Stress propagation in sand

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.

Development of normal pressure and frictional traction along the walls of a steep conical hopper during filling

“…Particulate solids display various behaviours and the mechanical description of such assemblies is an old but still open problem. A general feature observed both in experiments and in simulation is the very heterogeneous and anisotropic character of the force network arising from the inter-granular contacts [8,9,10,23,24,25,26,27]. Recently, strong interest has developed in both the engineering and physics communities to try to develop a new understanding from a description of such particulate contacts and force distribution to a macroscopic description of the stress-strain relations [26,27,28,29].…”

Prediction of flow patterns during silo discharges using a finite element approach and its preliminary experimental verification

“…This is mainly because the behavior of complex particulate solids under static and flow scenarios is not understood when obtaining an analytical solution (Campbell, 2006;Cates & Wittmer, 1998;Edwards & Mounfield, 1996). As an alternative, numerical modeling is considered in this study for predicting the effects of flow aid devices on flow patterns.…”

Granular Matter Instability: A Structural Rigidity Point of View

“…A large number of theoretical approaches to this problem are formulated on a continuum [12,27,28,29,30] and thus rest on the assumption that a length scale exists, below which fluctuations are negligible when compared to averages. It is not clear whether this assumption is easily justified for granular matter, where stress fluctuations seem to be at least as large as average stresses [20,21].…”