Table of Contents. Foreword... xiii Introduction... xv

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1 Foreword.... xiii Introduction.... xv Chapter 1. Controllability of Geotechnical Tests and their Relationship to the Instability of Soils... 1 Roberto NOVA 1.1. Introduction Load control Displacement control and mixed control Conditions for loss of controllability under mixed control Loss of controllability example Linear combinations of stresses and strains Instability line and spontaneous generation of pore water pressure Other cases of volumetric instability Drained shear bands Undrained shear bands Total stress analysis: effectiveness of the undrained strength concept in light of the loss of controllability notion Compaction bands Conclusions Bibliography Chapter 2. Multiscale Analysis of Failure François NICOT and Félix DARVE 2.1. Introduction Physical meaning of the notion of instability Hill s material instability... 36

2 vi Micromechanics of Failure in Granular Geomaterials Loss of controllability and loss of sustainability The notion of sustainability Macroscopic point of view Loss of sustainability criterion The fundamental micro macro relation The contact scale The granular assembly scale Micromechanical analysis of the vanishing of second-order work Conclusion Bibliography Chapter 3. Continuous and Discrete Modeling of Failure in Geomaterials 65 Luc SIBILLE, Florent PRUNIER, François NICOT and Félix DARVE 3.1. Definition of failure in geomechanics Material instability: definition and criterion Continuous analysis of stability with phenomenological constitutive relations Undrained loading paths on loose sand Axisymmetric loading paths Plane strain conditions Modeling instability with a discrete numerical model Proportional strain loading paths in axisymmetric conditions Unstable stress directions Application to the case of loading paths at constant stress deviator Phenomenological approach Discrete numerical modeling Conclusion Bibliography Chapter 4. Failure analysis using an Elastoplastic Micromechanical Model Richard WAN, PeiJun GUO, Mauricio PINHEIRO and Qian LI 4.1. Introduction Experimental results revealing the microstructure role Micromechanical analysis of dilatancy Micro macro relations Conservation of energy at both macro and micro scales Stress dilatancy relationship from the energy equation Case of regular assembly of particles Case of random particle packing Micromechanical elastoplastic model Yield surfaces

3 vii Plastic flow rate Hardening laws Evolution of fabric Incremental relationship Simulation results highlighting the effect of fabric Non-uniqueness of characteristic dilatancy curves Undrained triaxial compression test responses Modeling cyclic phenomena Dilatancy in both loading and unloading regimes Loading surface and kinematic hardening Comments on the plastic potential and the plastic modulus Evaluation of an elastoplastic model in cyclic loading Effect of fabric on the cyclic response of sand in drained conditions Conclusion Bibliography Chapter 5. Damage of Geomaterials: Induced Anisotropy and Coupling with Plasticity Djimédo KONDO, Qizhi ZHU and Vincent MONCHIET 5.1. Introduction Anisotropic elastic damage model with unilateral effects Homogenization and application to elastic microcracked media Micromechanics of media with random microstructure Application to microcracked media Mircrocracked closure effects and unilateral damage Impact of microcracking on the directional moduli E(n) Damage criterion and evolution law Nonlocal micromechanics-based damage model Application of the model and comparison to data Simulation of uniaxial tensile tests Predictions of anisotropic micro macro damage model for Willam s test Numerical analysis of Hassanzadeh s direct tension test A new model for ductile microcracked materials Introductory comments Limit analysis-based approach to the macroscopic yield function Studied cell of porous materials in the case of oblate voids The Eshelby-like trial velocity field Determination of the macroscopic yield surface Discussion of the boundary conditions

