## 4 Analysis of the Field Measurement Data
### Analysis of the Monitoring Data  
#### 4.3.1 Vertical Displacement  
The researcher organized the vertical displacement values of the existing tunnel monitoring points at each construction stage. The monitoring of each point is impacted by factors like the accuracy of measuring instruments, the vibration of operating subway trains, and the error of manual retesting. Furthermore, some points are discrete, and adjacent monitoring points revealed the phenomenon of up-and-down vibration and jumping. For the regression of the monitoring points of each section, the researcher utilized polynomials to fit the data:  
\[y=intercept+B_{1}x^{1}+B_{2}x^{2} \tag{3}\]  
where \(intercept\) is the intercept coefficient and \(B_{1},B_{2}\) is the slope coefficient. The fitted curve is presented in Figure 10.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Stage** & **Construction Activity** & **Date** & **Remark** \\ \hline S1: Excavation and structural work at the shield’s initial well foundation pit. S2: The new tunnel passes above the existing tunnel. S3: The new tunnel intersects with the existing tunnel. S4: New tunnel left-line tunneling & Excavation of the foundation pit and construction of the structure. S5: October 2019 & There is a great disturbance to the existing line. S6: New tunnel right-line tunneling & There is a great disturbance to the existing line. S7: New tunnel right-line tunneling & There is a great disturbance to the existing line. S8: New tunnel right-line tunneling & There is a great disturbance to the existing line. S9: New tunnel right-line tunneling & There is a great disturbance to the existing line. S10: New tunnel right-line tunneling & There is a great disturbance to the existing line. In Figure 10, during the excavation stage of the foundation pit of the shield initial well, the up-line of the existing tunnel exhibits a settlement trend, with a large settlement in the middle and a small settlement at both ends, and a maximum settlement value of \(-1.35\) mm. This measurement result is consistent with those of [PERSON] et al. [59] and [PERSON] et al. [60], which indicated the same conclusion. After the new right-line shield tunneling, the existing tunnel as a whole uplifts and the middle of the up-line of the existing tunnel returns to its initial position after floating. One end of the tunnel floats, while the other end settles slightly. After the above-crossing tunneling of the left-line shield, the existing tunnel exhibits a trend of partial upward floating and partial settlement. Generally, floating occurs in the middle of the up-line of the existing tunnel, and the two ends return to their initial positions. When the final data converged to meet the requirements of the stop test, the  
Figure 10: Vertical displacement of existing tunnels subjected to multiple disturbances. (**a**) Vertical displacement of up-line ballast bed subjected to multiple disturbances (**b**) Vertical displacement of down-line ballast bed subjected to multiple disturbances. middle of the existing tunnel up-line uplifted, the maximum floating value was 3.35 mm, and the two ends returned to the initial position. This observed outcome aligns with the findings reported by [PERSON] et al. (2016). Vertical settlement occurred in the middle part of the down-line of the existing tunnel, and a slight uplift occurred at both ends during the excavation stage of the shield initial well. After the new right-line shield tunneling, the overall vertical displacement trend of the down-line remained consistent with the foundation pit excavation stage and did not change. After the above-crossing tunneling of the left-line shield, the middle part of the down-line was still in a slight settlement. However, the two ends changed significantly, from the original uplift to settlement. Considering that all the values were within the range \([-2,+2]\), the change was still not significant.