## 3 Description of FE Model and Verification  
### Modeling Method  
The lateral resistance requirement of a CWR track on an open-deck steel plate girder bridge is determined using FE analyses. In this study, the commercial FE analysis program ABAQUS [12] was used to perform numerical simulations. The FE model for the CWR track on the bridge is constructed based on the modeling approach of previous research [13]. The model consists of bridge and embankment regions, as shown in Figure 7. The length of the embankment region is set as a total of 200 m (100 m for each side) so that it can reflect CWR behavior. Rails, sleepers, and the bridge members are modeled using 3D beam elements. The connection between the rail and the sleeper, i.e., the rail fastener, is modeled by a connector element, CONN3D2, which is provided by ABAQUS [12]. This connector element can simulate elastic and plastic behaviors between two nodes in six directions (3 translations and 3 rotations). For the track on the embankment region, the ballast and subgrade are modeled using CONN3D2, considering only translations in three directions (no rotations). Similarly, for the girder-sleeper fastener in the bridge region, only the translational degrees of freedom are considered and modeled by CONN3D2. Figure 6: Theoretical evaluation of the min. lateral resistance: (a) \(R=1500\) m; (b) \(R=700\) m; and (c) \(R=300\) m.  
UIC 60 rail was used in the analysis. The area and the moment of inertia in the strong and weak axes of the UIC 60 rail were 76.86 cm\({}^{2}\), 3055 cm\({}^{4}\) and 513 cm\({}^{4}\), respectively. The elastic modulus, thermal expansion coefficient, and Poisson's ratio of the rail were 210,000 MPa, 1.14 \(\times\) 10\({}^{-5}\)/\({}^{\circ}\)C, and 0.3, respectively. For the rail fastener, the properties shown in Table 2 were used [14; 15; 16]. In Table 2, \(K_{x,f}\), \(K_{y,f}\), and \(K_{z,f}\) are the translational stiffness of the rail fastener in the \(x,y,\) and \(z\) directions, respectively. \(R_{x,f}\), \(R_{y,f}\), and \(R_{z,f}\) represent the corresponding rotational stiffness of the rail fastener in each direction. Note that the directions can be recognized in Figure 7. In KRS TR 0014-20R [14], the minimum peak longitudinal resistance of the rail fastener is defined as 7 kN with an elastic limit of 0.5 mm. Thus, \(K_{x,f}\) is calculated as 1.4 \(\times\) 10\({}^{7}\) N/m, as shown in Table 2. Note that the perfect elasto-plastic behavior of the rail fastener is used only for the longitudinal direction, while the elastic behavior is assumed for the other degrees of freedom. The snap-through buckling behavior of the CWR mainly depends on the lateral behavior of the ballast (or the girder-sleeper fastener in this study). The longitudinal material behavior of the rail fastener is not an important factor for the buckling analysis of the CWR track, and the elastic behavior of rail fastener is usually used for analysis [3]. However, it is the main parameter for track-bridge interaction (TBI) analysis and the perfect elasto-plastic behavior of the rail fastener is considered in this study for further applications of this model to TBI analysis. Figure 7: Schematic view of FE model: (**a**) side view; (**b**) cross-section; and (**c**) example of FE model. In the case of the girder-sleeper fastener, the vertical stiffness was infinite since the sleeper was connected to the girder directly. For the longitudinal and lateral directions, the perfect elasto-plastic behavior was applied. To identify the influence on the buckling characteristics of the CWR track, the peak lateral resistance, which is the main parameter of this study, was varied from 14 kN/m/track to 22 kN/m/track with 2 mm of elastic limit, while the peak longitudinal resistance was fixed as 20 kN/m/track with 2 mm of elastic limit, which is the normal peak longitudinal resistance of the ballasted track for a high-speed train line.