## 4 Analysis of Simulation Results
### Displacement Field Calculation Results  
Based on the above-mentioned research, the temperature evolution characteristics and moisture migration patterns during the freezing process have been revealed. However, the study of the project's freezing law necessitates an analysis of soil freezing displacement, particularly vertical displacement. The magnitude of vertical displacement and ground surface uplift is a crucial index for assessing the stability and safety of the construction project and a prerequisite for the study of freezing displacement control, serving as an effective reference. In calculating the ground deformation displacement field, the initial ground stress is generally caused by the self-gravity stress of the soil body. Given that the soil is typically consolidated before freezing, it can be assumed that its initial displacement is zero, and any subsequent displacement is mainly due to freezing expansion. If gravity is directly applied in the calculation, the software will automatically calculate a large initial displacement. Therefore, before calculating the displacement due to freezing and expansion effects, the initial displacement caused by gravity must be deducted to ensure the accuracy of the simulation results. In this section, it is necessary to balance the ground stress through two steps before calculating the displacement due to freezing and expansion. First, the stress and displacement under gravity are calculated. The self-gravitational stress calculated in the first step is then extracted as the initial stress for the second study, and the displacement value from the first step is deducted. This ensures that the initial displacement in the calculation of freezing and expansion is nearly zero and that only the initial ground stress remains, as shown in Figure 12.  
As shown in Figure 13, vertical displacement spatial cloud maps and vertical displacement contour maps (\(Z=5\)) were extracted and analyzed for freezing times of 11, 25, 35, and 45 days. According to Figure 13, the vertical freezing expansion area of the stratum increases gradually with the development of the freezing curtain. The soil near the frozen pipe concentration area in the upper part of the stratum exhibits larger vertical freezing displacement. This is primarily because the pipe curtain inhibits soil freezing displacement, but the overburden depth is shallow. Consequently, the freezing curtain volume and moisture accumulation area are larger. As freezing time progresses, the upward vertical displacement continually accumulates, leading to greater displacement at the top and surface location of the soil. In contrast, the bottom experiences smaller freezing displacement for two main reasons: the model's boundary conditions limit the displacement, and the ground pipe curtain structure suppresses the freezing expansion at the bottom. Additionally, the effective stress of the soil body increases with depth, counteracting some of the freezing expansion forces generated during the freezing process. Figure 12: (a) Initial stress displacement; (b) displacement after geostress equilibrium. The contour plot shows that at 11 days of freezing, the soil body only produces a small displacement due to the recent onset of the phase transition process. The freezing expansion occurs primarily near the freezing pipe, and the soil near the surface shows a vertical displacement of only 0.66 mm. By 25 days of freezing, the maximum vertical displacement of the soil near the surface reaches 244 mm. At 35 days of freezing, this maximum vertical displacement increases to 320 mm. During the 11-to-35-day interval, the phase change process is rapid, resulting in larger displacements. At 45 days of freezing, the development of the freezing curtain slows, the moisture accumulation area expands, and moisture migration continues. The maximum vertical displacement near the surface reaches 358 mm, indicating that the freezing displacement develops more slowly at this stage. The internal ice and water phase change gradually reaches an equilibrium state.