Assessing entrainment of bed material in a debris-flow event: A theoretical approach incorporating Monte Carlo method

Entrainment of underlying bed sediment by a debris flow can significantly increase the debris-flow magnitude. To study this phenomenon, a theoretical approach to assessing bed-sediment entrainment is presented. The approach is based on a static approximation that bed-sediment entrainment occurs when the shearing stress of the flow is sufficiently high to overcome the basal resistance of the bed sediment. In order to delineate erodible zones in a channel, we analyze the critical condition of this static equilibrium model, and subsequently propose a new concept of a critical line to detect the entrainment reaches in a channel. Considering the spatial and temporal uncertainties of the input parameter, the approach is further incorporated within a Monte Carlo method, and the distribution of entrainment zones and post-entrainment volumes can be analyzed. This approach is illustrated by back-analysis of the 2010 Yohutagawa debris-flow event, Japan. Results from 10 000 trials of Monte Carlo simulation are compared with the in situ surveys. It is shown that the present approach can be satisfactorily used to delineate erodible zones and estimate possible entrainment volume of the event. Discussion regarding the sensitivities and limitations of the approach concludes the paper.