## 3 Results and Discussion
### Numerical Simulations  
The results of the calculations that have been conducted in sandstone and shale rock masses, in transversal tunnels, the central tunnel and the junction zone between them are shown in this section. Table 3 shows the properties of the support system used in the numerical analysis (bolt diameter, \begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline
**Lithology** & _RQD_ & \(\mathbf{J_{n}}\) & \(\mathbf{J_{r}}\) & \(\mathbf{J_{a}}\) & \(\mathbf{J_{w}}\) & _SRF_ & \(\mathbf{Q}\) & \(\mathbf{Q_{N}}\) & _GSI_ \\ \hline Shale & 31 & 15 & 1 & 2 & 0.4 & 1.8 & 0.23 & 0.41 & 35 \\ Sandstone & 48 & 12 & 1.4 & 2.2 & 0.5 & 1 & 1.27 & 1.27 & 50 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Evaluating results using the Q-system. \begin{table}
\begin{tabular}{l l} \hline \hline  & \multicolumn{3}{c}{**Shale Rock Mass**} \\ \hline Central tunnel & Systematic bottle 245 kN, \(\phi\) = 25 mm, \(L\) = 3 m, Reinforced shotcrete 150 mm \\ Transversal tunnels & Systematic bottle 245 kN, \(\phi\) = 25 mm, \(L\) = 3 m, Reinforced shotcrete 120 mm \\ \hline \hline \multicolumn{3}{c}{**Sandstone Rock Mass**} \\ \hline Central tunnel & Systematic bottle 245 kN, \(\phi\) = 25 mm, \(L\) = 3 m, Reinforced shotcrete 80 mm \\ Transversal tunnels & Systematic bottle 245 kN \(\phi\) = 25 mm, \(L\) = 3 m, Reinforced shotcrete 60 mm \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Support system design. \begin{table}
\begin{tabular}{l l} \hline \hline  & \multicolumn{3}{c}{**Shale Rock Mass**} \\ \hline Central tunnel & Systematic bottle 245 kN, \(\phi\) = 25 mm, \(L\) = 3 m, Reinforced shotcrete 150 mm \\ Transversal tunnels & Systematic bottle 245 kN, \(\phi\) = 25 mm, \(L\) = 3 m, Reinforced shotcrete 120 mm \\ \hline \hline \multicolumn{3}{c}{**Sandstone Rock Mass**} \\ \hline Central tunnel & Systematic bottle 245 kN, \(\phi\) = 25 mm, \(L\) = 3 m, Reinforced shotcrete 80 mm \\ Transversal tunnels & Systematic bottle 245 kN \(\phi\) = 25 mm, \(L\) = 3 m, Reinforced shotcrete 60 mm \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Empirical analysis. Support categories for shale and sandstone formations. length, spacing, load capacity, and thickness of the sprayed concrete layer). Figure 4 shows the vertical and horizontal displacements in the transversal tunnels for shale rock mass according to the model indicated in Figure 3a. The maximum displacement is located at the tunnel walls (17.4 mm). Table 6 shows the summary of the numerical simulations results in transversal tunnels for shale and sandstone rock masses: vertical and horizontal displacements, thickness of the EDZ, axial load in rock bolts and axial force, bending moment and shear force in the shotcrete layer at the walls, roof and floor of tunnels for unsupported and supported cases. By installation of the support, the EDZ and total displacements (vertical and horizontal) notably decreased. Because of the lower quality of the rock mass, in shale formation the displacement values are higher than in sandstone rock mass. The maximum value of displacement reached 17.5 mm at the walls of the tunnels in shale rock mass. The maximum thickness of EDZ is located at the tunnel walls in shale formation, reaching 2.1 m. In shale formation, the vertical and horizontal displacements are reduced to 12.5 mm (27%) and 14.8 mm (15%), respectively. In sandstone formation, the vertical (roof) and horizontal (walls) displacements are reduced to 1.92 mm (34%) and 2.27 mm (22%), respectively. In addition, the thickness of the EDZ is also reduced by 38% in shale formation when the support system is applied. Figure 5a also shows the rock bolts force for sandstone rock mass. The maximum load in the grouted rock bolts reached 30.5 kN at the tunnel walls. Figure 5b shows the failure states for transversal tunnels in sandstone formation as the model reaches equilibrium. A combination of shear and tensile