# Dynamic Damage Mechanism and Seismic Fragility Analysis of an Aqueduct Structure
## 4 Conclusions  
The dynamic damage mechanism and damage development law of an aqueduct under the impact of a rare earthquake are investigated in this research and the weak spots of the aqueduct structure where concrete cracking may occur. Seventeen seismic waves are selected based on the factors such as magnitude, shear wave velocity, epicentral distance, and site type. We use the IDA and MSA methods to analyze the seismic fragility of the aqueduct, respectively, with \(S_{a}(T_{1},5\%)\) as the IM and the pier shaft top offset ratio under structural response to quantify the index limit, which mutually verifies the rationality of the fragility results and studies the probability of damage to the structure under different IM. The aqueduct selected in this paper is universal in the SNWDP. However, the aqueduct is located in an earthquake-prone area. The research results apply to the aqueduct, bridges, and other structures similar to the structural model and conditions in this paper. The following are the main conclusions:  
* Penetrating damage is most likely to occur on both sides of the pier cap and around the pier shaft in the event of a rare earthquake, followed by the top of the aqueduct  
Figure 13: Comparison of IDA and MSA. \begin{table}
\begin{tabular}{c c c c c c c c c c c c} \hline \hline
**Limit** & \multirow{2}{*}{**IM**} & **0.00** & **0.05** & **0.08** & **0.10** & **0.15** & **0.17** & **0.20** & **0.23** & **0.30** & **0.40** & **0.50** \\
**States** & & **5 g** & **5 g** & **8 g** & **5 g** & **5 g** & **2 g** & **5 g** & **0 g** & **5 g** & **5 g** \\ \hline \multirow{2}{*}{LS1} & IDA & 0 & 10.49 & 46.88 & 64.18 & 86.99 & 91.20 & 94.98 & 96.77 & 99.40 & 99.99 & 100 \\  & MSA & 0 & 11.82 & 34.38 & 48.76 & 70.52 & 76.21 & 84.24 & 88.41 & 95.21 & 98.37 & 99.42 \\  & IDA & 0 & 0 & 2.36 & 6.15 & 28.51 & 37.92 & 53.38 & 62.50 & 81.36 & 93.77 & 97.10 \\  & MSA & 0 & 0.94 & 5.92 & 11.76 & 27.02 & 33.07 & 44.29 & 51.96 & 69.92 & 84.07 & 91.68 \\  & IDA & 0 & 0 & 0 & 0.24 & 3.25 & 5.65 & 12.59 & 19.55 & 41.35 & 64.89 & 78.50 \\  & MSA & 0 & 0 & 0 & 1.52 & 5.63 & 7.92 & 13.27 & 17.91 & 32.93 & 51.51 & 66.55 \\  & IDA & 0 & 0 & 0 & 0 & 0.19 & 0.36 & 0.98 & 1.77 & 6.18 & 16.53 & 29.76 \\  & MSA & 0 & 0 & 0 & 0 & 0.43 & 0.72 & 1.43 & 2.23 & 5.89 & 13.10 & 22.50 \\
**Limit** & & **0.53** & **0.58** & **0.63** & **0.75** & **0.85** & **1.05** & **1.09** & **1.17** & **1.40** & **1.80** & **2.03** \\
**States** & & **3 g** & **8 g** & **0 g** & **5 g** & **5 g** & **4 g** & **2 g** & **5 g** & **5 g** & **5 g** \\  & IDA & 100 & 100 & 100 & 100 & 100 & 100 & 100 & 100 & 100 & 100 & 100 \\  & MSA & 99.53 & 99.71 & 99.80 & 99.93 & 99.96 & 99.99 & 100 & 100 & 100 & 100 & 100 \\  & IDA & 97.80 & 98.79 & 99.37 & 100 & 100 & 100 & 100 & 100 & 100 & 100 & 100 & 100 \\ LS2 & MSA & 92.75 & 94.76 & 95.89 & 97.93 & 98.78 & 99.54 & 99.62 & 99.73 & 99.90 & 100 & 100 \\  & IDA & 81.78 & 85.40 & 87.75 & 92.70 & 95.23 & 97.65 & 98.40 & 99.10 & 99.90 & 99.99 & 100 \\ LS3 & MSA & 69.22 & 74.80 & 78.37 & 86.23 & 90.34 & 95.12 & 95.80 & 96.67 & 98.39 & 99.49 & 99.71 \\  & IDA & 33.60 & 41.03 & 46.46 & 60.76 & 69.91 & 82.69 & 84.50 & 87.55 & 93.52 & 97.81 & 98.78 \\  & MSA & 24.64 & 29.75 & 33.61 & 44.50 & 52.29 & 65.10 & 67.50 & 71.00 & 79.92 & 89.19 & 92.18 \\ \hline \hline \end{tabular}
\end{table} 
Table 9: Probability under various earthquake intensities (%). body, which will require the most concern during the earthquake. The entire aqueduct structure may collapse once the damage and cracks get severe. Therefore, in the process of seismic design, relevant damping measures should be taken to control the damage development and prevent the overall aqueduct structure from being damaged or collapsed. For easily damaged parts, appropriate structural reinforcement is required to meet the needs of earthquake resistance. * Two fragility analysis methodologies are used to investigate the aqueduct structure separately. The results reveal that the fragility curves obtained by IDA and MSA are very similar.