# 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 c} \hline \hline  & & & \multicolumn{10}{c}{**Embankment Height (Crest Width \(B\) = 24 m)**} \\ \cline{3-14}  & & **Soil ID** & \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** & **ds2** & **ds3** & **ds1** & **ds2** & **ds3** & **ds1** & **ds2** & **ds3** & **ds1** & **ds2** & **ds3** \\ \cline{3-14}  & & & \(\theta\) & 0.44 & 0.60 & 1.23 & 0.38 & 0.51 & 0.85 & 0.36 & 0.49 & 0.82 & 0.35 & 0.46 & 0.71 \\ \cline{3-14}  & & \(\beta\) & 0.40 & 0.33 & 0.59 & 0.35 & 0.40 & 0.36 & 0.32 & 0.41 & 0.37 & 0.27 & 0 Some cells in Tables 4-9 are empty (_/_) or have values highlighted in red, indicating less reliable results, because the adopted damage state criteria were either too strict or too flexible with respect to the range of intensity levels considered in this study. The number of exceedances was either very low over the entire intensity range or, on the other hand, the limit states were exceeded at very low intensities. In both cases, the fragility curve could not be properly derived. Tables 4-9 summarize fragility curve parameters for both damage state criteria (roads and railways) and all performed analyses, where peak ground acceleration at bedrock was used as IM for the derivation of fragility curves. Some of the obtained fragility curves were verified on the case history of CAR Canal site, located in Adapazari, Turkey [30]. In general, the site was strongly affected by the 1999 Kocaeli Earthquake, but at the location of the CAR Canal river embankments no sign of complete failure or heavy destruction was observed. According to [PERSON] [39] and [PERSON] et al. [40], no severe ground deformations (displacements not exceeding 10 cm) occurred at the site for a 4-5 m high river embankment lying on the 1-1.5 m thick liquefiable layer covered by a clayey crust. The same conclusions are reached with the proposed fragility curves (similar geometry to our model variation 9, medium dense soil, road criteria), where it was shown that the probability of damage due to liquefaction for a bedrock acceleration of 0.4 g corresponds to an exceedance probability of approximately 5-8% for minor damage state (ds1) (probability of experiencing less sever or equal damage to ds1, i.e., ground deformations below or equal to 5 cm, is thus around 95%), which is in agreement with the field evidence. Typical examples of a fragility curve response to variations in the selected model variables are presented in Figures 7-10. The trends observed in changes in the fragility curves with variation in the model parameters (e.g., embankment height, thickness of liquefiable layer) are similar for the damage state criteria of roads and railways. Therefore, in some figures, the damage state criteria for roads were used and in the others, the damage state criteria for railways were used. Fragility curves were derived for three different damage states representing minor (ds1), moderate (ds2) and significant (ds3) damage to the road/railway infrastructure, due to settlements at the embankment crest. Light green, blue and red colors were selected to differentiate between these three damage states, while for the other model variations (width and height of the embankment, thickness and relative density of the liquefiable layer, presence of crust layer), various line types were used in the figures.