# Dynamic Response of Railway Subgrade Under Train Load and Freeze-Thaw Action
## 1 Introduction  
With the continuous advancement of global infrastructure construction, railways, as a crucial means of transportation, play a vital role in ensuring the safe and efficient transportation of people and goods. Their stability is of utmost importance. Particularly in seasonally frozen soil regions, railways are constantly affected by freeze-thaw cycles, facing severe challenges to their long-term stability, which has attracted extensive attention from academia and the engineering community [1, 2]. Globally, seasonally frozen soil regions are widely distributed, covering large areas of many countries such as China, Russia, and Canada. Statistics show that the area of seasonally frozen soil regions in China accounts for approximately 53.5% of the total national territory. In these regions, the mileage of railway construction has been increasing [3]. However, freeze-thaw cycles bring numerous problems to railway infrastructure. When the temperature drops, the water in the subgrade freezes and expands, generating frost heave forces. When the temperature rises, the frozen soil thaws, reducing the strength of the soil and causing thawing settlement. This repeated freeze-thaw action can lead to subgrade deformationand track irregularities, seriously threatening the long-term stable operation of railways. Previous studies have explored railway-related issues from various perspectives. In the aspect of railway subgrade vibration response, some scholars have used a combination of numerical simulation and field monitoring to study the impact of train vibrations on the subgrade [4; 5; 6; 7]. [PERSON] et al. used ABAQUS to build a vehicle-track-subgrade coupled model. It analyzed the vibration response of high-speed railway subgrades in karst areas with and without soil holes. Results showed that soil holes decrease dynamic displacement and acceleration amplitudes while increasing the dominant frequency. Monitoring points 0-10 m from the slope toe and relevant indicators can detect subgrade defects [8]. [PERSON] et al. combined field monitoring and numerical simulation to study the dynamic response of soil around a curve-section tunnel under train vibration [9]. The results showed that train vibration affects pore water pressure and soil displacement, and the response is related to location, depth, and curve radius [10; 11; 12; 13; 14]. [PERSON] et al. employed a 2.5D finite element model to explore soil vibrations from trains. By analyzing different speeds of constant and harmonic loads, the critical speed was determined. Conclusions showed its relation to soil properties and clarified how speed/load type influences ground and track responses [15]. [PERSON] et al. established a 2.5D model based on [PERSON]'s theory to study the dynamic response of saturated soft soil foundation under high-speed train loads. They found that the responses of excess pore pressure, effective stress, and displacement are affected by factors such as train speed and permeability coefficient, and there is a critical speed [16; 17; 18]. [PERSON] et al. centered on the ballastless track-subgrade system of high-speed railways. A 3D finite element model was built based on the Beijing-Shanghai section. By varying the parameters of subgrade layers and fasteners, the impacts on dynamic vertical displacement are analyzed. Results showed that enhancing the subgrade/embankment modulus reduces total displacement. Fastener stiffness mainly affects rail displacement. The modulus ratio of subgrade layers and foundation modulus notably influence subgrade surface displacement. Thus, the proper selection of materials and control of fastener stiffness are crucial for system stability [19; 20; 21]. [PERSON] et al. proposed a deep, long short-term memory network to predict railway bridge dynamic responses. The results showed that displacement prediction is more accurate and robust than acceleration prediction. Also, factors like network structure, training samples, and train-related variables affect prediction accuracy [22].