# Experimental Study on Freezing Front Model of Alpine Tunnel under Wind Field
## 1 Introduction
(2016) established an unsteady finite reference calculation model according to the unsteady finite difference equation of heat transfer and heat convection in the cold zone railway tunnel; the heat convection between air and tunnel wall and the heat conduction at the interface between surrounding rock and different materials in the tunnel structure are studied [6]. In practical engineering, when determining the insulation material and the suitable range of grouting in alpine tunnels, the predicted scale of tunnel structure under freezing temperature must be determined by predicting the temperature field before construction, and the freezing front becomes an inevitable discussion object [18; 19]. As an important reference for thermal insulation design of alpine tunnels, freezing front has important guiding value for thermal insulation construction of alpine tunnel engineering. The current research results on the freezing front of alpine tunnels need to be explored further, as the existing research mainly focuses on single tube freezing and a small part of frozen soil freezing. The single-tube freezing theory considers the freezing point of soil, proposes the freezing front and considers that the temperature at the front is constant. This theory is only applicable to the solution of the freezing radius before the freezing front is closed, while the flat plate freezing theory is needed for the freezing radius after the freezing front is closed. The main reason is that the diameter of the freezing tube can be ignored in the calculation of the single-tube freezing problem. Thus, it can be simplified into a linear heat source model with analytical solutions, and the setting of a frozen soil temperature boundary can be simplified into a flat plate theory and the movement law of freezing front with freezing time can be obtained. [PERSON] and [PERSON] (1981), [PERSON] and [PERSON] (2004),[PERSON] et al. (2009) proposed an analytical solution of the freezing temperature field of a single tube under the condition of a constant heat flow boundary [20; 21; 22]. [PERSON] and [PERSON] (2012) established an analytical solution to the single pipe freezing temperature field considering the presence of some unfrozen water in the frozen soil [23]. [PERSON] et al. (2019) established an improved ground frost heave analysis and prediction method based on the formation process of freezing front in combination with the analysis and prediction proposed by [PERSON] et al. (2014) [24; 25]. In order to obtain the distribution law of freezing front under tunnel ventilation in cold regions, [PERSON] et al. (2018) carried out model tests under different air temperatures and inlet wind speed, and established the radial three domain control equation and the longitudinal parabolic control equation of the freezing front [26]. The accuracy of the equation was verified by comparing the research results with the field measurement results. [PERSON] et al. (2018) established the analytical solution of the single tube freezing temperature field considering the constant soil freezing temperature and freezing tube wall temperature [27]. The finite element program Abaqus was used to conduct numerical simulation of the single tube liquid nitrogen freezing temperature field, and the functional relationship between the freezing front radius, freezing time and freezing temperature was obtained. However, in practice, the overall radius of the tunnel section is large, the longitudinal temperature in the tunnel is different, and the temperature of the section cannot be ignored, so it is difficult to obtain the analytical solution to the freezing front. At present, it is difficult to carry out field research on the freezing front of tunnels in alpine areas, and the physical model test can be used as an important means to obtain test data of freezing front research because of various simulated working conditions and convenient operation and construction.