# Dynamic Damage Mechanism and Seismic Fragility Analysis of an Aqueduct Structure
## 3 Seismic Fragility Analysis of the Aqueduct Structure
### Determination of Structural Performance Indicators  
Studies have shown that PGA, PGV, and spectral acceleration \(S_{4}(T_{1},5\%)\) can serve as common ground motion intensity measures [41; 42; 43]. [PERSON] [44] chose 60 ground motion IM related to structural performance to construct ground motion parameter evaluation models. He believes that the analysis results involving the spectral acceleration could accurately describe the probability statistic relationship between IM and DM and avoid dispersion between analysis results. The aqueduct structure is similar to bridge structures in terms of engineering design. The pier shaft is responsible for sustaining the superstructure and affecting the overall stability of both structures. Bridge damage can be measured using a variety of indicators, including pier top displacement, pier top offset ratio, cracking degree, curvature ductility ratio, and displacement ductility ratio. [PERSON] and [PERSON] [45] proposed the pier top offset ratio during their research, using it to indicate the pier shaft's  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**No.** & **Event** & **Station** & **M** & **R (km)** & **Time (s)** & **Mech** & **Year** \\ \hline
1 & San Fernando & Fairmont Dam & 6.61 & 25.58 & 0.01 & RN & 1971 \\
2 & Taiwan SMART1(45) & SMART1 E02 & 7.3 & 51.35 & 0.01 & RN & 1986 \\
3 & Christchurch-New & MQZ & 6.2 & 13.91 & 0.02 & RO & 2011 \\
4 & Zealand & Parkfield-Fault Zone 11 & 6.36 & 27.1 & 0.01 & RN & 1983 \\
5 & Coalinga-01 & Parkfield-Gold Hill 3W & 6.36 & 38.1 & 0.01 & RN & 1983 \\
6 & Coalinga-01 & Parkfield-Stone Corral & & & & & \\
7 & Northridge-01 & Burbank-Howard Rd & 6.69 & 15.87 & 0.01 & RN & 1994 \\
8 & Northridge-01 & Baldwin Park-N Holly & 6.69 & 47.72 & 0.01 & RN & 1994 \\
9 & Northridge-01 & Rancho Palos & & & & & \\
10 & Northridge-01 & Verdes-Hauth & & & & & \\
11 & Northridge-01 & Rando Palos & 6.69 & 50.47 & 0.01 & RN & 1994 \\  & & Verdes-Luconia & & & & & \\
11 & Northridge-01 & Lake Hughes \#4-Camp & & & & & \\  & & Mend & & & & & \\
12 & Northridge-01 & Whittier–S.Alta Dr & 6.69 & 48.36 & 0.01 & RN & 1994 \\
13 & Duzce-Turkey & Lamont 531 & 7.14 & 8.03 & 0.01 & SS & 1999 \\
14 & San Fernando & Lake Hughes\#4 & 6.61 & 19.45 & 0.01 & RN & 1971 \\
15 & San Fernando & Pearlbossom Pump & 6.61 & 35.54 & 0.01 & RN & 1971 \\
16 & RHITG040 & - & - & - & - & - & - \\
17 & THITG040 & - & - & - & - & - & - \\ \hline \hline \end{tabular} Note: R: epicentral distance; M: moment magnitude; Mech: focal mechanisms; SS: strike slip; RN: reverse thrust; RO: reverse oblique.  
\end{table}
Table 4: Ground-motion records for \(6.0\leq\text{M}\leq 8.0\) and \(0\leq\text{R}\leq 105\text{ km}\).  
Figure 7: Response spectrum curves.  
deformation capacity. It is the ratio of the maximum displacement of the pier top to the pier shaft height during the earthquake. The limit values are shown in Table 5. The joint rotation features, structural damage degree, and deformation performance in the dynamic analysis are all directly related to displacement in the structure. Therefore, referring to the four limit states divided by FEMA356 and combined with the existing achievement of previous scholars [45; 46; 47], this paper divides structural earthquake-resistant performance into four grades: normal occupancy (NO), immediate occupancy (IO), life safety (LF), and collapse prevention (CP). We use the \(S_{a}(T_{1},5\%)\) as ground motion IM and the aqueduct pier shaft top offset ratio to quantify the structural damage index limit to reflect the specific damage degree to a structure in case of exceedance probability. The limit state values of the quantitative indicators of the structural performance level can be found in Table 5.