## 4 Analysis of Simulation Results
### Moisture Field Calculation Results
As external and internal moisture continues to gather in the cold zone, the internal moisture of the curtain essentially freezes, leading to significantly lower saturation. Overall, the soil saturation decreases with a smaller decrease observed further from the freezing pipe. Closer to the cold zone, the migration phenomenon becomes more pronounced. On the 30 th day of freezing, the permafrost saturation distribution within the freezing curtain is uniform, approaching a very low value (near zero). In actual projects, saturation may not reach zero entirely because water in the soil exists in complex forms, such as adsorbed water and capillary water, which strongly interact with soil particles. Additionally, when water freezes into ice, it expands, causing the soil to expand and potentially altering the pore structure. Thus, even if the water freezes, the remaining pore space may not be empty, preventing the saturation from reaching zero. By the 45 th day of freezing, the area of lower saturation further expands, enhancing the thickness of the frozen curtain. The 'foggy' appearance in the figure characterizes water migration. The inner edge of the frozen curtain appears smooth, with uniformly distributed soil saturation inside the curtain, indicating that water migration is nearing equilibrium. In contrast, the outer edge of the curtain has an obvious 'tooth-like' appearance, and the nearby soil shows a 'foggy' appearance, indicating intense water migration. The saturation at the outer edge of the curtain is higher than at the inner edge because the soil inside the curtain is a closed  
Figure 9: Cloud maps of soil saturation change. system with limited water migration and a small volume. In contrast, the soil outside the curtain is larger in volume, allowing for more significant water migration. By analyzing the variation pattern of the volumetric water content of the soil, the range of locations susceptible to freezing can be obtained to intuitively reflect the freezing process of unfrozen water volume content changes. Considering the above analysis, seven representative typical paths were selected, namely 1-5 for the strong freezing zone monitoring points, 6-7 and 8-9 for the weak freezing zone monitoring points, 10-14 and 15-19 for the internal soil monitoring points, and 20-24 and 25-29 for the external soil monitoring points; each monitoring point was separated by a 1 m interval. Twenty-nine external soil monitoring points were used, and each monitoring point was separated by a 1 m interval, as shown in Figure 10.  
The water content change curves for each monitoring point throughout the freezing process are illustrated in Figure 11. This figure shows that before the brine temperature of the freezing tube is reduced to the ice-water phase transition temperature, the water content at each monitoring point remains consistent with the original soil water content. When the brine temperature of the freezing tube reaches the phase transition temperature, the soil closer to the freezing tube experiences a rapid decline in water content, which tends to stabilize after a certain period of freezing. This phenomenon occurs because under the cooling effect of the freezing tube, the neighboring soil rapidly freezes, triggering a sharp soil moisture-to-pore ice phase change and causing a faster decrease in water content. In the later stages of freezing and in conjunction with the previous analysis results of the temperature field, it is evident that the lower the freezing temperature, the smaller the water content at that location, as more moisture in the soil undergoes a phase change into ice. Monitoring point 3, which is farther from the freezing pipe, exhibits the lowest water content in the late freezing stage. This is attributed to its position in the gap of the pipe curtain structure, forming a closed area when the complete frozen soil curtain is established. The freezing wall prevents moisture migration from the unfrozen soil to this area, resulting in lower water content.