Stability in geomechanics, experimental and numerical analyses
Résumé
One of the main consequences of the nonassociative character of plastic strains in geomaterials is the existence of failure states strictly inside the Mohr-Coulomb plastic limit surface. This point is first emphasized by considering proportional strain loading paths as generalizations of the classical undrained triaxial path. It is shown that the sign of the second-order work is a proper criterion for analyzing these particular failure states. Then, experimental results and theoretical curves (obtained from an incrementally nonlinear constitutive relation) are compared for the case of proportional stress paths in axisymmetric conditions. Main features of the second-order work criterion are identified, such as the existence of a bifurcation domain together with a number of instability cones inside the Mohr-Coulomb surface. Furthermore, decomposing the second-order work into its isotropic and deviatoric parts makes it possible to compare each of the respective contributions to material instability. Finally, a heuristic boundary value problem is simulated via finite element modelling. A spectral analysis of the symmetric part of the stiffness matrix is conducted to extract the first vanishing eigenvalue and its associated eigenvector. It is found that the displacement field related to this eigenvector appears to be very close to the displacement computed just before global numerical breakdown signalling an effective failure. A plausible explanation is that, considering a material point, the flow rule at the boundary of the bifurcation domain almost coincides with the one describing the failure mechanism on the Mohr-Coulomb plastic limit surface.