SOMESOME OBSERVATIONS ON OBSERVATIONS ON

COMPUTATIONAL COMPUTATIONAL GEOMECHANICS RESEARCH GEOMECHANICS RESEARCH

(1980-2010)(1980-2010)

Gyan N PandeGyan N PandeSwansea University, UKSwansea University, UK

Stan PietruszczakStan PietruszczakMcMaster University, CanadaMcMaster University, Canada

Dubrovnik, 29 April, 2011Dubrovnik, 29 April, 2011

OUTLINE OF PRESENTATIONOUTLINE OF PRESENTATION

• Introduction Introduction

• Constitutive models, modelling Constitutive models, modelling anisotropy anisotropy

• Strain localisation in engineering practiceStrain localisation in engineering practice

• Observations on research on partially Observations on research on partially saturated soilssaturated soils

• On Discrete Element MethodOn Discrete Element Method

• Wish list of future research effortsWish list of future research efforts

INTRODUCTION INTRODUCTION

• Purpose of researchPurpose of research– Training the young minds to study in Training the young minds to study in

depth and think independentlydepth and think independently– Appreciate the relevance of research Appreciate the relevance of research

conducted to engineering practiceconducted to engineering practice– Develop skills of innovation & effective Develop skills of innovation & effective

communicationcommunication• Our tools of (computational) researchOur tools of (computational) research

– Educational software, source codesEducational software, source codes– Commercial software, black boxesCommercial software, black boxes

Introduction (contd.)Introduction (contd.)

• Verification & validation of resultsVerification & validation of results– Solutions obtained from alternative Solutions obtained from alternative

methodologiesmethodologies– Laboratory experimentsLaboratory experiments– Analytical solutionsAnalytical solutions– Field tests and observationsField tests and observations

We want to assess our achievements We want to assess our achievements based on the above criteria.based on the above criteria.

Some observationsSome observations

Constitutive models for Constitutive models for geomaterialsgeomaterials

Historical backgroundHistorical background

• Pre-1980 An era of scepticism Pre-1980 An era of scepticism

• The eighties (NUMOGs I, II & III) The eighties (NUMOGs I, II & III) – Nonlinear elasticity models, simple Nonlinear elasticity models, simple

elasto-plastic models (modified flow elasto-plastic models (modified flow rules)rules)

– Critical state based models (isotropic, Critical state based models (isotropic, volumetric hardening)volumetric hardening)

The eighties (contd.)The eighties (contd.)

• Two, multi- and infinite surface models Two, multi- and infinite surface models (Mroz, Pietruszczak; Dafalias) (Mroz, Pietruszczak; Dafalias)

• Multi-mechanism frameworkMulti-mechanism framework– Spatially Mobilised Plane (SMP) concept Spatially Mobilised Plane (SMP) concept

(Matsuoka, Nakai et al) (Matsuoka, Nakai et al) – Multilaminate framework (Pande, Sharma, Multilaminate framework (Pande, Sharma,

Schweiger et al.)Schweiger et al.)– Micro-plane framework (Bazant, Pratt)Micro-plane framework (Bazant, Pratt)

• Endochronic theory (Bazant, Valianis et al.) Endochronic theory (Bazant, Valianis et al.)

Historical background Historical background (contd.)(contd.)

•The nineties (NUMOGs IV, V & VI) The nineties (NUMOGs IV, V & VI) – Modifications and enhancements of Modifications and enhancements of

elasto-plastic modelselasto-plastic models– Development of models for partially Development of models for partially

saturated soilssaturated soils– Issues relating to instabilities and Issues relating to instabilities and

localisationlocalisation

Historical background Historical background (contd.)(contd.)

– Other models (not discussed in NUMOGs)Other models (not discussed in NUMOGs)

•Brick model (Simpson – Rankine Brick model (Simpson – Rankine Lecture)Lecture)

•MIT Model (Whittle & co-workers)MIT Model (Whittle & co-workers)

•Some liquefaction modelsSome liquefaction models

•Hardening soil modelHardening soil model

•Soft soil modelSoft soil model

•Damage theory based modelsDamage theory based models

Historical review (contd.)Historical review (contd.)• The first decade of 21The first decade of 21stst century century

– Anisotropy (inherent and induced)Anisotropy (inherent and induced)•Modelling in multi-laminate framework Modelling in multi-laminate framework

•Critical plane approachCritical plane approach

•Microstructure tensor approachMicrostructure tensor approach – Small strain stiffness and its consequencesSmall strain stiffness and its consequences– Continuing research on PSS Continuing research on PSS – Neural network based constitutive modelsNeural network based constitutive models– NN based inverse analyses NN based inverse analyses

Huge choice of models but are we finally there?

