# Evaluation of Structural Stresses of Mountain-Embedded Railway Systems
## 2 Simulation Model for the Mountain-ERS Track
### Boundary Conditions  
The safety and structural behavior of railway track systems can be influenced by the ground conditions. Accordingly, the interaction between the railway track system and ground is crucial. In the structural analysis model, the presence of ground beneath the subgrade layer was assumed in two cases, and the differences between them were analyzed, as shown in Figure 12. First, it was assumed that the ground was sufficiently compacted during construction. Based on this assumption, the boundary condition of the bottom section of the subgrade layer was modeled with a fixed-end support (\(U_{x}=U_{y}=U_{z}=UR_{x}=UR_{y}=UR_{z}=0\)). In the second case, considering the actual ground conditions at the site where the mountain-ERS was installed, an elastic spring support condition was assumed (\(U_{x}=U_{z}=UR_{x}=UR_{y}=UR_{z}=0\)). In the study, the spring coefficient of the ground was considered and applied to the structural analysis model (\(k_{s}=0.029\)) [17].  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Load** & **Calculated Load Value** & **Applied Load Value** \\ \hline starting load (180\%) & 44.899 kN & 89.798 kN \\ braking load (180\%) & 38.150 kN & \\ \hline \hline \end{tabular}
\end{table}
Table 4: Starting/braking loads of the mountain train under development for a gradient of 180%.  
Figure 11: Gradient load schematic.  
Parametric Study for the Establishment of the Track Boundary Conditions of the Reference Model of the Mountain-ERS  
To examine the safety of the mountain-ERS track structure subjected to service loads, the maximum principal tensile stresses of the concrete elements were analyzed by comparing the tensile strength values of the concrete materials based on their brittleness. The von Mises stress values were examined for reinforcing bars inside a precast concrete panel. The major points in the concrete elements were investigated by analyzing the structural behavior of the railway system, as shown in Figure 13. The stresses in each axis of the concrete components were defined as shown in this figure. S11, S22, and S33 denote the normal stresses perpendicular to the \(x,y,\) and \(z\) axes, respectively.  
Figure 12: Boundary conditions considered in the structural analysis model: (**a**) fixed-end support condition; (**b**) spring support condition.  
The vertical loads transmitted by the rails constitute the major loads of the mountain-ERS; therefore, points were chosen from a section where vertical loads were applied to the 50-kg rails. For the precast concrete panel, Point A (Point D) was in direct contact with the rails, Point B (Point E) was where the reinforcing bars were embedded, and Point C (Point F) was the lowest point, all of which were selected as review points. In the bedding layer, Points G (H) (C (F)) were investigated. In the case of the subgrade layer, the lowest points of the section were chosen as Points I and J. By investigating the vertical stress values of these points, the behavior of the structures was analyzed in each direction (S11, \(x\)-direction; S22, \(y\)-direction; S33, \(z\)-direction).