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 Rd (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 θₘₐₓ and ends at the neutral angle θₙ, where θₙ is the angle at which erosion balances accretion and is smaller than θₘₐₓ (θₙ=θₘₐₓ-δ); and (iii) avalanches with a closed end (where the flow stops), for which the angle of repose is not θₙ but θₙ-δ=θₘₐₓ-2δ. Each avalanche involves a cascade of successive regimes that are described analytically.
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Boutreux et al. (1998) studied this question.