There are quite a few pending There are quite a few pending issues!issues!

IssuesIssues

• AnisotropyAnisotropy– Inherent due to deposition history, fabric Inherent due to deposition history, fabric

structure, joints and discontinuitiesstructure, joints and discontinuities– Induced due to plastic flowInduced due to plastic flow

• Influence of Rotation of Principal Influence of Rotation of Principal Stress AxesStress Axes

ANISOTROPY

Deformational Strength

(due to internal microstructure)

Anisotropy Anisotropy

• Any anisotropic Any anisotropic formulation should formulation should invoke a parameter invoke a parameter defining orientation defining orientation of principal material of principal material axis with respect to axis with respect to principal stress principal stress axesaxes

(e.g. Pietruszczak, (e.g. Pietruszczak, Mroz)Mroz)

α

Material anisotropy axes

Principal stress axes

σ1

σ1

σ3 σ3

0 1 2 3 4 5 6H orizonta l d isp lacem ent (m m )

0

0.4

0.8

1.2

1.6

2

0 1 2 3 4 5 6H orizonta l d isp lacem ent (m m )

0

0.4

0.8

1.2

1.6

Ver

tical

dis

plac

emen

t (m

m)

= 0 0

= 90 0

= 60 0

= 0 0

= 90 0

= 60 0

(a ) (b )

– Inherent & inducedInherent & induced– Both are equally important! Both are equally important!

Primary manifestation: directional dependence of Primary manifestation: directional dependence of deformation/strength characteristicsdeformation/strength characteristics

AnisotropyAnisotropy

• Three possible waysThree possible ways– Incorporation of microstructure/fabric tensorIncorporation of microstructure/fabric tensor– Critical plane approachCritical plane approach– Casting the constitutive model in the multilaminate Casting the constitutive model in the multilaminate

frameworkframework

• Only a few aspects of plastic flow induced Only a few aspects of plastic flow induced anisotropy (e.g. Bauschinger effect) in initially anisotropy (e.g. Bauschinger effect) in initially isotropic materials can be modelled by kinematic isotropic materials can be modelled by kinematic hardening hardening

• Directional dependence of mechanical behaviour Directional dependence of mechanical behaviour cannot be achieved by manipulating yield cannot be achieved by manipulating yield surfacessurfaces

ROPSAROPSA

• In most practical problems, the In most practical problems, the orientation of principal stress axes orientation of principal stress axes rotates, through 45rotates, through 4500 in tunnels and in tunnels and through 90through 9000 in earthquake problems in earthquake problems – A change in strains takes place due to A change in strains takes place due to

ROPSAROPSA– This will affect strength in undrained This will affect strength in undrained

conditionsconditions– It will lead to liquefaction at lower stress It will lead to liquefaction at lower stress

levels than the case when no rotation takes levels than the case when no rotation takes placeplace

ROPSAROPSA

• The ways to account for ROPSA areThe ways to account for ROPSA are– To use mixed invariants of stress and To use mixed invariants of stress and

fabric tensors in the evolution of yield fabric tensors in the evolution of yield function (Pietruszczak, Mroz)function (Pietruszczak, Mroz)

– Alternatively, cast constitutive models in Alternatively, cast constitutive models in the multilaminate frameworkthe multilaminate framework

Kinematic hardening models do not Kinematic hardening models do not account for ROPSA which is very account for ROPSA which is very important in liquefaction problems.important in liquefaction problems.

Self-learning finite Self-learning finite elements/ Inverse analysiselements/ Inverse analysis

Some observationsSome observations

Constitutive models for Constitutive models for partially saturated soilspartially saturated soils

Historical backgroundHistorical background

• Hardly any reference to PSS in text books Hardly any reference to PSS in text books • Intense research activity in the 15 yearsIntense research activity in the 15 years

– Basic Barcelona Model by Alonso et al Basic Barcelona Model by Alonso et al established suction as an independent established suction as an independent parameter (1990) parameter (1990)

– Many extensions & modifications proposed Many extensions & modifications proposed sincesince

However, Pietruszczak & Pande (1992, 94, 95) had However, Pietruszczak & Pande (1992, 94, 95) had come to a conclusion around 1996 that there come to a conclusion around 1996 that there was no need to develop ab initio constitutive was no need to develop ab initio constitutive models for PSS.models for PSS.

