# Evaluation of Structural Stresses of Mountain-Embedded Railway Systems
## 2 Simulation Model for the Mountain-ERS Track
### Finite Element Analysis Model for the Mountain-ERS Track  
A three-dimensional structural analysis model for railway tracks was developed using Abaqus 2022, a commonly used structural analysis program. As shown in Figure 4, the 50-kg rails, precast concrete panel, reinforcement bars inside the concrete panel, bedding layer, and concrete subgrade layer were modeled. The precast concrete panel, bedding layer, and subgrade layer were modeled using solid elements (C3D8R). Regarding the steel material components, transverse, and longitudinal reinforcing bars (arranged inside a precast concrete panel with a diameter of 13 mm) were modeled using beam elements (T3D2), and 50-kg rails were modeled using solid elements (C3D8R). By applying the load factors suggested in [10], factored service loads were applied, and a static analysis was conducted. Considering the objectives of this research, that is, the examination of the safety profile of the mountain-ERS and the analysis of the behavior of the entire structure under factored loads, some structural elements constituting the railway track system were not modeled based on several assumptions. First, we did not explicitly model the shear anchors in the structural analysis model because we assumed that their performance was optimal. This signifies the assumption that the interactions between the constituent structural elements were fully integrated, and that the entire structural system operated as a fully composite section. The tie option in the Abaqus program was used to integrate the structural elements. Figure 4: Schematic of the mountain railway track system. Figure 3: Schematic of the mountain train. Nodes on different surfaces were paired to connect the translational and rotational degrees of freedom between the adjacent nodes. This was applied to the surfaces between the 50-kg rail and precast concrete panel, between the concrete panel and bedding layer, and between the bedding layer and subgrade in the structural analysis model. Owing to the assumption that no slip occurred between the layers, the lateral boundary conditions of these components were not determined. Rails do not affect the strength or stiffness of railway track systems. However, the rails were modeled to consider the localized stresses that may be generated by concentrated train loads on the precast concrete panel, which do not occur in real structures. Similar to conventional railway track systems, synthetic resins act as rail fasteners, maintaining rail spacings and reducing vibrations. Therefore, based on the assumption that synthetic resins did not affect the safety of the railway track system, they were not modeled. Instead, a lateral load (wind load) transmitted from the rails to the concrete panel that did not induce local stresses was directly applied to the concrete panel as a distributed load with the same area as the synthetic resin material. The rack rail installed at the center of the track system, which engaged with the pinions of mountain trains to transfer loads from the slope to the concrete panel, was not modeled based on the assumption that its effect on the safety and behavior of the concrete panel was not significant. Instead, the starting or braking loads transmitted by the rack rail to the concrete panel were applied at the points where the rack rails were connected to the concrete panel. For the reinforcing bars placed inside a concrete panel, the embedded option in the Abaqus program was used in the analysis model to simulate the embedded reinforcing bars. If the node of the embedded element is located within the element containing it, the deformation degrees of freedom are removed, and the node functions as an embedded node. Using the corresponding constraint option, the internal nodes (i.e., the nodes of the embedded elements) can be configured for inclusion in a concrete panel. The ground was not directly modeled to construct a structural analysis model of the railway track system.