997) Figure 27 shows fractal analysis by the

dividing method The length of the fractal line can be defined as

N

1n

nn0 )nsinbncosa(a)(R

RD1n)(P

Figure 25 Feret measurement technique is defined by two parallel lines turning

around the particle to define the shortest and longest Feret diameter (Janoo 1988)

Figure 26 Fourier technique with two radiuses at one angle (Bowman et al 2001)

(43)

(44)

24

o Orthogonal image analysis This technique is basically the use of two images

orthogonal between them to acquire the three particle dimensions (Fernlund

2005) any of the above techniques can be used in this orthogonal way

o Laser Scanning Technique this kind of laser scanning 3D is one of the most

advanced techniques In figures 28a) we have the laser head scanning the rock

particles the particles have control points in order to keep a reference point

when move them to scan the lower part in figure 28b) we can see the laser

path followed (Lanaro and Tolppanen 2002)

Another technique is the Laser-Aided Tomography (LAT) in this case a laser sheet is

used to obtain the particles surveying (see figure 29) This technique is different and

has special requirements as to use liquid with same refractive index as the particles

particles must let the laser or certain percent of light go through (Matsushima et al

2003)

a) b)

Figure 27 Fractal analysis by the dividing method at different scrutiny scale (Hyslip and Vallejo 1997)

Figure 28 a) Scanning head b) scanning path (Lanaro and Tolppanen 2002)

Figure 30 3D scan completed ready to

use for any further measure

(Matsushima et al 2003)

Figure 29 LAT scaning particles

(Matsushima et al 2003)

25

Both 3D techniques obtain the particle shape that is later used to achieve measures as

we can see in figure 30

All these previous techniques are easily written in codes or scripts to be interpreted in

a digital way obtaining the desired measurement but there are some interesting points

in the image analysis regarding on the errors involve among them are image

resolution and orientation of the particles orientation is not relevant when it is

random and large number of particles are involve resolution have an influence on the

accuracy (Zeidan et al 2007)

When resolution is increase more accuracy is obtain and the object representation

match better with the real form in the other hand more resolution means more

spending on memory and time thus resolution needs to be according with the goal

and precision needed in any work (Schaumlfer 2002)

Schaumlfer (2002) conclude that attributes like length when measuring digital images

present relative high errors It can be vanish or at least diminish using high resolution

just for diameter but not for perimeter that keep the error as big as initially Johansson

and Vall (2011) obtain similar results when 3 different resolutions were used in the

same particle obtaining an unstable output for those termsquantities that involve the

perimeter Thus all quantities relating the perimeter should be treated with care

5 EFFECT OF SHAPE ON SOIL PROPERTIES

51 INTRODUCTION

In laboratory test on the effect on particle size on basic properties has been

investigated in several studies this relation has been discussed and various

mechanisms had been proposed to explain the behaviour of the soil in dependency

also with the shape Basically there are two mechanisms proposed The arrangement

of particles and the inter-particle contact (Santamarina and Cho 2004) and

subsequence breakage

The arrangement of particles

Arrangement of the particles can be presented in three different forms loose dense

and critical this arrangement determines the soil properties (eg density increase with

more dense arrangement) Loose and dense states are easy understandable when

figure 31 is explained while in the upper part of the figure the particles are arranged

using the minimum space needed in the lower part a span is created using the flaky

particle as a bridge this phenomena is known as ldquobridgingrdquo Bridging can produce

different geotechnical results when just the shape of the particle is changed eg void

ratio (Santamarina and Cho 2004) Particles are able to rearrange this could be done

applying pressure (energy) to the soil the pressure (energy) will create such forces

that soil particles will rotate and move (see figure 34) finishing in a more dense state

26

A loose soil will contract in volume on shearing and may not develop any peak

strength (figure 32 left) In this case the shear strength will increase gradually until

the residual shear strength is revealed once the soil has ceased contracting in volume

A dense soil may contract slightly (figure 32 right) before granular interlock prevents

further contraction (granular interlock is dependent on the shape of the grains and

their initial packing arrangement) In order to continue shearing once granular

interlock has occurred the soil must dilate (expand in volume) As additional shear

force is required to dilate the soil a peak shear strength occurs (figure 32 left) Once

this peak shear strength caused by dilation has been overcome through continued

shearing the resistance provided by the soil to the applied shear stress reduces

(termed strain softening) Strain softening will continue until no further changes in

volume of the soil occur on continued shearing Peak shear strengths are also

observed in overconsolidated clays where the natural fabric of the soil must be

destroyed prior to reaching constant volume shearing Other effects that result in peak

strengths include cementation and bonding of particles The distinctive shear strength

called the critical state is identified where the soil undergoing shear does so at a

constant volume (Schofield and Wroth 1968)

The inter-particle contact

For frictional soil ie coarse grained soil the friction between particles is the

dominating factor for strength Materials usually consisting of coarse grains (diameter

Figure 31 Bridging effect when flaky particles are combined in the bulk material (Santamarina and

Cho 2004)

Figure 32 The left part of the figure show a typical behaviour of loose and dense material over shear stress

while at the right the figures illustrate the typical volume changes

27

gt 006mm) behave as a frictional soil it means that the strength of coarse soils (silt

sand gravel etc) comes from an inter-particle mechanical friction thus ideally they

do not have traction strength In figure 33 the inter-particle contact is illustrated here

the pressure (P) is applied and two more components are found the normal load (N)

and the tangential load (T) described as the friction coefficient (μF) The forces stand

in equilibrium (Johansson and Vall 2011)

When particles equilibrium is disturbed (friction coefficient is not enough to keep

particles unmoved) the rotation is imminent and it is necessary in order to compact

the soil in figure 34 can be seen that the arrangement is a fact that inhibit or allow this

rotation and the shape in the 3 different scales are also factors because the more

spherical andor more rounded andor less roughness more easy is the rotation

(Santamarina and Cho 2004)

Breakage

Breakage is a side effect of the inter-particle contact and rotation when pressure

exceed the rock strength it can happened when the particles are tight together and

there is not enough space to rotate it is more obvious in angular particles (mesh form)

or as in figure 31 where the flaky particle ldquobridgingrdquo is not able to rotate but it can

brake by the pressure increase Yoginder et al (1985) notice that the angular particle

break during his experiments and they turn more rounded changing the original size

and form configuration at the same time there was a soil properties loosening

Figure 33 Inter-particle contact and forces acting (Axelsson 1998)

Figure 34 Rotation inhibition by the particles compaction or low void ratio (Santamarina and Cho 2004)

28

52 INFLUENCE OF SIZE AND SHAPE

Wenworth (1922a) and Pellegrino (1965) among others suggest that agent transport of

the rocks (rigor of transport temperature and moisture changes etc) determine its

shape but also the particle genesis itself (rock structure mineralogy hardness etc) It

is not possible to determine the shape of the particles based on the agent transport or

genesis but generally a shape behaviour is expected according to Mitchell and Soga

(2005) specially when the particle size is in the clay size (gt2μm) The shapes of the

most common clay minerals are platy (figure 35) with some exceptions (eg

halloysite occurs as tubes kaolinite are large thick and stiff Smectites are composed

of small very thin and filmy particles Illites are intermediate between kaolinite and

smectite and attapulgite occurs in lathlike particle shapes) Some clay minerals

photographs are presented in figure 35

Figure 35 Clay mineral shape a) hallosite b) Kaoline c) Smactites d) Illites and e) attapulgite (Modified

from Mitchell and Soga 2005)

Figure 36 Particle size range in soils Generally the particles of clay size are plate shaped (Mitchell and

Soga 2005)

a) b) c)

e) d)

29

53 VOID RATIO AND POROSITY

The void ratio (e) is the ratio of the volume of voids to the volume of solid it is

defined by the equation

Porosity (n) is the ratio of the volume of voids to the total volume of the soil it is

represented by the equation

Holubec and DrsquoAppolonia (1973) found a relation between the void ratio and

sphericity (referred in the paper as coefficient of angularity ratio of particle surface

and equivalent sphere surface) their results show that the maximum and the minimum

void ratio increases as the shpericity decreases In this study the surface was obtained

for an indirect method based on the permeability developed by Hoffman in 1959

described in the same document Rouseacute et al (2008) defined the roundness as

Wadell (1935) and he found it as an important factor controlling the minimum and

maximum void ratios Some other authors as Youd (1973) and Cho et al (2006)

conclude the same minimum and maximum void ratios increase when sphericity and

roundness decrease Another interesting result (all above authors) was the bigger

influence of the form (sphericity circularity) and roundness on the maximum void

ratio The change of the maximum void ratio is more pronounced than the change of

the minimum void ratio when the form and roundness changes (See figure 39)

Particles arrangement and interlocking are probably the factor that controls the void

ratio bridge effect permit the existence of void among the particles while interlocking

allowed the particles to form arches avoiding the possibility to rotate and stay in a

more stable configuration eg as it happens with marbles

Figures 36 37 and 38 shows proposed empirical relationships between void ratio and

shape from tables 5 and 6 (graphically the scale goes from 0 to 1 when cero mean

high angularity shpericity or circularity and one means low angularity circularity or

sphericity) Holubec and DrsquoAppolonia (1973) data was taken to obtain a power curve

and describe a tendency Santamarina and Cho (2004) show Youd equations in the

original paper Youd (1973) never presented the equation but it is easy to use the

information to draw a trend

The graphics presented in this document (figures 36 37 and 38) must be used with

certain reserves due the fact that the original data was modified in order to fit all

information in one graphic what the figures shows is just the general trend of the

behaviourrsquos material regarding on the shape If more accurate description and

information is required the author recommends consulting the reference data In the

same way equations from Holubec and DrsquoApollonia (1973) and Youd (1973) were not

presented by the authors but the use of the information was taken in order to build up

those equations on tables 6 and 7

S

V

V

V

= e

V

V

=nV

(45)

(46)

30

Table 6 Minimum void ratio equations regarding on the quantity (Ψ for sphericity C for circularity R

for roundness SF for Sukumaran shape factor and AF for Sukumaran angularity factor)

EQUATION NUMBER REFERENCE

Figure 34 (left)

4340

minΨ45490e =

47

Holubec amp DrsquoAppolonia 1973 (Ψ

was obtained using equation 2)

SF06340

mine021903180e +=

48

Sukumaran amp Ashmawy 2001 (SF

obtained using equation 21)

C05101emin

= 49

Cho etal 2006 (C obtained using

figure 12)

Figure 34 (right)

1

minR08203590e +=

50

Youd 1973 (R obtained from figure

11 and table 3)

R34080emin

= 51

Cho et al 2006 (R obtained using

figure 12)

1

minR05104330e +=

52

Rouseacute et al 2008 (R obtained by

equation 21)

AF02330

mine372004160e +=

53

Sukumaran amp Ashmawy 2001 (AF

obtained using equation 37)

Table 7 Maximum void ratio equations regarding on the quantity (Ψ for sphericity C for circularity R

for roundness SF for Sukumaran shape factor and AF for Sukumaran angularity factor)

EQUATION NUMBER REFERENCE

Figure 35 (left)

51520

max Ψ61120e = 54

Holubec and DrsquoAppolonia 1973 (Ψ

was obtained using equation 2)

SF1190

max e0016907180e += 55

Sukumaran amp Ashmawy 2001 (SF

obtained using equation 21)

C86061emax = 56

Cho etal 2006 (C obtained using

figure 12)

Figure 35 (right)

1

max R1505540e += 57

Youd 1973 (R obtained from figure

11 and table 3)

R62031emax= 58

Cho et al 2006 (R obtained using

figure 12)

1

max R107106150e += 59

Rouseacute et al 2008 (R obtained by

equation 21)

AF0530

max e12506090e += 60

Sukumaran amp Ashmawy 2001 (AF

obtained using equation 37)

Comparing figures 37 and 38 (minimum and maximum void ratio) it can be seen on

the right scheme of both figures 37 and 38 (when the factor is roundnessangularity)

that all the empirical relations has a common initial point close to 1 (it means that

particles are well rounded) while this common agreement disappear when the

roundness factor decreases (when the particles become more angular) Same figures

(37 and 38) on the left graphs (when the factor is sphericitycircularityshape) do not

present the same behaviour in fact there is more disperse initial point close to 1(when

the particles tend to be more sphericalcircular)

31

In Figure 39 the Δe (emax-emin) has been plotted to show how the maximum void ratio

and the minimum void ratio has different rate change when the particle shape

changes Maximum void ratio increases more than minimum void ratio when the

particle shape becomes less spherical andor more angular Comparing figure 39 left

and right graphics it can be seen that right present a common initial point when the

quantity (roundnessangularity) is close to one while in the left graphic the initial

point is more disperse Both ending points in both graphics (close to zero) are

dispersed

Figures 37 38 and 39 present the same behaviour right graphics (when the factor is

roundness angularity) in each figure have an initial common point while the left

graphics do not (when the factor is sphericity circularity shape)

Figure 37 Minimum void ratio based upon the relation of shape factor proposed by the authors indicated

in the figure

Figure 38 Maximum void ratio based upon the relation of shape factor proposed by the authors indicated

in the figure

04

06

08

1

12

14

16

18

2

005

015

025

035

045

055

065

075

085

095

Factor (roundness angularity)

min

imu

m v

oid

rati

o

Youd 1973 roundness

Rouse 2008 roundness

Cho 2006 roundness

Sukumaran 2001 AF

03

04

05

06

07

08

09

1

11

12

13

05

015

025

035

045

055

065

075

085

095

Factor (sphericity circularity shape)

min

imu

m v

oid

rati

oHolubec 1973 sphericity

Cho 2006 circularity

Sukumara 2001 SF

05

07

09

11

13

15

17

19

21

00

150

250

350

450

550

650

750

850

95

Factor (sphericity circularity shape)

Maxim

um

vo

id r

ati

o

Holubec 1973 sphericity

Cho 2006 circularity

Sukumara 2001 SF

05

1

15

2

25

3

35

005

015

025

035

045

055

065

075

085

095

Factor (roundness angularity)

Maxim

um

vo

id r

ati

o

Youd 1973 roundness

Rouse 2008 roundness

Cho 2006 roundness

Sukumaran 2001 AF

32

54 ANGLE OF REPOSE

The angle of repose of a granular material is the steepest angle of descent or dip of the

slope relative to the horizontal plane when material on the slope face is on the verge

of sliding as show in figure 40

According to Qazi (1975) there are five types of forces which may act between the

particles in soils

1 Force of friction between the particles

2 Force due to presence of absorbed gas andor moisture of particle

3 Mechanical forces caused by interlocking of particles of irregular shape

4 Electrostatic forces arising from friction between the particles themselves and

the surface with which they come in contact

5 Cohesion forces operating between neighbouring particles

Rouseacute et al (2008) found a decrease of angle of repose with increase roundness

based upon ASTM C1444 test (Standard Test Method for Measuring the Angle of

Repose of Free-Flowing Mold Powders) The method consist in pouring sand on a

surface cover by paper trough a funnel of specific dimensions (the nozzle diameter

depend on the sandrsquos particle size) from an altitude of 15 inches (381 mm) The sand

is release from the funnel until the peak of the cone formed by the sand stops the flow

The repose angle is obtained with the equation

H represent the 15 inches D and d represent the diameter of the cone formed by the

sand and the diameter of the funnel respectively

Figure 39 Maximum minus minimum void ratio based upon the relation of shape factor proposed by the

authors indicated in the figure

0

01

02

03

04

05

06

07

08

09

1

005

015

025

035

045

055

065

075

085

095

Factor (sphericity circularity shape)

Maxim

um

- M

inim

um

Vo

id r

ati

oHolubec 1973 sphericity

Cho 2006 circularity

Sukumara 2001 SF

0

02

04

06

08

1

12

14

16

18

005

015

025

035

045

055

065

075

085

095

Factor (roundness angularity)

Maxim

um

- M

inim

um

Vo

id r

ati

o

Youd 1973 roundness

Rouse 2008 roundness

Cho 2006 roundness

Sukumaran 2001 AF

dD

H2

tan=φ1

rep(61)

33

Rouseacute (2008) shows an empirical relation to obtain the angle of repose based on the

roundness of the particles

55 SHEAR STRENGTH

The MohrndashCoulomb failure criterion represents the linear envelope that is obtained

from a plot of the shear strength of a material versus the applied normal stress This

relation is expressed as

where τ is the shear strength σn is the normal stress co is the intercept of the failure

envelope with the τ axis and is the slope of the failure envelope The quantity c is

often called the cohesion and the angle is called the angle of internal friction

Studies show that the internal friction angle (under drained triaxial tests) increases

more rapidly on those materials having higher angularity increasing the relative

density The internal friction angle is a function of the relative density and the particle

shape (Holubec and DrsquoAppolonia 1973)

Chan and Page (1997) found in a study made with dry copper (using different shapes

and sizes ranging from 180 to 106 μm) using a direct shear test (ring share test) that

the internal friction angle increases as the angularity increases

Shinohara et al (2000) did some experiments with steel powder different shapes

using a triaxial cell in the test Shinohara never used the roundness or angularity on

the work but apply the shape factor (relation long axisshort axis) and the results were

that as this relation deviate from factor 1 the internal friction angle increases

The following empirical relations were found in the literature showing the behaviour

of the friction angle (obtained under different conditions)

)tan( noc

Figure 40 Representation of the angle of repose

(63)

(62)

34

Cho et al (2006)

(64)

(R is obtain by comparing the Krumbein chart figure 13)

Rouseacute (2008)

(65)

(66)

(R is defined using Wadell equation 22)

In figure 41 the suggested empirical relations above and lines constructed using

author data from Holubec and DrsquoAppolonia (1973) and Sukumara and Ashmawy

(2001) are plotted together to display the general trend on the particle shape and

friction angle relation Sukumaran reports two lines one based on the shape factor

(SF) and the second referring the angularity factor (AF) Sukumaran performed the

tests at constant volume

The scale used for Holubec and DrsquoAppolonia (1973) have lower and upper limits of 1

and 2 respectively (angularity form) and a scale change was applied to be able to

presented in the actual figure 41 As in the previous section (52) the author

recommend to use the original data from the references due that the figure just follows

the general trend of the behaviourrsquos particle regarding on the shape

Figure 41 The changes on the internal friction angle shows a general increase when the particle roundness

becomes angular or in the case of Sakamuran less spheric (Shape factor SF)

35

Barton and Kjaernsli (1981) suggested a model (equation 67) to predict the peak

friction angle (φrsquo) based upon numerous trixial and direct shear data tests

where

Se equivalent strength of particle

Re equivalent roughness of particle

φb basic friction angle (obtained from basic tilting test)

σn normal load

The information required for the model is (1) the uniaxial compressive strength of the

rock (2) the d50 particle size (mesh size where 50 of the particles pass through)

required to define Se (figure 42) (3) the degree of particle roundness and (4) the

porosity following compaction All data can be estimated by simple index tests

Barton and Kjaernsli (1981) suggest that particle size and sample scale has an effect

on the friction angle and includes them to obtain the equivalent strength (Se) figure 42

shows the method to obtain this value Compressive strength (σc) was chosen to be the

factor affecting the scale because micro fractures influence this property while

samples are bigger more micro fractures contain and its compressive strength reduces

The equivalent roughness is obtain using figure 43 where is required to know the

porosity (n) and the origin of the particles (a small chart is provided in the same figure

to compare the particles profile)

b

n

ee

SLogR

Figure 42 Method of estimating Equivalent Strength (Se) of rockfill based on uniaxial compressive strength

(σc ) and d50 particle size (Barton amp Kjaernsli 1981)

(67)

36

56 SEDIMENTATION PROPERTIES

A particle released in a less dense Newtonian fluid initially accelerate trough the fluid

due to the gravity Resistances to deformation of the fluid transmitted to the particle

surface drag generate forces that act to resist the particle motion The force due to the

weight (Fw) can be written as

Where ρp ρ are density of the particle and fluid (water) respectively g is the

gravitational force and Vp is the volume of the particle

And the resistance force (FD) is

Where CD is the dimensionless drag coefficient W is the weight of the particle and A

is the cross section area

Particlersquos shape has been assumed to be spherical when equations are applied on the

settling velocity Correlation deviates when particle shape departs from spherical form

Figure 43 Method of estimating Equivalent Roughness (Roe) based on porosity of rockfill

origin material degree of roundedness and smoothness of particle (Barton amp Kjaernsli 1981)

PPW ρ)gV(ρF

A2

WρCF

2

DD

(68)

(69)

37

(Dietrich 1982) and it is known that natural particles depart from spherical form

thus it is evident that this departure would have consequences

The below equation is proposed to account the shape (in this case the Corey shape

factor equation 8) in the settling velocity (Jimenez and Madsen 2003)

Jimenez and Madsen (2003) Dietrich (1982) Briggs and McCulloch (1962) and

others were working in the hydraulic shape of particles to solve problems as sediment

transport It is obvious that the equation presented and the researcherrsquos investigation

works under certain conditions (eg grain size between 0063-1 mm)

Dietrich (1982) suggests an empirical relation that accounts settling velocity size

density shape and roundness of a particle

R1 R2 and R3 are fitted equations for size and density shape and roundness

respectively

57 HYDRAULIC CONDUCTIVITY PERMEABILITY

Darcyrsquos Law Permeability is one component of Darcyrsquos law Darcys law is a simple

proportional relationship between the instantaneous discharge rate through a porous

medium the viscosity of the fluid and the pressure drop

The total velocity Ve is equal to the product of the permeability of the medium

(porous media) k the pressure drop ∆p all divided by the viscosity μ (Muskat

1937)

Darcys law is only valid for slow viscous flow most groundwater flow cases fall in

this category Typically Darcyrsquos law is valid at any flow with laminar flow (see figure

44)

Reynoldrsquos number (Laminar and turbulent Flow) Typically any laminar flow is

considered to have a Reynoldrsquos number less than one and it would be valid to apply

Darcys law Experimental tests have shown that flow regimes with Reynolds numbers

1

ND

S

S

ZY

gd1s

WW

NDN

gd)1s(4

dS

2R1R

3 10RW

pk

Ve

(70)

(71)

(72)

(73)

38

up to 10 may still be Darcian (laminar flow) as in the case of groundwater flow The

Reynolds number (a dimensionless parameter) for porous media flow is typically

expressed as

where ρ is the density of water (units of mass per volume) υ is the specific discharge

(with units of length per time) d is a representative average grain diameter for the

porous media (often taken as the 30 passing size from a grain size analysis using

sieves - with units of length) and μ is the viscosity of the fluid (Muskat 1937)

Shape effects Permeability as Head and Epps (2011) suggested is affected by the

shape and texture of soil grains Elongated or irregular particles create flow paths

which are more tortuous than those spherical particles Particles with a rough surface

texture provide more frictional resistance to flow Both effects tend to reduce the

water flow through the soil

Kozeny-Carman empirical relation accounts for the dependency of permeability on

void ratio in uniformly graded sands serious discrepancies are found when it is

applied to clays due the lack of uniform pores (Mitchell and Soga 2005)

There are various formulations of the Kozeny-Carman equation one published by

Head and Epps (2011) takes the void ratio e the specific surface area Ss and an

angularity factor F into account of permeability k

The angularity factor F considers the shape of the particles and ranges from 11 for

rounded grains 125 for sub rounded to 14 for angular particles The specific surface

Ss is defined as

d1 and d2 represent the maximum and minimum size particle in mm

Kane amp Sternheim (1988) suggest that the inclusion of the shape factor (F) has

probably the background on the Reynolds number due this factor is dependent

significantly on the shape of the obstacles and Reynolds number determines the

presence of laminar or turbulent flow Figure 44 show how the laminar flow has low

energy dissipation while turbulent flow (eg the roughness and path tortuosity) has

high energy dissipation

e1

e

FSs

2k

3

2

dRe

21

6

ddSs

(74)

(75)

(76)

39

According to Nearing and Parker (1994) the amount of soil detached during laminar

and turbulent flow is dependent on each soil and also greater on turbulent flow due the

greater shear strength generated during this kind of flow this could suggest the

greater erosion when turbulent flow is present

58 LIQUEFACTION

Soil liquefaction is a phenomenon in which soil loses much of its strength or stiffness

for a generally short time by earthquake shaking or other rapid loading Static and

dynamic liquefactions occur been the second one the most regular known

Liquefaction often occurs in saturated soils that is soils in which the space between

individual particles is completely filled with water This water exerts a pressure on the

soil particles that influences how tightly the particles themselves are pressed together

Shaking or other rapid loading can cause the water pressure to increase to the point

where the soil particles can readily move with respect to each other (Jefferies and

Been 2000)

Jefferies and Been (2000) state that it is clear that minor variation in intrinsic

properties of sand have major influence on the critical state These might be variations

on grain shape mineralogy grain size distribution surface roughness of grains etc

Yoginder et al (1985) found that substantial decrease on liquefaction resistance

occur with increase in confining pressure for rounded and angular sands (1600 kPa)

also rounded sands show an rapidly build up of resistance against liquefaction with

increasing density while angular tailing sand in contrast show such rapid increase

only at low confining pressures At low confining pressure angular material is more

resistant to liquefaction Probably the breakage of the corners on the angular particles

in tailings is ruling the lost in resistance at high confining pressures (sieve analysis

Figure 44 The figure show the extremes of flow behaviour First turbulent conditions where the flow is

essentially random and unpredictable and second the well defined Laminar flow conditions

40

after test identify the breakage of angular particles while on rounded particles the

sieve analysis was practically the same)

59 GROUNDWATER AND SEEPAGE MODELLING

In groundwater flow the particlersquos shape affects the soilrsquos pore size distribution

hence the flow characteristics (Sperry and Peirce 1995) Tortuosity and permeability

(also see section 57) are two significant macroscopic parameters of granular medium

that affect the passing flow (Hayati et al 2012) Current models incorporating the

effects of particle shape have failed to consider irregular particles such as those that

would prevail in a natural porous medium (Sperry and Peirce 1995)

Hayati et al (2012) suggested based on his results that tortuosity effect converge

when the porosity increases indicating that the shape have dominance at low and mid

porosity ranges

Sperry and Peirce (1995) research conclusions suggest that particle size and porosity

are more important predictors for hydraulic conductivity explaining the 69 of the

variability but particle shape appears to be the next most important This however

apparently comprises particles larger than 295-351 μm Differences for particle size

295-351 μm and smaller are not detectable Another interesting result in the research

was the interaction effect of the particle size and particle shape It suggests a different

packing configuration for particles of the same shape but different size (scale

dependent)

6 DISCUSSION

61 TERMS QUANTITIES AND DEFINITIONS

In order to describe the particle shape in detail there are a number of terms quantities

and definitions (qualitative and quantitative) used in the literature (eg Wadell 1932

1934 Krumbein 1941 Sneed amp Folk 1958) All mathematical definitions

(quantitatives) are models used to simplify the complexity of shape description Some

authors (Mitchell amp Soga 2005 Arasan et al 2010) are using three sub-quantities

one and each describing the shape but at different scales The terms are

morphologyform roundness and surface texture (figure 1) The three sub-quantities

are probably the best way to classify and describe a particle because not a single

definition can interpret the whole morphology Common language is needed when

descriptors are explained and these three scales represent an option It is evident in

the reviewed literature that many of the shape descriptors are presented with the same

name but also that there is not a clear meaning on what this descriptor defines eg

when there is no upper limit in the roundness does it means that the angularity never

ends Could they be more and more angular Probably they could be on theory but

not in reality

41

62 PROPERTIES

Trough various articlersquos review done in the present investigation it is recognized that

the particlersquos shape has an effect on the material properties among these are

1 Porosity (Tickell 1938 Fraser 1935 Kolbuszewski 1948) and void ratio

(Cho et al 2006 Shergold 1953 Rouseacute et al 2008 Santamarina and Cho

2004)

2 Permeability (Witt and Brauns 1983)

3 Internal friction angle (Shinohara et al 2000 Chan and Page 1997

Cheshomi et al 2009)

4 Density (Youd 1973 Holubec and DrsquoAppolonia 1973)

5 Drag coefficient Hydraulics (Briggs and McCulloch 1962)

In Table 5 is a short resume of the properties and shape effect found in peer review

articles trough different journals Most of the reviewed articles based its research on

uniform graded sands

Table 8 Compilation of properties influenced by particle shape

Repose

angle

Friction

angle

Porosity and

Void ratio Density Permeability

Settling velocity

Drag coefficient Deformation

Sphericity (3D)shape factor

NI x x x x x x

Circularity (2D)

