Two-dimensional mathematical model of debris flow

Debris flow is the gravity flow of water, clay, granular and rock mixtures and often triggered by torrential rains in mountainous areas. It is a catastrophic disaster that consists of grain-fluid mixtures and moves rapidly across three-dimensional terrain. Most debris flows move downslope as fluids. To predict the runout distance and extent of the hazard area of rainfall-induced debris flows, we proposed a depth-averaged two-dimensional mathematical model, in which the debris and water mixture is assumed to be uniform continuous, incompressible, unsteady Newtonian turbulence fluid. Based on mass balance equation and Navier-Stokes equations, the mathematical model is derived using the method of depth-integrated equations. The finite difference method is necessary to solve the all equations. Based on GIS, the two-dimensional mathematical model of debris flow can be used to estimate the flow range, the potentially dangerous homes and roads for hazard and risk analysis.