Surface flows of granular materials: A modified picture for thick avalanches

Some time ago, Bouchaud et al. [J. Phys. I 4, 1383 (1994)] proposed a basic set of equations to describe surface flows. They assumed in particular that the rate of erosion (or accretion, depending on the slope) was proportional to the local amount R of rolling species. This is natural for thin avalanches, but not for thick avalanches. We discuss here the thick limit and assume that for R much greater than d (the grain diameter) the rates become independent of R. This leads to some different features: (i) filling of a silo, for which the steady-state slope is a (decreasing) function of the feeding rate; (ii) avalanches with a sink at the bottom end (''open cells''), for which the profile starts at a certain angle theta(max) and ends at the neutral angle theta(n), where theta(n) is the angle at which erosion balances accretion and is smaller than theta(max) (theta(n)=theta(max)-delta); and (iii) avalanches with a closed end (where the flow stops), for which the angle of repose is not theta(n) but theta(n) - delta=theta(max)-2 delta. Each avalanche involves a cascade of successive regimes that are described analytically. [S1063-651X(98)03910-5].