Local Coulomb versus Global Failure Criterion for Granular Packings

TL;DR

This study links local contact instability at Coulomb thresholds to the global failure of granular packings, showing that local failure clusters grow and destabilize the entire system as it approaches an avalanche.

Contribution

It reveals how local failure mechanisms relate to global stability criteria in granular materials, emphasizing the role of heterogeneities and cluster growth.

Findings

Failure clusters are locally marginal and grow to span the system before avalanches.

Avalanches occur when local clusters reach the generalized isostaticity threshold.

Large heterogeneities influence the destabilization process leading to failure.

Abstract

Contacts at the Coulomb threshold are unstable to tangential perturbations and thus contribute to failure at the microscopic level. How is such a local property related to global failure, beyond the effective picture given by a Mohr-Coulomb type failure criterion? Here, we use a simulated bed of frictional disks slowly tilted under the action of gravity to investigate the link between the avalanche process and a global generalized isostaticity criterion. The avalanche starts when the packing as a whole is still stable according to this criterion, underlining the role of large heterogeneities in the destabilizing process: the clusters of particles with fully mobilized contacts concentrate local failure. We demonstrate that these clusters, at odds with the pile as a whole, are also globally marginal with respect to generalized isostaticity. More precisely, we observe how the condition of their stability from a local mechanical proprety progressively builds up to the generalized isostaticity criterion as they grow in size and eventually span the whole system when approaching the avalanche.