Discrete numerical analysis of failure modes in granular materials

The question of failure for geomaterials, and more generally for nonassociativematerials, is revisited through the second-order work criterion defining,for such media, a whole domain of bifurcation included in the plastic limit surface.In a first theoretical part of the chapter, relations between the vanishing ofthe second-order work, the existence of limit states and the occurrence of failurescharacterized by a transition from a quasi-static pre-failure regime to a dynamicpost-failure regime, are presented and illustrated from discrete element computations.Then boundaries of the bifurcation domain and cones of unstable loadingdirections are given in fully three-dimensional loading conditions for a phenomenologicalincrementally non-linear relation, and in axisymmetric loading conditionsfor a numerical discrete element model. Finally, conditions for the triggering andthe development of failure inside the bifurcation domain are described and emphasizedfrom direct simulations with the discrete element method for proportional stressloading paths