Instabilities Modeling in Geomechanics

Ioannis Stefanou is Associate Professor and Researcher at Laboratoire Navier, Ecole des Ponts Paris Tech, France. Jean Sulem is Full Professor and Senior Researcher at Laboratoire Navier, Ecole des Ponts Paris Tech, France.

• Introduction xiIoannis STEFANOU and Jean SULEMChapter 1. Multiphysics Role in Instabilities in Geomaterials: a Review 1Tomasz HUECKEL1.1. Introduction 11.2. General remarks 21.3. Solid phase material criteria 51.4. Material sample stability: experimental 101.5. Boundary value problems: uniqueness and stability at the field scale 191.5.1. Landslides 191.5.2. Thermal pressurization problem 241.5.3. Localization during drying of geomaterials 251.6. Conclusion 271.7. References 27Chapter 2. Fundamentals of Bifurcation Theory and Stability Analysis 31Ioannis STEFANOU and Sotiris ALEVIZOS2.1. Introduction 312.2. Bifurcation and stability of dynamical systems 352.2.1. Definition of stability 362.2.2. Linear systems of ODEs 372.2.3. Nonlinear systems of ODEs 392.2.4. An example of LSA 412.3. Stability of two-dimensional linear dynamical systems 422.3.1. Classification of fixed points 432.3.2. Love mechanics: Romeo and Juliet 462.4. Common types of bifurcations 482.4.1. Saddle-node bifurcation 482.4.2. Transcritical bifurcation 502.4.3. Supercritical and subcritical pitchfork bifurcation 512.4.4. From one to two dimensions – limit cycles 532.4.5. Bifurcations in two dimensions – supercritical and subcritical Hopf bifurcation 542.4.6. Mathematical bifurcations in PDEs 592.5. From ODEs to PDEs 612.5.1. Deformation bands and the acoustic tensor 612.5.2. Deformation bands as an instability problem 652.6. Summary 682.7. Appendix 692.8. References 69Chapter 3. Material Instability and Strain Localization Analysis 73Jean SULEM3.1. Introduction 733.2. Shear band model 753.2.1. Strain localization criterion 763.2.2. Strain localization, loss of ellipticity and vanishing speed of acceleration waves 793.3. Shear band formation in element tests on rocks 803.3.1. Drucker–Prager model 803.3.2. Non-coaxial plasticity 823.3.3. Cataclastic shear banding 823.3.4. Postlocalization behavior 833.4. Strain localization in fluid-saturated porous media 843.4.1. Strain localization criterion in fluid-saturated porous media 843.4.2. Stability analysis of undrained shear on a saturated layer 863.5. Conclusion 903.6. References 90Chapter 4. Experimental Investigation of the Emergence of Strain Localization in Geomaterials 95Pierre BÉSUELLE4.1. Introduction 954.2. Methods 984.2.1. Digital image correlation 994.2.2. X-ray computed tomography 1034.2.3. Experimental devices for in situ full-field measurements 1044.3. Selected materials 1104.3.1. Hostun sand 1104.3.2. Caicos ooids sand 1114.3.3. Vosges sandstone 1114.3.4. Callovo–Oxfordian clayey rock 1114.4. Strain localization in sands 1124.4.1. Plane strain compression by FRS 1124.4.2. Triaxial compression by X-ray CT and DIC 1164.4.3. Triaxial compression by X-ray CT, the critical void ratio 1224.5. Strain localization in porous rocks 1244.5.1. Strain localization in Vosges sandstone 1244.5.2. Strain localization in a clayey rock 1304.6. Conclusion 1354.7. References 136Chapter 5. Numerical Modeling of Strain Localization 141Panos PAPANASTASIOU and Antonis ZERVOS5.1. Introduction 1425.2. Cosserat continuum 1455.2.1. Governing equations 1455.2.2. Finite element formulation of Cosserat model 1485.2.3. Material parameters 1505.2.4. Failure in thick-walled cylinder test 1515.2.5. Stability analysis of elliptical shape perforations 1545.3. Gradient elastoplasticity 1565.3.1. Governing equations 1565.3.2. Finite element formulation 1605.3.3. Material model 1625.3.4. Modeling of the biaxial test 1635.3.5. Modeling cavity expansion 1675.4. Conclusion 1695.5. Acknowledgments 1705.6. References 170Chapter 6. Numerical Modeling of