Development of Modified Particles Method for Simulation of Debris Flow Using Constitutive Equations

We propose a numerical simulation method for calculating the vertical distributions of the flow velocity and the sediment concentration in debris flows. Our method is based on the moving particle semi-implicit (MPS) method. We introduce the constitutive equations of Egashira et al. to the MPS method. Numerical simulations of the debris flow are performed by using an existing model based on a shallow water equation, along with our model based on the MPS method. In the condition where the riverbed gradient becomes less steep, there is good agreement with experimental results, including those involving the formation of a convex upward deposition shape in the initial deposition process. Results for the initial deposition process are not produced with existing simulation method based on a shallow water equation. Further, our model can yield clear results when the upper and lower layers have different flow directions in a numerical simulation of the collapse of a natural dam by overtopping.