## 5 Conclusions  
Based on the secondary development functions of the PDE module in COMSOL finite element software, this study performed three-field coupling simulations to preliminarily assess the freezing and expansion characteristics of a tunnel reinforcement process in Hainan, China. This study focused on analyzing the development of the freezing wall, changes in the moisture field, and vertical freezing and expansion displacement. The main conclusions that can be drawn from this study are as follows:  
1. On the 25 th day of freezing, temperature variation cycles from \(-1\) to \(-10\)\({}^{\circ}\)C were completed. By the 30 th day, a fully frozen curtain had formed, meeting the design requirements for thickness. This indicates that the original cooling plan for the project was relatively conservative. Future optimizations could consider shortening the freezing period and reducing costs, referring to the temperature field analysis for improvements. The soil in the strong freezing zone exhibited a faster cooling rate and greater permafrost thickness than the weak freezing zone. The intervals between the pipe curtains in the strong freezing zone enhance the stability of the gaps and the water-stopping capability, aligning with the project's requirements. 2. The influence of the freezing pipes on the soil area resulted in changes in the cooling rate at specific time nodes during the freezing process. Different monitoring points showed varying cooling rates due to differences in the influence of the cold source. Based on monitoring data, specific areas can be targeted for freezing control measures, allowing for adjustments to the freezing program in this project or similar ones. 3. The ice content in the strong freezing area was higher than that in the weak freezing area. Due to the temperature gradient, moisture in the soil migrated toward the cold area, causing the saturation and water content of the surrounding soil to decline. Near the freezing pipe, moisture migration led to temporary water accumulation and increased saturation. By the 30 th day of freezing, saturation within the curtain became uniform and approached zero with higher ice content marking the primary area of freezing and expansion effects. The saturation along the inner and outer edges of the curtain was slightly higher than inside the curtain due to moisture  
Figure 17: Comparison of surface frozen vertical displacement under different freeze plans for 45 d of freezing. migration. Analyzing the saturation changes during freezing effectively elucidates the relationship between moisture migration and freeze-up. 4. The soil closer to the freezing pipe experienced a faster rate of water content reduction, eventually reaching a stable water content stage. The soil farther from the freezing pipe initially showed a slight decrease in water content. If later affected by the freezing front's cold source, a change in the water content reduction rate can be observed; otherwise, only a slight decrease due to water migration occurs. Our analysis of moisture field changes suggests that regions with a rapidly increasing water content decrease, indicating significant moisture phase change to ice, corresponding to strong freezing effects. 5. In the early-phase change phase, frost heave was observed only near the freezing pipe, with the soil near the surface experiencing a vertical displacement of 0.66 mm. By the 35 th day of freezing, upward freezing displacement continued accumulating after forming a stable freezing curtain with the maximum vertical displacement near the surface reaching 320 mm. On the 45 th day, maximum freezing displacement reached 358 mm, indicating a decreased freezing heave effect in the later stages. Therefore, in actual projects, the focus should be on controlling the freezing effect before the 35 th day. Additionally, dense contour lines near the freezing pipe indicated strong freezing displacement in that area, causing significant surface uplift.