# Parameter Analysis on Seismic Response of Long Lined Tunnel by 2.5D Substructure Method
## 1 Introduction
For the long lined underground structure with a constant longitudinal direction, special numerical calculation methods such as the 2.5D finite element method can be considered. At first, [PERSON] and [PERSON] [15] proposed a special wave transmission element to denote the traveling wave effect of seismic wave propagation. Some researchers used this idea to further analyze the scattering effect of seismic waves in irregular sites [16; 17; 18; 19]. Through Fourier transform, [PERSON] and [PERSON] [20] established a two-dimensional (2D) plane element with three degrees of freedom to solve the soil-structure dynamic interaction, and named it the 2.5D method. Subsequently, [PERSON] et al. [21] used the 2.5D finite element method to study the influence of soil nonlinearity on the dynamic response of a high-speed railway track. [PERSON] et al. [22] and [PERSON] et al. [23] solved the dynamic interaction between a longitudinally uniform structure and soil under moving load by using the 2.5D finite element-boundary element coupling method. [PERSON] et al. [24] studied the seismic response of underground structures using the 2.5-dimensional finite element infinite element method. Recently, [PERSON] et al. [25; 26] adopted a 2.5D indirect boundary element method to study the dynamic response of structures under earthquake action. In order to reduce the size of the finite field in the computational model and effectively improve the computational efficiency, the method of setting artificial boundaries is usually used to simulate the radiation damping effect. The purpose is to ensure that scattered waves generated in soil media pass through artificial boundaries from within the finite computational area without reflection. [PERSON] [27] proposed a viscous boundary with dampers on the truncated boundary according to the wave equation. [PERSON] [28] assumed that the scattered wave was a 2D cylindrical wave, and put forward the definition of a 2D viscous spring artificial boundary; that is, the equivalent viscous damper-spring-concentrated mass system is arranged on the truncated boundary. [PERSON] and [PERSON] [29] assumed that the scattered wave was a 3D spherical wave, and proposed a 3D viscous spring artificial boundary. In addition, the Perfectly Matched Layer is an absorbing boundary model, which absorbs external traveling waves by setting a layer of boundary zone with an energy dissipation effect [30]. An effective seismic input method is the key to the dynamic response analysis of the tunnel foundation system. [PERSON] and [PERSON] [31] proposed to transform the incident ground motion into the equivalent load acting on the viscous artificial boundary to realize the wave input of the one-dimensional model. [PERSON] et al. [32] proposed a two-dimensional substructure input method for two-phase media. The rest of this paper is as follows. In Section 2, the interaction between soil and long linear underground tunnel under the oblique incidence of a seismic wave is described. The 2.5D finite element substructure analysis method using a high-precision artificial boundary is given in Section 3. The accuracy of the 2.5D finite element substructure model is verified in Section 4 by comparing the site response with the analytical solution and the substructure model with the analytical solution. Section 5 carries out parameter analysis. According to different incident angles and different locations of soil-rock interface, the seismic response of an urban underground long linear tunnel is discussed. The conclusion is given in Section 6.