## 4 Application
### Risk Assessment  
The first step was to calculate LBRI to assess the degree of river blockage. According to Table 1, \(A_{C}=0.8\). Using Equation (2), LBRI was found to be 5.027, thus the river was blocked completely and a landslide dam formed. The Baige landslide was formed by gravitational deformation of several slopes during erosion of the river [43]. Equations (7)-(11) and (13) were used to predict the geometries of the landslide dam. The calculated and actual geometries are compared in Table 7.  
The calculated values were in good agreement with the actual values. According to Table 2, \(M=0.6\). Using Equation (6), LDSI was found to be 4.78, so the landslide dam was unstable. \begin{table}
\begin{tabular}{c c c c} \hline
**Parameter** & **Value** & **Parameter** & **Value** \\ \hline Width of the valley \(W_{V}\) (m) & 150 & Reservoir capacity of the barrier lake \(V_{I}\) (10\({}^{8}\) m\({}^{3}\)) & 2.9 \\ \hline Width of the dam \(W_{d}\) (m) & 1200 & Average steepness of the landslide slope \(\varphi\) (\({}^{\circ}\)) & 33 \\ \hline Depth of the river \(h\) (m) & 10 & Upstream riverbed slope \(i_{u}\) & 0.00135 \\ \hline Height of the dam \(H_{d}\) (m) & 61 & Volume of the dam \(V_{D}\) (10\({}^{6}\) m\({}^{3}\)) & 10 \\ \hline Length of the dam \(L_{d}\) (m) & 470 & Shape of the valley & V \\ \hline Materials & Earth and debris & Volume of the landslide (10\({}^{6}\) m\({}^{3}\)) & 27.95 \\ \hline \end{tabular}
\end{table} 
Table 6: Measured parameters of the river channel and the landslide dam. \begin{table}
\begin{tabular}{c c c c c c} \hline  & \(H_{d}\) **(m)** & \(W_{d}\) **(m)** & \(L_{d}\) **(m)** & \(V_{D}\) **(10\({}^{6}\) m\({}^{3}\))** & \(V_{I}\) (10\({}^{8}\) m\({}^{3}\))** & \(S_{C}\) **(10\({}^{6}\) m\({}^{2}\))** \\ \hline Actual values & 61 & 1200 & 470 & 10 & 2.9 & — \\ \hline Calculated values & 67.21 & 1004.63 & 494.66 & 10.24 & 2.76 & 12.31 \\ \hline \end{tabular}
\end{table} 
Table 7: Calculated and actual geometries of the Baige landslide dam. Figure 8: Overhead view of the Baige landslide and the landslide dam (photo credit: Yangtze River Water Resources Commission). The Baige landslide dam breached on 13 October 2018 (Figure 9). Because the value of \(H_{d}\) was 67.21 m, \(Q_{p}\) was calculated to be 10,786.35 m\({}^{3}\)/s, which is close to the actual value of 10,000 m\({}^{3}\)/s. Yebatan hydropower station and Lawa hydropower station recorded comparatively detailed information, except for the maximum average flow velocity during the flood period [38; 43]. The information recorded by the two hydropower stations and the results calculated using Equations (19) and (21)-(23) are listed in Table 8.  
Yebatan hydropower station is a national facility. Nearby, there are two counties: Gongjue County and Baiyu County. The total population of the two counties is 110,000, and the GDP per capita is CNY 26361. Lawa hydropower station is also a national facility. Nearby, there are two counties: Kangmang County and Batang County. The total population of the two counties is 130,000, and the GDP per capita is CNY 35,613. According to Tables 4 and 5 and Equations (20) and (24), the values of the vulnerability factors and the risk level for the two hydropower stations were calculated and are listed in Table 9.  
In fact, only a local bank slope collapse occurred at the Yebatan hydropower station during the flood period and fortunately did not cause casualties. For the Lawa hydropower station, there was almost no impact. The calculated results were in line with the actual situation.