# Research on Lateral Deformation Control Criteria of Metro Shield Tunnels with Excessive Ellipticity
## 5 Conclusions  
This study evaluates damage emergence and reinforcement of a case with significant lateral deformation in the Guangzhou Metro. It also suggests structural safety limits for the ellipticity, drawing from a three-dimensional refined finite-element model analysis of the shield tunnel segment. The following conclusions are drawn:  
1. The circular shield is most susceptible to cracking based on both observed cases and finite-element model loading results. This vulnerability is most visible from the inside, specifically within the arch. When the tunnel is located in a weak stratum, the arch's interior waist is more likely to experience joint compression collapse. The stratum conditions can significantly restrict the lateral deformation of the tunnel segment. 2. The variance in bolt stress across different surrounding rock conditions is minimal within the finite-element simulation. However, this difference underscores the deformation characteristics of the shield tunnel structure. The reinforcement ratio has a lesser effect on the bearing capacity of the entire ring compared to a single piece of the segment. Consequently, neither significantly impacts the segment's overall deformation trend or the establishment of deformation limit values. 3. The steel plate reinforcement technique proves highly effective in reinforcing shield tunnels with extensive elliptical variations. Monitoring data affirms that, post-reinforcement, the entire structure remains safe and stable during regular operations for an extended period. 4. Determining appropriate deformation limit values for varying external conditions of the shield tunnel is crucial. When integrated with real-world conditions, the Guangzhou Metro shield tunnel's ellipticity-based lateral deformation warning value is set at 20%, with the control value at 25%. The deformation control value should be adjusted based on the criteria above if the tunnel lies within a hard soil layer. \begin{table}
\begin{tabular}{c c} \hline
**Control Level** & **Gauge** \\ \hline I & Normal service and good performance \\ II & Beginning of cracks and leaks in a working condition with micro-cracks \\ III & Cracks and leaks have further increased, requiring increased attention and \\  & health monitoring \\ IV & Further deterioration of structural cracking, severe leakage from adjacent \\  & rings, urgent need for reinforcement \\ V & The whole ring structure will start to yield, and the loaded stiffness will \\  & decrease significantly \\ \hline \end{tabular}
\end{table} 
Table 2: Safety and health status control levels of subway shield tunnels. \begin{table}
\begin{tabular}{c c c c c c} \hline
**Convergent Deformation** & **\textless{}30 mm** & **30–40 mm** & **40–55 mm** & **55–70 mm** & **70–85 mm** & **\textgreater{}85 mm** \\ \hline
**Ellipticity** & **\textless{}10\%** & **10–15\%** & **15–20\%** & **20–25\%** & **25–30\%** & **\textgreater{}30\%** \\ \hline \(k=5\) MPa/m & I & II & III & III & IV & IV, V \\ \(k=10\) MPa/m & I & II & III & III & IV & IV, V \\ \(k=20\) MPa/m & I, II & III & III & III & IV & V \\ \(k=30\) MPa/m & I, II & III & III & IV & V & V \\ \hline \end{tabular}
\end{table} 
Table 3: Corresponding levels of safety limits for lateral deformation in metro shield tunnels. **Author Contributions:** S.K. : conceptualization, review, and editing: J.C.: methodology and writing the original draft. ; Y.L. and Y.W. : data curation; H.Z. : software and validation. All authors have read and agreed to the published version of the manuscript. **Funding:** This research was funded by the Guangdong Provincial Key Laboratory of New Technology in Urban Rail Transit Engineering Construction (2017B030302009) and the Guangzhou Academician Expert Workstation (2021 CZX030). **Institutional Review Board Statement:** Not applicable. **Informed Consent Statement:** Not applicable. **Data Availability Statement:** Data are contained within the article.