Probability distribution of measured debris-flow velocity in Jiangjia Gully, Yunnan Province, China

Abstract

Debris flow moves in the form of surge waves and consists of dozens or even hundreds of surges that are separated in time and space and have a variety of appearances, as exemplified in Jiangjia Gully, China. Observations there indicate that the deposit is made up by superposition of successive surges and deposit of a single surge is in effect a "frozen" surge. Then the study of debris flow is reduced to the study of surge sequence, which leads to a probabilistic picture of debris flow. This study attempts to find the probability distribution of velocity of surge using a huge data set of Jiangjia Gully. Statistics of the data shows that the velocity satisfies the Weibull distribution, which is believed to be universally valid because the distribution parameters vary little between events, with the shape parameter being well related to the average of velocity. It follows that the same distribution applies also to other quantities of debris flow, such as the flow depth and the discharge. Therefore, the distribution can be used to assess the magnitude and overflow range of a potential debris flow, as well as to the parameter calculation for engineering design.