## 1 Introduction  
With the rapid development of large and medium-sized cities in the world and the increasing population, the traditional ground transportation system has been unable to meet people's traffic needs. Therefore, a lot of cities have built or are building a large number of underground railways. As a result of the limitations of early urban traffic planning, in the process of subway construction, the line planning needs to bypass some large buildings that have been built, resulting in a large number of curved tunnels. Compared with a straight section tunnel, the seismic response of a curved tunnel is more complex, especially for a small-radius curved tunnel; because of its small bending radius and irregular trend, the influence factors of its seismic performance are more complex. Therefore, it is necessary to conduct in-depth research on the seismic response of small-radius curve tunnels under different influence factors to ensure the stability of subway lines and surface buildings. Finite element numerical simulation technology is extensively utilized for the seismic analysis of underground structures owing to its economy and easy operation. After many years of research, a large number of researchers have made great progress regarding the seismic performance to tunnels. [PERSON] et al. [1] combined ANSYS finite element simulation (FEM) software with linear soil-structure interaction (SSI) codes for studying the nonlinear seismic dynamic response of subterranean box constructions and determined the relevant factors affecting their seismic performance. [PERSON] et al. [2] examined the seismic response of a tunnel model of an integrated pipe corridor driven by uneven seismic stimulation by means of numerical simulation for comparison with experimental results. It was found that the integrated pipe corridor underwent bending deformation, and the acceleration response was greater than the surrounding soil, and the modelling approach in this study was reasonable for shaking table tests. [PERSON] et al. [3] proposed a numerical simulation method pertaining to massive seismic response calculations in sunken tube tunnels. The finite element LS-DYNA analysis software was applied to add flexible joints to the weak parts of the tunnel under seismic excitation, which effectively controlled the displacement of the tunnel section. [PERSON] et al. [4] investigated the seismic response of a double tunnel using statically and dynamically plane strain finite element analysis, respectively, and compared the results with seismic field observations. It was found that the tunnel deformation was predominantly elliptical and that the interaction of the tunnel pillars with the wave reflection between the columns had little effect on its seismic performance. In addition, many academicians have carried out research on the seismic response, seismic design and calculation methods for subterranean constructions such as tunnels. [PERSON] et al. [5] investigated the seismic load effects on tunnels and shafts under seismic excitation by proposing a closed form idea, which is applicable to tunnels and shafts of small length. [PERSON] et al. [6] examined the non-linear response of deep sunken tunnels subject to strong earthquakes. [PERSON] et al. [7] investigated the lengthwise seismic response of tunnel interlined structures under frontal waves. [PERSON] and [PERSON] [8] studied the damage of rock tunnels under ground shaking. However, most of the above researchers have based their studies on straight-line tunnels. Research into the seismic response of curved tunnels has been in its infancy in recent years, and researchers have only proposed relevant research ideas, without forming a complete research system.