Development of Stresses in Cohesionless Poured Sand

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.Comment: 25 pages, latex RS.tex with rspublic.sty, 7 figures in Rsfig.ps. Philosophical Transactions A, Royal Society, submitted 02/9

Jamming and Stress Propagation in Granular Materials

We have recently developed some simple continuum models of static granular media which display "fragile" behaviour: they predict that the medium is unable to support certain types of infinitesimal load (which we call "incompatible" loads) without plastic rearrangement. We argue that a fragile description may be appropriate when the mechanical integrity of the medium arises adaptively, in response to a load, through an internal jamming process. We hypothesize that a network of force chains (or "granular skeleton") evolves until it can just support the applied load, at which point it comes to rest; it then remains intact so long as no incompatible load is applied. Our fragile models exhibits unusual mechanical responses involving hyperbolic equations for stress propagation along fixed characteristics through the material. These characteristics represent force chains; their arrangement expressly depends on the construction history. Thus, for example, we predict a large difference in the stress pattern beneath two conical piles of sand, one poured from a point source and one created by sieving.Comment: 40 pages, 9 figures, LATE

An explanation for the central stress minimum in sand piles

URL: http://www-spht.cea.fr/articles/s96/119International audienc