Numerical simulation of debris flow over erodible bed

The erosion rate equation is usually used to close a system of the governing equations for debris flow. The shear stress formula in the equation of motion, which is derived based on the uniform flow condition, has two terms: the Coulomb shear stress and the dynamic shear stress. The sediment concentration is determined so that the Coulomb shear stress accords with an external shear stress on the theoretical bed. It is found that numerical and unreasonable disturbances take place because of the dependency of the dynamic shear stress on the Coulomb shear stress, when this system of the equations is applied to an unsteady debris flow. In order to solve these problems, we derived a new expression for the dynamic shear stress, which does not depend on the Coulomb shear stress. Numerical simulation of debris flow for erosion and deposition processes is conducted. An illustration of the calculated results indicates that the dynamic behavior of a debris flow can be clearly explained by the proposed method.