*3.2. 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, length, spacing, load capacity, and thickness of the spayed concrete layer). Figure 4 shows the vertical

*3.2. Numerical Simulations* 

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). length, spacing, load capacity, and thickness of the spayed 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 3 shows the properties of the support system used in the numerical analysis (bolt diameter,

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The results of the calculations that have been conducted in sandstone and shale rock masses, in

**Figure 4.** Transversal tunnels in shale formation: (**a**) vertical displacements [m]; (**b**) horizontal displacements [m]. **Figure 4.** Transversal tunnels in shale formation: (**a**) vertical displacements [m]; (**b**) horizontal displacements [m].

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. 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.


**Table 6.** Numerical simulations results in transversal tunnels. **Table 6.** Numerical simulations results in transversal tunnels.

grouted rock bolts reached 30.5 kN at the tunnel walls. Figure 5b shows the failure states for 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 failure initiation mechanisms are observed at the floor and walls. The failure mode changes to

Figure 5a also shows the rock bolts force for sandstone rock mass. The maximum load in the

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. formation. The simulation results indicate that the designed support systems can guarantee the tunnels stability. tunnels stability.

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

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transversal tunnels in sandstone formation as the model reaches equilibrium. A combination of shear and tensile failure initiation mechanisms are observed at the floor and walls. The failure mode

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**Figure 5.** Transversal tunnels in sandstone formation: (**a**) rock bolts axial force [N]; (**b**) state of **Figure 5.** Transversal tunnels in sandstone formation: (**a**) rock bolts axial force [N]; (**b**) state of plasticity. plasticity.

plasticity. 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 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. 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.

**Figure 6.** Transversal tunnels in shale 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.

**Figure 6.** Transversal tunnels in shale formation: (**a**) rock bolts axial force [N]; (**b**) state of plasticity. 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 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 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.

Table 3.

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 7.** Numerical simulation results in the central tunnel.

**Shale Sandstone Shale Sandstone** 

**Variable Unsupported Case Supported Case** 

Vertical displacements (mm) 20.92 3.29 12.97 2.51 Horizontal displacements (mm) 18.32 2.72 11.62 1.54 Thickness of EDZ (m) 2.9 1.1 1.75 0.65 Axial load rock bolts (kN) 188.9 18.5

Axial force (kN) 883.64 56.29

Shear force (kN) 22.35 0.42

883.64 kN, 8.08 kNm, and 22.35 kN, respectively, in shale rock mass.

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

**Figure 7.** The central tunnel in shale formation: (**a**) rock bolts axial force [N]; (**b**) state of plasticity. **Figure 7.** The central tunnel in shale formation: (**a**) rock bolts axial force [N]; (**b**) state of plasticity.


Finally, the stability analysis was carried out in the junction zone between the central and **Table 7.** Numerical simulation results in the central tunnel.

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.

capacity designed).

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**Figure 8.** Junction zone in shale formation: (**a**) horizontal displacements; (**b**) shear force in shotcrete. **Figure 8.** Junction zone in shale formation: (**a**) horizontal displacements; (**b**) shear force in shotcrete.

Table 8 shows the results for the junction zone between the central and transversal tunnels. The maximum value of displacement reached 18.20 mm at the roof of the tunnels in shale rock mass. By installation of support, the thickness of the EDZ and deformations are reduced. In shale formation, the vertical and horizontal displacements decreased down to 13.84 mm at the roof and 11.51 mm in the walls, when the support system is applied. The axial force, bending moment and shear force in reinforced shotcrete layer have also been analyzed in the junction zone, reaching 1570 kN, 9.31 kNm, and 27.13 kN, respectively, in shale rock mass. The shear force indicated in Figure 8b shows peaks due to the head of the rock bolts. Table 8 shows the results for the junction zone between the central and transversal tunnels. The maximum value of displacement reached 18.20 mm at the roof of the tunnels in shale rock mass. By installation of support, the thickness of the EDZ and deformations are reduced. In shale formation, the vertical and horizontal displacements decreased down to 13.84 mm at the roof and 11.51 mm in the walls, when the support system is applied. The axial force, bending moment and shear force in reinforced shotcrete layer have also been analyzed in the junction zone, reaching 1570 kN, 9.31 kNm, and 27.13 kN, respectively, in shale rock mass. The shear force indicated in Figure 8b shows peaks due to the head of the rock bolts.


**Table 8.** Numerical simulation results in the junction zone. **Table 8.** Numerical simulation results in the junction zone.

Figure 9 shows the rock bolts force in the central tunnel and the transversal tunnels depending on the distance from the rock bolt head. Rock bolts located at the walls in shale and sandstone formations have been selected. The maximum axial load is reached in shale rock mass, at the central tunnel. It has been observed that in all scenarios the axial load reached is less than 245 kN (load Figure 9 shows the rock bolts force in the central tunnel and the transversal tunnels depending on the distance from the rock bolt head. Rock bolts located at the walls in shale and sandstone formations have been selected. The maximum axial load is reached in shale rock mass, at the central tunnel. It has been observed that in all scenarios the axial load reached is less than 245 kN (load capacity designed).

