## 4 Analysis of the Effect of TBM Crossing Fault Fracture Zone Under Different Treatment Methods
### Analysis of Calculation Results
#### 4.3.2 Analysis of Tunnel Deformation and Ground Displacement  
At a depth of 30 m (y = 30 m), the tunnel deformation under four working conditions was calculated, and the deformation cloud map is shown in Figure 14a. The deformation trends of the surrounding rock are similar across all four conditions before reaching the fault fracture zone. Specifically, the arch crown deforms by 5 mm to 7 mm, the arch waist by 4 mm to 7 mm, and the arch bottom lifts by about 7 mm. Preliminary analysis suggests that this similarity is due to the consistent geological conditions at this depth, which minimizes the impact of different grouting methods. Before conducting further calculations and analysis, we first standardize the model by unifying the grid and normalizing other variables to eliminate their influence on the results. This ensures the analysis focuses on the core research variables, improving the accuracy and reliability of the model. The deformation calculation results validate the model's effectiveness in assessing the stability of surrounding rock at fault locations. Figure 13: Schematic diagram of plastic zone development. (**a**) Plastic zone computing development depth cloud map. (**b**) Viewable depth distribution of computational development in the plastic zone. We calculate the deformation of the tunnel at the position of y = 75 m (tunnel model excavation 75 m, fault fracture zone) for four working conditions, and calculate the deformation cloud map as shown in Figure 14b. It is not difficult to see that the first three working conditions all use the pipe shed grouting model, while the fourth working condition uses the surface pre-grouting model. According to the calculation, the deformation of the surrounding rock at the left and right arch waist positions is relatively obvious, about 14-17 mm. Due to the grouting reinforcement effect, the load is evenly distributed on the initial support structure of the upper surrounding rock of the tunnel. The deformation at the arch crown is 2-3 mm smaller than that at the arch waist, and the uplift at the bottom of the arch in condition II is higher than in other conditions. It is not difficult to see that using the surface pre-grouting scheme results in a much smaller overall deformation of the tunnel surrounding rock. We calculate the deformation of the tunnel at the position of y = 100 m (100 m in the excavation direction of the tunnel model) for four working conditions, and the deformation cloud map is shown in Figure 14c. The difference between this calculation section and the position of y = 30 m is that the surface pre-grouting range of working condition IV still includes the position of the 100 m section. So, analyzing the deformation cloud map shows that using surface pre-grouting can still effectively reinforce the surrounding rock when the tunnel passes through ordinary strata. Compared with the other three working conditions, the deformation of the tunnel surrounding rock can be reduced by 52.3%. The deformation cloud map helps visualize the differences In surrounding rock deformation caused by various grouting schemes. Comparative analysis is conducted on the deformation at different positions--arch crown, arch waist, and arch bottom--under four working conditions (Figure 15), with different line styles used to distinguish between conditions I-IV. First, the deformation at the arch positions under different working conditions is analyzed. As shown in Figure 15a, the deformation curve at the fault fracture zone (y = 75 m) is significantly higher than at other positions, indicating greater overall deformation at the fault. Among the four working conditions at the fault fracture zone, Condition II (pre-grouting reinforcement with a pipe shed) results in the highest surrounding rock deformation, reaching 14.2 mm. The grouting schemes of double-layer pipe shed, chemical grouting + shield tail small pipe grouting + advanced pipe shed, and surface pre-grouting reduced the deformation by 2.12%, 3.97%, and 50.78%, respectively, compared to Condition II.