## 3 Simulation Result Analysis
### Temperature Field Evolution Analysis of the Pipe-Soil System During the Freeze-Thaw Process
While this study primarily focuses on short-term freeze-thaw dynamics (3-year cycles), the potential for cumulative residual deformation under prolonged cycles is acknowledged. Numerical simulations reveal a ratchet effect characterized by progressive soil restructuring, wherein each freeze-thaw cycle induces an incremental vertical displacement of 0.4-0.6 mm/year. The observed displacement reduction proximal to the pipeline (40.8% attenuation relative to distal zones) corroborates its thermal buffering capacity through conductive heat transfer. However, the persistence of residual displacement underscores the irreversible nature of frost-induced soil fabric reorganization, necessitating long-term monitoring strategies to mitigate structural risk accumulation. Furthermore, the results show that the frost heave displacement at the top of the pipeline is 2.12 mm greater than at the bottom of the pipeline, indicating uneven deformation of the pipeline during the frost heave process. The top of the pipeline is closer to the surface, where the cooling effect is stronger, resulting in more heat loss, while the bottom is limited by the freezing depth, which reduces the frost heave force. Additionally, the soil at the pipeline bottom has a higher bearing capacity, which helps mitigate the bottom deformation caused by freezing. To reduce such uneven deformation, the materials surrounding the pipeline can be optimized. For example, a frost heave prevention cushion layer (such as gravel or coarse-grained soil) can be placed around the pipeline to reduce the generation of frost heave forces. Alternatively, the thermal conductivity of the surrounding soil can be improved to rapidly release heat and reduce the unevenness of the freezing depth. Figure 10: The cloud map of displacement variation with time (mm). Figure 12 illustrates the displacement variation of the ground surface and the top of the pipeline during the frost heave and thawing stages. The displacement behavior of the ground surface and the pipeline top during the freeze-thaw cycle follows completely different patterns. As frost heave progresses, the displacement of the ground surface gradually increases, while the displacement of the pipeline top is significantly influenced by the pipeline's internal water temperature, leading to certain non-uniformity in frost heave deformation. Since the water temperature inside the pipeline is maintained at 10 \({}^{\circ}\)C, it effectively reduces the freezing depth, and as a result, the frost heave displacement of the soil directly above the pipeline is relatively small. At the same time, the frost heave displacement on the upper side of the pipeline shows a gradually increasing trend, reaching a maximum at the centerline of the pipeline and then decreasing toward both sides. Beyond 0.6 m from the pipeline, the displacement increases again, indicating that the frost heave force primarily extends outward from the center of the pipeline. The displacement on both sides of the pipeline includes both vertical and horizontal components. Since only the vertical displacement is shown in the figure, the vertical displacement components at 1 m and 3 m are smaller. Beyond 0.6 m from the pipeline, the influence of water temperature on soil freezing gradually weakens, causing the frost heave displacement in this area to begin increasing. Combining the data from Figure 11, it can be seen that the pipeline undergoes both vertical stretching and horizontal compression. This indicates that the multi-dimensional nature of the force direction during the frost heave process cannot be ignored. Figure 11: Effect of freeze–thaw cycles on the displacement field. During the thawing stage, the soil at the surface near the pipeline centerline settles more quickly, while the soil on top of the pipeline shows a trend of displacement, first increasing and then decreasing. This is because the temperature transfer at the ground surface takes some time.