NI x x x x NI NI

Roundness x x x x NI NI x

x influence

NI no information available

Shape of particles has an effect on the arrangement producing bridging or avoiding

the rotation of the particles and the resulting geotechnical property is affected eg

including flaky particles can result in a higher void ratio due the bridging effect

(Santamarina and Cho 2004) and depending on the loads even the size distribution is

changed due the breakage (Yoginder et al 1985) in similar way angular particles

produce higher void ratio due the avoided possibility of the particles to rotate and

compact

The influence of the chosen shape descriptor appears in this review to have minor

influence on the soil properties in the reviewed studies except on the void ratio and

the friction angle Influence of particle shape in some cases is hider by other factors

(eg size distribution) also the particle shape probably does not have influence when

particle size is in the clay order (eg hydraulic conductivity) the reason could be due

to forces as electrostatic or capillarity become more important at this level

Among the shape descriptors some are chosen more often in literature (eg aspect

ratio) there is no apparent scientific basis to use it (probably due to the simplicity of

the measurement it becomes one of the most use) but there are still some other

descriptors that may or may not show better correlation with the soil properties

Instead empirical relations had been developed regarding roundness or shape to

describe the soil behaviour it is clear that the mechanism behind the results is still not

completely understood

42

There is necessity to define the best(s) shape descriptor(s) to be used for particular

geotechnical properties

63 IMAGE ANALYSIS

Many image analysis techniques had been used to describe the particle shape eg

Fourier analysis fractal dimension tomography etc (Hyslip and Vallejo 1997) but

there is not agreement on the usage or conclusion to ensure the best particle descriptor

for geotechnical applications

There are several shape descriptors and also various techniques to capture the

particles profile (3-dimensions 3-dimension orthogonal and 2-dimensions) Each

technique presents advantages and disadvantages 3-dimensions is probably the

technique that provide more information about the particle shape but the precision

also lies in the resolution the equipment required to perform such capture could be

more or less sophisticated (scanning particles laying down in one position and later

move to complete the scanning or just falling down particles to scan it in one step)

3-dimensions orthogonal this technique use less sophisticated equipment (compare

with the previous technique) but its use is limited to particles over 1cm also

information between the orthogonal pictures is not capture 2-dimensions require non

sophisticated equipment but at the same time the shape information diminish compare

with the previous due the fact that it is possible to determine only the outline as the

particle measurements are performed in 2-dimensions it is presumed that they will lie

with its shortest axis perpendicular to the laying surface when they are flat but when

the particle tends to have more or less similar axis the laying could be random

Advantages on the use of image analysis are clear there is not subjectivity because it

is possible to obtain same result over the same images Electronic files do not loose

resolution and it is important when collaboration among distant work places is done

files can be send with the entire confidence and knowing that file properties has not

been changed Technology evolutions allowed to work with more information and it

also applies to the image processing area were the time consumed has been shortened

(more images processed in less time)

One important aspect in image analysis is the used resolution in the analysis due the

fact that there are measurements dependent and independent on resolution Thus

those dependent measurements should be avoided due the error included when they

are applied or avoid low resolution to increase the reliability Among these

parameters length is the principal parameter that is influences by resolution (eg

perimeter diameter axis etc) Resolution also has another aspect with two faces

quality versus capacity more resolution (quality) means more storage space a

minimum resolution to obtain reasonable and reliable data must be known but it

depend on each particular application

43

64 APPLICATIONS

Quantify changes in particles in the authorrsquos thought is one of the future applications

due the non-invasive methods of taking photographs in the surface of the damrsquos slope

rail road ballast or roads Sampling of the material and comparing with previous

results could show volume (3D analysis) or area (2D analysis) loss of the particles as

well as the form roundness and roughness This is important when it has been

suggested that a soil or rock embankment decrees their stability properties (eg

internal friction angle) with the loss of sphericity roundness or roughness

Seepage stock piling groundwater etc should try to include the particle shape while

modelling seepage requires grading material to not allow particles move due the

water pressure but in angular materials as it is known the void ratio is great than the

rounded soil it means the space and the possibilities for the small particles to move

are greater stock piling could be modelled incorporating the particle shape to

determine the binrsquos capacity when particle shape changes (void ratio changes when

particle shape changes) Modelling requires all information available and the

understanding of the principles that apply

Industry is actually using the particle shape to understand the soil behaviour and

transform processes into practical and economic image analysis has been included in

the quality control to determine particle shape and size because the advantages it

brings eg the acquisition of the sieving curve for pellets using digital images taken

from conveyor this allows to have the information in a short period of time with a

similar result at least enough from the practical point of view as the traditional

sieving

7 CONCLUSIONS

The conclusions of this literature review are

It has been shown that particle shape has influence on the soil behaviour

despite of partial knowledge of the mechanism behind Understanding of the

particle shape and its influence needs to be accomplished

A common language needs to be built up to standardize the meaning on

geotechnical field that involve the particle shape General relationships

between shape and properties should be developed

Based on this review it is not clear which is the best descriptor to use in

geotechnical engineering affecting he related shape to properties Instead of a

couple of standards there is no shape descriptor in geotechnical field fully

accepted

Image analysis tool is objective make the results repeatable obtain fast results

and work with more amount of information

44

Resolution needs to be taken in consideration when image analysis is been

carried out because the effects could be considerable Resolution must be set

according to the necessities Parameters as perimeter can be affected by

resolution

There are examples where particle shape has been incorporated in industries

related to geotechnical engineering eg in the ballast and asphalt industry for

quality control

8 FURTHER WORK

Three main issues have been identified in this review that will be further investigated

the limits of shape descriptors influence of grading and choice of descriptor for

relation to geotechnical properties

Shape descriptors have low and high limits frequently the limits are not the same and

the ability to describe the particlersquos shape is relative The sensitivity of each descriptor

should be compare to apply the most suitable descriptor in each situation

Sieving curve determine the particle size in a granular soil particle shape could differ

in each sieve size There is the necessity to describe the particle shape on each sieve

portion (due to practical issues) and included in the sieve curve Obtain an average

shape in determined sieve size is complicated (due to the possible presence of several

shapes) and to obtain the particle shape on the overall particlersquos size is challenging

how the particle shape should be included

Since several descriptors have been used to determine the shape of the particles and

the relation with the soil properties it is convenient to determine the descriptorrsquos

correlation with the soil properties

9 ACKNOWLEDGMENT

I would like to thanks to Lulearing University of Technology (LTU) the time I had spent

in its facilities and the kind environment it offers and University of Sonora

(UNISON) that has been providing me the financial support and the time to conclude

this journey

10 REFERENCES

Andersson T (2010) Estimating particle size distributions based on machine vision

Doctoral Thesis Departament of Computer Science and Electrical Engineering Lulearing

University of Technology ISSN 1402-1544 ISBN 978-91-7439-186-2

45

Arasan Seracettin Hasiloglu A Samet Akbulut Suat (2010) Shape particle of

natural and crished aggregate using image analysis International Journal of Civil and

Structural Engineering Vol 1 No 2 pp 221-233 ISSN 0970-4399

Aschenbrenner BC (1956) A new method of expressing particle sphericity Journal

of Sedimentary Petrology Vol 26 No 1 pp 15-31

Axelsson K (1998) Introduktion till jordmekaniken jaumlmte jordmateriallaumlran Skrift

984 Lulearing Avdelningen foumlr Geoteknologi Lulearing Tekniska Universitet (In Swedish)

Barton Nick amp Kjaernsli Bjorn (1981) Shear strength of rockfill Journal of the

Geotechnical Engineering Division Proceedings of the American Society of Civil

Engineers (ASCE) Vol 107 No GT7

Barrett P J (1980) The shape of rock particles a critical review Sedimentology

Vol 27 pp 291-303

Blott S J and Pye K (2008) Particle shape a review and new methods of

characterization and classification Sedimentology Vol 55 pp 31-63

Bowman E T Soga K and Drummond W (2001) Particle shape characterization

using Fourier descriptor analysis Geotechnique Vol 51 No 6 pp 545-554

Briggs L I McCulloch D S (1962) Hydraulic shape of sand particles Journal of

Sedimentary Petrology Vol 32 pp 645-656

Chan Leonard C Y and Page Neil W (1997) Particle fractal and load effects on

internal friction in powders Powder Technology Vol 90 pp 259-266

Cheshomi A Fakher A Jones C J F P (2009) A correlation between friction

angle and particle shape metrics in quaternary coarse alluvia Quarterly Journal of

Engineering Geology and Hydrogeology Vol 42 pp 145-155

Cho G Dodds J and Santamarina J C (2006) Particle shape effects on packing

density stiffness and strength Natural and crushed sands Journal of Geotechnical

and Geoenvironmental Engineering May 2006 pp 591-602

Dietrich William E (1982) Settling velocity of natural particles Water Resources

Research Vol 18 No 6 pp 1615-1626

Dobkins J E and Folk R L (1970) Shape development on Tahiti-nui Journal of

Sedimentary Petrology Vol 40 No 2 pp 1167-1203

Folk R L (1955) Student operator error in determining of roundness sphericity and

grain size Journal of Sedimentary Petrology Vol 25 pp 297-301

Fernlund J M R (1998) The effect of particle form on sieve analysis A test by

image analysis Engineering Geology Vol 50 No 1-2 pp 111-124

46

Fernlund J M R (2005) Image analysis method for determining 3-D shape of

coarse aggregate Cement and Concrete Research Vol 35 Issue 8 pp 1629-1637

Fernlund J M R Zimmerman Robert and Kragic Danica (2007) Influence of

volumemass on grain-size curves and conversion of image-analysis size to sieve size

Engineering Geology Vol 90 No 3-4 pp 124-137

Fraser H J (1935) Experimental study of the porosity and permeability of clastic

sediments The Journal of Geology Vol 43 pp 910-1010 ISSN 0022-1376

Hayati Ali Nemati Ahmadi Mohammad Mehdi and Mohammadi Soheil (2012)

American Physical Society Physical review E 85 036310 DOI

101103PhysRevE85036310

Hawkins A E (1993) The Shape of Powder-Particle Outlines Wiley New York

Head K H and Epps R J (2011) Manual of soil Laboratory testing Volum II

Permeability shear strength and compressibility test 3rd

edition Whittles Publishing

Scotland UK 3rd

edition

Holubec I and DrsquoAppolonia E (1973) Effect of particle shape on the engineering

properties of granular soils ASTM STP 523 pp 304-318

Hyslip James P Vallejo Luis E (1997) Fractal analysis of the roughness and size

distribution of granular materials Engineering Geology Vol 48 pp 231-244

Janoo Vincent C (1998) Quantification of shape angularity and surface texture of

base course materials US Army Corps of Engineers Cold Region Research and

Engineering Laboratory Special report 98-1

Jefferies Mike and Been Ken (2000) Soil liquefaction A critical state approach

Taylor amp Francis Group London and New York

Jimenez Jose A Madsen Ole S (2003) A simple formula to estimate settling

velocity of natural sediments Journal of Waterway Port Coastal and Ocean

Engineering Vol 129 No 2 pp 70-78

Johansson Jens and Vall Jakob (2011) Jordmaterials kornform Inverkan paring

Geotekniska Egenskaper Beskrivande storheter bestaumlmningsmetoder

Examensarbete Avdelningen foumlr Geoteknologi Institutionen foumlr Samhaumlllsbyggnad

och naturresurser Lulearing Tekniska Universitet Lulearing (In Swedish)

Kane Joseph W and Sternheim Morton M (1988) Physics John Wiley amp Sons Inc

Third edition

Kolbuszewski J (1948) An experimental study of the maximum and minimum

porosities of sands Proceedings of the Second International Conference on Soil

Mechanics and Foundation Engineering Rotterdam June 21 to 30 Sub-section IIb

pp 158-165

47

Krumbein W C and Pettijohn FJ (1938) Manual of sedimentary petrography

Appleton-Century Crofts Inc New York

Krumbein W C (1941) Measurement and geological significance of shape and

roundness of sedimentary particles Journal of Sedimentary Petrology Vol 11 No 2

pp 64-72

Krumbein W C and Sloss L L (1963) Stratigraphy and Sedimentation 2nd

ed

WH Freeman San Francisco

Kuo Chun-Yi and Freeman Reed B (1998a) Image analysis evaluation of

aggregates for asphalt concrete mixtures Transportation Research Record Vol 1615

pp 65-71

Kuo Chun-Yi Rollings Raymond and Lynch Larry N (1998b) Morphological

study of coarse aggregates using image analysis Journal of Materials in Civil

Engineering Vol 10 No 3 pp 135-142

Lanaro F Tolppanen P (2002) 3D characterization of coarse aggregates

Engineering Geology Vol 65 pp 17-30

Lees G (1964a) A new method for determining the angularity of particles

Sedimentology Vol 3 pp 2-21

Lees G (1964b) The measurement of particle shape and its influence in engineering

materials British Granite Whinstone Federation Vol 4 No 2 pp 17-38

Matsushima Takashi Saomoto Hidetaka Matsumoto Masaaki Toda Kengo

Yamada Yasuo (2003) Discrete element simulation of an assembly of irregular-

shaped grains Quantitative comparison with experiments 16th ASCE Engineering

Mechanics Conference University of Washington Seattle July 16-18

Mitchell James K and Soga Kenichi (2005) Fundamentals of soil behaviour Third

edition WILEY

Mora C F Kwan A K H Chan H C (1998) Particle size distribution analysis of

coarse aggregate using digital image processing Cement and Concrete Research Vol

28 pp 921-932

Mora C F and Kwan A K H (2000) Sphericity shape factor and convexity

measurement of coarse aggregate for concrete using digital image processing Cement

and Concrete Research Vol 30 No 3 pp 351-358

Muskat Morris (1937) The Flow of fluids through porous media Journal of Applied

Physics Vol 8 pp 274

Nearing M A and Parker S C (1994) Detachment of soil by flowing water under

turbulent and laminar conditions Soil Science Society of American Journal Vol 58

No 6 pp 1612-1614

48

Pan Tongyan Tutumluer Erol Carpenter Samuel H (2006) Effect of coarse

aggregate morphology on permanent deformation behavior of hot mix asphalt Journal

of Transportation Engineering Vol 132 No 7 pp 580-589

Pellegrino A (1965) Geotechnical properties of coarse-grained soils Proceedings

International Conference of Soil Mechanics and Foundation Engineering Vol 1 pp

97-91

Pentland A (1927) A method of measuring the angularity of sands MAG MN AL

Acta Eng Dom Transaction of the Royal Society of Canada Vol 21 Ser3xciii

Persson Anna-Lena (1998) Image analysis of shape and size of fine aggregates

Engineering Geology Vol 50 pp 177-186

Powers M C (1953) A new roundness scale for sedimentary particles Journal of

Sedimentary Petrology Vol 23 No 2 pp 117-119

Pye W and Pye M (1943) Sphericity determination of pebbles and grains Journal

of Sedimentary Petrology Vol 13 No 1 pp 28-34

Qazi M A (1975) Flow properties of granular masses A review on the angle of

repose The Arabian Journal for Science and Engineering Vol 1 No 2

Quiroga Pedro Nel and Fowle David W (2003) The effects of aggregate

characteristics on the performance of portland cement concrete Report ICAR 104-1F

Project number 104 International Center for Aggregates Research University of

Texas

Riley N A (1941) Projection sphericity Journal of Sedimentary Petrology Vol 11

No 2 pp 94-97

Rouseacute P C Fennin R J and Shuttle D A (2008) Influence of roundness on the

void ratio and strength of uniform sand Geotechnique Vol 58 No 3 227-231

Santamarina J C and Cho G C (2004) Soil behaviour The role of particle shape

Proceedings Skempton Conf London

Schofield and Wroth (1968) Critical state soil mechanics McGraw Hill

Shaumlfer Michael (2002) Digital optics Some remarks on the accuracy of particle

image analysis Particle amp Particle Systems Characterization Vol 19 No 3 pp 158-

168

Shergold F A (1953) The percentage of voids in compacted gravel as a measure of

its angularity Magazine of Concrete Research Vol 5 No 13 pp 3-10

Shinohara Kunio Oida Mikihiro Golman Boris (2000) Effect of particle shape on

angle of internal friction by triaxial compression test Powder Technology Vol 107

pp131-136

49

Skredcommisionen (1995) Ingenjoumlrsvetenskapsakademinen rapport 395 Linkoumlping

1995

Sneed E D and Folk R L (1958) Pebbles in the Colorado river Texas A study in

particle morphogenesis Journal of Geology Vol 66 pp 114-150

Sperry James M and Peirce J Jeffrey (1995) A model for estimating the hydraulic

conductivity of granular material based on grain shape grain size and porosity

Ground Water Vol 33 No 6 pp 892-898

Sukumaran B and Ashmawy A K (2001) Quantitative characterisation of the

geometry of discrete particles Geotechnique Vol 51 No 7 pp 619-627

Szaacutedeczy-Kardoss E Von (1933) Die bistimmung der abrollungsgrades Geologie

und palaumlontologie Vol 34B pp 389-401 (in German)

Teller J T (1976) Equantcy versus sphericity Sedimentology Vol 23 pp 427-428

Tickell F G (1938) Effect of the angularity of grain on porosity and permeability

bulletin of the American Association of Petroleum Geologist Vol 22 pp 1272-1274

Tutumluer E Huang H Hashash Y Ghaboussi J (2006) Aggregate shape effects

on ballast tamping and railroad track lateral stability AREMA 2006 Annual

Conference Louisville KY

Wadell H (1932) ldquoVolume Shape and roundness of rock particlesrdquo Journal of

Geology Vol 40 pp 443-451

Wadell H (1933) Sphericity and roundness of rock Particles Journal of Geology

Vol 41 No 3 pp 310ndash331

Wadell H (1934) Shape determination of large sedimental rock fragments

The Pan-American Geologist Vol 61 pp 187-220

Wadell H (1935) ldquoVolume shape and roundness of quartz particlesrdquo Journal of

Geology Vol 43 pp 250-279

Wentworth W C (1922a) The shape of beach pebbles Washington US Geological

Survey Bulletin Vol 131C pp 75-83

Wentworth W C (1922b) A method of measuring and plotting the shape of pebbles

Washington US Geological Survey Bulletin Vol 730C pp 91-114

Wentworth W C (1933) The shape of rock particle A discussion Journal of

Geology Vol 41 pp 306-309

Witt K J Brauns J (1983) Permeability-Anisotropy due to particle shape Journal

of Geotechnical Engineering Vol 109 No 9 pp 1181-1187

12

Wadell (1935) describes his methodology calling it total degree or roundness to

obtain the roundness of a particle using the average radius of the corners in relation

with the inscribed circle diameter (see figure 11) on the equation

In the same study Wadell (1935) has used the equation

This two last equation shows slightly differences on the results (Wadell 1935)

Powers (1953) also published a graphic scale to illustrate the qualitative measure

(figure 12) It is important to highlight that any comparing chart to describe particle

properties has a high degree of subjectivity Folk (1955) concludes that when charts

are used for classification the risk of getting errors is negligible for sphericity but

large for roundness

N

R

r

Rinmax

r

R

NR

inmax

Figure 10 Form (shape) Roundness and Texture graphical description (Bowman et al 2001)

Figure 11 Wadellrsquos method to estimate the roundness corners radius and inscribed circle

(Hawkins 1993)

(22)

(23)

13

Some authors as Russel amp Taylor in 1937 Pettijohn in 1957 and Powers in 1953

developed a classification based on five and six classes (Hawkins 1993) each one

with its own class limits it is important to denote that the way they measure the

roundness is the developed by Wadell (1935) This classification and class limits are

showed in the table 4

Table 4 Degrees of roundness Wadell Values (Hawkins 1993) NA = no-applicable

Grade terms Russell amp Taylor (1937) Pettijohn (1957) Powers (1953)

Class

limits (R)

Arithmetic

midpoint

Class limits

(R)

Arithmetic midpoint Class

limits (R)

Arithmetic

midpoint

Very angular

NA

NA

NA

NA

012-017

014

Angular

000-015

0075

000-015

0125

017-025

021

Subangular

015-030

0225

015-025

0200

025-035

030

Subrounded

030-050

0400

025-040

0315

035-049

041

Rounded

050-070

0600

040-060

0500

049-070

059

Well rounded

070-100

0800

060-100

0800

070-100

084

Krumbein and Sloss (1963) published a graphical chart easy to determine the

sphericity and roundness parameters using comparison See figure 13 (Cho et al

2006)

Figure 12 A Roundness qualitative scale (Powers 1953)

Figure 13 Sphericity and roundness chart (Cho et al 2006) The roundness equation that appears here in

the chart is the wadellrsquos equation number 22

14

Fischer in 1933 (Hawkins 1993) used a straightforward method to quantify roundness

using a central point in the outline and dividing the outline in angles around this point

that were subtended by the straight or non curved parts of the profile were measured

This is illustrated in figure 14

To express the angularity value Fischer used the ratio of angles standing linear parts

on the outlines and concave respectively

Figure 14 left (A) and right (B) gives a similar angularity of approximately 042

using the above equations (Hawkins 1993)

Wentworth in 1922 used the maximum projection to define the position of the particle

to obtain the outline or contour (Barret 1980) The equation reflects the relation of the

diameter of a circle fitting the sharpest corner and the longest axis plus the shortest

axis c (minimum projection)

Wentworth (Hawkins 1993) expressed the roundness as the ratio of the radius of

curvature of the most convex part and the longest axis plus short axis

Actually these last two equations are the same just expressed in different terms when

the particle is in its maximum projection

Dimensions can be seen on figure 15 L and B represents the mayor axis a and

intermediate axis b The intention is to make difference between the 2 and 3

dimensions (L and B are for 2D as a b and c are for 3D)

deg360

ANG

=R

sumPLA

PLA

CON

ANG

ANGR

2)S(L

DR

M

S

B)4(L

RR CON

Figure 14 Fischerrsquos methods of angularity computation (Hawkins 1993)

A=inscribed circle B=circumscribed circle

(24)

(25)

(26)

(27)

15

Wentworth 1919 has a second way to express the roundness called Shape index

(Barrett 1980) and it relates the sharpest corner and the diameter of a pebble trough

the sharpest corner

Wentworth (1922b) used define the roundness as the ratio of the sharpest corner and

the average radius of the pebble

Cailleux (Barrett 1980) relates the radius of the most convex part and the longest

axis

Kuenen in 1956 show his roundness index (Barrett 1980) between the sharpest corner

and the breath axis

Dobkins amp Folk (1970) used a modified Wentworth roundness with the relation of

sharpest corner and inscribed circle diameters

AVG

CON

R

RR

x

s

D

DR

L2

RR CON

B

DR s

i

s

D

DR

3AVGAVG cbaDR2

Figure 15 Description of L and B axes (Hawkins 1993)

(28)

(29)

(30)

(31)

(32)

(33)

16

Swan in 1974 shows his equation (Barrett 1980) relating the sharpest (or the two

sharpest) corner(s) and inscribed circle diameter

Szadeczsky-Kardoss has his Average roundness of outline (Krumbein and Pettijohn

1938) relating the concave parts perimeter and the actual perimeter

Lees (1964a) developed an opposite definition to roundness it means that he

measures the angularity instead of the roundness and he calls it Degree of angularity

Figure 16 shows the items considered when equation 36 applies as the angles (α)

inscribed circle (Rmax-in) and the distance (x) The main formula is

In order to apply the last equation corners needs to be entered in the formula and each

individual result will add to each other to obtain the final degree of angularity

A roundness index appears on Janoo (1998) Kuo and Freeman (1998a) and Kuo et

al (1998b) it is described as

The last equation is on section 34 also because there is not a general agreement on the

definition furthermore some authors had used to define the roughness this is not the

only equation that has been used trying to define different aspects (sphericity

roundness or roughness) but it is a good example of the misuse of the quantities and

definitions

inmaxR

x)180(R

2P

A4R

i

ss

D

DDR

221

100P

PR CON

Figure 16 Degree of angularity measurement technique (Blot and Pye 2008)

(34)

(35)

(36)

(17)

17

Sukumaran and Ashmawy (2001) present an angularity factor (AF) calculated from

the number of sharpness corners Angles βi required to obtain the angularity factor are

shown in figure 9

Sukumaran and Ashmawy (2001) also suggested use not bigger sampling interval of

N=40 because it is the cut off between angularity factor and surface roughness If so

this equation could be used to describe the roughness

Table 5 General chronological overview of the particle roundness

Aspect Name Author Year Based on

Roundness shape index Wentworth 19191

diameter of sharper corner

shape index Wentworth 1922b sharpest corner and axis

roundness Wentworth 1933 convex parts

Fischer 19332

noncurved parts outline

Fischer 19332

noncurved-streigth parts outline

Average roundness of outline

Szadeczsky-Kardoss 19333

convex parts-perimeter

roundness Wadell 1935 diameter of corners

roundness Wadell 1935 diameter of corners

roundness Russel amp Taylor 19372

class limit table

roundness Krumbein 1941 chart

Cailleux 19471

convex parts

roundness Pettijohn 19494 class limit table

roundness Powers 1953 chart and class limit table

Kuenen 19561

axis-convex corner

roundness Krumbein and Sloss 1963 chart

degree of angularity Lees 1964a corners angles and inscribed circle

Dobkins amp Folk 1970 diameter of sharper corner

Swan 19741

diameter of sharper corners

Angularity factor Sukumaran and

Ashmawy 2001

Segmentation of particles and angles

1) Barret 1980 2) Hawkins 1993 3) Krumbein and Pettijohn 1938 4) Powers 1953

sum

sumsumN

1=i

2

i

2

N

1=i

2

i

2N

1=ii

)ordm180 -circleβ( - )(180ordm x 3

)ordm180-circleβ(-)ordm180 -Particleβ(

= AF (37)

18

36 ROUGHNESS OR SURFACE TEXTURE

A third property called texture appears early in the literature with the sphericity and

roundness properties since then texture property was longed described but it was in

accordance with the authors at that time not measurable

Wright in 1955 developed a method to quantify the surface texture or roughness of

concrete aggregate using studies done on 19 mm stones The test aggregates were first

embedded in a synthetic resin The stones were cut in thin sections The sections

projection was magnified 125 times The unevenness of the surface was traced and the

total length of the trace was measured The length was then compared with an uneven

line drawn as a series of chords (see figure 17) The difference between these two

lines was defined as the roughness factor (Janoo 1998)

However with the advance of technology it has become easier measure the roughness

and here is presented some researcherrsquos ideas how this property should be calculated

One technique used by Janoo (1988) to define the roughness can be seen in figure 18a

and is defined as the ratio between perimeter and convex perimeter

The convex perimeter is obtained using the Feretrsquos box (or diameter) tending a line in

between the touching points that the Feretrsquos box describes each time it is turn (figure

18b)

PER

OC

PR

Figure 17 Measurement method for characterizing the surface texture of an aggregate (Janoo 1998)

a) Convex perimeter (CPER) b) Feret measurement Figure 18 a) Convex perimeter (CPER) b) Feret measurement (modified after Janoo 1998)

(38)

a)

b)

19

Kuo and Freeman (1998a) and Kuo et al (1998b) use the roughness definition as the

ratio perimeter and average diameter

Erosion and dilatation image processing techniques are used to obtain the surface

texture Erosion is a morphological process by which boundary image pixels are

removed from an object surface which leaves the object less dense along the

perimeter or outer boundary Dilatation is the reverse process of erosion and a single

dilatation cycle increases the particle shape or image dimension by adding pixels

around its boundary (Pan etal 2006)

The ldquonrdquo erosion and dilatation cycles are not standardized

Mora and Kwan (2000) used the ldquoconvexity ratio CRrdquo (equation 41) and the ldquofullness

ratio FRrdquo (equation 42) in their investigation they are

The convex area is the area of the minimum convex boundaries circumscribing the

particle This is illustrated in the figure 19 The convex area is obtained in a similar

way as the convex perimeter but in this case the area between the original outline and

the convex perimeter is our convex area

AVG

OD

PR

100A

1AARO

CONo A

AR =

CONo A

AR =

Figure 19 Evaluation of area and convex area (Mora and Kuan 2000)

(39)

(40)

(41)

(42)

20

4 TECHNIQUES IN ORDER TO DETERMINE PARTICLE

SHAPE

41 HAND MEASUREMENT

Hand measurement technique was the first used by obvious reasons in order to

improve the accuracy special devices developed as the ldquosliding rod caliperrdquo used by

Krumbein (1941) it works placing the sample on the sliding road calliper as show

figure 20b the length in different positions can be obtain by using the scale provided

in the handle the ldquoconvexity gagerdquo that was actually used by opticians to measure the

curvature of lenses but easily applicable to the particle shape analysis (Wentworth

