## 3 Results and Discussion
### Numerical Simulations
\begin{table}
\begin{tabular}{l c c c c} \hline \hline \multirow{2}{*}{**Variable**} & \multicolumn{2}{c}{**Unsupported Case**} & \multicolumn{2}{c}{**Supported Case**} \\ \cline{2-5}  & **Shale** & **Sandstone** & **Shale** & **Sandstone** \\ \hline Vertical displacements (mm) & 17.1 & 2.93 & 12.5 & 1.92 \\ Horizontal displacements (mm) & 17.4 & 2.91 & 14.8 & 2.27 \\ Thickness of EDZ (m) & 2.1 & 0.72 & 1.3 & 0.37 \\ \hline Axial load rock bolts (kN) & & & 130.0 & 30.5 \\ \hline \multirow{3}{*}{Shotcrete} & Axial force (kN) & & 699.46 & 62.41 \\  & Bending moment & & 1.5 & 0.03 \\ \cline{1-1}  & (KNm) & & 5.02 & 0.08 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Numerical simulations results in transversal tunnels. Figure 4: Transversal tunnels in shale formation: (**a**) vertical displacements [m]; (**b**) horizontal displacements [m]. failure initiation mechanisms are observed at the floor and walls. The failure mode changes to only shear at the roof of the tunnels. The thickness of the EDZ is 0.72 m in sandstone formation. The simulation results indicate that the designed support systems can guarantee the tunnels stability. Figure 6a indicates the rock bolt axial force for transversal tunnels in shale formation. The maximum bolt force is located at the walls of the tunnels (130 kN). Figure 6b shows the plasticity zones for shale formation after reaching balance. Shear failure is observed at the roof, walls and floor of the transversal tunnels. The thickness of the EDZ is larger in shale rock mass, reaching a value of 2.1 m. After support installation the thickness of the EDZ is reduced to 1.3 m in shale formation and 0.37 m in sandstone formation. In addition to the stability analysis in the transversal tunnels, the state of plasticity and the total displacements have also been analyzed in the central tunnel. Figure 7 shows the axial force in the rock bolts and the state of plasticity in the central tunnel for shale formation. A combination of shear and tensile failure initiation mode is seen at the roof, walls and floor of the central tunnel. Table 7 shows the summary of the numerical simulations results in the central tunnel in shale and sandstone formations for unsupported and supported cases, with the support system indicated previously in Table 3.  
Figure 5: Transversal tunnels in sandstone formation: (**a**) rock bolts axial force [N]; (**b**) state of plasticity. Figure 6: Transversal tunnels in shale formation: (**a**) rock bolts axial force [N]; (**b**) state of plasticity. The maximum value of displacement reached is 20.92 mm at the roof of the tunnel in shale rock mass. The thickness of the EDZ reached is 2.9 m is shale formation for the unsupported case. The vertical and horizontal displacements in sandstone formation reach 3.29 and 2.72 mm, respectively. The area of the EDZ and the maximum displacements notably decreased when the support system is applied. In shale formation, the vertical (roof) and horizontal displacements decreased down to 12.97 mm (38%) and 11.62 mm (36.5%), respectively. The rock bolt load reaches a value of 188.9 kN at the walls, while the elastic capacity of the rock bolts is 245 kN (safety factor of 1.29). The axial force, bending moment and shear force in reinforced shotcrete layer have also been analyzed, reaching 883.64 kN, 8.08 kNm, and 22.35 kN, respectively, in shale rock mass. Finally, the stability analysis was carried out in the junction zone between the central and transversal tunnels. Figure 8a shows the horizontal displacement and Figure 8b shows the shear force in the fibre reinforced shotcrete layer.