## 4 Deformation Characteristics of Site
### Ground Settlement Trough  
During shield tunneling, the ground settlement perpendicular to the tunnel axis tends to be the shape of a settlement trough with a large center and small sides. The method suggested by [PERSON] [1] is widely used to predict ground settlement trough in tunnel construction, and its typical expression [3] is shown in Formulas (1)-(3):  
\[\mathrm{S}(x)=S_{max}exp\left[\frac{-x^{2}}{2i^{2}}\right] \tag{1}\]\[S_{max}=\frac{V_{s}}{\sqrt{2\pi i}} \tag{2}\]  
\[V_{s}=\frac{V_{I}\pi D^{2}}{4} \tag{3}\]  
in which S(x) presents the ground settlement value at the monitoring point, \(x\) is the horizontal distance between the monitoring point and tunnel axis, \(V_{I}\) is the volume loss rate of the stratum, and \(i\) is the transverse profile inflexion distance. Figure 7a shows the measured ground settlement of three monitoring sections caused by the tunneling of the right tube, as well as the corresponding curves fitted by Formula (1). As shown in Figure 7a, the ground settlements are symmetrical to the tunnel axis in the form of a normal distribution, which conforms to the description of Formula (1), except that the value of parameters in Formula (1) are different. At section A, the maximum ground settlement (\(S_{max}\)) is 7.95 mm, \(i\) is 11.65 m, and \(V_{I}\) is 0.75%. At section B, \(S_{max}\) is 6.98 mm, \(i\) is 10.89 m, and \(V_{I}\) is 0.62%. At section C, \(S_{max}\) is 9.01 mm, \(i\) is 10.48 m, and \(V_{I}\) is 0.76%. In other words, \(V_{I}\) in this project ranges from 0.62% to 0.76% during shield tunneling. Figure 7b shows the development of ground settlement trough at section C during the construction of parallel twin tunnels. As shown in Figure 7b, ground settlement increases gradually with the former shield tunneling of the right tube; when the excavation of the right tube is completed, the ground settlement trough is symmetrical to the axis of the right  
Figure 7: Ground settlement trough. (**a**) Ground settlement trough of the right tube; (**b**) Development of transverse ground settlement trough at section C; (**c**) final ground settlement curve at section C.  
tube. Then, with the subsequent shield tunneling of the left tube, the ground settlement further increases, and the position of the maximum settlement moves to the left tube. After the completion of the double-tube construction, the ground settlement trough is approximately in a normal distribution, and the maximum ground settlement lies in the area between the two tubes. Figure 7c gives the final ground settlement at section C and the fitting curve from Formula (1), which demonstrates that the ground settlement caused by the double tunneling is a U-shaped settlement trough. After excavation, the maximum ground settlement is 13.87 mm, and the transverse profile inflexion distance is 15.94 m. In order to reveal the disturbance of shield tunneling to the site, the ground settlement trough induced by the shield tunneling of the left tube (\(S_{left}\)) is also shown in Figure 7c. The value of \(S_{left}\) is of the residual settlement after deducting the ground settlement induced by the former excavation of the right tube (\(S_{right}\)) from the total ground settlement (\(S_{total}\)), i.e., \(S_{left}=S_{total}-S_{right}\). It can be seen that the maximum ground settlement induced by the shield tunneling of the left tube is 9.68 mm, which is larger than that induced by the former excavation of the right tube. The transverse profile inflexion distance caused by the shield tunneling of the left tube is 10.21 m, which is slightly smaller than that caused by the former excavation of the right tube. The volume loss rate of the stratum caused by the shield tunneling of the left tube is 0.80%, which is higher than that caused by the former excavation of the right tube. These results demonstrate that the former excavation of the right tube disturbs the surrounding strata, which leads to an increase in stratum loss and in ground subsidence during the shield tunneling of the left tube.