Annual risk assessment on high-frequency debris-flow fans

An empirical model of debris-flow risk assessment is developed to estimate annual loss ratio on high-frequency debris-flow fans where more than one hazard events occur every year. Based on observations of debris flows in Jiangjia Ravine, Yunnan Province, China, it is found that Gamma distribution is more appropriate for describing the annual frequency than the exponential distribution, which is supposed to be a good description of the low-frequency cases. Further analyses reveal that the two parameters of Gamma distribution can be explained, respectively, as the number of factors which dominate debris-flow occurrence and one-third of the mean annual frequency. Given the expectation of loss ratio is unchanged for each event we deduced a simple relationship between the expectations of one-event and annual loss ratios. Combined with the Gamma model, an equation is proposed to calculate the expectation of the annual loss ratio, which can be also used to assess the potential risk of fans formed by high-frequency debris flows.