## 2 Materials and Methods
### Case Study
#### 2.5.1 Taum Sauk Dam  
The study object is the upper reservoir of the Taum Sauk Pumped Storage Power Station in Reynolds County, Missouri State, United States. The project was completed in 1962 and put into operation in 1963. On 14 December 2005, the stage sensors of the upper reservoir failed to turn off the pumps employed to convey water from the lower reservoir during the overnight filling, resulting in the water overflowing the wall top of Upper Taum Sauk dam. When the dam breached, 5.30 million m\({}^{3}\) of water was released within 25 min and flowed into the Black River. After the dam break occurred, the US Geological Survey (USGS), the local natural resources department, and many flood research institutions conducted investigations on the accident and obtained detailed data on the dam break [54]. At the same time, the Oak Ridge Laboratory in the United States was developing a multi-architecture (multi-CPU and GPU) open-source two-dimensional flood model based on the source term full shallow water equation analysis (TRITON), and in this model, Taum Sauk is simulated as a typical case [39; 55]. The hydrograph in TRITON is from the USGS analysis of the event [56], in which the discharge is developed from a volume analysis of the reservoir and knowledge of the embankment failure. The location of Taum Sauk dam and the shape of the breach are shown in Figure 6.  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Basic Information** & **Taum Sauk Dam** & **Tangjiashan Landslide Dams** \\ \hline Location & \(90^{\circ}49^{\prime}6^{\prime\prime}\) E, \(37^{\circ}32^{\prime}8^{\prime\prime}\) N & \(104^{\circ}25^{\prime}57^{\prime\prime}\) E, \(31^{\circ}50^{\prime}40^{\prime\prime}\) N \\ \hline Volume (m\({}^{3}\)) & \(5.366\times 10^{6}\) & \(2.3\times 10^{7}\) \\ \hline Dam crest elevation (m) & 487.38 & 742.5 \\ \hline Dam bottom elevation (m) & 455.37 & 639.5 \\ \hline Dam height (m) & 32.01 & 103 \\ \hline Dam crest width (m) & 3.7 & 300 \\ \hline Dam breach bottom elevation (m) & 456 & 717.5 \\ \hline Final breach depth (m) & 31.38 & 25 \\ \hline Upstream slope ratio (vertical/horizontal) & 1:1.3 & 1:1.5 \\ \hline Downstream slope ratio (vertical/horizontal) & 1:1.3 & 1:1.5 \\ \hline Initial breach width (m) & 10 & 8 \\ \hline Initial breach depth (m) & 2 & 13 \\ \hline Average particle size (m) & 0.01 & 0.03 \\ \hline Porosity \(e\) & 0.46 & 0.4 \\ \hline Average density of dam material (kg/m\({}^{3}\)) & \(2.65\times 10^{3}\) & \(2.6\times 10^{3}\) \\ \hline Internal friction angle (\({}^{\circ}\)) & 38 & 45 \\ \hline Cohesive force (kPa) & 20 & 60 \\ \hline Erosion parameter & a = 1.0, b = 0.0005 & a = 1.1, b = 0.0007 \\ \hline \hline \end{tabular}
\end{table}
Table 2: Information of the Taum Sauk and the Tangjiashan landslide dams.  
The terrain for this study is a 9.36 m USGS DEM covering the 62 km\({}^{2}\) extent of the flood event with 708,864 model grid cells (624 \(\times\) 1136). The instability area of the dam is selected, and the initial position of the breach is determined. The initial breach is 10 m wide and 2 m deep in the middle of the dam, and the final breach width is 274 m. The profile of the dam is shown in Figure 7.  
Figure 6: The Taum Sauk dam location and the shape of the breach: (**a**) breach frontal view; (**b**) breach top view; (**c**) dam location; (**d**) study area remote sensing image.  
Figure 7: The diagram of the dam profile and initial breach: (**a**) side view; (**b**) top view.