Development of Stresses in Cohesionless Poured Sand

Details Development of Stresses in Cohesionless Poured Sand Development of Stresses in Cohesionless Poured Sand

1998-03-21

arxiv.org/abs/cond-mat/9803266v1

Physics

Condensed Matter

Statistical Mechanics

25 pages, latex RS.tex with rspublic.sty, 7 figures in Rsfig.ps. Philosophical Transactions A, Royal Society, submitted 02/98

Scientific paper

10.1098/rsta.1998.0285

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 of 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 .... 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 .... Our hyperbolic models are based instead on a physical picture of the material, in which (a) the load is supported by a skeletal network of force chains ("stress paths") whose geometry depends on construction history; (b) this network is `fragile' or marginally stable, in a sense that we define. .... 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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