1922b) works measuring the movement of the central pivot as figure 20a shows (the

two adjacent pivots are invariable) as many the central pivot moves more is the

curvature or the ldquoSzadeczky-Kardossrsquos apparatusrdquo develop in 1933 that traces the

profile of the rock fragment so the outline traced is then analyzed (Krumbein and

Pettijohn 1938) figure 20c show equipment

Another helpful tool to determine the particle dimensions was the ldquocamera lucidardquo to

project the particlersquos contour over a circle scale appearing in Figure 21 thus it is

possible to measure the particlersquos diameter

a)

c) b)

Figure 20 a) convexity gage used to determine the curvature in particle corners (Wenworth 1922b)

b)sliding rod caliper device to measure the particle axis length (Krumbein 1941) and c)Szadeczky-

Kardoss (1933) apparatus it was utilized to obtain the particle outline

Figure 21 Circle scale used by Wadell (1935) to determine particlersquos diameter and roundness

21

42 SIEVE ANALYSIS

Bar sieving eg according to EN 933-31997 can be used to determine simple large

scale properties By combining mesh geometries the obtained results can be used to

quantify flakiness and elongation index ASTM D4791 (Flat and elongated particles

are defined as those coarse aggregate particles that have a ratio of length to thickness

equal to or greater than a specified value such as 51 The index represents the

percentage on weight of these particles) The method is not suitable for fine materials

This due to the difficulty to get the fine grains passed through the sieve and the great

amount of particles in relation to the area of the sieve (Persson 1998) eg EN 933-

31997 related to flakiness index The test is performed on aggregates with grain size

from 4 mm and up to 63 mm two sieving operations are necessary the first separates

on size fraction and the second use a bar sieve after the first sieving the average

maximum diameter of the particles is obtain and with the second sieving (bar sieving)

the shortest axis diameter is found finally with this two parameters the flakiness

index is determined

There are more standards related with the particle shape (see appendix A) but this

above presented are probably the most known using sieve analysis to determine

particlersquos geometrical properties

Sieve analysis is facing the computers age and image analysis sieving research is

taking place (Andersson 2010 Mora and Kwan 2000 Persson 1998) Industry is

also applying the image analysis sieving with decrees on the testing time compare

with the traditional sieving method An inconvenient of image analysis is the error

due the overlapping or hiding of the particles during the capture process but the

advantages are more compare with disadvantages (Anderson 2010)

43 CHART COMPARISON

Charts developed over the necessity of faster results because the long time consuming

required when measuring each particle

Krumbein (1941) present a comparison roundness chart for pebbles which were

measured by Wadellrsquos method because this property was the most difficult to measure

due to the second order scale that roundness represents (See figure 22)

Figure 22 Krumbein (1941) comparision chart for roundness

22

A qualitative chart by Powers (1953) try to include both (sphericity and roundness)

particlersquos characteristics it was divided on six roundness ranges (very angular

angular sub-angular sub-rounded rounded and well rounded) and two sphericity

series (high and low sphericity) This chart was prepared with photographs to enhance

the reader perspective (See figure 23)

A new chart including sphericity and roundness appear this time it was easier to

handle the two mean properties of particlersquos shape furthermore there was included

the numerical values that eliminated the subjectivity of qualitative description The

chart is based on Wadellrsquos definitions (Krumbein and Sloss 1963) (See figure 24)

Folk (1955) worried about the personrsquos error on the chartrsquos comparison studied the

determination of sphericity and angularity (he used the Powers 1953 comparison

chart) he found that the sphericity determination by chart comparison has a negligible

error while the roundness he concluded it was necessary to carry out a more wide

research due the high variability show by his study

Figure 23 Powers (1953) qualitative shpericity-roundness chart

Figure 24 Sphericity-roundness comparison chart (Krumbein and sloss 1963)

23

44 IMAGE ANALYSIS

Image analysis is a practical method to use for shape classification since it is fast and

can be automated Different techniques appear to process these images among them

are

o Feret Diameter the Feret diameter is the longitude between two parallel lines

this lines can rotate around one particle or outline to define dimensions as it

is shown in figure 25 these method is not a fine descriptor but as it was say

above it is a helpful tool to determine diameters (Janoo 1988)

o Fourier Mathematical Technique It produces mathematical relations that

characterize the profile of individual particles This method favours the

analysis of roughness and textural features for granular soils The problem in

the methodology remains in the re-entrant angles in order to complete the

revolution (Bowman et al 2001) see figure 26

o Fractal Dimension Irregular line at any level of scrutiny is by definition

fractal (Hyslip and Vallejo 1997) Figure 27 shows fractal analysis by the

dividing method The length of the fractal line can be defined as

N

1n

nn0 )nsinbncosa(a)(R

RD1n)(P

Figure 25 Feret measurement technique is defined by two parallel lines turning

around the particle to define the shortest and longest Feret diameter (Janoo 1988)

Figure 26 Fourier technique with two radiuses at one angle (Bowman et al 2001)

(43)

(44)

24

o Orthogonal image analysis This technique is basically the use of two images

orthogonal between them to acquire the three particle dimensions (Fernlund

2005) any of the above techniques can be used in this orthogonal way

o Laser Scanning Technique this kind of laser scanning 3D is one of the most

advanced techniques In figures 28a) we have the laser head scanning the rock

particles the particles have control points in order to keep a reference point

when move them to scan the lower part in figure 28b) we can see the laser

path followed (Lanaro and Tolppanen 2002)

Another technique is the Laser-Aided Tomography (LAT) in this case a laser sheet is

used to obtain the particles surveying (see figure 29) This technique is different and

has special requirements as to use liquid with same refractive index as the particles

particles must let the laser or certain percent of light go through (Matsushima et al

2003)

a) b)

Figure 27 Fractal analysis by the dividing method at different scrutiny scale (Hyslip and Vallejo 1997)

Figure 28 a) Scanning head b) scanning path (Lanaro and Tolppanen 2002)

Figure 30 3D scan completed ready to

use for any further measure

(Matsushima et al 2003)

Figure 29 LAT scaning particles

(Matsushima et al 2003)

25

Both 3D techniques obtain the particle shape that is later used to achieve measures as

we can see in figure 30

All these previous techniques are easily written in codes or scripts to be interpreted in

a digital way obtaining the desired measurement but there are some interesting points

in the image analysis regarding on the errors involve among them are image

resolution and orientation of the particles orientation is not relevant when it is

random and large number of particles are involve resolution have an influence on the

accuracy (Zeidan et al 2007)

When resolution is increase more accuracy is obtain and the object representation

match better with the real form in the other hand more resolution means more

spending on memory and time thus resolution needs to be according with the goal

and precision needed in any work (Schaumlfer 2002)

Schaumlfer (2002) conclude that attributes like length when measuring digital images

present relative high errors It can be vanish or at least diminish using high resolution

just for diameter but not for perimeter that keep the error as big as initially Johansson

and Vall (2011) obtain similar results when 3 different resolutions were used in the

same particle obtaining an unstable output for those termsquantities that involve the

perimeter Thus all quantities relating the perimeter should be treated with care

5 EFFECT OF SHAPE ON SOIL PROPERTIES

51 INTRODUCTION

In laboratory test on the effect on particle size on basic properties has been

investigated in several studies this relation has been discussed and various

mechanisms had been proposed to explain the behaviour of the soil in dependency

also with the shape Basically there are two mechanisms proposed The arrangement

of particles and the inter-particle contact (Santamarina and Cho 2004) and

subsequence breakage

The arrangement of particles

Arrangement of the particles can be presented in three different forms loose dense

and critical this arrangement determines the soil properties (eg density increase with

more dense arrangement) Loose and dense states are easy understandable when

figure 31 is explained while in the upper part of the figure the particles are arranged

using the minimum space needed in the lower part a span is created using the flaky

particle as a bridge this phenomena is known as ldquobridgingrdquo Bridging can produce

different geotechnical results when just the shape of the particle is changed eg void

ratio (Santamarina and Cho 2004) Particles are able to rearrange this could be done

applying pressure (energy) to the soil the pressure (energy) will create such forces

that soil particles will rotate and move (see figure 34) finishing in a more dense state

26

A loose soil will contract in volume on shearing and may not develop any peak

strength (figure 32 left) In this case the shear strength will increase gradually until

the residual shear strength is revealed once the soil has ceased contracting in volume

A dense soil may contract slightly (figure 32 right) before granular interlock prevents

further contraction (granular interlock is dependent on the shape of the grains and

their initial packing arrangement) In order to continue shearing once granular

interlock has occurred the soil must dilate (expand in volume) As additional shear

force is required to dilate the soil a peak shear strength occurs (figure 32 left) Once

this peak shear strength caused by dilation has been overcome through continued

shearing the resistance provided by the soil to the applied shear stress reduces

(termed strain softening) Strain softening will continue until no further changes in

volume of the soil occur on continued shearing Peak shear strengths are also

observed in overconsolidated clays where the natural fabric of the soil must be

destroyed prior to reaching constant volume shearing Other effects that result in peak

strengths include cementation and bonding of particles The distinctive shear strength

called the critical state is identified where the soil undergoing shear does so at a

constant volume (Schofield and Wroth 1968)

The inter-particle contact

For frictional soil ie coarse grained soil the friction between particles is the

dominating factor for strength Materials usually consisting of coarse grains (diameter

Figure 31 Bridging effect when flaky particles are combined in the bulk material (Santamarina and

Cho 2004)

Figure 32 The left part of the figure show a typical behaviour of loose and dense material over shear stress

while at the right the figures illustrate the typical volume changes

27

gt 006mm) behave as a frictional soil it means that the strength of coarse soils (silt

sand gravel etc) comes from an inter-particle mechanical friction thus ideally they

do not have traction strength In figure 33 the inter-particle contact is illustrated here

the pressure (P) is applied and two more components are found the normal load (N)

and the tangential load (T) described as the friction coefficient (μF) The forces stand

in equilibrium (Johansson and Vall 2011)

When particles equilibrium is disturbed (friction coefficient is not enough to keep

particles unmoved) the rotation is imminent and it is necessary in order to compact

the soil in figure 34 can be seen that the arrangement is a fact that inhibit or allow this

rotation and the shape in the 3 different scales are also factors because the more

spherical andor more rounded andor less roughness more easy is the rotation

(Santamarina and Cho 2004)

Breakage

Breakage is a side effect of the inter-particle contact and rotation when pressure

exceed the rock strength it can happened when the particles are tight together and

there is not enough space to rotate it is more obvious in angular particles (mesh form)

or as in figure 31 where the flaky particle ldquobridgingrdquo is not able to rotate but it can

brake by the pressure increase Yoginder et al (1985) notice that the angular particle

break during his experiments and they turn more rounded changing the original size

and form configuration at the same time there was a soil properties loosening

Figure 33 Inter-particle contact and forces acting (Axelsson 1998)

Figure 34 Rotation inhibition by the particles compaction or low void ratio (Santamarina and Cho 2004)

28

52 INFLUENCE OF SIZE AND SHAPE

Wenworth (1922a) and Pellegrino (1965) among others suggest that agent transport of

the rocks (rigor of transport temperature and moisture changes etc) determine its

shape but also the particle genesis itself (rock structure mineralogy hardness etc) It

is not possible to determine the shape of the particles based on the agent transport or

genesis but generally a shape behaviour is expected according to Mitchell and Soga

(2005) specially when the particle size is in the clay size (gt2μm) The shapes of the

most common clay minerals are platy (figure 35) with some exceptions (eg

halloysite occurs as tubes kaolinite are large thick and stiff Smectites are composed

of small very thin and filmy particles Illites are intermediate between kaolinite and

smectite and attapulgite occurs in lathlike particle shapes) Some clay minerals

photographs are presented in figure 35

Figure 35 Clay mineral shape a) hallosite b) Kaoline c) Smactites d) Illites and e) attapulgite (Modified

from Mitchell and Soga 2005)

Figure 36 Particle size range in soils Generally the particles of clay size are plate shaped (Mitchell and

Soga 2005)

a) b) c)

e) d)

29

53 VOID RATIO AND POROSITY

The void ratio (e) is the ratio of the volume of voids to the volume of solid it is

defined by the equation

Porosity (n) is the ratio of the volume of voids to the total volume of the soil it is

represented by the equation

Holubec and DrsquoAppolonia (1973) found a relation between the void ratio and

sphericity (referred in the paper as coefficient of angularity ratio of particle surface

and equivalent sphere surface) their results show that the maximum and the minimum

void ratio increases as the shpericity decreases In this study the surface was obtained

for an indirect method based on the permeability developed by Hoffman in 1959

described in the same document Rouseacute et al (2008) defined the roundness as

Wadell (1935) and he found it as an important factor controlling the minimum and

maximum void ratios Some other authors as Youd (1973) and Cho et al (2006)

conclude the same minimum and maximum void ratios increase when sphericity and

roundness decrease Another interesting result (all above authors) was the bigger

influence of the form (sphericity circularity) and roundness on the maximum void

ratio The change of the maximum void ratio is more pronounced than the change of

the minimum void ratio when the form and roundness changes (See figure 39)

Particles arrangement and interlocking are probably the factor that controls the void

ratio bridge effect permit the existence of void among the particles while interlocking

allowed the particles to form arches avoiding the possibility to rotate and stay in a

more stable configuration eg as it happens with marbles

Figures 36 37 and 38 shows proposed empirical relationships between void ratio and

shape from tables 5 and 6 (graphically the scale goes from 0 to 1 when cero mean

high angularity shpericity or circularity and one means low angularity circularity or

sphericity) Holubec and DrsquoAppolonia (1973) data was taken to obtain a power curve

and describe a tendency Santamarina and Cho (2004) show Youd equations in the

original paper Youd (1973) never presented the equation but it is easy to use the

information to draw a trend

The graphics presented in this document (figures 36 37 and 38) must be used with

certain reserves due the fact that the original data was modified in order to fit all

information in one graphic what the figures shows is just the general trend of the

behaviourrsquos material regarding on the shape If more accurate description and

information is required the author recommends consulting the reference data In the

same way equations from Holubec and DrsquoApollonia (1973) and Youd (1973) were not

presented by the authors but the use of the information was taken in order to build up

those equations on tables 6 and 7

S

V

V

V

= e

V

V

=nV

(45)

(46)

30

Table 6 Minimum void ratio equations regarding on the quantity (Ψ for sphericity C for circularity R

for roundness SF for Sukumaran shape factor and AF for Sukumaran angularity factor)

EQUATION NUMBER REFERENCE

Figure 34 (left)

4340

minΨ45490e =

47

Holubec amp DrsquoAppolonia 1973 (Ψ

was obtained using equation 2)

SF06340

mine021903180e +=

48

Sukumaran amp Ashmawy 2001 (SF

obtained using equation 21)

C05101emin

= 49

Cho etal 2006 (C obtained using

figure 12)

Figure 34 (right)

1

minR08203590e +=

50

Youd 1973 (R obtained from figure

11 and table 3)

R34080emin

= 51

Cho et al 2006 (R obtained using

figure 12)

1

minR05104330e +=

52

Rouseacute et al 2008 (R obtained by

equation 21)

AF02330

mine372004160e +=

53

Sukumaran amp Ashmawy 2001 (AF

obtained using equation 37)

Table 7 Maximum void ratio equations regarding on the quantity (Ψ for sphericity C for circularity R

for roundness SF for Sukumaran shape factor and AF for Sukumaran angularity factor)

EQUATION NUMBER REFERENCE

Figure 35 (left)

51520

max Ψ61120e = 54

Holubec and DrsquoAppolonia 1973 (Ψ

was obtained using equation 2)

SF1190

max e0016907180e += 55

Sukumaran amp Ashmawy 2001 (SF

obtained using equation 21)

C86061emax = 56

Cho etal 2006 (C obtained using

figure 12)

Figure 35 (right)

1

max R1505540e += 57

Youd 1973 (R obtained from figure

11 and table 3)

R62031emax= 58

Cho et al 2006 (R obtained using

figure 12)

1

max R107106150e += 59

Rouseacute et al 2008 (R obtained by

equation 21)

AF0530

max e12506090e += 60

Sukumaran amp Ashmawy 2001 (AF

obtained using equation 37)

Comparing figures 37 and 38 (minimum and maximum void ratio) it can be seen on

the right scheme of both figures 37 and 38 (when the factor is roundnessangularity)

that all the empirical relations has a common initial point close to 1 (it means that

particles are well rounded) while this common agreement disappear when the

roundness factor decreases (when the particles become more angular) Same figures

(37 and 38) on the left graphs (when the factor is sphericitycircularityshape) do not

present the same behaviour in fact there is more disperse initial point close to 1(when

the particles tend to be more sphericalcircular)

31

In Figure 39 the Δe (emax-emin) has been plotted to show how the maximum void ratio

and the minimum void ratio has different rate change when the particle shape

changes Maximum void ratio increases more than minimum void ratio when the

particle shape becomes less spherical andor more angular Comparing figure 39 left

and right graphics it can be seen that right present a common initial point when the

quantity (roundnessangularity) is close to one while in the left graphic the initial

point is more disperse Both ending points in both graphics (close to zero) are

dispersed

Figures 37 38 and 39 present the same behaviour right graphics (when the factor is

roundness angularity) in each figure have an initial common point while the left

graphics do not (when the factor is sphericity circularity shape)

Figure 37 Minimum void ratio based upon the relation of shape factor proposed by the authors indicated

in the figure

Figure 38 Maximum void ratio based upon the relation of shape factor proposed by the authors indicated

in the figure

04

06

08

1

12

14

16

18

2

005

015

025

035

045

055

065

075

085

095

Factor (roundness angularity)

min

imu

m v

oid

rati

o

Youd 1973 roundness

Rouse 2008 roundness

Cho 2006 roundness

Sukumaran 2001 AF

03

04

05

06

07

08

09

1

11

12

13

05

015

025

035

045

055

065

075

085

095

Factor (sphericity circularity shape)

min

imu

m v

oid

rati

oHolubec 1973 sphericity

Cho 2006 circularity

Sukumara 2001 SF

05

07

09

11

13

15

17

19

21

00

150

250

350

450

550

650

750

850

95

Factor (sphericity circularity shape)

Maxim

um

vo

id r

ati

o

Holubec 1973 sphericity

Cho 2006 circularity

Sukumara 2001 SF

05

1

15

2

25

3

35

005

015

025

035

045

055

065

075

085

095

Factor (roundness angularity)

Maxim

um

vo

id r

ati

o

Youd 1973 roundness

Rouse 2008 roundness

Cho 2006 roundness

Sukumaran 2001 AF

32

54 ANGLE OF REPOSE

The angle of repose of a granular material is the steepest angle of descent or dip of the

slope relative to the horizontal plane when material on the slope face is on the verge

of sliding as show in figure 40

According to Qazi (1975) there are five types of forces which may act between the

particles in soils

1 Force of friction between the particles

2 Force due to presence of absorbed gas andor moisture of particle

3 Mechanical forces caused by interlocking of particles of irregular shape

4 Electrostatic forces arising from friction between the particles themselves and

the surface with which they come in contact

5 Cohesion forces operating between neighbouring particles

Rouseacute et al (2008) found a decrease of angle of repose with increase roundness

based upon ASTM C1444 test (Standard Test Method for Measuring the Angle of

Repose of Free-Flowing Mold Powders) The method consist in pouring sand on a

surface cover by paper trough a funnel of specific dimensions (the nozzle diameter

depend on the sandrsquos particle size) from an altitude of 15 inches (381 mm) The sand

is release from the funnel until the peak of the cone formed by the sand stops the flow

The repose angle is obtained with the equation

H represent the 15 inches D and d represent the diameter of the cone formed by the

sand and the diameter of the funnel respectively

Figure 39 Maximum minus minimum void ratio based upon the relation of shape factor proposed by the

authors indicated in the figure

0

01

02

03

04

05

06

07

08

09

1

005

015

025

035

045

055

065

075

085

095

Factor (sphericity circularity shape)

Maxim

um

- M

inim

um

Vo

id r

ati

oHolubec 1973 sphericity

Cho 2006 circularity

Sukumara 2001 SF

0

02

04

06

08

1

12

14

16

18

005

015

025

035

045

055

065

075

085

095

Factor (roundness angularity)

Maxim

um

- M

inim

um

Vo

id r

ati

o

Youd 1973 roundness

Rouse 2008 roundness

Cho 2006 roundness

Sukumaran 2001 AF

dD

H2

tan=φ1

rep(61)

33

Rouseacute (2008) shows an empirical relation to obtain the angle of repose based on the

roundness of the particles

55 SHEAR STRENGTH

The MohrndashCoulomb failure criterion represents the linear envelope that is obtained

from a plot of the shear strength of a material versus the applied normal stress This

relation is expressed as

where τ is the shear strength σn is the normal stress co is the intercept of the failure

envelope with the τ axis and is the slope of the failure envelope The quantity c is

often called the cohesion and the angle is called the angle of internal friction

Studies show that the internal friction angle (under drained triaxial tests) increases

more rapidly on those materials having higher angularity increasing the relative

density The internal friction angle is a function of the relative density and the particle

shape (Holubec and DrsquoAppolonia 1973)

Chan and Page (1997) found in a study made with dry copper (using different shapes

and sizes ranging from 180 to 106 μm) using a direct shear test (ring share test) that

the internal friction angle increases as the angularity increases

Shinohara et al (2000) did some experiments with steel powder different shapes

using a triaxial cell in the test Shinohara never used the roundness or angularity on

the work but apply the shape factor (relation long axisshort axis) and the results were

that as this relation deviate from factor 1 the internal friction angle increases

The following empirical relations were found in the literature showing the behaviour

of the friction angle (obtained under different conditions)

)tan( noc

Figure 40 Representation of the angle of repose

(63)

(62)

34

Cho et al (2006)

(64)

(R is obtain by comparing the Krumbein chart figure 13)

Rouseacute (2008)

(65)

(66)

(R is defined using Wadell equation 22)

In figure 41 the suggested empirical relations above and lines constructed using

author data from Holubec and DrsquoAppolonia (1973) and Sukumara and Ashmawy

(2001) are plotted together to display the general trend on the particle shape and

friction angle relation Sukumaran reports two lines one based on the shape factor

(SF) and the second referring the angularity factor (AF) Sukumaran performed the

tests at constant volume

The scale used for Holubec and DrsquoAppolonia (1973) have lower and upper limits of 1

and 2 respectively (angularity form) and a scale change was applied to be able to

presented in the actual figure 41 As in the previous section (52) the author

recommend to use the original data from the references due that the figure just follows

the general trend of the behaviourrsquos particle regarding on the shape

Figure 41 The changes on the internal friction angle shows a general increase when the particle roundness

becomes angular or in the case of Sakamuran less spheric (Shape factor SF)

35

Barton and Kjaernsli (1981) suggested a model (equation 67) to predict the peak

friction angle (φrsquo) based upon numerous trixial and direct shear data tests

where

Se equivalent strength of particle

Re equivalent roughness of particle

φb basic friction angle (obtained from basic tilting test)

σn normal load

The information required for the model is (1) the uniaxial compressive strength of the

rock (2) the d50 particle size (mesh size where 50 of the particles pass through)

required to define Se (figure 42) (3) the degree of particle roundness and (4) the

porosity following compaction All data can be estimated by simple index tests

Barton and Kjaernsli (1981) suggest that particle size and sample scale has an effect

on the friction angle and includes them to obtain the equivalent strength (Se) figure 42

shows the method to obtain this value Compressive strength (σc) was chosen to be the

factor affecting the scale because micro fractures influence this property while

samples are bigger more micro fractures contain and its compressive strength reduces

The equivalent roughness is obtain using figure 43 where is required to know the

porosity (n) and the origin of the particles (a small chart is provided in the same figure

to compare the particles profile)

b

n

ee

SLogR

Figure 42 Method of estimating Equivalent Strength (Se) of rockfill based on uniaxial compressive strength

(σc ) and d50 particle size (Barton amp Kjaernsli 1981)

(67)

36

56 SEDIMENTATION PROPERTIES

A particle released in a less dense Newtonian fluid initially accelerate trough the fluid

due to the gravity Resistances to deformation of the fluid transmitted to the particle

surface drag generate forces that act to resist the particle motion The force due to the

weight (Fw) can be written as

Where ρp ρ are density of the particle and fluid (water) respectively g is the

gravitational force and Vp is the volume of the particle

And the resistance force (FD) is

Where CD is the dimensionless drag coefficient W is the weight of the particle and A

is the cross section area

Particlersquos shape has been assumed to be spherical when equations are applied on the

settling velocity Correlation deviates when particle shape departs from spherical form

Figure 43 Method of estimating Equivalent Roughness (Roe) based on porosity of rockfill

origin material degree of roundedness and smoothness of particle (Barton amp Kjaernsli 1981)

PPW ρ)gV(ρF

A2

WρCF

2

DD

(68)

(69)

37

(Dietrich 1982) and it is known that natural particles depart from spherical form

thus it is evident that this departure would have consequences

The below equation is proposed to account the shape (in this case the Corey shape

factor equation 8) in the settling velocity (Jimenez and Madsen 2003)

Jimenez and Madsen (2003) Dietrich (1982) Briggs and McCulloch (1962) and

others were working in the hydraulic shape of particles to solve problems as sediment

transport It is obvious that the equation presented and the researcherrsquos investigation

works under certain conditions (eg grain size between 0063-1 mm)

Dietrich (1982) suggests an empirical relation that accounts settling velocity size

density shape and roundness of a particle

R1 R2 and R3 are fitted equations for size and density shape and roundness

respectively

57 HYDRAULIC CONDUCTIVITY PERMEABILITY

Darcyrsquos Law Permeability is one component of Darcyrsquos law Darcys law is a simple

proportional relationship between the instantaneous discharge rate through a porous

medium the viscosity of the fluid and the pressure drop

The total velocity Ve is equal to the product of the permeability of the medium

(porous media) k the pressure drop ∆p all divided by the viscosity μ (Muskat

1937)

Darcys law is only valid for slow viscous flow most groundwater flow cases fall in

this category Typically Darcyrsquos law is valid at any flow with laminar flow (see figure

44)

Reynoldrsquos number (Laminar and turbulent Flow) Typically any laminar flow is

considered to have a Reynoldrsquos number less than one and it would be valid to apply

Darcys law Experimental tests have shown that flow regimes with Reynolds numbers

1

ND

S

S

ZY

gd1s

WW

NDN

gd)1s(4

dS

2R1R

3 10RW

pk

Ve

(70)

(71)

(72)

(73)

38

up to 10 may still be Darcian (laminar flow) as in the case of groundwater flow The

Reynolds number (a dimensionless parameter) for porous media flow is typically

expressed as

where ρ is the density of water (units of mass per volume) υ is the specific discharge

(with units of length per time) d is a representative average grain diameter for the

porous media (often taken as the 30 passing size from a grain size analysis using

sieves - with units of length) and μ is the viscosity of the fluid (Muskat 1937)

Shape effects Permeability as Head and Epps (2011) suggested is affected by the

shape and texture of soil grains Elongated or irregular particles create flow paths

which are more tortuous than those spherical particles Particles with a rough surface

texture provide more frictional resistance to flow Both effects tend to reduce the

water flow through the soil

Kozeny-Carman empirical relation accounts for the dependency of permeability on

void ratio in uniformly graded sands serious discrepancies are found when it is

applied to clays due the lack of uniform pores (Mitchell and Soga 2005)

There are various formulations of the Kozeny-Carman equation one published by

Head and Epps (2011) takes the void ratio e the specific surface area Ss and an

angularity factor F into account of permeability k

The angularity factor F considers the shape of the particles and ranges from 11 for

rounded grains 125 for sub rounded to 14 for angular particles The specific surface

Ss is defined as

d1 and d2 represent the maximum and minimum size particle in mm

Kane amp Sternheim (1988) suggest that the inclusion of the shape factor (F) has

probably the background on the Reynolds number due this factor is dependent

significantly on the shape of the obstacles and Reynolds number determines the

presence of laminar or turbulent flow Figure 44 show how the laminar flow has low

energy dissipation while turbulent flow (eg the roughness and path tortuosity) has

high energy dissipation

e1

e

FSs

2k

3

2

dRe

21

6

ddSs

(74)

(75)

(76)

39

According to Nearing and Parker (1994) the amount of soil detached during laminar

and turbulent flow is dependent on each soil and also greater on turbulent flow due the

greater shear strength generated during this kind of flow this could suggest the

greater erosion when turbulent flow is present

58 LIQUEFACTION

Soil liquefaction is a phenomenon in which soil loses much of its strength or stiffness

for a generally short time by earthquake shaking or other rapid loading Static and

dynamic liquefactions occur been the second one the most regular known

Liquefaction often occurs in saturated soils that is soils in which the space between

individual particles is completely filled with water This water exerts a pressure on the

soil particles that influences how tightly the particles themselves are pressed together

