## 1 Introduction  
In recent years, Northeast China's high-speed railway has entered a period of large-scale development [1], with the operating mileage over 2000 km, the majority of which covers seasonally frozen ground [2]. Field tests (shown in Figure 1) demonstrated that the water in the surface layer of the bed is frozen in winter, which makes subgrade heave [3]. The operation experience of the Harbin-Dalian high-speed railway shows that subgrade frost heave makes it difficult to maintain the stability and safety of vehicles [4; 5; 6; 7]. Specifically, subgrade frost heave causes deformation of rails, which deteriorates the regularity state of the track system [8] and increases the dynamic response of wheels and rails. Then, both the deformation from the subgrade and the increased dynamic response aggravate the structural damage, which further affects the operation state of the whole system. To accurately evaluate the service state of high-speed railways in cold regions, it is necessary to clarify the influences of frost heave on the vehicle-track system [9; 10; 11]. To date, several studies have investigated the effect of subgrade frost heave on slab track; according to existing research, slab track is a typical three-dimensional belt-shaped structure [12; 13]. Subgrade frost heave could be simplified as a displacement boundary condition on the surface of the subgrade [14]. Based on the actual monitoring results [15; 16; 17; 18; 19], uneven subgrade frost heave could be simulated with an upper convex cosine curve in most research, as shown in Equation (1) and Figure 2. With this calculation hypothesis, many researchers have evaluated the service states of different ballastless tracks under subgrade frost heave. [PERSON] [20] analyzed the influence of frost heave deformation on the mechanical characteristics of the CRTS (China Railway Track System) I slab track, and a management standard of the ballastless track on the high-speed railway (HSR) was proposed. [PERSON] et al. [14] calculated the mechanical characteristics of different types of ballastless tracks under frost heave and proposed suggestions to optimize the CRTS III slab track. [PERSON] et al. [21] studied the deformations and interlayer separation fractures of CRTS I slab track under frost heave deformation. [PERSON] et al. [22] also developed a flexible track system model to calculate the dynamic response of the vehicle-track system, and the upper convex cosine curve was used as an indicator of the track irregularity to reveal the effects of subgrade frost heave on vehicle dynamic behaviors. [PERSON] et al. [23] presented a vehicle dynamic model to study the influence of uneven frost heave on train vibration, and the frost-induced irregularity was considered as a major influential factor in the dynamic model. [PERSON] et al. [24] studied the influence of frost heave on track irregularity and interlayer seam and evaluated the dynamic response of the vehicle-track system through a dynamic model; a standard of safety management of CRTS III slab track in the seasonally frozen ground was also presented. There are also a number of studies focusing on the influence mechanism of the foundation settlement on the dynamic system, which provide some references for this study [25; 26; 27; 28; 29]. However, in terms of the influence mechanism of frost heave on the vehicle-track dynamic system, there are so far few investigations which take into account the change in the stress and constraint state of the ballastless track itself after the occurrence of subgrade frost heave, and only track irregularity and interlayer contact loss area caused by frost heave are included in existing dynamic models [14; 21; 22; 23; 24]; the explicit mechanisms of frost heave have not been fully disclosed. \[y= \begin{cases}f_{0}\Big{[}\dfrac{1}{2}-\dfrac{1}{2}\cos\Big{(}\dfrac{2\pi Z}{ L}\Big{)}\Big{]},\ Z\in Frozen\ ground\\ 0,\ Z\in Non-frozen\ ground\end{cases}