## Materials and Methods
### Method of Measuring Thermal Conductivity of Sandy Soil in the Near-Phase-Transition Zone  
In this study, the thermal conductivity of sandy soil specimens in the near-phase-transition zone was calculated using the test results of thermal diffusivity and specific heat capacity:  
\[\lambda=\alpha C, \tag{1}\]  
where \(\lambda\) is the thermal conductivity of a sandy soil specimen, \(\alpha\) is its thermal diffusivity, and \(C\) is its volumetric specific heat capacity. The thermal diffusivity was measured using the transient plane source method. The experimental system consisted of a Hot Disk TPS1500s Thermal Conductivity Analyzer, a high-precision environmental cabinet and a data acquisition system, as shown in Figure 3. According to geotechnical testing standards, the remolded testing soil specimens were fabricated using the hydraulic press demundding method. In order to improve the test accuracy, cylindrical specimens with a diameter of 80 mm and a height of 30 mm and a circular Kapton sensor with a diameter of 29.4 mm were adopted. The testing temperatures were divided into two ranges, positive temperatures and negative temperatures, in which the controlling temperature of the positive temperature range was 10 \({}^{\circ}\)C. The negative temperature range was defined from initial freezing temperature point of the tested sample (\(T_{f}\)) to \(-\)15 \({}^{\circ}\)C. Since the initial freezing temperatures of the tested soil specimens were all around \(-\)0.5 \({}^{\circ}\)C, the starting point of the negative temperature range was set to \(-\)0.5 \({}^{\circ}\)C to simplify the experimental protocol and facilitate analysis. Furthermore, in order to more accurately capture the trends in thermal diffusivity of the tested samples in the near-phase-transition zone, an experimental strategy using small temperature intervals was applied in this temperature range. The specific test temperature points were \(-\)15 \({}^{\circ}\)C, \(-\)11 \({}^{\circ}\)C, \(-\)8 \({}^{\circ}\)C, \(-\)6 \({}^{\circ}\)C, \(-\)4 \({}^{\circ}\)C, \(-\)3 \({}^{\circ}\)C, \(-\)2 \({}^{\circ}\)C, \(-\)1.5 \({}^{\circ}\)C, \(-\)1 \({}^{\circ}\)C, \(-\)0.7 \({}^{\circ}\)C, and \(-\)0.5 \({}^{\circ}\)C. \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline
**Mileage** & **Specimen** & \multicolumn{3}{c}{**Natural Water Content/\%**} & \multicolumn{3}{c}{**Density/g\(\cdot\)cm\({}^{-3}\)**} \\ \cline{3-8}
**Range** & **Number** & _Max._ & _Min._ & _Ave._ & _Max._ & _Min._ & _Ave._ \\ \hline K2881\(-\)K2920 & 9 & 28.3 & 9.1 & 15.6 & 2.17 & 1.88 & 2.03 \\ K2920\(-\)K2985 & 12 & 21.3 & 7.9 & 13.9 & 2.27 & 1.90 & 2.04 \\ K2985\(-\)K3070 & 8 & 19.4 & 11.0 & 13.3 & 2.39 & 1.83 & 2.11 \\ K3070\(-\)K3150 & 7 & 18.5 & 13.5 & 15.3 & 2.24 & 1.86 & 2.05 \\ K3150\(-\)K3220 & 8 & 19.6 & 13.2 & 15.2 & 2.14 & 1.84 & 2.00 \\ K3220\(-\)K3307 & 7 & 11.5 & 7.3 & 9.4 & 2.20 & 2.07 & 2.11 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Basic physical properties of the tested soil specimens. Figure 3: Thermal diffusivity testing instrument. The volumetric specific heat capacity was calculated using the theoretical calculation method [10]. In this calculation method, it is assumed that the soil's volumetric specific heat capacity is the mass-weighted average of its multiphase components, including the soil skeleton, water and ice. The calculation formula is as follows:  
\[C_{u}=\frac{C_{su}+W_{0}\cdot C_{w}}{1+W_{0}}\rho_{u}, \tag{2}\]  
\[C_{f}=\frac{C_{sf}+(W_{0}-W_{u})\cdot C_{i}+W_{u}\cdot C_{w}}{1+W_{0}}\rho_{f}, \tag{3}\]  
where \(C_{u}\) and \(C_{f}\) are the volumetric specific heat capacity of unfrozen and frozen soil samples, respectively; \(C_{su}\), \(C_{sf}\), \(C_{w}\) and \(C_{i}\) are the mass specific heat capacity of unfrozen soil skeleton, frozen soil skeleton, water, and ice, respectively, for which specific values are listed in Table 2; \(\rho_{u}\) and \(\rho_{f}\) are the natural density of unfrozen soil and frozen soil, respectively; and \(W_{0}\) and \(W_{u}\) are total water content and unfrozen water content, respectively.