Shaking or other rapid loading can cause the water pressure to increase to the point

where the soil particles can readily move with respect to each other (Jefferies and

Been 2000)

Jefferies and Been (2000) state that it is clear that minor variation in intrinsic

properties of sand have major influence on the critical state These might be variations

on grain shape mineralogy grain size distribution surface roughness of grains etc

Yoginder et al (1985) found that substantial decrease on liquefaction resistance

occur with increase in confining pressure for rounded and angular sands (1600 kPa)

also rounded sands show an rapidly build up of resistance against liquefaction with

increasing density while angular tailing sand in contrast show such rapid increase

only at low confining pressures At low confining pressure angular material is more

resistant to liquefaction Probably the breakage of the corners on the angular particles

in tailings is ruling the lost in resistance at high confining pressures (sieve analysis

Figure 44 The figure show the extremes of flow behaviour First turbulent conditions where the flow is

essentially random and unpredictable and second the well defined Laminar flow conditions

40

after test identify the breakage of angular particles while on rounded particles the

sieve analysis was practically the same)

59 GROUNDWATER AND SEEPAGE MODELLING

In groundwater flow the particlersquos shape affects the soilrsquos pore size distribution

hence the flow characteristics (Sperry and Peirce 1995) Tortuosity and permeability

(also see section 57) are two significant macroscopic parameters of granular medium

that affect the passing flow (Hayati et al 2012) Current models incorporating the

effects of particle shape have failed to consider irregular particles such as those that

would prevail in a natural porous medium (Sperry and Peirce 1995)

Hayati et al (2012) suggested based on his results that tortuosity effect converge

when the porosity increases indicating that the shape have dominance at low and mid

porosity ranges

Sperry and Peirce (1995) research conclusions suggest that particle size and porosity

are more important predictors for hydraulic conductivity explaining the 69 of the

variability but particle shape appears to be the next most important This however

apparently comprises particles larger than 295-351 μm Differences for particle size

295-351 μm and smaller are not detectable Another interesting result in the research

was the interaction effect of the particle size and particle shape It suggests a different

packing configuration for particles of the same shape but different size (scale

dependent)

6 DISCUSSION

61 TERMS QUANTITIES AND DEFINITIONS

In order to describe the particle shape in detail there are a number of terms quantities

and definitions (qualitative and quantitative) used in the literature (eg Wadell 1932

1934 Krumbein 1941 Sneed amp Folk 1958) All mathematical definitions

(quantitatives) are models used to simplify the complexity of shape description Some

authors (Mitchell amp Soga 2005 Arasan et al 2010) are using three sub-quantities

one and each describing the shape but at different scales The terms are

morphologyform roundness and surface texture (figure 1) The three sub-quantities

are probably the best way to classify and describe a particle because not a single

definition can interpret the whole morphology Common language is needed when

descriptors are explained and these three scales represent an option It is evident in

the reviewed literature that many of the shape descriptors are presented with the same

name but also that there is not a clear meaning on what this descriptor defines eg

when there is no upper limit in the roundness does it means that the angularity never

ends Could they be more and more angular Probably they could be on theory but

not in reality

41

62 PROPERTIES

Trough various articlersquos review done in the present investigation it is recognized that

the particlersquos shape has an effect on the material properties among these are

1 Porosity (Tickell 1938 Fraser 1935 Kolbuszewski 1948) and void ratio

(Cho et al 2006 Shergold 1953 Rouseacute et al 2008 Santamarina and Cho

2004)

2 Permeability (Witt and Brauns 1983)

3 Internal friction angle (Shinohara et al 2000 Chan and Page 1997

Cheshomi et al 2009)

4 Density (Youd 1973 Holubec and DrsquoAppolonia 1973)

5 Drag coefficient Hydraulics (Briggs and McCulloch 1962)

In Table 5 is a short resume of the properties and shape effect found in peer review

articles trough different journals Most of the reviewed articles based its research on

uniform graded sands

Table 8 Compilation of properties influenced by particle shape

Repose

angle

Friction

angle

Porosity and

Void ratio Density Permeability

Settling velocity

Drag coefficient Deformation

Sphericity (3D)shape factor

NI x x x x x x

Circularity (2D)

NI x x x x NI NI

Roundness x x x x NI NI x

x influence

NI no information available

Shape of particles has an effect on the arrangement producing bridging or avoiding

the rotation of the particles and the resulting geotechnical property is affected eg

including flaky particles can result in a higher void ratio due the bridging effect

(Santamarina and Cho 2004) and depending on the loads even the size distribution is

changed due the breakage (Yoginder et al 1985) in similar way angular particles

produce higher void ratio due the avoided possibility of the particles to rotate and

compact

The influence of the chosen shape descriptor appears in this review to have minor

influence on the soil properties in the reviewed studies except on the void ratio and

the friction angle Influence of particle shape in some cases is hider by other factors

(eg size distribution) also the particle shape probably does not have influence when

particle size is in the clay order (eg hydraulic conductivity) the reason could be due

to forces as electrostatic or capillarity become more important at this level

Among the shape descriptors some are chosen more often in literature (eg aspect

ratio) there is no apparent scientific basis to use it (probably due to the simplicity of

the measurement it becomes one of the most use) but there are still some other

descriptors that may or may not show better correlation with the soil properties

Instead empirical relations had been developed regarding roundness or shape to

describe the soil behaviour it is clear that the mechanism behind the results is still not

completely understood

42

There is necessity to define the best(s) shape descriptor(s) to be used for particular

geotechnical properties

63 IMAGE ANALYSIS

Many image analysis techniques had been used to describe the particle shape eg

Fourier analysis fractal dimension tomography etc (Hyslip and Vallejo 1997) but

there is not agreement on the usage or conclusion to ensure the best particle descriptor

for geotechnical applications

There are several shape descriptors and also various techniques to capture the

particles profile (3-dimensions 3-dimension orthogonal and 2-dimensions) Each

technique presents advantages and disadvantages 3-dimensions is probably the

technique that provide more information about the particle shape but the precision

also lies in the resolution the equipment required to perform such capture could be

more or less sophisticated (scanning particles laying down in one position and later

move to complete the scanning or just falling down particles to scan it in one step)

3-dimensions orthogonal this technique use less sophisticated equipment (compare

with the previous technique) but its use is limited to particles over 1cm also

information between the orthogonal pictures is not capture 2-dimensions require non

sophisticated equipment but at the same time the shape information diminish compare

with the previous due the fact that it is possible to determine only the outline as the

particle measurements are performed in 2-dimensions it is presumed that they will lie

with its shortest axis perpendicular to the laying surface when they are flat but when

the particle tends to have more or less similar axis the laying could be random

Advantages on the use of image analysis are clear there is not subjectivity because it

is possible to obtain same result over the same images Electronic files do not loose

resolution and it is important when collaboration among distant work places is done

files can be send with the entire confidence and knowing that file properties has not

been changed Technology evolutions allowed to work with more information and it

also applies to the image processing area were the time consumed has been shortened

(more images processed in less time)

One important aspect in image analysis is the used resolution in the analysis due the

fact that there are measurements dependent and independent on resolution Thus

those dependent measurements should be avoided due the error included when they

are applied or avoid low resolution to increase the reliability Among these

parameters length is the principal parameter that is influences by resolution (eg

perimeter diameter axis etc) Resolution also has another aspect with two faces

quality versus capacity more resolution (quality) means more storage space a

minimum resolution to obtain reasonable and reliable data must be known but it

depend on each particular application

43

64 APPLICATIONS

Quantify changes in particles in the authorrsquos thought is one of the future applications

due the non-invasive methods of taking photographs in the surface of the damrsquos slope

rail road ballast or roads Sampling of the material and comparing with previous

results could show volume (3D analysis) or area (2D analysis) loss of the particles as

well as the form roundness and roughness This is important when it has been

suggested that a soil or rock embankment decrees their stability properties (eg

internal friction angle) with the loss of sphericity roundness or roughness

Seepage stock piling groundwater etc should try to include the particle shape while

modelling seepage requires grading material to not allow particles move due the

water pressure but in angular materials as it is known the void ratio is great than the

rounded soil it means the space and the possibilities for the small particles to move

are greater stock piling could be modelled incorporating the particle shape to

determine the binrsquos capacity when particle shape changes (void ratio changes when

particle shape changes) Modelling requires all information available and the

understanding of the principles that apply

Industry is actually using the particle shape to understand the soil behaviour and

transform processes into practical and economic image analysis has been included in

the quality control to determine particle shape and size because the advantages it

brings eg the acquisition of the sieving curve for pellets using digital images taken

from conveyor this allows to have the information in a short period of time with a

similar result at least enough from the practical point of view as the traditional

sieving

7 CONCLUSIONS

The conclusions of this literature review are

It has been shown that particle shape has influence on the soil behaviour

despite of partial knowledge of the mechanism behind Understanding of the

particle shape and its influence needs to be accomplished

A common language needs to be built up to standardize the meaning on

geotechnical field that involve the particle shape General relationships

between shape and properties should be developed

Based on this review it is not clear which is the best descriptor to use in

geotechnical engineering affecting he related shape to properties Instead of a

couple of standards there is no shape descriptor in geotechnical field fully

accepted

Image analysis tool is objective make the results repeatable obtain fast results

and work with more amount of information

44

Resolution needs to be taken in consideration when image analysis is been

carried out because the effects could be considerable Resolution must be set

according to the necessities Parameters as perimeter can be affected by

resolution

There are examples where particle shape has been incorporated in industries

related to geotechnical engineering eg in the ballast and asphalt industry for

quality control

8 FURTHER WORK

Three main issues have been identified in this review that will be further investigated

the limits of shape descriptors influence of grading and choice of descriptor for

relation to geotechnical properties

Shape descriptors have low and high limits frequently the limits are not the same and

the ability to describe the particlersquos shape is relative The sensitivity of each descriptor

should be compare to apply the most suitable descriptor in each situation

Sieving curve determine the particle size in a granular soil particle shape could differ

in each sieve size There is the necessity to describe the particle shape on each sieve

portion (due to practical issues) and included in the sieve curve Obtain an average

shape in determined sieve size is complicated (due to the possible presence of several

shapes) and to obtain the particle shape on the overall particlersquos size is challenging

how the particle shape should be included

Since several descriptors have been used to determine the shape of the particles and

the relation with the soil properties it is convenient to determine the descriptorrsquos

correlation with the soil properties

9 ACKNOWLEDGMENT

I would like to thanks to Lulearing University of Technology (LTU) the time I had spent

in its facilities and the kind environment it offers and University of Sonora

(UNISON) that has been providing me the financial support and the time to conclude

this journey

10 REFERENCES

Andersson T (2010) Estimating particle size distributions based on machine vision

Doctoral Thesis Departament of Computer Science and Electrical Engineering Lulearing

University of Technology ISSN 1402-1544 ISBN 978-91-7439-186-2

45

Arasan Seracettin Hasiloglu A Samet Akbulut Suat (2010) Shape particle of

natural and crished aggregate using image analysis International Journal of Civil and

Structural Engineering Vol 1 No 2 pp 221-233 ISSN 0970-4399

Aschenbrenner BC (1956) A new method of expressing particle sphericity Journal

of Sedimentary Petrology Vol 26 No 1 pp 15-31

Axelsson K (1998) Introduktion till jordmekaniken jaumlmte jordmateriallaumlran Skrift

984 Lulearing Avdelningen foumlr Geoteknologi Lulearing Tekniska Universitet (In Swedish)

Barton Nick amp Kjaernsli Bjorn (1981) Shear strength of rockfill Journal of the

Geotechnical Engineering Division Proceedings of the American Society of Civil

Engineers (ASCE) Vol 107 No GT7

Barrett P J (1980) The shape of rock particles a critical review Sedimentology

Vol 27 pp 291-303

Blott S J and Pye K (2008) Particle shape a review and new methods of

characterization and classification Sedimentology Vol 55 pp 31-63

Bowman E T Soga K and Drummond W (2001) Particle shape characterization

using Fourier descriptor analysis Geotechnique Vol 51 No 6 pp 545-554

Briggs L I McCulloch D S (1962) Hydraulic shape of sand particles Journal of

Sedimentary Petrology Vol 32 pp 645-656

Chan Leonard C Y and Page Neil W (1997) Particle fractal and load effects on

internal friction in powders Powder Technology Vol 90 pp 259-266

Cheshomi A Fakher A Jones C J F P (2009) A correlation between friction

angle and particle shape metrics in quaternary coarse alluvia Quarterly Journal of

Engineering Geology and Hydrogeology Vol 42 pp 145-155

Cho G Dodds J and Santamarina J C (2006) Particle shape effects on packing

density stiffness and strength Natural and crushed sands Journal of Geotechnical

and Geoenvironmental Engineering May 2006 pp 591-602

Dietrich William E (1982) Settling velocity of natural particles Water Resources

Research Vol 18 No 6 pp 1615-1626

Dobkins J E and Folk R L (1970) Shape development on Tahiti-nui Journal of

Sedimentary Petrology Vol 40 No 2 pp 1167-1203

Folk R L (1955) Student operator error in determining of roundness sphericity and

grain size Journal of Sedimentary Petrology Vol 25 pp 297-301

Fernlund J M R (1998) The effect of particle form on sieve analysis A test by

image analysis Engineering Geology Vol 50 No 1-2 pp 111-124

46

Fernlund J M R (2005) Image analysis method for determining 3-D shape of

coarse aggregate Cement and Concrete Research Vol 35 Issue 8 pp 1629-1637

Fernlund J M R Zimmerman Robert and Kragic Danica (2007) Influence of

volumemass on grain-size curves and conversion of image-analysis size to sieve size

Engineering Geology Vol 90 No 3-4 pp 124-137

Fraser H J (1935) Experimental study of the porosity and permeability of clastic

sediments The Journal of Geology Vol 43 pp 910-1010 ISSN 0022-1376

Hayati Ali Nemati Ahmadi Mohammad Mehdi and Mohammadi Soheil (2012)

American Physical Society Physical review E 85 036310 DOI

101103PhysRevE85036310

Hawkins A E (1993) The Shape of Powder-Particle Outlines Wiley New York

Head K H and Epps R J (2011) Manual of soil Laboratory testing Volum II

Permeability shear strength and compressibility test 3rd

edition Whittles Publishing

Scotland UK 3rd

edition

Holubec I and DrsquoAppolonia E (1973) Effect of particle shape on the engineering

properties of granular soils ASTM STP 523 pp 304-318

Hyslip James P Vallejo Luis E (1997) Fractal analysis of the roughness and size

distribution of granular materials Engineering Geology Vol 48 pp 231-244

Janoo Vincent C (1998) Quantification of shape angularity and surface texture of

base course materials US Army Corps of Engineers Cold Region Research and

Engineering Laboratory Special report 98-1

Jefferies Mike and Been Ken (2000) Soil liquefaction A critical state approach

Taylor amp Francis Group London and New York

Jimenez Jose A Madsen Ole S (2003) A simple formula to estimate settling

velocity of natural sediments Journal of Waterway Port Coastal and Ocean

Engineering Vol 129 No 2 pp 70-78

Johansson Jens and Vall Jakob (2011) Jordmaterials kornform Inverkan paring

Geotekniska Egenskaper Beskrivande storheter bestaumlmningsmetoder

Examensarbete Avdelningen foumlr Geoteknologi Institutionen foumlr Samhaumlllsbyggnad

och naturresurser Lulearing Tekniska Universitet Lulearing (In Swedish)

Kane Joseph W and Sternheim Morton M (1988) Physics John Wiley amp Sons Inc

Third edition

Kolbuszewski J (1948) An experimental study of the maximum and minimum

porosities of sands Proceedings of the Second International Conference on Soil

Mechanics and Foundation Engineering Rotterdam June 21 to 30 Sub-section IIb

pp 158-165

47

Krumbein W C and Pettijohn FJ (1938) Manual of sedimentary petrography

Appleton-Century Crofts Inc New York

Krumbein W C (1941) Measurement and geological significance of shape and

roundness of sedimentary particles Journal of Sedimentary Petrology Vol 11 No 2

pp 64-72

Krumbein W C and Sloss L L (1963) Stratigraphy and Sedimentation 2nd

ed

WH Freeman San Francisco

Kuo Chun-Yi and Freeman Reed B (1998a) Image analysis evaluation of

aggregates for asphalt concrete mixtures Transportation Research Record Vol 1615

pp 65-71

Kuo Chun-Yi Rollings Raymond and Lynch Larry N (1998b) Morphological

study of coarse aggregates using image analysis Journal of Materials in Civil

Engineering Vol 10 No 3 pp 135-142

Lanaro F Tolppanen P (2002) 3D characterization of coarse aggregates

Engineering Geology Vol 65 pp 17-30

Lees G (1964a) A new method for determining the angularity of particles

Sedimentology Vol 3 pp 2-21

Lees G (1964b) The measurement of particle shape and its influence in engineering

materials British Granite Whinstone Federation Vol 4 No 2 pp 17-38

Matsushima Takashi Saomoto Hidetaka Matsumoto Masaaki Toda Kengo

Yamada Yasuo (2003) Discrete element simulation of an assembly of irregular-

shaped grains Quantitative comparison with experiments 16th ASCE Engineering

Mechanics Conference University of Washington Seattle July 16-18

Mitchell James K and Soga Kenichi (2005) Fundamentals of soil behaviour Third

edition WILEY

Mora C F Kwan A K H Chan H C (1998) Particle size distribution analysis of

coarse aggregate using digital image processing Cement and Concrete Research Vol

28 pp 921-932

Mora C F and Kwan A K H (2000) Sphericity shape factor and convexity

measurement of coarse aggregate for concrete using digital image processing Cement

and Concrete Research Vol 30 No 3 pp 351-358

Muskat Morris (1937) The Flow of fluids through porous media Journal of Applied

Physics Vol 8 pp 274

Nearing M A and Parker S C (1994) Detachment of soil by flowing water under

turbulent and laminar conditions Soil Science Society of American Journal Vol 58

No 6 pp 1612-1614

48

Pan Tongyan Tutumluer Erol Carpenter Samuel H (2006) Effect of coarse

aggregate morphology on permanent deformation behavior of hot mix asphalt Journal

of Transportation Engineering Vol 132 No 7 pp 580-589

Pellegrino A (1965) Geotechnical properties of coarse-grained soils Proceedings

International Conference of Soil Mechanics and Foundation Engineering Vol 1 pp

97-91

Pentland A (1927) A method of measuring the angularity of sands MAG MN AL

Acta Eng Dom Transaction of the Royal Society of Canada Vol 21 Ser3xciii

Persson Anna-Lena (1998) Image analysis of shape and size of fine aggregates

Engineering Geology Vol 50 pp 177-186

Powers M C (1953) A new roundness scale for sedimentary particles Journal of

Sedimentary Petrology Vol 23 No 2 pp 117-119

Pye W and Pye M (1943) Sphericity determination of pebbles and grains Journal

of Sedimentary Petrology Vol 13 No 1 pp 28-34

Qazi M A (1975) Flow properties of granular masses A review on the angle of

repose The Arabian Journal for Science and Engineering Vol 1 No 2

Quiroga Pedro Nel and Fowle David W (2003) The effects of aggregate

characteristics on the performance of portland cement concrete Report ICAR 104-1F

Project number 104 International Center for Aggregates Research University of

Texas

Riley N A (1941) Projection sphericity Journal of Sedimentary Petrology Vol 11

No 2 pp 94-97

Rouseacute P C Fennin R J and Shuttle D A (2008) Influence of roundness on the

void ratio and strength of uniform sand Geotechnique Vol 58 No 3 227-231

Santamarina J C and Cho G C (2004) Soil behaviour The role of particle shape

Proceedings Skempton Conf London

Schofield and Wroth (1968) Critical state soil mechanics McGraw Hill

Shaumlfer Michael (2002) Digital optics Some remarks on the accuracy of particle

image analysis Particle amp Particle Systems Characterization Vol 19 No 3 pp 158-

168

Shergold F A (1953) The percentage of voids in compacted gravel as a measure of

its angularity Magazine of Concrete Research Vol 5 No 13 pp 3-10

Shinohara Kunio Oida Mikihiro Golman Boris (2000) Effect of particle shape on

angle of internal friction by triaxial compression test Powder Technology Vol 107

pp131-136

49

Skredcommisionen (1995) Ingenjoumlrsvetenskapsakademinen rapport 395 Linkoumlping

1995

Sneed E D and Folk R L (1958) Pebbles in the Colorado river Texas A study in

particle morphogenesis Journal of Geology Vol 66 pp 114-150

Sperry James M and Peirce J Jeffrey (1995) A model for estimating the hydraulic

conductivity of granular material based on grain shape grain size and porosity

Ground Water Vol 33 No 6 pp 892-898

Sukumaran B and Ashmawy A K (2001) Quantitative characterisation of the

geometry of discrete particles Geotechnique Vol 51 No 7 pp 619-627

Szaacutedeczy-Kardoss E Von (1933) Die bistimmung der abrollungsgrades Geologie

und palaumlontologie Vol 34B pp 389-401 (in German)

Teller J T (1976) Equantcy versus sphericity Sedimentology Vol 23 pp 427-428

Tickell F G (1938) Effect of the angularity of grain on porosity and permeability

bulletin of the American Association of Petroleum Geologist Vol 22 pp 1272-1274

Tutumluer E Huang H Hashash Y Ghaboussi J (2006) Aggregate shape effects

on ballast tamping and railroad track lateral stability AREMA 2006 Annual

Conference Louisville KY

Wadell H (1932) ldquoVolume Shape and roundness of rock particlesrdquo Journal of

Geology Vol 40 pp 443-451

Wadell H (1933) Sphericity and roundness of rock Particles Journal of Geology

Vol 41 No 3 pp 310ndash331

Wadell H (1934) Shape determination of large sedimental rock fragments

The Pan-American Geologist Vol 61 pp 187-220

Wadell H (1935) ldquoVolume shape and roundness of quartz particlesrdquo Journal of

Geology Vol 43 pp 250-279

Wentworth W C (1922a) The shape of beach pebbles Washington US Geological

Survey Bulletin Vol 131C pp 75-83

Wentworth W C (1922b) A method of measuring and plotting the shape of pebbles

Washington US Geological Survey Bulletin Vol 730C pp 91-114

Wentworth W C (1933) The shape of rock particle A discussion Journal of

Geology Vol 41 pp 306-309

Witt K J Brauns J (1983) Permeability-Anisotropy due to particle shape Journal

of Geotechnical Engineering Vol 109 No 9 pp 1181-1187

13

Some authors as Russel amp Taylor in 1937 Pettijohn in 1957 and Powers in 1953

developed a classification based on five and six classes (Hawkins 1993) each one

with its own class limits it is important to denote that the way they measure the

roundness is the developed by Wadell (1935) This classification and class limits are

showed in the table 4

Table 4 Degrees of roundness Wadell Values (Hawkins 1993) NA = no-applicable

Grade terms Russell amp Taylor (1937) Pettijohn (1957) Powers (1953)

Class

limits (R)

Arithmetic

midpoint

Class limits

(R)

Arithmetic midpoint Class

limits (R)

Arithmetic

midpoint

Very angular

NA

NA

NA

NA

012-017

014

Angular

000-015

0075

000-015

0125

017-025

021

Subangular

015-030

0225

015-025

0200

025-035

030

Subrounded

030-050

0400

025-040

0315

035-049

041

Rounded

050-070

0600

040-060

0500

049-070

059

Well rounded

070-100

0800

060-100

0800

070-100

084

Krumbein and Sloss (1963) published a graphical chart easy to determine the

sphericity and roundness parameters using comparison See figure 13 (Cho et al

2006)

Figure 12 A Roundness qualitative scale (Powers 1953)

Figure 13 Sphericity and roundness chart (Cho et al 2006) The roundness equation that appears here in

the chart is the wadellrsquos equation number 22

14

Fischer in 1933 (Hawkins 1993) used a straightforward method to quantify roundness

using a central point in the outline and dividing the outline in angles around this point

that were subtended by the straight or non curved parts of the profile were measured

This is illustrated in figure 14

To express the angularity value Fischer used the ratio of angles standing linear parts

on the outlines and concave respectively

Figure 14 left (A) and right (B) gives a similar angularity of approximately 042

using the above equations (Hawkins 1993)

Wentworth in 1922 used the maximum projection to define the position of the particle

to obtain the outline or contour (Barret 1980) The equation reflects the relation of the

diameter of a circle fitting the sharpest corner and the longest axis plus the shortest

axis c (minimum projection)

Wentworth (Hawkins 1993) expressed the roundness as the ratio of the radius of

curvature of the most convex part and the longest axis plus short axis

Actually these last two equations are the same just expressed in different terms when

the particle is in its maximum projection

Dimensions can be seen on figure 15 L and B represents the mayor axis a and

intermediate axis b The intention is to make difference between the 2 and 3

dimensions (L and B are for 2D as a b and c are for 3D)

deg360

ANG

=R

sumPLA

PLA

CON

ANG

ANGR

2)S(L

DR

M

S

B)4(L

RR CON

Figure 14 Fischerrsquos methods of angularity computation (Hawkins 1993)

A=inscribed circle B=circumscribed circle

(24)

(25)

(26)

(27)

15

Wentworth 1919 has a second way to express the roundness called Shape index

(Barrett 1980) and it relates the sharpest corner and the diameter of a pebble trough

the sharpest corner

Wentworth (1922b) used define the roundness as the ratio of the sharpest corner and

the average radius of the pebble

Cailleux (Barrett 1980) relates the radius of the most convex part and the longest

axis

Kuenen in 1956 show his roundness index (Barrett 1980) between the sharpest corner

and the breath axis

Dobkins amp Folk (1970) used a modified Wentworth roundness with the relation of

sharpest corner and inscribed circle diameters

AVG

CON

R

RR

x

s

D

DR

L2

RR CON

B

DR s

i

s

D

DR

3AVGAVG cbaDR2

Figure 15 Description of L and B axes (Hawkins 1993)

(28)

(29)

(30)

(31)

(32)

(33)

16

Swan in 1974 shows his equation (Barrett 1980) relating the sharpest (or the two

sharpest) corner(s) and inscribed circle diameter

Szadeczsky-Kardoss has his Average roundness of outline (Krumbein and Pettijohn

1938) relating the concave parts perimeter and the actual perimeter

Lees (1964a) developed an opposite definition to roundness it means that he

measures the angularity instead of the roundness and he calls it Degree of angularity

Figure 16 shows the items considered when equation 36 applies as the angles (α)

inscribed circle (Rmax-in) and the distance (x) The main formula is

In order to apply the last equation corners needs to be entered in the formula and each

individual result will add to each other to obtain the final degree of angularity

A roundness index appears on Janoo (1998) Kuo and Freeman (1998a) and Kuo et

al (1998b) it is described as

The last equation is on section 34 also because there is not a general agreement on the

definition furthermore some authors had used to define the roughness this is not the

only equation that has been used trying to define different aspects (sphericity

roundness or roughness) but it is a good example of the misuse of the quantities and

definitions

inmaxR

x)180(R

2P

A4R

i

ss

D

DDR

221

100P

PR CON

Figure 16 Degree of angularity measurement technique (Blot and Pye 2008)

(34)

(35)

(36)

(17)

17

Sukumaran and Ashmawy (2001) present an angularity factor (AF) calculated from

the number of sharpness corners Angles βi required to obtain the angularity factor are

shown in figure 9

Sukumaran and Ashmawy (2001) also suggested use not bigger sampling interval of

N=40 because it is the cut off between angularity factor and surface roughness If so

this equation could be used to describe the roughness

Table 5 General chronological overview of the particle roundness

Aspect Name Author Year Based on

Roundness shape index Wentworth 19191

diameter of sharper corner

shape index Wentworth 1922b sharpest corner and axis

roundness Wentworth 1933 convex parts

Fischer 19332

noncurved parts outline

Fischer 19332

noncurved-streigth parts outline

Average roundness of outline

Szadeczsky-Kardoss 19333

convex parts-perimeter

roundness Wadell 1935 diameter of corners

roundness Wadell 1935 diameter of corners

roundness Russel amp Taylor 19372

class limit table

roundness Krumbein 1941 chart

Cailleux 19471

convex parts

roundness Pettijohn 19494 class limit table

roundness Powers 1953 chart and class limit table

Kuenen 19561

axis-convex corner

roundness Krumbein and Sloss 1963 chart

degree of angularity Lees 1964a corners angles and inscribed circle

Dobkins amp Folk 1970 diameter of sharper corner

Swan 19741

diameter of sharper corners

Angularity factor Sukumaran and

Ashmawy 2001

Segmentation of particles and angles

1) Barret 1980 2) Hawkins 1993 3) Krumbein and Pettijohn 1938 4) Powers 1953

sum

sumsumN

1=i

2

i

2

N

1=i

2

i

2N

1=ii

)ordm180 -circleβ( - )(180ordm x 3

)ordm180-circleβ(-)ordm180 -Particleβ(

= AF (37)

