## 3 Engineering Case Analysis
### Case History 2  
There was a foundation pit adjacent to Hangzhou Metro Line 2 at Shixinzhong Road and Jincheng Road in Xiaoshan District. The plane excavation size of the foundation pit was \(L\) = 68 m, \(B\) = 72 m, with a 15.8-m excavation depth. The continuous underground wall penetrates 37.2 m below the ground. The minimum distance between the enclosure structure and the shield tunnel axis was \(s\) = 12.6 m [25]. The shield tunnel lining outer diameter was \(D\) = 6.2 m, using C50 concrete segments, a thickness \(t\) = 0.35 m, and ring width \(D_{\text{t}}\) = 1.2 m. Sixteen M30 longitudinal bolts connect the segment rings, according to the calculations \(k_{\text{sl}}\) = 2.23 \(\times\) 10\({}^{6}\) kN/m, \(k_{\text{t}}\) = 9.39 \(\times\) 10\({}^{5}\) kN/m, and \((EI)_{\text{eq}}\) = 1.1 \(\times\) 10\({}^{8}\) kN\(\cdot\)m\({}^{2}\). The tunnel axis was buried 14.3 m deep and was located in a layer of silt mixed with silt and sandy silt. Miscellaneous fill, silly clay, sandy silt, and silly sand are mainly distributed within the excavation area of the foundation pit. According to the actual engineering geology, the Poisson's ratio of soil \(\mu\) = 0.4, \(E_{\text{s}}\) = 6.39 MPa. In this foundation pit, the excavation process was divided into four layers of soil for layered excavation. The thickness of each layer from top to bottom was 1.6 m, 4.9 m, 4.8 m, and 4.5 m.  
Figure 9 shows the comparison between the value calculated and the data measured of the horizontal displacement of the adjacent shield tunnel. As Figure 9 shows, the calculated values are in reasonable agreement with measured data. The control parameter is \(v_{\text{max}}/d\) = 0.6% for the deformation of the enclosure structure in the calculation case. The rotation effect ratio coefficient of the adjacent shield tunnel \(j_{\text{x}}\) is 0.2. The horizontal displacement value of the adjacent shield tunnel is mainly negative in Figure 8, which means that the displacement is along the negative direction of the \(x\)-axis. The maximum horizontal displacement calculated is 11.46 mm, and the maximum value measured is 11.90 mm. The horizontal displacement presents a normal distribution. The horizontal displacement near the excavation center is relatively large, and it decreases successively on both sides. The length of the central uplift affected area of the tunnel is about twice the length of the enclosure structure along the tunnel axis. The values of the dislocation and rotation angles between the rings are essential to the security of the tunnel structure and waterproof system. The greater the rotation angle between the rings, the larger the opening of the ring seam. The probability of leakage in the shield tunnel will be significantly increased when the seam opening and dislocation values between the rings are large. Therefore, it is necessary to estimate the amount of  
Figure 8: Comparison of the calculated and measured values of the horizontal displacement of the tunnel beside the foundation pit in case 1.  
seam opening and dislocation between the rings. Figure 10 shows the calculated curve of the offset of the shield tunnel segments and rotation angle between the rings. It can be seen that the segment displacement and inter-ring rotation angle at the maximum horizontal displacement of the side tunnel corresponding to the excavation center of the foundation pit is close to 0, with almost no misalignment deformation and relative rotation deformation. The maximum misalignment amount of the segment is 0.24 mm, and the maximum ring-to-ring corner is \(5\times 10^{-5}\) rad. Refer to [PERSON] et al. [26] for the classification of the safety assessment level of the misalignment and corners. The corresponding evaluation level of the misalignment and corners is Level IV. There is a more significant potential safety hazard.