## 5 Analysis of Numerical Results
### Spatiotemporal Evolution Law of the Temperature Field before Exaxation
#### 5.2.3 Temporal and Spatial Evolution Laws of the Temperature Field along Main Pathways  
Figures 11 and 12 show the temperature variation curves for the fine sand layer with a burial depth of 3 m and for the medium sand layer with a burial depth of 11 m. For ease of analysis, the main surface one could be divided into three zones: A, B, and C. Zone A was located outside the U-row plugging holes; Zone B was between the two rows of plugging holes U and V; and Zone C was where the middle-row holes were located. The main surface two could be divided into five zones: D, E, F, G, and H. Zones D and H were located outside the P-row and S-row, respectively, while Zone E was between the P and Q rows of the side-row holes. Zone G was between the R and S rows of the side-row holes. Zone F was located between Zones E and G. The figures show that, as the freezing progresses, the cooling capacity of the freezing pipe continues to output, and the temperature in each zone consistently decreases. When the freezing time reached 88 days, the temperature of the fine sand layer with a depth of 3 m dropped to below \(-12\)\({}^{\circ}\)C, while the temperature of the medium sand layer with a depth of 11 m decreased to below \(-6\)\({}^{\circ}\)C. This indicates that the arrangement of the freezing pipes was effective and that it produced a satisfactory  
Figure 10: Relationship between the average temperature and the effective thickness of the frozen wall with time. (**a**) Relationship between the average temperature of the frozen wall and the freezing time. (**b**) Relationship between side-wall thickness of the effective frozen wall and the freezing time. freezing outcome. The temperature was lowest when the path passed through the freezing pipe owing to the cooling capacity of the freezing pipe diffusing around it. In this case, the temperature was approximately \(-25\)\({}^{\circ}\)C.  
When the freezing time was the same, in the main surface one, Zone A had the lowest freezing efficiency, followed by Zone C, while Zone B exhibited the highest freezing efficiency; the order of the freezing efficiency was B \(>\) C \(>\) A. Zone A was located outside the plugging holes, and since the external soil temperature was high, the heat was continuously transferred to Zone A, causing its freezing efficiency to be lower than that in other areas on the main surface one. Zone C, where the middle-row holes were located, had more densely arranged freezing holes, resulting in better freezing effects. After 88 days of freezing, the temperatures of the fine and medium sand layers decreased to below \(-12\)\({}^{\circ}\)C and \(-6\)\({}^{\circ}\)C, respectively. Zone B was located between two rows of plugging holes, and the freezing  
Figure 11: Temporal and spatial variations in the temperature at a burial depth of 3 m (fine sand layer). (**a**) Main surface one. (**b**) Main surface two. Figure 12: Temporal and spatial variations in the temperature at a burial depth of 11 m (medium sand layer). (**a**) Main surface 1. (**b**) Main surface 2.  
holes were the most densely arranged. Consequently, the freezing efficiency of the soil in Zone B was the highest when the cooling capacities of the two rows of plugging holes were superimposed. After 88 days of freezing, the temperature in both the soil layers dropped to below \(-24\)\({}^{\circ}\)C. On the main surface two, the temperature field exhibited a symmetrical distribution. Zones E and G, which were located between the two rows of side-row holes, exhibited the highest freezing efficiency. After 88 days of freezing, the temperature of both the soil layers dropped to below \(-20\)\({}^{\circ}\)C. Zone F, which was located in the middle-row hole area, had a lower freezing efficiency than Zones E and G. After 88 days of freezing, the temperatures of the fine and medium sand layers decreased to \(-12\)\({}^{\circ}\)C and \(-6\)\({}^{\circ}\)C, respectively. The freezing efficiency in Zones D and H, which were located outside the side-row holes, was the lowest.