18

36 ROUGHNESS OR SURFACE TEXTURE

A third property called texture appears early in the literature with the sphericity and

roundness properties since then texture property was longed described but it was in

accordance with the authors at that time not measurable

Wright in 1955 developed a method to quantify the surface texture or roughness of

concrete aggregate using studies done on 19 mm stones The test aggregates were first

embedded in a synthetic resin The stones were cut in thin sections The sections

projection was magnified 125 times The unevenness of the surface was traced and the

total length of the trace was measured The length was then compared with an uneven

line drawn as a series of chords (see figure 17) The difference between these two

lines was defined as the roughness factor (Janoo 1998)

However with the advance of technology it has become easier measure the roughness

and here is presented some researcherrsquos ideas how this property should be calculated

One technique used by Janoo (1988) to define the roughness can be seen in figure 18a

and is defined as the ratio between perimeter and convex perimeter

The convex perimeter is obtained using the Feretrsquos box (or diameter) tending a line in

between the touching points that the Feretrsquos box describes each time it is turn (figure

18b)

PER

OC

PR

Figure 17 Measurement method for characterizing the surface texture of an aggregate (Janoo 1998)

a) Convex perimeter (CPER) b) Feret measurement Figure 18 a) Convex perimeter (CPER) b) Feret measurement (modified after Janoo 1998)

(38)

a)

b)

19

Kuo and Freeman (1998a) and Kuo et al (1998b) use the roughness definition as the

ratio perimeter and average diameter

Erosion and dilatation image processing techniques are used to obtain the surface

texture Erosion is a morphological process by which boundary image pixels are

removed from an object surface which leaves the object less dense along the

perimeter or outer boundary Dilatation is the reverse process of erosion and a single

dilatation cycle increases the particle shape or image dimension by adding pixels

around its boundary (Pan etal 2006)

The ldquonrdquo erosion and dilatation cycles are not standardized

Mora and Kwan (2000) used the ldquoconvexity ratio CRrdquo (equation 41) and the ldquofullness

ratio FRrdquo (equation 42) in their investigation they are

The convex area is the area of the minimum convex boundaries circumscribing the

particle This is illustrated in the figure 19 The convex area is obtained in a similar

way as the convex perimeter but in this case the area between the original outline and

the convex perimeter is our convex area

AVG

OD

PR

100A

1AARO

CONo A

AR =

CONo A

AR =

Figure 19 Evaluation of area and convex area (Mora and Kuan 2000)

(39)

(40)

(41)

(42)

20

4 TECHNIQUES IN ORDER TO DETERMINE PARTICLE

SHAPE

41 HAND MEASUREMENT

Hand measurement technique was the first used by obvious reasons in order to

improve the accuracy special devices developed as the ldquosliding rod caliperrdquo used by

Krumbein (1941) it works placing the sample on the sliding road calliper as show

figure 20b the length in different positions can be obtain by using the scale provided

in the handle the ldquoconvexity gagerdquo that was actually used by opticians to measure the

curvature of lenses but easily applicable to the particle shape analysis (Wentworth

1922b) works measuring the movement of the central pivot as figure 20a shows (the

two adjacent pivots are invariable) as many the central pivot moves more is the

curvature or the ldquoSzadeczky-Kardossrsquos apparatusrdquo develop in 1933 that traces the

profile of the rock fragment so the outline traced is then analyzed (Krumbein and

Pettijohn 1938) figure 20c show equipment

Another helpful tool to determine the particle dimensions was the ldquocamera lucidardquo to

project the particlersquos contour over a circle scale appearing in Figure 21 thus it is

possible to measure the particlersquos diameter

a)

c) b)

Figure 20 a) convexity gage used to determine the curvature in particle corners (Wenworth 1922b)

b)sliding rod caliper device to measure the particle axis length (Krumbein 1941) and c)Szadeczky-

Kardoss (1933) apparatus it was utilized to obtain the particle outline

Figure 21 Circle scale used by Wadell (1935) to determine particlersquos diameter and roundness

21

42 SIEVE ANALYSIS

Bar sieving eg according to EN 933-31997 can be used to determine simple large

scale properties By combining mesh geometries the obtained results can be used to

quantify flakiness and elongation index ASTM D4791 (Flat and elongated particles

are defined as those coarse aggregate particles that have a ratio of length to thickness

equal to or greater than a specified value such as 51 The index represents the

percentage on weight of these particles) The method is not suitable for fine materials

This due to the difficulty to get the fine grains passed through the sieve and the great

amount of particles in relation to the area of the sieve (Persson 1998) eg EN 933-

31997 related to flakiness index The test is performed on aggregates with grain size

from 4 mm and up to 63 mm two sieving operations are necessary the first separates

on size fraction and the second use a bar sieve after the first sieving the average

maximum diameter of the particles is obtain and with the second sieving (bar sieving)

the shortest axis diameter is found finally with this two parameters the flakiness

index is determined

There are more standards related with the particle shape (see appendix A) but this

above presented are probably the most known using sieve analysis to determine

particlersquos geometrical properties

Sieve analysis is facing the computers age and image analysis sieving research is

taking place (Andersson 2010 Mora and Kwan 2000 Persson 1998) Industry is

also applying the image analysis sieving with decrees on the testing time compare

with the traditional sieving method An inconvenient of image analysis is the error

due the overlapping or hiding of the particles during the capture process but the

advantages are more compare with disadvantages (Anderson 2010)

43 CHART COMPARISON

Charts developed over the necessity of faster results because the long time consuming

required when measuring each particle

Krumbein (1941) present a comparison roundness chart for pebbles which were

measured by Wadellrsquos method because this property was the most difficult to measure

due to the second order scale that roundness represents (See figure 22)

Figure 22 Krumbein (1941) comparision chart for roundness

22

A qualitative chart by Powers (1953) try to include both (sphericity and roundness)

particlersquos characteristics it was divided on six roundness ranges (very angular

angular sub-angular sub-rounded rounded and well rounded) and two sphericity

series (high and low sphericity) This chart was prepared with photographs to enhance

the reader perspective (See figure 23)

A new chart including sphericity and roundness appear this time it was easier to

handle the two mean properties of particlersquos shape furthermore there was included

the numerical values that eliminated the subjectivity of qualitative description The

chart is based on Wadellrsquos definitions (Krumbein and Sloss 1963) (See figure 24)

Folk (1955) worried about the personrsquos error on the chartrsquos comparison studied the

determination of sphericity and angularity (he used the Powers 1953 comparison

chart) he found that the sphericity determination by chart comparison has a negligible

error while the roundness he concluded it was necessary to carry out a more wide

research due the high variability show by his study

Figure 23 Powers (1953) qualitative shpericity-roundness chart

Figure 24 Sphericity-roundness comparison chart (Krumbein and sloss 1963)

23

44 IMAGE ANALYSIS

Image analysis is a practical method to use for shape classification since it is fast and

can be automated Different techniques appear to process these images among them

are

o Feret Diameter the Feret diameter is the longitude between two parallel lines

this lines can rotate around one particle or outline to define dimensions as it

is shown in figure 25 these method is not a fine descriptor but as it was say

above it is a helpful tool to determine diameters (Janoo 1988)

o Fourier Mathematical Technique It produces mathematical relations that

characterize the profile of individual particles This method favours the

analysis of roughness and textural features for granular soils The problem in

the methodology remains in the re-entrant angles in order to complete the

revolution (Bowman et al 2001) see figure 26

o Fractal Dimension Irregular line at any level of scrutiny is by definition

fractal (Hyslip and Vallejo 1997) Figure 27 shows fractal analysis by the

dividing method The length of the fractal line can be defined as

N

1n

nn0 )nsinbncosa(a)(R

RD1n)(P

Figure 25 Feret measurement technique is defined by two parallel lines turning

around the particle to define the shortest and longest Feret diameter (Janoo 1988)

Figure 26 Fourier technique with two radiuses at one angle (Bowman et al 2001)

(43)

(44)

24

o Orthogonal image analysis This technique is basically the use of two images

orthogonal between them to acquire the three particle dimensions (Fernlund

2005) any of the above techniques can be used in this orthogonal way

o Laser Scanning Technique this kind of laser scanning 3D is one of the most

advanced techniques In figures 28a) we have the laser head scanning the rock

particles the particles have control points in order to keep a reference point

when move them to scan the lower part in figure 28b) we can see the laser

path followed (Lanaro and Tolppanen 2002)

Another technique is the Laser-Aided Tomography (LAT) in this case a laser sheet is

used to obtain the particles surveying (see figure 29) This technique is different and

has special requirements as to use liquid with same refractive index as the particles

particles must let the laser or certain percent of light go through (Matsushima et al

2003)

a) b)

Figure 27 Fractal analysis by the dividing method at different scrutiny scale (Hyslip and Vallejo 1997)

Figure 28 a) Scanning head b) scanning path (Lanaro and Tolppanen 2002)

Figure 30 3D scan completed ready to

use for any further measure

(Matsushima et al 2003)

Figure 29 LAT scaning particles

(Matsushima et al 2003)

25

Both 3D techniques obtain the particle shape that is later used to achieve measures as

we can see in figure 30

All these previous techniques are easily written in codes or scripts to be interpreted in

a digital way obtaining the desired measurement but there are some interesting points

in the image analysis regarding on the errors involve among them are image

resolution and orientation of the particles orientation is not relevant when it is

random and large number of particles are involve resolution have an influence on the

accuracy (Zeidan et al 2007)

When resolution is increase more accuracy is obtain and the object representation

match better with the real form in the other hand more resolution means more

spending on memory and time thus resolution needs to be according with the goal

and precision needed in any work (Schaumlfer 2002)

Schaumlfer (2002) conclude that attributes like length when measuring digital images

present relative high errors It can be vanish or at least diminish using high resolution

just for diameter but not for perimeter that keep the error as big as initially Johansson

and Vall (2011) obtain similar results when 3 different resolutions were used in the

same particle obtaining an unstable output for those termsquantities that involve the

perimeter Thus all quantities relating the perimeter should be treated with care

5 EFFECT OF SHAPE ON SOIL PROPERTIES

51 INTRODUCTION

In laboratory test on the effect on particle size on basic properties has been

investigated in several studies this relation has been discussed and various

mechanisms had been proposed to explain the behaviour of the soil in dependency

also with the shape Basically there are two mechanisms proposed The arrangement

of particles and the inter-particle contact (Santamarina and Cho 2004) and

subsequence breakage

The arrangement of particles

Arrangement of the particles can be presented in three different forms loose dense

and critical this arrangement determines the soil properties (eg density increase with

more dense arrangement) Loose and dense states are easy understandable when

figure 31 is explained while in the upper part of the figure the particles are arranged

using the minimum space needed in the lower part a span is created using the flaky

particle as a bridge this phenomena is known as ldquobridgingrdquo Bridging can produce

different geotechnical results when just the shape of the particle is changed eg void

ratio (Santamarina and Cho 2004) Particles are able to rearrange this could be done

applying pressure (energy) to the soil the pressure (energy) will create such forces

that soil particles will rotate and move (see figure 34) finishing in a more dense state

26

A loose soil will contract in volume on shearing and may not develop any peak

strength (figure 32 left) In this case the shear strength will increase gradually until

the residual shear strength is revealed once the soil has ceased contracting in volume

A dense soil may contract slightly (figure 32 right) before granular interlock prevents

further contraction (granular interlock is dependent on the shape of the grains and

their initial packing arrangement) In order to continue shearing once granular

interlock has occurred the soil must dilate (expand in volume) As additional shear

force is required to dilate the soil a peak shear strength occurs (figure 32 left) Once

this peak shear strength caused by dilation has been overcome through continued

shearing the resistance provided by the soil to the applied shear stress reduces

(termed strain softening) Strain softening will continue until no further changes in

volume of the soil occur on continued shearing Peak shear strengths are also

observed in overconsolidated clays where the natural fabric of the soil must be

destroyed prior to reaching constant volume shearing Other effects that result in peak

strengths include cementation and bonding of particles The distinctive shear strength

called the critical state is identified where the soil undergoing shear does so at a

constant volume (Schofield and Wroth 1968)

The inter-particle contact

For frictional soil ie coarse grained soil the friction between particles is the

dominating factor for strength Materials usually consisting of coarse grains (diameter

Figure 31 Bridging effect when flaky particles are combined in the bulk material (Santamarina and

Cho 2004)

Figure 32 The left part of the figure show a typical behaviour of loose and dense material over shear stress

while at the right the figures illustrate the typical volume changes

27

gt 006mm) behave as a frictional soil it means that the strength of coarse soils (silt

sand gravel etc) comes from an inter-particle mechanical friction thus ideally they

do not have traction strength In figure 33 the inter-particle contact is illustrated here

the pressure (P) is applied and two more components are found the normal load (N)

and the tangential load (T) described as the friction coefficient (μF) The forces stand

in equilibrium (Johansson and Vall 2011)

When particles equilibrium is disturbed (friction coefficient is not enough to keep

particles unmoved) the rotation is imminent and it is necessary in order to compact

the soil in figure 34 can be seen that the arrangement is a fact that inhibit or allow this

rotation and the shape in the 3 different scales are also factors because the more

spherical andor more rounded andor less roughness more easy is the rotation

(Santamarina and Cho 2004)

Breakage

Breakage is a side effect of the inter-particle contact and rotation when pressure

exceed the rock strength it can happened when the particles are tight together and

there is not enough space to rotate it is more obvious in angular particles (mesh form)

or as in figure 31 where the flaky particle ldquobridgingrdquo is not able to rotate but it can

brake by the pressure increase Yoginder et al (1985) notice that the angular particle

break during his experiments and they turn more rounded changing the original size

and form configuration at the same time there was a soil properties loosening

Figure 33 Inter-particle contact and forces acting (Axelsson 1998)

Figure 34 Rotation inhibition by the particles compaction or low void ratio (Santamarina and Cho 2004)

28

52 INFLUENCE OF SIZE AND SHAPE

Wenworth (1922a) and Pellegrino (1965) among others suggest that agent transport of

the rocks (rigor of transport temperature and moisture changes etc) determine its

shape but also the particle genesis itself (rock structure mineralogy hardness etc) It

is not possible to determine the shape of the particles based on the agent transport or

genesis but generally a shape behaviour is expected according to Mitchell and Soga

(2005) specially when the particle size is in the clay size (gt2μm) The shapes of the

most common clay minerals are platy (figure 35) with some exceptions (eg

halloysite occurs as tubes kaolinite are large thick and stiff Smectites are composed

of small very thin and filmy particles Illites are intermediate between kaolinite and

smectite and attapulgite occurs in lathlike particle shapes) Some clay minerals

photographs are presented in figure 35

Figure 35 Clay mineral shape a) hallosite b) Kaoline c) Smactites d) Illites and e) attapulgite (Modified

from Mitchell and Soga 2005)

Figure 36 Particle size range in soils Generally the particles of clay size are plate shaped (Mitchell and

Soga 2005)

a) b) c)

e) d)

29

53 VOID RATIO AND POROSITY

The void ratio (e) is the ratio of the volume of voids to the volume of solid it is

defined by the equation

Porosity (n) is the ratio of the volume of voids to the total volume of the soil it is

represented by the equation

Holubec and DrsquoAppolonia (1973) found a relation between the void ratio and

sphericity (referred in the paper as coefficient of angularity ratio of particle surface

and equivalent sphere surface) their results show that the maximum and the minimum

void ratio increases as the shpericity decreases In this study the surface was obtained

for an indirect method based on the permeability developed by Hoffman in 1959

described in the same document Rouseacute et al (2008) defined the roundness as

Wadell (1935) and he found it as an important factor controlling the minimum and

maximum void ratios Some other authors as Youd (1973) and Cho et al (2006)

conclude the same minimum and maximum void ratios increase when sphericity and

roundness decrease Another interesting result (all above authors) was the bigger

influence of the form (sphericity circularity) and roundness on the maximum void

ratio The change of the maximum void ratio is more pronounced than the change of

the minimum void ratio when the form and roundness changes (See figure 39)

Particles arrangement and interlocking are probably the factor that controls the void

ratio bridge effect permit the existence of void among the particles while interlocking

allowed the particles to form arches avoiding the possibility to rotate and stay in a

more stable configuration eg as it happens with marbles

Figures 36 37 and 38 shows proposed empirical relationships between void ratio and

shape from tables 5 and 6 (graphically the scale goes from 0 to 1 when cero mean

high angularity shpericity or circularity and one means low angularity circularity or

sphericity) Holubec and DrsquoAppolonia (1973) data was taken to obtain a power curve

and describe a tendency Santamarina and Cho (2004) show Youd equations in the

original paper Youd (1973) never presented the equation but it is easy to use the

information to draw a trend

The graphics presented in this document (figures 36 37 and 38) must be used with

certain reserves due the fact that the original data was modified in order to fit all

information in one graphic what the figures shows is just the general trend of the

behaviourrsquos material regarding on the shape If more accurate description and

information is required the author recommends consulting the reference data In the

same way equations from Holubec and DrsquoApollonia (1973) and Youd (1973) were not

presented by the authors but the use of the information was taken in order to build up

those equations on tables 6 and 7

S

V

V

V

= e

V

V

=nV

(45)

(46)

30

Table 6 Minimum void ratio equations regarding on the quantity (Ψ for sphericity C for circularity R

for roundness SF for Sukumaran shape factor and AF for Sukumaran angularity factor)

EQUATION NUMBER REFERENCE

Figure 34 (left)

4340

minΨ45490e =

47

Holubec amp DrsquoAppolonia 1973 (Ψ

was obtained using equation 2)

SF06340

mine021903180e +=

48

Sukumaran amp Ashmawy 2001 (SF

obtained using equation 21)

C05101emin

= 49

Cho etal 2006 (C obtained using

figure 12)

Figure 34 (right)

1

minR08203590e +=

50

Youd 1973 (R obtained from figure

11 and table 3)

R34080emin

= 51

Cho et al 2006 (R obtained using

figure 12)

1

minR05104330e +=

52

Rouseacute et al 2008 (R obtained by

equation 21)

AF02330

mine372004160e +=

53

Sukumaran amp Ashmawy 2001 (AF

obtained using equation 37)

Table 7 Maximum void ratio equations regarding on the quantity (Ψ for sphericity C for circularity R

for roundness SF for Sukumaran shape factor and AF for Sukumaran angularity factor)

EQUATION NUMBER REFERENCE

Figure 35 (left)

51520

max Ψ61120e = 54

Holubec and DrsquoAppolonia 1973 (Ψ

was obtained using equation 2)

SF1190

max e0016907180e += 55

Sukumaran amp Ashmawy 2001 (SF

obtained using equation 21)

C86061emax = 56

Cho etal 2006 (C obtained using

figure 12)

Figure 35 (right)

1

max R1505540e += 57

Youd 1973 (R obtained from figure

11 and table 3)

R62031emax= 58

Cho et al 2006 (R obtained using

figure 12)

1

max R107106150e += 59

Rouseacute et al 2008 (R obtained by

equation 21)

AF0530

max e12506090e += 60

Sukumaran amp Ashmawy 2001 (AF

obtained using equation 37)

Comparing figures 37 and 38 (minimum and maximum void ratio) it can be seen on

the right scheme of both figures 37 and 38 (when the factor is roundnessangularity)

that all the empirical relations has a common initial point close to 1 (it means that

particles are well rounded) while this common agreement disappear when the

roundness factor decreases (when the particles become more angular) Same figures

(37 and 38) on the left graphs (when the factor is sphericitycircularityshape) do not

present the same behaviour in fact there is more disperse initial point close to 1(when

the particles tend to be more sphericalcircular)

31

In Figure 39 the Δe (emax-emin) has been plotted to show how the maximum void ratio

and the minimum void ratio has different rate change when the particle shape

changes Maximum void ratio increases more than minimum void ratio when the

particle shape becomes less spherical andor more angular Comparing figure 39 left

and right graphics it can be seen that right present a common initial point when the

quantity (roundnessangularity) is close to one while in the left graphic the initial

point is more disperse Both ending points in both graphics (close to zero) are

dispersed

Figures 37 38 and 39 present the same behaviour right graphics (when the factor is

roundness angularity) in each figure have an initial common point while the left

graphics do not (when the factor is sphericity circularity shape)

Figure 37 Minimum void ratio based upon the relation of shape factor proposed by the authors indicated

in the figure

Figure 38 Maximum void ratio based upon the relation of shape factor proposed by the authors indicated

in the figure

04

06

08

1

12

14

16

18

2

005

015

025

035

045

055

065

075

085

095

Factor (roundness angularity)

min

imu

m v

oid

rati

o

Youd 1973 roundness

Rouse 2008 roundness

Cho 2006 roundness

Sukumaran 2001 AF

03

04

05

06

07

08

09

1

11

12

13

05

015

025

035

045

055

065

075

085

095

Factor (sphericity circularity shape)

min

imu

m v

oid

rati

oHolubec 1973 sphericity

Cho 2006 circularity

Sukumara 2001 SF

05

07

09

11

13

15

17

19

21

00

150

250

350

450

550

650

750

850

95

Factor (sphericity circularity shape)

Maxim

um

vo

id r

ati

o

Holubec 1973 sphericity

Cho 2006 circularity

Sukumara 2001 SF

05

1

15

2

25

3

35

005

015

025

035

045

055

065

075

085

095

Factor (roundness angularity)

Maxim

um

vo

id r

ati

o

Youd 1973 roundness

Rouse 2008 roundness

Cho 2006 roundness

Sukumaran 2001 AF

32

54 ANGLE OF REPOSE

The angle of repose of a granular material is the steepest angle of descent or dip of the

slope relative to the horizontal plane when material on the slope face is on the verge

of sliding as show in figure 40

According to Qazi (1975) there are five types of forces which may act between the

particles in soils

1 Force of friction between the particles

2 Force due to presence of absorbed gas andor moisture of particle

3 Mechanical forces caused by interlocking of particles of irregular shape

4 Electrostatic forces arising from friction between the particles themselves and

the surface with which they come in contact

5 Cohesion forces operating between neighbouring particles

Rouseacute et al (2008) found a decrease of angle of repose with increase roundness

based upon ASTM C1444 test (Standard Test Method for Measuring the Angle of

Repose of Free-Flowing Mold Powders) The method consist in pouring sand on a

surface cover by paper trough a funnel of specific dimensions (the nozzle diameter

depend on the sandrsquos particle size) from an altitude of 15 inches (381 mm) The sand

is release from the funnel until the peak of the cone formed by the sand stops the flow

The repose angle is obtained with the equation

H represent the 15 inches D and d represent the diameter of the cone formed by the

sand and the diameter of the funnel respectively

Figure 39 Maximum minus minimum void ratio based upon the relation of shape factor proposed by the

authors indicated in the figure

0

01

02

03

04

05

06

07

08

09

1

005

015

025

035

045

055

065

075

085

095

Factor (sphericity circularity shape)

Maxim

um

- M

inim

um

Vo

id r

ati

oHolubec 1973 sphericity

Cho 2006 circularity

Sukumara 2001 SF

0

02

04

06

08

1

12

14

16

18

005

015

025

035

045

055

065

075

085

095

Factor (roundness angularity)

Maxim

um

- M

inim

um

Vo

id r

ati

o

Youd 1973 roundness

Rouse 2008 roundness

Cho 2006 roundness

Sukumaran 2001 AF

dD

H2

tan=φ1

rep(61)

33

Rouseacute (2008) shows an empirical relation to obtain the angle of repose based on the

roundness of the particles

55 SHEAR STRENGTH

The MohrndashCoulomb failure criterion represents the linear envelope that is obtained

from a plot of the shear strength of a material versus the applied normal stress This

relation is expressed as

where τ is the shear strength σn is the normal stress co is the intercept of the failure

envelope with the τ axis and is the slope of the failure envelope The quantity c is

often called the cohesion and the angle is called the angle of internal friction

Studies show that the internal friction angle (under drained triaxial tests) increases

more rapidly on those materials having higher angularity increasing the relative

density The internal friction angle is a function of the relative density and the particle

shape (Holubec and DrsquoAppolonia 1973)

Chan and Page (1997) found in a study made with dry copper (using different shapes

and sizes ranging from 180 to 106 μm) using a direct shear test (ring share test) that

the internal friction angle increases as the angularity increases

Shinohara et al (2000) did some experiments with steel powder different shapes

using a triaxial cell in the test Shinohara never used the roundness or angularity on

the work but apply the shape factor (relation long axisshort axis) and the results were

that as this relation deviate from factor 1 the internal friction angle increases

The following empirical relations were found in the literature showing the behaviour

of the friction angle (obtained under different conditions)

)tan( noc

Figure 40 Representation of the angle of repose

(63)

(62)

34

Cho et al (2006)

(64)

(R is obtain by comparing the Krumbein chart figure 13)

Rouseacute (2008)

(65)

(66)

(R is defined using Wadell equation 22)

In figure 41 the suggested empirical relations above and lines constructed using

author data from Holubec and DrsquoAppolonia (1973) and Sukumara and Ashmawy

(2001) are plotted together to display the general trend on the particle shape and

friction angle relation Sukumaran reports two lines one based on the shape factor

(SF) and the second referring the angularity factor (AF) Sukumaran performed the

tests at constant volume

The scale used for Holubec and DrsquoAppolonia (1973) have lower and upper limits of 1

and 2 respectively (angularity form) and a scale change was applied to be able to

presented in the actual figure 41 As in the previous section (52) the author

recommend to use the original data from the references due that the figure just follows

the general trend of the behaviourrsquos particle regarding on the shape

Figure 41 The changes on the internal friction angle shows a general increase when the particle roundness

becomes angular or in the case of Sakamuran less spheric (Shape factor SF)

35

Barton and Kjaernsli (1981) suggested a model (equation 67) to predict the peak

friction angle (φrsquo) based upon numerous trixial and direct shear data tests

where

Se equivalent strength of particle

Re equivalent roughness of particle

φb basic friction angle (obtained from basic tilting test)

σn normal load

The information required for the model is (1) the uniaxial compressive strength of the

rock (2) the d50 particle size (mesh size where 50 of the particles pass through)

required to define Se (figure 42) (3) the degree of particle roundness and (4) the

porosity following compaction All data can be estimated by simple index tests

Barton and Kjaernsli (1981) suggest that particle size and sample scale has an effect

on the friction angle and includes them to obtain the equivalent strength (Se) figure 42

shows the method to obtain this value Compressive strength (σc) was chosen to be the

factor affecting the scale because micro fractures influence this property while

samples are bigger more micro fractures contain and its compressive strength reduces

The equivalent roughness is obtain using figure 43 where is required to know the

porosity (n) and the origin of the particles (a small chart is provided in the same figure

to compare the particles profile)

b

n

ee

SLogR

Figure 42 Method of estimating Equivalent Strength (Se) of rockfill based on uniaxial compressive strength

(σc ) and d50 particle size (Barton amp Kjaernsli 1981)

(67)

36

56 SEDIMENTATION PROPERTIES

A particle released in a less dense Newtonian fluid initially accelerate trough the fluid

due to the gravity Resistances to deformation of the fluid transmitted to the particle

surface drag generate forces that act to resist the particle motion The force due to the

weight (Fw) can be written as

Where ρp ρ are density of the particle and fluid (water) respectively g is the

gravitational force and Vp is the volume of the particle

And the resistance force (FD) is

Where CD is the dimensionless drag coefficient W is the weight of the particle and A

is the cross section area

Particlersquos shape has been assumed to be spherical when equations are applied on the

settling velocity Correlation deviates when particle shape departs from spherical form

Figure 43 Method of estimating Equivalent Roughness (Roe) based on porosity of rockfill

origin material degree of roundedness and smoothness of particle (Barton amp Kjaernsli 1981)

PPW ρ)gV(ρF

A2

WρCF

2

DD

(68)

(69)

37

(Dietrich 1982) and it is known that natural particles depart from spherical form

thus it is evident that this departure would have consequences

The below equation is proposed to account the shape (in this case the Corey shape

factor equation 8) in the settling velocity (Jimenez and Madsen 2003)

