A continuum model of discrete granular avalanches

Abstract

A simple continuum model is proposed for discrete granular avalanches, as observed in slowly rotating drums. Subject to granular transfer across the basal interface, the model evolves the transient surface inclination and mid-slope velocity profile of the avalanches, from failure to arrest. This is done using new boundary conditions that allow entrainment or detrainment contingent on the basal shear rate. For entrainment to occur, the basal shear stress must overcome the erosion resistance of the jammed deposit, while for detrainment to take place the basal shear rate must vanish. The resulting avalanche dynamics is controlled by a single dimensionless number, the ratio of excess slope at failure to excess resistance to erosion, that can be determined from inclination history data. This number provides a measure of slope brittleness, from which the peak flow rate and arrest inclination can be predicted. Analytical techniques are used to derive model solutions, and clarify the resulting behaviour. Finally, the model is tested by comparing solutions with laboratory experiments and discrete particle simulations.