4 viii Micromechanics of Failure in Granular Geomaterials Principle of the determination of the yield function closed form expression for the macroscopic yield function The case of penny-shaped cracks Conclusions Appendix Bibliography Chapter 6. Continuous Damage Modeling and Discrete Approaches to Failure Gilles PIJAUDIER-CABOT 6.1. Introduction Damage in disordered lattices Global response of lattices Invariance and local distribution of forces in the lattice Correlations during the failure process Continuum damage General setting Explicit formulation Discrete modeling of crack propagation Localization limiters Integral model Gradient damage model Failure and structural size effect Conclusions Acknowledgements Bibliography Chapter 7. Effect of Particle Breakage on the Behavior of Granular Materials Bernard CAMBOU, Cécile NOUGUIER-LEHON and Eric VINCENS 7.1. Introduction Experimental results concerning the breakage of a single grain Different kinds of particle breakage Determining the block breaking strength Parameters influencing grain breakage Nature and state of the rock Size and shape of grains Effect of loading Experimental results on breakage within a REV Definition of the amount of breakage Parameters causing breakage Grading curve

5 ix Initial density State of stress and loading path Consequences for global behavior Compressibility increase Dilatancy decrease Internal friction angle decrease Phenomenological models of the representative elementary volume taking into account particle crushing Micromechanical approach of particle breakage in granular materials Particle breakage due to the applied stress, clastic yielding Hydric environment influence Phenomenological model of oedometric loading Analysis considering only the applied stress Taking into account hydric environment Complete phenomenological modeling Elastoplastic modeling using one mechanism of plasticity only Elastic-plastic modeling considering several plastic mechanisms Distinct numerical modeling of granular materials allowing particle breakage to be considered Modeling the breakage of a single particle Distinct numerical modeling using a simplified breakage local mechanism Difficulties linked to the use of a 2D numerical model Results obtained from simulations performed on representative elementary volumes Model of work in actual conditions Numerical model of ageing effects Local numerical model Numerical model Some results Conclusion Bibliography Chapter 8. Mechanical Behavior of Granular Materials with Soft Grains. 235 Ioannis-Orestis GEORGOPOULOS and Ioannis VARDOULAKIS 8.1. Introduction Definition of constitutive stress for granular media Taylor s intergranular stress Skempton s constitutive stress Biot s constitutive stress

6 x Micromechanics of Failure in Granular Geomaterials Constitutive stress for a soft-rained material Expanded perlite the case of a highly compressible granular medium Origin of raw material Physical properties of expanded perlite Isotropic triaxial compression tests on expanded perlite Discussion of Terzaghi s effective stress principle based on drained and undrained triaxial compression tests Drained triaxial compression tests on dry specimens Drained triaxial compression tests on water-saturated specimens Undrained triaxial tests on water-saturated specimens Structural cohesion and shear softening Main results and conclusions Acknowledgements Bibliography Chapter 9. Capillary Cohesion of Wet Granular Media Moulay Saïd EL YOUSSOUFI, Farhang RADJAÏ, Vincent RICHEFEU and Fabien SOULIÉ Introduction Capillary cohesion at the local scale Modeling the capillary interaction Liquid bridge and capillary force Model of capillary cohesion Experimental study of a single liquid bond Influence of parameters Implementation of capillarity in a DEM code Capillary-type interaction law Distribution of liquid inside a numerical sample Shearing weakly confined cohesive materials Experimental study Experimental setup and materials Experimental results Discrete numerical simulations Numerical sample Presentation and analysis of numerical results Microscopic origins of the macroscopic cohesion Force transmission Analysis of macroscopic stresses in the presence of capillary forces Rupture of a granular sample under simple compression Experimental study

7 xi Discrete numerical simulations Comparison between simulations and experiments Effect of the distribution and number density of liquid bonds Conclusion Bibliography Chapter 10. Numerical Modeling of Failure Mechanisms José FERNÁNDEZ MERODO, Pablo MIRA, Manuel PASTOR and Laura TONNI Introduction Mathematical model Introduction General model Balance equations Swansea model: u-p w formulation Constitutive models Introduction Generalized plasticity A simple model for sand behavior Model of collapsible soils Model of unsaturated soils Numerical model Discretization of balance equations in space Computation of stress increments Other special numerical techniques Applications Localized failure in a drained biaxial test Diffuse failure of a soil layer of a very loose sand under seismic loading Diffuse failure in the foundation of a caisson-type dyke under wave action Conclusions Acknowledgements Bibliography List of Authors Index