## 4 Results and Discussion
### Mechanism of Isolation Piles Controlling the Tunnel Deformation
According to the mirror image method proposed by [PERSON] [27], increased soil deformation leads to greater tunnel deformation, which, in turn, reduces the control efficiency of the isolation piles. The trend of the curve obtained by flipping the one in Figure 16 along the \(x\)-axis aligns with the trend of the control efficiency of the isolation piles. This suggests that the control efficiency of the isolation piles is primarily influenced by the displacement of the soil at the pile locations. Additionally, based on the soil displacement vector and deviatoric strain, significant soil movement (within the influence zone [19]) around the retaining pile toe could be observed. This movement mainly occurred within an obliquely upward 45\({}^{\circ}\) zone, below which soil displacement decreased considerably. As a result, the blocking effects of the isolation piles diminished when the pile head depth exceeded 25 m. At this point, the maximum horizontal displacement of the soil approached that of a scenario without isolation piles, explaining why the control efficiency tends toward zero at such depths. Figure 15: Relationships between control efficiency and pile position (x = 9 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). Meanwhile, according to the numerical results, the vertical and horizontal displacements at various positions of the tunnel are presented in Figure 9:0 It is evident that these displacements vary significantly across the tunnel, suggesting that the tunnel's shape has deviated from its original circular geometry. Specifically, Figure 17 indicates that, regardless of the pile position, the maximum vertical displacements occurred near the tunnel crown, while the maximum horizontal displacements were observed near the tunnel waist. As shown in Figure 18, these critical locations were marked as points D and C, with additional points A and B selected to further illustrate the tunnel's deformation. The tunnel deformation has been amplified by a factor of 1600 to highlight the significant rotation and elongation of the tunnel towards the foundation pit following excavation. This phenomenon can help explain the observed discrepancies in the vertical and horizontal control efficiencies of the isolation piles. Figure 18b further illustrates that the trend in horizontal displacement of the soil for the case with x = 9 m closely mirrors that of the case with x = 2 m. However, the trend in control efficiency for these two cases differs significantly. This suggests that other factors may influence the control efficiency of the isolation piles. In addition to reducing  
Figure 9:1 Evolutions of the maximum horizontal displacement of soil at the isolation piles with the depth of the pile head for cases with x = 2 (**a**) and 9 m (**b**). Figure 9:2 Evolutions of vertical (**a**) and horizontal (**b**) displacement of the tunnel with the center angel (**a**). soil displacement, the isolation piles also affected the direction of soil movement, which played a crucial role in the development of tunnel deformation, particularly when the piles were situated near the tunnel. According to the numerical results, the directions of soil movement before and after excavation are presented in Figure 18c. As shown in the figure, as the depth of the pile head increased, the soil near the isolation piles moved in various directions: from the lower left to lower, from the lower left to upper left, and from upper left to left. These movements resulted in the tunnel shifting to the lower right, upper right, and lower right, respectively. At the same time, the tunnel's deformation was influenced by both the soil displacement at the isolation piles and the changing geometric shape of the tunnel. Consequently, the vertical control efficiency first decreased, then increased, decreased again, and finally increased as the pile head depth increased.