Static multiplicity of stress states in granular heaps

Abstract

As a summary and extension of previous work on arching in granular heaps, an analysis is given of statically admissible stress distributions in infinite planar wedges and axisymmetric cones composed of an isotropic linear–elastic material subject to a noncohesive Mohr–Coulomb yield criterion. The treatment is based on a combination of analytical solutions for elastic and simple plastic states, together with numerical integration of the (Sokolovskii–Kötter) ordinary differential equations appropriate to more complex plastic states. For wedges, we obtain a one–parameter family of continuous elastoplastic solutions, 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 continuous elastoplastic state is found, and it exhibits an arch. In addition to the above continuous solutions, a class of discontinuous plastic–limit states is considered, which exhibit a central pressure dip associated with the discontinuous transition from active to passive states proposed by Savage. The only solutions of this type found for symmetric wedges and cones involve central pressure dips. A brief discussion is given of the relation of this work to an extensive recent literature on the central pressure dip observed in certain experiments on granular heaps.