## 4 Results and Analyses
### Settlement of Ground Surface  
During construction, the additional soil stress caused by the excavation of the following tunnel is transmitted through the ground movements and thus affects the stability of the preceding tunnel. Therefore, in order to understand the twin tunnels' interactions, it is important to investigate the ground surface settlement (vertical downward displacement at the ground surface), and especially, ground movements between the twin tunnels [4; 20; 38; 39]. Figure 5 shows the settlement of the ground surface at the transverse monitoring section under different scenarios. Figure 5a shows the surface settlements for the ring reinforcement of the right tunnel (RR). It can be clearly seen that the surface settlement profile is asymmetric but still approximately conforms to Peck's curve. An asymmetric profile of the settlement has also been observed through field measurements at shield tunneling sites [37]. The maximum settlement, \(S_{\max}\), is 35.78, 32.60, 30.30, 28.66, 27.54, and 26.95 mm for \(t\) = 0.0 \(D\), 0.05 \(D\), 0.10 \(D\), 0.15 \(D\), 0.20 \(D\), and 0.30 \(D\), respectively. When \(t\) = 0.30 \(D\), the \(S_{\max}\) is reduced by about 24.6% compared with the case of \(t\) = 0.0 \(D\), indicating that the RR has some effect on decreasing the surface settlement. Figure 4: Comparison between numerical and analytical results [37]. The surface settlement for the cases with the ring reinforcement of the left tunnel (LR) and the twin tunnels (TR) are shown in Figure 5b,c. The shapes and values of two sets of profiles are relatively close. During the excavation process of the following tunnel, the accumulated ground loss was mainly caused by the following tunnel, and the stress release zone was concentrated around the following tunnel. Therefore, the LR could effectively hinder the transmission of soil stress and reduce the disturbance to the ground surface. It suggests that the reinforcement of the following tunnel plays a more important role in surface settlement, while the reinforcement of the preceding tunnel plays an auxiliary role. When \(t\) is relatively small (\(t<0.10\)\(D\)), the surface is subject to settlement. However, with the increase in \(t\) (\(t>0.10\)\(D\)), the surface starts to heave. This is because the stiffness and thickness of the reinforcement layer are relatively large, and the accumulated ground loss caused by excavation of the following tunnel is small, but the rebound of the soil layer due to the release of soil stress is relatively large. In Figure 5b, \(S_{\text{max}}\) is 35.78, 16.25, 2.45, 2.81, 3.38, and 3.49 mm for \(t=0.0\)\(D\), 0.05 \(D\), 0.10 \(D\), 0.15 \(D\), 0.20 \(D\), and 0.30 \(D\), respectively. When \(t=0.30\)\(D\), the \(S_{\text{max}}\) is reduced by about 90.2% compared with the case of \(t=0.0\)\(D\). The degree of impact by the TR is similar. The results indicate that the LR and TR can play a significant role in reducing surface settlement. Figure 5d shows the surface settlement for the cases with cement wall reinforcement (CR). It is seen that the left and right sides of the settlement curve are not symmetrical with respect to the symmetrical axis of the left tunnel. The CR has blocked the transmission of the soil displacement caused by the loss of soil layer around the following tunnel, but the heaving of soil due to stress release during excavation of the following tunnel still  
Figure 5: Settlement of ground surface at the transverse monitoring section: (a) RR; (b) LR; (c) TR; (d) CR. propagates to the right side of the wall reinforcement. This results in having of the ground surface on the right. However, the accumulated loss of the soil layer still causes a certain surface settlement on the left side of the wall reinforcement. Generally, with the increase in \(t\), the ground settlement has not changed significantly. The \(S_{\text{max}}\) is 35.78, 39.81, 32.09, 30.26, 29.68, and 29.28 mm for \(t=0.0\)\(D\), 0.05 \(D\), 0.10 \(D\), 0.15 \(D\), 0.20 \(D\), and 0.30 \(D\), respectively.