## 4 Results and Discussion
### Mechanism of Isolation Piles Controlling the Tunnel Deformation  
To investigate the mechanism by which isolation piles control tunnel deformation induced by excavation, the foundation pit dimensions were simplified to \(20\times 40\) m (Figure 11), and a corresponding finite element model with dimensions of \(140\times 100\times 50\) m (Figure 12) was established, consisting of 33,510 elements. All other parameters and model settings were maintained, consistent with the original configuration. Additionally, a meshing sensitivity analysis was conducted to ensure the accuracy of the results. Specifically, when the number of elements was doubled, the change in the maximum tunnel deformation was less than 3%, indicating that the mesh used was sufficiently refined. Meanwhile,  
Figure 10: Comparison between the predicted and measured values. Figure 9: Evolutions of the horizontal displacement (**a**) and vertical displacement (**b**) of the tunnel with the monitoring point along the tunnel. to avoid inconsistent meshing and potential increased analysis errors when analyzing different isolation pile parameters, all scenarios were considered within one model. During analysis, only the relevant conditions for each scenario were activated. The parameters of the soil layer, tunnel, and beam were consistent with those in the above model. The working conditions were primarily categorized based on the distance (x) between the foundation pit and the isolation piles, with three key values: 2 m, 5.5 m, and 9 m. Additionally, the effects of the pile head depth (u) and pile toe depth (w) were also considered. The specific parameters are summarized in Table 4, and a total of 108 cases were analyzed. The horizontal and vertical control efficiencies of isolation piles with x = 2 m are presented in Figure 13. For cases with a pile length of 5 m, both the vertical and horizontal control efficiencies initially increased, then decreased, and gradually approached zero as  
Figure 11: Simplified finite-element model for parametric study. Figure 12: Three-dimensional finite-element model for parametric analysis. the pile head depth. For longer pile lengths, from a global perspective, the vertical control efficiency decreased as the pile head depth increased, while the horizontal control efficiency exhibited either a fluctuating or decreasing trend. This behavior differs from the patterns observed in Figure 13.  
The vertical and horizontal control efficiencies with x = 9 m are shown in Figure 15. For cases with a pile length of 5 m, the vertical control efficiency initially decreased, then increased, decreased again, and finally increased once more as the depth of the pile head increased. In contrast, the horizontal control efficiency first increased, then decreased, increased again, and ultimately decreased as the depth of the pile head increased. For longer pile lengths, the vertical control efficiency generally showed a downward trend, while the horizontal control efficiency either increased or decreased with increasing pile head depth. These trends differ from those presented in Figures 13 and 14, which can be attributed to the combined effects of pile blocking and alterations in the tunnel's geometric configuration. A more detailed explanation for these observations is provided below:  
Figure 14: Relationships between control efficiency and pile position (x = 5.5 m) for varying pile lengths: 5 m (**a**), 10 m (**b**), 15 m (**c**), 20 m (**d**), 25 m (**e**), 30 m (**f**), and 35 m (**g**). The maximum horizontal displacement of soil at the position of the isolation piles for cases with a pile length of 5 m and x = 2 m is plotted in Figure 16. As shown in Figure 16, due to the blocking effects of the isolation piles, the maximum horizontal displacement of soil at the position of the isolation piles initially decreased and then increased, as the depth of the pile head increased.