Stress Propagation in Sand

TL;DR

This paper introduces a new continuum model for stress propagation in static granular media, specifically sandpiles, emphasizing the role of construction history and fixed eigendirections in stress tensor organization.

Contribution

It proposes the FPA model, a novel approach assuming fixed eigendirections of the stress tensor determined at burial, aligning well with experimental data.

Findings

Stresses propagate along archlike structures within the medium.

The FPA model quantitatively matches experimental stress measurements.

The model links stress paths to microscopic grain arrangements.

Abstract

We describe a new continuum approach to the modelling of stress propagation in static granular media, focussing on the conical sandpile created from a point source. We argue that the stress continuity equations should be closed by means of scale-free, local constitutive relations between different components of the stress tensor, encoding the construction history of the pile: this history determines the organization of the grains, and thereby the local relationship between stresses. Our preferred model FPA (Fixed Principle Axes) assumes that the eigendirections (but not the eigenvalues) of the stress tensor are determined forever when a material element is first buried. Stresses propagate along a nested set of archlike structures within the medium; the results are in good quantitative agreement with published experimental data. The FPA model is one of a larger class, called OSL (Oriented Stress Linearity) models, in which the direction of the characteristics for stress propagation are fixed at burial. We speculate on the connection between these characteristics and the stress paths observed microscopically.