## 5 Conclusions  
In this paper, the effects of geometric factors such as buried depth, curve angle and curve radius on the seismic response of a small-radius curved tunnel are discussed by using response surface methodology (RSM) through experimental design and finite element simulation calculation. The displacement and acceleration of the small-radius curved tunnel under seismic excitation are modelled as a function of the corresponding geometrical parameters by means of the RSM. Based on this model, a MOD approach is used to study the optimal geometric parameter configuration of the small-radius curved tunnel. The main conclusions thus obtained are as follows.  
1. The buried depth of the small-radius curved tunnel is the most important factor affecting displacement. When the buried depth increases, the displacement response of the small-radius curved tunnel under seismic excitation decreases, while the displacement response of the curved tunnel increases slightly as the angle increases. For point A of the small-radius curved tunnel, the angle of the curved tunnel and the radius of the curve do not offer significant implications for the displacement response. For point B of the small-radius curved tunnel, the effect of curve angle on the displacement response is more significant, while the effect of curve radius on the displacement response is not significant. As the buried depth increases, the displacement response of the small-radius curved tunnel under seismic excitation decreases, while the displacement response of the curved tunnel increases slightly as the angle increases.
2. The buried depth of the small-radius curved tunnel is the key parameter affecting the acceleration response values. For point A of the small-radius curved tunnel, the radius of the curve has a significant effect on the acceleration response values and the angle of the curve does not offer significant implications for the acceleration response values. The minimum acceleration is obtained when both the buried depth and the radius of the curve are taken to be the minimum values. For point B of the small-radius curved tunnel, the effect of curve angle on the acceleration response value is slightly significant and the implication of curve radius on the acceleration response is not significant. As the buried depth increases, the overall acceleration response of the small-radius curved tunnel under seismic excitation tends to increase, with the minimum value of the acceleration response occurring around the minimum point of the buried depth, and the minimum acceleration is obtained when the buried depth is taken to be the minimum and the curve angle is taken to be the maximum.
3. The optimum geometric parameter configuration for the small-radius curved tunnel can be obtained by taking the maximum buried depth, the maximum curve angle and the maximum curve radius within the domain.  
Conceptualization, methodology, X.F, Y.X. and F.Y.; software, Y.X., S.L. and F.Y.; validation, Y.X., S.L. and F.Y.; formal analysis, Y.X. and S.L.; investigation, Y.X.; resources, funding acquisition, S.L. All authors have read and agreed to the published version of the manuscript.  
This research was funded by the Natural Science Research of Higher Education Institutions in Jiangsu Province, China (grant number 18 KJB560001). Changzhou Leading Innovative Talents Introduction and Cultivation Project (grant number CQ20220100).  
**Informed Consent Statement:** Not applicable.  
**Data Availability Statement:** The results presented in this study are available on request from the corresponding author. The data are not publicly available due to the reason that the authors are conducting further analysis on the same structural model.  
**Conflicts of Interest:** The authors declare no conflict of interest.