Abstract
The immense destructive impact induced by debris flow in mountainous region endangers human lives and infrastructure facilities. The previous studies have indicated that the fatalities in a debris-flow event depend on the volume of debris flow, which may be conspicuously amplified by entraining bed-sediment along the trajectory as it descending the slope. Several lines of evidence by the previous studies have also highlighted this viewpoint that debris flow can grow dramatically in magnitude as accompanying by the entrainment. In this paper, we present an elementary model to estimate the dynamic entrainment rate of bed-sediment when overridden by debris flow. Following the preliminary studies done by Iverson (2012) and Medina et al. (2008), a temporal entrainment rate can be computed basing on the momentum conservation of the two-layer system. To represent the influence of the pore water pressure on the entrainment rate, we employ two parameters λ1 and λ2 into the model, which denote the saturate degree of debris flow and bed-sediment, respectively. Our approach demonstrates that if flow layer and bed layer shares the same friction angle, the condition λ2>λ1 should be satisfied to provoke the entrainment. The performance of the approach is prior tested on a simple scenario with the parameters of typical value, and then a debris-flow event that occurred in 2010 at the Yohutagawa torrent, Japan. The computed entrainment rate and accumulated depth show a good agreement with the in-situ surveys. Another advantage of our approach rests on the fact that entrainment rate is written in a differential form, thus it can be easily incorporated to the mass constitutive equation of the numerical model using a shallow water approximation.
