## 3 Quantitative Analysis of Support Effect of the Tunnel Face
### Strengthening Effect of Grouting Support  
The grouting strengthening effect of the tunnel surface is closely related to the cohesion (\(c_{g}\)), grouting filling rate (\(\zeta\)) and grouting depth (\(L_{g}\)). Figure 8 shows the relationship  
Figure 6: Operation flow chart of support optimization system. Figure 7: Relationship between stability coefficient (\(K\)) and pressure reduction factor (\(a_{1}\)) under pipe roofing support. between stability coefficient and grouting depth under grouting support. As can be concluded from Figure 8, the grouting depth causes the stability coefficient to go through a linear growth and a steady development with a stage demarcation point of 5.94 m. The evolution characteristics of the stability coefficient show that when the tunnel face does not have grouting support (\(L_{g}=0\)), its stability coefficient (0.86) is significantly less than 1.20, showing that the tunnel face cannot reach a self-stable state. The stability coefficient linearly increases when the grouting depth increases from 0 to 6 m, and the strengthening effect of tunnel face is significantly improved when the grouting depth is greater than 2.40 m. The maximum stability coefficient reaches a maximum of 1.75 when the grouting depth is 6 m. This indicates that the tunnel face has the best reinforcement effect. However, the stability coefficient remains around 1.75 when the grouting depth exceeds 6 m, indicating that the reinforcement effect does not continue to improve. The reason analysis shows that the grouting support improves the stability and bearing strength of tunnel face by increasing the cohesion of the wedge sliding body. The grouting effect cannot be fully utilized by the wedge sliding body and sliding surface when the grouting depth exceeds the sliding surface. The stability of the tunnel face cannot significantly improve if the grouting depth continues to increase, but the utilization rate of the grouting material is reduced [29]. Therefore, the precise position of sliding surface of the wedge sliding body should be considered when strengthening the grouting of the tunnel surface, and the grouting depth should be comprehensively determined in combination with factors such as excavation footage and grouting equipment performance. Based on a consideration of the potential instability of the tunnel face, a sufficient grouting depth was preserved, and the grouting depth (\(L_{g}\)) is 8 m. Figure 9 shows the relationship between the stability coefficient and cohesion and grouting filling rate. It can be seen from the 3D distribution cloud map that the stability coefficient of the tunnel face has spatial division characteristics, indicating that there are differences in the reinforcement effect of grouting. Figure 9 shows the relationship between the stability coefficient and grouting filling rate when the mortar cohesion is 1000-4000 kPa, revealing that the stability coefficient linearly increases with the increasing grouting filling rate when the mortar cohesion is determined. When the mortar cohesion is 1000 kPa, the grouting filling rate increases from 0 to 0.075, and the stability coefficient increases from 0.86 to 1.20. Existing studies show that the grouting filling rate of surrounding rock in practical engineering is generally between 0.15 and 0.20 [38]. It can be seen that the stability coefficient increases to 1.75 as the grouting filling rate increases to 0.20, indicating that the reinforcement effect is significantly improved. Figure 8: Relationship between stability coefficient (\(K\)) and grouting depth (\(L_{g}\)) under grouting support. Figure 9c shows that the stability coefficient also has a good linear correlation with mortar cohesion when the grouting filling rate is determined. When the grouting filling ratio is taken as 0.15, the stability coefficient increases from 0.86 to 1.22 when the mortar cohesion increases from 0 to 550 kPa. When the mortar cohesion increases to 4000 kPa, the stability coefficient can reach 3.52, which is 4.09 times higher than initial stability coefficient.