A discrete element analysis of collapse mechanisms in granular materials
Résumé
This paper attempts to numerically examine the concept of diffuse failure using a numerical approach based on a discrete element method. First, the theoretical background is reviewed, and it is shown how the kinetic energy of a system, initially at rest after a loading history, is likely to increase under the effect of disturbances. The vanishing of the second-order work thus constitutes a basic ingredient, related to both the pioneering work of Hill (1958) and the notion of bifurcation applied to geomechanics (Vardoulakis and Sulem, 1995). Discrete numerical simulations were performed on homogeneous three-dimensional specimens, and the three basic conditions that must be satisfied in order to observe a failure mechanism are numerically checked: (i) the equilibrium state belongs to the bifurcation domain, in which the symmetric part of the tangent constitutive operator admits at least one negative eigenvalue; (ii) the loading is controlled by mixed parameters, some being composed of stress components, the other of strain components; and, (iii) the mixed control parameters, when maintained constant, impose a loading direction associated with a negative value of the second-order work.
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