## 3 Results and Discussion  
### Trends in Sandy Soil Thermal Conductivity in the Near-Phase-Transition Zone  
Based on the proposed testing method, the thermal conductivity of sandy soil specimens in the near-phase-transition zone was obtained and analyzed. The natural density of the sandy soil samples tested in this study ranged from 1.83 to 2.39 g/cm\({}^{3}\), with an average of 2.05 g/cm\({}^{3}\), and the water content range was 7.3%-28.3%, with an average of 13.9%. According to the classification standard of frozen soil [45], the test soil samples \begin{table}
\begin{tabular}{c c c c c c} \hline \multirow{2}{*}{\(W_{0}\)**\%**} & \multirow{2}{*}{\(\rho_{d}\)/g\(\cdot\)cm\({}^{-3}\)} & \multicolumn{3}{c}{**Test Error in the Near-Phase-Transition Zone/\%**} & \multicolumn{1}{c}{**Test Error at Room**} \\ \cline{3-6}  & & _Min._ & _Max._ & _Ave._ & **Temperature/\%** \\ \hline \multirow{4}{*}{8} & 1.70 & 7.52 & 8.80 & 8.27 & 5.20 \\  & 1.75 & 9.10 & 10.13 & 9.54 & 2.37 \\  & 1.80 & 8.73 & 9.66 & 9.08 & 3.79 \\  & 1.70 & 7.53 & 8.02 & 7.86 & 3.38 \\
10 & 1.75 & 7.27 & 7.85 & 7.65 & 7.83 \\  & 1.80 & 6.31 & 7.28 & 6.87 & 2.99 \\  & 1.70 & 5.50 & 6.37 & 5.87 & 3.41 \\
12 & 1.75 & 4.65 & 5.53 & 5.18 & 2.68 \\  & 1.80 & 4.24 & 5.20 & 4.93 & 2.09 \\ \hline \end{tabular}
\end{table} 
Table 5: Comparison of errors of the method developed in the present work and the method in ref. [42]. Figure 6: Comparison of soil thermal conductivities predicted by the transient method developed in the present work and those predicted by the steady-state heat flow method in ref. [42]: (**a**) room temperature; (**b**) near-phase-transition zone. were divided into four types, namely ice-poor (W\({}_{0}\)\(\leq\) 12%), icy (12 \(<\) W\({}_{0}\)\(\leq\) 18%), ice-rich (18 \(<\) W\({}_{0}\)\(\leq\) 25%), and ice-saturated (W\({}_{0}\)\(>\) 25%) frozen soil. Figure 7 shows the variation in thermal conductivity of different soil types in the negative temperature range. It can be seen that, as the temperature decreases, the thermal conductivity of sandy soil specimens decreases. When the temperature is far away from the phase transition point (e.g., \(>\)\(-\)4 \({}^{\circ}\)C), the soil thermal conductivity remains relatively stable and resistant to temperature changes. When approaching the phase transition temperature point (e.g., \(<\)\(-\)2 \({}^{\circ}\)C), the soil thermal conductivity changes dramatically with temperature, and the magnitude of the change rapidly increases as the temperature approaches the phase change point. This is because, when the temperature drops, the unfrozen water in the soil sample transforms from liquid to solid. The volume of ice is 1.1 times that of water, and the increased amount of ice fills the pores inside the soil sample, thereby increasing the contact area for heat transfer. The solid ice also enhances the thermal conductivity of the soil itself (the thermal conductivity of ice is four times that of water). Therefore, the soil thermal conductivity significantly increases as the temperature decreases, especially in the near-phase-transition zone where the liquid water undergoes considerable changes. It can also be observed that the thermal conductivity of the soil specimens increases as the dry density increases. In addition, the thermal conductivity increase caused by the increase in dry density is greater for ice-poor and icy frozen soils, but relatively insignificant for ice-rich and ice-saturated frozen soils. As shown in Figure 7, when the  
Figure 7: Variation in thermal conductivity of different soil types in the negative temperature range: (**a**) ice-poor frozen soil; (**b**) icy frozen soil; (**c**) ice-rich frozen soil; (**d**) ice-saturated frozen soil.