# Research on the Safety Assessment of Corbel Beams of Reservoir Radial Gates Based on Real States
## 3 Finite Element Simulation and Safety Review of the Corbel Beam of the Radial Gate
### Analysis of Calculation Results and Safety Review
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**b (mm)** & **B (mm)** & **The Standard Value of Concrete Tensile Strength \(f_{kk}\) (N/mm\({}^{2}\))** & **Eccentric Distance of Thrust to Gate Pier Thickness Centerline \(e_{0}\) (mm)** \\ \hline
800 & 1000 & 2.01 & 950 \\  & \(\frac{0.55f_{k}B}{2}\) & & Model 2 Equivalent standard value \(F_{k}\) (KN) & Security judgment result \\  & 769.04 & & 679.53 & Normal \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Crack control test results in the local tension area of the gate pier (method (1)). Figure 11: Detail of the maximum tensile stress of the corbel beam and gate pier of the joint force structure model. subjected to the center point of the support strut thrust was calculated, and then the shear force was calculated by integration, as shown in Table 5.  
Then the shear force is brought into Equation (4) for calculation, and the calculation process and results are shown in Table 6.  
Finally, considering the site inspection data, the stress analysis of finite element simulation, and the results of the review calculation, the surface of the corbel beam structure of this reservoir is intact, no corrosion of reinforcement has occurred, no cracks are found in the stress concentration area, and the results of review calculation are in accordance with the specification, so it can be judged that the corbel beam structure of this reservoir has good engineering quality and operates normally, and there is no need to carry out danger removal and reinforcement. Method (2) requires experimental analysis of the concrete performance of the corbel beam structure, finite element simulation to be carried out based on the experimental data, the stress distribution to be analyzed under the real state, and then the review calculation to be carried out. The process is more complicated, but the real working state of the corbel beam structure can be accurately evaluated, and then the targeted danger removal and reinforcement can be carried out, which is suitable for the safety assessment of large and medium-scale reservoirs with a complex stress state. The current calculation method for the corbel beam safety review is to disconnect the corbel beam from the middle and treat it as a corbel for review calculation. Therefore, the calculation results of the current method are compared with the two methods proposed in this paper, as shown in Figure 12: \begin{table}
\begin{tabular}{c c c c} \hline \hline
**b (mm)** & **B (mm)** & **The Standard Value of Concrete Tensile Strength \(f_{kk}\) (N/mm\({}^{2}\))** & **The Eccentricity of Thrust to Gate Pier Thickness Centerline \(\epsilon_{0}\) (mm)** \\ \hline
800 & 1000 & 2.01 & 950 \\  & \(\frac{0.55f_{abB}}{\frac{3}{2}+0.20}\) & & Model 4 standard value \(F_{k}\) (kN) & Security judgment result \\  & 769.04 & & 526.91 & Normal \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Crack control test results in the local tension area of the gate pier (method (2)). Figure 12: Comparison of the results of different calculation methods. Figure 12 illustrates that method (1) yields a calculation result 32% lower than that of the current method, while method (2) yields a result 47% lower than that of the current method. Furthermore, the current method exceeds the safety limit. This discrepancy demonstrates that the combined force structure of the corbel beam and gate pier possesses significantly higher load-bearing capacity than the corbel's cantilever structure. If the calculation is performed using the current method, it may lead to a misjudgment that the project fails to meet the safety assessment specifications, which will affect the danger removal and reinforcement. The safety inspection information shows that this reservoir sand discharge vent has good appearance quality after more than 40 years of operation, no cracks or concrete breakage are evident, and the strength meets the requirements.