influence of the particle shape on the ......fig. 6: definition of different particle size...

INFLUENCE OF THE PARTICLE SHAPE ON THE PACKING DENSITY OF AGGREGATES

Tilo Proske, Peter Ramge

SUMMARY

The influence of the particle shape on the packing density was analysed in the research program. Hereby fine and coarse aggregates with particle diameter from 0,25 mm up to 32 mm of different aggregate materials were tested. The computerized particle analysis (CPA) as well as the classic methods according to DIN EN 933 were used for the evaluation of the particle shape. The determination of the packing density is based on the compressible packing model (CPM), a semi-empirical method. A correlation between the photo-optical parameter sphericity and the packing density of the aggregates was found. The influence of the particle size is considered thereby.

1. INTRODUCTION

The properties of fresh and hardened concrete are highly influenced by the packing density of the granular particles. Thereby the aggregates as well as the fine particles like cement and filler are included in the granular system. To provide the workability of the concrete, at least all voids have to be filled with a fluid phase respectively water. Further on a minimal paste content (consisting of water and powders), is required to keep the aggregates at distance. Due to the hardening properties and the sedimentation risk the water-cement ratio is limited. As a consequence a higher cement volume must be provided if the packing density of the aggregates is lower.

Beside the particle size distribution, the packing density of the aggregates is influenced by the packing process and the particle shape. In the past many attempts were made to find a correlation between the particle shape and the packing density of granular particles. Though there is already a difficulty to classify and quantify the particle shape and to qualify the packing density.

Proske, T.; Ramge, P.: Influence of the particle shape on the packing density of aggregates 19 (2004). http://www.darmstadt-concrete.de/2004/packing.html

http://www.massivbau.tu-darmstadt.de/user/proske/web/proske.htm

mailto:[email protected]

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2. RESEARCH PROGRAM

2.1 Overview

The research program included the investigation of the shape and the packing density of different crushed and rounded fine and coarse aggregates. The particle diameter ranged from 0,25 mm up to 32 mm. The computerized particle analyse (CPA) as well as the classic method according to DIN EN 933-4 [1] were used for the evaluation of the particle shape. The following determination of the packing density was realized by the compressible packing model (CPM), a semi-empirical method. The calculations and experimental tests are based on the refined model by de Larrard [4].


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2.2 Materials

An overview about the properties of the used materials is given in Tab. 1. The optical impression of the fine and coarse particles can be found in Fig. 1 - Fig. 4.

Gabbro Grano-diorite

Limestone Marble Quartz River gravel

Fraction [mm]

0,125/0,25 - (X) - - X X 0,25/0,50 - X - - X X 0,50/1,0 - X - - X X 1,0/2,0 - X (X) - X X 2,0/3,15 X X - - X X 3,15/5,0 X X - - X X 5,0/8,0 X X X - X X 8,0/11,2 X X X - - X 11,2/16,0 X X X X - X 16,0/22,4 X - X - - 22,4/32,0 - - - - -

(X)

Colour Grey Back/ White

Light grey White White/ honey

Light grey Ochre

Density [Mg/m³]

2,875

2,715 2,686 2,700 2,605 Variable

Mineral structure

Fine-crystalline

Coarse- crystalline

Not visible Not visible Fine-crystalline

Not visible

Crusher Jaw-, Cone type

gyratory crusher

No infor-mation

Baffle mill Mecha- nical

rounded

Baffle mill -

Region Odenwald Odenwald Sauerland No infor-mation

Lahntal

Rhine (Hessen)

Tab. 1: Tested aggregate fractions


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b) Granodiorite 2/5 mm

a) Gabbro 2/5 mm

d) River gravel 2/5 mm

c) Quartz 2/5mm

e) Limestone 5/8 mm f) Marble

Fig. 1: Macroscopic images of coarse aggregates on scale paper (1 mm)


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a) b)

d) c)

g) e) f)

Fig. 2: Tested coarse aggregates

a) Gabbro - fraction 2/5, 5/8, 8/11, 11/16 and 16/22

b) Limestone - fraction 5/8, 8/11, 11/16 and 16/22

c) Granodiorite - fraction 2/5, 5/8, 8/11 and 11/16

d) River gravel - fraction 2/5, 5/8, 8/11 and 11/16

e) Quartz - fraction 2/5 und 5/8

f) Mechanical rounded marble - fraction 11/16

g) River gravel platy - fraction 8/16


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River sand 0,25/0,5 mm

River sand 0,5/1,0mm River sand 1,0/2,0 mm

River sand 0,125/0,25 mm

Fig. 3: Macroscopic images of River sand fractions on scale paper (1 mm)

