## 4 Analysis of Simulation Results
### Displacement Field Calculation Results
In the region affected by the upward force of the pipe curtain structure, the contour interval is larger, indicating that the pipe curtain structure inhibits freezing and expansion displacement to some extent. The soil near the freezing pipe has dense contour lines, reflecting this region's intense phase change process and the obvious freezing and expansion effect. The soil within the freezing curtain is directly subjected to minimal freezing effects with the displacement changes primarily being influenced by the lower freezing region and the effects of the curtains on both sides. Consequently, its displacement growth is slow, and the contour interval is larger. To further analyze the vertical displacement pattern of the soil in the area near the surface during freezing, three monitoring paths, DP1 to DP3, and four monitoring points in the Z = 5 m section, point 1 to point 4, were selected, as shown in Figure 14.  
The vertical displacement change for points 1 to 4 under different freezing times, as shown in Figure 15a, reveals that in the early-phase change phase, the surface area soil is influenced by all freezing pipes. The combined effect of freezing and the expansion of the underlying soil causes a significant uplift displacement in the surface area soil. Point 4, affected by the lower freezing zone, exhibits a displacement of 125 mm throughout the freezing process. There is no drastic increase in displacement between points 4 and 3 due to the minimal influence of the freezing pipes. The substantial displacement increase at the early freezing stage primarily occurs between points 3 and 2. No significant displacement difference is observed between points 1 and 2 because the freezing area has yet to develop to the top of point 2. However, the soil above point 2 experiences significant displacement with prolonged freezing time. As the freezing time continues, the freezing curtain develops  
Figure 13: Cloud maps and contour maps of vertical displacement at different freezing times. further, and the moisture accumulation area expands, increasing displacement differences above the monitoring points. Once moisture migration reaches dynamic equilibrium, the displacement difference stabilizes, and the vertical displacement of the soil body below develops slowly. From the vertical displacement observed after 45 days of freezing in Figure 15b, it is evident that larger vertical displacement differences primarily occur in areas directly affected by the cold source and the moisture accumulation area. Above DP2, no significant displacement changes are observed, which is mainly because the soil is already at the edge of the freezing curtain's influence, where minimal phase change effects occur. Contour plots and path analysis diagrams indicate that the soil displacement is not symmetrically distributed along the center plane (X = 0), and the maximum displacement is not at the center point. This asymmetry is due to the denser distribution of freezing tubes on the left side, resulting in a greater freezing effect. Finally, the analysis of vertical freezing displacement changes suggests that freezing causes significant surface uplift due to water migration. This phenomenon poses substantial engineering challenges, necessitating freezing control measures in the soil layers most adversely affected. Such measures are essential to prevent the deformation and rupture of pipelines in the upper ground and significant settlement during foundation thawing.