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**Figure 9.** Axial load in rock bolts. Shale and sandstone rock masses. **Figure 9.** Axial load in rock bolts. Shale and sandstone rock masses.

## **4. Conclusions 4. Conclusions**

Flexible energy storage systems allow increasing the generation of electricity by means of intermittent renewable energy sources. A closed coal mine in the Asturian Central Coal Basin (NW Spain) is proposed as a subsurface water reservoir of underground pumped storage hydropower plants. Underground pumped storage hydropower plants provide a large amount of electrical energy with rapid response and low environmental impacts. An underground reservoir conformed by a network of tunnels with an arched roof cross section of 30 m2 has been designed. For the construction of the underground water reservoir it is necessary to analyze the stability of the excavation of the Flexible energy storage systems allow increasing the generation of electricity by means of intermittent renewable energy sources. A closed coal mine in the Asturian Central Coal Basin (NW Spain) is proposed as a subsurface water reservoir of underground pumped storage hydropower plants. Underground pumped storage hydropower plants provide a large amount of electrical energy with rapid response and low environmental impacts. An underground reservoir conformed by a network of tunnels with an arched roof cross section of 30 m<sup>2</sup> has been designed. For the construction of the underground water reservoir it is necessary to analyze the stability of the excavation of the network of tunnels. Transversal tunnels, the central tunnel and junction zones have been analyzed.

network of tunnels. Transversal tunnels, the central tunnel and junction zones have been analyzed. Empirical analysis and three-dimensional numerical simulations have been carried out in this work. According to the empirical analysis, grouted rock bolts and a layer of fibre reinforced shotcrete were recommended as the support system. The rock mass properties used as input parameters for numerical modeling were obtained from laboratory tests and estimated from rock mass classification systems. In the numerical model, the state of plasticity, the axial load in rock bolts and the deformations around the tunnels were analyzed. In addition, the axial force, the bending moment and the shear force were also checked in the reinforced shotcrete layer. The maximum displacements and thickness of the excavation damage zone were reached in shale formation. As shown by the numerical simulations, the proposed support from empirical analysis was feasible. By applying the designed support system, the area of the excavation damage zone and the maximum displacements significantly decreased. The results of the numerical analysis show that no significant failure is expected. All this shows that a combination of empirical and numerical methods is appropriate to Empirical analysis and three-dimensional numerical simulations have been carried out in this work. According to the empirical analysis, grouted rock bolts and a layer of fibre reinforced shotcrete were recommended as the support system. The rock mass properties used as input parameters for numerical modeling were obtained from laboratory tests and estimated from rock mass classification systems. In the numerical model, the state of plasticity, the axial load in rock bolts and the deformations around the tunnels were analyzed. In addition, the axial force, the bending moment and the shear force were also checked in the reinforced shotcrete layer. The maximum displacements and thickness of the excavation damage zone were reached in shale formation. As shown by the numerical simulations, the proposed support from empirical analysis was feasible. By applying the designed support system, the area of the excavation damage zone and the maximum displacements significantly decreased. The results of the numerical analysis show that no significant failure is expected. All this shows that a combination of empirical and numerical methods is appropriate to design a proper support system in underground infrastructures.

design a proper support system in underground infrastructures. Based on further rock lab testing, a softening factor for the rock mass after failure should be applied in order to get more precise predictions for displacements and the extension of the excavation damage zone as well as the support loads. Based on further rock lab testing, a softening factor for the rock mass after failure should be applied in order to get more precise predictions for displacements and the extension of the excavation damage zone as well as the support loads.

**Author Contributions:** Conceptualization, J.M.; investigation, J.M., F.S., H.K., A.B.S. and J.L.; methodology, J.M. F.S.; software, J.M., F.S.; validation, J.M, F.S., H.K. and A.B.S.; writing original draft, J.M. and F.S.; writing review **Author Contributions:** Conceptualization, J.M.; investigation, J.M., F.S., H.K., A.B.S. and J.L.; methodology, J.M. and F.S.; software, J.M., F.S.; validation, J.M, F.S., H.K. and A.B.S.; writing original draft, J.M. and F.S.; writing review and editing, J.M., A.B.S. and J.L.; supervision, F.S., H.K., A.B.S. and J.L. All authors have read and agreed to the published version of the manuscript.

and editing, J.M. A.B.S. and J.L.; supervision, F.S., H.K., A.B.S. and J.L. All authors have read and agreed to the published version of the manuscript. **Funding:** This research received no external funding.

**Funding:** This research received no external funding. **Conflicts of Interest:** The authors declare no conflict of interest.

**Conflicts of Interest:** The authors declare no conflict of interest.
