# Evaluation of Structural Stresses of Mountain-Embedded Railway Systems
## 4 Analytical Investigation of the Behavioral Characteristics of the Mountain-ERS Track System
### Effects of Thickness of the Subgrade Layer on the Stress of the Mountain-ERS Track  
Based on the results presented above, it was concluded that the precast concrete panels of the mountain-ERS exhibited sufficient robustness against factored service loads. Based on this consideration, safety assessment and behavioral analysis of mountain-ERS were conducted by reducing the thickness of the subgrade layer. A parametric study was conducted by reducing the thickness of the subgrade of the reference model (total thickness = 200 mm) at 25-mm intervals. This study accounted for thickness reductions of \(-25\) mm (subgrade thickness:175 mm), \(-50\) mm (subgrade thickness:150 mm), \(-75\) mm (subgrade thickness:125 mm), and \(-100\) mm (subgrade thickness:100 mm). The stress distributions in the track sections are shown in Figure 25. \begin{table}
\begin{tabular}{c c c c c c c} \hline
**Gradient (\%)** & **0** & **50** & **100** & **150** & **180** & **200** \\ \hline concrete panel & 3.90 & 3.91 & 3.91 & 3.91 & 3.91 & 3.91 \\ bedding layer & 4.02 \(\times\) 10\({}^{-1}\) & 4.03 \(\times\) 10\({}^{-1}\) & 4.04 \(\times\) 10\({}^{-1}\) & 4.04 \(\times\) 10\({}^{-1}\) & 4.04 \(\times\) 10\({}^{-1}\) & 4.04 \(\times\) 10\({}^{-1}\) \\ subgrade layer & 4.25 \(\times\) 10\({}^{-1}\) & 4.25 \(\times\) 10\({}^{-1}\) & 4.25 \(\times\) 10\({}^{-1}\) & 4.25 \(\times\) 10\({}^{-1}\) & 4.25 \(\times\) 10\({}^{-1}\) \\ reinforcing bars & 3.69 \(\times\) 10\({}^{1}\) & 3.69 \(\times\) 10\({}^{1}\) & 3.69 \(\times\) 10\({}^{1}\) & 3.69 \(\times\) 10\({}^{1}\) & 3.69 \(\times\) 10\({}^{1}\) & 3.69 \(\times\) 10\({}^{1}\) \\ \hline Unit: MPa. & & & & & & \\ \end{tabular}
\end{table} 
Table 7: Maximum principal tensile stresses of concrete elements and von Mises stresses of reinforcing bars inside the concrete panel (parametric study cases: variation of gradients). Figure 22: Comparison of analyzed results obtained subject to variations in the gradient of the mountain-ERS track: (**a**) S22 (\(y\)-axis), (**b**) S11 (\(x\)-axis), and (**c**) S33 (\(z\)-axis). Figure 23: Principal stress contours and location of the maximum principal tensile stress of concrete elements (example: slope = 0): (**a**) precast concrete panel, (**b**) bedding layer, and (**c**) subgrade layer. Figure 24: Von Mises stress contours and locations of the maximum stress values of reinforcing bars inside the precast concrete panel (example: slope = 0). As the thickness of the subgrade layer decreased, the distribution of S22 generally exhibited a consistent trend in each case study. The vertical loads applied to the rails were the same in the parametric cases; the distributions of S22 exhibited similar trends. For S11, the tensile stresses in the precast concrete panel, bedding layer, and subgrade tended to decrease with the increasing thickness of the subgrade layer. Similarly, for S33, the tensile stress decreased, whereas the compressive stress increased. This is attributable to the conditions applied to the structural analysis model. A tie option that enabled each concrete component to be fixed to the connected surface was used to prevent slippage between them. Additionally, owing to the boundary conditions applied at the bottom section of the subgrade, localized behavior occurred in these sections. The principal stress contours and the location of the maximum principal stress of the concrete elements are shown in Figure 26. The von Mises stress contour and location of the maximum stress value of the reinforcing bars are shown in Figure 27. The stress distribution and locations of the maximum principal tensile stress within the concrete components and the locations of the reinforcing bars were similar in all studied cases; the values are listed in Table 8. The results of these analyses indicated that even when the thickness of the subgrade of the mountain-ERS track was reduced to half of its original value, the maximum tensile stress in the concrete members did not exceed the tensile strength of the concrete materials.