# Fragility Assessment of Traffic Embarkments Exposed to Earthquake-Induced Liquefaction
## 4 Results and Discussion
### Fragility Curves
\begin{table}
\begin{tabular}{c c c c c c c c c c c c c c c} \hline \hline  & & & & \multicolumn{8}{c}{**Embankment Height (Crest Width \(B\) = 24 m)**} \\ \cline{3-14}  & & & \multirow{2}{*}{**Soil ID**} & \multirow{2}{*}{
\begin{tabular}{c} **Fragility** \\ **Curve** \\ **Parameters** \\ \end{tabular} } & \multicolumn{3}{c}{**2 m**} & \multicolumn{3}{c}{**4 m**} & \multicolumn{3}{c}{**6 m**} & \multicolumn{3}{c}{**8 m**} \\ \cline{3-14}  & & & **ds1** & & & & & & & & & & & \\ \cline{3-14}  & & & & **ds2** & & & & & & & & & & \\ \cline{3-14}  & & & & **ds3** & & & & & & & & & & \\ \cline{3-14}  & & & & **ds1** & & & & & & & & & & \\ \cline{3-14}  & & & & **ds2** & & & & & & & & & & \\ \cline{3-14}  & & & & **ds3** & & & & & & & & & & \\ \cline{3-14}  & & & & **ds1** & & & & & & & & & & \\ \cline{3-14}  & & & & **ds2** & & & & & & & & & & \\ \cline{3-14}  & & & & **ds1** & & & & & & & & & & \\ \cline{3-14}  & & & & **ds1** & & & & & & & & & & & \\ \cline{3-14}  & & & & **ds2** & & & & & & & & & & & \\ \hline \hline \end{tabular}
\end{table} 
Table 9: FC parameters for different embankment heights (loose soil, PGA, railway criteria). Figure 8: Influence of embankment height on fragility curves (damage state criteria for railway embankments). Figure 7: Influence of embankment width on fragility curves (damage state criteria for road embankments). Figure 9: Influence of thickness of liquefiable layer on fragility curves (damage state criteria for road embankments). Initially, the influence of embankment width was studied for the case with a 4 m high embankment, situated on soil profile S1 (7 m thick liquefiable layer beneath a 1 m thick clayev crust layer) for a medium dense state of the sandy soil (Figure 7). From the figure, it is clear that the displacement of the central point of the embankment crest for this particular case decreased with an increase in embankment width, since the impact of less stable slopes was smaller. Consequently, the curves for the wider embankments move to the right, indicating lower vulnerability. All further analyses were performed using 24 m wide embankment crests. The effect of embankment height on settlements at the top midpoint is expressed by the fragility curves in Figure 8. These curves were derived for 2 m, 4 m, 6 m and 8 m high embankments, situated above soil profile S1 and containing a medium-density liquefiable layer. The probability of exceeding the examined limit states increased with increasing height of the embankment. There was a similar impact on the fragility curves with an increase in the thickness of the liquefiable layer, for the examined range in the study (2, 4 and 7 m). The greater the thickness of the liquefiable layer, the larger the vertical displacement at the crest. Consequently, there was a higher-numbered limit-state exceedance at each intensity, causing a shift of the fragility curves to the left. Even larger displacements were obtained in the absence of the crust layer (\(H_{C}\) = 0 m). The effect of the thickness of the sandy layer is presented in Figure 9 for the case of a 6 m high embankment and loose sandy material. The curves were derived on the basis of damage state criteria for road embankments using the PGA at bedrock as the IM. Due to the relatively high embankment and the loose density state of the liquefiable layer, the minimum threshold value was exceeded rapidly in all the soil profiles, which also caused a significant overlap of the curves for damage state ds1 (Figure 9). Figure 10 shows the fragility curves for medium-density and loose state liquefiable layers. A comparison was made with a model with a 4 m thick sandy layer beneath a 1 m thick crust layer (soil profile S4) and a 6 m high embankment on top. As expected, with the embankments situated above saturated, loose sand deposits are highly vulnerable because liquefaction can develop to its full potential in loose soil, even at lower earthquake intensities.