1

International Society for Rock Mechanics

Rock Properties and Their Role in RockCharacterization, Modelling and Design

Prof. Dr. Reşat UlusayHacettepe University, Turkey

President of the ISRM Commission on Testing Methods

CONTENT

- ROCK MATERIAL, ROCK MASS AND SIZE OF THE PROBLEM IN ROCK ENGINEERING

- MAIN DESIGN AND MODELLING METHODOLOGIES IN ROCK ENGINEERING

- ACCESS TO THE ROCK

- THE USE OF ROCK PROPERTIES IN CHARACTERIZATION, DESIGN AND MODELLING IN ROCK ENGINEERING

Despite the global nature of today’s problems, Geotechnology alsoincluding ROCK ENGINEERING has remained divided into disciplinessuch as mining, civil and petroleum engineering, geology andgeophysics.

REMIFICATINOS OF GEOTECHNOLOGY

(Amadei et al., 2000)

MAIN ARAES OF INTEREST IN ROCK ENGINEERING

) y şRock Slopes Shafts & Tunnels Foundations Dams

Caverns Mining Geothermal EnergyRadioactive Waste

Disposal

(Rearranged from Hudson, 1989)

2

Historical and recent man-made underground and semi-underground rockstructures and settlements in the soft tuffs of the Cappadocia Region of Turkey

Church

Congress center under constructionPoliceofficein a fairychimney

Cliff settlement

Rock-hewnhotel

Underground city

Rocks and rock-hewn openings have been used as a construction materialand settlement since down of civilization.

(Photos: R. Ulusay)

Different structures have been built on, in or of rock, includinghouses, bridges, dams, tunnels and caverns.

Millau Viaduct (France)Vaiont dam (Italy)

Hoosac Tunnel (USA)Saint Gotthardt Tunnel (Alps)

Rocks differ from most engineering materials because they containdiscontinuities. Therefore, a clear distinction must be madebetween rock material and rock mass.

When dealing with the mechanical behaviour of solids, a commomassumption is that they are:

. Homogeneous

. Continuous

. Isotropic

But rocks are much more complex and their physical andmechanical properteis vary according to scale.

(Eberhartd, 2009)

ROCK MATERIAL A continium or polycrystalline solid betweendiscontinuities consisting of an aggregate of minerals or grains.

Its properties are governed by the physical properties of the materialsof which it is composed.

Terzaghi’s intact rock

Tunnel

Rock massROCK MASS An assemblageof rock blocks separated bydifferent types of geologicaldiscontinuities.

Intact rock

Discontinuity

3

MASSIVE ROCK

. Rock masses with few discontinuities, OR

. Excavation dimension < discontinuity spacing

Because rock masses are discontinuous and varibale in space, it is important to choose the right domain that is representative of therock mass affected by the structure analyzed.

JOINTED OR BLOCKY ROCKJOINTED OR BLOCKY ROCK•• Rock masses with moderate number of Rock masses with moderate number of

discontinuitiesdiscontinuities•• Excavation dimension Excavation dimension >> discontinuity discontinuity

spacingspacing

HEAVILY JOINTED ROCKHEAVILY JOINTED ROCK•• Rock masses with a large number of Rock masses with a large number of

discontinuitiesdiscontinuities•• Excavation dimension Excavation dimension >>>> discontinuity discontinuity

spacingspacing

When the problem domain ismuch smaller than rock blocks(excavation of rock by drilling)

Intact rock material

When the structure is much largerthan the blocks

Rock mass properties

Discontinuity propertiesgovern

Relation of Discontinuity Spacing and Size of the Problem

(Arr

anged

from

Hoek

& B

row

n,

1980)

MAIN DESIGN AND MODELLING METHODOLOGIES IN ROCK ENGINEERING

OBSERVATIONAL APPROACH

EMPIRICAL METHODS

ANALYTICAL METHODS

NUMERICALMETHODS/ MODELLING

KINEMATIC ANALYSIS

If necessary, as a Logistic Tool

4

The term “observational method” appears to have been coined by Terzaghi in the 1940’s.

1. OBSERVATIONAL APPROACH

OBSERVATIONAL APPROACH provides a “Learnas you go” alternative.

