## 5 Analysis and Discussion of Calculation Results  
### Formation Law of Frozen Soil Curtain  
Figure 6 depicts the cloud map of the temperature field distribution throughout the freezing phase. To study the changing features of the frozen soil curtain, the soil layer region around the 6# hollow pipe and 7# concrete pipe were intercepted. The frozen soil boundary (\(-1.5\)\({}^{\circ}\)C) is denoted by the black line in each illustration. Figure 6: Temperature field distribution during freezing phase: (**a**) 32 days; (**b**) 45 days; (**c**) 90 days. According to the cooling plan, only the circular freezing tubes in the concrete pipe were opened in the first 32 days, as shown in Figure 6a. As the freezing time progresses, frozen soil forms near the circular freezing tubes at the two waist positions of each concrete pipe, and its range gradually expands from the pipe to the inside and outside of the pipe curtain. On day 32, the soil temperature in the pipe curtain area significantly decreased, particularly around the concrete pipes. The frozen soil curtain region has begun to \"wrap\" the concrete pipe and \"overlap\" with the neighboring hollow pipe but its size and temperature have not yet met the design requirements. The soil temperature in the pipe curtain region rapidly decreased after the opening of the profiled freezing tubes in the hollow pipe from day 32 to day 45, and the distribution of the frozen soil curtain exhibited substantial changes compared to previously, as shown in Figure 6b. A frozen soil curtain of varying thickness has formed around the concrete pipes, with an average thickness range of 1.80 m to 1.87 m; the part of the hollow pipe located on the inner side of the pipe curtain has also been \"wrapped\" by the frozen soil; while a small portion on the outside has not been \"wrapped\", the inner frozen soil curtain is developing faster than the outer side. The frozen soil between neighboring pipes also develops quite quickly, with an average thickness range of 1.82 m to 1.91 m and a temperature range of \(-0.2\)\({}^{\circ}\)C to \(-17.3\)\({}^{\circ}\)C.  
After the frozen soil curtain has completely \"wrapped\" the hollow pipe, the frozen soil range on the inner and outer sides of the pipe curtain continues to expand but at a slower rate, and the temperature of the frozen soil between the adjacent pipes decreases further. When frozen for 90 days, the development of the frozen soil curtain begins to stabilize, as shown in Figure 6c. The average thickness increased somewhat, ranging from 2.32 m to 2.58 m, and the temperature range of the frozen soil between pipes is \(-7.2\)\({}^{\circ}\)C to \(-22.1\)\({}^{\circ}\)C, meeting the freezing design requirements. The interface and axial plane between 6# hollow pipe and 7# concrete pipe were chosen as research subjects to explore the spatiotemporal impacts of temperature variations in frozen soil between adjacent pipes, as illustrated in Figure 7a. The distance between interface points was 0.4 m, while the distance between axial plane points was 0.09 m.  
Figure 7: Analysis of temporal and spatial variation of frozen soil temperature between jacked pipes: (**a**) Schematic diagram of measuring points; (**b**) Temperature–time curve of interface measurement points; (**c**) Temperature–time curve of axial plane measurement points. Figure 7b depicts the temperature-time curves for each point on the interface. Because of the varying distances from point 0#, each curve shows \"layering\" and \"symmetry\" features from 0 d to 32 d. The average cooling rate at point 0# is \(-\)0.83 \({}^{\circ}\)C/d; the average cooling rates of Z3 and Z4, Z2 and Z5, and Z1 and Z6 are \(-\)0.74 \({}^{\circ}\)C/d, \(-\)0.57 \({}^{\circ}\)C/d, and \(-\)0.41 \({}^{\circ}\)C/d, respectively. When the profiled freezing tube in the hollow pipe was opened for operation after 32 days, all curves revealed a dramatic change in curvature, indicating that the cooling rate at each location had been increased once again.