## 5 Analysis of Numerical Results  
Due to the lack of on-site monitoring data on deep strata and the internal force of tunnel segments in shield tunneling in the project, a numerical simulation was employed as a supplement. The detailed numerical modeling process can be seen in another article [26]. Figure 9 shows the ground settlement on section C formed by shield tunneling. It can be seen that the distribution pattern of the settlement curve obtained from numerical simulation is basically consistent with the monitoring data, whether it is induced by the former right tunneling or by the twin tunneling. Due to the simplification of the geological strata in numerical simulation, there is a slight difference between the measured and numerical values, but the difference between them is less than 1.0 mm. This result proves that the numerical model is correct and reasonable. Since we have analyzed the deep deformation characteristics of the site in reference [26], we only analyze the interaction between the twin tubes in shield tunneling in this section. Figure 10 shows the mechanical responses of the right tube induced by the shield tunneling of the left tube, in which Figure 10a presents the horizontal displacement change in the side wall of the right tube with the advance of the working face, and Figure 10b gives the change in circumferential stresses of the right tube. It can be seen from Figure 10a that the right tube has a displacement pointing to the left tube being excavated. As the working face moves forward, the displacement difference between the left wall and the right wall of right tube, i.e., the lateral convergence, becomes more and more obvious, and cannot remain  
Figure 8: The response of the right tube under shield driving in the left tube. (**a**) Heaving of the floor; (**b**) lateral convergence. In figures, the red line shows the trend of changes in the heaving of the floor or lateral convergence. stable until the working face is more than 2D in front of the monitoring point. Except for values smaller than those in the monitoring results, the change in lateral convergence of the tube is consistent with that in the field monitoring results shown in Figure 8b. As shown in Figure 10b, the circumferential stress at different positions of the right tube is different under the shield tunneling of the left tube. Taking point A as an example, when the working face reaches about 1D behind the monitoring point, the circumferential stress begins to increase, which is manifested as tensile stress with a maximum value of 30 kPa; when the working face reaches about 1D in front of the monitoring point, the circumferential stress begins to decrease, and when the working face reaches the front of the monitoring point at more than 1.5D, the circumferential stress maintains a stable value of about 20 kPa. The changes in circumferential stress at point B and point D are similar to that at point A except that they are forms of compressive stress. Point C is located at the bottom of the right tube, and the value of circumferential stress at the position fluctuates near zero with the advance of the working face. Shield tunneling will lead to the inconsistent deformation of the adjacent tunnel. Therefore, the lateral deformation ratio (abbreviated as LDR) is defined, as shown in Formula (4), by normalizing the horizontal displacement difference at two monitoring points by using the distance between them. \[\gamma_{i}=\frac{d_{i}-d_{i+1}}{L} \tag{4}\]  
where \(d_{i}\) and \(d_{i+1}\) are the lateral displacements of point \(i\) and of point \(i+1\) respectively. \(L\) is the distance between the two monitoring points; the value is taken as the width of a single segment in this article. Figure 11 shows the change in the LDR of the left wall of the right tube, which indicates that the LDR increases first, then decreases until it disappears with the advance of the working face, and decreases with the increase in the axis spacing of the twin tunnels.