SOME OBSERVATIONS ON COMPUTATIONAL GEOMECHANICS RESEARCH (1980-2010)

1. SOME OBSERVATIONS ON COMPUTATIONAL GEOMECHANICS RESEARCH (1980-2010) Gyan N Pande Swansea University, UK Stan Pietruszczak McMaster University, Canada Dubrovnik, 29 April, 2011

2. OUTLINE OF PRESENTATION • Introduction • Constitutive models, modelling anisotropy • Strain localisation in engineering practice • Observations on research on partially saturated soils • On Discrete Element Method • Wish list of future research efforts

3. INTRODUCTION • Purpose of research • Training the young minds to study in depth and think independently • Appreciate the relevance of research conducted to engineering practice • Develop skills of innovation & effective communication • Our tools of (computational) research • Educational software, source codes • Commercial software, black boxes

4. Introduction (contd.) • Verification & validation of results • Solutions obtained from alternative methodologies • Laboratory experiments • Analytical solutions • Field tests and observations We want to assess our achievements based on the above criteria.

5. Some observations Constitutive models for geomaterials

6. Historical background • Pre-1980 An era of scepticism • The eighties (NUMOGs I, II & III) • Nonlinear elasticity models, simple elasto-plastic models (modified flow rules) • Critical state based models (isotropic, volumetric hardening)

7. The eighties (contd.) • Two, multi- and infinite surface models (Mroz, Pietruszczak; Dafalias) • Multi-mechanism framework • Spatially Mobilised Plane (SMP) concept (Matsuoka, Nakai et al) • Multilaminate framework (Pande, Sharma, Schweiger et al.) • Micro-plane framework (Bazant, Pratt) • Endochronic theory (Bazant, Valianis et al.)

8. Historical background (contd.) • The nineties (NUMOGs IV, V & VI) • Modifications and enhancements of elasto-plastic models • Development of models for partially saturated soils • Issues relating to instabilities and localisation

9. Historical background (contd.) • Other models (not discussed in NUMOGs) • Brick model (Simpson – Rankine Lecture) • MIT Model (Whittle & co-workers) • Some liquefaction models • Hardening soil model • Soft soil model • Damage theory based models

10. Historical review (contd.) The first decade of 21st century Anisotropy (inherent and induced) Modelling in multi-laminate framework Critical plane approach Microstructure tensor approach Small strain stiffness and its consequences Continuing research on PSS Neural network based constitutive models NN based inverse analyses

11. Huge choice of models but are we finally there? There are quite a few pending issues!

12. Issues • Anisotropy • Inherent due to deposition history, fabric structure, joints and discontinuities • Induced due to plastic flow • Influence of Rotation of Principal Stress Axes

13. (due to internal microstructure)

14. σ1 Material anisotropy axes α σ3 σ3 Principal stress axes σ1 Anisotropy • Any anisotropic formulation should invoke a parameter defining orientation of principal material axis with respect to principal stress axes (e.g. Pietruszczak, Mroz)

15. Inherent & induced • Both are equally important! Primary manifestation: directional dependence of deformation/strength characteristics

16. Anisotropy • Three possible ways • Incorporation of microstructure/fabric tensor • Critical plane approach • Casting the constitutive model in the multilaminate framework • Only a few aspects of plastic flow induced anisotropy (e.g. Bauschinger effect) in initially isotropic materials can be modelled by kinematic hardening • Directional dependence of mechanical behaviour cannot be achieved by manipulating yield surfaces

17. ROPSA • In most practical problems, the orientation of principal stress axes rotates, through 450 in tunnels and through 900 in earthquake problems • A change in strains takes place due to ROPSA • This will affect strength in undrained conditions • It will lead to liquefaction at lower stress levels than the case when no rotation takes place

18. ROPSA • The ways to account for ROPSA are • To use mixed invariants of stress and fabric tensors in the evolution of yield function (Pietruszczak, Mroz) • Alternatively, cast constitutive models in the multilaminate framework Kinematic hardening models do not account for ROPSA which is very important in liquefaction problems.

19. Self-learning finite elements/ Inverse analysis

22. Some observations Constitutive models for partially saturated soils

23. Historical background • Hardly any reference to PSS in text books • Intense research activity in the 15 years • Basic Barcelona Model by Alonso et al established suction as an independent parameter (1990) • Many extensions & modifications proposed since However, Pietruszczak & Pande (1992, 94, 95) had come to a conclusion around 1996 that there was no need to develop ab initio constitutive models for PSS. Their line of research was largely ignored.

24. Background • Our research followed Occam’s principle Occam’s principle (After William of Occam (derived from the name of a village (Ockham) in Surrey, England, a fourteenth century logician) "Pluralitas non est ponenda sine neccesitate". Or in plain English: "Entities should not be multiplied unnecessarily." The argument is that additional entities (theories or postulates) may contradict the existing ones.

