# Evaluation of Structural Stresses of Mountain-Embedded Railway Systems
## 2 Simulation Model for the Mountain-ERS Track
### Load Conditions  
Among the loads considered in the railway track design, those corresponding to the mountain-ERS track were selected and applied to the structural analysis model, as listed in Table 3. For the load factors corresponding to each load, the coefficients presented in the DIN Technical Report 101 (Actions on Bridges, 2009) [12] were applied. The loads, including the dead load, which is the self-weight of the components; the live load (train loads); the starting/braking load of the train; the loads owing to the gradient; and the wind load were considered. The snake load owing to train hunting was not considered because the mountain train moved at a low speed. In addition, the load arising from drying shrinkage was not considered because a precast concrete panel was utilized in the mountain-ERS track. The loads listed in Table 3 were applied to the structural analysis model, as shown in Figure 8. They were applied in the vertical (\(y\)-), transverse (\(x\)-), and longitudinal (\(z\)-) directions. For vertical loads, the analysis included both dead and live loads. The dead load included the weight of various components, including the 50-kg rails, precast concrete panels, synthetic resin materials, a mortar filler layer (bedding layer), and a subgrade layer. In this structural analysis model, the weights of these components were factored into the gravity loads based on their respective densities. To account for the 180% slope, the gravity loads were divided into two directions using this angle as a reference. As shown in Figure 9, the live train load was 90 kN. Similar to gravity loads, a live load was applied as a force component based on the gradient. \begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Loads**} & \multicolumn{3}{c}{**Partial Safety Factor**} & **Combination** \\ \cline{2-5}  & **ULS 1** & **SLS 2** & **Coefficient** \\ \hline dead load & & & & \\ (self-weights) & & 1.35 & 1.00 & 1.00 \\ live load & & & & \\ (train loads) & applied at rails & 1.45 & 1.00 & 1.00 \\ starting/braking load & & 1.50 & 1.00 & 1.00 \\ load owing to gradient & & 1.35 & 1.00 & 1.00 \\ snake load & & 1.50 & 1.00 & 1.00 \\ (hunting oscillation) & & applied & & \\  & & with train & & \\ wind load & applied at rails & & 1.50 & 1.00 & 1.00 \\  & & taneously & & \\ loads owing to drying & & & & \\ shrinkage & & & 1.00 & 1.00 & 1.00 \\ \hline \hline \end{tabular} \({}^{1}\) Ultimate limit state. 2 Service limit state.  
\end{table} 
Table 3: Loads and corresponding factors considered in mountain-ERS analysis (Deutsches Institut für Normung (DIN) Technical Report-Actions on Bridges, 2009) [12]. The wind load (transverse load) was calculated using the train dimensions. To calculate the wind load (\(q_{w}\)), the following equation presented in KR C 08020 [16] was used to calculate the wind load (\(q_{w}\)):  
\[q_{w}=1.50\cdot H, \tag{9}\]  
where \(H\) denotes the height of the train, as shown in Figure 10. As discussed in Section 2.2, the transverse loads applied to the 50-kg rails were assumed to be distributed across the sections of the precast concrete panel. Figure 8: Schematic for the applied loads along the vertical (\(y\)-axis), transverse (\(x\)-axis), and longitudinal (\(z\)-axis) directions. Figure 10: Wind load schematic. Figure 9: Schematic of mountain train load. In the case of longitudinal loads, the loads owing to the slope and starting/braking loads were considered, as shown in Figure 11. The longitudinal load (\(P_{G}\)) was calculated using Equation (10), as follows:  
\[P_{G}=(P_{t}+P_{D})\times\frac{S}{1000}, \tag{10}\]  
where \(P_{G}\) denotes the longitudinal load, \(P_{t}\) is the train load, \(P_{D}\) is the dead load, and \(S\) is the slope. As previously mentioned, the longitudinal loads were divided into force components. For the starting/braking loads, the load occurring at one bogie of the train was calculated based on the length of the precast concrete panel and its system.