# Probabilistic Seismic Safety Assessment of Railway Embarnments
## 1 Introduction
(2016) [26] studied the seismic behavior of embankments under earthquake loading using numerical analysis. They also conducted a shaking table test to validate their numerical results. To obtain the seismic behavior of an embankment, they evaluated the dynamic displacement response alongside horizontal and vertical acceleration responses, and the block state of the embankment during earthquake loading. The results showed that the value of the horizontal acceleration response calculated by the numerical study was coincident with the one obtained by the test. [PERSON] & [PERSON] (2015) [27] presented a numerical seismic fragility curve for embankments. In that research, the soil conditions, the geo-construction and the embankment geometry are considered the first objective in evaluating the vulnerability of highway and railway embankments. [PERSON] et al. [28] performed a response failure analysis on a collapsed railway embankment considering tensile cracks during the 1968 Tokachi-Oki earthquake. The result is entirely consistent with the damaged state reported. [PERSON] et al. [29] performed a vulnerability analysis of embankments to liquefaction-induced deformations. In addition to the above studies, several researchers have shown the different failure mechanisms of embankments during earthquakes, including slipping of the slope surface, piping failure, crest settlements and lateral spreading [30; 31]. In order to reduce the socio-economic loss due to earthquakes and enhance the resilience of society to these events, it is necessary to ensure the serviceability of traffic systems as soon as possible. All the above mentioned studies are focused on performing fragility curves under earthquake loading. However, according to the authors' literature survey, no investigation has been conducted so far regarding the influence of soil material properties on fragility curves. This research aims to present the effect of several model parameters, particularly soil cohesion and friction angle, on the response of an embankment on a probabilistic platform. The following noteworthy contributions have been made in this research study. The first main contribution is to develop fragility curves for railway embankments and present the effect of several soil material properties on the embankment response during earthquakes. The effect of embankment geometry, including embankment height and width, on embankment response during an earthquake, is investigated. The fragility functions are derived utilizing an incremental dynamic analysis [32] approach considering a set of near-field and far-field earthquake ground motions. The rest of the paper is organized as follows. Section 2 shows the methodology to perform the fragility curves. In Section 3, the definition of intensity measure, damage index and damage limit states are explained. Permanent vertical displacement of the embankment is selected as a damage index, while peak ground acceleration is considered the intensity measure. Section 4 summarizes the selected ground motions. Ten appropriate records of natural earthquakes considering near- and far-field records are selected and utilized for incremental dynamic analysis. For each embankment-earthquake set, an IDA was conducted. In Section 5, the seismic safety of three typical railway embankments is numerically evaluated using nonlinear response history analyses, and numerical models are provided in Section 6. The selected railway embankments are categorized into three groups with respect to their heights. Moreover, several friction angles and cohesions are considered for each group. Finally, fragility analyses are performed for railway embankments according to damage data simulated by numerical computations, as presented in Section 8.