# Characteristics of Plane Gate Vibration and Holding Force in Closing Process by Experiments
## 3 Results and Discussion
### Characteristics of Holding Force
#### 3.2.3 Crawl Vibration in Closing Process  
In the closing process, the length of steel cable, water weight in gate lattice and water column on the gate top increase gradually. These changes directly reflect the increase of length \(L\) and mass \(m\) in Equation (3), which makes the nature frequency of the simplified system decrease. Besides, the flow boundary deformation and unsteady flow under the gate result in the variation of fluid inertia and make flow pulsation pressure acting on the gate bottom edge intensify significantly. [PERSON] et al. [23] studied that the seismic waves had influenced on the maximum hydrodynamic pressure in curved gate. The results indicate that maximum hydrodynamic pressure of gate panel, considering the fluid-solid coupling effect, was 4-5 times higher than the theoretical value by the additional mass method. Thus, strong fluid-solid coupling effect could increase the hydrodynamic loads and crawl vibration appears in small gate opening. [PERSON] et al. [32] regarded that the difference of dynamic and static friction coefficient was the main factor for crawl vibration. The necessary condition for the vibration is given as follows: \(\Delta\mu\times P/(v\times\sqrt{mk})>1\) (where \(\Delta\mu\) is the difference of dynamic and static friction coefficient, \(P\) is the horizontal panel thrust, \(v\) is the closing gate speed, \(m\) is the gate mass and \(k\) is the transmission rod stiffness). Table 3 provides the time parameters about the crawl vibration in the physical model test. With the upstream water depth increase, the gate-closing time decreases and duration of crawl vibration increases gradually. We regard that crawl vibration should be related to the upstream water depth and happen at specific external loads. When the gate structure and upstream water depth are determined, the horizontal panel thrust can be viewed as a control index for the crawl vibration. From the results in [32], horizontal panel thrust also played an important role in the crawl vibration. Once panel thrust exceeds the critical threshold, crawl vibration will appear. As upstream water depth increases, the time for panel thrust reaching the threshold decreases gradually so that initial crawl time decreases, as shown in Table 3.  
After the gate intermittent motion, the gate stopped moving at a certain distance from the chamber floor. The higher is the upstream water depth, the larger is the distance. The gate is not fully closed and the failure of gate-closing appears, which seriously threatens the operation of the projects. The failure has also happened in other physical model tests and engineering practices [33; 34]. Because steel cable cannot provide the vertical downward loads, the gate can only utilize the self-weight, additional weight, water column on the gate top and water weight in the gate girder to close. Especially for the heavily sediment-carrying river, the sediment deposited in the gate slots exacerbates the above \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Upstream Water** & **16 m** & **18 m** & **20 m** & **23 m** \\ \hline Gate closed time & 115.3 & 107.6 & 100.3 & 95.78 \\ Initial crawl time & 95.05 & 87.13 & 73.78 & 69.81 \\ Duration of crawl vibration & 20.25 & 20.47 & 26.52 & 25.96 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: The time parameters about the gate crawl vibration. Unit: s.  
phenomenon [33]. [PERSON] et al. [31] and [PERSON] et al. [35] both suggested increasing gate speed can improve gate stability, avoid or delay the crawl vibration to a certain extent, which was good for the gate-closing. To solve the above problem, increasing vertical downward loads by modified gate shape or additional mass is a common technical method. [PERSON] et al. [34] proposed the method shown in Figure 10a. Placing a protruding boundary in front of the gate bottom edge and making full use of the water column could increase the vertical downward loads. Figure 10b provides the holding force for three body shapes in the physical model test.