25. Constitutive model for PSS • Partially saturated soil consists of three phases - soil skeleton, water & air • We know the mechanical behaviour of a soil skeleton, we know the constitutive model for water, we know the constitutive model for air (Boyle’s law) • The relative measures of the three phases are dealt with in elementary soil mechanics

26. Constitutive model for PSS (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 constitutive model for partially saturated soils? (The danger is that if you propose one, it might conflict with the one already existing and well established theories/postulates)

27. Constitutive model for PSS (contd.) • Two models were proposed • PSS at high degrees of saturation Here, the assumption is that the water phase is continuous but the air phase is discontinuous (Validated with undrained triaxial tests on partially saturated Ottawa sand) • PSS at low degrees of saturation Here, the assumption is that the air phase is continuous but water phase is discontinuous (Only qualitative verification)

32. Remarks on tests with constant suction • Constant suction tests are essentially drained tests • They simply reflect the response of soil skeleton • Of course the influence of suction should be accounted for in the form of a fictitious ‘cohesion’ • Let us re-visit tests of Barcelona group conducted with constant suction (1990)

33. 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.

34. Some remarks • The crucial parameter in characterizing the behaviour of partially saturated soils, is the ‘average pore size’, defined as n/Svwhere Sv is the ‘specific surface area by volume’ of the soil skeleton.  • Determination of Sv for a granular as well as a porous solid materials is a routine test carried out in many fields of engineering sciences and can be conveniently adapted for soils (Santamarina et al., 2002).

35. Remarks (contd.) • Techniques for measuring Sv • Nitrogen adsorption (maximum pore size limit of about 0.2 m) • Mercury intrusion porosimetry (range 0.0036m to 1000m) • -CT scanning techniques Correlations between particle and pore size distributions for soils will also be useful

36. Remarks (contd.) • A number of companies manufacture stand-alone equipment for the determination of Sv.   • Use of particle size analysers for soils needs to be explored • They have a facility for calculation of specific surface area based on the assumption that the particles are non porous spheres, and that all of the particles have been analysed.  

37. Remarks (contd.) • In authors’ opinion there appears to be no need to develop and refine procedures for testing partially saturated soils and to develop new instruments for in-situ measurement of ‘suction’.  All field measurements are notoriously deceptive.

38. Concluding remarks Particle size distribution or ‘gradation curve’ is a fundamental characteristic of soils • Pore size distribution is related to particle size distribution • Average pore size used in the formulation is simply porosity divided by ‘specific internal surface area’ used in many branches of engineering • Many techniques for the above parameters are already available Efforts to develop instruments to measure in-situ suctions are perhaps mis-guided

39. Permeability variation with c.o.v.

41. Last minute remarks • Intuition/speculation • Even in PS rocks, joints asperity tips, sharp edges in rock fill are microscopically fully saturated and are regions of undrained response • They should exhibit creep as localised stresses are a few orders of magnitude higher • Can we do some Brazilian tests on rocks under different levels of humidity?

42. Some observations Instability and strain localisation

43. Historical background • The most common form of strain localisation is tensile cracking which invariably occurs in most practical problems • A scale parameter needs to be introduced to retain objectivity of the finite element mesh. • Approaches proposed • Cosserat Media (de Borst) • Higher gradient plasticity • Viscoplastic approach • Homogenisation (Pietruszczak) No facility is available in any commercial code to overcome mesh dependence

44. Homogenisation technique • The orientation of cracking (most common form of localisation) is assumed as normal to the major principal stress • The orientation of shear band is calculated on the basis of Rudinicki & Rice criterion • The interface characteristics are established in terms of normal and tangential displacements • The fracture/shear zone is smeared in the intact material and characteristics of the composite are derived using homogenisation based on respective volumes of the constituents

45. Homogenisation technique (contd.) • In our view this is only way to solve practical problems • We have implemented the procedure in COSMOS and developed a User Defined Model for ABAQUS • The procedure has been applied for the analysis of concrete and reinforced concrete structures

46. Some observations Discrete Element Method

47. Discrete Element Method • This method has become increasingly popular since early eighties and has been applied to a large number of engineering problems of continua and discontinua • Its popularity can be largely attributed to • availability of free or cheap versions of software • impressive real time computer graphics • The results of the analysis can of course be matched to experimental results, if known a-priori by playing with parameters many of which are usually unknown or arbitrary

48. Discrete Element Method (contd.) However, • It is often forgotten that the results obtained are qualitative only • The engineers at higher levels in industry get easily charmed by its amazing capabilities and are unaware of its pitfalls Admittedly, there are situations where a qualitative result is better than nothing. It is then a legitimate use of the method.

49. Discrete Element Method (contd.) • The method is qualitative as • There is no proof of convergence • Contact parameters are mostly arbitrary • Algorithmic parameters are also arbitrary and can change collapse mechanism However, DEM has led to useful studies on non-spherical contact problems and contact detection algorithms

50. Wish list - research • Neural Network based Constitutive Models (NNCM) should be explored further • Role of NNCM in inverse analysis • Development of a new breed of testing equipment • Integration of a particle size or pore size distribution curve in constitutive models • Make a universal lattice analogy model for the study of cracking and crack propagation