Full two-dimensional rapid chute flows of simple viscoplastic granular materials with a pressure-dependent dynamic slip-velocity and their numerical simulations

Abstract

We present a fully two-dimensional, novel Coulomb-viscoplastic sliding model, which includes some basic features and observed phenomena in dense granular flows like the exhibition of a yield strength and a non-zero slip velocity. The interaction of the flow with the solid boundary is modelled by a pressure and rate-dependent Coulomb-viscoplastic sliding law. The bottom boundary velocity is required for a fully two-dimensional model, whereas in classical, depth-averaged models its explicit knowledge is not needed. It is observed in experiments and in the field that in rapid flow of frictional granular material down the slopes even the lowest particle layer in contact with the bottom boundary moves with a non-zero and non-trivial velocity. Therefore, the no-slip boundary condition, which is generally accepted for simulations of ideal fluid, e.g., water, is not applicable to granular flows. The numerical treatment of the Coulomb-viscoplastic sliding model requires the set up of a novel pressure equation, which defines the pressure independent of the bottom boundary velocities. These are dynamically and automatically defined by our Coulomb-viscoplastic sliding law for a given pressure. A simple viscoplastic granular flow down an inclined channel subject to slip or no-slip at the bottom boundary is studied numerically with the marker-and-cell method. The simulation results demonstrate the substantial influence of the chosen boundary condition. The Coulomb-viscoplastic sliding law reveals completely different flow dynamics and flow depth variations of the field quantities, mainly the velocity and full dynamic pressure, and also other derived quantities, such as the bottom shear-stress, and the mean shear-rate, compared to the commonly used no-slip boundary condition. We show that for Coulomb-viscoplastic sliding law observable shearing mainly takes place close to the sliding surface in agreement with observations but in contrast to the no-slip boundary condition.