A simplified model for static/flowing dynamics in thin-layer flows of granular materials with yield

We introduce a simplified model for thin-layer flows of granular materials with yield. The model is based on a viscoplastic rheology with Drucker-Prager yield stress and describes the dynamics of the velocity profile as well as the transition between static and flowing material. As opposed to most models developed to describe the static/flowing transition in thin-layer flows, the variable Z in the direction normal to the topography is conserved in our model. To evaluate the respective role of yield and viscosity in this problem, we compare both the analytical solution for the inviscid case and the numerical solution for the viscous case (with a constant viscosity or the variable viscosity of the μ(I) rheology), with experimental data. Although the model does not describe variations in the flow direction, it is able to reproduce the essential features of experiments on granular flow over an inclined static layer of grains, including the stopping time and the erosion of the initial static bed, which is shown to be closely related to the viscosity.