###### Abstract  
Due to their advantages, artificial ground freezing methods are widely used in deep shaft construction and repair with the continuous exploitation of coal and other mineral resources. The boundary convection due to ventilation conditions will affect the formation and development of this frozen soil wall, which needs to be studied systematically. Thus, in this study, a numerical calculation model of a freezing temperature field was established based on the actual conditions of the east ventilation shaft in the Chengjiao coal mine during repair by the freezing method, and the temperature and thickness laws of the frozen soil wall and the shaft wall were studied by changing the influencing parameters. The results indicated that the thickness of the outside position gradually exceeded that of the inside position of the frozen soil wall due to the ventilation effect, and the difference between these two parameters was approximately 0.2-0.3 m, while the temperature difference was no more than 1 \({}^{\circ}\)C. The frozen soil wall did not complete a cross-loop within 180 d under ventilation conditions when the freezing tube pitch exceeded a certain threshold, which was about 2.3-2.5 m for this ventilation shaft. The soil moisture content played an important role in the initial freezing under ventilation conditions in the full combination calculation. This paper provides theoretical support for studying the application of the artificial ground freezing method for shaft construction and repair under ventilation conditions. s +
Footnote †: journal: Applied sciences  
definition  
a constant cold source to reduce the ground's temperature to below the freezing point of groundwater, resulting in a hydraulic boundary that enhances and stabilizes the ground structure and restricts the flow of groundwater. This method was widely used in deep shaft construction and repair due to its multiple advantages [6; 7; 8; 9; 10; 11; 12; 13]. The frozen soil wall formed by this method can effectively prevent water and quicksand in water-rich soft rock from flowing into the shaft, and the wall can also bear lateral pressure from the soil layer to protect the shaft wall during shaft wall construction and repair [14; 15; 16; 17; 18; 19], as shown in Figure 1. In addition, the formation and development characteristics of frozen soil walls are of great significance when evaluating the reliability and economy of artificial ground freezing methods, which have been systematically studied. To date, the mechanical properties of frozen soil have been increasingly established due to their central role in the construction and design of artificial ground freezing in underground projects [20; 21]. A statistical damage constitutive model of artificial frozen silt was studied to analyze its mechanical properties, considering the effects of temperature and confining pressures [22]. Many triaxial compression tests of frozen sand were completed under confining pressures to study the mechanical properties of artificial frozen soils [23; 24]. A series of laboratory experiments and theoretical analyses were conducted to study the temperature and thickness laws of frozen soil walls, and a more complete basic theoretical system was obtained. A higher precision semi-analytical solution in the dimensionless freezing zone of a temperature field was derived from equations of a single tube frozen soil wall and an analysis of the relationship between the freezing radius and heat flow density and various other factors under the condition of constant wall temperature [25; 26; 27; 28]. In addition, the controlling equations of heat conduction and the analytical solution of the soil temperature around the freezing tube are based on a single-tube freezing temperature field model [29]. However, frozen soil walls have a nonstationary temperature field. An analytical method based on mathematical analysis is relatively rigorous and can be expressed by a function showing the results, but it may not solve complex engineering problems.