## 3 Numerical Calculation Analysis
### The Comprehensive Effect of Different Parameters  
To better study the influence of various factors on the frozen soil wall and shaft wall under ventilation conditions, a full combination numerical simulation of different parameters that affects the freezing temperature field is studied, which includes 384 sets of numerical experiments. The typical simulation results are extracted and analyzed as follows:  
The effect of the thermal conductivity of unfrozen soil (\(\lambda\)) and the soil moisture content (\(\omega\)) on the thickness (\(\delta\)) and the average temperature (\(\overline{T}\)) of the frozen soil wall are presented in Figures 21 and 22. The change in the thicknesses in the inside (\(l_{2}\)) and outside (\(O_{2}\)) of frozen soil walls, caused by the variation in the thermal conductivity of unfrozen soil and the soil moisture content, are similar. These two parameters show a nearly linear relationship with the thickness (\(\delta\)) and the average temperature (\(\overline{T}\)) of the frozen soil wall when the cross-loop of the frozen soil wall is completed. The increase in the conductivity of unfrozen soil will accelerate the cross-loop of the frozen soil wall, boosting the increase in the thickness and the decrease in the temperature inside and outside the freezing tube. An increase in soil moisture content would achieve the exact opposite effect. Figure 21: Variance in thickness and temperature of frozen soil wall under different thermal conductivity values of unfrozen soil: (**a**) the effect of thermal conductivity of unfrozen soil on the thickness of frozen soil wall, (**b**) the effect of thermal conductivity of unfrozen soil on the temperature of frozen soil wall. In addition, the thickness (\(\delta\)) has a power function relationship with freezing time, while the average temperature (\(\overline{T}\)) has a logarithmic function relationship with freezing time after the cross-loop of the adjacent frozen soil wall, as shown in Figure 23. The thickness gradually increases, and the average temperature gradually decreases in the inner and outer areas of the freezing tube with an increase in freezing time. The thickness of the outer frozen soil wall (\(\delta_{w}\)) and the thickness of the inner frozen soil wall (\(\delta_{n}\)) are basically the same under ventilation conditions, and the thickness of the frozen soil wall inside and outside the freezing tube remains within 1.5\(\sim\)2.1 m after 180 d of freezing. However, the average temperature of the outer frozen soil wall (\(\overline{T}_{w}\)) is slightly higher than the average temperature of the inner frozen soil wall (\(\overline{T}_{n}\)) by 1-2 \({}^{\circ}\)C after the cross-loop of the adjacent frozen soil wall. Figure 22: Variance in thickness and temperature of frozen soil wall under different soil moisture contents: (**a**) the effect of soil moisture content on the thickness of frozen soil wall, (**b**) the effect of soil moisture content on the temperature of frozen soil wall. Figure 24 shows the relationship between the cross-loop time and different parameters. The layout radius of the freezing tube has a relatively small effect on the cross-loop time of the frozen soil wall when the combined effect of the layout radius of freezing tube and freezing tube pitch is considered in the full combination calculation. The thermal conductivity of unfrozen soil (\(\lambda\)) and soil moisture content (\(\omega\)) has a linear relationship with the cross-loop time of the frozen soil wall. The cross-loop time of the frozen soil wall becomes shorter with the increase in the thermal conductivity of unfrozen soil and becomes longer with the increase in the soil moisture content when other parameters are determined.