Jean Sulem - Instabilities Modeling in Geomechanics

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1 Chapter 5Table 5.1. Normalized shear band thickness for different dilatancy angles and c...Table 5.2. Theoretically predicted and numerically determined shear band inclin...Table 5.3. Comparison of numerical results (third column) on shear band inclina...

2 Chapter 8Table 8.1. Parameter values for lizardite dehydration at a depth of around 30 km...Table 8.2. Indicative material properties of a carbonate grainstone

3 Chapter 10Table 10.1. Model parameter values for a fault gouge (Rice 2006; Sulem et al. 20...

1 Chapter 1 Figure 1.1. Multiple shear bands and a volume increase due to diffuse dilatancy Figure 1.2. Relationships between criteria for uniqueness, second-order work, st... Figure 1.3. Triaxial compression of Wombeyan marble. (a) Axial stress–strain cur... Figure 1.4. Axial and lateral stress measured on a set of argillaceous quartzite... Figure 1.5. Biaxial compression of sand with visible localized shear band (Vardo... Figure 1.6. (a) Low and (b) high confining stress compression of a quartz sand: ... Figure 1.7. Comparison of uniaxial compression of rock salt, granite and marble... Figure 1.8. Evolution of the distribution of acoustic emission during uniaxial c... Figure 1.9. Unstable behavior during an undrained test of Hostun sand (Daouadji... Figure 1.10. Stress–strain curves in a q = cons. drained test with instability (... Figure 1.11. General view of the Maierato landslide site (Borrelli et al. 2014)... Figure 1.12. A geological profile across the area prior to the landslide. The gr... Figure 1.13. Evolution of factor of safety of the slope at Mount Turtle along th... Figure 1.14. Top left: view of the landslide scarp (2014). Top right: a crack (5... Figure 1.15. Top: predicted tempearture and excess pore pressure arising in the ... Figure 1.16. Evolution with time of the effective internal friction angle and co... Figure 1.17. (a) Effective stress paths during undrained heating of Boom clay (H... Figure 1.18. Evolution of the water body between eight glass spheres subjected t...

2 Chapter 2 Figure 2.1. Different types of stability. Solid lines depict the fixed points an... Figure 2.2. Spring – rigid beam system. For a color version of this figure, see ... Figure 2.3. Bifurcation diagram. Dashed lines represent unstable braches and sol... Figure 2.4. Phase diagram for (a) a <���–1, (b) –1 < a <... Figure 2.5. (a) Unstable fixed point with non-orthogonal eigenvectors (saddle), ... Figure 2.6. Stable (a) and unstable (b) spiral fixed points Figure 2.7. Degenerate cases: (a) star node and (b) degenerate node Figure 2.8. Classification of fixed points of a two-dimensional dynamical sy... Figure 2.9. Sketch of beam buckling due to high load. Here, the load acts as a ... Figure 2.10. Saddle-node bifurcation. A half full circle denotes half stable fix... Figure 2.11. Transcritical bifurcation Figure 2.12. Supercritical pitchfork bifurcation Figure 2.13. Bifurcation diagram of the subcritical pitchfork bifurcation Figure 2.14. (a) Phase diagram of the system of equation [2.22]. We observe the... Figure 2.15. (a) Phase diagram of the van der Pol equation for μ = 1. (b) Evolut... Figure 2.16. Sketch of a pair of complex eigenvalues crossing the imaginary axi... Figure 2.17. Phase diagram of the supercritical Hopf bifurcation. We observe the... Figure 2.18. Phase diagram of the subcritical Hopf bifurcation. In (a) Figure 2.19. (a) Experiments on hydrothermal convection where the famous Bénard ... Figure 2.20. Schematic representation of a deformation band and of the discontin... Figure 2.21. Elastoplastic yield envelope with hardening/softening (dotted lines... Figure 2.22. Critical hardening values as a function of the β and μ for strain l...Figure 2.23. Shear band formation and mesh dependency for a rate-independent el...

3 Chapter 3Figure 3.1. Model of a deforming shear band with heat and fluid fluxesFigure 3.2. Localized deformation with shear, compaction and dilation modes (Du ...Figure 3.3. Cataclastic shear banding in Fontainebleau sandstone (El Bied et al...Figure 3.4. Saturated rock layer under constant normal stress and sheared at con...Figure 3.5. Shear stress–plastic shear strain curves in drained and undrained co...

