## 3 Simulation Result Analysis
### Temperature Field Evolution Analysis of the Pipe-Soil System During the Freeze-Thaw Process  
Numerical simulations were conducted using the above parameters, and the hydrothermal-mechanical coupling simulation results at the soil locations of line1 and line2 were analyzed. Figure 7 shows the temperature field evolution over time, with the vertical axis representing soil depth and the horizontal axis representing time. From the simulation results, it can be seen that due to the periodic variation of the surface temperature, the soil temperature also exhibits seasonal fluctuations. During a single freeze-thaw cycle, the lowest and highest temperatures occur around days 90 and 270, respectively. These points correspond to the extreme winter and summer temperatures, with heat conduction effects causing heat transfer within the soil layers, resulting in a delayed response to surface temperature changes. Additionally, the variation of the freeze-thaw interface is directly influenced by the thermal properties and phase change characteristics of the soil layers. The thickened contour lines in the figure represent the freeze-thaw interface. In the silty clay layer, the pipeline water temperature is 10 \({}^{\circ}\)C, providing a localized heat source. Heat is transferred from the pipeline to the surrounding soil, significantly reducing the freezing depth of the soil above the pipeline, with the maximum freeze-thaw depth reaching only 0.87 m. In contrast, the right boundary of the model, which is farther from the heat source and lacks additional heat, experiences a maximum freeze-thaw depth exceeding the pipeline burial depth. This figure demonstrates the thermal buffering effect of the pipeline, which reduces frost penetration and associated heave forces. The delayed temperature response in deeper soil layers underscores the importance of burial depth in mitigating frost heave risks. Analysis of the Temporal Evolution of Volumetric Water Content and Volumetric Ice Content During the Freeze-Thaw Process of the Pipe-Soil Systemthe changes in volumetric water content primarily occur in the clay layer, with a smaller impact in the gravelly fill layer with larger porosity. Since the variation in volumetric water content directly affects the changes in the mechanical properties of the soil, further analysis is needed on the deformation of the silty clay layer and its interaction with the pipeline. Analysis of the Temporal Evolution of Displacement During the Freeze-Thaw Process of the Pipe-Soil System  
Figure 10 shows the cloud map of displacement variation with time. It can be observed that frost heave displacement is closely related to heat transfer. The maximum frost heave displacement of the soil above the pipeline is only 7.6 mm, which is about 40.8% less than the displacement of the soil at the right boundary (10.7 mm). This is because the heat from the water inside the pipeline alleviates the freezing effect on the surrounding soil through conduction, thereby reducing the frost heave displacement. This indicates that the heat source from the pipeline has a significant impact on the frost heave displacement of the soil, and the constant temperature state of the water inside the pipeline plays a positive role in reducing the frost heave of the surrounding soil. Figure 8: The cloud map of volumetric water content variation with time. Figure 9: The cloud map of volumetric ice content variation with time. For 3-year cycles, the simulation results show that after each freeze-thaw cycle, a portion of irreversible residual displacement occurs in the soil (as shown in Figure 11). The accumulation of this residual displacement indicates that the soil structure is gradually compacted and rearranged. The main reason for this is the migration of water and the expansion effect caused by freezing within the soil pores. During each freezing stage, pore water migrates to the colder regions, causing the soil to expand; after thawing, some of the water flows back, but the soil structure cannot fully recover.