Depth-resolved model for debris flows based on a two-phase fluid

Debris flows are prevalent natural hazards in mountainous regions, posing threats to human safety and resulting in property damage. Recent research has focused increased attention on characterizing the dynamic properties of these flows, especially in the vertical direction. The present study puts forth a mathematical model to describe the physics of debris flows. Specifically, concentration-weighted averaging is employed to represent the mass and momentum balance equations of the bulk granular-fluid mixture. Furthermore, an evolution equation for the slip velocity between the granular solid and liquid phases is derived in order to capture the separation between these constituents. The model determines the particle pressure based on frictional-collisional relations and the fluid stress via a Herschel-Bulkley rheological formulation. The coupled differential equations are solved numerically using a two-step finite difference projection method. The free surface profile is tracked using a volume of fluid approach. Favorable comparisons with experimental measurements validate the numerical model. Finally, analyses provide insight into the influence of the slip velocity on the dynamics of granular-liquid flows.