###### Abstract
Thus, it is necessary to build a numerical calculation model that can meet engineering needs and solve complex engineering problems [30; 31; 32]. Figure 1: Schematic diagram of shaft construction by the artificial ground freezing method. A series of numerical calculation analyses were conducted to study the temperature and thickness laws of frozen soil walls. The influence of the soil moisture content, thermal conductivity, initial ground temperature, and changing temperature of a frozen soil wall on the distribution of a freezing temperature field was studied by ANSYS software based on experimental data in the Xinzhuang coal mine [33]. The influence of thermal conductivity and specific heat capacity on the distribution of the freezing temperature field and the freezing rate was considered and studied using finite element software based on a two-dimensional planar numerical model of a ventilation shaft in the Tashendian mine area [13]. The effect of the mesoscale internal structure on the effective thermal conductivity of anisotropic geomaterials and a numerical method to estimate the effective thermal conductivity of a multiphase composite material under the steady-state heat transfer condition were studied [34; 35]. Numerical calculation analyses were carried out to observe the changing thickness law of a frozen soil wall under the effect of different parameters. The influence of the freezing tube's outside diameter, brine temperature, and initial ground temperature on the thickness of the frozen soil wall was studied based on a numerical simulation of PVC tubes [36]. The influence of the phase change latent heat of the soil, thermal conductivity, specific heat capacity, and initial ground temperature on the thickness of a frozen soil wall was considered and studied based on a numerical calculation of the freezing finite element temperature field at Nanjing station [37]. Several studies were conducted to summarize the extent to which different parameters on a frozen soil wall were affected. The extent to which different parameters affected on the freezing efficiency, from largest to smallest, is as follows: brine temperature, initial soil temperature, thermal conductivity, and specific heat capacity [38]. The factors affecting the development of the frozen soil wall, from large to small, are as follows: brine temperature, freezing tube arrangement spacing, freezing tube diameter, and water content of the formation [39]. As a shaft wall failure has become increasingly severe with the increase in shaft service time, the application of the freezing method in shaft repair has become more widespread and has proven to be reliable. However, most numerical simulations have focused on the development law of the temperature field around the frozen soil wall in the main shaft and auxiliary shaft, as shown in Figure 2, but the ventilation shaft is more complicated than the main shaft and auxiliary shaft due to the continuous operation of the ventilation shaft during repair, the high total volume of return air, and the wet, high wind, year-round environment. Meanwhile, the development law of frozen soil wall, applied to the ventilation shaft using the freezing method, is not yet clear. The shaft remains within a relatively stable temperature range, and there is a continuous heat exchange during shaft ventilation which is not conducive to the normal development of a frozen soil wall [40]. Hence, the development of the temperature field around the frozen soil wall during ventilation shaft repair was studied by ANSYS software, based on the actual data of the Chengjiao east ventilation shaft combined with the shaft environment, with convective heat exchange conditions used to simulate ventilation. The effect of various influencing factors on the development laws of the frozen soil wall was studied, including the convective heat transfer coefficient, layout radius of freezing tube, freezing tube pitch, freezing tube diameter, thermal conductivity of unfrozen soil, soil moisture content, and shaft wall thickness.