Granodiorite 0,5/1,0mm

Quartz 0,5/1,0mm

Fig. 4: Macroscopic images of Quartz and Granodiorite, fraction 0,5/1,0 mm, on scale paper (1 mm)


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2.3 Photo optical analyse

The photo optical investigations by CPA [2] were realized with the device HAVER CPA 4 (year of construction 2001, manufactured by Taurus, Weimar) [3] and supported by the Bauhaus-University Weimar. The device has the option of two measurement ranges. Range 1 is to prefer for particles from 0,063 mm up to 15 mm, range 2 for particles from 0,25 mm up to 100 mm. In the tests range 1 was used for the particles with d ≤ 2 mm, range 2 for the particles with d > 2 mm. Fig. 5 shows the functionality of the test machine. The CCD-line camera works with a frequency of 10.000 Hz, so the shade projection of the objects can be measured quasi-continually. The size distribution of the particles are determined assuming the particles are spheres. Additionally the shade projections can be reconstructed and analysed regarding the particle shape. The optical parameters of the camera are summarized in Tab. 2.

3

2

1

4

5

1 – Box with aggregates 2 – Vibration chamfer 3 – Light source 4 – CCD-camera 5 – Controlling and Analysis

Fig. 5: Functionality of the photo optical test machine

Contrary to the classical sieve analyse the size of the particles can be described by different parameters, for example FERET-diameter (XFe), MARTIN- diameter (XMa), maximal chord (XC) and the equivalent diameter (dequ). Further on the widest dimension of the projection Lk and the orthographic width Bk are informative. Fig. 6 shows the definition of these parameters.


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Projection

däqu

Circle of equal area

LK

BK

XMa

Direction of the chord

Dire

ctio

n of

fal

ling

X Fe

Xc

XMa Length of the projection in the bisector

XFe Distance of the tangents on the projection in the direction of falling

XC Length of the maximal chord

däqu Diameter of the circle of equal area

Lk Maximal length of the particle and corresponding width Bk

Fig. 6: Definition of different particle size parameters using the CCD-line camera

The highest degree of information about the shape of a particle is given by the ratio XFe / XC respectively Lk / Bk or the sphericity index SPHT. The problem is always the reduction from the 3D reality to a 2D problem. Reliable results are only achievable if the sample quantity is high. Due to the rotation of the particles all projections are well distributed then. But the direct comparison between the manual analyse according to DIN EN 933-3 or DIN EN 933-4 and CPA-analyse is not possible.

The sphericity index SPHT is defined by equation (1).

p

p

A

USPHT

⋅π⋅=

2 (1)

Up perimeter of the projection Ap area of the projection

The sphericity index SPHT is generally independent of the projection scale, but is influenced by the optical resolution. First of all the determination of the particle perimeter is affected thereby.

The measured sphericity index SPHT against the average particle diameter (by sieve analyse) is presented in Fig. 7. Significant is the effect of the particle size on the measured sphericity. This is explainable by the scale effect or respectively the pixel resolution.


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p

p

AU

SPHT⋅π⋅

=2

measurement range 2 measurement range 1

Fig. 7: Measured sphericity index SPHT against the average particle diameter

It was found out that the sphericity is significantly influenced (beside the pixel resolution) by the structure of the particles and their fracture behaviour. Stone is composed of minerals, fractions of minerals or fractions of stone material. During the crushing process the material is breaking at the weak points. The surface of the aggregates is structured accordingly. The influence of the aggregate size on the sphericity can be pointed out in Fig. 8. Here the particle A and the larger particle B have the same sphericity SPHT. In reality the large particle C is composed of several particles A. Therefore the surface of C is higher then the surface of B. Finally the sphericity SPHT of C is higher than of A despite the same basic shape.

CB A

SPHT(A) < SPHT(C)SPHT(A) = SPHT(B)

Real:Theoretically:

A

Fig. 8: Schematic illustration of the influence of the particle size and structure on the sphericity


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It was pointed out that SPHT generally increases with the size. The river gravel represents an exception, first of all in fact of the natural abrasion. Because of the smooth surface there is only a low influence of the particle size. Further on the fraction 2/8 mm has a relatively high content of broken material. The consequence is an increasing sphericity.

