Numerical simulation of debris-flow behavior incorporating a dynamic method for estimating the entrainment

• A 2-D numerical model of debris-flow behavior over complex topography is developed.
• A method for estimating sediment entrainment is proposed and incorporated into the model.
• The dam-breaking problem with analytical solution is used to verify the stability of the model.
• The described model is applied to simulate the 2010 Yohutagawa debris-flow event in Japan.

There is a pressing need to estimate debris-flow entrainment because several lines of studies have substantiated that the magnitude of a debris flow may grow manyfold due to sediment entrainment. In this paper, we present a two-dimensional numerical model of debris-flow behavior for estimating entrainment over complex topography. The model is governed by a numerical integration of the depth-average motion equations using shallow water approximation. The governing equations are numerically solved using the semi-Lagrangian method in an explicit finite difference grid. Compared to previous models, the presented model highlights the importance of entrainment, and incorporates a physically-based dynamic method to estimate the entrainment rate. The entrainment rate can be predicted using reasonable assumptions regarding the velocity profile of the debris flow and the rapidly changing pore pressure of the bed sediment. The stability of the presented model is first illustrated by a hypothesized dam-breaking problem; the effectiveness of the implemented model entrainment process is subsequently tested on the 2010 Yohutagawa debris-flow event in Japan. The test indicates that the presented method can be satisfactorily used to simulate debris-flow behavior and the entrainment process. A discussion regarding the advantages and limitations of the model concludes the paper.