## 4 Numerical Simulation
### Parametric Study of Controls
#### 4.4.1 Grouting Layer Thickness  
In conjunction with current relevant research findings, this section focused on selecting grouting reinforcement surrounding the tunnel rock with grouting layer thicknesses of 2 m, 4 m, and 6 m as seismic fortification measures for the tunnel, and investigated the anti-vibration mechanism of grouting reinforcement surrounding the rock. For the calculation results of peak values of horizontal acceleration (positive and negative) and principal stress at key positions of the tunnel under different grouting thickness conditions, refer to Figures 16 and 17. Figure 16: Effect of grouting thickness on horizontal acceleration in (a) positive and (b) negative directions. Figure 15: Validation of numerical simulation: (a) lining cross section and monitoring points; (b) comparison of numerical simulation results with model test results. The results in Figure 16 indicated that radial grouting had a similar effect on reducing acceleration at the vault, arch toe, and inverted arch. The maximum acceleration in the fault fracture zone notably decreased with an increase in grouting layer thickness. When the grouting layer thickness was 6 m, the maximum acceleration response peak value of the tunnel lining was only 5.35 m/s\({}^{2}\), approximately 17% lower than that without a grouting layer. This was attributed to the significantly enhanced strength of the surrounding rock in the fracture zone after grouting reinforcement, gradually strengthening the constraint of the surrounding rock on the lining structure and reducing the lithological difference between the fracture zone and the intact surrounding rock on both sides. Furthermore, the acceleration distribution along the longitudinal direction of the tunnel was analyzed. In general, the acceleration response at the fracture zone was larger than that at positions far away from the fracture zone. When the grouting layer thickness was 6 m, the acceleration response peak at the fracture zone position approached that at the intact section of surrounding rock, and the acceleration longitudinal distribution curve became gentler. It could be inferred that when the grouting layer thickness increased to a certain extent, the influence of the fracture zone on the lining essentially disappeared due to the reinforcement of the fractured rock mass around the tunnel over a large range, and the acceleration response curve along the longitudinal direction of the tunnel tended to become horizontal. In Figure 17, it was evident that the first principal stress and the third principal stress in the tunnel lining structure decreased significantly with the continuous increase in the thickness of the grouting layer at the location of the fault zone and its vicinity. When the thickness of the grouting layer was 2 m, 4 m, and 6 m, respectively, the maximum reduction in the first principal stress was 34%, 41%, and 46%, with the largest reduction occurring at the crown and the base of the wall. The reduction in stress at the crown and invert was not significant. The highest reduction rate of the third principal stress was close to 73%, with the largest reduction occurring at the crown and invert. Through comparative analysis, it was concluded that the decrease in stress response due to the grouting layer was more significant than the acceleration. This was attributed to the enhanced self-stabilizing ability of the surrounding rock after grouting reinforcement, which increased the constraint force on the tunnel and reduced the external load transmitted from the surrounding rock to the lining under seismic action. In summary, when the thickness of the grouting layer is 6 m, the principal stress in the tunnel meets the code requirements, the acceleration response of the tunnel along the full length fluctuates within a small range, and the amplification effect of the acceleration  
Figure 17: Effect of grouting thickness on (**a**) first and (**b**) third principal stresses. on the lining at the fault zone is already minimal.