A Model for Granular Flows over an Erodible Surface

Source abstract

Geophysical mass flows, such as debris flows, volcanic avalanches, and landslides, can be initiated consequent to volcanic activities. These flows can be tens of meters in depth and hundreds of meters in length and contain $O(10^6$–$10^8)\,\mathrm{m}^3$ or more of material. The bulk flow can easily erode the volcanic rocks and soil on the slopes of mountains, thereby increasing their size several fold. The range of scales and the rheology of these flows, especially with erosion, present significant modeling and computational challenges. This paper describes an approach to incorporate the interaction between a mass flow, an erodible bed, and the topography of that bed. The kinetic theory for rapid granular flow is employed to model a “mixing” layer, the interface between the flowing material and the basal surface and the area where erosion occurs. A tractable set of equations is derived, a hyperbolic system that describes the motion of a granular flow and the elevation of erodible bed.