# Dynamic Response Analysis of Soil around Curve Section Tunnel under Train Vibration Load
## 1 Introduction  
During the operation of trains on curved sections within tunnels, centrifugal forces are generated. To counterbalance these forces, excessive settlement may occur as a result of the elevated height of the outer rail. This is more likely to occur compared to straight sections. In saturated soils, the pore water pressure is particularly sensitive to the effects of vibration loads. Consequently, it can further cause the soil around the tunnel to become soft, increase the pore water pressure, and even cause soil fluidization, leading to excessive settlement of the underlying soil layer, which has a significant impact on safety. Currently, there are few studies on the response of the pore water pressure in the underlying soil layer caused by the vibration loads of subway trains on curves. The changes in pore pressure within the soil layer directly impact tunnel settlement. Therefore, there is a need to conduct research on the response of pore water pressure to train vibrations on curves and understand the underlying dynamic response patterns. Recently, there have been notable advancements in research regarding the pore water pressure and dynamic response of the soil surrounding tunnels caused by the vibrationloads of underground train vehicles [1; 2; 3; 4; 5]. [PERSON] [6; 7] conducted indoor GDS tests and corrected the actual field measurement data to obtain the pore water pressure change development model in saturated soft silt under the cyclic vibration load of underground trains, and calculated the soil settlement value caused by the walking load of the train. [PERSON] [8] established a numerical model using the FLAC3D finite difference software, considering the fluid-solid coupling effect, to study the dynamic response characteristics of the soil layer due to the vibration load of underground trains, and analyzed the changes in soil pore water pressure and void ratio during high-speed passage of trains through the tunnel. [PERSON] [9] combined the numerical simulation of ADINA with field experiments to study the development rules of soil settlement and pore water pressure changes in the tunnel and its surrounding soil due to the vibration load of underground trains. [PERSON] [10] used the finite element software ABAQUS to establish a numerical model to study and analyze the deformation of soil mass in horizontal and vertical directions at different distances between the soil layer around the tunnel and the tunnel. [PERSON] [11] took the saturated clay in Tianjin as the research object, carried out an indoor cyclic triaxial undrained test, and analyzed the dynamic response of saturated clay under the intermittent action of cyclic load. [PERSON] [12] used a dynamic model based on multi-body mechanics and finite element methods to study the dynamic response of a low-speed magnetic levitation vehicle on an overhead track in a small radius curve. The model considered the vibration behavior of the track key components and the space dynamic magnetic field effects. The research and analysis of the dynamic response of the vehicle-track coupling system in a small radius curve were conducted. [PERSON] [13] established a coupling dynamic analysis model of the vehicle-track-foundation system using a 2.5D thin layer element finite element model, and derived the equation of the rolling interaction force between the wheel and rail considering the irregular track surface. Taking the Beijing-Shanghai high-speed railway as the research background, the new high-speed railway track was found to have good track linearity due to the application of grinding operations, and the vehicle parameters determined the dynamic response characteristics of the track structure. [PERSON] [14] proposed an effective method for predicting train-induced vibrations in circular tunnels within porous elastic half-space. This method was applied to investigate soil vibrations caused by train loads on tracks and simple harmonic loads. In addition to this, numerous studies have been conducted by scholars abroad.