## 5 Conclusions  
The incident angle and SSI have a significant impact on site seismic response. Using the FEM and time-domain wave method, this study combined the analytical solution of the free-field seismic response of the soil when the SV wave is obliquely incident in the half-space with the VSAB. The numerical simulation of an SV wave with oblique incidence was realized by applying equivalent nodal loads on the boundary. The simulation technology can be used for the seismic response analysis of an SSI system. The rationality and accuracy of the simulation technique were verified using a free-field example. On this basis, a 3D FE model of a soil-immersed tunnel is established. Considering the coupling effect of static-dynamic load, the seismic response of the HZM immersed tunnel under an oblique incident SV wave was studied. The main conclusions of the simulation are as follows:  
1. The proposed method can effectively simulate the seismic response of engineering site under oblique incidence of the SV wave. This method can consider the impact of incident angle and SSI, which is useful for the seismic design of tunnel structures.
2. The oblique incident SV wave amplifies the vertical and longitudinal seismic responses of the structure, and the influence reaches maximum when the incident angle is close to the critical angle. Moreover, the oblique incident SV wave reduces the response frequency of the tunnel structure, making it closer to the natural frequency of the soil-tunnel system.
3. With an increase in the incident angle, the horizontal displacement and force of tunnel structure decrease and tend to be stable. The difference between the incident angle of \(15^{\circ}\) and \(30^{\circ}\) is small.
4. The oblique incidence of seismic wave causes the asymmetric shearing force in symmetric parts of the structure, resulting in the change of the shear bearing ratio in the shear key. The root of the shear key is prone to tensile cracks, and the end angle may also be partially damaged due to stress concentration. Therefore, the  
Figure 24: Tensile stress time history of the shear key: (**a**) shear key B; (**b**) shear key E.  
Figure 25: Compressive stress time history of the shear key: (**a**) shear key B; (**b**) shear key E.  
influence of oblique incidence of seismic waves should be considered in seismic design. Furthermore, attention should be paid to the configuration of anti-crack reinforcement at the connection between the shear key and immersed segment and the structural optimization of the end angle of shear key.
* Further improvements of the factors (e.g., the oblique incidence direction parallel to the \(y\)-\(z\) plane and multilayered foundation) will be investigated to establish a more general model and obtain more accurate results.  
Conceptualization: C.H.; methodology, C.H.; validation, C.H. and G.X.; formal analysis, C.H.; investigation, Z.Z.; resources, Z.Z.; data curation, C.H.; writing--original draft preparation, C.H.; writing--review and editing, C.H.; visualization, C.H. and W.L.; supervision, G.X.; project administration, G.X.; funding acquisition, W.L. All authors have read and agreed to the published version of the manuscript.  
This research was funded by the National Natural Science Foundation of China (Grant No. 51508200).  
Not applicable.  
The data that support the findings of this study are available from the first author upon reasonable request.  
We thank the Cosmos Virtual Data Center for sharing their data. We thank the anonymous reviewers for their comments, which were of substantial help to the improvement of the paper.  
The authors declare no conflict of interest.