## 2 Statistical Analyses of Individual Hazards
### Assessing the Stability of Landslide Dams  
A landslide dam's stability increases with the dam's volume or the ratio of the dam's width to its height. Obviously, the longer the dam is, with the higher hydraulic thrust, the lower the stability of the dam will be. Meanwhile, as the ratio of the reservoir capacity of the barrier lake to the dam's volume increases, the landslide dam's stability decreases [30]. [PERSON] et al. [14] proposed the blockage index (BI) to assess a dam's stability. The formulation of BI is expressed as follows:  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**Shape of**} & \multicolumn{6}{c}{**Landslide Materials**} \\ \cline{2-7}  & **Rock** & **Rock and Debris** & **Debris** & **Debris and Earth** & **Earth and Debris** & **Earth** \\ \hline V & 1 & 0.95 & 0.9 & 0.85 & 0.8 & 0.75 \\ \hline U & 0.9 & 0.85 & 0.8 & 0.75 & 0.7 & 0.65 \\ \hline \hline \end{tabular}
\end{table}
Table 1: Suggested values of \(A_{C}\).  
Figure 3: Critical conditions of river blockages caused by landslides.  
\[\text{BI}=\log_{10}\left(\frac{V_{D}}{S_{C}}\right) \tag{3}\]  
where \(V_{D}\) is the dam's volume (m\({}^{3}\)) and \(S_{C}\) is the catchment area (\(10^{6}\) m\({}^{2}\)). [PERSON] et al. [14] suggested that when BI \(>5\), the dam is stable; when \(4\leq\text{BI}\leq 5\), the stability is unsure; and when \(3<\text{BI}<4\), the dam is unstable.  
The dam volume is easily measured, and the catchment area is easily calculated. The BI is instructive for the rapid assessment of the stability of landslide dams, so it is widely used [13; 16; 31]. However, the accuracy of the BI is poor. Only 50.0% of the cases in the database could be assessed correctly (Table A2).  
[PERSON] [17] developed a rapid assessment model of the stability of landslide dams by collecting the geometric information and breach times of 110 landslide dams worldwide. The model consists of two parts [17], i.e., [PERSON]'s discriminant model \(Y_{A}\) and the logistics regression model \(Z_{B}\).  
\[Y_{A}=-8.935+2.453\log_{10}H_{d}-0.832\log_{10}V_{D}+0.4911\log_{10}V_{l}+0.4 71\log_{10}S_{C} \tag{4}\]  
\[Z_{B}=-8.542+3.704\log_{10}H_{d}-0.732\log_{10}V_{D}+0.801\log_{10}S_{C} \tag{5}\]  
where \(V_{l}\) is the reservoir capacity of the barrier lake (m\({}^{3}\)) and \(H_{d}\) is the dam's height (m).  
[PERSON]'s discriminant model considered the influences of the dam's height \(H_{d}\), the landslide dam's volume \(V_{D}\), the reservoir capacity of the barrier lake \(V_{l}\), and the catchment area \(S_{C}\) on the stability of landslide dams. The logistic regression model considered the influences of the dam's height \(H_{d}\), the landslide dam's volume \(V_{D}\), and the catchment area \(S_{C}\) on the stability of landslide dams. In [PERSON]'s discriminant model, if \(Y_{A}<0\), the landslide dam is stable; if \(Y_{A}>0\), the landslide dam is unstable. In the logistic regression model, if \(Z_{B}<0.5\), the landslide dam is stable; if \(Z_{B}>0.5\), the landslide dam is unstable.  
Dam materials originate from the landslide's materials, so they have almost the same material composition. Dams made up of earth or soft rock have a low shear strength and are prone to breaching, and dams made up of rock or debris are more stable [32]. Therefore, it is also necessary to consider the influence of the dam materials.