## 4 Analysis of Simulation Results
### Moisture Field Calculation Results  
In the freezing project, changes in the moisture field directly impact the effectiveness of the freezing process. Analyzing the changes in the moisture field can concretely reveal the moisture migration phenomena that occur during the formation of the freezing wall. Therefore, volume changes in ice content distribution were extracted at intervals of 11, 13, 20, 25, 30, and 45 days, as shown in Figure 8.  
From this figure, it can be observed that by the 11 th day of freezing, the temperature of the frozen tube had dropped below 0 \({}^{\circ}\)C, initiating fluctuations in the volumetric ice content centered around the frozen tube. By the 13 th day of freezing, the temperature of the freezing tube continued to fall, causing the liquid water in the surrounding soil to condense into ice, although the ice content in the frozen soil column remained low at this stage. On the 20 th day of freezing, the ice content in the soil of the strong freezing zone reached 35%, compared to the 40% volumetric water content before freezing. This indicated higher ice content-soil associations within the strong freezing zone. Conversely, the weak freezing zone only exhibited further expansion of the frozen soil column due to differences in the distribution of freezing tubes. By the 25 th day of freezing, the surrounding soil had gradually formed a permafrost curtain rich in ice content. The ice content in the strong freezing zone was fuller and richer than in the weak freezing zone. Additionally, the volumetric ice content exceeded 40%, which is attributed to the approximately 9% volume expansion when water transitions to ice. On the 30 th day of freezing, the ice content in the soil between the interconnecting steel pipes and the independent steel pipes within the pipe curtains increased significantly. In contrast, the ice content at the edge of the freezing front was smaller than that near the frozen tube. This indicated that after freezing commenced, internal water migration occurred within the soil due to the temperature difference. The formation of a temperature gradient between the frozen and unfrozen areas led to the development of a moisture potential gradient. The moisture potential was lower in the freezing area and higher in the unfrozen area. Consequently, moisture migrated from the higher moisture potential in the unfrozen area to the lower in the freezing area, causing liquid moisture in the surrounding soil to spontaneously move toward the freezing front. This migration resulted in a higher unfrozen water content at the edge of the freezing front. By the 45 th day of freezing,  
Figure 8: Volumetric ice content cloud maps at different freezing times. continuous moisture migration from the external and internal unfrozen soil and ongoing phase changes caused the freezing front to advance further. The thickness of the ice-bearing permafrost increased significantly, and the concavity of the inner and outer walls of the permafrost curtain became smoother, leading to a more uniform ice content distribution. To further analyze the changing pattern of the moisture field, cloud plots of saturation changes were extracted for 20, 25, 30, and 45 days of freezing, as shown in Figure 9.  
This figure shows that by the 20 th day of freezing, the strong and weak freezing zones form a frozen soil structure. The weak freezing zone exhibits higher saturation around it due to differences in freezing efficiency. The soil saturation around the freezing pipe within the strong freezing zone is lower. The soil near the freezing pipe along the edge shows a temporary increase in saturation due to continuous moisture migration from the unfrozen soil to the cold zone, resulting in a decrease in soil saturation around the curtain. By the 25 th day of freezing, a continuous freezing wall gradually forms around the freezing pipe. During this process, the outer edge of the curtain expands outward, and the inner edge expands inward.