## 4 Results and Discussion
### Verification of Numerical Simulation
#### 4.1.3 Verification  
The evolution of horizontal displacement of the retaining wall (monitoring point C1) with depth is presented in Figure 7. Positive horizontal displacement indicates movement toward the foundation pit. As shown in Figure 7, the predicted values from the numerical simulation closely align with the measured data. The maximum horizontal displacements occur at the bottom of the foundation pit.  
The evolution of horizontal displacement of the soil at a distance of 15 m from the excavation (monitoring point C2) with depth is presented in Figure 8. The results in Figure 8 show that the deformation curve under various excavation depths exhibits a \"cantilever\" shape, with the maximum displacement occurring near the shallow surface. When the excavation reached a depth of 2.9 m, the maximum horizontal displacement of the soil was approximately 9 mm. At a depth of 7.6 m, the maximum horizontal displacement increased to around 20 mm, and at 10 m, it further increased to 23 mm. Abnormal fluctuations are observed in the measured data at a depth of 5 m. This is likely due to the influence of the surrounding construction loads. From a global perspective, the finite element calculation results align reasonably well with the measured deformation curves. Additionally, it can also be observed in Figure 8 that the predicted horizontal displacement without isolation piles is obviously higher than that with isolation piles, indicating that the isolation piles effectively rest  
Figure 7: Evolutions of the horizontal displacement of the retaining wall (C1) and the depth.  
The evolution of both horizontal and vertical displacements of the tunnel with respect to the monitoring points is presented in Figure 9. Positive horizontal displacement indicates movement towards the foundation pit, while negative vertical displacement represents settlement of the tunnel. Overall, the predicted values from the numerical simulations are in good agreement with the measured data. However, notable fluctuations in both the horizontal and vertical displacements are observed, which are not captured by the numerical simulation. This discrepancy may be attributed to construction-induced disturbances and the uneven stiffness of the tunnel. Additionally, it can be observed in Figure 7 that the tunnel deformation without isolation piles is noticeably greater than that with isolation piles, further confirming the beneficial role of isolation piles in mitigating tunnel deformation. The underlying mechanisms of isolation piles are explored in the subsequent section.  
To quantitatively analyze the accuracy of the predicted results in Figures 5-7, the relationship between the predicted values and measure values is plotted in Figure 10, where the coefficient of determination (\(R^{2}\)) is calculated. An \(R^{2}\) value close to 1 means the model explains most of the variance in the measured data, suggesting a good fit.  
\[R^{2}=1-\frac{\sum(y_{m}-y_{p})^{2}}{\sum(y_{m}-y_{m-ave})^{2}} \tag{10}\]  
where \(y_{m}\) is the measured value, \(y_{p}\) is the predicted value, and \(y_{m-ave}\) is the average measured value.  
It can be observed that the fitting curve \(y=x\) could well simulate the scatter plots and the \(R_{2}\) value was 0.96, indicating the high accuracy of the model. Additionally, the number of elements was increased by 100%, and the maximum tunnel deformation changed by less than 3%, demonstrating that the current mesh resolution is sufficient to ensure the model's accuracy.  
Figure 8: Evolutions of the horizontal displacement of the soil at a distance of 15 m away from the excavation (C2) and the depth.