-The procedure is to base the design on whateverinformation can be secured

- Make note of all possible diferrences betweenreality and the assumptions, then

- Based on the original assumptions, computevarious quantities that can be measured in the field

- Based on the results of the measurements, gradually close the gaps in knowledge and, ifnecessary, modify the design during construction

Example: Numerical modelling and performance monitoring for a tunnel.

(www.gpiko.ru)

IF NECESSARY CHANGE IN

DESIGN

(www.finesoftware.eu)

Monitoring

Modelling

Mainly based on previous experience as derived fromconstruction of rock structures having similar characteristicsas the one to be designed ROCK MASS CLASSIFICATION(such as RMR, Q, GSI)

2. EMPIRICAL METHODS

RMCS today form an integral part of the most predominantdesign approach INDIRECT METHODS

Rock Mass Characterization, Classification and Design

Rock massclassification

DescribeDescribe thethediscontnuitiesdiscontnuities

RMR RMR oror QQ

ClassifyClassify thethe rockrockmassmass usingusing:: EmpiricalEmpirical databasedatabase

SupportSupport requirementsrequirements

DESIGNDESIGN

Rock massbehaviour

H&B H&B FailureFailure CriterionCriterion-- mm

-- SS-- σσcici

GSIGSINumericalNumerical ModellingModelling, LEM, LEM

AnalysisAnalysis

DESIGN DESIGN

Stand-up time (RMR)

Line survey/Boring

(Bieniawski, 1989,

5

3. ANALYTICAL METHODS

Complexity of the nature of stress has to be fully considered in thedesign of underground excavations.

The problem can be initilally simplified through the assumptions of Continuous, Homogenous, Isotropic, Linear Elastic behaviour

(CHILE)

However

Successfully used solutions, especially in those excavations at depth, where high stresses have closed the fractures and the rock mass is relatively homogeneous and isotropic.

However, for near surfaceexcavations, where the rock stressesare lower, their fractures are morefrequent,and the rock mass is disturbed and weathered, there is more concern about the validity of the CHILE.

(a) CHILE

Deep UG openings

EXAMPLES: Estimation of Radius of Plastic Zone

(Hoek & Brown, 1980)

Rock-support InteractionAnalysis

(b) LIMIT EQUILIBRIUM METHODS (LEM)

The most widely applied analytical technique used for slope stabilityassessments.

Force and/or moment equilibrium conditions for different modes offailure are examined on the basis of statics.

The typical output from LEM analyses is the Factor of Safety

FS = Resisting forces

Driving forces

FS = Shear strength

Shear stress

Tansiyon çatlağışev

aynasında

Kayma düzlemi

H

ZZwv

u

wψpψf

(a) Tansiyon çatlağı şev tepesinin gerisinde

Slope face

Failure surface

Tension crack

(Hoe

k&

Bra

y, 1

977)

Circular F.

Planar F.Wedge F.

Toppling F.

R

These methods consist in applying the state of stress-strain in the engineering structure, with consideration given to the strength and deformability properties of the rock mass and of the discontinuities.

4. NUMERICAL METHODS / MODELLING

- A way to gain understanding of governing deformation andfailure mechanisms- Exploring alternatives rather than making absolute predictions- Making changes in the input data to see how the changes affectthe overall response of rock structure (e.g. parametric studies).

STRESS σ

STRAIN є

DISPL. u

Useful for analysis and design in cases where analytical solutions arenot available Examples

Design of high slopes, rock burst prone tunnels, soft rock slopes

MAIN PURPOSES

6

Numerical methods of stress and deformation analysis fall into two categories

INTEGRAL METHODS- Only problem boundary is definedand discretized- Restricted to elastic analyses

DIFFERENTIAL METHODS-Problem domain is defined and

discretized-Non-linear and heterogeneous

material properties accomodated

As a continuum, the failure path passes throughthe rock mass.

As a discontinuum, the failure surface is dictatedmore directly by the presence of pre-existingdiscontinuities.

