## 7 Conclusions  
Based on the statistics of 44 case histories, 732 FEM numerical simulations are conducted to determine the influenced zone of deep excavation under different conditions of excavation depth (\(H_{\text{e}}\)) and the maximum retaining wall deflection (\(\delta_{\text{hm}}\)). On this basis, the effects of \(H_{\text{e}}\) and \(\delta_{\text{hm}}\) on the scope of the influenced zone are studied, and a prediction method for the scope of the influenced zone under any \(H_{\text{e}}\) and \(\delta_{\text{hm}}\) conditions is proposed. Then, the reliability of the proposed method is verified by comparing it with the current research and case histories. Finally, the proposed method is applied to an actual project, and the application effect is evaluated. The conclusions are as follows:  
1. The range outside the pit can be divided into: I (primary influenced zone), II (secondary influenced zone), III (general influenced zone), and IV (weak influenced zone), corresponding to the three-level tunnel displacement control standards of 20 mm, 10 mm, and 5 mm;
2. The influenced zone can be simplified as a right-angled trapezoid shape, and the isoline of tunnel displacement can be simplified as a polyline. By defining the coordinates of three points on the polyline: width coefficient \(M\), depth coefficients \(N_{1}\) and \(N_{2}\), the scope of the influenced zone can be quickly determined;
3. \(M\) and \(N_{2}\) basically have a linear relationship with the \(H_{\text{e}}\) and \(\delta_{\text{hm}}\), but \(N_{1}\) is less affected by \(H_{\text{e}}\) and \(\delta_{\text{hm}}\), and it can be taken as a constant of 1.5. Based on these relationships and the division results of the influenced zone under different simulation conditions, the scope of the influenced zone under any \(H_{\text{e}}\) and \(\delta_{\text{hm}}\) conditions can be determined by linear interpolation;
4. In practice, using the proposed method to predict the influenced zone of deep excavation and the excavation-induced tunnel displacement and then taking some control measures, the effect of deep excavation on the adjacent tunnel can be reduced, and the tunnel displacement can be kept within a reasonable range.  
Conceptualization, B.L.; methodology, B.L.; software, B.L.; validation, B.L.; formal analysis, B.L.; investigation, B.L.; resources, C.S. and N.W.; data curation, D.Z.; writing--original draft preparation, B.L.; writing--review and editing, D.Z.; visualization, B.L.; supervision, D.Z.; project administration, C.S. and N.W.; funding acquisition, C.S. and N.W. All authors have read and agreed to the published version of the manuscript.  
This work was supported by the National Natural Science Foundation of China (52208334), the Natural Science Foundation of Jiangsu Province (BK20220856), the China Postdoctoral Science Foundation (2021M690624), the Jiangsu Planned Projects for Postdoctoral Research Funds (2021K146B), and the Research Fund of Key Laboratory of Water Management and Water Security for Yellow River Basin, Ministry of Water Resources (2022-SYSJ)-07).  
Not applicable.  
The data presented in this study are available from the corresponding author upon request.  
The authors thank all reviewers for their great help in this article.  
The authors declare no conflict of interest.