## 4 Numerical Modelling and Calculation Methodology
### Calculation Results and Analysis of GRCs  
#### 4.2.1 GRCs Under Different Spacing Conditions  
To investigate the influence of tunnel group spacing on the GRC, the maximum deformation values and support stress data of the tunnels were extracted and plotted to generate the GRCs for the surrounding rock. The impact of tunnel group spacing on the GRC was analyzed by taking the GRC of the 400 m deep Tunnel 1 as an example, as shown in Figure 5.  
For Grade III surrounding rock, under the same stress level, the displacement decreased gradually as the spacing increased, although the rate of decrease slowed. Taking the support stress of 2 MPa as an example, the spacing increased from 20 m to 125 m, with the displacements of Tunnel 1 being 1.3657 cm, 1.322 cm, 1.298 cm, 1.283 cm, 1.254 cm, 1.262 cm, 1.231 cm, and 1.191 cm, respectively. The displacement reduction was most significant when the spacing increased from 20 m to 35 m, but only by 3.14%. Overall, for a 400 m burial depth condition with Grade III surrounding rock, the influence of tunnel spacing \(\geq\) 35 m on the displacement of the same tunnel was not significant.  
Figure 5: GRCs of 400 m depth tunnels with different spacing in Grade III to V surrounding rock. (**a**) Grade III; (**b**) Grade IV; and (**c**) Grade V.  
For Grade IV surrounding rock, under the same stress level, the displacement decreased gradually as the spacing increased, but the rate of decrease slowed. Taking the support stress of 2 Mpa as an example, the spacing increased from 20 m to 125 m, with the displacements of Tunnel 1 being 5.726 cm, 5.056 cm, 4.841 cm, 4.748 cm, 4.568 cm, 4.223 cm, and 4.091 cm, respectively. When the spacing increased from 20 m to 35 m, the displacement reduction was most significant at 11.70%, but after that, the decrease in displacement remained below 5% when the spacing was increased. The tunnel group effect was more pronounced when D = 20 m and became less significant when D > 35 m.  
For Grade V surrounding rock, under the same stress level, the displacement decreased gradually as the spacing increased, but the rate of decrease slowed. Taking the support stress of 6 Mpa as an example, the spacing increased from 20 m to 125 m, with the displacements of Tunnel 1 being 28.195 cm, 25.85 cm, 24.52 cm, 23.400 cm, 22.372 cm, 21.516 cm, 20.827 cm, and 20.107 cm, respectively. When the spacing increased from 20 m to 35 m, the displacement reduction was most significant at 8.30%, but after that, the decrease in displacement remained below 5% when the spacing was increased. The tunnel group effect was more pronounced when D \(\leq\) 50 m and became less significant when D > 50 m, as shown in Figure 6.  
Overall, for a 400 m burial depth condition with Grade V surrounding rock, the influence of tunnel spacing > 50 m on the displacement of the same tunnel was not significant. It is evident that under the same burial depth condition, the poorer the quality of the surrounding rock, the more pronounced the tunnel group effect. Considering that, with increasing depth, the tunnel faces an environment with increased ground stress, the tunnel group effect may be more significant. To minimize the tunnel group effect during the design stage, based on the analysis in the previous sections, a preliminary calculation of D = 65 m is conducted for the GRCs of Grade V surrounding rock at a 1600 m burial depth for Tunnels 1 to 3. It can be seen that under a support stress of 20 Mpa, the displacements of the surrounding rock for Tunnels 1 to 3 are 97.55 cm, 102.47 cm, and 103.28 cm, respectively, with a maximum displacement error of 5.87% between the tunnels. The tunnel group effect is not significant. Therefore, it can be preliminarily determined that the tunnel group effect is negligible under tunnel spacing D = 65 m.  
Figure 6: GRC of V-grade surrounding rock of each tunnel under the condition of a buried depth of 1600 m and spacing D = 65 m.