Thick surface flows of granular materials: Effect of the velocity profile on the avalanche amplitude

A few years ago, Bouchaud et al. introduced a phenomenological model to des cribe surface flows of granular materials [J. Phys. I 4, 1383 (1994)]. Acco rding to this model, one can distinguish between a static phase and a rolli ng phase that are able to exchange grains through an erosion or accretion m echanism. Boutreux et al. [Phys. Rev. E 58, 4692 (1998)] proposed a modific ation of the exchange term in order to describe thicker flows where saturat ion effects are present. However, these approaches assumed that the downhil l convection velocity of the grains is constant inside the rolling phase, a hypothesis that is not verified experimentally. In this article, we theref ore modify the above models by introducing a velocity profile in the flow, and study the physical consequences of this modification in the simple situ ation of an avalanche in an open cell. We present: a complete analytical de scription of the avalanche in the case of a linear velocity profile, and ge neralize the results for a power-law dependency. We show, in particular, th at the amplitude of the avalanche is strongly affected by the velocity prof ile. [S1063-651X(99)69508-2].