# Dynamic Response Analysis of Soil around Curve Section Tunnel under Train Vibration Load
## 1 Introduction
[PERSON] [15] studied the response of soil pore water pressure under saturated and unsaturated conditions through triaxial tests, and proposed a model that could predict the accumulated excess pore water pressure under saturated and unsaturated conditions. [PERSON] [16] established a two-dimensional finite element vibration propagation model to study the influence of vibration propagation in the frequency range below 200 Hz in dug and drilled tunnels. [PERSON] [17] proposed a modular model composed of three sub-models: the propagation model, orbit model, and static deflection model. The propagation model has also been used to study the effects of parameters such as soil stiffness, mesh size, boundary conditions, damping, and finite element analysis techniques on the vibration characteristics of a subway tunnel in Japan. [PERSON] [18] established an efficient modular numerical model for predicting the impact of vibration and radiated noise of subway trains on adjacent buildings in existing and new tunnels. The object of this study is a shallow buried tunnel in Paris. The dynamic response of soil mass and tunnel is analyzed using Floquet transform. [PERSON] [19] used a coupled periodic boundary-finite element model for the numerical modeling of the London Underground Bakerloo Tunnel. The model is induced by underground railway, and the interaction among soil, tunnel, track, and train is fully considered. The free field vibration of trains traveling at different speeds is predicted, and the results are compared with the measured results. The results show that the coupled periodic finite element model with boundary is suitable for the practical prediction of subway vibration. [PERSON] [20] used a Line 3 curve segment of the Hangzhou metro under a middle school as an engineering background, using the finite element software ABAQUS train-track-vehicle vibration response research system coupling model. By using finite element software MIDAS to establish a double-parallel curve tunnel, hole-soil-pile 3D model structure, [PERSON] calculated the vibration response of the subway train runtime. The propagation mode of the vibration wave generated by the subway in the foundation soil and the dynamic response characteristics of the building were analyzed, and the vibration comfort of the building was evaluated according to the relevant environmental vibration control standards. [PERSON] [21] investigated the effects of ground vibration generated by high-speed trains on mast structures by combining finite element models with semi-empirical formulas. The results indicate that the transverse effects of train-induced vibrations on mast structures are more significant than the longitudinal effects. [PERSON] [22] demonstrated the practical impact of dynamic material properties on train-track vibration interaction based on the principles of multibody simulation and the finite element method using LS-DYNA. The study confirmed that dynamic material properties have a significant influence on the interaction between train and track vibrations when the train speed exceeds 70 km/h. In order to analyze the accelerated track degradation caused by variations in track stiffness and increased dynamic wheel loads, [PERSON] [23] developed a hybrid method that combines 3D finite element modeling with empirical settlement equations in an iterative manner. This method enables the simulation of the degradation process of ballasted tracks. [PERSON] [24] established a three-dimensional calculation model by using the scaled proportional boundary finite element method (SBFEM) to study the dynamic response of tunnel structures and soil under train vibration load. In order to fully understand the development law of pore water pressure and its influence on tunnel settlement, it is necessary to carry out long-term field monitoring.