Fundamentals of Plasticity in Geomechanics

The book presents a concise, yetreasonably comprehensive,overview of fundamentalnotions of plasticity in relation to geomechanics. The primary objective of this work is to provide the reader with a general background in soil/rock plasticity and, as such, should be perceived as an introduction to the broad area of inelastic response of geomaterials. The book is divided into eight chapters. Chapters 1 & 2 start with an outline of the basic concepts and fundamental postulates, followed by a review of the elastic-perfectly plastic formulations in geomechanics. The isotropic strain-hardening framework and isotropic-kinematic hardening rules, the latter formulated within the context of bounding surface plasticity, are discussed in Chapters 3 & 4. Chapter 5 outlines the basic techniques for numerical integration, whereas Chapter 6 gives an overview of procedures for limit analysis that include applications of lower and upper bound theorems. Both these chapters are introductory in nature and are intended to provide a basic background in the respective areas. Chapter 7 deals with description of inherent anisotropy in geomaterials. Finally, Chapter 8 provides an overview of the experimental response of geomaterials. The text is intended primarily for Ph.D./M.Sc. students as well as researchers working in the areas of soil/rock mechanics. It may also be of interest to practicing engineers familiar with established notions of contemporary continuum mechanics.

ContentsPreface Chapter 1. Basic concepts of the theory of plasticity1.1 Typical approximations of uniaxial response of the material1.2 The notion of generalized yield/failure criterion1.3 Generalization of the concept of elastic-perfectly plastic and strain hardening material1.4 Determination of plastic strain; deformation and flow theories of plasticity1.5 Review of fundamental postulates of plasticity; uniqueness of the solution Chapter 2. Elastic-perfectly plastic formulations in geomechanics2.1 General considerations2.2 Geometric representation of the failure surface2.3 Selection of stress invariants for the mathematical description2.4 Typical failure criteria for geomaterials2.4.1 Mohr-Coulomb failure criterion2.4.2 Drucker-Prager and other derivative criteria2.4.3 Modified criteria based on smooth approximations to Mohr-Coulomb envelope2.4.4 Non-linear approximations in meridional section2.5 Derivation of constitutive relation2.5.1 Matrix formulation2.6 Consequences of a non-associated flow rule Chapter 3. Isotropic strain-hardening formulations3.1 ‘Triaxial’ tests and their mathematical representation3.1.1 Mohr-Coulomb criterion in ‘triaxial’ space3.1.2 On the behaviour of a perfectly plastic Mohr-Coulomb material3.1.3 Review of typical mechanical characteristics of granular materials3.2 Volumetric hardening; Critical State model3.2.1 Formulation in the ‘triaxial’ {p,q} space3.2.2 Comments on the performance3.2.3 Generalization and specification of the constitutive matrix3.3 Deviatoric hardening model3.3.1 Formulation in the ‘triaxial’ {p,q} space3.3.2 Comments on the performance3.3.3 Generalization and specification of the constitutive matrix3.4 Combined volumetric-deviatoric hardening3.5 Specification of constitutive matrix under undrained conditions Chapter 4. Combined isotropic-kinematic hardening rules4.1 Bounding surface plasticicty; volumetric hardening framework4.1.1 Formulation in the ‘triaxial’ {p,q} space4.1.2 Comments on the performance4.1.3 Generalization and specification of the constitutive matrix4.2 Bounding surface plasticicty; deviatoric hardening framework4.2.1 Formulation in the ‘triaxial’ {P,Q} space4.2.2 Comments on the performance4.2.3 Generalization and specification of the constitutive matrix Chapter 5. Numerical integration of constitutive relations5.1 Euler’s integration schemes5.2 Numerical integration of {p,q} formulation5.2.1 Stress-controlled scheme5.2.2 Strain-controlled schemes5.3 Numerical examples of integration in {p,q}-space5.3.1 Critical State model; drained p=const. compression5.3.2 Deviatoric hardening model; drained ‘triaxial’ compression5.3.3 Deviatoric hardening model; undrained ‘triaxial’ compression5.4 General methods for numerical integration5.4.1 Statement of algorithmic problem5.4.2 Notion of closest point projection5.4.3 Return-mapping algorithms Chapter 6. Introduction to limit analysis6.1 Formulation of lower and upper bound theorems6.2 Examples for applications of limit theorems in geotechnical engineering Chapter 7. Description of inherent anisotropy in geomaterials7.1 Formulation of anisotropic failure criteria7.1.1 Specification of failure criteria based on critical plane approach7.1.2 Formulation of failure criteria incorporating a microstructure tensor7.2 Description of inelastic deformation process7.2.1 Plasticity formulation for critical plane approach7.2.2 Plasticity formulation incorporating a microstructure tensor7.2.3 Numerical examples Chapter 8. Experimental trends in the mechanical behaviour of soils and rocks8.1 Basic mechanical characteristics in monotonic tests under drained conditions 8.1.1 Influence of confining pressure; compaction/dilatancy8.1.2 Influence of Lode’s angle and the phenomenon of strain localization8.2 Undrained response of granular media; pore pressure evolution, liquefaction8.3 Basic mechanical characteristics in cyclic tests; hysteresis and liquefaction8.4 Inherent anisotropy; strength characteristics of sedimentary rocks8.5 Identification of basic material parameters for soils/rocks8.5.1 General remarks on identification procedure8.5.2 Examples involving deviatoric hardening framework Bibliography Appendix: Suggested exercises

Dr. Stan Pietruszczak is professor of Civil Engineering at McMaster University in Canada. His research interests are in the following areas: Geotechnical Engineering: Modelling of mechanical response of geomaterials (soils, rocks, etc) to both monotonic and fluctuating loads. Description of inherent and induced anisotropy through incorporation of some tensorial functions reflecting the evolution of material microstructure. Modelling of the chemo-mechanical interaction in rocks / soils. Description of strain localization phenomenon, in dry and saturated soils, through a homogenization technique. Structural Mechanics: Numerical analysis of concrete structures, including nuclear containment structures. Assessment of seismic stability of masonry structures. Modelling of the mechanical effects of alkali-aggregate reaction in hydraulic structures. Description of the response of saturated cemented aggregate mixtures, including localized deformation.Biomechanics: Description of aging and functional adaptation of bone. Evaluation of risk of fracture of bones; modelling of bone-implant interaction. He has published over 140 refereed papers.