## 4 Influenced Zone of Deep Excavation on Adjacent Tunnel Displacement
### Effects of \(H_{\rm e}\) and \(\delta_{\rm 1m}\) on the Scope of Influenced Zone  
Figure 10 shows the effect of \(H_{\rm e}\) on \(M\), \(N_{1}\) and \(N_{2}\). It is observed from Figure 10a when the maximum retaining wall deflection and the tunnel displacement control standards are constant, \(M\) has a trend towards increasing linearly with \(H_{\rm e}\), i.e., the deeper of excavation, the wider the influenced zone obtained. It is observed from Figure 10b, \(H_{\rm e}\) has no obvious effect on \(N_{1}\), and \(N_{1}\) varies between 1-2 with an average of about 1.5. It is observed from Figure 10c that when the maximum retaining wall deflection and the tunnel displacement control standards are constant, \(N_{2}\) has a trend towards increasing linearly with \(H_{\rm e}\), and this trend is more obvious when the tunnel displacement control standards are 20 mm and 10 mm. Figure 11 shows the effect of \(\delta_{\rm 1m}\) on \(M\), \(N_{1}\) and \(N_{2}\). It is observed from Figure 11a that when the excavation depth and the tunnel displacement control standards are constant, \(M\) a the trend towards increasing linearly with \(\delta_{\rm 1m}\), i.e., the deeper of excavation, the deeper the influenced zone obtained. It is observed from Figure 11b that the effect of \(\delta_{\rm 1m}\) on \(N_{1}\) has no obvious rule, and \(N_{1}\) varies between 1-2 with an average of about 1.5. It is observed from Figure 11c that when the excavation depth and the tunnel displacement control standards are constant, \(N_{2}\) has a trend toward increasing linearly with \(\delta_{\rm 1m}\). \begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \multirow{2}{*}{\(H_{\rm e}\) (m)} & \multirow{2}{*}{\(\delta_{\rm 1m}\) (mm)} & \multicolumn{4}{c}{**20 mm**} & \multicolumn{4}{c}{**10 mm**} & \multicolumn{4}{c}{**5 mm**} \\ \cline{3-10}  & & \(M\) & \(N_{1}\) & \(N_{2}\) & \(M\) & \(N_{1}\) & \(N_{2}\) & \(M\) & \(N_{1}\) & \(N_{2}\) \\ \hline \multirow{3}{*}{\(H_{\rm e}\) = 18 m} & 0.18\%\(H_{\rm e}\) & 0.60 & 1.30 & 1.75 & 1.35 & 1.30 & 2.35 & 2.15 & 1.50 & 3.30 \\  & 0.3\%\(H_{\rm e}\) & 0.90 & 1.25 & 1.80 & 1.45 & 1.35 & 2.40 & 2.30 & 1.50 & 3.40 \\  & 0.7\%\(H_{\rm e}\) & 1.15 & 1.25 & 2.00 & 1.75 & 1.35 & 2.50 & 2.55 & 1.50 & 3.45 \\  & 0.18\%\(H_{\rm e}\) & 0.50 & 1.40 & 1.60 & 1.10 & 1.30 & 2.20 & 1.90 & 1.75 & 3.30 \\ \multirow{3}{*}{\(H_{\rm e}\) = 15 m} & 0.3\%\(H_{\rm e}\) & 0.80 & 1.20 & 1.80 & 1.20 & 1.30 & 2.30 & 2.00 & 1.60 & 3.40 \\  & 0.7\%\(H_{\rm e}\) & 1.10 & 1.30 & 2.00 & 1.50 & 1.50 & 2.50 & 2.30 & 1.80 & 3.40 \\  & 0.18\%\(H_{\rm e}\) & — & — & — & 1.00 & 1.50 & 2.10 & 1.75 & 1.75 & 3.30 \\ \multirow{3}{*}{\(H_{\rm e}\) = 12 m} & 0.3\%\(H_{\rm e}\) & 0.70 & 1.30 & 1.75 & 1.10 & 1.60 & 2.25 & 1.75 & 2.0 & 3.40 \\  & 0.7\%\(H_{\rm e}\) & 0.85 & 1.40 & 1.80 & 1.20 & 1.50 & 2.30 & 2.00 & 1.75 & 3.40 \\ \multirow{3}{*}{\(H_{\rm e}\) = 9 m} & 0.18\%\(H_{\rm e}\) & — & — & — & 0.75 & 1.30 & 1.70 & 1.250 & 1.50 & 3.10 \\  & 0.3\%\(H_{\rm e}\) & — & — & — & 0.90 & 1.50 & 2.10 & 1.30 & 1.60 & 3.20 \\ \multirow{3}{*}{\(H_{\rm e}\) = 9 m} & 0.7\%\(H_{\rm e}\) & — & — & — & 1.00 & 1.60 & 2.10 & 1.30 & 1.75 & 3.20 \\ \hline \end{tabular}
\end{table} 
Table 3: Determination parameters of influenced zones under different simulation conditions. Prediction Method of Influenced Zone under any \(H_{\rm e}\) and \(\delta_{\rm hm}\) Conditions  
As described above, the determination parameters, \(M\) and \(N_{2}\), of the influenced zone have a linear relationship with \(H_{\rm e}\) and \(\delta_{\rm hm}\); \(N_{1}\) is less affected by \(H_{\rm e}\) and \(\delta_{\rm hm}\) and varies between 1-2 with an average of about 1.5, so it can be taken a constant. Based on these conclusions, a method for predicting the scope of the influenced zone under any \(H_{\rm e}\) and \(\delta_{\rm hm}\) conditions is proposed through linear interpolation, as shown in Figure 12.  
The prediction process can be described as follows.