Their line of research was largely ignored. Their line of research was largely ignored.

Background Background

• Our research followed Occam’s principleOur research followed Occam’s principle

Occam’s principleOccam’s principle(After William of Occam (derived from the name of a village (After William of Occam (derived from the name of a village (Ockham) in Surrey, England, a fourteenth century logician)(Ockham) in Surrey, England, a fourteenth century logician)

"Pluralitas non est ponenda sine neccesitate". "Pluralitas non est ponenda sine neccesitate". Or in plain English:Or in plain English:

"Entities should not be multiplied unnecessarily.""Entities should not be multiplied unnecessarily."

The argument is that additional entities (theories The argument is that additional entities (theories or postulates) may contradict the existing ones. or postulates) may contradict the existing ones.

Constitutive model for Constitutive model for PSSPSS• Partially saturated soil consists of three Partially saturated soil consists of three

phases - soil skeleton, water & air phases - soil skeleton, water & air

• We know the mechanical behaviour of a We know the mechanical behaviour of a soil skeleton, we know the constitutive soil skeleton, we know the constitutive model for water, we know the constitutive model for water, we know the constitutive model for air (Boyle’s law)model for air (Boyle’s law)

• The relative measures of the three The relative measures of the three phases are dealt with in elementary soil phases are dealt with in elementary soil mechanicsmechanics

Constitutive model for PSS Constitutive model for PSS (contd.)(contd.)

• From the above, response of a partially saturated soil (at any degree of saturation), including evolution of suction, can be derived

So, why do we need a separate, new So, why do we need a separate, new constitutive model for partially constitutive model for partially saturated soils?saturated soils?

(The danger is that if you propose one, it might conflict (The danger is that if you propose one, it might conflict with the one already existing and well established with the one already existing and well established theories/postulates) theories/postulates)

Constitutive model for PSS Constitutive model for PSS (contd.)(contd.)

•Two models were proposedTwo models were proposed– PSS at high degrees of saturationPSS at high degrees of saturationHere, the assumption is that the water phase is Here, the assumption is that the water phase is

continuous but the air phase is discontinuous continuous but the air phase is discontinuous (Validated with undrained triaxial tests on (Validated with undrained triaxial tests on partially saturated Ottawa sand)partially saturated Ottawa sand)

– PSS at low degrees of saturationPSS at low degrees of saturationHere, the assumption is that the air phase is Here, the assumption is that the air phase is

continuous but water phase is discontinuouscontinuous but water phase is discontinuous(Only qualitative verification)(Only qualitative verification)

0 100 200 300 400

p ' (kP a)

0

100

200

300

400

q (k

Pa)

S r = 1 .0N um erica lExperim enta l

0 2 4 6 8 10

1

(% )

0

40

80

120

160

200

q (k

Pa

)

0 100 200 300 400

p ' (kP a)

0

100

200

300

400

q (k

Pa)

Sr = 0.96

N um erica lExperim enta l

0 4 8 12

1

(% )

0

100

200

300

q (k

Pa

)

%

q (

kPa)

dry sam ple S ro=1.0

S ro=0.4

soaking

%

%

%

q (k

Pa)

S ro=1.0

S ro=0.8

S ro=0.4

dra ined response (at S ro=0.4)

dry sam ple

%

V%

Remarks on tests with constant Remarks on tests with constant suctionsuction

• Constant suction tests are essentially Constant suction tests are essentially drained testsdrained tests– They simply reflect the response of soil skeletonThey simply reflect the response of soil skeleton– Of course the influence of suction should be Of course the influence of suction should be

accounted for in the form of a fictitious ‘cohesion’ accounted for in the form of a fictitious ‘cohesion’

• Let us re-visit tests of Barcelona group Let us re-visit tests of Barcelona group conducted with constant suction (1990) conducted with constant suction (1990)

Test # P (kPa) Suction (kPa) qf (kPa)Exp.

qf (kPa)calc.