Bifurcation: Applications to Borehole Stability, Multilayer Buckling and Rock Bursting 175Euripides PAPAMICHOS6.1. Introduction 1756.2. Borehole stability 1766.2.1. Primary loading path 1776.2.2. Hole failure 1806.2.3. Simulation of hollow cylinder experiments 1836.3. Folding of elastic media as a bifurcation problem 1876.3.1. Buckling of a layer under initial stress 1886.3.2. Eigen-displacements and tractions at layer boundaries 1906.3.3. Buckling of a layer system – the transfer matrix technique 1916.3.4. Buckling of layered half-space 1926.4. Axial splitting and spalling 1946.4.1. Buckling of a half-space with surface parallel cracks 1956.5. Conclusion 1996.6. Acknowledgments 2006.7. References 200Chapter 7. Numerical Modeling of Multiphysics Couplings and Strain Localization 203Frédéric COLLIN, Panagiotis KOTRONIS and Benoît PARDOEN7.1. Introduction 2037.2. Experimental evidences of strain localization 2057.3. Regularization methods 2057.3.1. Enrichment of the constitutive law 2067.3.2. Enrichment of the kinematics 2097.4. Coupled local second gradient model for microstructure saturated media 2127.4.1. Balance equations for microstructure poromechanics 2137.4.2. Coupled finite element formulation 2197.4.3. Two-dimensional specimen under compression 2247.5. Coupled local second gradient model for an unsaturated medium 2297.5.1. Partial saturation conditions 2297.5.2. Anisotropy of the intrinsic permeability 2307.5.3. Compressibility of the solid grains 2317.6. Modeling of a gallery excavation 2337.6.1. Numerical model 2337.6.2. Influence of stress and permeability anisotropies 2377.6.3. Influence of second gradient boundary condition 2397.6.4. Influence of Biot’s coefficient 2397.6.5. Influence of gallery ventilation 2407.7. Conclusion 2467.8. References 246Chapter 8. Multiphysics Couplings and Strain Localization in Geomaterials 253Jean SULEM and Ioannis STEFANOU8.1. Introduction 2538.2. Thermo-chemo-chemical couplings and stability of shear zones 2558.2.1. Problem statement 2558.2.2. Stability of adiabatic undrained shear 2578.2.3. Chemical weakening and earthquake nucleation 2598.3. Dissolution weakening and compaction banding 2648.3.1. Multiscale modeling of strong chemo-poro-mechanical coupling 2648.3.2. Compaction banding in oedometric compression 2688.4. Conclusion 2738.5. References 274Chapter 9. On the Thermo-poro-mechanics of Chemically Active Faults 279Manolis VEVEAKIS9.1. Introduction 2809.2. Time-independent formation of shear zones from solid mechanics 2829.2.1. Shear zone thickness at boundary temperature conditions 2839.2.2. Shear zone thickness at elevated temperature 2849.3. Time-dependent evolution of shear zones 2859.3.1. Energy considerations 2879.3.2. The Taylor–Quinney coefficient 2889.3.3. Chemical reactions 2899.4. Postfailure evolution of a shear zone 2909.4.1. Analysis of the system’s response 2939.4.2. Time scales of the system 2959.5. Comparison to field observations 2969.6. Application to ETS sequences 2989.6.1. Regular sequences – Cascadia ETS sequence 2999.7. Discussion 3029.8. Appendix: poro-chemical model 3059.9. References 306Chapter 10. Analysis of Instabilities in Faults 313Hadrien RATTEZ, Ioannis STEFANOU, Jean SULEM, Manolis VEVEAKIS and Thomas POULET10.1. Introduction 31410.2. Description of the model 31610.2.1. Cosserat continuum theory 31610.2.2. Constitutive equations for a Cosserat continuum 31710.2.3. Mass balance equation 31910.2.4. Energy balance equation 31910.3. Bifurcation analysis 32010.3.1. LSA for a Cosserat continuum with THM couplings 32010.3.2. Localization conditions for a fault zone 32210.3.3. Shear band thickness evolution in a fault zone 32410.4. Numerical analysis 32610.4.1. Regularization of the mesh dependency 32610.4.2. Response and shear band thickness of a fault gouge 32910.5. Conclusion 33410.6. Bibliography 334List of Authors 337Index 339