A Simplex Multi-Phase Approach for Modelling Debris Flows in Smoothed-Terrain-Following Coordinate System

Herewith we present a multi-phase model for debris flows, of which the flow body is supposed to be composed of water, fine sediment (clay/silt) and grains. The rheology of debris flows varies due to the dynamical variation of the composition concentrations. In the present study the component of silt/clay is an individual phase, and its concentration plays a key role in determining the rheology of the interstitial fluid. Hence, there are three phases in the mixture, the grain phase, the clay phase and the water phase from the viewpoint of mass conservation. Only the grain phase and fluid phase are considered in the momentum conservation, since the clay is suspended in the fluid and the relative motion is negligible within the interstitial fluid. The grain constituent is treated as a frictional Coulomb-like continuum, and the viscosity of the interstitial depends on the clay concentration. The resultant models are given in a smoothed-terrain-following coordinate system, a compromise between the constraint of shallow curvature for the terrain-fitting coordinate system and retaining the high resolution of the topography. The numerical implementation is developed with the CUDA-library for GPU-high-performance computations. The feasibility and applicability will be presented by back calculation of a historical event.