10 Pages

Stress propagation through frictionless granular material

The nature of the forces within a static pile of grains has proven more subtle than one might expect. Such a pile is an assembly of many hard, spheroidal bodies that maintain their positions via a balance of gravitational forces and contact forces with their neighbors [1,2]. On the one hand, determin­ ing these forces is a prosaic equilibrium problem. Since the number of grains is large, the long-established notions of continuum solid mechanics appear applicable. On the other hand, a pile of grains or beads is not a solid. The forces between beads are more problematic than those between the atoms of a conventional solid. These latter forces are smoothly varying on the scale of the separation and they arise from a potential energy that includes attraction. The forces on a grain are different. First, they vary sharply with interparticle distance, and there is no attraction. Second, the frictional part of a contact force is not determined by the macroscopic positions of the grains. Rather, it depends on how each contact was formed. The resulting macroscopic behavior of the pile is also clearly different from that of a conventional solid. Arbitrarily slight forces can disturb the pile, so that the notion of stable equilibrium is suspect. De­ spite these complexities, we expect the mechanics of a granular pile to be universal. Hard, round grains appear to form piles of the same nature independent of their composi­ tion or detailed shape. We are led to think of these as nondeformable objects that exert normal forces of constraint and transverse forces limited by Coulomb’s static friction limit.