Numerical investigations of the force experienced by a wall subject to granular lid-driven flows: regimes and scaling of the mean force

Discrete element simulations are used to model a two-dimensional gravity-free granular sample, which is trapped between two smooth sidewalls and one bottom rough wall while being subject to a constant shearing velocity at the top under a given confinement pressure. This system, inspired by conventional fluid mechanics, is called a granular lid-driven cavity. Attention is firstly paid to the time-averaged dynamics of the grains once a steady-state is reached. Strong spatial heterogeneities associated with a large-scale vortex formed within the whole volume of the lid-driven cavity are observed. The mean steady force on the sidewall facing the shearing velocity is then investigated in detail for different cavity lengths, shearing velocities and confinement pressures at the top. The ratio of the force on the latter wall to the top confinement pressure force is not constant but depends on both the shearing velocity and the confinement pressure. Above a critical value of the cavity length relative to the wall height and over a wide range of both shearing velocity and top confinement pressure, all data merge into a one-to-one relation between the mean force scaled by the top pressure force and the macroscopic inertial number of the lid-driven cavity. This result reveals the key role played by the inertial rheology of the granular material in the granular force transmission.