Stress Propagation and Arching in Static Sandpiles

TL;DR

This paper introduces a new stress propagation model for static sandpiles, emphasizing the role of local constitutive relations that encode the pile's construction history, aligning with experimental stress patterns.

Contribution

It proposes a novel approach to modeling stress in static granular media using local constitutive relations that incorporate construction history effects.

Findings

Stress patterns exhibit RSF scaling across different pile sizes.

The proposed model aligns with experimental stress measurements.

Microscopic indeterminacy influences macroscopic stress distribution.

Abstract

We present a new approach to the modelling of stress propagation in static granular media, focussing on the conical sandpile constructed from a point source. We view the medium as consisting of cohesionless hard particles held up by static frictional forces; these are subject to microscopic indeterminacy which corresponds macroscopically to the fact that the equations of stress continuity are incomplete -- no strain variable can be defined. We propose that in general the continuity equations should be closed by means of a constitutive relation (or relations) between different components of the (mesoscopically averaged) stress tensor. The primary constitutive relation relates radial and vertical shear and normal stresses (in two dimensions, this is all one needs). We argue that the constitutive relation(s) should be local, and should encode the construction history of the pile: this history determines the organization of the grains at a mesoscopic scale, and thereby the local relationship between stresses. To the accuracy of published experiments, the pattern of stresses beneath a pile shows a scaling between piles of different heights (RSF scaling) which severely limits the form the constitutive relation can take ...