# Fragility Assessment of Traffic Embarkments Exposed to Earthquake-Induced Liquefaction
## 5 Conclusions  
The dynamic response of embankments built on soil deposits susceptible to liquefaction was studied through vulnerability analysis. A large set of fragility curves was derived based on the results of numerical calculations using the software package FLAC 2D and the PM4 Sand material model for simulating the behavior of the liquefiable layer during dynamic excitation. The width and height of the embankment, thickness and density state of the liquefiable layer, and effect of a 1 m thick crust layer were examined in this parametric study. In order to derive fragility curves, each variation of the model was loaded by at least eight intensities of a set of 30 GMs. Permanent vertical displacement of midpoint at embankment crest was selected as the EDP, while peak ground acceleration at bedrock was used as the IM. Threshold values for assessing three damage states, from minor to extensive deformation of the embankment, were taken from the literature ([14]). According to the presented results, similar tendencies were observed when the criteria for road or railway embankments were applied in the fragility analysis. Generally, all the curves for the railway embankments shifted to the left compared to the curves for the road embankments due to the more severe serviceability limitations of railway transportation. Despite the limited number of model variations, certain trends in embankment response were identified. Both the height of the embankment and the thickness of the liquefiable sandy layer increase the vulnerability, while increasing the crest width and the relative density of the sandy layer reduced settling at the central top point, thus diminishing the vulnerability of the embankment. A positive effect of the clayey crust layer on top of the liquefiable layer was also observed. Since it was not clear in advance whether vertical displacement at crest midpoint would be a robust representative parameter for assessing the overall performance of the traffic embankment in the case of seismic loading and liquefiable ground, some correlations between different embankment displacements were analyzed. The results showed that the settling of the crest midpoint correlated well with the maximum settlement of the crest edge points and with the differential horizontal displacements. On the other hand, it was observed that differential vertical settlements could not be reliably predicted based on vertical displacements at the embankment midpoint. Based on that finding, other EDPs (e.g., rotation or differential settlement) should be used when differential vertical displacement is important for assessing the damage state of an embankment. The results of the presented fragility analyses may be of limited value for specific locations, but they may be relevant for preliminary vulnerability assessments of traffic embankments. The main purpose of this paper was to present the influence of key variables regarding model geometry and material properties on the behavior of embankments on liquefiable ground exposed to seismic excitation by mean of fragility curves. The study is useful for assessing the vulnerability of the entire transport network of a wider area, as time and financial constraints make it difficult to afford detailed analyses of each embankment separately. A generic parametric study is needed to capture the spatial variability of soil properties and geometry of the embankments, the results of which can later be applied to different scenarios in a vulnerability analysis of transport network systems. Fragility curves and other outcomes of the study related to the effects of model variables might serve as an input parameter to an integrated framework of a comprehensive study dealing with infrastructure or traffic network resilience [41; 42] as well as overall societal flexibility to recover from a natural disaster. In addition, the outcomes of such studies enable a rapid assessment of vulnerability, which can serve as a starting point for a detailed analysis of critical embankments.