% Error

1 142 9.7 132 131 0

2 142 14.2 149 135 9

3 137 95 228 200 12

4 280 16 241 255 6

5 340 0 293 293 0

7 390 95 377 418 10

8 325 91 384 360 6

9 544 40 500 503 1

10 557 41 500 515 3

11 558 16 508 495 3

12 590 97 567 590 4

13 540 95 567 549 3

This value appears to be too low since even without suction the strength should have been higher than 410 kPa in view of test# 5.

Some remarksSome remarks

• The crucial parameter in characterizing The crucial parameter in characterizing the behaviour of partially saturated soils, the behaviour of partially saturated soils, is the ‘average pore size’, defined as n/Svis the ‘average pore size’, defined as n/Sv where Sv is the ‘specific surface area by where Sv is the ‘specific surface area by volume’ of the soil skeleton.  volume’ of the soil skeleton. 

• Determination of Sv for a granular as well Determination of Sv for a granular as well as a porous solid materials is a routine test as a porous solid materials is a routine test carried out in many fields of engineering carried out in many fields of engineering sciences and can be conveniently adapted sciences and can be conveniently adapted for soils (Santamarina et al., 2002). for soils (Santamarina et al., 2002).

Remarks (contd.)Remarks (contd.)

• Techniques for measuring STechniques for measuring Svv

– Nitrogen adsorption (maximum pore size Nitrogen adsorption (maximum pore size limit of about 0.2 limit of about 0.2 m)m)

– Mercury intrusion porosimetry (range Mercury intrusion porosimetry (range 0.00360.0036m to 1000m to 1000m)m)

– -CT scanning techniques-CT scanning techniques

Correlations between particle and pore Correlations between particle and pore size distributions for soils will also be size distributions for soils will also be useful useful

Remarks (contd.)Remarks (contd.)

• A number of companies manufacture stand-A number of companies manufacture stand-alone equipment for the determination of Sv. alone equipment for the determination of Sv.   

• Use of particle size analysers for soils needs Use of particle size analysers for soils needs to be exploredto be explored

• They have a facility for calculation of specific They have a facility for calculation of specific surface area based on the assumption that surface area based on the assumption that the particles are non porous spheres, and the particles are non porous spheres, and that all of the particles have been analysed.  that all of the particles have been analysed.  

Remarks (contd.)Remarks (contd.)

• In authors’ opinion there appears to In authors’ opinion there appears to be no need to develop and refine be no need to develop and refine procedures for testing partially procedures for testing partially saturated soils and to develop new saturated soils and to develop new instruments for in-situ measurement instruments for in-situ measurement of ‘suction’.  of ‘suction’. 

All field measurements are notoriously All field measurements are notoriously deceptive.deceptive.

Concluding remarks Concluding remarks

Particle size distribution or ‘gradation curve’ is a Particle size distribution or ‘gradation curve’ is a fundamental characteristic of soilsfundamental characteristic of soils

• Pore size distribution is related to particle size Pore size distribution is related to particle size distributiondistribution

• Average pore size used in the formulation is Average pore size used in the formulation is simply porosity divided by ‘specific internal simply porosity divided by ‘specific internal surface area’ used in many branches of surface area’ used in many branches of engineering engineering

• Many techniques for the above parameters are Many techniques for the above parameters are already availablealready available

Efforts to develop instruments to measure Efforts to develop instruments to measure in-situ suctions are perhaps mis-guided in-situ suctions are perhaps mis-guided

Permeability variation with c.o.v.

Permeability variation with c.o.v.

Variation of permeability with c.o.v. of pore sizes (Tests L4 & DB1)L4 mean diam. = 25.149 microns, DB1 mean diam. = 7.976 microns

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

0.0 0.5 1.0 1.5 2.0 2.5

c.o.v.

Nor

mal

ised

per

mea

bilit

y

Last minute remarksLast minute remarks

• Intuition/speculationIntuition/speculation– Even in PS rocks, joints asperity tips, sharp Even in PS rocks, joints asperity tips, sharp

edges in rock fill are microscopically fully edges in rock fill are microscopically fully saturated and are regions of undrained saturated and are regions of undrained responseresponse

– They should exhibit creep as localised They should exhibit creep as localised stresses are a few orders of magnitude stresses are a few orders of magnitude higherhigher

– Can we do some Brazilian tests on rocks Can we do some Brazilian tests on rocks under different levels of humidity? under different levels of humidity?