BoundaryElement Method(BEM)

FEM, FDM,DEM

(Eber

hard

t, 2

009)

DIFFERENTIAL METHODSContinuum Methods

- Rock mass bahaviour is representedas a continuum- Approximations to the connectivity of elements, and continuity of displacements and stresses betweenelements

Discontinuum Methods

Rock mass is represented as assemblageof distinct interacting blocks or bodiesthat are subjected to external loads andare expected to undergo significantmotion with time.

Blocks are subdivided into finite-difference mesh which follows linaeror non-linear stress-strain laws

Finite Element Method-FEM (PHASE)Finite Difference Method-FDM (FLAC)

Distinct Element Method-DEM (UDEC)

Time step 1 Time step 2 Time step 3

Time step 4 Time step 5

(Eber

hard

t, 2

009)

Numerical methods include consideration of the followings, dependingon the type of the model used (continuum or discontinuum):

GeologyDiscontinuities (spacing/persistence)

Constitutive equations & failure criteriaGroundwater pressure/Seismic loadingIn-situ stresses and external loads

Material and mass properties (intact/discontinuity)ROCK

PROPERTIES

FEM-FDM DEM FEM-BEM

Continuum Discontinuum Continuum

(Bar

ton,

1998)

METHOD OF KINEMATIC ANALYSIS(A Logistic Tool)

Rock Mass Failure MechanismsStructurally-controlled

Stress-controlled

Structurally-controlled instability: Blocks formed by discontinuitiesmay be free to either fall or slide from the excavation under a set of body forces.

Analysis of kinematic addmissibility of poteantial wedges or planesintersecting the excavation face(s) KINEMATICAL ANALYSIS

Wedge failure in slopes

Block falls in underground openings

J1

J2

J1J2

7

Stereographic Projection Technique:

200

200

φ

fαpψ

fψ

pα

Süreksizlik

Şev

Discontinuity

Slope

Kinematic analysis of blocks in U/Gopenings

φ φ

Kinematic analysis for rock slopes

(Hoek & Brown, 1980)

(Nor

rish

& W

yllie

, 1996)

ACCESS TO THE ROCK

İKZ

İKZ

Rock Exposures Borehole Cores Borehole Wall Images

Intact rockBlock samples for testing

Intact rockCores for testing

Discontinuity masurementsfor Rock Mass

Characterization

Measurement of disconttinuityproperties is limited and no possibility

of measuring rock mass properties

Flat-jack stress determination,larger-scale modulus and

permeability tests

In situ stress on corescan not be measured

Indirect methodsare nedded forassessing the

rock massproperties

There are always limitations on resources Therefore, when optimizing the rockcharacterization procedures it is necessary to consider the requirements and to choosethe rock access method and testing techniques in accordance with the engineeringobjective.

INTACT ROCK AND ROCK MASS PROPERTIESCOMMONLY USED IN ROCK ENGINEERING

1. Determined from laboratory tests (Intact Rock and Discontinuites):

(a) Classification and characterization of intact rock(i) Porosity, unit weight, water content, absorbtion

(ii) Hardness, abrasivity(iii) Durability(iv) Point load strength index(v) BPI

(vi) UCS and deformability(viii) Sound velocity (vp, vs)(ix) Permeability

(b) Rock engineering design(i) Shear strength of intact rock

(ii) UCS and deformability (E, ν, G, K) (iii) Shear strength and stiffness of

discontinuities(iv) Tensile strength (direct or indirect)

.

(www.sfu.ca/~tafgrc/Courses/Easc313)

2. Determined from in-situ measurements and tests (Rock Mass)

(a) Characterization of rock mass(i) Properties of discontinuities(ii) In-situ sound velocity(iii) Properties obtained from geophysical borehole tests

(b) Design(i) In-situ deformability(ii) Rock mass strength(iii) Field permeability(iv) In-situ stresses

(www.sfu.ca/~tafgrc/Courses/Easc313)

8

TAILORING TESTING TO ENGINEERING REQUIREMENT

Objective: To tailor the testing to the engineering objective by consideringa number of testing methods.

Importance of rock mechanics parameters for HYDROELECTRIC SCHEME PRESSURE TUNNEL design

(Hudson & Harrison, 2000)

In situ stress is most important and should be determined

Slope or surface blasting case: Not an importantparameter

Rock engineersmust decide

Whether theyare going to

make particularmeasurementson the basis of

the overallobjective

ANOTHER IMPORTANT ISSUE !