Fig. 7 shows further the differences between the materials. River gravel and Quartz have low but Gabbro and Granodiorite high SPHT values. The 2D-shade projection of several fractions 8/11 mm are presented in Fig. 9. The shape as well as the pixel resolution are visible.

a) b) c)

Fig. 9: Enlarged shade projection of the fraction 8/11 mm; a) Gabbro, b) Limestone and c) River gravel

The ratio Lk/Bk against the average particle size is presented in Fig. 10. There are no significant differences considering the particle size dm ≥ 8 mm. With a diameter lower than 8 mm the Lk/Bk - ratio of Limestone, Granodiorite and Gabbro is significantly higher than the Lk/Bk - ratio of Quartz and River gravel. Marble has the lowest Lk/Bk – value, the highest value has the platy River gravel.


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Fig. 10: Lk/Bk – ratio of the tested aggregates against the average particle diameter

CPA 4-5 Comment

Machine No. 459

Measurement range 1 2

Height of falling [mm] 26 70

Pixel length [mm] (Hardware) 0,013 0,013

Pixel height [mm] (Hardware) 0,026 0,026

Projection scale 1:2,5 1:9,1

Pixel length in the optical system [mm] 0,0325 0,1183 Equal to the horizontal resolution

Line frequency in [kHz] 9,638 9,638

Velocity of the particle in [m/s1] 0,714 1,172

Height of the chord [mm] 0,074 0,122 Equal to the vertical resolution

Tab. 2: Optical parameters of the used device HAVER CPA 4, company HAVER & BOECKER


1 At the entrance of the particle in the measurement section with hgv ∗∗= 2

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2.4 The packing density by the compressible packing model (CPM)

In the experimental tests an aggregate diameter ratio of was chosen. Thereby the mass of the aggregates in the range 0,063 mm ≤ d ≤ 4 mm amounted 3 kg and in the range d > 4 mm 7,5 kg.

4≤minmax d/d

The aggregates were filled in a steel cylinder which was fixed on the vibrating table according to DIN EN 196-1 (1995). Fig. 11 und Fig. 12 display the test machine. The aggregates were vibrated at a frequency of 50 Hz and a normal pressure of 10 kPa.

Fig. 11: The test device, Vibration table (a), Clamping jig (b), Steel weight (c),

Cylindrical container (d)

a b

d

c

V0

hi

dz

h0

h0 = Depth before vibrahi = Depth after vibratiodz = Inner diameter of th

Fig. 12: Compression tes

Proske, T.; Ramge, P.: Influaggregates 19 (2004). http:/

Vibration

tion n e steel cylinder, dz = 160,25 mm

t

ence of the particle shape on the packing density of /www.darmstadt-concrete.de/2004/packing.html

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The filled volume of the cylindrical container V0 is determined by the total volume Vges less the immersing volume part of the cylindrical steel weight. The immersing volume part is calculated on basis of the average penetration depth hi. The position of the steel weight is measured thereby on 4 measuring points by means of a caliper gauge. The reading precision of the caliper gauge amounted to 0,05 mm. The packing density Φi is calculated according to equation (2).

( )AhVV

VV

iges

kki ⋅−

==Φ0

(2)

with

hi average penetration depth in the state i of compaction

A inner cross-section area of the container

Vk pure grain volume of the aggregate sample V k,rdkk /M ρ= with Mk = mass of the aggregate sample and ρrd,k = particle density of the aggregate on furnace-dry basis according to DIN EN 1097-6 (2001)

To obtain the aimed compaction intensity of K = 9, several vibration times and amplitudes were examined in preliminary tests. The calibration resulted in a three-step compression program with 60 seconds vibration at 0,8 mm amplitude, 120 seconds at 0,4 mm amplitude and 60 seconds at 0,2 mm amplitude. For each aggregate fraction at least two measurements were accomplished.

The packing density under various compaction intensities was calculated with the software René-LCPC. Therefore the sieve passages of the R10-range according to DIN ISO 565 (1998) respectively DIN 323 (1974) are needed. For the used aggregate fractions the appropriate grading curves were determined according to DIN EN 933-1 (1997). The software considers the wall-effect, which results in the container geometry.

