## 4 Conclusions  
Three centrifugal model tests have been conducted to investigate the mechanical characteristics of the mainline tunnel influenced by different types of lateral openings under different buried depths. There are three types of the opening, namely, rectangular opening, small circular opening, and big circular opening. External earth pressures, structural deformations, dislocations, and structural stresses were monitored during the tests. The main conclusions are as follows.  
1. The vertical earth pressures on the tunnel vault demonstrated that the soil arching effect occurred in the overlying soil. The reduction coefficients of the actual pressure to the theoretical pressure were obtained for different buried depths, namely, 0.926, 0.796, and 0.74 for 1.0 D, 1.5 D, and 2.0 D, respectively, which can provide a reference for the structural design or theoretical analysis. The lateral pressure coefficients changed barely with the buried depth, which is because in the scaled model test, the lateral expansion displacement of the tunnel is limited, and the increase of the lateral passive earth pressures can be neglected.
2. The vertical deformation of the mainline tunnel increased with the size of the opening. For the big circular opening, the vertical deformation ratio to the diameter reached 3.86% under the buried depth of 2.0 D and 50 g acceleration, and may even exceed the limit (4%) specified in the specification. Thus, temporary support methods should be adopted during the construction of the cross passages.
3. The dislocations between the semi-split ring and the adjacent rings also increased with the opening size. The dislocations close to the three openings all exceeded 5 mm when the buried depth reached 2.0 D. As excessive locations between segments may cause waterproof failure, the longitudinal connections should be enhanced in practical engineering to resist the trend of dislocations.
4. Significant stress concentration occurred close to the opening and was approximately limited in the opening rings. The larger the opening size, the more severe the stress concentration, and the greater the compressive stress at the inner surface. The inner compressive stresses at BC-Op-R0 are 31.7 MPa and 41.9 MPa under the buried depths of 1.5 D and 2.0 D, while 32.3 MPa at SC-Op-R0 under the buried depth of 2.0 D, which may exceed the limited strength of C60 concrete (27.5 MPa). Thus, higher-strength materials or other reinforcement measures should be adopted for segments around the openings.  
In summary, the lateral openings on the shield tunnel will increase the stresses and deformations of the structure, and the larger the opening, the more unfavorable is the influence. Therefore, targeted measures should be taken, such as temporary support, longitudinal connections, and high-strength materials near the openings.  
Conceptualization, P.L. and D.Y.; methodology, P.L.; software, P.L.; validation, W.L. and D.J.; formal analysis, P.L.; investigation, P.L. and W.L.; resources, M.L.; data curation, P.L.; writing--original draft preparation, P.L.; writing--review and editing, W.L.; visualization, D.J.; supervision, D.Y.; project administration, M.L.; funding acquisition, D.Y. All authors have read and agreed to the published version of the manuscript.  
This study was supported by the Key Project of High-speed Rail Joint Fund of National Natural Science Foundation of China under Grant No. U1834208.  
Not applicable.  
Data Availability Statement: The data presented in this study are available from the corresponding author upon request.  
The authors gratefully acknowledge financial support from the Key Project of High-speed Rail Joint Fund of National Natural Science Foundation of China under Grant No. U1834208.  
The authors declare no conflict of interest.