Rock engineer should consider whether emphasis is to be placed on INDEX TESTS, FUNDAMENTAL TESTS or COMBINATION OF THE TWO

INDEX TESTS Cheap, performed quickly Do not determine an intrinsicproperty

UCS= k Is50

Point LoadTest FUNDAMENTAL TESTS

More expensive, time consuming

Measure the property directly

UCS

Carry out a few UCS tests and more PLT, and use the calibrated values

HOW WE CAN CHARACTERIZE ROCK MASSESAND ESTIMATE THEIR STRENGTH?

For the determination of rock mass properties we have two alternative ways:

(a) via the properties of the intact rock and the properties of the discontinui-ties which together make up the rock mass properties OR

(b) Via the properties of the rock mass as measured or estimated directly(STRENGTH, DEFORMABILITY & PERMEABILITY)

A) ROCK MASS PROPERTIES DETERMINED FROM IN-SITU MEASUREMENTS

Because rock masses are usually anisotropic, essential device must bothapply load and measure displacement in different radial directions.

Install some form of loading within the borehole to obtain force-displacementcurve and estimate the associated elastic parameters of the rock

(ww

w.s

lopei

ndic

ato

r.co

m)

(Hudson & Harrison, 2000)

Testing of strength of rock mass is difficultbecause of the high loads involved. Alsotime consuming and expansive tests

GOODMAN BOREHOLE JACK

9

PLATE LOADING TEST

On a surface of rock exposure Underground

(ISRM

, 1981)

Hysteresis is directly associatedwith discontinuities

B) CHARACTERIZATION OF ROCK MASSES AND CLASSIFICATION

Depending on the rock mass classification used, determinediscontinuity properties

Scan-line survey

(Hudson, 1989)

BoreholeOutcrop

S

İKZ

İKZ

Orientation Spacing

AperturePersistence

Roughness (JRC)

Joint wall strength(JCS)

Weathering

Block size

RQD

ROCK MASSCLASSIFICATION(RMR, Q and others)

Set number

>10 cm

A Basic RMR = R ( σci) + R (RQD) + R (spacing) + R (JC) + R (GW)RMR SYSTEM

Adjustments(Orientation, blasting etc.)

Final RMR

Q=(RQD/Jn) (Jr/Ja) (Jw/SRF)Q SYSTEM

Q

(Support & Span)

RMR

Estimation of Erm fromclassification

(Support)

Stand-up time

JRC, JCS

Disc. Stiffness

(Serafim & Pereira, 1983)

(Grim

stad

and

Bart

on,

1993)

(Bienaiwski, 1989)

10

C) ROCK MASS STRENGTH (Hoek & Brown Failure Criterion)

a

c

'3

bc'3

'1 sm ⎟⎟

⎠

⎞⎜⎜⎝

⎛+

σσ

σ+σ=σ

Generalized H&B equation

⎟⎟⎠

⎞⎜⎜⎝

⎛ −=

mib b

100GSIexpmm

⎟⎟⎠

⎞⎜⎜⎝

⎛ −=

sb100GSIexps

D1428bm −=

D39bs −=

( )3/2015/GSI ee61

21a −− −+=

(Barla & Barla, 2005)

GEOLOGICAL STRENGTH INDEX (GSI)(Hoek, 1999) (Sönmez & Ulusay, 2002)Quantitative GSI ChartOriginal GSI Chart

ROCK MASS

Ground response

ROCK MASS

Ground response

How to incorporate modeof failure and rock massstrength

Slope

UG

UG

Slope

IN SITU SOUND VELOCITY

Closely reated to rock mass characteristics and one of the most importantindex properties Seismic Characterization Method

(www.winona.edu)

(Whitley, 1990)

11

Vp-Q-RQD-λ relationships for hard, near-surface, low porosity rock masses

(Bart

on,

2007)

(Bart

on,

2007)

Dynamic E-Q-RMR

(Bart

on,

1995)

Relationships between Vp androck mass characteristics

(Bart

on,

2007)

Intact samples of rock may be selected for index testing

- To further aid in geological classification and as indicators of rock massbehavior

- To provide a measure of the “quality” of the rock,- To indirectly estimate fundamental properties by empirical relationships- They are not directly used in design.

