## 4 Conclusions  
To study the development law of the temperature field around the frozen soil wall under ventilation conditions, a numerical calculation model of the 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 effects of various factors on the development laws regarding the temperature and thickness of the frozen soil wall were studied and analyzed. The detailed conclusions are shown below:  
(1) The temperature of the frozen soil wall inside the freezing tube is higher than that outside the freezing tube due to the continuous cooling capacity loss of inner shaft wall surface induced by ventilation. The thickness of the frozen soil wall outside the freezing tube gradually exceeds that inside the freezing tube, and the difference between these two parts is approximately 0.2-0.3 m, while the temperature difference is no more than 1 \({}^{\circ}\)C.  
(2) The layout radius of the freezing tube and the freezing tube pitch show a greater impact on the temperature distribution of the shaft wall and frozen soil wall. The decrease in these two parameters could reduce the temperature of the shaft wall and boost the variance of the temperature in the interlayer and outside surface of the shaft wall. In addition, the frozen soil wall did not complete the cross-loop in 180 d under ventilation condition when the freezing tube pitch exceeds 2.3-2.5 m, at this point, the thicker strata make it difficult for the cooling capacity to pass through. (3) The temperature reduction of the frozen soil wall is mainly concentrated in the initial freezing stage due to the huge temperature difference between the freezing tube and topsoil. The higher thermal conductivity of unfrozen soil and the lower soil moisture content could clearly enhance the cooling capacity transfer from the low-temperature region, reducing the temperature of the frozen soil wall, and then thickening this material at a higher speed. In addition, the soil moisture content plays an important role in the initial freezing generation under ventilation conditions due to the energy required for latent heat of the phase transition. (4) The full combination numerical simulation results present that the layout radius of the freezing tube shows relatively small effect on the cross-loop time of the frozen soil wall when the combination effect of layout radius of freezing tube and freezing tube pitch is comprehensively considered. (5) For the artificial ground freezing project, the frozen soil wall can complete the cross-loop even if the inside surface of the shaft wall is ventilated and the cross-loop time is mainly affected by the freezing tube pitch, which is the primary factor of the freezing project. This paper is expected to provide theoretical support in predicting the development law of the temperature field around the frozen soil wall and serving the field operation of freezing construction under ventilation conditions. Meanwhile, the findings of this study are mainly derived from numerical simulations of a certain artificial ground freezing project, and the influence of groundwater seepage and other factors has not been considered. More research methods and research factors will be considered in our future study. In addition, the artificial ground freezing method is not recommended when there is a high flow rate in groundwater, low-strength permafrost walls, and extremely low moisture content conditions. Conceptualization, T.H. ; Methodology, T.Z. ; Software, T.H. and T.L. ; Formal analysis, Y.X. and T.L. ; Resources, T.L. ; Data curation, T.H. and T.Z. ; Writing--original draft, Y.X. ; Writing--review and editing, T.H., T.Z. and T.L. All authors have read and agreed to the published version of the manuscript.