Arches and contact forces in a granular pile

TL;DR

This study investigates how arches in granular piles influence stress distribution, revealing that in-arch particles bear larger isotropic stresses and exhibit different contact force distributions compared to out-of-arch particles.

Contribution

It provides new insights into the stress and contact force distributions within arches in granular assemblies, challenging previous assumptions about stress shielding.

Findings

In-arch particles withstand larger isotropic stresses.

Out-of-arch contacts follow an exponential force distribution.

In-arch contacts are compatible with a Gaussian force distribution.

Abstract

Assemblies of granular particles mechanically stable under their own weight contain arches. These are structural units identified as sets of mutually stable grains. It is generally assumed that these arches shield the weight above them and should bear most of the stress in the system. We test such hypothesis by studying the stress born by in-arch and out-of-arch grains. We show that, indeed, particles in arches withstand larger stresses. In particular, the isotropic stress tends to be larger for in-arch-grains whereas the anisotropic component is marginally distinguishable between the two types of particles. The contact force distributions demonstrate that an exponential tail (compatible with the maximization of entropy under no extra constraints) is followed only by the out-of-arch contacts. In-arch contacts seem to be compatible with a Gaussian distribution consistent with a recently introduced approach that takes into account constraints imposed by the local force balance on grains.