## 6 Conclusions  
In this study, the performance of twin-line shield tunnel excavation below an existing multi-arch culvert bridge in close vicinity was analyzed through numerical analysis. The following conclusions are drawn.  
1. The lateral surface settlement caused by tunnel excavation follows a Gaussian distribution curve in areas outside the multi-arch culvert bridge, and the settlement is greater compared to the area beneath the arch culvert. The maximum settlement in these areas is approximately 9 mm. The ground improvement scheme employed in the engineering design involves high values of the ground deformation modulus and load-bearing capacity, which results in a relatively high overall stiffness of the multi-arch culvert bridge, making it less susceptible to the effects of tunnel excavation. The reinforcement measures of the foundation can be appropriately reduced to improve the economic benefits while ensuring safety.  
Figure 16: Transverse foundation settlement under different grouting pressures.  
Figure 15: Foundation settlement curves under different grouting pressures. (**a**) 1-hole; (**b**) 4-hole.  
2. Due to the varying deformation modulus of the soil on both sides of the multi-arch culvert bridge, the soil outside the foundation of the multi-arch culvert bridge is more affected by tunnel excavation. The deformation of the 1-hole at the edge of the steel corrugated pipes is more significantly influenced by the tunnel excavation. The transverse ground settlement trough exhibits an asymmetric distribution, with the maximum settlement trough shifting by approximately 5 m to the right tunnel. The later excavation of the right tunnel has a greater impact on the ground settlement compared to the earlier excavation of the left tunnel.
3. The range of influence of the ground disturbance extended approximately 7 m in front of the excavation face before the tunnel passed through. The range of ground disturbance decreased to 4-6 m in front of the excavation face after the tunnel passed through. Compared to the excavation face support pressure, the influence of grouting pressure on the ground is more significant. A reasonable grouting pressure can effectively control ground settlement. The foundation reinforced design with a high deformation modulus and high bearing capacity in this project resulted in relatively small settlement deformation caused by tunnel excavation, with the settlement of the multi-arch culvert bridge remaining within 2 mm. The chosen foundation reinforcement design appears to be reasonable.  
Some simplifications were applied to the establishment of the finite element model to solve the computational workload, which may affect the calculation results in this study. Field monitoring data should be collected for the verification of the analysis in a following study. Furthermore, the spatial effects of shield tunnel excavation can be further considered based on this study after validating the model with on-site monitoring data.  
Conceptualization, X.B. and X.C.; methodology, Z.B.; validation, J.S., S.W. and S.Y.; formal analysis, S.W.; investigation, Z.B.; data curation, Z.B.; writing--original draft preparation, S.W.; writing--review and editing, J.S., Z.B.; supervision, X.B.; project administration, X.C.; funding acquisition, X.B. All authors have read and agreed to the published version of the manuscript.  
This research was funded by the National Key R&D Program of China, grant number 2019 YFC1511104, the National Natural Science Foundation of China (Grant No. 52090084) and the Technical Innovation Foundation of Shenzhen, grant number JCYJ20220531101214031.  
Not applicable.  
Data availability Statement: Data are contained within the article.  
Author [PERSON] was employed by the company China Railway 22 nd Bureau Group Shenzhen Construction Co., Ltd. The remaining authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.