# Probabilistic Seismic Safety Assessment of Railway Embarnments
## 7 Development of Fragility Curves
### Sensitivity to Cohesion  
The previous section shows that the vulnerability of embankments increases with decreasing friction angle, and when \(\phi\) = 30\({}^{\circ}\), the maximum vulnerability occurs. The main focus of this section is to consider \(\phi\) = 30\({}^{\circ}\) and vary the cohesion as 16, 32 and 40 kPa and perform the fragility curves for the near-field and far-field seismic sources. Therefore, all further analyses are performed using \(\phi\) = 30\({}^{\circ}\). Table 8 presents the fragility curve parameters by considering the different cohesion of the embankment soil properties for near-field and far-field ground motion records. Figure 7 shows the fragility curve for three embankments due to cohesion variation. From the results presented in these figures, it is possible to infer that the maximum vertical displacement for this particular case enhances with an increase in cohesion. Consequently, the curves for the higher cohesion of the embankment soil move to the left, indicating higher vulnerability. Moreover, as can be seen in Figure 7, E1 with the highest ratio of H/B is more vulnerable than E2 and E3 for both near- and far-field seismic sources.  
\begin{table}
\begin{tabular}{c c c c c c c c c c c} \hline \hline \multirow{3}{*}{**Field**} & \multirow{3}{*}{**Fragility Curve Parameters**} & \multicolumn{8}{c}{\(\phi\) = 30\({}^{\circ}\)} \\ \cline{3-10}  & & & \multicolumn{3}{c}{**c = 16 kPa**} & \multicolumn{3}{c}{**c = 32 kPa**} & \multicolumn{3}{c}{**c = 40 kPa**} \\ \cline{3-10}  & & & **DS1** & **DS2** & **DS3** & **DS1** & **DS2** & **DS3** & **DS1** & **DS2** & **DS3** \\ \hline \multirow{3}{*}{E1} & Near-field & \(\beta\) & 0.46 & 0.45 & 0.32 & 0.71 & 0.51 & 0.49 & 0.46 & 0.52 & 0.47 \\ \cline{2-10}  & & \(\theta\) & \(-\)2.28 & \(-\)1.58 & \(-\)1.43 & \(-\)2.69 & \(-\)2.19 & \(-\)1.20 & \(-\)2.28 & \(-\)2.04 & \(-\)1.23 \\ \cline{2-10}  & Far-field & \(\beta\) & 0.46 & 0.41 & 0.32 & 0.29 & 0.19 & 0.30 & 0.46 & 0.48 & 0.36 \\ \cline{2-10}  & & \(\theta\) & \(-\)2.28 & \(-\)2.05 & \(-\)1.43 & \(-\)1.39 & \(-\)1.12 & \(-\)0.81 & \(-\)2.28 & \(-\)1.70 & \(-\)1.03 \\ \hline \multirow{3}{*}{E2} & Near-field & \(\beta\) & 0.47 & 0.45 & 0.34 & 0.74 & 0.62 & 0.77 & 0.36 & 0.28 & 0.51 \\ \cline{2-10}  & Far-field & \(\theta\) & \(-\)2.26 & \(-\)1.67 & \(-\)1.41 & \(-\)2.47 & \(-\)1.94 & \(-\)1.43 & \(-\)1.97 & \(-\)1.50 & \(-\)1.02 \\ \cline{2-10}  & Far-field & \(\beta\) & 0.32 & 0.41 & 0.33 & 0.46 & 0.36 & 0.28 & 0.33 & 0.31 & 0.28 \\ \cline{2-10}  & & \(\theta\) & \(-\)1.43 & \(-\)2.05 & \(-\)1.35 & \(-\)2.28 & \(-\)1.97 & \(-\)0.80 & \(-\)1.79 & \(-\)1.23 & \(-\)0.76 \\ \hline \multirow{3}{*}{E3} & Near-field & \(\beta\) & 0.46 & 0.36 & 0.55 & 0.08 & 0.06 & 0.08 & 0.33 & 0.32 & 0.40 \\ \cline{2-10}  & & \(\theta\) & \(-\)2.28 & \(-\)1.97 & \(-\)1.31 & \(-\)0.39 & \(-\)0.16 & \(-\)0.38 & \(-\)1.79 & \(-\)1.44 & \(-\)0.92 \\ \cline{2-10}  & Far-field & \(\beta\) & 0.30 & 0.33 & 0.32 & 0.42 & 0.28 & 0.43 & 0.28 & 0.24 & 0.26 \\ \cline{2-10}  & & \(\theta\) & \(-\)1.89 & \(-\)1.79 & \(-\)1.29 & \(-\)1.71 & \(-\)1.36 & \(-\)0.93 & \(-\)1.39 & \(-\)1.03 & \(-\)0.67 \\ \hline \end{tabular}
\end{table}
Table 8: Fragility curve parameters considering the different cohesion of the soil properties subjected to near-field and far-field earthquake ground motions.  
Figure 6: Fragility curves of the embankments due to friction angle variation, (**a**) E1, near-field, c = 32.5 kPa (**b**) E3, near-field, c = 0 kPa (**c**), E1, far-field, c = 32.5 kPa (**d**) E3, far-field, c = 0 kPa.