Mass conservation equations for a debris]flow body and for bed sediment, in addition to an equation of motion, constitute the governing equations for debris flow. The erosion rate equation is generally added to close the governing equation system. However, it is impossible to conduct numerical simulations with just the governing equation system, because points that are highly unsteady locally and are not assumed in the process of developing the existing erosion rate equation occur in numerical simulation. Analysis of the existing erosion rate equation clarifies that there is a high possibility of occurrence of abnormal values at the front of debris flow because the deposition volume calculated using the existing erosion rate equation becomes larger than the existing volume. Therefore, a processing method for the erosion rate equation is necessary. Use of a method that only modifies abnormal values to normal values results in problems related to the conservation law, such as an increase in flow volume or sediment volume. Thus, two methods were examined in this study. One method entails limiting the erosion rate so as to avoid introducing abnormal values and the other entails adjusting the riverbed level corresponding to the extent of modification of abnormal values to normal values. These two methods were evaluated by numerical simulations performed at the transition point of the riverbed gradient. The simulation results clarified that the method of limiting the erosion rate did not obey the conservation law in the case of a large time step value. In comparison, the method of adjusting the riverbed level was able to obey the conservation law almost completely. Moreover, the minimum concentration and equilibrium concentration, taken as target modification values of the sediment concentration, were examined by the numerical simulation. Then, the simulation results indicated that numerical oscillation occurred with the minimum concentration but not with the equilibrium concentration. Therefore, the method of adjusting the riverbed level using the equilibrium concentration as the target modification value was the most effective method under the calculation conditions considered in this study.

Key wordsFdebris flow, numerical simulation, erosion rate equation, processing method