## 5 Conclusions  
Based on the actual position of freezing holes in the Qingdong Mine, combined with the real-time monitoring of the brine temperature of freezing holes, a numerical model was established for calculating the transient thermal temperature field considering latent heat of phase transformation. The calculated values of temperature measurement points and side-wall temperature were verified by the field measured data. The distribution and development of freezing temperature field of fine sand, sandy clay, and clay layers were studied by the proposed numerical method. At the same time, the stability of the frozen wall during the excavation of the control layer was analyzed theoretically. The main results of this study are summarized as follows:  
Figure 12: Variation in the displacement of shaft wall with time. Under the same freezing time, the average effective freezing temperature of the fine sand layer was 0.2-1 and 0.5-2.5 \({}^{\circ}\)C lower than that of the sandy clay layer and clay layer, respectively. The effective frozen wall thickness of the fine sand layer was 0.04-0.17 and 0.17-0.33 m larger than that of the sandy clay layer and clay layer, respectively. The temperature field at the main surface and interface of the fine sand layer had the fastest decrease, while that of the sandy clay layer had the slowest decrease. Therefore, the fine sand layer had the best freezing effect, while the sandy clay layer had the worst freezing effect. 2. Based on the main freezing holes and auxiliary holes, the freezing temperature field could be divided into three characteristic areas in the radial direction. Due to the superposition effect of the cooling capacity of double-ring freezing holes, the cooling of soil in the frozen zone II was the fastest, followed by that in the frozen zone I without external heat source, and the frozen zone III without superposition effect of the cooling capacity of freezing holes with external heat source had the slowest cooling. The deflection of the freezing holes had a minor influence on the symmetry of the temperature field II zone of the main surface, but it had a significant influence on the symmetry of the temperature field II zone of the interface. Therefore, the drilling process should be strictly controlled in the freezing construction to minimize the deflection of freezing holes. 3. The brine temperature had a considerable influence on the temperature field of the frozen wall. At a high brine temperature, the average temperature and thickness of the effective frozen wall could not meet the design requirements. A lower brine temperature ensured the safety of shaft excavation, but greatly increased the cost of freezing construction. According to the theoretical analysis, the temperature of brine during the active freezing period of the project should be \(-\)25 to \(-\)30 \({}^{\circ}\)C, and the temperature of brine during the active freezing period was finally determined to be \(-\)25 to \(-\)27 \({}^{\circ}\)C based on the actual on site situation in the middle and late period of freezing during the maintenance freezing period. Consequently, to ensure an appropriate effective thickness and average temperature of frozen wall, the brine temperature of auxiliary holes should be controlled in real time to reduce the expansion of frozen soil into the excavation section, decrease the difficulty in excavation, and save the freezing cost. 4. According to the actual freezing situation at the site, the safety of the frozen wall in the \(-\)216 m sandy clay control layer during excavation was evaluated.