Time-varying force from dense granular avalanches on a wall.

We studied avalanches of cohesionless granular materials down a rough inclined plane and overflowing a wall normal to the incoming flow and to the bottom. This paper focuses on the transient time-varying mean force exerted by the granular stream on the obstacle at various slope inclinations. A nearly triangular dead zone is formed upstream of the obstacle. It largely contributes to the overall force signal at low slope inclinations. It also drives the residual force corresponding to the avalanche tail until its standstill whatever the slope inclination. An analytical hydrodynamic model based on depth-averaged momentum conservation was successfully developed for steady-flow conditions to predict the steady-state force computed from discrete numerical simulations [T. Faug, R. Beguin, and B. Chanut, Phys. Rev. E 80, 021305 (2009)]. The basic equations of the model are briefly reviewed and adapted to transient time-varying flows. The modified hydrodynamic model quite accurately represents the force peak produced by the granular avalanche flows computed from discrete numerical simulations reported in previous studies. A fitting procedure is needed to represent the decrease of the force after the force peak, thus quantifying the different contributions to the mean force on the wall. We show that the weight of each contribution is largely dependent on the slope inclination.