In order to obtain the actual packing densities ci of the aggregate fractions of the R10 row on the basis of the actual packing density of the particle mix, an iterative calculation has to be done with René-LCPC. Therefore an appropriate compaction index K has to be chosen. It is approximately assumed that each single grain fraction of the R10 range of a larger examined grain fraction exhibits the same packing density. The densities βi of the single fractions can be calculated by equation (3). Equation (3) is valid for all granular mixes with an equal packing density of all single fractions that means for all mixes with ci = c and βi = β.


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+⋅=

Kc 11β

(3)

with

c actual packing density of a single fraction K compaction index

The measured packing density as well as the virtual packing densities of the R10 fractions by René-LCPC are summarized in [5]. Fig. 13 shows the average grain diameters of the R10 fractions versus the virtual packing densities. The average grain diameter dm is described through the geometrical mean value of the fraction borders according to equation (4).

Dddm ⋅= (4)

with

d lower sieve opening, respectively smallest particle diameter D upper sieve opening, respectively largest particle diameter

It is noticeable that rounded aggregates like river gravel and marble show the highest packing densities of all types of aggregates. Quartz respectively Quartz sand reaches the highest packing densities among the crushed aggregates, Granodiorite in comparison the lowest values. One explanation is given by the different particle shape, which was dealt with in chapter 2.3. At the same particle diameter higher SPHT-values as well as higher Lk/Bk-ratios lead to a decreasing packing densities.

In Fig. 13 it is further on noticeable that the packing density is strongly influenced by the particle diameter. Using Granodiorite the virtual packing density increases significantly from 0,565 at a grain diameter of dm = 0,4 mm up to 0,655 at a grain diameter of dm = 13,4 mm. This behaviour is less significant in the experiments with the naturally rounded aggregates and with Quartz.

Theoretically the packing density is independent of the grain size for particles with a similar geometrical particle shape. Due to the mineralogical structure and the processing procedure of the aggregates, there are deviations in the particle shape noticeable for the different particle size fractions. Detailed explanations of this behaviour are given in section 4.


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Fig. 13: Virtual packing densities of the grain fractions of the R10 range determined by CPM versus the average grain diameter


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4. RESULTS

In the research program it was tried to formulate a numeric relation between the particle shape and the packing density of aggregates. Therefore aggregate samples with a grain diameter range from 0,25 mm to 16 mm were examined. Particles with a diameter lower than 0,25 mm could not be included in the considerations because their photo-optical particle shape parameters turned out to be unusable.

In Fig. 14 and Fig. 15 the determined virtual packing density of the grain fractions of the R10 range is shown versus the Lk / Bk -ratio respectively versus the SPHT of the aggregates. It is noticeable that there exists no direct correlation between the particle shape parameters and the virtual packing density. Generally the virtual packing density decreases with increasing Lk / Bk -ratio respectively increasing SPHT-values.

Fig. 14: Virtual packing density of the grain fractions of the R10 range versus the Lk / Bk -ratio

For the evaluation of the analytic relations it is to be considered that the sphericity index SPHT includes also surface deviations that have only minor effect on the packing density. Fig. 16 shows that the packing density is mainly influenced by the basic particle shape. The fine surface roughness is only of secondary importance. Grain A shows the same geometrical basic shape as grain B. Due to the higher roughness of the surface of grain B a higher perimeter is measured with means of CPA. Therefore the absolute grain size has


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always to be included in the evaluation of the surface structure respectively the measuring value SPHT.

Comparing Limestone and Gabbro the described problem is significantly noticeable. For both aggregates the packing densities are nearly identical. The aggregates show a similar basic particle shape. A closer comparison of the surface shows however that Gabbro is much more uneven than Limestone. This results in an appropriate influence on the SPHT-values (see chapter 2.3). For the determination of the packing density in dependence oft the SPHT-value a certain inaccuracy has to be accepted. A particle shape analyse according to the chord-angel-method would be much more useful. Here the surface roughness can be separated in several levels and classes.

