Bounds on the shear load of cohesionless granular matter

TL;DR

This paper derives theoretical bounds on the maximum shear stress sustainable by cohesionless granular materials, linking microscopic force networks and contact anisotropies to macroscopic shear resistance.

Contribution

It introduces an optimization-based approach to relate force network properties to shear strength, establishing an upper bound influenced mainly by friction coefficient.

Findings

Maximum shear stress is bounded by the force network ensemble.

Contact network anisotropies have a subdominant effect on shear resistance.

Force anisotropies relate to elastic constants in experiments.

Abstract

We characterize the force state of shear-loaded granular matter by relating the macroscopic stress to statistical properties of the force network. The purely repulsive nature of the interaction between grains naturally provides an upper bound for the sustainable shear stress, which we analyze using an optimization procedure inspired by the so-called force network ensemble. We establish a relation between the maximum possible shear resistance and the friction coefficient between individual grains, and find that anisotropies of the contact network (or the fabric tensor) only have a subdominant effect. These results can be considered the hyperstatic limit of the force network ensemble and we discuss possible implications for real systems. Finally, we argue how force anisotropies can be related quantitatively to experimental measurements of the effective elastic constants.