A Pareto–Poisson process model for intermittent debris flow surges developing from slope failures

Abstract

Many debris flows originate from shallow slope failures over the source area of valley and move in form of successive surges. In order to understand the behavior of such failures, we conducted seven sets of experiments of rainfall-induced soil failures in a 4 × 8 m spot on a slope under different rainfall intensities ranging from 12 to 60 mm/h, according to the local rainfall conditions in the valley of Jiangjia Gully, and this work is based on the experimental data. It is found that the failures are realization of a Poisson process with failure volume satisfying the Pareto distribution, thus the failure process can be simulated using a combinative Pareto-Poisson process (PPP) model. The PPP model incorporates a Poisson process determining the failure time, and a Pareto distribution characterizing the fluctuation of failure volume. The developing course of a debris flow surge is reduced to the hierarchic evolution of the failures from their source to the mainstream, which amounts to a cascade thinning process of the Poisson sequence in the PPP model framework. Given the controlling parameters (i.e., the Poisson intensity, Pareto distribution parameters, and thinning ratio), the model is capable of predicting surge sequences that agree well with the monitored surges in terms of time interval, magnitude fluctuation, and probability distribution. This study represents the first attempt to formulate a stochastic framework for debris flows developing from source to mainstream, which applies to debris flows fed by discontinuous material supplies from shallow slope failures.