# Parameter Analysis on Seismic Response of Long Lined Tunnel by 2.5D Substructure Method
## 1 Introduction  
With the increasing scale of urban underground space construction, the safety performance of underground structures has been of wide concern by researchers [1; 2; 3]. The observation results of the 1995 Kobe earthquake show that subway stations and interstation tunnels will suffer serious damage under strong earthquakes [4]. At present, researchers mainly use model tests [5], analytical methods [6; 7] and numerical methods [8] to study the dynamic interaction of underground structures. Due to the lack of prototype observation data, there is not enough data to reveal the earthquake damage mechanism and failure mode. The model experiment can simulate the damage process during an earthquake. It is a widely used seismic research method at present. However, it is limited by the geometric scale of the model, the boundary effect and other conditions, so the results will have a certain impact. The analytical method established to analyze the soil-structure dynamic interaction under seismic waves has the characteristics of a clear concept and physical meaning, but the research work is only applicable to elastic half-space, simple site conditions or ideal geometric conditions. The rapid development of computer and numerical analysis technology has significantly improved the ability to use numerical methods to obtain quantitative results. Therefore, the numerical simulation method has become one of the most efficient methods in the engineering field [9; 10]. When the numerical method is used to solve the soil-structure dynamic interaction problem,the whole analysis method or substructure method based on the finite element method is often used. The whole analysis method refers to the establishment of the near-field whole model including the structure and a part of surrounding media. At the cut-off boundary of the near field model, dynamic artificial boundary conditions are applied to simulate the radiation damping effect of truncated far field media. At the same time, the earthquake input at the artificial boundary of the near field model is realized based on the free field response. Different from the whole analysis method, the substructure analysis method only establishes the structural finite element model. The truncated infinite domain is simulated through the foundation impedance function or the frequency domain dynamic stiffness. The impedance function or the frequency domain dynamic stiffness are integrated into the structural finite element model through the soil-structure interface condition. The earthquake input is realized at the soil-structure interface based on the free field response. A suitable method for the seismic design of a tunnel isometric underground structure is to use a three-dimensional (3D) finite element model to conduct the whole dynamic time-history analysis of the tunnel-soil interaction system. This method can effectively simulate the dynamic interaction between tunnel and soil [11]. The deformation and internal force at each moment can be obtained in the process of structural seismic response. In order to improve the computational efficiency, [PERSON] et al. [12] proposed a multi-scale finite element method that combines coarse mesh division with local fine mesh division. Based on the multi-scale finite element method, the seismic response of a long water transmission pipeline is analyzed. [PERSON] et al. [13] used three-dimensional dynamic finite element time-history analysis to study the influence of the incident P-wave of seismic wave on the internal force and deformation of a long lined tunnel. At the same time, the truncation effect at the end of the tunnel is discussed in detail. The large size of the three-dimensional finite element model in practical engineering applications, the large number of divided units and the high cost of calculation put forward high requirements of the computing ability, thus limiting the application of the three-dimensional dynamic finite element analysis method [14].