## 4 Results  
### Results of Physical Model Test  
The experiment results, as revealed in Figure 4, showed that the holding force of the emergency gate has three typical curves in the closing process:  
(1) The holding force gradually decreased with the decrease in opening rate \(e\) (opening rate \(e\) equals opening height dividing spillway tunnel height) and the maximum appeared under the opening rate \(e\) = 1.0 in Figure 4a. When the emergency gate approached full closure, the holding force suddenly dropped to zero. The flow behind the emergency gate was always full flow in the closing process. The flow pattern was relatively stable and the hydrodynamic loads acting on the gate body altered little. (2) The holding force decreased slowly with a decrease in the opening rate, and decreased with drastic fluctuation before the gate was completely closed. The maximum holding force still appeared at the opening rate \(e\) = 1.0 (Figure 4b). With the upstream water depth increased, the panel thrust increased and friction force increased, making the holding force decrease the large opening rate. In terms of the small opening rate, nevertheless, the fluctuation intensity of the holding force increased gradually. (3) With the opening rate decreased, the holding force decreased slowly at first, then reached the peak, and finally decreased to zero (Figure 4c). The peak was larger than the initial stage and it was the maximum holding force for the low water head. For the high water head, however, the maximum holding force still appeared at the initial stage. As depicted in Figure 4d, the variation in the holding force was consistent with that in Figure 4c. The reason for the situation was the lift force at the gate bottom. The lift force was related to the flow pattern behind the emergency gate. When the service gate was at a large opening rate and upstream water depth was low, the flow pattern would change from full-flow to open-flow and the lift force decreased rapidly. The decreased lift force was larger than the increased friction force, making the holding force peak significantly. While the service gate had a large opening rate and upstream water depth was high, nevertheless, the holding force was influenced by many factors and its regularity became worse. Thus, it is necessary to adopt the numerical simulation to study the characteristics of hydrodynamic loads in the closing process. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Minimum Grid Size of Gate Boundary** & **Force (kN)** & **Relative Error (\%)** \\ \hline M1 (80 mm) & 38,473.53 & 0.48 \\ M2 (60 mm) & 38,274.68 & \(-\)0.04 \\ M3 (40 mm) & 38,435.01 & 0.38 \\ \hline \hline \end{tabular}  
The hinge forces of the service gate were obtained under the service gate height of 1.0 m and 4.0 m, as shown in Table 3. Compared to the experiment results, it can be used to validate the reliability of the simulation results. It can be seen from Table 3 that the maximum relative error between the simulation and the experiment was less than 7.08%, which indicates that the simulation results were reliable and can meet the requirements of engineering precision.  
\end{table} 
Table 2: Mesh dependence check. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Upstream** & \multicolumn{3}{c}{**Service Gate Height 1.0 m**} & \multicolumn{3}{c}{**Service Gate Height 4.0 m**} \\ \cline{2-7}
**Water Depth** & **Experiment** & **Simulation** & **Relative Error/\%** & **Experiment** & **Simulation** & **Relative Error/\%** \\ \hline
49 m & 18,335.80 & 18,549.44 & \(-\)1.16 & 6216.14 & 6194.58 & 0.34 \\
65 m & 24,128.58 & 24,847.90 & \(-\)2.98 & 8794.52 & 8745.52 & 0.56 \\
85 m & 30,601.46 & 31,946.04 & \(-\)4.39 & 11,048.52 & 11,336.64 & \(-\)2.60 \\
100 m & 38,288.60 & 39,619.44 & \(-\)3.47 & 14,732.36 & 13,659.24 & 7.08 \\ \hline \hline \end{tabular}  
\end{table} 
Table 3: Simulation validation with experiment results. Unit: kN.