Relaxation dynamics of water-immersed granular avalanches

We study water-immersed granular avalanches in a long rectangular cell of small thickness. By video means, both the angle of the granular pile and the velocity profiles of the grains across the depth are recorded as a function of time. These measurements give access to the instantaneous granular flux. By inclining the pile at initial angles larger than the maximum angle of stability, avalanches are triggered and last for a long time, up to several hours for small grains, during which both the slope angle and the granular flux relax slowly. We show that the relaxation is quasi-steady so that there is no inertia: the relaxation at a given time is controlled only by the slope angle at that time. This allows us to adapt a frictional model developed recently for dry or water-immersed grains flowing in stationary conditions. This model succeeds well in reproducing our unsteady avalanche flows, namely the flowing layer thickness, the granular flux and the temporal relaxation of the slope. When a water counter-flow is applied along the pile, the granular avalanches are slowed down and behave as if granular friction were increased by an amount proportional to the water flow. All these findings are also reproduced well with the same friction model by taking into account the additional fluid force.