International audienceThis paper presents a synthesis of the works performed by various teams from France, Italy and Canada around the question of second-order work criterion. Because of the non-associative character of geomaterials plastic strains, it is now recognized that a whole bifurcation domain exists in the stress space with various possible modes of failure. In a first part these failure modes are observed in lab experimental tests and in discrete element modelling. Then a theoretical study of second-order work allows to establish a link with the kinetic energy, giving a basis to explain the transition from a prefailure (quasi)static regime to a postfailure dynamic regime. Eventually the main features of geomaterials failure are obtained by applying second-order work criterion to five different constitutive rate-independent models-three being phenomenological and two micromechanical. As a whole this paper tries to gather together all the elements for a proper understanding and use of second-order work criterion in geomechanics
International audienceOne 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
It is now recognized that some collapses can occur before the Mohr-Coulomb plastic limit criterion is reached, and our recent results highlight that these collapses occur under a diffuse mode of failure. We present and discuss experimental data on constant shear drained tests. A non-associated elastoplastic multimechanism model is briefly presented and numerical results are compared with our data obtained constant shear drained tests. These simulations are in agreement with experiments. The second order work is computed and the loss of stability, corresponding to the vanishing of the second order work, is very close to the experimental collapse point. RÉSUMÉ. Des effondrements se produisent avant que le critère de rupture de Mohr-Coulomb ne soit atteint. Nous avons récemment mis en évidence le fait que ces ruptures se produisent en mode diffus. Des résultats d'essais de laboratoire à contrainte déviatoire constante sont présentés et analysés. Nous simulons ces essais en utilisant une loi de comportement élastoplastique multimécanisme non associée. Nous observons une bonne concordance entre la réponse du modèle et les courbes expérimentales. De plus, le travail du second ordre est calculé à partir de la réponse du modèle et coïncide avec la perte de stabilité du matériau.
In this study, we present a device designed to investigate the behavior of very loose sand subjected to strain and stress loading paths. The influence of these loading paths is analyzed with particular attention to potential instabilities. Comparisons are made with results obtained from experimental data from literature. A particular stress path, i.e. a constant shear undrained path, is then detailed and results are discussed. Experimental results show that diffuse mode failure occurs before the Mohr-Coulomb failure surface is reached. It is shown for these undrained tests that excess pore pressure results from collapse and it is not a trigger parameter.
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