## 5 Conclusions  
This paper establishes a foundation pit sidewall deformation prediction model that takes the ratio of the cumulative maximum deformation of the enclosure structure to the excavation depth \(v_{\rm max}/d\) as the control parameter. The soil displacement caused by sidewall deformation is calculated based on the virtual image technique. Meanwhile, the collaborative deformation model considering the rotating and dislocation of the shield tunnel is used to establish a calculation method of the horizontal displacement of a shield tunnel adjacent to a foundation pit. Additionally, the case verification and influencing factor analysis were carried out, and the following conclusions have been obtained.  
1. The method of calculation in this paper has the advantage of making full use of onsite monitoring data, solving the problem that the size of sidewall unloading could not be verified in the past, and the calculation is relatively simple. The calculated values are in good agreement with the measured data, and the curve of horizontal displacement of the shield tunnel beside a foundation pit shows a normal distribution. The method of calculation in this paper can be used to evaluate the safety status of adjacent tunnels before excavation of the foundation pit.
2. The horizontal displacement of the adjacent shield tunnel near the center of the excavation of the foundation pit is relatively large, but the amount of dislocation between the segments and the relative rotation angle is slight; the maximum inter-ring rotation angle, the maximum dislocation amount, and shear force value between the segments all appear near the two inflection points of the horizontal displacement curve of the adjacent shield tunnel.
3. As the deformation of the enclosure structure, the effect value, and the scope of the longitudinal deformation of the side shield tunnel also increase, the longitudinal deformation of the side shield tunnel decreases nonlinearly with the distance between the axis of the shield tunnel and the enclosure structure increases; the excavation of the foundation pit has a more significant influence on an adjacent shield tunnel with a shallower buried depth. The influence diminishes gradually as the buried depth of the side shield tunnel increases.  
In this paper, several simplifications have been made in the analysis process. For example, the influence of tunnels, precipitation, layering of the foundation soil, the nonlinear effect of the tunnels and soil is not considered, and the nonuniformity of soil convergence is also neglected. The theoretical results may contain certain errors that can be studied further.  
Figure 20: The calculated curve of the maximum horizontal displacement of the shield tunnel by the side of the foundation pit changing with \(h\).  
**Author Contributions:** Conceptualization, Z.W. and B.G.; methodology, G.W.; software, B.G.; validation, D.Y., B.G. and G.W.; formal analysis, D.Y.; investigation, C.H.; data curation, Z.W.; writing--original draft preparation, D.Y.; writing--review and editing, B.G.; visualization, Z.W.; supervision, B.G.; project administration, D.Y.; and funding acquisition, Z.W. and G.W. All authors have read and agreed to the published version of the manuscript.  
This research was funded by the Basic Public Welfare Research Projects in Zhejiang Province (LGF22E080012), the General Scientific Research Projects for Agriculture and Social Development in Hangzhou (grant number 20201203B127), and the Joint Fund of Zhejiang Natural Science Foundation Committee and Power China Huadong Engineering Corporation (grant number LHZ19E090001).  
**Institutional Review Board Statement:** Not applicable.  
**Informed Consent Statement:** Not applicable.  
**Data Availability Statement:** Not applicable.  
**Acknowledgments:** We would like to thank [PERSON] for the support in obtaining the engineering cases.  
**Conflicts of Interest:** The authors declare no conflict of interest.