Some observationsSome observations

Instability and strain Instability and strain localisationlocalisation

Historical backgroundHistorical background

• The most common form of strain The most common form of strain localisation is tensile cracking which localisation is tensile cracking which invariably occurs in most practical problemsinvariably occurs in most practical problems

• A scale parameter needs to be introduced A scale parameter needs to be introduced to retain objectivity of the finite element to retain objectivity of the finite element mesh.mesh.

• Approaches proposedApproaches proposed– Cosserat Media (de Borst)Cosserat Media (de Borst)– Higher gradient plasticityHigher gradient plasticity– Viscoplastic approachViscoplastic approach– Homogenisation (Pietruszczak)Homogenisation (Pietruszczak)No facility is available in any commercial No facility is available in any commercial

code to overcome mesh dependencecode to overcome mesh dependence

Homogenisation techniqueHomogenisation technique

• The orientation of cracking (most common form The orientation of cracking (most common form of localisation) is assumed as normal to the of localisation) is assumed as normal to the major principal stressmajor principal stress

• The orientation of shear band is calculated on The orientation of shear band is calculated on the basis of Rudinicki & Rice criterionthe basis of Rudinicki & Rice criterion

• The interface characteristics are established in The interface characteristics are established in terms of normal and tangential displacementsterms of normal and tangential displacements

• The fracture/shear zone is smeared in the intact The fracture/shear zone is smeared in the intact material and characteristics of the composite material and characteristics of the composite are derived using homogenisation based on are derived using homogenisation based on respective volumes of the constituents respective volumes of the constituents

Homogenisation technique Homogenisation technique (contd.)(contd.)

• In our view this is only way to solve In our view this is only way to solve practical problemspractical problems

• We have implemented the procedure We have implemented the procedure in COSMOS and developed a User in COSMOS and developed a User Defined Model for ABAQUS Defined Model for ABAQUS

• The procedure has been applied for The procedure has been applied for the analysis of concrete and the analysis of concrete and reinforced concrete structuresreinforced concrete structures

Some observationsSome observations

Discrete Element Method Discrete Element Method

Discrete Element MethodDiscrete Element Method

• This method has become increasingly popular This method has become increasingly popular since early eighties and has been applied to a since early eighties and has been applied to a large number of engineering problems of large number of engineering problems of continua and discontinua continua and discontinua

• Its popularity can be largely attributed toIts popularity can be largely attributed to– availability of free or cheap versions of software availability of free or cheap versions of software – impressive real time computer graphicsimpressive real time computer graphics

• The results of the analysis can of course be The results of the analysis can of course be matched to experimental results, if known a-matched to experimental results, if known a-priori by playing with parameters many of priori by playing with parameters many of which are usually unknown or arbitrarywhich are usually unknown or arbitrary

Discrete Element Method Discrete Element Method (contd.)(contd.)However,However,• It is often forgotten that the results It is often forgotten that the results

obtained are qualitative onlyobtained are qualitative only• The engineers at higher levels in industry The engineers at higher levels in industry

get easily charmed by its amazing get easily charmed by its amazing capabilities and are unaware of its pitfalls capabilities and are unaware of its pitfalls

Admittedly, there are situations where a Admittedly, there are situations where a qualitative result is better than nothing. qualitative result is better than nothing. It is then a legitimate use of the method.It is then a legitimate use of the method.

Discrete Element Method Discrete Element Method (contd.)(contd.)

• The method is qualitative asThe method is qualitative as– There is no proof of convergence There is no proof of convergence – Contact parameters are mostly arbitrary Contact parameters are mostly arbitrary – Algorithmic parameters are also arbitrary Algorithmic parameters are also arbitrary

and can change collapse mechanismand can change collapse mechanism

However, DEM has led to useful studies However, DEM has led to useful studies on non-spherical contact problems on non-spherical contact problems and contact detection algorithms and contact detection algorithms

Wish list - research Wish list - research

• Neural Network based Constitutive Models Neural Network based Constitutive Models (NNCM) should be explored further(NNCM) should be explored further

• Role of NNCM in inverse analysisRole of NNCM in inverse analysis• Development of a new breed of testing Development of a new breed of testing

equipmentequipment• Integration of a particle size or pore size Integration of a particle size or pore size

distribution curve in constitutive modelsdistribution curve in constitutive models• Make a universal lattice analogy model for Make a universal lattice analogy model for

the study of cracking and crack the study of cracking and crack propagationpropagation

Thank you Thank you