## 4 Influenced Zone of Deep Excavation on Adjacent Tunnel Displacement
### Verification by Comparing with the Results in Case Histories  
A total of 42 case histories were collected to study the effect of deep excavation on the adjacent tunnel [7]. Due to the limitation of field monitoring data, few case histories contain displacements of both deep excavation and existing tunnels. Therefore, only Cases 1-3 are chosen as representatives to verify the proposed method. In these 3 case histories, the strata are silty clay and muddy clay, which have similar properties to the soil conditions of silty clay adopted in this study. The supporting structures are the diaphragm wall and horizontal struts, which are consistent with the simulation conditions adopted in this study. The form of the existing tunnel is a subway shield tunnel with a diameter of 6.2 m, which \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Strata** & \(\omega\) **(\%)** & \(e\) & \(\gamma\) **(kN/m3)** & \(c\) **(kPa)** & \(\varphi\) **(\({}^{\circ}\))** & \(I_{\mathbf{P}}\) & \(E_{\mathbf{s}}\) **(MPa)** \\ \hline \hline
1�1 & — & — & 18.5 & 6 & 15 & — & — \\
1�2 & 30.1 & 0.86 & 19.1 & 15 & 12 & 16.0 & 4.95 \\
2�1 & 31.2 & 0.87 & 19.1 & 15 & 16 & 16.6 & 4.46 \\
3�2 & 38.4 & 1.07 & 18.1 & 12 & 15 & 15.2 & 3.27 \\
3�3 & 36.3 & 1.05 & 18.2 & 11 & 18 & 13.8 & 3.48 \\
4�4 & 30.3 & 0.86 & 18.8 & 8.2 & 31 & — & 11.56 \\
5�5 & 25.1 & 0.77 & 19 & 8.3 & 32 & — & 14.36 \\ \hline \hline \end{tabular} Note: \(u\)—water content, \(e\)—porosity ratio, \(\gamma\)—unit weight, \(c\)—cohesive force, \(\varphi\)—internal friction angle, \(I_{\mathbf{P}}\)—plasticity index, \(E_{\mathbf{s}}\)—compression modulus.  
\end{table} 
Table 6: Physical and mechanical parameters of strata at the site. Figure 13: Comparison of the predicted influenced zone with the results in current research: (**a**) \(H_{\mathrm{e}}\) = 18 m, \(\delta_{\mathrm{hm}}\) = 30 mm; (**b**) \(H_{\mathrm{e}}\) = 18 m, \(\delta_{\mathrm{hm}}\) = 45 mm; (**c**) \(H_{\mathrm{e}}\) = 18 m, \(\delta_{\mathrm{hm}}\) = 60 mm [27]. is also basically consistent with the simulation conditions in this study. Therefore, it is reasonable to use them for verification. In Case 1 [41], \(H_{\text{e}}\) = 21.1 m, \(\delta_{\text{hm}}\) = 53 mm = 0.25%\(H_{\text{e}}\), \(H_{\text{t}}\) = 17.5 m, and \(L_{\text{t}}\) = 10 m. According to the prediction process of the influenced zone in Figure 12, the referenced depth range [15 m, 18 m] and the referenced displacement range [0.18%\(H_{\text{e}}\), 0.3%\(H_{\text{e}}\)] are chosen for calculation. Figure 14a shows the predicted influenced zone and the actual position of the tunnel in the influenced zone. It can be seen that the tunnel is in the primary influenced zone, i.e., the excavation-induced tunnel displacement may exceed 20 mm. It is reported that no protection measures are taken for the tunnel during the adjacent excavation, and the maximum horizontal displacement and settlement of the tunnel are 27 mm and 33 mm, respectively; after excavation is completed, both have exceeded the displacement control thresholds of 20 mm, which is consistent with the predicted results. In Case 2 [42], \(H_{\text{e}}\) = 15.9 m, \(\delta_{\text{hm}}\) = 54 mm = 0.34%\(H_{\text{e}}\), \(H_{\text{t}}\) = 19.1 m, and \(L_{\text{t}}\) = 10.3 m. According to the prediction process of the influenced zone in Figure 12, the referenced depth range [15 m, 18 m] and the referenced displacement range [0.3%\(H_{\text{e}}\), 0.7%\(H_{\text{e}}\)] are chosen for calculation. Figure 14b shows the predicted influenced zone and the actual position of the tunnel in the influenced zone. It can be seen that the tunnel is in the primary influenced zone, i.e., the excavation-induced tunnel displacement may exceed 20 mm. It is reported that no protection measures were taken for the tunnel during the adjacent excavation, and the maximum horizontal displacement and settlement of the tunnel were 50 mm and 100 mm.