# Dynamic Damage Mechanism and Seismic Fragility Analysis of an Aqueduct Structure
## Dynamic Response Analysis
### Damage Mechanism of Aqueduct Structures under Ground Motion  
Figure 4 depicts the progression of the aqueduct structure's dynamic damage as a result of significant earthquakes. The pier shaft and pier cap were severely damaged because they functioned as the principal supports. Penetrating damage occurred on both sides of the pier cap and around the pier shaft, and minor damage near the cushion cap, as indicated by the damage development range. Because of the aqueduct's high rigidity, damage only emerged near the top. The damage development pattern shows that the seismic excitation was weak at the early stages of the earthquake, and the structure was in the elastic stage, implying that damage has little impact on the result. The damage first showed on both sides of the pier shaft and at the bottom of the pier cap when the earthquake struck 3.70 s. It is due to the introduction of CDP constitutive, which describes the phenomenon of the concrete structure after damage. The structure was undergoing \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**And** & **Station Name** & **EPA** & **EPV** & \(\mathbf{T_{g}}\) & \(\mathbf{\beta_{max}}\) \\ \hline Northridge\(-\)01 & Whittier\(-\)S. Alta Dr & 0.67 & 0.06 & 0.56 & 2.25 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Ground motion parameters of natural wave Northridge-01. Figure 3: Time history records of seismic accelerations. (**a**) Transverse; (**b**) Vertical. irreversible plastic damage. The damage range extended on both sides of the pier shaft in both directions throughout 4.22 s-8.20 s, reaching from the top and bottom of the aqueduct body to the middle, as illustrated in Figure 4a-d. Penetrating damage appeared on both sides of the pier shaft and the pier cap almost simultaneously throughout 8.20 s-10.44 s. However, due to the effect of foundations, the aqueduct body and cushion cap showed damage later than the pier shafts and pier caps, and the damage expanded slower than the aqueduct body. The damage ranges gradually increased throughout the entire aqueduct during the period 11.00 s-25.00 s, under the continuous action of the seismic force, as shown in Figure 4c,d. At the later stage of the earthquake, the damage ranges eventually stabilized when the earthquake duration curve shifted. Changes in acceleration cause the structural stress state to vary during the seismic wave motion process, an important component of dynamic load time history calculation. The feature points on one side of the structure are chosen for analysis to examine the development process and laws of aqueduct structural damage during seismic wave motion. Figure 5 depicts the evolution and changes in damage value at each point. The slope of the damage development process curve of the pier cap is the largest, and it is also the position where the damage occurs first. The damage range quickly increases over the entire aqueduct construction as the seismic force continues, and the pier shaft and pier cap are damaged almost simultaneously, and entirely. Compared to the pier shaft and pier cap, the cushion cap is damaged later and has a smaller damage range. The damage to the aqueduct structure proliferates, as evidenced by the damage development curves of characteristic points. The structural damage aggravates rapidly when the ground motion acceleration reaches its peak, indicating that the peak acceleration of ground motion can considerably impact the damage to the structure, and the seismic damage is severe. When comparing the development trend of damage to various elements, pier caps and pier shafts exceed the aqueduct body and cushion caps significantly. Since pier shafts and pier caps are responsible for sustaining the upper structure and affecting its overall stability, it is hypothesized that the rapid progression of damage to pier shafts and pier caps is due to their increased displacement under seismic forces.