Instabilities Modeling in Geomechanics. Jean Sulem

      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 1Figure 1.1. Multiple shear bands and a volume increase due to diffuse dilatancyFigure 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 2Figure 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 pointsFigure 2.7. Degenerate cases: (a) star node and (b) degenerate nodeFigure 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 bifurcationFigure 2.12. Supercritical pitchfork bifurcationFigure 2.13. Bifurcation diagram of the subcritical pitchfork bifurcationFigure 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