Depth-averaged analytic solutions for free-surface granular flows impacting rigid walls down inclines

In the present paper, flows of granular materials impacting wall-like obstacles down inclines are described by depth-averaged analytic solutions. Particular attention is paid to extending the existing depth-averaged equations initially developed for frictionless and incompressible fluids down a horizontal plane. The effects of the gravitational acceleration along the slope, and of the retarding acceleration caused by friction as well, are systematically taken into account. The analytic solutions are then used to revisit existing data on rigid walls impacted by granular flows. This approach allows establishing a complete phase diagram for granular flow-wall interaction.