## 4 Analysis of Simulation Results
### Sensitivity Analysis  
According to previous research, the cooling plan is the most significant factor affecting the temperature change in freezing construction. Considering that the focus of the freezing  
Figure 14: Schematic diagram of freeze-up displacement monitoring path and monitoring points. Figure 15: (**a**) Variation in freezing vertical displacement of monitoring points under different times; (**b**) frozen vertical displacement map of each path after 45 d of freezing. project was on keeping the other material parameters of the soil body unchanged, we set the final brine temperatures to \(-23\)\({}^{\circ}\)C and \(-33\)\({}^{\circ}\)C and compared the results with those corresponding to the original \(-28\)\({}^{\circ}\)C brine temperature to discuss the effect of the difference in the final temperature of the cooling plan on the temperature field and the displacement field. The cooling plan is shown in Table 3.  
Temperature variations measured in points 2 and 7 under different brine cooling plans were extracted and plotted, as shown in Figure 16 (certain details have been omitted for brevity). Analyzing the temperatures at the measurement points, it can be seen that due to the cooling plans all being the same at the beginning of freezing, differences between the cooling plans start to appear only after the cooling plans reach the lowest design plan, and the temperature differences are gradually shown after five days of active freezing: Plan 2 reaches the phase transition temperature faster and enters into the latent heat of the phase transition stage earlier than the original plan, while Plan 3 reaches the phase transition temperature slower and enters into the latent heat of phase transition stage at a time lag compared with the original plan. Afterward, as the minimum temperature of the brine cooling plan decreases, the temperature difference between the temperature measurement points gradually becomes larger. The overall law of cooling maintains the pre-freezing temperature decline speed; the soil body reaches the latent heat stage after slowing down and then starts to become faster before finally slowing down to a constant temperature, being lower than the design requirements of the permafrost temperature. The brine cooling program has a more obvious influence on the final freezing temperature. The temperature difference between the lowest temperature of the cooling program is 5\({}^{\circ}\)C, and the final temperature difference between the temperature measurement points is about 5\({}^{\circ}\)C.  
The frozen vertical displacement variation curves of the DP1 path after freezing for 45 d under different brine cooling plans were extracted and plotted, as shown in Figure 17. As can be seen in this figure, the surface's maximum vertical displacements of 379 and 213 mm were produced by 45-day freezing via Plans 2 and 3, respectively. The lower brine temperature has a wider range of influence, and the difference in displacement between the soils is farther away from the center of influence, while that of the center soil  
Figure 16: (**a**) Comparison of temperature changes at point 2 under different freeze plans; (**b**) comparison of temperature changes at point 7 under different freeze plans. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Time/d** & 0 & 20 & 30 & 45 \\ \hline
**Plan 1/\({}^{\circ}\)C** & 18 & \(-20\) & \(-28\) & \(-28\) \\ \hline
**Plan 2/\({}^{\circ}\)C** & 18 & \(-25\) & \(-33\) & \(-33\) \\ \hline
**Plan 3/\({}^{\circ}\)C** & 18 & \(-15\) & \(-23\) & \(-23\) \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Salt water cooling program. is smaller. In addition, the decrease in freezing displacement brought about by the increase in the minimum brine temperature is larger than the increase in displacement brought about by the decrease in the minimum brine temperature because when the minimum brine temperature increases, the thickness of its permafrost curtain decreases, and the phenomenon of soil freezing shrinkage is less obvious.