Development of stresses in cohesionless poured sand

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Abstract
The pressure distribution beneath a conical sandpile, created by pouring sand from a point source onto a rough rigid support, shows a pronounced minimum 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 the medium. We discuss the fundamental difference between such approaches, which lead to hyperbolic differential equations, and elastoplastic models, for 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 (of given construction history), on a rough rigid support, is uniquely determined by the body forces and the boundary condition at the free (upper) surface. In simple elastoplastic treatments, one must in addition specify, at the base of the pile, a displacement field (or some equivalent data). This displacement field appears to be either ill–defined, or defined relative to a reference state whose physical existence is in doubt. Insofar as their predictions depend on physical factors unknown and outside experimental control, such elastoplastic models predict that the observations should be intrinsically irreproducible. This view is not easily reconciled with the existing experimental data on conical sandpiles, which we briefly review. Our hyperbolic models are based instead on a physical picture of the material, in which: (1) the load is supported by a skeletal network of force chains (‘stress paths’) whose geometry depends on construction history; (2) this network is ‘fragile’ or marginally stable, in a sense that we define. Although perhaps oversimplified, these assumptions may lie closer to the true physics of poured cohesionless grains than do those of conventional elastoplasticity. We point out that our hyperbolic models can nonetheless be reconciled with elastoplastic ideas by taking the limit of an extremely anisotropic yield condition.
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