# Probabilistic Seismic Safety Assessment of Railway Embarnments
## 8 Conclusions  
A fragility analysis has been generated for railway embankments in this study. For this purpose, the seismic safety of three typical railway embankments was numerically evaluated using nonlinear response history analyses. The selected railway embankments  
Figure 7: Fragility curves of the embankments due to cohesion variation and \(\phi\) = 30\({}^{\circ}\), (**a**) E1, near-field, (**b**) E2, near-field, (**c**) E3, near-field (**d**), E1, far-field, (**e**) E2, far-field, (**f**) E3, far-field. were categorized into three groups based on their heights (H = 2, 3 and 4 m). Moreover, several friction angles (\(\phi\) = 30\({}^{\circ}\), 32\({}^{\circ}\), 34\({}^{\circ}\)) and cohesions (c = 16, 32, 40 kPa) were considered for each group. In other words, the height to width ratio of the embankment, soil material properties and different ground motion sources were examined in this parametric study. Ten appropriate records of natural earthquakes considering near-field and far-field records were selected and utilized for IDA. For each embankment-earthquake set, an incremental dynamic analysis was conducted. To perform fragility curves, each model was subjected to ten intensities of a set of ten ground motions. The displacement of the embankment in a vertical direction served as the damage index, while PGA was considered the intensity measure. Based on the literature, threshold values were set for assessing three damage states, including slight, moderate and extensive deformation of the embankment [27]. Hence, 2400 analysis cases were implemented. Finally, fragility functions were derived according to damage data simulated by numerical analyses. The results of the study lead to the following conclusions. * As a result of this study, it was determined that railway embankments' mechanical properties could be considered significant sources of uncertainty in seismic fragility analyses. * The results of this study indicate that embankments with a high H/B ratio were more susceptible to earthquakes than embankments with a low H/B ratio. * As a result of the selected records, near-fault embankments were more prone to failure than far-fault ones. * The results show that by increasing cohesion, the vulnerability of the embankments is enhanced. However, curves for the embankments considering higher friction angles move to the right, indicating lower vulnerability. Although this study's results are limited to specific locations, they are suitable for assessing embankment vulnerability at the initial stage. It can also be mentioned that the outputs of this research are limited by the number of analyses performed, and to come by more reliable results, more analyses are required. This study aims to analyze the response behavior of embankments, considering geometry and material properties using fragility curves. A general parametric study is required to obtain the spatial variability of soil properties and embankment geometry. Furthermore, the results of a parametric study that considers different soil layers under the embankment can also be used in the analysis of transportation network vulnerability in future scenarios. Conceptualization, A.M., P.A.C., R.C. and M.S.R. ; methodology, A.M.; software, A.M. and M.S.R. ; validation, M.M. ; formal analysis, M.M. ; investigation, A.M., M.M. ; resources, R.C. ; data curation, M.M. ; writing--original draft preparation, A.M.; writing--review and editing, P.A.C., R.C. and M.S.R. ; visualization, A.M., P.A.C., R.C. and M.S.R. ; supervision, A.M., P.A.C., R.C. and M.S.R. ; project administration, R.C. ; funding acquisition, R.C. All authors have read and agreed to the published version of the manuscript. The work was financially supported by the IDB/04708/2020 and Programmatic Funding-of the CONSTRUCT--Instituto de I&D em Estruturas e Construcoes--funded by the FCT/MCTES (PIDDAC). The paper reflects research developed in the ambit of the project RISEN \"RISEN: Rail Infrastructure Systems Engineering Network\" (Grant No.