## 1 Introduction
[11] studied the influence of seawater depth, the thickness of overlying rock strata, and the permeability coefficient on the seismic dynamic stability safety coefficient and plastic zone variation of a cross-sea tunnel structure experiencing seepage flow and bidirectional seismic action. According to the study by [PERSON] et al. [12], the continuous disturbance of sea waves and currents has a significant impact on the soil-structure interaction, such as the EPWP response, seabed liquefaction mode above the contact area, uplift of the sinking tube tunnel, and subsidence. [PERSON] et al. [13] investigated the dynamic response of a submarine tunnel under the action of sea waves and an earthquake, considering the coupling effect of stress field and seepage field. As a type of long, linear structure, the internal forces and deformations of a shield tunnel in both the transverse and longitudinal directions are closely related to the site conditions along the line. Therefore, the seismic analysis of a shield tunnel in a complex site has an important reference value for its seismic design. Nowadays, among the construction methods for establishing undersea tunnels, the shield method has gradually developed into the most widely adopted method thanks to its advantages, which include a fast speed, fine quality, high geological adaptability, safe construction, and sound working environment [14; 15]. A shield tunnel is a tunnel structure composed of a large number of lining segments assembled by bolts and other connections. The rupture of a tunnel's joints under the influence of a seismic force is mainly caused by the uneven settlement of the soil layer and the traveling wave effect of seismic waves. In some specifications, therefore, it is recommended to use the diameter deformation rate of the shield tunnel lining structure as the lateral seismic performance control index and use the longitudinal response displacement method to calculate the longitudinal stress and distortion experienced by the tunnel. [PERSON] et al. [16] adopted the multi-mass-spring model while considering the influence of sinking tube tunnel joints to conduct a dynamic response analysis. [PERSON] et al. [17] utilized the mass-spring model to calculate the three-dimensional nonlinear seismic responses of 70-meter-deep submarine sinking tunnels. [PERSON] et al. [18] carried out a study on the response displacement method for two different types of rings--a homogeneous ring and jointed ring--and calculated that the internal force value of the shield tunnel model with homogeneous rings was greater than that of the shield tunnel model with jointed rings. [PERSON] et al. [PERSON] et al. (2019) used the response displacement method and ABAQUS software to establish a beam-spring finite element model, and the cross-sectional seismic analysis of a shield tunnel in a complex soft-soil site was carried out. The calculation was combined with the soft-soil shield tunnel of Tianjin Binhai Line Z2. [PERSON] et al. (2019) proposed a set of holistic to local numerical analysis processes to analyze the mechanical characteristics of the detailed structure of a longitudinal joint under the action of an earthquake. [PERSON] (2018) discussed the influence of bolt prestress, bolt strength, tunnel diameter, and other factors on the structural equivalent stiffness and used an iterative calculation to realize a longitudinal seismic calculation method for a shield tunnel that updated the structural stiffness. [PERSON] et al. [PERSON] et al. (2019) calculated the longitudinal dynamic response of shield tunnels in heterogeneous strata under the action of an earthquake by using the stratum structure model and the tunnel's longitudinal equivalent stiffness model. [PERSON] et al. [PERSON] et al.