Flow pattern of fast granular flow impacting a granular deposit

There are intricate and intriguing flow structures in interaction between fast granular flow and an existing deposit, significantly affecting the development of granular avalanches. This study examines the dynamic interaction for six different steep terrains using the depth-integrated Savage-Hutter model. Results reveal three distinct flow patterns, which are the propagating shock mode, stationary shock mode, and runup mode. In the propagating shock mode, a stable bow shock formed by the fast flow impacting propagates upstream. The stationary shock mode forms a nearly flat, stationary shock upon impact. A new normal shock relationship for granular flow is developed by considering the effect of earth pressure, which can be reduced to classical shock relationship for both stationary and propagating shocks on highly inclined slopes, and agrees well with the numerical predictions. However, on low-degree slopes, the predictions accord with the modified shock relationship accounting for different types of earth pressure.