## 4 Conclusions  
In this paper, the finite element strength-reduction method, which is widely used in slope stability analysis, was introduced into the stability study of tunnel excavation. The arch cover method was selected as the representative excavation method. For the damage characteristics of a tunnel-group, the safety factors of the tunnels after excavation of the areas 1, 3, and 5 were selected for the study. The calculated conditions refer to the moment when the excavation of each part is completed but before it is supported. The following conclusions were drawn from the present study.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Working Condition** & **Safety Factor** & **Instability Form** & **Increase Value** \\ \hline Excavation area 1 & 1.83 & Partial collapse of the roof & 9.80\% \\ Support area 1 & 2.01 & / & \\ \hline Excavation area 3 & 1.20 & Side wall collapse & 12.50\% \\ Support area 3 & 1.35 & / & \\ \hline Excavation area 5 & 1.41 & Partial collapse of the roof & 1.40\% \\ Support area 5 & 1.43 & / & \\ \hline \hline \end{tabular}
\end{table}
Table 2: Safety factor, form of instability, and increased value after support.  
When the finite element strength-reduction method was used for the analysis of the stability of the surrounding rock, a judgment method based on the convergence of the finite element calculation could be adopted, since the non-convergence is associated with either local instability of the rock surrounding the excavation area or overall instability of the rock of the connected plastic zones.  
For the form of instability under each working condition, designers should carefully select the crossing stratum of the tunnel vault and pay attention to the pre-reinforcement of the surrounding rock of the vault before construction. Pre-reinforcement approaches may include expanding the scope of the reinforcement area or increasing the reinforcement strength.  
For a large-span concealed tunnel, the initial support should be implemented in time. After the arch is excavated, the initial support of the section should be closed early.  
For this tunnel-group metro station, excavating in area 3 was the most dangerous construction step. The application of initial support in each excavation step will increase the safety factor of the surrounding rock to different degrees.  
There is no doubt that the SRM has wide applicability, and the results obtained in this case were only used for special tunnel structures. In the future, additional analyses are planned to perform sensitivity calculations on the model parameters. In addition, it is planned to analyze the seismic response of the tunnel-group metro stations during their operational period.  
Conceptualization, Q.L. and Y.Y.; Investigation, W.H. and X.G.; Methodology, Q.L. and J.Z.; Project administration, W.H. and X.G.; Validation, R.L. and X.Y.; Writing--original draft, R.L.; Writing--review & editing, X.Y., Y.Y. and J.Z. All authors have read and agreed to the published version of the manuscript.  
This research was funded by the Ministry of Science and Technology of China (grant No. 2021 YFE0114100) and by the Federal Ministry of Education, Science and Research (BMBWF) of Austria (grant No. CN11/2021), jointly provided for the project \"Intense Upgrades of the New Austrian Tunnelling Method (NATM) and Demonstration of its Applicability to High-Quality Urban Development\". In addition, the authors were indebted to the National Natural Science Foundation of China (grant No. U1934210) and the Science and Technology Commission of Shanghai Municipality (grant No. 21 DZ1203505) for financial support of this work.  
Not applicable.  
The datasets generated and/or analyzed during the current study are available from the corresponding author upon reasonable request.  
The authors declare no conflict of interest.