## 5 Analysis of Numerical Results
### Spatiotemporal Evolution Law of the Temperature Field before Exaxation  
#### 5.2.1 Overall Distribution and Development Law of the Temperature Field  
Figure 7 shows the overall distribution and development diagrams of the 3D freezing temperature field in the open-excavation section before excavation. In the initial freezing stage, the low-temperature brine flowing inside the freezing pipes transferred cold energy to the surrounding areas, leading to intense heat exchange between the pipes and the nearby soil. After 30 days of freezing, the soil temperature in the freezing zone decreased rapidly. The plugging hole area saw the highest temperature drop rate, followed by the side-row holes and, lastly, the middle-row holes. After freezing for 50 days, the freezing peak surface, with the freezing pipes at its center, expanded outward with increasing freezing time, gradually reducing the unfrozen soil thickness in the middle-row hole area. The denser the freezing pipes, the quicker the freezing temperature field develops and the thicker the frozen wall. At 88 days of freezing, the small spacing between the plugging and side-row holes contributed to a well-developed freezing wall. The middle-row hole area, which was designated for later excavation, had a larger freezing hole spacing, resulting in a lower development rate of the freezing wall. This indicates that the freezing pipe layout is reasonable and that the overall freezing effect is successful. Figure 5: Measured thermal changes at the measurement holes. (**a**) Three-dimensional diagram of the temperature at T1. (**b**) Three-dimensional diagram of the thermal change at T3. Figure 6: Comparison of the measured results with the numerical results. (**a**) T1 burial depth: 3 m. (**b**) T3 burial depth: 3 m. (**c**) T1 burial depth: 11 m. (**d**) T3 burial depth: 11 m.  
Figure 7: Overall distribution and development clouds of the 3D temperature field before excavation. To analyze the temperature field distribution within each soil layer before open excavation, the temperature-field nephograms of two soil layers with burial depths of 3 m (fine sand layer) and 11 m (medium sand layer) were chosen for comparison, as shown in Figure 8. In the early freezing stage, the formation rate of the frozen soil was relatively low, representing a process of cold energy storage. At 30 days of freezing, the freezing areas of the adjacent plugging holes and side-row holes in the fine sand layer began to intersect as time progressed. Meanwhile, the development rate of the frozen wall in the medium sand layer was notably lower than that of the frozen wall in the fine sand layer, and the frozen walls had not yet fully intersected. At 50 days of freezing, the freezing areas of each freezing hole gradually expanded, and the frozen walls of both the soil layers had entirely intersected to form a water-sealed curtain surrounding the open-excavation section. At 88 days of freezing, the middle-row hole area intersected, and excavation requirements were met. In summary, when the open-excavation section was frozen for 88 days, the sidewall thickness of the frozen wall could reach its corresponding design value (4 m), meeting the excavation demand for open-excavation sections. Figure 9 shows the overall shape and distribution of the frozen wall when the open-excavation section is frozen for 88 days. From the diagram, it is evident that at different burial depths within the range of the frozen pipe, the horizontal frozen wall intersected when the excavation area was frozen for 88 days. In the proposed excavation area, the thickness of the frozen wall at the bottom plate exceeded 5 m. Moreover, as shown in the cloud map of the frozen wall at various cross-sections of the burial depth, the sidewalls of the frozen wall of different layers could reach a thickness of over 4 m at 88 days of freezing. This indicates that both the floor and side walls of the frozen wall could reach their corresponding design values when excavating the open-excavation section after 88 days of freezing.