## 1 Introduction  
High-speed rail tunnels in cold areas are a special type of tunnel that is very difficult to construct, operate, and maintain. Due to the obvious piston wind effect in high-speed railway tunnels, the temperature inside the tunnels fluctuates violently [1]. The length and extreme value of the negative temperature section are significantly longer than those of ordinary railway tunnels and highway tunnels. In addition, high-speed railway tunnels have faster driving speeds, higher safety requirements, and colder temperatures. The problem of freezing damage in regional tunnels is more complex, and the harm is more serious. The main manifestations of frost damage to tunnels in cold regions include ice accumulation on the tunnel bed, ice hanging on the lining, surface peeling, cracking, and the loss of blocks [2]. Among these, cracks, loss of blocks, and even damage caused by frost heaving can be caused by water accumulation behind the lining. The hazards of collapse are particularly serious. The conditions for freezing damage in tunnels are groundwater and negative temperatures. When preventing and controlling freezing damage, measures such as thermal insulation, heating and anti-freezing, anti-drainage optimization, and de-icing are usually implemented. However, these measures usually do not consider the short cycle. Problems include temperature fluctuations, high energy consumption [3, 4],freezing of water in the drainage plate pores [5], potential safety hazards [6], and high costs [7; 8; 9]. Therefore, understanding the mechanism of frost-heave force caused by water accumulation in the lining and establishing models for its calculation and analysis are key prerequisites for the prevention and control of this type of frost damage. The accumulation of water in the cavity behind the lining is restricted in drainage during the freezing process, and the volume expands to generate frost-heave force [10]. Therefore, the formation and magnitude of the frost-heave force are directly related to the size and shape of the cavity, water drainage conditions, and temperature. The negative fluctuation process is directly related, and its formation mechanism and mechanical model are extremely complex. [PERSON] [11] studied the influence of the surrounding rock temperature on frost-heave force through on-site measurements of the surrounding rock temperature and lining pressure. [PERSON] [12] studied tunnels in seasonally frozen soil areas and found that the frost-heave force decreased as the ambient temperature increased. [PERSON] [13] used the semi-formulaic and semi-empirical \"elastic equivalent coefficient method\" to calculate the magnitude of the frost-heave force of water accumulated between the lining and the surrounding rock. [PERSON] [14] proposed a tunnel frost-heave force calculation model considering freeze/thaw damage and the lateral anisotropic characteristics of the surrounding rock. [PERSON] [15] comprehensively considered multiple factors, such as seasonal temperature changes and water body characteristics, and proposed a calculation model for the frost-heave force of freestanding water. The above studies all conducted certain analyses for the calculation of tunnel frost-heave force, but they did not comprehensively consider the effects of short-period temperature fluctuations, cavity size and shape, and water accumulation and drainage conditions on the frost-heave force. In order to reveal the frost-heave mechanism of voids and accumulated water behind the lining of high-speed railway tunnels in cold regions, voids were first classified according to the positional relationship between voids and waterproof panels; then, the supply and discharge conditions of accumulated water in different types of voids were investigated, and the supply and drainage were studied experimentally to determine the effects of these conditions on the frost-heave force.