Modeling Two‐Phase Debris Flows With Grain‐Fluid Separation Over Rugged Topography: Application to the 2009 Hsiaolin Event, Taiwan

Abstract

Landslides or debris flows usually arise in mountainous areas and slide over a rough topography. As the flow body is typically a mixture of particles and interstitial fluid, this paper aims at developing a binary mixture model and its numerical implementation for shallow debris flows on rugged topography. The mathematical formulation of this saturated solid‐fluid mixture is developed with respect to a terrain‐fitted coordinate system. Employing the thin layer assumption, a system of depth‐integrated equations is derived, where the interstitial fluid is supposed to be a viscous Newtonian fluid and the granular material is treated as a frictional Coulomb‐like continuum. At the basal surface, the Coulomb sliding condition for the granular constituent and Navier slip for the fluid phase are applied. The interaction between granular material and interstitial fluid is depicted by the buoyancy and a drag force induced by the velocity difference of both the phases. Numerical investigations are performed for studying the features of the proposed model, where a shock‐capturing nonoscillatory scheme is employed. A thorough parameter study of flows over three idealized terrain geometries illustrates the distinct impacts of the applied material parameters on the flow dynamics and deposit shapes. The phase separation such as the solid‐phase‐dominated flow front and how this changes with parameter values are presented. The simulation of the Hsiaolin landslide successfully retraces the approximate flow path recognized in satellite images as well as the measured deposition given in Kuo et al. (2011, https://doi.org/10.1029/2010JF001921).