The sandpile revisited: Computer assisted determination of constitutive relations and the breaking of scaling

TL;DR

This study uses numerical simulations to analyze stress distributions in granular sandpiles, revealing how bottom interactions and size-dependent effects influence the validity of scaling laws and constitutive relations.

Contribution

It introduces a new numerical model for granular assemblies and demonstrates the breakdown of classical scaling assumptions under certain conditions.

Findings

Interaction with the bottom surface influences pressure dip formation.

Scaling assumptions break down for small piles and low friction coefficients.

A predictive theory identifies when scaling solutions are valid or fail.

Abstract

We revisit the problem of the stress distribution in a frictional sandpile under gravity, equipped with a new numerical model of granular assemblies with both normal and tangential (frictional) inter-granular forces. Numerical simulations allow a determination of the spatial dependence of all the components of the stress field as a function of systems size, the coefficient of static friction and the frictional interaction with the bottom surface. Our study clearly demonstrates that interaction with the bottom surface plays a crucial role in the formation of a pressure dip under the apex of a granular pile. Basic to the theory of sandpiles are assumptions about the form of scaling solutions and constitutive relations for cohesive-less hard grains for which no typical scale is available. We find that these constitutive relations must be modified; moreover for smaller friction coefficients and smaller piles these scaling assumptions break down in the bulk of the sandpile due to the presence of length scales that must be carefully identified. After identifying the crucial scale we provide a predictive theory to when scaling solutions are expected to break down. At the bottom of the pile the scaling assumption always breaks, due to the different interactions with the bottom surface. The consequences for measurable quantities like the pressure distribution and shear stress at the bottom of the pile are discussed. For example one can have a transition from no dip in the base-pressure to a dip at the center of the pile as a function of the system size.