INDEX PROPERTIES OF ROCK MATERIAL

Water Content: Indirect indication of porosity of intact rock or clay content of sedimentary rock.

Unit Weight: Indirect indication of weathering and soundness, and is usedto estimate vertical stress

h σv = γh

Porosity: Indirect indication of weatheringand soundness, and governs permeability

Rebound Number:- Index of relative hardness and quality of rock mass on the exposedsurface when the rock is fragmented- Relative hardness and indirect strength of intact rock

Weak and highly weatheredrocks

Care is necessary

Abrasivity: Measures the abrasiveness of a rock material against other materialse.g., steel. It is an important measure toestimate wear of rock drilling and boringequipment.

(Deere & Miller, 1966)

Point Load Strength Index: Indirect method to determine unconfinedcompressive strength (UCS)

σc = kIs50 k=5-52 (?)

As a classification parameter in RMR system

(Bieniawski, 1989)

12

Block Punch Strength Index (BPI): To indirectly estimate the UCS

UCS= 5.1BPIc

BPI (MPa) < 1 Very weak1 - 5 Weak5 - 10 Moderate10 - 20 Medium20 - 50 High> 50 Very high

c Strength Class

(Ulusay et al., 2001)

Durability: Index of weatherability (degradability) of rock exposed in excavations.

Particularly important in soft andclay-bearing rocks (may cause collapse)

Outcrop

UG opening

Pillar

The loss of sample weight is a measure of the susceptibility of the rock to the combinedaction of slaking and mechanical erosion.

SLAKE DURABILITY TEST

Sound velocity: Closely reated to rock properties and one of the mostimportant index properties. They provide estimates of rock properties and/orare used as an index in their own right indicating anisotropy and/or inhomogenity

(ww

w.w

inona.e

du)

Estimation of dynamic elastic properties:

(Vp)

(Vs)

(Sassa et al., 1988)

NON-DESTRUCTIVE TEST

(νfield / νlab)2 = velocity index (an indicator of intensity of discontinuities)

UNIAXIAL COMPRESSIVE STRENGTH (Intact Rock)

- UCS is a rock property most oftenly used to characterize the mechanicalbehavior of rock. - It is most useful as a means for comparing rocks and classifying theirlikely behavior as an index property.

1. CLASSIFICATION OF INTACT ROCK

σci = F/A

F

Primary index testfor strength and

deformability of intactrock

(Dee

re&

Mill

er,

1966)

13

2. CHARACTERIZATION(a) Input Parameter for Rock Mass Classification

RMR System(Bieniawaski,

1989)

(Hudso

n,

1989)

(Bie

nia

wsk

i, 1

989)

(b) As an intact rock parameter to be used by the empirical rockmass failure criteria (σci)

Generalized Hoek-Brown failure criterion:

σ’1= σ’3+ σci (mb (σ’3/ σci)+s))a

(c) First estimate of the tensile strength

σt = - σci /10

(Barla &

Barla,

2005)

(d) Estimation of UCS and deformation modulus of rock masses:

σcrm = (sσci)0.5UCS of rock mass:

Deformation modulus of rock masses:

Erm= (σci / 10)0.5 10(GSI-10)/40 (Hoek & Brown, 1997)

Erm = (1-(D/2)) (σci / 100)0.5 10(GSI-10)/40 (Hoek et al., 2002)

Erm= 0.001 [ ((Ei/ σci) ((1+RQD/)100) /WD]1.5828(Gökçeoglu et al., 2003)

(e) Estimation of the tensile strength of intact rock with the H-Bstrength criterion:

σt = 0.5σci [mi- (mi2 + 4)0.5]

Erm = 10 (Qσci /100) 1/3 (Barton, 2002)

3. IN DESIGN AND MODELLING

(a) As a design parameter of rockstructures subjected to uniaxialcompressive stresses, such as pillars (intact or rock mass UCS)Strength of pillar is a function of material strength anddistribution of stresses in pillar.