Fig. 15: Virtual packing density of the grain fractions of the R10 range versus the SPHT-value


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Grain A Grain B

SPHT (A) < SPHT (B)

Φ (A) ≈ Φ (B)

Fig. 16: Schematic illustration of the influence of the different levels of surface roughness on the packing density

The influence of different levels of surface roughness on the measurable sphericity and the packing density is shown in Tab. 3. For simplification only three different levels of roughness are considered: the micro, meso and macro level. The micro level represents those deviations which, due to the pixel resolution, cannot be determined during the SPHT measuring. Little influence on the packing density has the surface roughness of the meso level.

Surface roughness

Micro level Meso level Macro level

Measured sphericity - + +

Virtual packing density - - +

- has non or minor influence

+ has significant influence

Tab. 3: Influence of the surface roughness on the measured sphericity and the packing density of aggregates


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On the basis of the test results an analytic relation between the measured sphericity and the packing density was derived. Consideration was given to the fact that the sphericity increases with increasing grain size (due to the inner grain structure and the pixel resolution) while the packing density is unaffected or not significantly effected of those phenomena.

Equation (5) describes the dependence between the sphericity and the virtual packing density on the basis of the R10 range, which was found by regression of the test results. The influence of the diameter is considered by the auxiliary value SPHT* which is the particle size dependent sphericity.

*8,1 SPHT−=β (5)

with

β virtual packing density of the examined fraction (R10)

The particle size dependent sphericity SPHT* is derived from the measured sphericity and the average particle diameter according to equation (6). For a particle diameter of dm = 5,6 mm is SPHT = SPHT*.

( )( ) ( )1ln27,046,11* −⋅−+= SPHTdSPHT m (6)

with

dm average particle diameter of the examined grain fraction Dddm ⋅=

Inserting (6) in (5) results in the following function:

( )( ) ( )1ln27,046,18,0 −⋅−−=β SPHTdm (7) In equation (7) the Lk / Bk - ratio is not considered directly. It is however noteworthy that a changing Lk / Bk - ratio also influences the sphericity SPHT.

Fig. 17 shows the determined virtual packing density versus the particle size dependent sphericity SPHT* according to equation (6). Noticeable is an almost linear correlation between both values.


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*SPHT, −=β 81

( )( ) ( )127046180 −⋅−−=β SPHTdln,,, m

Fig. 17: Virtual packing density of the particles (R 10) against the particle size dependent sphericity SPHT* (6)

Equation (7) is only valid for the examined range of data (SPHT-values between 1,05 and 1,25 and grain size between 0,25 mm and 16 mm). It is conditioned that the SPHT-values have been measured with an equal measurement method. Further on this correlation is valid only for single grain fractions with fraction borders according to the sieve openings of the R10 range. If the calculation of the packing density is based on other fraction borders or the sphericity is measured by an other method equation (7) may have to be adjusted. The calculated packing densities versus the measurement result data are shown in Fig. 18. A good accordance of the respective values is noticeable.


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Fig. 18: The experimental measuring data versus the calculations according to equation (7)


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5. CONCLUSION

The research project was supported by “Deutscher Beton- und Bautechnik-Verein E.V.”

and “Arbeitsgemeinschaft industrieller Forschungsvereinigungen e.V.”. Further we thank

Dr.-Ing. U. Stark, Bauhaus-Universität Weimar very much for the kindly support.

6. LITERATURE

[1] DIN 933-4, Prüfverfahren für geometrische Eigenschaften von Gesteinskörnungen – Teil 4: Bestimmung der Kornform Kornformkennzahl, Berlin, Dezember, 1999.

[2] Stark. U., Reinhold, A., Müller, A.: Neue Methoden zur Messung der Korngröße und Kornform von Mikro bis Makro, In: Tagungsbericht, 15. Internationale Baustofftagung, Band 1, Weimar, 2003.

[3] HAVER-CPA-4 Photooptisches ONLINE – Partikelanalysegerät Firmenprospekt Haver + Boecker Drahtweberei und Maschinenfabrik Oelde.

[4] de Larrard, F.: Concrete Mixture-Proportion – Scientific Approach, E & FN SPON, London, 1999.

[5] Ramge, P.: Untersuchungen zum Einfluss der Kornform auf die Packungsdichte, Studienarbeit TU Darmstadt, Darmstadt, 2004

Contact to the authors:

[email protected]

[email protected]

Homepage of Darmstadt Concrete:

http://www.darmstadt-concrete.de



http://www.darmstadt-concrete.de/

influence of the particle shape on the ......fig. 6: definition of different particle size...

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