## 2 Experimental Study
### Experimental Results  
Figure 5 shows the plot of the results of the measured thermal conductivity of the specimens at different porosities and the water contents of 0%, 5%, 10%, and 15%, respectively. It shows that the measurements using the needle probe method and those using the hot-plate method are in a good agreement at low water contents. In the range of four water contents, the measurements of the probe method present a more stable and consistent trend in variation. It can be seen that two curves of the hot-plate measurements crossed at high water content and porosity. This result may be related to the moisture migration in the tests using the hot-plate method. The comparison demonstrates that the needle probe method is more suitable for unsaturated soils and can provide good accuracy. In conclusion, all the modelling, analyses, and discussion in the rest of the paper will use the data of the needle probe method. Compared with similar sands, the sample D of [PERSON] [18] and the Ottawa C-190 of [PERSON] et al. [16], it can be noticed that the measurements in this study are very close to the two previous studies at the fully dry condition. For example, all the sands in the three studies have a similar thermal conductivity of about 0.3-0.4 Wm\({}^{-1}\).K\({}^{-1}\) at the porosity of about 0.4-0.5 at \begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**The Order No. of the Needle Probe**} & \multicolumn{2}{c}{**The Standard Value**} & \multirow{2}{*}{**Measurement**} & \multirow{2}{*}{**Absolute Error \({}^{*}\)**} & \multirow{2}{*}{**Relative Error \({}^{**}\)**} \\ \cline{2-2} \cline{5-5}  & & & & 0.292 & 0.003 & 0.87\% \\
2 & & & & 0.291 & 0.002 & 0.55\% \\
3 & 0.2872 & 0.2897 & 0.290 & 0.001 & 0.17\% \\
4 & & & 0.284 & \(-\)0.005 & \(-\)1.76\% \\
5 & & & 0.291 & 0.002 & 0.76\% \\ \hline \hline \end{tabular} \({}^{*}\) The measurement—the average of the two standard values at 20 and 40 \({}^{\circ}\)C, \({}^{**}\) the absolute error/the average of the two standard values at 20 and 40 \({}^{\circ}\)C.  
\end{table} 
Table 2: The comparison of the measurement of the thermal conductivity of glycerol. Figure 4: Hot-plate measuring system, (**a**) illustration; (**b**) products. the dry condition. This demonstrates in another way that the three compared sands are quite close in composition and particle distribution. However, it is also noticed that at other unsaturated and fully saturated states, the thermal conductivity of the specimens in this study is much smaller than that of the two similar samples of [PERSON] [18] and [PERSON] et al. [16]. For example, at porosity of 0.466, the fully saturated specimen of this work has a thermal conductivity of 1.6 Wm\({}^{-1}\).K\({}^{-1}\), however, the fully saturated thermal conductivity of the sample D of [PERSON] [18] is about 2.46 Wm\({}^{-1}\).K\({}^{-1}\) at porosity of 0.43, while the fully saturated thermal conductivity of the Ottawa C-190 of [PERSON] et al. [16] is about 3.4 Wm\({}^{-1}\).K\({}^{-1}\) at porosity of 0.4. The big difference is attributed to the difference in pore size distribution of the used specimens because this study took a significantly different preparation procedure from that of the two previous studies. Figure 5 also shows that at 0% water content the variation of porosity presents the smallest influence on the thermal conductivity. This can be explained in that the air content in soils has no significant effect on the thermal conductivity due to its own low thermal transfer capacity. It is noticed that water thermal conductivity is about 0.6 (W/(m\(\cdot\)C)) and air thermal conductivity one order of magnitude less and near 0.024 (W/(m\(\cdot\)C)) at 25 \(\cdot\)C. Therefore, the higher the water content level, the more the conductive phase in the pore space and consequently the greater the thermal conductivity. For that of the 5% and 10% water contents, the thermal conductivity decreases relatively quickly with increasing porosity at the low porosity region.