Abstract
A depth-integrated theory is derived for the gravity-driven two-phase debris flows over complex shallow topography. The mixture theory is adopted to describe the mass and momentum conservation of each phase. The model employs the Mohr-Coulomb plasticity for the solid rheology, and assumes the Newtonian fluid for the fluid phase. The interactive forces assumed here consist of viscous drag force linear to velocity difference between the both phases, and buoyancy force. The well-established governing equations are built in 3D topography; as a result, they are expressed in the curvilinear coordinate system. Considering the characteristics of flows, a shallow layer assumption is made to simplify the depth-integrated equations. The final resulting equations are solved numerically by a high-resolution TVD scheme. The dynamic behaviors of the mixture are investigated. Numerical results indicate that the model can adequately describe the flows of dry granular material, the pure water and general two-phase debris flows.
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