## 6 Conclusions  
Taking the frozen open-excavation section of the main inclined shaft of Shengfu Mine in Shaanxi Province as the engineering background, this study utilized field-measured data and the finite element software COMSOL Multiphysics to build a 3D numerical calculation model of the freezing temperature field. The spatiotemporal evolution of the temperature field during the construction of the open-excavation section of the frozen inclined shaft was evaluated. The main conclusions drawn from this study are as follows:  
1. The field measured data revealed that the initial ground temperature of the fine sand layer was approximately 3.7 \({}^{\circ}\)C lower than that of the medium sand layer, resulting in a higher freezing rate for the fine sand layer compared with that of the medium sand layer. Due to the sealing effect of the frozen wall, the fine and medium sand layers at the T1 temperature measurement holes experienced freezing for 13 to 27 days, with phase change platforms appearing sequentially. However, there was no evident phase change platform in the soil at the T3 temperature measurement holes. During the 50-to-60-day freezing period, the overall temperatures of the soil on both sides of the point decreased to approximately \(-20\)\({}^{\circ}\)C and \(-8\)\({}^{\circ}\)C, respectively. Subsequently, the soil temperature stabilized.
2. Under the same freezing time, the average temperature and effective frozen wall thickness, as per the numerical simulation results, showed that freezing was more efficient in the fine sand layer than in the medium sand layer. Both the numerical calculations and field measurements showed that, after 88 days of freezing, the average temperature of the frozen wall for each soil layer was lower than \(-12\)\({}^{\circ}\)C. The thickness of the frozen wall could reach over 4 m for the side walls of different layers and over 5 m for the bottom plate. Consequently, it was found to be reasonable and safe to excavate the open-excavation section after 88 days of freezing.
3. A partial-step excavation method was employed for the excavation area of the open-excavation section, involving six excavation steps. During soil excavation, the section was exposed, and the freezing pipes were suspended for cooling. The soil experienced \"heat flow erosion,\" resulting in an increase in the temperature at the well side. However, this temperature rise was limited, and the well-side temperature could still maintain a low negative level with a quick cooling recovery from the freezing pipes. This prevented spalling at the well side, and the effective thickness of the frozen wall did not decrease. The average temperature of the frozen wall remained below \(-10\)\({}^{\circ}\)C. Consequently, there was no extensive \"softening\" of the frozen wall during the excavation process, ensuring construction safety.  
Methodology, C.R.; Software, W.L.; Investigation, S.Y.; Writing--original draft, J.Z.; Writing--review & editing, B.W. All authors have read and agreed to the published version of the manuscript.  
This work was supported by the Anhui Province Postdoctoral Fund Project (2022B635), China Postdoctoral Fund General Project (2021M703621), Anhui Province Natural Science Fund Project (2108085 QE251), Anhui University Natural Science Research Key Project (KJ2021A0425), Mine Underground Engineering Ministry of Education Engineering Research Center Open Fund Project (JYBGCZX2022103), Anhui Province Science, Technology Major Project Funding Project (202003C08020007) and College student innovation and entrepreneurship program (S202210361048).  
Not applicable.  
The authors declare that they have no known competing financial interest or personal relationships that could have appeared to influence the work reported in this paper.