Compare the computed stresses with estimated rock massstrength in discontiuum media or intact rock strength in weakand not jointed media

σc Pillar stresses

Pillar

Pillar

(Hoek & Brown, 1980)

14

(b) In numerical codes such as UDEC, simulating the response of discontinuous media (jointed rock mass) subjected to either staticor dynamic loading UCS is as one of the parameters used by Barton-Bandis model.

For estimation of initial normal stiffness

Kni= -7.15+1.75 JRC+0.02 (JCS/e)

e≈ (JRC (0.04 σci)-0.02)

Discontinuity aperture (mm)

Co

mp

ress

ion

(Zhang, 2005)

(c) Rock fragmentation and rock cutting

Fractures by disc cutters:-Effect of rock strength on tool forces Fnormal/σc =0.15p-0.21(Snowdoown et al., 1982) (p:Penetration, mm)

-The thrust force affecting penetration (Roxborough & Philips, 1975):

Ft= 4 σc tan (θ/2)(Dp3-p4))0.5

(D: Disc diameter, mm)

In rock indentation assessments

(d) Rock-support interaction analysis (as an input parameter)

(Hoek & Brown, 1980)

TENSILE STRENGTH

(a) Analysis of rock structures subjected to tensile stresses, such as wide roof spans

σti = P/AFor underground stability, the tensile strength is not assignificant parameter as the UCS for rocks. Generally, tensile rock strength is low enough when rock is in tension,it splits and tensile stresses are relieved.

In jointed rock masses, the jointing may very well eliminate the tensilestrength of the rock mass, in which case the in situ rock should be considered as having zero tensile strength.

1) DESIGN

(Hudso

n &

Harr

ison,

2000)

15

(b) Input parameter in numerical analyses:

- In analysis of flexural toppling:As an input parameter Bending of the slabs induces tensile cracking in their upper face.

(Hutc

hin

son

et a

l.,

2009)

- Continuum models such as FLAC (Mohr-Coulomb model )- Discontinuous model such as UDEC (Mohr-Coulomb model)

(Hoek & Bray, 1977)

DEFORMABILITY PROPERTIES

1. CLASSIFICATION (Intact rock)

A) MODULUS OF ELASTICITY OF INTACT ROCK AND MODULUS OF DEFORMATION OF THE ROCK MASS

(Deere & Miller, 1966)

Modulus Ratio

(b) Estimation of rock mass deformation modulus from that ofintact rock

Nicholson & Bieniawski (1983)

Mitri et al. (1994)

Sonmez et al. (2004)

Hoek and Diederichs (2006)

Sonmez et al. (2006)

Em = f(Ei)

2. DESIGN

(a) Estimation of deformations in various rock engineering designs

- Estimation of deformations around underground openings/Rock-support(analytical) interaction analysis (Analytical solutions)

If the medium is jointed rock mass Use Erm

(Hoe

k&

Bro

wn,

1980)

16

-Settlement for founadtions in homogeneous, isotropic rockconditions

δv = (CdqB(1-ν2))/E

(Wyl

lie,

1992)

(b) An important input parameter in numerical methods:

Depending on the continuum and discontinuum media under investigation,Young’s modulus of the intact rock or deformation modulus of rockmass is used by all models for stress and deformation analyses such as PHASE, FLAC and UDEC for different types of rock engineering problems

- Other Elastic Properties:

G (Shear modulus)= E/2(1+ν) K (Bulk modulus)= E/(3(1-2ν)Describes the material's responseto shearing strains.

G

dx

y

Shear strain

Shear stressMeasures the substance's resistance to uniform compression

(B) POISSON’S RATIO

It is a mechanical property playing a role in the deformation of elasticmaterials and utilized in rock engineering problems associated withthe deformation of rocks such as an input parameter for the numericalstress analyses.

Poisson’s ratio for rock masses is not required in majority of rock engineeringapplications. Indeed, in Overcoring Methods employing “CSIR doorstopper”,“USBR borehole deformation gauge”, “CSIR triaxial strain cell” and “CSIROhollow incluison cell”, the value of Poisson’s ratio of intact rock is requiredfor evaluation and interpretation of mesaurements.

