Development of stresses in cohesionless poured sand

The pressure distribution beneath a conical sandpile, created by pouring sa nd from a point source onto a rough rigid support, shows a pronounced minim um below the apex ('the dip'). Recent work by the authors has attempted to explain this phenomenon by invoking local rules for stress propagation that depend on the local geometry, and hence on the construction history, of th e medium. We discuss the fundamental difference between such approaches, wh ich lead to hyperbolic differential equations, and elastoplastic models, fo r which the equations are elliptic within any elastic zones present. In the hyperbolic case, the stress distribution at the base of a wedge or cone (o f given construction history), on a rough rigid support, is uniquely determ ined by the body forces and the boundary condition at the free (upper) surf ace. In simple elastoplastic treatments, one must in addition specify, at t he base of the pile, a displacement field (or some equivalent data). This d isplacement held appears to be either ill-defined, or defined relative to a reference state whose physical existence is in doubt. Insofar as their pre dictions depend on physical factors unknown and outside experimental contro l, such elastoplastic models predict that the observations should be intrin sically irreproducible. This view is not easily reconciled with the existin g experimental data on conical sandpiles, which we briefly review. Our hype rbolic models are based instead on a physical picture of the material, in w hich: (1) the load is supported by a skeletal network of force chains ('str ess paths') whose geometry depends on construction history; (2) this networ k is 'fragile' or marginally stable, in a sense that we define. Although pe rhaps oversimplified, these assumptions may lie closer to the true physics of poured cohesionless grains than do those of conventional elastoplasticit y. We point out that our hyperbolic models can nonetheless be reconciled wi th elastoplastic ideas by taking the limit of an extremely anisotropic yiel d condition.