4 Chapter 4Figure 4.1. Material deformation of the subset (from Bornert et al. (2004))Figure 4.2. Schematic of a 2D-surface DIC analysis approach (from Hall (2012)). ...Figure 4.3. Schematic diagram of the plane strain apparatus for soils (from Desr...Figure 4.4. Schematic diagram of the plane strain apparatus for rocks (from Bésu...Figure 4.5. (a) Photograph of the silicon membrane that separates the specimen f...Figure 4.6. Schematic of the X-ray microtomography setup for triaxial testing (f...Figure 4.7. Tomography setup for triaxial testing at the beamline ID15A at ESRF....Figure 4.8. Stress strain responses from various tests; the numbers noted on eac...Figure 4.9. Test shf00: stereophotogrammetry-based incremental fields of shear s...Figure 4.10. Test shf03: stereophotogrammetry-based incremental fields of shear ...Figure 4.11. Test shf06: stereophotogrammetry-based incremental fields of shear ...Figure 4.12. Test COEA01: Slices of the X-ray CT scan of specimen COEA01 in its ...Figure 4.13. Test COEA01: Stress strain response; the numbers noted on curve are...Figure 4.14. Test COEA01: (top) slice of the grain displacement field during th...Figure 4.15. Test COEA01: (top) slice of the strain field during the test, measu...Figure 4.16. Comparison of the strain field during tests on three sands: (top) ...Figure 4.17. Deformation stress curve and incremental shear strain fields in an...Figure 4.18. Comparison of triaxial tests on loose and dense Hostun sand specime...Figure 4.19. Test BxR_GVR_06: (top) differential stress (σ i– σ 3) versus axial s...Figure 4.20. Test BxR_GVR_06: (the two first lines) incremental second strain t...Figure 4.21. Test BxR_GVR_11: (top) differential stress (σ i– σ 3) vs axial strai...Figure 4.22. Test BxR_GVR_11: (the two first lines) incremental second strain te...Figure 4.23. Test BxR_COx_06: (top) differential stress (σ i– σ 3) versus axial s...Figure 4.24. Test BxR_COx_06: (the two first lines) incremental second strain te...Figure 4.25. Test BxR_COx_13: (top) differential stress (σ 1– σ 3) versus axial s...Figure 4.26. Test BxR_COx_13: (the two first lines) incremental second strain te...

5 Chapter 5Figure 5.1. Primary branch (I), secondary branch (II) and branch for the “imperf...Figure 5.2. (a) Displacement and rotation fields, and (b) stresses and couple st...Figure 5.3. External pressure versus normalized hole closure in a thick walled c...Figure 5.4. Contours of the shear plastic strain after localization of deformati...Figure 5.5. Bifurcation load and peak load versus normalized hole radius predict...Figure 5.6. Hole closure versus applied stress for a circular hole and elliptica...Figure 5.7. Incremental displacement field after localization of deformation aro...Figure 5.8. Contours of shear plastic strain around a circular hole (left) and ...Figure 5.9. Biaxial geometry, loading and boundary conditionsFigure 5.10. Vertical load versus vertical displacementFigure 5.11. Contours of the equivalent plastic strain: (a) associative case; (b...Figure 5.12. Radial displacement increment at bifurcation (left) and final mater...Figure 5.13. Internal pressure versus hole expansion for the Ri = 10 cm model

6 Chapter 6Figure 6.1. Vertical (left) and horizontal (right) X-ray CT scan images of hollo...Figure 6.2. Geometric layout of the thick wall hollow cylinder configuration: (a...Figure 6.3. Experimental data and theoretical results for lateral hole failure f...Figure 6.4. External radial stress at bifurcation failure versus bifurcation mod...Figure 6.5. Isotropic and plane-strain loading. Numerical simulations and experi...Figure 6.6. Theoretical predictions of scale effect for lateral hole failure du...Figure 6.7. A single layer under initial stress σ 1and σ 2Figure 6.8. Multilayered medium under compressive initial stressesFigure 6.9. (a) Buckling of a layer on top of a half-space, and (b) critical buc...Figure 6.10. Critical buckling stress of a viscoelastic layer on a viscoelastic ...Figure 6.11. Deformed shape of crack and free surface due to buckling of the hal...Figure 6.12. Half-space with periodic array of collinear cracks compressed by un...Figure 6.13. Critical buckling stress ξ = –σ∕G of a half-space with a periodic a...