(Ger

cek,

2008)

Lateral strain

Axial strain

- There is no correlation between the values of Poisson’s ratio of rockmass and intact rock.

- ν (rockmass) ≈ 1.2 ν (intact rock) (Kulatilake et al. (2004)

The intact rock value constitutes a limit for the values that may be assumed by the jointed rock mass (Gercek, 2008)

1. CHARACTERIZATION

Intact rock classification(Gercek, 2008) can be usefulfor a qualitative assessment of labortaory test results. Thisclassifications are applicableto isotropic rocks only.

(Gercek, 2008)

00≤≤νν<0.1<0.10.10.1≤≤νν<0.2<0.20.20.2≤≤νν<0.3<0.30.30.3≤≤νν<0.4<0.40.40.4≤≤νν<0.5<0.5

VeryVery lowlowLowLowMediumMediumHighHighVeryVery highhigh

PoissonPoisson’’ss ratioratioCategoryCategory

17

2. DESIGN (Analytical-Numerical)

Poisson’s ratio of the medium influences the distribution of stresses in somesolutions that are widely applied to geomechanics problem.

(a) In analytical solutions: Estimation of deformations aroundunderground openings – Rock-support (analytical) interactionanalysis (ν of rock mass)

(Hoek & Brown, 1980)

(d) An important input parameter used by numerical methods:

Depending on the continuum and discontinuum media under investigation,Poisson’s ratio of the intact rock and/or deformation modulus of rockmass is used by all models for stress and deformation analyses such as PHASE, FLAC and UDEC.

Poisson’s ratio influences the normalized elastic radial displacements aroundthe excavation face of a circular tunnel located in a hydrostatic in-situ stressfield

(Unlu

& G

erce

k, 2

003)

SHEAR STRENGTH

A) SHEAR STRENGTH OF INTACT ROCK

- DESIGN: Particularly those of weak rocks in numerical methods

B) SHEAR STRENGTH OF DISCONTINUITIES

Cohesion and Friction Angle: Commonly used properties in dicontinuum media (both as peak cp & φp, and residual cr & φp)

Planardiscontinuities

Peak

Residual

18

Undulateddiscontinuities

Barton’s criteria

In-situ shear strength determination

(ISRM, 1981)

Input parameter for analytical, numerical and kinematicmethods of analysis

200

200

φ

fαpψ

fψ

pα

Süreksizlik

Şev

Discontinuity

Slope

(a) Kinematic Analysis of Structurally-Controlled Slopes

EXAMPLES

(Nor

rish

& W

yllie

, 1996)

(b) Analysis of Structurally-Controlled Instabilities in Underground Openings

(Hoek’s Corner)

φ

(Hoek & Brown, 1981)

(c) In Analytical Methods:

Example 1: Structurally-controlled rock slopes

Tansiyon çatlağışev

aynasında

Kayma düzlemi

H

ZZwv

u

wψpψf

(a) Tansiyon çatlağı şev tepesinin gerisindeTension crack in upper surfaceof slope

Failure surface

Slope face

Geometry of slope with tension crack in upper slope surface

pp

pp

vCossinWtan)vSinuWCos(cA

Fψ+ψ

φψ−−ψ+=

Discontinuity Discontinuity(Hoek & Bray, 1977) (Ulusay, 1991)

19

Example 2: Bearing capacity of shallow dipping bedded rocks

qa=σ3Nφ1 + (c1/tan φ1 ) (Nφ1 -1)

F

σ3A = (γB/2tanψ1) Nφ2 + (c2/tan φ1) (Nφ2 - 1)

c1, φ1, c2, φ2 Discontinuity shear strength parameters

(Wyl

lie,

1992)

(Allowable bearing capacity)

(d) In Numerical Analyses:

Particularly in the analysis of rock engineering structures such as underground openings and slopes in discontinuum media (UDEC) shearstrength of discontinuities are important parameters.

