Granular slumping in a fluid : focus on runout distances

We investigate the effect of an ambient fluid on the dynamics of collapse and spread of a granular column simulated by means of a recently developed model which takes into account both fluid forces that act on each grain and contacts between grains. The model couples the contact dynamics method for discrete element modeling of the grains and their interactions with the finite element method for the integration of Navier-Stokes equations in 2D. The coupling is based on the fictitious domain approach in which the fluid domain is extended to that of grains, and the rigid-body motion of the grains is imposed by means of distributed Lagrange multipliers. As in similar numerical and experimental works with dry grains, we focus here on the run-out distances and avalanche durations for different column aspect ratios (height vs width). We consider three options for the surrounding fluid: 1) no fluid, 2) water and 3) a viscous fluid that allows us to perform our simulations in the grain-inertial, fluid-inertial and viscous regimes, respectively. The run-out distance is found to increase as a power law with the aspect ratio of the column, and surprisingly, for a given aspect ratio and packing fraction, it may be similar in the grain-inertial regime and fluid inertial regimes but with considerably longer duration in the latter case. We show that the effect of the fluid in viscous and fluid-inertial regimes is both to reduce the kinetic energy during the collapse and enhance the flow by lubrication during the spread. Hence, the run-out distance in a fluid may be below or equal to that in the absence of fluid due to compensation between those effects