# Probabilistic Seismic Safety Assessment of Railway Embarnments
## 7 Development of Fragility Curves
### Sensitivity to H/B
\begin{table}
\begin{tabular}{c c c c c c c c c c c c} \hline \hline  & \begin{tabular}{c} **Field** \\ **Parameters** \\ \end{tabular} & \multicolumn{3}{c}{**Fragility Curve**} & \multicolumn{3}{c}{**\(\Phi\) = 30\({}^{\circ}\)**} & \multicolumn{3}{c}{**\(\Phi\) = 32\({}^{\circ}\)**} & \multicolumn{3}{c}{**\(\Phi\) = 34\({}^{\circ}\)**} \\ \cline{3-11}  & \begin{tabular}{c} **Field** \\ **Parameters** \\ \end{tabular} & \begin{tabular}{c} **P3** \\ \end{tabular} & \begin{tabular}{c} **DS1** \\ \end{tabular} & \begin{tabular}{c} **DS2** \\ \end{tabular} & \begin{tabular}{c} **DS3** \\ \end{tabular} & \begin{tabular}{c} **DS1** \\ \end{tabular} & \begin{tabular}{c} **DS2** \\ \end{tabular} & \begin{tabular}{c} **DS3** \\ \end{tabular} & \begin{tabular}{c} **DS1** \\ \end{tabular} & \begin{tabular}{c} **DS2** \\ \end{tabular} & \
\begin{tabular}{c} **DS3** \\ \end{tabular} \\ \hline \multirow{4}{*}{E1} & \multirow{2}{*}{Near-field} & \(\beta\) & 0.7 & 0.5 & 0.47 & 0.25 & 0.32 & / & 0.41 & 0.22 & / \\ \cline{2-11}  & & \(\theta\) & \(-2.54\) & \(-2.09\) & \(-1.23\) & \(-1.46\) & \(-1.29\) & / & \(-1.20\) & \(-0.24\) & / \\ \cline{2-11} c & \multirow{2}{*}{Far-field} & \(\beta\) & 0.72 & 0.61 & 0.79 & 0.22 & 0.24 & / & 0.24 & 0.38 & / \\ \cline{2-11}  & & \(\theta\) & \(-2.49\) & \(-1.92\) & \(-1.41\) & \(-1.18\) & \(-0.86\) & / & \(-0.86\) & \(-0.40\) & / \\ \hline \multirow{4}{*}{
\begin{tabular}{c} E3 \\ \text{c} = 0 kPa \\ \end{tabular} } & \multirow{2}{*}{Near-field} & \(\beta\) & 0.36 & 0.34 & 0.52 & 0.08 & 0.06 & / & 0.22 & 0.31 & / \\ \cline{2-11}  & & \(\theta\) & \(-1.97\) & \(-1.69\) & \(-1.07\) & \(-0.39\) & \(-0.16\) & / & \(-0.36\) & \(-0.02\) & / \\ \cline{1-1} \cline{2-11}  & & \(\beta\) & 0.28 & 0.19 & 0.3 & 0.07 & 0.05 & / & 0.27 & 0.08 & / \\ \cline{1-1} \cline{2-11}  & & \(\theta\) & \(-1.39\) & \(-1.12\) & \(-0.81\) & \(-0.33\) & \(-0.15\) & / & \(-0.25\) & \(-0.09\) & / \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Fragility curve parameters considering several friction angles of the soil properties subjected to near-field and far-field earthquake ground motions. Figure 5: Fragility curves of the embankments due to H/B ratio (**a**) near-ground motions (**b**) far-ground motions. As an example of the influence of the H/B ratio and the seismic sources on the probability of reaching the limit, Figure 5a shows that, for PGA = 0.7 g, the probabilities of reaching or exceeding DS1 (slight) for three embankments subjected to near ground motion are 97, 75, and 56%, respectively. In other words, increasing the H/B ratio leads to the enhancement of the probabilities of reaching or exceeding for both seismic sources. This outcome is consistent with the embankment responses observed by previous researchers [27; 29]. Moreover, the embankments subjected to near-fault records were more vulnerable than those subjected to the far-fault ones. The reason is related to the response spectra of the selected ground motion records. As illustrated in Figure 2, the response spectra of the near-field seismic records are higher than the response spectra of the selected far-field ground motion records. Therefore, less deformation occurred for embankments subjected to far-field ground motion records. Moreover, the results show that E3 is less vulnerable than E1 and E2. The reason for such a result is the cohesion of embankment E3, which is 0.