# Bridge Assessment under Earthquake and Flood-Induced Scour
## 4. Results
### Generation of Fragility  
#### 4.2.1 Element-Level Fragility  
Critical elements of the structure are subjected to seismic assessments at various depths of local scour to develop fragility curves, utilizing specific engineering demand parameters. Bents, abutments, and bearings are recognized as elements with a high damage potential. The threshold limits specified in Table 1 are utilized to compare the structural response of elements, aiding in determining the damage states of the bridge. The results of non-linear response history analyses, conducted under the influence of generated accelerograms at various seismic levels, are utilized to develop fragility curves at the element level. The maximum structural response for each ground motion of the bridge element is determined by identifying the absolute maximum from the response non-linear time history analysis for each ground motion, considering the relevant engineering demand parameters. In this research work, truncated incremental dynamic analysis is performed only up to the maximum intensity measure \(IM_{\text{max}}=0.5\) g, above which no further analyses are performed [12]. In the analysis of the bridge, \(n=10\) ground motions were applied, among which \(m\) motions led to collapse at \(IM\) (\(x_{\text{j}}\)) values less than \(IM_{\text{max}}\) (\(x_{\text{max}}\)). Meanwhile, the remaining \(n-m\) ground motions did not result in collapse before the end of the analysis. The given data are  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Flood Probability of** & \multirow{2}{*}{**No Flood**} & \multirow{2}{*}{**1\%**} & \multirow{2}{*}{**2\%**} & \multirow{2}{*}{**5\%**} & \multirow{2}{*}{**10\%**} & \multirow{2}{*}{**20\%**} \\
**Exceedance** & & & & & & \\ \hline
**Maximum Bent Scour [m]** & **-** & **3.62** & **3.07** & **2.72** & **2.45** & **2.27** \\ \hline First mode (long.) [s.] & 0.955 & 0.975 & 0.970 & 0.967 & 0.966 & 0.966 \\ Second mode (long.) [s.] & 0.902 & 0.915 & 0.912 & 0.910 & 0.909 & 0.908 \\ Third mode (long.) [s.] & 0.894 & 0.904 & 0.901 & 0.900 & 0.899 & 0.898 \\ Fourth mode (transv.) [s.] & 0.853 & 0.854 & 0.854 & 0.854 & 0.854 & 0.853 \\ \hline \hline \end{tabular}
\end{table}
Table 4: Fundamental modal periods.  
Figure 8: Fundamental periods of bridge.  
assessed using the maximum likelihood method. Equation (9) provides the mathematical expression for estimating the fragility function parameters for a specific damage limit state.  
\[\{\hat{\theta}_{\mathrm{k}},\hat{\beta}_{\mathrm{k}}\}=\mathrm{argmax}_{\Theta, \beta}\sum_{j=1}^{m}\left\{\ln\Phi\left(\frac{\ln(x_{\mathrm{j}}/\theta_{ \mathrm{k}})}{\beta_{\mathrm{k}}}\right)\right\}+(n-m)\ln\left\{1-\Phi\left( \frac{\ln(x_{\mathrm{max}}/\theta_{\mathrm{k}})}{\beta_{\mathrm{k}}}\right) \right\} \tag{9}\]  
Figure 9 illustrates the fragility curves of structural elements at different local scour depths. The parameters, including median and log-normal values, are provided in these figures.  
This figure highlights that bents are the sole elements of the bridge affected by seismic activity, regardless of the local scour depths, which could potentially lead to complete collapse. Variations in the fragility of the element are noted in the scenario without local scour compared to bents with varying scour depths at different flood hazard levels. The heightened bents with scour depths enhance the flexibility of bridge bents, consequently decreasing vulnerability to seismic actions in this bridge's case.