## 1 Introduction  
Korea experienced the 2016 Gyeongiu earthquake (magnitude 5.8) and the 2017 Pohang earthquake (magnitude 5.3). Globally, major earthquakes such as the 2019 Alaska earthquake (magnitude 7.0), the 2021 Haiti earthquake (magnitude 7.2), and the Turkey-Syria earthquake (magnitude 7.8) were observed. The Turkey-Syria earthquake included aftershocks ranging from magnitude 6.0 to 7.0, with the largest main earthquake reaching magnitude of approximately 7.5, indicating intense seismic activity. Such large-scale earthquakes and aftershocks have heightened anxiety about earthquakes and increased the need for preparedness and pre-disaster damage assessments. The recent increase in the construction of various railway facilities, such as the GTX and Shinansan lines, has expanded railway networks, increasing the need for studies on the seismic behavior of individual railway components [1]. Based on such seismic behavior evaluations, seismic fragility curves--which represent the exceedance probability of various damage states caused by earthquakes--have been proposed by several researchers and are widely used as quantitative indicators of structural damage [2, 3, 4]. When railway networks are damaged by earthquakes, the physical structures suffer direct damage, and socioeconomic losses such as disruptions of logistics due to the functionality degradation of network components occur. Studies on structural behavior during earthquakes and seismic fragility functions have been conducted by numerous researchers. [PERSON] et al. [5] studied the dynamic behavior of pile structures, while [PERSON] et al. [6] investigated the dynamic behavior of underground structures during earthquakes and proposed methods for risk assessment. Additionally, various studies on seismic fragility have been conducted. [PERSON] et al. [7] developed seismic fragility functions for railway structures, presenting methods for evaluating seismic damage and developing fragility functions for tracks, bridges, and tunnels. [PERSON] [8] assessed seismic performance and developed fragility functions for tunnels on the Gyeongbu high-speed railway line, comparing them with those of other studies. [PERSON] and [PERSON] [9] analyzed the 2004 Niigata earthquake and developed seismic fragility curves for high-speed rail systems, concluding that long-period seismic waves significantly damage tunnels and bridges. [PERSON] and [PERSON] [2] developed seismic fragility curves for shallow tunnels to evaluate their vulnerability based on ground conditions, while [PERSON] et al. [10] proposed fragility curves for steel fiber reinforced concrete segment tunnel linings, analyzing the impact of reinforcement materials on seismic performance. [PERSON] and [PERSON] [11] used seismic fragility curves for mountain tunnels to study methods for assessing tunnel vulnerability in seismic risk analyses. However, prior research on seismic fragility curves has primarily focused on the physical damage sustained by structures during earthquakes; limited studies quantitatively evaluated the socioeconomic impact, such as logistics disruptions, based on functionality loss of network components. [PERSON] et al. [12] evaluated the impact of buried depth on the seismic fragility of tunnels embedded in soft soil. [PERSON] et al. [13] investigated fragility functions for various railway structures and proposed and applied a direct damage propagation model; however, the study only analyzed direct damage and did not evaluate the functionality loss of structures. [PERSON] et al. [14] proposed a procedure to evaluate the recovery performance of tunnel structures; however, their study focused on analyzing the recovery performance of individual tunnel structures without examining the functionality loss at the network level. In this study, we established a new railway network system and proposed a model to evaluate functionality loss during earthquakes by leveraging statistical data on existing seismic fragility curves and recovery times for bridges, embankments, and tunnels.