Similarity solutions for granular avalanches of finite mass with variable bed friction
Abstract
This paper continues a series of studies on the plane flow of a pile of cohesionless granular material down a rough inclined plane. Internal and basal friction laws are assumed to obey the MohrCoulomb yield criterion but in contrast to previous investigations the angle of friction at the bottom of the pile is considered to depend on the position or on the velocity or on both. Similarity, i.e. shape preserving solutions are constructed. The depth of the pile and the profile of the total minus the centre of mass velocity are determined analytically, but the total length and the position of the centre of mass are calculated numerically. If the basal friction angle is constant, the centre of mass moves with constant acceleration and the length of the pile extends monotonically. These motions change, when the angle of friction varies along the pile — the length of the pile may extend, contract or remain stationary and the centre of mass motion may decelerate or even reach steady state. Eight special cases are exhibited which demonstrate the influence of the friction law on the speed and spread of the pile.
 Publication:

Continuum Mechanics and Thermodynamics
 Pub Date:
 December 1989
 DOI:
 10.1007/BF01125776
 Bibcode:
 1989CMT.....1..239N