Mean steady granular force on a wall overflowed by free-surface gravity-driven dense flows

We studied free-surface gravity-driven recirculating flows of cohesionless granular materials down a rough inclined plane and overflowing a wall normal to the incoming flow and to the bottom. We performed two-dimensional spherical particle discrete element simulations using a linear damped spring law between particles with a Coulomb failure criterion. High-frequency force fluctuations were observed. This paper focuses on the mean steady force exerted by the flow on the obstacle versus the macroscopic inertial number of the incoming flow, where the inertial number measures the ratio between a macroscopic deformation time scale and an inertial time scale. A triangular stagnant zone is formed upstream of the obstacle and sharply increases the mean force at low incoming inertial numbers. A simple hydrodynamic model based on depth-averaged momentum conservation is proposed. This analytical model predicts the numerical data fairly well and allows us to quantify the different contributions to the mean force on the wall. Beyond this model, our study provides an example of the ability of simple hydrodynamic approaches to describe the macroscopic behavior of an assembly of discrete particles not only in terms of kinematics but also in terms of forces.