## 4 Numerical Simulation Verification and Discussion
### Analysis of Numerical Simulation Results  
In the process of model simulation operation, several typical working conditions are selected, as shown in Table 2.  
Figure 10 shows the stratigraphic subsidence diagrams under different working conditions. From Figure 10a-c, it can be seen that the ground settlement curve shows a single peak (\"V\" shape), while in Figure 10d-f, the ground settlement curve shows a double peak (\"W\" shape). Then, with the increase in tunnel excavation distance, the trend of the settlement curve becomes more and more obvious. The reason for this is that the impact of left tunnel excavation on the ground settlement is smaller than that of right tunnel excavation, and both of them interact with each other. Finally, the superposition of the ground settlement curve shows a bimodal shape [21]. With the increase in the tunnel excavation distance, the soil around the tunnel becomes subjected to increased force, and thus the settlement trend becomes larger and larger. Figure 11 shows the vertical deformation of the pipeline under different working conditions. As can be seen from the figure, under different working conditions, the trend of pipeline deformation is consistent, showing a \"single peak\": the middle section of the deformation is large, and the two ends are small. As the pipeline has a certain stiffness, it will produce a resisting moment so that the pipeline and the foundation between the complex deformation coordination achieve force balance when the pipeline deformation trend is similar to the soil settlement in the plane. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Working Condition** & \
\begin{tabular}{c} **Left Line Tunnel Shield** \\ **Tunneling Distance/m** \\ \end{tabular} &
\begin{tabular}{c} **Right Line Tunnel Shield** \\ **Tunneling Distance/m** \\ \end{tabular} \\ \hline Case1 & 1.2 & 0 \\ Case2 & 30 & 0 \\ Case3 & 60 & 0 \\ Case4 & 60 & 1.2 \\ Case5 & 60 & 30 \\ Case6 & 60 & 60 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Parameters of soil layers. Figure 10: Ground settlement for different working conditions: (**a**) Case 1; (**b**) Case 2; (**c**) Case 3; (**d**) Case 4; (**e**) Case 5; (**f**) Case 6. (1) In Case 1, the pipeline deformation value is 0. This is because before tunnel excavation, the pipeline maintains force equilibrium under the interaction of Earth pressure and the foundation reaction force, and the loss of stratum caused by Case 1 conditions and the additional stresses introduced by it are within the equilibrium range. However, with the increase in tunnel excavation distance, the force equilibrium state of the pipeline is destroyed, so force rebalance is realized by employing its deformation. Under Case 2 and Case 3 conditions, because the pipeline is far away from the left tunnel, its influence on pipeline deformation is limited, and the deformation value of the pipeline is below 2.2 mm, with a maximum difference of 1.2 mm. (2) In Cases 4, 5, and 6, the excavation of the left tunnel is completed and the excavation of the right tunnel is started, during which the deformation of the pipeline over 45 m in the longitudinal direction reaches its maximum value. Under Case 5 and Case 6, the maximum values of pipeline deformation are 5 mm and 9.25 mm, which are two and four times more than the maximum values of pipeline deformation under Case 3, respectively. [PERSON] et al. [22] found that with the shortening of the distance between the tubes and tunnels, the pipeline becomes more affected by shield tunnel excavation, and the shear force and bending moment of the pipeline will become larger, which will lead to a larger vertical deformation of the pipeline. Therefore, because the right tunnel is closer to the pipeline and it is affected by the distance between the tubes and tunnels, the vertical deformation of the pipeline caused by the shield machine in the process of right tunneling will be greater.