Jimenez and Madsen (2003) Dietrich (1982) Briggs and McCulloch (1962) and

others were working in the hydraulic shape of particles to solve problems as sediment

transport It is obvious that the equation presented and the researcherrsquos investigation

works under certain conditions (eg grain size between 0063-1 mm)

Dietrich (1982) suggests an empirical relation that accounts settling velocity size

density shape and roundness of a particle

R1 R2 and R3 are fitted equations for size and density shape and roundness

respectively

57 HYDRAULIC CONDUCTIVITY PERMEABILITY

Darcyrsquos Law Permeability is one component of Darcyrsquos law Darcys law is a simple

proportional relationship between the instantaneous discharge rate through a porous

medium the viscosity of the fluid and the pressure drop

The total velocity Ve is equal to the product of the permeability of the medium

(porous media) k the pressure drop ∆p all divided by the viscosity μ (Muskat

1937)

Darcys law is only valid for slow viscous flow most groundwater flow cases fall in

this category Typically Darcyrsquos law is valid at any flow with laminar flow (see figure

44)

Reynoldrsquos number (Laminar and turbulent Flow) Typically any laminar flow is

considered to have a Reynoldrsquos number less than one and it would be valid to apply

Darcys law Experimental tests have shown that flow regimes with Reynolds numbers

1

ND

S

S

ZY

gd1s

WW

NDN

gd)1s(4

dS

2R1R

3 10RW

pk

Ve

(70)

(71)

(72)

(73)

38

up to 10 may still be Darcian (laminar flow) as in the case of groundwater flow The

Reynolds number (a dimensionless parameter) for porous media flow is typically

expressed as

where ρ is the density of water (units of mass per volume) υ is the specific discharge

(with units of length per time) d is a representative average grain diameter for the

porous media (often taken as the 30 passing size from a grain size analysis using

sieves - with units of length) and μ is the viscosity of the fluid (Muskat 1937)

Shape effects Permeability as Head and Epps (2011) suggested is affected by the

shape and texture of soil grains Elongated or irregular particles create flow paths

which are more tortuous than those spherical particles Particles with a rough surface

texture provide more frictional resistance to flow Both effects tend to reduce the

water flow through the soil

Kozeny-Carman empirical relation accounts for the dependency of permeability on

void ratio in uniformly graded sands serious discrepancies are found when it is

applied to clays due the lack of uniform pores (Mitchell and Soga 2005)

There are various formulations of the Kozeny-Carman equation one published by

Head and Epps (2011) takes the void ratio e the specific surface area Ss and an

angularity factor F into account of permeability k

The angularity factor F considers the shape of the particles and ranges from 11 for

rounded grains 125 for sub rounded to 14 for angular particles The specific surface

Ss is defined as

d1 and d2 represent the maximum and minimum size particle in mm

Kane amp Sternheim (1988) suggest that the inclusion of the shape factor (F) has

probably the background on the Reynolds number due this factor is dependent

significantly on the shape of the obstacles and Reynolds number determines the

presence of laminar or turbulent flow Figure 44 show how the laminar flow has low

energy dissipation while turbulent flow (eg the roughness and path tortuosity) has

high energy dissipation

e1

e

FSs

2k

3

2

dRe

21

6

ddSs

(74)

(75)

(76)

39

According to Nearing and Parker (1994) the amount of soil detached during laminar

and turbulent flow is dependent on each soil and also greater on turbulent flow due the

greater shear strength generated during this kind of flow this could suggest the

greater erosion when turbulent flow is present

58 LIQUEFACTION

Soil liquefaction is a phenomenon in which soil loses much of its strength or stiffness

for a generally short time by earthquake shaking or other rapid loading Static and

dynamic liquefactions occur been the second one the most regular known

Liquefaction often occurs in saturated soils that is soils in which the space between

individual particles is completely filled with water This water exerts a pressure on the

soil particles that influences how tightly the particles themselves are pressed together

Shaking or other rapid loading can cause the water pressure to increase to the point

where the soil particles can readily move with respect to each other (Jefferies and

Been 2000)

Jefferies and Been (2000) state that it is clear that minor variation in intrinsic

properties of sand have major influence on the critical state These might be variations

on grain shape mineralogy grain size distribution surface roughness of grains etc

Yoginder et al (1985) found that substantial decrease on liquefaction resistance

occur with increase in confining pressure for rounded and angular sands (1600 kPa)

also rounded sands show an rapidly build up of resistance against liquefaction with

increasing density while angular tailing sand in contrast show such rapid increase

only at low confining pressures At low confining pressure angular material is more

resistant to liquefaction Probably the breakage of the corners on the angular particles

in tailings is ruling the lost in resistance at high confining pressures (sieve analysis

Figure 44 The figure show the extremes of flow behaviour First turbulent conditions where the flow is

essentially random and unpredictable and second the well defined Laminar flow conditions

40

after test identify the breakage of angular particles while on rounded particles the

sieve analysis was practically the same)

59 GROUNDWATER AND SEEPAGE MODELLING

In groundwater flow the particlersquos shape affects the soilrsquos pore size distribution

hence the flow characteristics (Sperry and Peirce 1995) Tortuosity and permeability

(also see section 57) are two significant macroscopic parameters of granular medium

that affect the passing flow (Hayati et al 2012) Current models incorporating the

effects of particle shape have failed to consider irregular particles such as those that

would prevail in a natural porous medium (Sperry and Peirce 1995)

Hayati et al (2012) suggested based on his results that tortuosity effect converge

when the porosity increases indicating that the shape have dominance at low and mid

porosity ranges

Sperry and Peirce (1995) research conclusions suggest that particle size and porosity

are more important predictors for hydraulic conductivity explaining the 69 of the

variability but particle shape appears to be the next most important This however

apparently comprises particles larger than 295-351 μm Differences for particle size

295-351 μm and smaller are not detectable Another interesting result in the research

was the interaction effect of the particle size and particle shape It suggests a different

packing configuration for particles of the same shape but different size (scale

dependent)

6 DISCUSSION

61 TERMS QUANTITIES AND DEFINITIONS

In order to describe the particle shape in detail there are a number of terms quantities

and definitions (qualitative and quantitative) used in the literature (eg Wadell 1932

1934 Krumbein 1941 Sneed amp Folk 1958) All mathematical definitions

(quantitatives) are models used to simplify the complexity of shape description Some

authors (Mitchell amp Soga 2005 Arasan et al 2010) are using three sub-quantities

one and each describing the shape but at different scales The terms are

morphologyform roundness and surface texture (figure 1) The three sub-quantities

are probably the best way to classify and describe a particle because not a single

definition can interpret the whole morphology Common language is needed when

descriptors are explained and these three scales represent an option It is evident in

the reviewed literature that many of the shape descriptors are presented with the same

name but also that there is not a clear meaning on what this descriptor defines eg

when there is no upper limit in the roundness does it means that the angularity never

ends Could they be more and more angular Probably they could be on theory but

not in reality

41

62 PROPERTIES

Trough various articlersquos review done in the present investigation it is recognized that

the particlersquos shape has an effect on the material properties among these are

1 Porosity (Tickell 1938 Fraser 1935 Kolbuszewski 1948) and void ratio

(Cho et al 2006 Shergold 1953 Rouseacute et al 2008 Santamarina and Cho

2004)

2 Permeability (Witt and Brauns 1983)

3 Internal friction angle (Shinohara et al 2000 Chan and Page 1997

Cheshomi et al 2009)

4 Density (Youd 1973 Holubec and DrsquoAppolonia 1973)

5 Drag coefficient Hydraulics (Briggs and McCulloch 1962)

In Table 5 is a short resume of the properties and shape effect found in peer review

articles trough different journals Most of the reviewed articles based its research on

uniform graded sands

Table 8 Compilation of properties influenced by particle shape

Repose

angle

Friction

angle

Porosity and

Void ratio Density Permeability

Settling velocity

Drag coefficient Deformation

Sphericity (3D)shape factor

NI x x x x x x

Circularity (2D)

NI x x x x NI NI

Roundness x x x x NI NI x

x influence

NI no information available

Shape of particles has an effect on the arrangement producing bridging or avoiding

the rotation of the particles and the resulting geotechnical property is affected eg

including flaky particles can result in a higher void ratio due the bridging effect

(Santamarina and Cho 2004) and depending on the loads even the size distribution is

changed due the breakage (Yoginder et al 1985) in similar way angular particles

produce higher void ratio due the avoided possibility of the particles to rotate and

compact

The influence of the chosen shape descriptor appears in this review to have minor

influence on the soil properties in the reviewed studies except on the void ratio and

the friction angle Influence of particle shape in some cases is hider by other factors

(eg size distribution) also the particle shape probably does not have influence when

particle size is in the clay order (eg hydraulic conductivity) the reason could be due

to forces as electrostatic or capillarity become more important at this level

Among the shape descriptors some are chosen more often in literature (eg aspect

ratio) there is no apparent scientific basis to use it (probably due to the simplicity of

the measurement it becomes one of the most use) but there are still some other

descriptors that may or may not show better correlation with the soil properties

Instead empirical relations had been developed regarding roundness or shape to

describe the soil behaviour it is clear that the mechanism behind the results is still not

completely understood

42

There is necessity to define the best(s) shape descriptor(s) to be used for particular

geotechnical properties

63 IMAGE ANALYSIS

Many image analysis techniques had been used to describe the particle shape eg

Fourier analysis fractal dimension tomography etc (Hyslip and Vallejo 1997) but

there is not agreement on the usage or conclusion to ensure the best particle descriptor

for geotechnical applications

There are several shape descriptors and also various techniques to capture the

particles profile (3-dimensions 3-dimension orthogonal and 2-dimensions) Each

technique presents advantages and disadvantages 3-dimensions is probably the

technique that provide more information about the particle shape but the precision

also lies in the resolution the equipment required to perform such capture could be

more or less sophisticated (scanning particles laying down in one position and later

move to complete the scanning or just falling down particles to scan it in one step)

3-dimensions orthogonal this technique use less sophisticated equipment (compare

with the previous technique) but its use is limited to particles over 1cm also

information between the orthogonal pictures is not capture 2-dimensions require non

sophisticated equipment but at the same time the shape information diminish compare

with the previous due the fact that it is possible to determine only the outline as the

particle measurements are performed in 2-dimensions it is presumed that they will lie

with its shortest axis perpendicular to the laying surface when they are flat but when

the particle tends to have more or less similar axis the laying could be random

Advantages on the use of image analysis are clear there is not subjectivity because it

is possible to obtain same result over the same images Electronic files do not loose

resolution and it is important when collaboration among distant work places is done

files can be send with the entire confidence and knowing that file properties has not

been changed Technology evolutions allowed to work with more information and it

also applies to the image processing area were the time consumed has been shortened

(more images processed in less time)

One important aspect in image analysis is the used resolution in the analysis due the

fact that there are measurements dependent and independent on resolution Thus

those dependent measurements should be avoided due the error included when they

are applied or avoid low resolution to increase the reliability Among these

parameters length is the principal parameter that is influences by resolution (eg

perimeter diameter axis etc) Resolution also has another aspect with two faces

quality versus capacity more resolution (quality) means more storage space a

minimum resolution to obtain reasonable and reliable data must be known but it

depend on each particular application

43

64 APPLICATIONS

Quantify changes in particles in the authorrsquos thought is one of the future applications

due the non-invasive methods of taking photographs in the surface of the damrsquos slope

rail road ballast or roads Sampling of the material and comparing with previous

results could show volume (3D analysis) or area (2D analysis) loss of the particles as

well as the form roundness and roughness This is important when it has been

suggested that a soil or rock embankment decrees their stability properties (eg

internal friction angle) with the loss of sphericity roundness or roughness

Seepage stock piling groundwater etc should try to include the particle shape while

modelling seepage requires grading material to not allow particles move due the

water pressure but in angular materials as it is known the void ratio is great than the

rounded soil it means the space and the possibilities for the small particles to move

are greater stock piling could be modelled incorporating the particle shape to

determine the binrsquos capacity when particle shape changes (void ratio changes when

particle shape changes) Modelling requires all information available and the

understanding of the principles that apply

Industry is actually using the particle shape to understand the soil behaviour and

transform processes into practical and economic image analysis has been included in

the quality control to determine particle shape and size because the advantages it

brings eg the acquisition of the sieving curve for pellets using digital images taken

from conveyor this allows to have the information in a short period of time with a

similar result at least enough from the practical point of view as the traditional

sieving

7 CONCLUSIONS

The conclusions of this literature review are

It has been shown that particle shape has influence on the soil behaviour

despite of partial knowledge of the mechanism behind Understanding of the

particle shape and its influence needs to be accomplished

A common language needs to be built up to standardize the meaning on

geotechnical field that involve the particle shape General relationships

between shape and properties should be developed

Based on this review it is not clear which is the best descriptor to use in

geotechnical engineering affecting he related shape to properties Instead of a

couple of standards there is no shape descriptor in geotechnical field fully

accepted

Image analysis tool is objective make the results repeatable obtain fast results

and work with more amount of information

44

Resolution needs to be taken in consideration when image analysis is been

carried out because the effects could be considerable Resolution must be set

according to the necessities Parameters as perimeter can be affected by

resolution

There are examples where particle shape has been incorporated in industries

related to geotechnical engineering eg in the ballast and asphalt industry for

quality control

8 FURTHER WORK

Three main issues have been identified in this review that will be further investigated

the limits of shape descriptors influence of grading and choice of descriptor for

relation to geotechnical properties

Shape descriptors have low and high limits frequently the limits are not the same and

the ability to describe the particlersquos shape is relative The sensitivity of each descriptor

should be compare to apply the most suitable descriptor in each situation

Sieving curve determine the particle size in a granular soil particle shape could differ

in each sieve size There is the necessity to describe the particle shape on each sieve

portion (due to practical issues) and included in the sieve curve Obtain an average

shape in determined sieve size is complicated (due to the possible presence of several

shapes) and to obtain the particle shape on the overall particlersquos size is challenging

how the particle shape should be included

Since several descriptors have been used to determine the shape of the particles and

the relation with the soil properties it is convenient to determine the descriptorrsquos

correlation with the soil properties

9 ACKNOWLEDGMENT

I would like to thanks to Lulearing University of Technology (LTU) the time I had spent

in its facilities and the kind environment it offers and University of Sonora

(UNISON) that has been providing me the financial support and the time to conclude

this journey

10 REFERENCES

Andersson T (2010) Estimating particle size distributions based on machine vision

Doctoral Thesis Departament of Computer Science and Electrical Engineering Lulearing

University of Technology ISSN 1402-1544 ISBN 978-91-7439-186-2

45

Arasan Seracettin Hasiloglu A Samet Akbulut Suat (2010) Shape particle of

natural and crished aggregate using image analysis International Journal of Civil and

Structural Engineering Vol 1 No 2 pp 221-233 ISSN 0970-4399

Aschenbrenner BC (1956) A new method of expressing particle sphericity Journal

of Sedimentary Petrology Vol 26 No 1 pp 15-31

Axelsson K (1998) Introduktion till jordmekaniken jaumlmte jordmateriallaumlran Skrift

984 Lulearing Avdelningen foumlr Geoteknologi Lulearing Tekniska Universitet (In Swedish)

Barton Nick amp Kjaernsli Bjorn (1981) Shear strength of rockfill Journal of the

Geotechnical Engineering Division Proceedings of the American Society of Civil

Engineers (ASCE) Vol 107 No GT7

Barrett P J (1980) The shape of rock particles a critical review Sedimentology

Vol 27 pp 291-303

Blott S J and Pye K (2008) Particle shape a review and new methods of

characterization and classification Sedimentology Vol 55 pp 31-63

Bowman E T Soga K and Drummond W (2001) Particle shape characterization

using Fourier descriptor analysis Geotechnique Vol 51 No 6 pp 545-554

Briggs L I McCulloch D S (1962) Hydraulic shape of sand particles Journal of

Sedimentary Petrology Vol 32 pp 645-656

Chan Leonard C Y and Page Neil W (1997) Particle fractal and load effects on

internal friction in powders Powder Technology Vol 90 pp 259-266

Cheshomi A Fakher A Jones C J F P (2009) A correlation between friction

angle and particle shape metrics in quaternary coarse alluvia Quarterly Journal of

Engineering Geology and Hydrogeology Vol 42 pp 145-155

Cho G Dodds J and Santamarina J C (2006) Particle shape effects on packing

density stiffness and strength Natural and crushed sands Journal of Geotechnical

and Geoenvironmental Engineering May 2006 pp 591-602

Dietrich William E (1982) Settling velocity of natural particles Water Resources

Research Vol 18 No 6 pp 1615-1626

Dobkins J E and Folk R L (1970) Shape development on Tahiti-nui Journal of

Sedimentary Petrology Vol 40 No 2 pp 1167-1203

Folk R L (1955) Student operator error in determining of roundness sphericity and

grain size Journal of Sedimentary Petrology Vol 25 pp 297-301

Fernlund J M R (1998) The effect of particle form on sieve analysis A test by

image analysis Engineering Geology Vol 50 No 1-2 pp 111-124

46

Fernlund J M R (2005) Image analysis method for determining 3-D shape of

coarse aggregate Cement and Concrete Research Vol 35 Issue 8 pp 1629-1637

Fernlund J M R Zimmerman Robert and Kragic Danica (2007) Influence of

volumemass on grain-size curves and conversion of image-analysis size to sieve size

Engineering Geology Vol 90 No 3-4 pp 124-137

Fraser H J (1935) Experimental study of the porosity and permeability of clastic

sediments The Journal of Geology Vol 43 pp 910-1010 ISSN 0022-1376

Hayati Ali Nemati Ahmadi Mohammad Mehdi and Mohammadi Soheil (2012)

American Physical Society Physical review E 85 036310 DOI

101103PhysRevE85036310

Hawkins A E (1993) The Shape of Powder-Particle Outlines Wiley New York

Head K H and Epps R J (2011) Manual of soil Laboratory testing Volum II

Permeability shear strength and compressibility test 3rd

edition Whittles Publishing

Scotland UK 3rd

edition

Holubec I and DrsquoAppolonia E (1973) Effect of particle shape on the engineering

properties of granular soils ASTM STP 523 pp 304-318

Hyslip James P Vallejo Luis E (1997) Fractal analysis of the roughness and size

distribution of granular materials Engineering Geology Vol 48 pp 231-244

Janoo Vincent C (1998) Quantification of shape angularity and surface texture of

base course materials US Army Corps of Engineers Cold Region Research and

Engineering Laboratory Special report 98-1

Jefferies Mike and Been Ken (2000) Soil liquefaction A critical state approach

Taylor amp Francis Group London and New York

Jimenez Jose A Madsen Ole S (2003) A simple formula to estimate settling

velocity of natural sediments Journal of Waterway Port Coastal and Ocean

Engineering Vol 129 No 2 pp 70-78

Johansson Jens and Vall Jakob (2011) Jordmaterials kornform Inverkan paring

Geotekniska Egenskaper Beskrivande storheter bestaumlmningsmetoder

Examensarbete Avdelningen foumlr Geoteknologi Institutionen foumlr Samhaumlllsbyggnad

och naturresurser Lulearing Tekniska Universitet Lulearing (In Swedish)

Kane Joseph W and Sternheim Morton M (1988) Physics John Wiley amp Sons Inc

Third edition

Kolbuszewski J (1948) An experimental study of the maximum and minimum

porosities of sands Proceedings of the Second International Conference on Soil

Mechanics and Foundation Engineering Rotterdam June 21 to 30 Sub-section IIb

pp 158-165

47

Krumbein W C and Pettijohn FJ (1938) Manual of sedimentary petrography

Appleton-Century Crofts Inc New York

Krumbein W C (1941) Measurement and geological significance of shape and

roundness of sedimentary particles Journal of Sedimentary Petrology Vol 11 No 2

pp 64-72

Krumbein W C and Sloss L L (1963) Stratigraphy and Sedimentation 2nd

ed

WH Freeman San Francisco

Kuo Chun-Yi and Freeman Reed B (1998a) Image analysis evaluation of

aggregates for asphalt concrete mixtures Transportation Research Record Vol 1615

pp 65-71

Kuo Chun-Yi Rollings Raymond and Lynch Larry N (1998b) Morphological

study of coarse aggregates using image analysis Journal of Materials in Civil

Engineering Vol 10 No 3 pp 135-142

Lanaro F Tolppanen P (2002) 3D characterization of coarse aggregates

Engineering Geology Vol 65 pp 17-30

Lees G (1964a) A new method for determining the angularity of particles

Sedimentology Vol 3 pp 2-21

Lees G (1964b) The measurement of particle shape and its influence in engineering

materials British Granite Whinstone Federation Vol 4 No 2 pp 17-38

Matsushima Takashi Saomoto Hidetaka Matsumoto Masaaki Toda Kengo

Yamada Yasuo (2003) Discrete element simulation of an assembly of irregular-

shaped grains Quantitative comparison with experiments 16th ASCE Engineering

Mechanics Conference University of Washington Seattle July 16-18

Mitchell James K and Soga Kenichi (2005) Fundamentals of soil behaviour Third

edition WILEY

Mora C F Kwan A K H Chan H C (1998) Particle size distribution analysis of

coarse aggregate using digital image processing Cement and Concrete Research Vol

28 pp 921-932

Mora C F and Kwan A K H (2000) Sphericity shape factor and convexity

measurement of coarse aggregate for concrete using digital image processing Cement

and Concrete Research Vol 30 No 3 pp 351-358

Muskat Morris (1937) The Flow of fluids through porous media Journal of Applied

Physics Vol 8 pp 274

Nearing M A and Parker S C (1994) Detachment of soil by flowing water under

turbulent and laminar conditions Soil Science Society of American Journal Vol 58

No 6 pp 1612-1614

48

Pan Tongyan Tutumluer Erol Carpenter Samuel H (2006) Effect of coarse

aggregate morphology on permanent deformation behavior of hot mix asphalt Journal

of Transportation Engineering Vol 132 No 7 pp 580-589

Pellegrino A (1965) Geotechnical properties of coarse-grained soils Proceedings

International Conference of Soil Mechanics and Foundation Engineering Vol 1 pp

97-91

Pentland A (1927) A method of measuring the angularity of sands MAG MN AL

Acta Eng Dom Transaction of the Royal Society of Canada Vol 21 Ser3xciii

Persson Anna-Lena (1998) Image analysis of shape and size of fine aggregates

Engineering Geology Vol 50 pp 177-186

Powers M C (1953) A new roundness scale for sedimentary particles Journal of

Sedimentary Petrology Vol 23 No 2 pp 117-119

Pye W and Pye M (1943) Sphericity determination of pebbles and grains Journal

of Sedimentary Petrology Vol 13 No 1 pp 28-34

Qazi M A (1975) Flow properties of granular masses A review on the angle of

repose The Arabian Journal for Science and Engineering Vol 1 No 2

Quiroga Pedro Nel and Fowle David W (2003) The effects of aggregate

characteristics on the performance of portland cement concrete Report ICAR 104-1F

Project number 104 International Center for Aggregates Research University of

Texas

Riley N A (1941) Projection sphericity Journal of Sedimentary Petrology Vol 11

No 2 pp 94-97

Rouseacute P C Fennin R J and Shuttle D A (2008) Influence of roundness on the

void ratio and strength of uniform sand Geotechnique Vol 58 No 3 227-231

Santamarina J C and Cho G C (2004) Soil behaviour The role of particle shape

Proceedings Skempton Conf London

Schofield and Wroth (1968) Critical state soil mechanics McGraw Hill

Shaumlfer Michael (2002) Digital optics Some remarks on the accuracy of particle

image analysis Particle amp Particle Systems Characterization Vol 19 No 3 pp 158-

168

Shergold F A (1953) The percentage of voids in compacted gravel as a measure of

its angularity Magazine of Concrete Research Vol 5 No 13 pp 3-10

Shinohara Kunio Oida Mikihiro Golman Boris (2000) Effect of particle shape on

angle of internal friction by triaxial compression test Powder Technology Vol 107

pp131-136

49

Skredcommisionen (1995) Ingenjoumlrsvetenskapsakademinen rapport 395 Linkoumlping

1995

Sneed E D and Folk R L (1958) Pebbles in the Colorado river Texas A study in

particle morphogenesis Journal of Geology Vol 66 pp 114-150

Sperry James M and Peirce J Jeffrey (1995) A model for estimating the hydraulic

conductivity of granular material based on grain shape grain size and porosity

Ground Water Vol 33 No 6 pp 892-898

Sukumaran B and Ashmawy A K (2001) Quantitative characterisation of the

geometry of discrete particles Geotechnique Vol 51 No 7 pp 619-627

Szaacutedeczy-Kardoss E Von (1933) Die bistimmung der abrollungsgrades Geologie

und palaumlontologie Vol 34B pp 389-401 (in German)

Teller J T (1976) Equantcy versus sphericity Sedimentology Vol 23 pp 427-428

Tickell F G (1938) Effect of the angularity of grain on porosity and permeability

bulletin of the American Association of Petroleum Geologist Vol 22 pp 1272-1274

Tutumluer E Huang H Hashash Y Ghaboussi J (2006) Aggregate shape effects

on ballast tamping and railroad track lateral stability AREMA 2006 Annual

Conference Louisville KY

Wadell H (1932) ldquoVolume Shape and roundness of rock particlesrdquo Journal of

Geology Vol 40 pp 443-451

Wadell H (1933) Sphericity and roundness of rock Particles Journal of Geology

Vol 41 No 3 pp 310ndash331

Wadell H (1934) Shape determination of large sedimental rock fragments

The Pan-American Geologist Vol 61 pp 187-220

Wadell H (1935) ldquoVolume shape and roundness of quartz particlesrdquo Journal of

Geology Vol 43 pp 250-279

Wentworth W C (1922a) The shape of beach pebbles Washington US Geological

Survey Bulletin Vol 131C pp 75-83

Wentworth W C (1922b) A method of measuring and plotting the shape of pebbles

Washington US Geological Survey Bulletin Vol 730C pp 91-114

Wentworth W C (1933) The shape of rock particle A discussion Journal of

Geology Vol 41 pp 306-309

Witt K J Brauns J (1983) Permeability-Anisotropy due to particle shape Journal

of Geotechnical Engineering Vol 109 No 9 pp 1181-1187

14

Fischer in 1933 (Hawkins 1993) used a straightforward method to quantify roundness

using a central point in the outline and dividing the outline in angles around this point

that were subtended by the straight or non curved parts of the profile were measured

This is illustrated in figure 14

To express the angularity value Fischer used the ratio of angles standing linear parts

on the outlines and concave respectively

Figure 14 left (A) and right (B) gives a similar angularity of approximately 042

using the above equations (Hawkins 1993)

Wentworth in 1922 used the maximum projection to define the position of the particle

to obtain the outline or contour (Barret 1980) The equation reflects the relation of the

diameter of a circle fitting the sharpest corner and the longest axis plus the shortest

axis c (minimum projection)

Wentworth (Hawkins 1993) expressed the roundness as the ratio of the radius of

curvature of the most convex part and the longest axis plus short axis

Actually these last two equations are the same just expressed in different terms when

the particle is in its maximum projection

Dimensions can be seen on figure 15 L and B represents the mayor axis a and

intermediate axis b The intention is to make difference between the 2 and 3

dimensions (L and B are for 2D as a b and c are for 3D)

deg360

ANG

=R

sumPLA

PLA

CON

ANG

ANGR

2)S(L

DR

M

S

B)4(L

RR CON

Figure 14 Fischerrsquos methods of angularity computation (Hawkins 1993)

A=inscribed circle B=circumscribed circle

(24)

(25)

(26)

(27)

15

Wentworth 1919 has a second way to express the roundness called Shape index

(Barrett 1980) and it relates the sharpest corner and the diameter of a pebble trough

the sharpest corner

Wentworth (1922b) used define the roundness as the ratio of the sharpest corner and

the average radius of the pebble

Cailleux (Barrett 1980) relates the radius of the most convex part and the longest

axis

Kuenen in 1956 show his roundness index (Barrett 1980) between the sharpest corner

and the breath axis

Dobkins amp Folk (1970) used a modified Wentworth roundness with the relation of

sharpest corner and inscribed circle diameters

AVG

CON

R

RR

x

s

D

DR

L2

RR CON

B

DR s

i

s

D

DR

3AVGAVG cbaDR2

Figure 15 Description of L and B axes (Hawkins 1993)

(28)

(29)

(30)

(31)

(32)

(33)