C) SHEAR STRENGTH OF ROCK MASS

(a) Analytical and numerical methods

φ

ci

SLOPE

TUNNEL

Bearing capacity of foundations on rock masses:

The usual method to determine allowable bearing pressures

Use published tables or building codes

Where the rock conditions do not match descriptions in the codes

Use analytical or numerical methods and rock mass strength

HOWEVER

Fractured rock:

qa= Cf1s0.5σu(r) [1+(ms0.5+1)0.5]

F

Weak rock with little fracturing:

qa= Cf1cNc + Cf2 (Bγ/2) Nγ + γDNq

F

φ dependent(Wyl

lie,

1992)

(D) JOINT STIFFNESS

The mechanical behaviour of discontinuities in generally plotted in theform of stress-displacement curves withthe result that discvontinuity stiffness(MPa/m) and strength (kPa) can be measured.

Normal stiffness:

kn= Δσ’n/ Δun

Shear stiffness:

ks = Δτ/ Δus

(Zhang,

2005)

20

Normal and shear joint stiffnes values are used in discontinuum modelssuch as UDEC (in Barton and Bandis Model)

DEM Terminology

(Eberhardt, 2009)

(Eberhardt, 2009)

PERMEABILITY

Hydraulicgradient

Permeability is concerned with fluid flowthrough a material or rocks and rockmasses, and is one of the most difficiulttopics facing the practicing rockengineers.

(a) Permeability of Intact Rock (PRIMARY PERMEABILITY):

Refers to matrix permeability and except in petroleum engineering, prime consideration is not paid to this type of permeability in rock engineering.

Because of the presence of discontinuities in rock mass, two types of permeability are considered: (i) PRIMARY, (ii) SECONDARY

Governed by

Porosity

Geological history

In-situ stress

K also varies with grain size

Permeability vs. porosity for intact rocks (ww

w.s

earc

handdis

cove

ry.c

om

)

PERMEAMETER

(b) Permeability of Discontinuities:

Infilled discontinuity Permeability of the infill material.

Unfilled discontinuities for a set of parallel discontinuities K:

K=g (e)3

12 vb

v: Kinematic viscosity (10-6 m2/s)b: Spacinge: Aperture

K is very sensitive to small changesin “e”

Variation of dfiscontinuity setpermeability as a function of the

aperture and discontiuityfrequencey

(Hoek & Bray, 1977)

21

(c) Permeability of Rock Mass (Secondary Permeability):

In rock masses consisting of discontinuities terminating against another,computatins are not only made for the permeability of a set of paralleldiscontinuties but also for the discontinuities meeting.

Commonly discontinuity permeability dominates over the intact rockpermeability, and therefore, the second term may often be neglected.

In-situ messurement of K

PackerTest

Single set

3 ortogonal setsK in x-direction

(Zhang, 2005)

(Hoe

k&

Bra

y, 1

977)

WHY WE DETERMINE IN SITU STRESS?

The basic reasons for in situ stress determination

Engineering analyses require boundary conditions. In situ stress is one of the most important boundaryconditions for the analyses of U/G excavations

To have basic knowledge of the stress state(e.g. direction and magnitude of the majorprincipal stresses, the direction in which therock is most likely to fail)

In situ stressstate

Failureσ1

σ3

FOS=StrengthStress

σ1

σ3

σ2

Civil & Mining Engg.Stability of U/G excavationsDrilling & blastingPillar designDesign of support systemsPrediction of rock burstDamsSlope stability

Energy DevelopmentBorehole stabilityFracturing & fracture propogationFluid flow and geothermal problemsReservoir production managementEnergy extraction and storage

σ1

σ2

σ3

STANDARDIZED TESTS

Determination of properties of intact rock and rock mass is the integral partof rock engineering studies. Although the strategy of rock characterization isa function of the engineering objectives, the tactical approach to individualtests can be standardized. The advantages of standardization are as follows(Hudson & Harrison, 2000):

The standardization guidance is helpful to anyone conducting the test,The results obtained by different organizations on rocks at different sitescan be compared in the knowledge that “like is being compared with like”, There is a source of recommended procedures for use in contracts, ifrequired.

“The use of some form of standard procedures provides rock engineersto determine the quality objectively”

ISRM SUGGESTED METHODS produced by the ISRM Commission onTesting Methods for rock testing and characterization since 1978

Such as

THE END