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

A layer of sand of thickness h flows down a rough surface if the inclination is larger than some threshold value _start which decreases with increasing h. A tentative microscopic model for the dependence of _start on 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 z_s of sliding contacts. Instability with respect to flow occurs when z- z_s=z_c. This criterion leads to a prediction for _start(h) in good agreement with empirical observations.