16

Swan in 1974 shows his equation (Barrett 1980) relating the sharpest (or the two

sharpest) corner(s) and inscribed circle diameter

Szadeczsky-Kardoss has his Average roundness of outline (Krumbein and Pettijohn

1938) relating the concave parts perimeter and the actual perimeter

Lees (1964a) developed an opposite definition to roundness it means that he

measures the angularity instead of the roundness and he calls it Degree of angularity

Figure 16 shows the items considered when equation 36 applies as the angles (α)

inscribed circle (Rmax-in) and the distance (x) The main formula is

In order to apply the last equation corners needs to be entered in the formula and each

individual result will add to each other to obtain the final degree of angularity

A roundness index appears on Janoo (1998) Kuo and Freeman (1998a) and Kuo et

al (1998b) it is described as

The last equation is on section 34 also because there is not a general agreement on the

definition furthermore some authors had used to define the roughness this is not the

only equation that has been used trying to define different aspects (sphericity

roundness or roughness) but it is a good example of the misuse of the quantities and

definitions

inmaxR

x)180(R

2P

A4R

i

ss

D

DDR

221

100P

PR CON

Figure 16 Degree of angularity measurement technique (Blot and Pye 2008)

(34)

(35)

(36)

(17)

17

Sukumaran and Ashmawy (2001) present an angularity factor (AF) calculated from

the number of sharpness corners Angles βi required to obtain the angularity factor are

shown in figure 9

Sukumaran and Ashmawy (2001) also suggested use not bigger sampling interval of

N=40 because it is the cut off between angularity factor and surface roughness If so

this equation could be used to describe the roughness

Table 5 General chronological overview of the particle roundness

Aspect Name Author Year Based on

Roundness shape index Wentworth 19191

diameter of sharper corner

shape index Wentworth 1922b sharpest corner and axis

roundness Wentworth 1933 convex parts

Fischer 19332

noncurved parts outline

Fischer 19332

noncurved-streigth parts outline

Average roundness of outline

Szadeczsky-Kardoss 19333

convex parts-perimeter

roundness Wadell 1935 diameter of corners

roundness Wadell 1935 diameter of corners

roundness Russel amp Taylor 19372

class limit table

roundness Krumbein 1941 chart

Cailleux 19471

convex parts

roundness Pettijohn 19494 class limit table

roundness Powers 1953 chart and class limit table

Kuenen 19561

axis-convex corner

roundness Krumbein and Sloss 1963 chart

degree of angularity Lees 1964a corners angles and inscribed circle

Dobkins amp Folk 1970 diameter of sharper corner

Swan 19741

diameter of sharper corners

Angularity factor Sukumaran and

Ashmawy 2001

Segmentation of particles and angles

1) Barret 1980 2) Hawkins 1993 3) Krumbein and Pettijohn 1938 4) Powers 1953

sum

sumsumN

1=i

2

i

2

N

1=i

2

i

2N

1=ii

)ordm180 -circleβ( - )(180ordm x 3

)ordm180-circleβ(-)ordm180 -Particleβ(

= AF (37)

18

36 ROUGHNESS OR SURFACE TEXTURE

A third property called texture appears early in the literature with the sphericity and

roundness properties since then texture property was longed described but it was in

accordance with the authors at that time not measurable

Wright in 1955 developed a method to quantify the surface texture or roughness of

concrete aggregate using studies done on 19 mm stones The test aggregates were first

embedded in a synthetic resin The stones were cut in thin sections The sections

projection was magnified 125 times The unevenness of the surface was traced and the

total length of the trace was measured The length was then compared with an uneven

line drawn as a series of chords (see figure 17) The difference between these two

lines was defined as the roughness factor (Janoo 1998)

However with the advance of technology it has become easier measure the roughness

and here is presented some researcherrsquos ideas how this property should be calculated

One technique used by Janoo (1988) to define the roughness can be seen in figure 18a

and is defined as the ratio between perimeter and convex perimeter

The convex perimeter is obtained using the Feretrsquos box (or diameter) tending a line in

between the touching points that the Feretrsquos box describes each time it is turn (figure

18b)

PER

OC

PR

Figure 17 Measurement method for characterizing the surface texture of an aggregate (Janoo 1998)

a) Convex perimeter (CPER) b) Feret measurement Figure 18 a) Convex perimeter (CPER) b) Feret measurement (modified after Janoo 1998)

(38)

a)

b)

19

Kuo and Freeman (1998a) and Kuo et al (1998b) use the roughness definition as the

ratio perimeter and average diameter

Erosion and dilatation image processing techniques are used to obtain the surface

texture Erosion is a morphological process by which boundary image pixels are

removed from an object surface which leaves the object less dense along the

perimeter or outer boundary Dilatation is the reverse process of erosion and a single

dilatation cycle increases the particle shape or image dimension by adding pixels

around its boundary (Pan etal 2006)

The ldquonrdquo erosion and dilatation cycles are not standardized

Mora and Kwan (2000) used the ldquoconvexity ratio CRrdquo (equation 41) and the ldquofullness

ratio FRrdquo (equation 42) in their investigation they are

The convex area is the area of the minimum convex boundaries circumscribing the

particle This is illustrated in the figure 19 The convex area is obtained in a similar

way as the convex perimeter but in this case the area between the original outline and

the convex perimeter is our convex area

AVG

OD

PR

100A

1AARO

CONo A

AR =

CONo A

AR =

Figure 19 Evaluation of area and convex area (Mora and Kuan 2000)

(39)

(40)

(41)

(42)

20

4 TECHNIQUES IN ORDER TO DETERMINE PARTICLE

SHAPE

41 HAND MEASUREMENT

Hand measurement technique was the first used by obvious reasons in order to

improve the accuracy special devices developed as the ldquosliding rod caliperrdquo used by

Krumbein (1941) it works placing the sample on the sliding road calliper as show

figure 20b the length in different positions can be obtain by using the scale provided

in the handle the ldquoconvexity gagerdquo that was actually used by opticians to measure the

curvature of lenses but easily applicable to the particle shape analysis (Wentworth

1922b) works measuring the movement of the central pivot as figure 20a shows (the

two adjacent pivots are invariable) as many the central pivot moves more is the

curvature or the ldquoSzadeczky-Kardossrsquos apparatusrdquo develop in 1933 that traces the

profile of the rock fragment so the outline traced is then analyzed (Krumbein and

Pettijohn 1938) figure 20c show equipment

Another helpful tool to determine the particle dimensions was the ldquocamera lucidardquo to

project the particlersquos contour over a circle scale appearing in Figure 21 thus it is

possible to measure the particlersquos diameter

a)

c) b)

Figure 20 a) convexity gage used to determine the curvature in particle corners (Wenworth 1922b)

b)sliding rod caliper device to measure the particle axis length (Krumbein 1941) and c)Szadeczky-

Kardoss (1933) apparatus it was utilized to obtain the particle outline

Figure 21 Circle scale used by Wadell (1935) to determine particlersquos diameter and roundness

21

42 SIEVE ANALYSIS

Bar sieving eg according to EN 933-31997 can be used to determine simple large

scale properties By combining mesh geometries the obtained results can be used to

quantify flakiness and elongation index ASTM D4791 (Flat and elongated particles

are defined as those coarse aggregate particles that have a ratio of length to thickness

equal to or greater than a specified value such as 51 The index represents the

percentage on weight of these particles) The method is not suitable for fine materials

This due to the difficulty to get the fine grains passed through the sieve and the great

amount of particles in relation to the area of the sieve (Persson 1998) eg EN 933-

31997 related to flakiness index The test is performed on aggregates with grain size

from 4 mm and up to 63 mm two sieving operations are necessary the first separates

on size fraction and the second use a bar sieve after the first sieving the average

maximum diameter of the particles is obtain and with the second sieving (bar sieving)

the shortest axis diameter is found finally with this two parameters the flakiness

index is determined

There are more standards related with the particle shape (see appendix A) but this

above presented are probably the most known using sieve analysis to determine

particlersquos geometrical properties

Sieve analysis is facing the computers age and image analysis sieving research is

taking place (Andersson 2010 Mora and Kwan 2000 Persson 1998) Industry is

also applying the image analysis sieving with decrees on the testing time compare

with the traditional sieving method An inconvenient of image analysis is the error

due the overlapping or hiding of the particles during the capture process but the

advantages are more compare with disadvantages (Anderson 2010)

43 CHART COMPARISON

Charts developed over the necessity of faster results because the long time consuming

required when measuring each particle

Krumbein (1941) present a comparison roundness chart for pebbles which were

measured by Wadellrsquos method because this property was the most difficult to measure

due to the second order scale that roundness represents (See figure 22)

Figure 22 Krumbein (1941) comparision chart for roundness

22

A qualitative chart by Powers (1953) try to include both (sphericity and roundness)

particlersquos characteristics it was divided on six roundness ranges (very angular

angular sub-angular sub-rounded rounded and well rounded) and two sphericity

series (high and low sphericity) This chart was prepared with photographs to enhance

the reader perspective (See figure 23)

A new chart including sphericity and roundness appear this time it was easier to

handle the two mean properties of particlersquos shape furthermore there was included

the numerical values that eliminated the subjectivity of qualitative description The

chart is based on Wadellrsquos definitions (Krumbein and Sloss 1963) (See figure 24)

Folk (1955) worried about the personrsquos error on the chartrsquos comparison studied the

determination of sphericity and angularity (he used the Powers 1953 comparison

chart) he found that the sphericity determination by chart comparison has a negligible

error while the roundness he concluded it was necessary to carry out a more wide

research due the high variability show by his study

Figure 23 Powers (1953) qualitative shpericity-roundness chart

Figure 24 Sphericity-roundness comparison chart (Krumbein and sloss 1963)

23

44 IMAGE ANALYSIS

Image analysis is a practical method to use for shape classification since it is fast and

can be automated Different techniques appear to process these images among them

are

o Feret Diameter the Feret diameter is the longitude between two parallel lines

this lines can rotate around one particle or outline to define dimensions as it

is shown in figure 25 these method is not a fine descriptor but as it was say

above it is a helpful tool to determine diameters (Janoo 1988)

o Fourier Mathematical Technique It produces mathematical relations that

characterize the profile of individual particles This method favours the

analysis of roughness and textural features for granular soils The problem in

the methodology remains in the re-entrant angles in order to complete the

revolution (Bowman et al 2001) see figure 26

o Fractal Dimension Irregular line at any level of scrutiny is by definition

fractal (Hyslip and Vallejo 1997) Figure 27 shows fractal analysis by the

dividing method The length of the fractal line can be defined as

N

1n

nn0 )nsinbncosa(a)(R

RD1n)(P

Figure 25 Feret measurement technique is defined by two parallel lines turning

around the particle to define the shortest and longest Feret diameter (Janoo 1988)

Figure 26 Fourier technique with two radiuses at one angle (Bowman et al 2001)

(43)

(44)

24

o Orthogonal image analysis This technique is basically the use of two images

orthogonal between them to acquire the three particle dimensions (Fernlund

2005) any of the above techniques can be used in this orthogonal way

o Laser Scanning Technique this kind of laser scanning 3D is one of the most

advanced techniques In figures 28a) we have the laser head scanning the rock

particles the particles have control points in order to keep a reference point

when move them to scan the lower part in figure 28b) we can see the laser

path followed (Lanaro and Tolppanen 2002)

Another technique is the Laser-Aided Tomography (LAT) in this case a laser sheet is

used to obtain the particles surveying (see figure 29) This technique is different and

has special requirements as to use liquid with same refractive index as the particles

particles must let the laser or certain percent of light go through (Matsushima et al

2003)

a) b)

Figure 27 Fractal analysis by the dividing method at different scrutiny scale (Hyslip and Vallejo 1997)

Figure 28 a) Scanning head b) scanning path (Lanaro and Tolppanen 2002)

Figure 30 3D scan completed ready to

use for any further measure

(Matsushima et al 2003)

Figure 29 LAT scaning particles

(Matsushima et al 2003)

25

Both 3D techniques obtain the particle shape that is later used to achieve measures as

we can see in figure 30

All these previous techniques are easily written in codes or scripts to be interpreted in

a digital way obtaining the desired measurement but there are some interesting points

in the image analysis regarding on the errors involve among them are image

resolution and orientation of the particles orientation is not relevant when it is

random and large number of particles are involve resolution have an influence on the

accuracy (Zeidan et al 2007)

When resolution is increase more accuracy is obtain and the object representation

match better with the real form in the other hand more resolution means more

spending on memory and time thus resolution needs to be according with the goal

and precision needed in any work (Schaumlfer 2002)

Schaumlfer (2002) conclude that attributes like length when measuring digital images

present relative high errors It can be vanish or at least diminish using high resolution

just for diameter but not for perimeter that keep the error as big as initially Johansson

and Vall (2011) obtain similar results when 3 different resolutions were used in the

same particle obtaining an unstable output for those termsquantities that involve the

perimeter Thus all quantities relating the perimeter should be treated with care

5 EFFECT OF SHAPE ON SOIL PROPERTIES

51 INTRODUCTION

In laboratory test on the effect on particle size on basic properties has been

investigated in several studies this relation has been discussed and various

mechanisms had been proposed to explain the behaviour of the soil in dependency

also with the shape Basically there are two mechanisms proposed The arrangement

of particles and the inter-particle contact (Santamarina and Cho 2004) and

subsequence breakage

The arrangement of particles

Arrangement of the particles can be presented in three different forms loose dense

and critical this arrangement determines the soil properties (eg density increase with

more dense arrangement) Loose and dense states are easy understandable when

figure 31 is explained while in the upper part of the figure the particles are arranged

using the minimum space needed in the lower part a span is created using the flaky

particle as a bridge this phenomena is known as ldquobridgingrdquo Bridging can produce

different geotechnical results when just the shape of the particle is changed eg void

ratio (Santamarina and Cho 2004) Particles are able to rearrange this could be done

applying pressure (energy) to the soil the pressure (energy) will create such forces

that soil particles will rotate and move (see figure 34) finishing in a more dense state

26

A loose soil will contract in volume on shearing and may not develop any peak

strength (figure 32 left) In this case the shear strength will increase gradually until

the residual shear strength is revealed once the soil has ceased contracting in volume

A dense soil may contract slightly (figure 32 right) before granular interlock prevents

further contraction (granular interlock is dependent on the shape of the grains and

their initial packing arrangement) In order to continue shearing once granular

interlock has occurred the soil must dilate (expand in volume) As additional shear

force is required to dilate the soil a peak shear strength occurs (figure 32 left) Once

this peak shear strength caused by dilation has been overcome through continued

shearing the resistance provided by the soil to the applied shear stress reduces

(termed strain softening) Strain softening will continue until no further changes in

volume of the soil occur on continued shearing Peak shear strengths are also

observed in overconsolidated clays where the natural fabric of the soil must be

destroyed prior to reaching constant volume shearing Other effects that result in peak

strengths include cementation and bonding of particles The distinctive shear strength

called the critical state is identified where the soil undergoing shear does so at a

constant volume (Schofield and Wroth 1968)

The inter-particle contact

For frictional soil ie coarse grained soil the friction between particles is the

dominating factor for strength Materials usually consisting of coarse grains (diameter

Figure 31 Bridging effect when flaky particles are combined in the bulk material (Santamarina and

Cho 2004)

Figure 32 The left part of the figure show a typical behaviour of loose and dense material over shear stress

while at the right the figures illustrate the typical volume changes

27

gt 006mm) behave as a frictional soil it means that the strength of coarse soils (silt

sand gravel etc) comes from an inter-particle mechanical friction thus ideally they

do not have traction strength In figure 33 the inter-particle contact is illustrated here

the pressure (P) is applied and two more components are found the normal load (N)

and the tangential load (T) described as the friction coefficient (μF) The forces stand

in equilibrium (Johansson and Vall 2011)

When particles equilibrium is disturbed (friction coefficient is not enough to keep

particles unmoved) the rotation is imminent and it is necessary in order to compact

the soil in figure 34 can be seen that the arrangement is a fact that inhibit or allow this

rotation and the shape in the 3 different scales are also factors because the more

spherical andor more rounded andor less roughness more easy is the rotation

(Santamarina and Cho 2004)

Breakage

Breakage is a side effect of the inter-particle contact and rotation when pressure

exceed the rock strength it can happened when the particles are tight together and

there is not enough space to rotate it is more obvious in angular particles (mesh form)

or as in figure 31 where the flaky particle ldquobridgingrdquo is not able to rotate but it can

brake by the pressure increase Yoginder et al (1985) notice that the angular particle

break during his experiments and they turn more rounded changing the original size

and form configuration at the same time there was a soil properties loosening

Figure 33 Inter-particle contact and forces acting (Axelsson 1998)

Figure 34 Rotation inhibition by the particles compaction or low void ratio (Santamarina and Cho 2004)

28

52 INFLUENCE OF SIZE AND SHAPE

Wenworth (1922a) and Pellegrino (1965) among others suggest that agent transport of

the rocks (rigor of transport temperature and moisture changes etc) determine its

shape but also the particle genesis itself (rock structure mineralogy hardness etc) It

is not possible to determine the shape of the particles based on the agent transport or

genesis but generally a shape behaviour is expected according to Mitchell and Soga

(2005) specially when the particle size is in the clay size (gt2μm) The shapes of the

most common clay minerals are platy (figure 35) with some exceptions (eg

halloysite occurs as tubes kaolinite are large thick and stiff Smectites are composed

of small very thin and filmy particles Illites are intermediate between kaolinite and

smectite and attapulgite occurs in lathlike particle shapes) Some clay minerals

photographs are presented in figure 35

Figure 35 Clay mineral shape a) hallosite b) Kaoline c) Smactites d) Illites and e) attapulgite (Modified

from Mitchell and Soga 2005)

Figure 36 Particle size range in soils Generally the particles of clay size are plate shaped (Mitchell and

Soga 2005)

a) b) c)

e) d)

29

53 VOID RATIO AND POROSITY

The void ratio (e) is the ratio of the volume of voids to the volume of solid it is

defined by the equation

Porosity (n) is the ratio of the volume of voids to the total volume of the soil it is

represented by the equation

Holubec and DrsquoAppolonia (1973) found a relation between the void ratio and

sphericity (referred in the paper as coefficient of angularity ratio of particle surface

and equivalent sphere surface) their results show that the maximum and the minimum

void ratio increases as the shpericity decreases In this study the surface was obtained

for an indirect method based on the permeability developed by Hoffman in 1959

described in the same document Rouseacute et al (2008) defined the roundness as

Wadell (1935) and he found it as an important factor controlling the minimum and

maximum void ratios Some other authors as Youd (1973) and Cho et al (2006)

conclude the same minimum and maximum void ratios increase when sphericity and

roundness decrease Another interesting result (all above authors) was the bigger

influence of the form (sphericity circularity) and roundness on the maximum void

ratio The change of the maximum void ratio is more pronounced than the change of

the minimum void ratio when the form and roundness changes (See figure 39)

Particles arrangement and interlocking are probably the factor that controls the void

ratio bridge effect permit the existence of void among the particles while interlocking

allowed the particles to form arches avoiding the possibility to rotate and stay in a

more stable configuration eg as it happens with marbles

Figures 36 37 and 38 shows proposed empirical relationships between void ratio and

shape from tables 5 and 6 (graphically the scale goes from 0 to 1 when cero mean

high angularity shpericity or circularity and one means low angularity circularity or

sphericity) Holubec and DrsquoAppolonia (1973) data was taken to obtain a power curve

and describe a tendency Santamarina and Cho (2004) show Youd equations in the

original paper Youd (1973) never presented the equation but it is easy to use the

information to draw a trend

The graphics presented in this document (figures 36 37 and 38) must be used with

certain reserves due the fact that the original data was modified in order to fit all

information in one graphic what the figures shows is just the general trend of the

behaviourrsquos material regarding on the shape If more accurate description and

information is required the author recommends consulting the reference data In the

same way equations from Holubec and DrsquoApollonia (1973) and Youd (1973) were not

presented by the authors but the use of the information was taken in order to build up

those equations on tables 6 and 7

S

V

V

V

= e

V

V

=nV

(45)

(46)

30

Table 6 Minimum void ratio equations regarding on the quantity (Ψ for sphericity C for circularity R

for roundness SF for Sukumaran shape factor and AF for Sukumaran angularity factor)

EQUATION NUMBER REFERENCE

Figure 34 (left)

4340

minΨ45490e =

47

Holubec amp DrsquoAppolonia 1973 (Ψ

was obtained using equation 2)

SF06340

mine021903180e +=

48

Sukumaran amp Ashmawy 2001 (SF

obtained using equation 21)

C05101emin

= 49

Cho etal 2006 (C obtained using

figure 12)

Figure 34 (right)

1

minR08203590e +=

50

Youd 1973 (R obtained from figure

11 and table 3)

R34080emin

= 51

Cho et al 2006 (R obtained using

figure 12)

1

minR05104330e +=

52

Rouseacute et al 2008 (R obtained by

equation 21)

AF02330

mine372004160e +=

53

Sukumaran amp Ashmawy 2001 (AF

obtained using equation 37)

Table 7 Maximum void ratio equations regarding on the quantity (Ψ for sphericity C for circularity R

for roundness SF for Sukumaran shape factor and AF for Sukumaran angularity factor)

EQUATION NUMBER REFERENCE

Figure 35 (left)

51520

max Ψ61120e = 54

Holubec and DrsquoAppolonia 1973 (Ψ

was obtained using equation 2)

SF1190

max e0016907180e += 55

Sukumaran amp Ashmawy 2001 (SF

obtained using equation 21)

C86061emax = 56

Cho etal 2006 (C obtained using

figure 12)

Figure 35 (right)

1

max R1505540e += 57

Youd 1973 (R obtained from figure

11 and table 3)

R62031emax= 58

Cho et al 2006 (R obtained using

figure 12)

1

max R107106150e += 59

Rouseacute et al 2008 (R obtained by

equation 21)

AF0530

max e12506090e += 60

Sukumaran amp Ashmawy 2001 (AF

obtained using equation 37)

Comparing figures 37 and 38 (minimum and maximum void ratio) it can be seen on

the right scheme of both figures 37 and 38 (when the factor is roundnessangularity)

that all the empirical relations has a common initial point close to 1 (it means that

particles are well rounded) while this common agreement disappear when the

roundness factor decreases (when the particles become more angular) Same figures

(37 and 38) on the left graphs (when the factor is sphericitycircularityshape) do not

present the same behaviour in fact there is more disperse initial point close to 1(when

the particles tend to be more sphericalcircular)

31

In Figure 39 the Δe (emax-emin) has been plotted to show how the maximum void ratio

and the minimum void ratio has different rate change when the particle shape

changes Maximum void ratio increases more than minimum void ratio when the

particle shape becomes less spherical andor more angular Comparing figure 39 left

and right graphics it can be seen that right present a common initial point when the

quantity (roundnessangularity) is close to one while in the left graphic the initial

point is more disperse Both ending points in both graphics (close to zero) are

dispersed

Figures 37 38 and 39 present the same behaviour right graphics (when the factor is

roundness angularity) in each figure have an initial common point while the left

graphics do not (when the factor is sphericity circularity shape)

Figure 37 Minimum void ratio based upon the relation of shape factor proposed by the authors indicated

in the figure

Figure 38 Maximum void ratio based upon the relation of shape factor proposed by the authors indicated

in the figure

04

06

08

1

12

14

16

18

2

005

015

025

035

045

055

065

075

085

095

Factor (roundness angularity)

min

imu

m v

oid

rati

o

Youd 1973 roundness

Rouse 2008 roundness

Cho 2006 roundness

Sukumaran 2001 AF

03

04

05

06

07

08

09

1

11

12

13

05

015

025

035

045

055

065

075

085

095

Factor (sphericity circularity shape)

min

imu

m v

oid

rati

oHolubec 1973 sphericity

Cho 2006 circularity

Sukumara 2001 SF

05

07

09

11

13

15

17

19

21

00

150

250

350

450

550

650

750

850

95

Factor (sphericity circularity shape)

Maxim

um

vo

id r

ati

o

Holubec 1973 sphericity

Cho 2006 circularity

Sukumara 2001 SF

05

1

15

2

25

3

35

005

015

025

035

045

055

065

075

085

095

Factor (roundness angularity)

Maxim

um

vo

id r

ati

o

Youd 1973 roundness

Rouse 2008 roundness

Cho 2006 roundness

Sukumaran 2001 AF

32

54 ANGLE OF REPOSE

The angle of repose of a granular material is the steepest angle of descent or dip of the

slope relative to the horizontal plane when material on the slope face is on the verge

of sliding as show in figure 40

According to Qazi (1975) there are five types of forces which may act between the

particles in soils

1 Force of friction between the particles

2 Force due to presence of absorbed gas andor moisture of particle

3 Mechanical forces caused by interlocking of particles of irregular shape

4 Electrostatic forces arising from friction between the particles themselves and

the surface with which they come in contact

5 Cohesion forces operating between neighbouring particles

Rouseacute et al (2008) found a decrease of angle of repose with increase roundness

based upon ASTM C1444 test (Standard Test Method for Measuring the Angle of

Repose of Free-Flowing Mold Powders) The method consist in pouring sand on a

surface cover by paper trough a funnel of specific dimensions (the nozzle diameter

depend on the sandrsquos particle size) from an altitude of 15 inches (381 mm) The sand

is release from the funnel until the peak of the cone formed by the sand stops the flow

The repose angle is obtained with the equation

H represent the 15 inches D and d represent the diameter of the cone formed by the

sand and the diameter of the funnel respectively

Figure 39 Maximum minus minimum void ratio based upon the relation of shape factor proposed by the

authors indicated in the figure

0

01

02

03

04

05

06

07

08

09

1

005

015

025

035

045

055

065

075

085

095

Factor (sphericity circularity shape)

Maxim

um

- M

inim

um

Vo

id r

ati

oHolubec 1973 sphericity

Cho 2006 circularity

Sukumara 2001 SF

0

02

04

06

08

1

12

14

16

18

005

015

025

035

045

055

065

075

085

095

Factor (roundness angularity)

Maxim

um

- M

inim

um

Vo

id r

ati

o

Youd 1973 roundness

Rouse 2008 roundness

Cho 2006 roundness

Sukumaran 2001 AF

dD

H2

tan=φ1

rep(61)

33

Rouseacute (2008) shows an empirical relation to obtain the angle of repose based on the

roundness of the particles

55 SHEAR STRENGTH

The MohrndashCoulomb failure criterion represents the linear envelope that is obtained

from a plot of the shear strength of a material versus the applied normal stress This

relation is expressed as

where τ is the shear strength σn is the normal stress co is the intercept of the failure

envelope with the τ axis and is the slope of the failure envelope The quantity c is

often called the cohesion and the angle is called the angle of internal friction

Studies show that the internal friction angle (under drained triaxial tests) increases

more rapidly on those materials having higher angularity increasing the relative

density The internal friction angle is a function of the relative density and the particle

shape (Holubec and DrsquoAppolonia 1973)

Chan and Page (1997) found in a study made with dry copper (using different shapes

and sizes ranging from 180 to 106 μm) using a direct shear test (ring share test) that

the internal friction angle increases as the angularity increases

Shinohara et al (2000) did some experiments with steel powder different shapes

using a triaxial cell in the test Shinohara never used the roundness or angularity on

the work but apply the shape factor (relation long axisshort axis) and the results were

that as this relation deviate from factor 1 the internal friction angle increases

The following empirical relations were found in the literature showing the behaviour

of the friction angle (obtained under different conditions)

)tan( noc

Figure 40 Representation of the angle of repose

(63)

(62)

34

Cho et al (2006)

(64)

(R is obtain by comparing the Krumbein chart figure 13)

Rouseacute (2008)

(65)

(66)

(R is defined using Wadell equation 22)

In figure 41 the suggested empirical relations above and lines constructed using

author data from Holubec and DrsquoAppolonia (1973) and Sukumara and Ashmawy

(2001) are plotted together to display the general trend on the particle shape and

friction angle relation Sukumaran reports two lines one based on the shape factor

(SF) and the second referring the angularity factor (AF) Sukumaran performed the

tests at constant volume

The scale used for Holubec and DrsquoAppolonia (1973) have lower and upper limits of 1

and 2 respectively (angularity form) and a scale change was applied to be able to

presented in the actual figure 41 As in the previous section (52) the author

recommend to use the original data from the references due that the figure just follows

the general trend of the behaviourrsquos particle regarding on the shape

Figure 41 The changes on the internal friction angle shows a general increase when the particle roundness

becomes angular or in the case of Sakamuran less spheric (Shape factor SF)

