# Dynamic Response of Railway Subgrade Under Train Load and Freeze-Thaw Action
## 1 Introduction
However, research on the long-term operation stability of railways under the action of freeze-thaw cycles still has limitations. Most existing studies focus on the impact of a single factor on railway infrastructure and fail to fully consider the coupling effects of freeze-thaw cycles with other factors, such as train loads and climate change [23; 24; 25]. [PERSON] et al. used dynamic triaxial tests to study the effects of freeze-thaw cycles (number and temperature) on frozen subgrade soil's dynamic responses. The results showed that these cycles significantly influence soil properties such as shear modulus, damping ratio, plastic strain, and resilient modulus. A theoretical model was developed, and the freeze-thaw attenuation coefficient was used to evaluate property deterioration, with good agreement between experimental and predicted data [26]. [PERSON] et al. investigated the vibration-induced settlement and permanent deformation accumulation of the permafrost subgrade of the Qinghai-Tibet Railway. They utilized ABAQUS to establish a finite element model considering factors such as seasonality, vibration frequency, train type, and global warming. Results showed that cumulative vibration-induced settlement mainly occurred near the ice-rich permafrost layer and was highly influenced by ground temperature. The embankment height, ice-rich permafrost thickness, and initial mean annual ground temperature of the site affected the settlement and deformation. Permanent deformation accumulation was mainly due to the thaw consolidation of the permafrost layer, with vibration-induced settlement contributing approximately 20% [27; 28]. [PERSON] et al. focused on the train-induced vibration and subsidence of the Qinghai-Tibet Railway's permafrost subgrade. By establishing train-track-subgrade coupling models and conducting laboratory tests, it analyzed the influence of factors such as embankment height, mean annual ground temperature (MAGT), and ice-rich permafrost layer thickness on subsidence. A prediction program is developed, and it is concluded that increasing embankment height and reducing MAGT can decrease subsidence. The appropriate embankment height for the section is 3-3.5 m [29]. [PERSON] et al. utilized monitoring data to analyze the thermal, unfrozen water, and deformation behaviors of a new high-speed railway anti-frost cutting bed. A frost model was built to assess its effectiveness under extreme weather. Results showed that cutting the top's frost depth is less than the center's, unfrozen water sensitivity delays, frost heave occurs early, more water infiltration increases peak frost, and slopes are unstable at the freeze-thaw interface [30; 31; 32]. [PERSON] et al. established mathematical and numerical models based on Daqing data to simulate the temperature field and vibration response of railway subgrades with insulation boards. The research found that the numerical method can predict the subgrade temperature field. The insulation layer can reduce the freeze-thaw effect, subgrade vibration, and prevent frost damage, and the shallower burial depth has better effects [33; 34]. According to the above discussion, there have been a lot of studies on the dynamic response of railway subgrade at home and abroad, but there are few studies on the dynamic response under the combined action of train load and freezing and thawing. Therefore, it is urgent and necessary to conduct research on the long-term operational stability of railways under the action of freeze-thaw cycles. This not only helps to deeply understand the mechanical behavior and performance evolution laws of railways in complex environments, providing a scientific basis for the design, construction, and maintenance of railway infrastructure, but also effectively ensures the safe operation of railways. This study constructs a three-dimensional finite-element model to analyze the dynamic response (vertical displacement, stress, and acceleration) of railway subgrades under single-track moving loads at 180 km/h, 200 km/h, and 220 km/h.