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 theta(start) which decreases with increasing h. A tentative microscopic model for the dependence of theta(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 theta(start)( h) in good agreement with empirical observations. Copyright (C) EPLA, 2009