Static multiplicity of stress states in granular heaps

As a summary and extension of previous work On arching in granular heaps, a n analysis is given of statically admissible stress distributions in infini te planar wedges and axisymmetric cones composed of an isotropic linear-ela stic material subject to a non-cohesive Mohr-Coulomb yield criterion. The t reatment is based on a combination of analytical solutions for elastic and simple plastic states, together with numerical integration of the (Sokolovs kii-Kotter) ordinary differential equations appropriate to more complex pla stic states. For wedges, we obtain a one-parameter family of continuous elastoplastic so lutions, with only three isolated symmetric solutions for symmetric wedges, one of which has a central pressure dip or 'arch'. For axisymmetric cones subject to a well-known closure for plastic hoop stress, only one continuou s elastoplastic state is found, and it exhibits an arch. In addition to the above continuous solutions, a class of discontinuous pla stic-limit states is considered, which exhibit a central pressure dip assoc iated with the discontinuous transition from active to passive states propo sed by Savage. The only solutions of this type found for symmetric wedges a nd cones involve central pressure dips. A brief discussion is given of the relation of this work to an extensive recent literature on the central pres sure dip observed in certain experiments on granular heaps.