# Fragility Assessment of Traffic Embarkments Exposed to Earthquake-Induced Liquefaction
## 4 Results and Discussion
### Fragility Curves  
The complete set of results for all studied examples are given in Tables 4-9 in terms of median value of fragility function (\(\theta\)) and standard deviation of \(\ln\)_IM_ (\(\beta\)). These two fragility-curve parameters completely define each fragility curve (see Equation (1)). It must be emphasized, however, that these results are only valid within the confines of the assumptions made in this study (e.g., material properties, geometry of ground layers and embankment) and cannot be readily extrapolated for other conditions. The main scope of the study was to show the influence in individual model variables on fragility curves. \begin{table}
\begin{tabular}{c c c c c c c c c c c c} \hline \hline  & & & & & & & & & & & & \\ \cline{3-11}  & \multirow{3}{*}{**Soil ID**} & \multirow{3}{*}{**Fraility Curve**} & \multicolumn{6}{c}{**Crest Width (Embankment Height \(H\) = 4 m)**} \\ \cline{3-11}  & & & & & & & & & & & & 24 m & \\ \cline{3-11}  & & & & & & & & & & & & & \\ \cline{3-11}  & \multirow{3}{*}{S1} & \multirow{3}{*}{**Fraility Curve**} & \multirow{3}{*}{**Parameters**} & **ds1** & **ds2** & **ds3** & **ds1** & **ds2** & **ds3** & **ds1** & **ds2** & **ds3** \\ \cline{3-11}  & & & \(\theta\) & 0.35 & 0.56 & 1.13 & 0.38 & 0.58 & 1.21 & 0.42 & 0.71 & 1.54 \\ \cline{3-11}  & & & \(\beta\) & 0.31 & 0.40 & 0.43 & 0.33 & 0.44 & 0.47 & 0.42 & 0.33 & 0.51 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Fragility curve (FC) parameters for different crest widths (medium dense soil, peak ground acceleration (PGA), road criteria). Figure 6: Vertical crest displacement (**a**), pore pressure ratio (**b**) and acceleration time (**c**) histories. \begin{table}
\begin{tabular}{c c c c c c c c c c c c c c c c} \hline \hline  & & & \multicolumn{10}{c}{**Fragility**} & \multicolumn{10}{c}{**Embankment Height (Crest Width \(B\) = 24 m)**} \\ \cline{3-14}  & & **Soil ID** &
\begin{tabular}{c} **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** & **ds2** & **ds3** & **ds1** & **ds2** & **ds3** & **ds1** & **ds2** & **ds3** & **ds1** & **ds2** & **ds3** \\ \cline{3-14}  & & & \(\theta\) & 0.21 & 0.37 & 1.03 & 0.18 & 0.31 & 0.68 & 0.18 & 0.30 & 0.59 & 0.18 & 0.24 & 0.50 \\ \cline{3-14}  & & \(\beta\) & 0.40 & 0.38 & 0.43 & 0.40 & 0.39 & 0.40 & 0.42 & 0.35 & 0.42 & 0.40 & 0.41 & 0.45 \\ \cline{3-14}  & & \(\theta\) & 0.17 & 0.31 & 0.86 & 0.17 & 0.26 & 0.56 & 0.17 & 0.24 & 0.49 & & & \\ \cline{3-14}  & & \(\beta\) & 0.37 & 0.41 & 0.41 & 0.38 & 0.40 & 0.42 & 0.39 & 0.43 & 0.46 & & & \\ \cline{3-14}  & & \(\beta\) & 0.84 & / & / & 0.23 & 0.54 & / & 0.20 & 0.38 & 0.87 & 0.18 & 0.29 & 0.81 \\ \cline{3-14}  & & \(\beta\) & 1.03 & / & / & 0.35 & 0.53 & / & 0.25 & 0.48 & 0.46 & 0.37 & 0.39 & 0.69 \\ \cline{3-14}  & & \(\theta\) & 0.35 & 1.15 & / & 0.22 & 0.50 & 1.26 & 0.19 & 0.40 & 0.80 & 0.19 & 0.27 & 0.55 \\ \cline{3-14}  & & \(\beta\) & 0.34 & 0.61 & / & 0.35 & 0.34 & 0.42 & 0.42 & 0.39 & 0.38 & 0.39 & 0.37 & 0.43 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: FC parameters for different embankment heights (loose soil, PGA, road criteria). \begin{table}
\begin{tabular}{c c c c c c c c c c c c c c c} \hline \hline  & & & \multicolumn{10}{c}{**Fragility**} & \multicolumn{10}{c}{**Crest Width (Embankment Height \(H\) = 4 m)**} \\ \cline{3-14}  & & **Soil ID** &
\begin{tabular}{c} **Curve** \\ **Parameters** \\ \end{tabular} & \multicolumn{3}{c}{**6 m**} & \multicolumn{3}{c}{**12 m**} & \multicolumn{3}{c}{**24 m**} \\ \cline{3-14}  & & **ds1** & **ds2** & **ds3** & **ds1** & **ds2** & **ds3** & **ds1** & **ds2** & **ds3** & **ds1** & **ds2** & **ds3** \\ \cline{3-14}  & & \(\beta\) & 0.31 & 0.42 & 0.70 & 0.37 & 0.51 & 0.85 & 0.38 & 0.51 & 0.85 \\ \cline{3-14}  & & \(\beta\) & 0.30 & 0.42 & 0.45 & 0.33 & 0.37 & 0.35 & 0.35 & 0.40 & 0.36 \\ \hline \hline \end{tabular}
\end{table} 
Table 7: FC parameters for different crest widths (medium dense soil, PGA, railway criteria).