35

Barton and Kjaernsli (1981) suggested a model (equation 67) to predict the peak

friction angle (φrsquo) based upon numerous trixial and direct shear data tests

where

Se equivalent strength of particle

Re equivalent roughness of particle

φb basic friction angle (obtained from basic tilting test)

σn normal load

The information required for the model is (1) the uniaxial compressive strength of the

rock (2) the d50 particle size (mesh size where 50 of the particles pass through)

required to define Se (figure 42) (3) the degree of particle roundness and (4) the

porosity following compaction All data can be estimated by simple index tests

Barton and Kjaernsli (1981) suggest that particle size and sample scale has an effect

on the friction angle and includes them to obtain the equivalent strength (Se) figure 42

shows the method to obtain this value Compressive strength (σc) was chosen to be the

factor affecting the scale because micro fractures influence this property while

samples are bigger more micro fractures contain and its compressive strength reduces

The equivalent roughness is obtain using figure 43 where is required to know the

porosity (n) and the origin of the particles (a small chart is provided in the same figure

to compare the particles profile)

b

n

ee

SLogR

Figure 42 Method of estimating Equivalent Strength (Se) of rockfill based on uniaxial compressive strength

(σc ) and d50 particle size (Barton amp Kjaernsli 1981)

(67)

36

56 SEDIMENTATION PROPERTIES

A particle released in a less dense Newtonian fluid initially accelerate trough the fluid

due to the gravity Resistances to deformation of the fluid transmitted to the particle

surface drag generate forces that act to resist the particle motion The force due to the

weight (Fw) can be written as

Where ρp ρ are density of the particle and fluid (water) respectively g is the

gravitational force and Vp is the volume of the particle

And the resistance force (FD) is

Where CD is the dimensionless drag coefficient W is the weight of the particle and A

is the cross section area

Particlersquos shape has been assumed to be spherical when equations are applied on the

settling velocity Correlation deviates when particle shape departs from spherical form

Figure 43 Method of estimating Equivalent Roughness (Roe) based on porosity of rockfill

origin material degree of roundedness and smoothness of particle (Barton amp Kjaernsli 1981)

PPW ρ)gV(ρF

A2

WρCF

2

DD

(68)

(69)

37

(Dietrich 1982) and it is known that natural particles depart from spherical form

thus it is evident that this departure would have consequences

The below equation is proposed to account the shape (in this case the Corey shape

factor equation 8) in the settling velocity (Jimenez and Madsen 2003)

Jimenez and Madsen (2003) Dietrich (1982) Briggs and McCulloch (1962) and

others were working in the hydraulic shape of particles to solve problems as sediment

transport It is obvious that the equation presented and the researcherrsquos investigation

works under certain conditions (eg grain size between 0063-1 mm)

Dietrich (1982) suggests an empirical relation that accounts settling velocity size

density shape and roundness of a particle

R1 R2 and R3 are fitted equations for size and density shape and roundness

respectively

57 HYDRAULIC CONDUCTIVITY PERMEABILITY

Darcyrsquos Law Permeability is one component of Darcyrsquos law Darcys law is a simple

proportional relationship between the instantaneous discharge rate through a porous

medium the viscosity of the fluid and the pressure drop

The total velocity Ve is equal to the product of the permeability of the medium

(porous media) k the pressure drop ∆p all divided by the viscosity μ (Muskat

1937)

Darcys law is only valid for slow viscous flow most groundwater flow cases fall in

this category Typically Darcyrsquos law is valid at any flow with laminar flow (see figure

44)

Reynoldrsquos number (Laminar and turbulent Flow) Typically any laminar flow is

considered to have a Reynoldrsquos number less than one and it would be valid to apply

Darcys law Experimental tests have shown that flow regimes with Reynolds numbers

1

ND

S

S

ZY

gd1s

WW

NDN

gd)1s(4

dS

2R1R

3 10RW

pk

Ve

(70)

(71)

(72)

(73)

38

up to 10 may still be Darcian (laminar flow) as in the case of groundwater flow The

Reynolds number (a dimensionless parameter) for porous media flow is typically

expressed as

where ρ is the density of water (units of mass per volume) υ is the specific discharge

(with units of length per time) d is a representative average grain diameter for the

porous media (often taken as the 30 passing size from a grain size analysis using

sieves - with units of length) and μ is the viscosity of the fluid (Muskat 1937)

Shape effects Permeability as Head and Epps (2011) suggested is affected by the

shape and texture of soil grains Elongated or irregular particles create flow paths

which are more tortuous than those spherical particles Particles with a rough surface

texture provide more frictional resistance to flow Both effects tend to reduce the

water flow through the soil

Kozeny-Carman empirical relation accounts for the dependency of permeability on

void ratio in uniformly graded sands serious discrepancies are found when it is

applied to clays due the lack of uniform pores (Mitchell and Soga 2005)

There are various formulations of the Kozeny-Carman equation one published by

Head and Epps (2011) takes the void ratio e the specific surface area Ss and an

angularity factor F into account of permeability k

The angularity factor F considers the shape of the particles and ranges from 11 for

rounded grains 125 for sub rounded to 14 for angular particles The specific surface

Ss is defined as

d1 and d2 represent the maximum and minimum size particle in mm

Kane amp Sternheim (1988) suggest that the inclusion of the shape factor (F) has

probably the background on the Reynolds number due this factor is dependent

significantly on the shape of the obstacles and Reynolds number determines the

presence of laminar or turbulent flow Figure 44 show how the laminar flow has low

energy dissipation while turbulent flow (eg the roughness and path tortuosity) has

high energy dissipation

e1

e

FSs

2k

3

2

dRe

21

6

ddSs

(74)

(75)

(76)

39

According to Nearing and Parker (1994) the amount of soil detached during laminar

and turbulent flow is dependent on each soil and also greater on turbulent flow due the

greater shear strength generated during this kind of flow this could suggest the

greater erosion when turbulent flow is present

58 LIQUEFACTION

Soil liquefaction is a phenomenon in which soil loses much of its strength or stiffness

for a generally short time by earthquake shaking or other rapid loading Static and

dynamic liquefactions occur been the second one the most regular known

Liquefaction often occurs in saturated soils that is soils in which the space between

individual particles is completely filled with water This water exerts a pressure on the

soil particles that influences how tightly the particles themselves are pressed together

Shaking or other rapid loading can cause the water pressure to increase to the point

where the soil particles can readily move with respect to each other (Jefferies and

Been 2000)

Jefferies and Been (2000) state that it is clear that minor variation in intrinsic

properties of sand have major influence on the critical state These might be variations

on grain shape mineralogy grain size distribution surface roughness of grains etc

Yoginder et al (1985) found that substantial decrease on liquefaction resistance

occur with increase in confining pressure for rounded and angular sands (1600 kPa)

also rounded sands show an rapidly build up of resistance against liquefaction with

increasing density while angular tailing sand in contrast show such rapid increase

only at low confining pressures At low confining pressure angular material is more

resistant to liquefaction Probably the breakage of the corners on the angular particles

in tailings is ruling the lost in resistance at high confining pressures (sieve analysis

Figure 44 The figure show the extremes of flow behaviour First turbulent conditions where the flow is

essentially random and unpredictable and second the well defined Laminar flow conditions

40

after test identify the breakage of angular particles while on rounded particles the

sieve analysis was practically the same)

59 GROUNDWATER AND SEEPAGE MODELLING

In groundwater flow the particlersquos shape affects the soilrsquos pore size distribution

hence the flow characteristics (Sperry and Peirce 1995) Tortuosity and permeability

(also see section 57) are two significant macroscopic parameters of granular medium

that affect the passing flow (Hayati et al 2012) Current models incorporating the

effects of particle shape have failed to consider irregular particles such as those that

would prevail in a natural porous medium (Sperry and Peirce 1995)

Hayati et al (2012) suggested based on his results that tortuosity effect converge

when the porosity increases indicating that the shape have dominance at low and mid

porosity ranges

Sperry and Peirce (1995) research conclusions suggest that particle size and porosity

are more important predictors for hydraulic conductivity explaining the 69 of the

variability but particle shape appears to be the next most important This however

apparently comprises particles larger than 295-351 μm Differences for particle size

295-351 μm and smaller are not detectable Another interesting result in the research

was the interaction effect of the particle size and particle shape It suggests a different

packing configuration for particles of the same shape but different size (scale

dependent)

6 DISCUSSION

61 TERMS QUANTITIES AND DEFINITIONS

In order to describe the particle shape in detail there are a number of terms quantities

and definitions (qualitative and quantitative) used in the literature (eg Wadell 1932

1934 Krumbein 1941 Sneed amp Folk 1958) All mathematical definitions

(quantitatives) are models used to simplify the complexity of shape description Some

authors (Mitchell amp Soga 2005 Arasan et al 2010) are using three sub-quantities

one and each describing the shape but at different scales The terms are

morphologyform roundness and surface texture (figure 1) The three sub-quantities

are probably the best way to classify and describe a particle because not a single

definition can interpret the whole morphology Common language is needed when

descriptors are explained and these three scales represent an option It is evident in

the reviewed literature that many of the shape descriptors are presented with the same

name but also that there is not a clear meaning on what this descriptor defines eg

when there is no upper limit in the roundness does it means that the angularity never

ends Could they be more and more angular Probably they could be on theory but

not in reality

41

62 PROPERTIES

Trough various articlersquos review done in the present investigation it is recognized that

the particlersquos shape has an effect on the material properties among these are

1 Porosity (Tickell 1938 Fraser 1935 Kolbuszewski 1948) and void ratio

(Cho et al 2006 Shergold 1953 Rouseacute et al 2008 Santamarina and Cho

2004)

2 Permeability (Witt and Brauns 1983)

3 Internal friction angle (Shinohara et al 2000 Chan and Page 1997

Cheshomi et al 2009)

4 Density (Youd 1973 Holubec and DrsquoAppolonia 1973)

5 Drag coefficient Hydraulics (Briggs and McCulloch 1962)

In Table 5 is a short resume of the properties and shape effect found in peer review

articles trough different journals Most of the reviewed articles based its research on

uniform graded sands

Table 8 Compilation of properties influenced by particle shape

Repose

angle

Friction

angle

Porosity and

Void ratio Density Permeability

Settling velocity

Drag coefficient Deformation

Sphericity (3D)shape factor

NI x x x x x x

Circularity (2D)

NI x x x x NI NI

Roundness x x x x NI NI x

x influence

NI no information available

Shape of particles has an effect on the arrangement producing bridging or avoiding

the rotation of the particles and the resulting geotechnical property is affected eg

including flaky particles can result in a higher void ratio due the bridging effect

(Santamarina and Cho 2004) and depending on the loads even the size distribution is

changed due the breakage (Yoginder et al 1985) in similar way angular particles

produce higher void ratio due the avoided possibility of the particles to rotate and

compact

The influence of the chosen shape descriptor appears in this review to have minor

influence on the soil properties in the reviewed studies except on the void ratio and

the friction angle Influence of particle shape in some cases is hider by other factors

(eg size distribution) also the particle shape probably does not have influence when

particle size is in the clay order (eg hydraulic conductivity) the reason could be due

to forces as electrostatic or capillarity become more important at this level

Among the shape descriptors some are chosen more often in literature (eg aspect

ratio) there is no apparent scientific basis to use it (probably due to the simplicity of

the measurement it becomes one of the most use) but there are still some other

descriptors that may or may not show better correlation with the soil properties

Instead empirical relations had been developed regarding roundness or shape to

describe the soil behaviour it is clear that the mechanism behind the results is still not

completely understood

42

There is necessity to define the best(s) shape descriptor(s) to be used for particular

geotechnical properties

63 IMAGE ANALYSIS

Many image analysis techniques had been used to describe the particle shape eg

Fourier analysis fractal dimension tomography etc (Hyslip and Vallejo 1997) but

there is not agreement on the usage or conclusion to ensure the best particle descriptor

for geotechnical applications

There are several shape descriptors and also various techniques to capture the

particles profile (3-dimensions 3-dimension orthogonal and 2-dimensions) Each

technique presents advantages and disadvantages 3-dimensions is probably the

technique that provide more information about the particle shape but the precision

also lies in the resolution the equipment required to perform such capture could be

more or less sophisticated (scanning particles laying down in one position and later

move to complete the scanning or just falling down particles to scan it in one step)

3-dimensions orthogonal this technique use less sophisticated equipment (compare

with the previous technique) but its use is limited to particles over 1cm also

information between the orthogonal pictures is not capture 2-dimensions require non

sophisticated equipment but at the same time the shape information diminish compare

with the previous due the fact that it is possible to determine only the outline as the

particle measurements are performed in 2-dimensions it is presumed that they will lie

with its shortest axis perpendicular to the laying surface when they are flat but when

the particle tends to have more or less similar axis the laying could be random

Advantages on the use of image analysis are clear there is not subjectivity because it

is possible to obtain same result over the same images Electronic files do not loose

resolution and it is important when collaboration among distant work places is done

files can be send with the entire confidence and knowing that file properties has not

been changed Technology evolutions allowed to work with more information and it

also applies to the image processing area were the time consumed has been shortened

(more images processed in less time)

One important aspect in image analysis is the used resolution in the analysis due the

fact that there are measurements dependent and independent on resolution Thus

those dependent measurements should be avoided due the error included when they

are applied or avoid low resolution to increase the reliability Among these

parameters length is the principal parameter that is influences by resolution (eg

perimeter diameter axis etc) Resolution also has another aspect with two faces

quality versus capacity more resolution (quality) means more storage space a

minimum resolution to obtain reasonable and reliable data must be known but it

depend on each particular application

43

64 APPLICATIONS

Quantify changes in particles in the authorrsquos thought is one of the future applications

due the non-invasive methods of taking photographs in the surface of the damrsquos slope

rail road ballast or roads Sampling of the material and comparing with previous

results could show volume (3D analysis) or area (2D analysis) loss of the particles as

well as the form roundness and roughness This is important when it has been

suggested that a soil or rock embankment decrees their stability properties (eg

internal friction angle) with the loss of sphericity roundness or roughness

Seepage stock piling groundwater etc should try to include the particle shape while

modelling seepage requires grading material to not allow particles move due the

water pressure but in angular materials as it is known the void ratio is great than the

rounded soil it means the space and the possibilities for the small particles to move

are greater stock piling could be modelled incorporating the particle shape to

determine the binrsquos capacity when particle shape changes (void ratio changes when

particle shape changes) Modelling requires all information available and the

understanding of the principles that apply

Industry is actually using the particle shape to understand the soil behaviour and

transform processes into practical and economic image analysis has been included in

the quality control to determine particle shape and size because the advantages it

brings eg the acquisition of the sieving curve for pellets using digital images taken

from conveyor this allows to have the information in a short period of time with a

similar result at least enough from the practical point of view as the traditional

sieving

7 CONCLUSIONS

The conclusions of this literature review are

It has been shown that particle shape has influence on the soil behaviour

despite of partial knowledge of the mechanism behind Understanding of the

particle shape and its influence needs to be accomplished

A common language needs to be built up to standardize the meaning on

geotechnical field that involve the particle shape General relationships

between shape and properties should be developed

Based on this review it is not clear which is the best descriptor to use in

geotechnical engineering affecting he related shape to properties Instead of a

couple of standards there is no shape descriptor in geotechnical field fully

accepted

Image analysis tool is objective make the results repeatable obtain fast results

and work with more amount of information

44

Resolution needs to be taken in consideration when image analysis is been

carried out because the effects could be considerable Resolution must be set

according to the necessities Parameters as perimeter can be affected by

resolution

There are examples where particle shape has been incorporated in industries

related to geotechnical engineering eg in the ballast and asphalt industry for

quality control

8 FURTHER WORK

Three main issues have been identified in this review that will be further investigated

the limits of shape descriptors influence of grading and choice of descriptor for

relation to geotechnical properties

Shape descriptors have low and high limits frequently the limits are not the same and

the ability to describe the particlersquos shape is relative The sensitivity of each descriptor

should be compare to apply the most suitable descriptor in each situation

Sieving curve determine the particle size in a granular soil particle shape could differ

in each sieve size There is the necessity to describe the particle shape on each sieve

portion (due to practical issues) and included in the sieve curve Obtain an average

shape in determined sieve size is complicated (due to the possible presence of several

shapes) and to obtain the particle shape on the overall particlersquos size is challenging

how the particle shape should be included

Since several descriptors have been used to determine the shape of the particles and

the relation with the soil properties it is convenient to determine the descriptorrsquos

correlation with the soil properties

9 ACKNOWLEDGMENT

I would like to thanks to Lulearing University of Technology (LTU) the time I had spent

in its facilities and the kind environment it offers and University of Sonora

(UNISON) that has been providing me the financial support and the time to conclude

this journey

10 REFERENCES

Andersson T (2010) Estimating particle size distributions based on machine vision

Doctoral Thesis Departament of Computer Science and Electrical Engineering Lulearing

University of Technology ISSN 1402-1544 ISBN 978-91-7439-186-2

45

Arasan Seracettin Hasiloglu A Samet Akbulut Suat (2010) Shape particle of

natural and crished aggregate using image analysis International Journal of Civil and

Structural Engineering Vol 1 No 2 pp 221-233 ISSN 0970-4399

Aschenbrenner BC (1956) A new method of expressing particle sphericity Journal

of Sedimentary Petrology Vol 26 No 1 pp 15-31

Axelsson K (1998) Introduktion till jordmekaniken jaumlmte jordmateriallaumlran Skrift

984 Lulearing Avdelningen foumlr Geoteknologi Lulearing Tekniska Universitet (In Swedish)

Barton Nick amp Kjaernsli Bjorn (1981) Shear strength of rockfill Journal of the

Geotechnical Engineering Division Proceedings of the American Society of Civil

Engineers (ASCE) Vol 107 No GT7

Barrett P J (1980) The shape of rock particles a critical review Sedimentology

Vol 27 pp 291-303

Blott S J and Pye K (2008) Particle shape a review and new methods of

characterization and classification Sedimentology Vol 55 pp 31-63

Bowman E T Soga K and Drummond W (2001) Particle shape characterization

using Fourier descriptor analysis Geotechnique Vol 51 No 6 pp 545-554

Briggs L I McCulloch D S (1962) Hydraulic shape of sand particles Journal of

Sedimentary Petrology Vol 32 pp 645-656

Chan Leonard C Y and Page Neil W (1997) Particle fractal and load effects on

internal friction in powders Powder Technology Vol 90 pp 259-266

Cheshomi A Fakher A Jones C J F P (2009) A correlation between friction

angle and particle shape metrics in quaternary coarse alluvia Quarterly Journal of

Engineering Geology and Hydrogeology Vol 42 pp 145-155

Cho G Dodds J and Santamarina J C (2006) Particle shape effects on packing

density stiffness and strength Natural and crushed sands Journal of Geotechnical

and Geoenvironmental Engineering May 2006 pp 591-602

Dietrich William E (1982) Settling velocity of natural particles Water Resources

Research Vol 18 No 6 pp 1615-1626

Dobkins J E and Folk R L (1970) Shape development on Tahiti-nui Journal of

Sedimentary Petrology Vol 40 No 2 pp 1167-1203

Folk R L (1955) Student operator error in determining of roundness sphericity and

grain size Journal of Sedimentary Petrology Vol 25 pp 297-301

Fernlund J M R (1998) The effect of particle form on sieve analysis A test by

image analysis Engineering Geology Vol 50 No 1-2 pp 111-124

46

Fernlund J M R (2005) Image analysis method for determining 3-D shape of

coarse aggregate Cement and Concrete Research Vol 35 Issue 8 pp 1629-1637

Fernlund J M R Zimmerman Robert and Kragic Danica (2007) Influence of

volumemass on grain-size curves and conversion of image-analysis size to sieve size

Engineering Geology Vol 90 No 3-4 pp 124-137

Fraser H J (1935) Experimental study of the porosity and permeability of clastic

sediments The Journal of Geology Vol 43 pp 910-1010 ISSN 0022-1376

Hayati Ali Nemati Ahmadi Mohammad Mehdi and Mohammadi Soheil (2012)

American Physical Society Physical review E 85 036310 DOI

101103PhysRevE85036310

Hawkins A E (1993) The Shape of Powder-Particle Outlines Wiley New York

Head K H and Epps R J (2011) Manual of soil Laboratory testing Volum II

Permeability shear strength and compressibility test 3rd

edition Whittles Publishing

Scotland UK 3rd

edition

Holubec I and DrsquoAppolonia E (1973) Effect of particle shape on the engineering

properties of granular soils ASTM STP 523 pp 304-318

Hyslip James P Vallejo Luis E (1997) Fractal analysis of the roughness and size

distribution of granular materials Engineering Geology Vol 48 pp 231-244

Janoo Vincent C (1998) Quantification of shape angularity and surface texture of

base course materials US Army Corps of Engineers Cold Region Research and

Engineering Laboratory Special report 98-1

Jefferies Mike and Been Ken (2000) Soil liquefaction A critical state approach

Taylor amp Francis Group London and New York

Jimenez Jose A Madsen Ole S (2003) A simple formula to estimate settling

velocity of natural sediments Journal of Waterway Port Coastal and Ocean

Engineering Vol 129 No 2 pp 70-78

Johansson Jens and Vall Jakob (2011) Jordmaterials kornform Inverkan paring

Geotekniska Egenskaper Beskrivande storheter bestaumlmningsmetoder

Examensarbete Avdelningen foumlr Geoteknologi Institutionen foumlr Samhaumlllsbyggnad

och naturresurser Lulearing Tekniska Universitet Lulearing (In Swedish)

Kane Joseph W and Sternheim Morton M (1988) Physics John Wiley amp Sons Inc

Third edition

Kolbuszewski J (1948) An experimental study of the maximum and minimum

porosities of sands Proceedings of the Second International Conference on Soil

Mechanics and Foundation Engineering Rotterdam June 21 to 30 Sub-section IIb

pp 158-165

47

Krumbein W C and Pettijohn FJ (1938) Manual of sedimentary petrography

Appleton-Century Crofts Inc New York

Krumbein W C (1941) Measurement and geological significance of shape and

roundness of sedimentary particles Journal of Sedimentary Petrology Vol 11 No 2

pp 64-72

Krumbein W C and Sloss L L (1963) Stratigraphy and Sedimentation 2nd

ed

WH Freeman San Francisco

Kuo Chun-Yi and Freeman Reed B (1998a) Image analysis evaluation of

aggregates for asphalt concrete mixtures Transportation Research Record Vol 1615

pp 65-71

Kuo Chun-Yi Rollings Raymond and Lynch Larry N (1998b) Morphological

study of coarse aggregates using image analysis Journal of Materials in Civil

Engineering Vol 10 No 3 pp 135-142

Lanaro F Tolppanen P (2002) 3D characterization of coarse aggregates

Engineering Geology Vol 65 pp 17-30

Lees G (1964a) A new method for determining the angularity of particles

Sedimentology Vol 3 pp 2-21

Lees G (1964b) The measurement of particle shape and its influence in engineering

materials British Granite Whinstone Federation Vol 4 No 2 pp 17-38

Matsushima Takashi Saomoto Hidetaka Matsumoto Masaaki Toda Kengo

Yamada Yasuo (2003) Discrete element simulation of an assembly of irregular-

shaped grains Quantitative comparison with experiments 16th ASCE Engineering

Mechanics Conference University of Washington Seattle July 16-18

Mitchell James K and Soga Kenichi (2005) Fundamentals of soil behaviour Third

edition WILEY

Mora C F Kwan A K H Chan H C (1998) Particle size distribution analysis of

coarse aggregate using digital image processing Cement and Concrete Research Vol

28 pp 921-932

Mora C F and Kwan A K H (2000) Sphericity shape factor and convexity

measurement of coarse aggregate for concrete using digital image processing Cement

and Concrete Research Vol 30 No 3 pp 351-358

Muskat Morris (1937) The Flow of fluids through porous media Journal of Applied

Physics Vol 8 pp 274

Nearing M A and Parker S C (1994) Detachment of soil by flowing water under

turbulent and laminar conditions Soil Science Society of American Journal Vol 58

No 6 pp 1612-1614

48

Pan Tongyan Tutumluer Erol Carpenter Samuel H (2006) Effect of coarse

aggregate morphology on permanent deformation behavior of hot mix asphalt Journal

of Transportation Engineering Vol 132 No 7 pp 580-589

Pellegrino A (1965) Geotechnical properties of coarse-grained soils Proceedings

International Conference of Soil Mechanics and Foundation Engineering Vol 1 pp

97-91

Pentland A (1927) A method of measuring the angularity of sands MAG MN AL

Acta Eng Dom Transaction of the Royal Society of Canada Vol 21 Ser3xciii

Persson Anna-Lena (1998) Image analysis of shape and size of fine aggregates

Engineering Geology Vol 50 pp 177-186

Powers M C (1953) A new roundness scale for sedimentary particles Journal of

Sedimentary Petrology Vol 23 No 2 pp 117-119

Pye W and Pye M (1943) Sphericity determination of pebbles and grains Journal

of Sedimentary Petrology Vol 13 No 1 pp 28-34

Qazi M A (1975) Flow properties of granular masses A review on the angle of

repose The Arabian Journal for Science and Engineering Vol 1 No 2

Quiroga Pedro Nel and Fowle David W (2003) The effects of aggregate

characteristics on the performance of portland cement concrete Report ICAR 104-1F

Project number 104 International Center for Aggregates Research University of

Texas

Riley N A (1941) Projection sphericity Journal of Sedimentary Petrology Vol 11

No 2 pp 94-97

Rouseacute P C Fennin R J and Shuttle D A (2008) Influence of roundness on the

void ratio and strength of uniform sand Geotechnique Vol 58 No 3 227-231

Santamarina J C and Cho G C (2004) Soil behaviour The role of particle shape

Proceedings Skempton Conf London

Schofield and Wroth (1968) Critical state soil mechanics McGraw Hill

Shaumlfer Michael (2002) Digital optics Some remarks on the accuracy of particle

image analysis Particle amp Particle Systems Characterization Vol 19 No 3 pp 158-

168

Shergold F A (1953) The percentage of voids in compacted gravel as a measure of

its angularity Magazine of Concrete Research Vol 5 No 13 pp 3-10

Shinohara Kunio Oida Mikihiro Golman Boris (2000) Effect of particle shape on

angle of internal friction by triaxial compression test Powder Technology Vol 107

pp131-136

49

Skredcommisionen (1995) Ingenjoumlrsvetenskapsakademinen rapport 395 Linkoumlping

1995

Sneed E D and Folk R L (1958) Pebbles in the Colorado river Texas A study in

particle morphogenesis Journal of Geology Vol 66 pp 114-150

Sperry James M and Peirce J Jeffrey (1995) A model for estimating the hydraulic

conductivity of granular material based on grain shape grain size and porosity

Ground Water Vol 33 No 6 pp 892-898

Sukumaran B and Ashmawy A K (2001) Quantitative characterisation of the

geometry of discrete particles Geotechnique Vol 51 No 7 pp 619-627

Szaacutedeczy-Kardoss E Von (1933) Die bistimmung der abrollungsgrades Geologie

und palaumlontologie Vol 34B pp 389-401 (in German)

Teller J T (1976) Equantcy versus sphericity Sedimentology Vol 23 pp 427-428

Tickell F G (1938) Effect of the angularity of grain on porosity and permeability

bulletin of the American Association of Petroleum Geologist Vol 22 pp 1272-1274

Tutumluer E Huang H Hashash Y Ghaboussi J (2006) Aggregate shape effects

on ballast tamping and railroad track lateral stability AREMA 2006 Annual

Conference Louisville KY

Wadell H (1932) ldquoVolume Shape and roundness of rock particlesrdquo Journal of

Geology Vol 40 pp 443-451

Wadell H (1933) Sphericity and roundness of rock Particles Journal of Geology

Vol 41 No 3 pp 310ndash331

Wadell H (1934) Shape determination of large sedimental rock fragments

The Pan-American Geologist Vol 61 pp 187-220

Wadell H (1935) ldquoVolume shape and roundness of quartz particlesrdquo Journal of

Geology Vol 43 pp 250-279

Wentworth W C (1922a) The shape of beach pebbles Washington US Geological

Survey Bulletin Vol 131C pp 75-83

Wentworth W C (1922b) A method of measuring and plotting the shape of pebbles

Washington US Geological Survey Bulletin Vol 730C pp 91-114

Wentworth W C (1933) The shape of rock particle A discussion Journal of

Geology Vol 41 pp 306-309

Witt K J Brauns J (1983) Permeability-Anisotropy due to particle shape Journal

of Geotechnical Engineering Vol 109 No 9 pp 1181-1187