On the dependence of the avalanche angle on the granular layer thickness

TL;DR

This paper investigates how the avalanche angle of a granular layer depends on its thickness, proposing a microscopic model that predicts the threshold angle based on grain stability and contact dynamics, aligning well with experimental data.

Contribution

It introduces a microscopic model linking granular stability and contact configurations to the avalanche angle dependence on layer thickness.

Findings

Model predicts theta(h) accurately

Threshold angle decreases with layer thickness

Agreement with empirical observations

Abstract

A layer of sand of thickness h flows down a rough surface if the inclination is larger than some threshold value theta which decreases with h. A tentative microscopic model for the dependence of theta with h is proposed for rigid frictional grains, based on the following hypothesis: (i) a horizontal layer of sand has some coordination z larger than a critical value z_c where mechanical stability is lost (ii) as the tilt angle is increased, the configurations visited present a growing proportion $_s of sliding contacts. Instability with respect to flow occurs when z-z_s=z_c. This criterion leads to a prediction for theta(h) in good agreement with empirical observations.