# Analysis of Shield Tunnels Undercrossing an Existing Building and Tunnel Reinforcement Measures
## 4 Model Validation
### Effect of Successive Excavation of Double Shield Tunnels on Displacements of Soil  
The vertical and lateral displacements of soil after the completion of the double shield tunnel excavation are shown in Figure 11. From Figure 11a, it can be found that the balance of soil stress was destroyed during the tunnel excavation, and the soil released stress to the excavation face, forming a \"bowl-shaped\" subsidence area above the excavation face and an \"inverted bowl-shaped\" uplift area below the excavation face. From Figure 11b, it can be found that due to the displacement of the soil above and below the tunnel in the direction of the tunnel, the soil outside the extrusion tunnel was displaced to both sides, making the lateral displacement of the soil in a \"butterfly shape\".  
The top of the tunnel vault was where the maximum subsidence of the soil was during the excavation of double shield tunnels. The cross-section in the middle of the model was selected to explore the law of subsidence of soil above the double tunnels. Figure 12 shows the subsidence of the soil at the plane directly above the tunnel. It can be found that the subsidence of soil on the left and right sides of the centerline of the double tunnels was basically symmetrically distributed, which was basically consistent with the conclusion in reference [28]. The maximum subsidence of the soil in reference [28] was close to 12 mm. From Figure 12, it can be seen that the maximum subsidence of the soil in this article was close to 17 mm. This is because there were no buildings above the shield tunnels in reference [28], while there was an existing building above the shield tunnels in this article. The gravity of the existing building will further increase the soil subsidence caused by tunnel excavation. The subsidence curve of soil above the tunnel with the distance from the center line shows the \"M\" shaped distribution. The two maximum subsidence of soil were located directly above the two tunnels. As the distance from the center line got closer, the subsidence of soil gradually reduced. This was due to the fact that the excavation of the double shield tunnels caused the surrounding soil to squeeze, causing the surrounding soil to have a tendency to converge towards the centerline of the tunnels.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline \begin{tabular}{c} **Monitoring** \\ **Points** \\ \end{tabular} & \begin{tabular}{c} **Measured** \\ **Results (mm)** \\ \end{tabular} & \
\begin{tabular}{c} **Simulation** \\ **Results (mm)** \\ \end{tabular} &
\begin{tabular}{c} **Deviation** \\ **Percentage** \\ \end{tabular} \\ \hline
1 & \(-1.89\) & \(2.06\) & \(0.17\) & \(8.99\%\) \\
2 & \(-6.28\) & \(-6.59\) & \(0.31\) & \(4.94\%\) \\
3 & \(-6.71\) & \(-6.97\) & \(0.26\) & \(3.87\%\) \\
4 & \(-6.75\) & \(-6.88\) & \(0.13\) & \(1.93\%\) \\
5 & \(-7.05\) & \(-6.93\) & \(0.12\) & \(1.70\%\) \\
6 & \(-6.87\) & \(-7.11\) & \(0.24\) & \(3.49\%\) \\
7 & \(-6.51\) & \(-6.22\) & \(0.29\) & \(4.45\%\) \\
8 & \(-2.27\) & \(-2.08\) & \(0.19\) & \(8.37\%\) \\ \hline \hline \end{tabular}
\end{table}
Table 2: Comparison of simulation and measured results.  
Figure 11: Nephogram of soil displacements after the completion of double shield tunnel excavation: (**a**) vertical displacement of soil during excavation of double shield tunnels; (**b**) lateral displacement of soil during excavation of double shield tunnels.  
Figure 12: Curve of the subsidence of soil layer directly above double shield tunnels for successive excavation.  
Effect of Successive Excavation of Double Shield Tunnels on Displacements and Internal Forces of Segment