Development of Stresses in Cohesionless Poured Sand

TL;DR

This paper investigates the stress distribution beneath a poured sandpile, contrasting hyperbolic stress propagation models based on force chains with elastoplastic models, and discusses their implications for understanding the observed stress dip.

Contribution

It introduces hyperbolic models based on force chains and compares them with elastoplastic models, highlighting the importance of construction history and material fragility.

Findings

Hyperbolic models explain the stress dip phenomenon.

Elastoplastic models face issues with displacement field definition.

Hyperbolic models can be related to elastoplastic models through anisotropic yield conditions.

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 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.