## 1 Introduction
In fact, when the distance between the epicenter and the structural engineering site is short, the incident angle of the ground motion is usually oblique, which has been confirmed in the statistics of many seismic observation records [20]. Several studies have been carried out on the seismic analysis of underground structures under oblique incident seismic waves. [PERSON] et al. [21] developed a numerical method to study the longitudinal seismic performance of tunnels by using the nonuniform input of oblique incidence seismic SH, \(P\), and SV waves. [PERSON] et al. [22; 23] proposed a method to realize the oblique incidence of the plane P wave, and studied its influence on long-lined tunnels and normal fault underground tunnels. [PERSON] et al. [24; 25] studied the damage evolution process of an underground powerhouse with an obliquely incident seismic wave, and found the coherence between the results of a numerical simulation and field observations. [PERSON] et al. [26] analyzed the influence of SV wave incident angle on the Nanchang Honggu immersed tunnel using time-domain FEM and a viscous-spring artificial boundary (VSAB), and the results showed that the seismic response of the immersed tunnel under oblique incidence of the SV wave was significantly different from that under vertical incidence. [PERSON] et al. [27] proposed a 2D structure-water-sediment-rock interaction model to evaluate the seismic response of submarine immersed tunnel under an oblique incident wave, with the result showing that the larger incident angle of P wave is more likely to cause large deformation of the tunnel. As mentioned above, the 2D plane model cannot fully reflect the performance of tunnel structure, especially the cooperative work of shear keys in an immersed tunnel. [PERSON] et al. [28] established the 3D FE model of Tianjin Haihe immersed tunnel, and studied the seismic variation law of the tunnel under the oblique incidence of an SV wave using the dynamic stiffness matrix of soil layer and half-space [29]. However, this method was performed in the frequency domain, it could not be used directly with timestep integration techniques to solve complex seismic problems, and the influence of hydrodynamic pressure was not considered. Under the action of a vertical incident wave, the hydrodynamic pressure has a greater impact on the stress of an immersed tunnel [30], and the obliquely incident seismic wave contains the seismic excitation of the vertical component. In light of this, the present study aims to establish a 3D time-domain numerical model under oblique incidence of a seismic SV wave using FEM and analyze the seismic response of an immersed tunnel. The model assumes that the ground is a half-space with uniform elasticity and starts with the calculation of the free field ground motion. The equivalent nodal load based on VSAB is obtained by programming with FORTRAN language, and then imported into the ABAQUS FE software to realize the input of the seismic wave into the finite region to be analyzed, so as to carry out a 3D simulation of an elastic half-space site response under an oblique plane SV wave. The accuracy of this simulation is verified using a free-field numerical example. On this basis, a 3D SSI model is established to simulate the seismic response of an immersed tunnel with obliquely incident SV wave, which provides a reference for the seismic design.