## 4 Conclusions  
In the present work, a method of determining the thermal conductivity of sandy soils in the near-phase-transition zone was proposed, and the temperature variation trends and parameter influence laws of thermal conductivity were investigated. Moreover, prediction models based on MR and RBFNN methods were established, and the prediction accuracies of the different models were compared. The conclusions are as follows:  
1. The average error between the proposed method and the steady-state heat flow method for soil thermal conductivity in the near-phase-transition zone is 7.25% and the maximum error is 10.1%, which verifies the reliability of the proposed test method. 2. The unfrozen water content in fine sandy soil changes drastically in the near-phase-transition zone, and the amplitude of this change in the range of 0\(\rightarrow\)\(-\)3 \({}^{\circ}\)C accounts for over 80% of the total change in the entire negative temperature range. The changes in unfrozen water content and thermal conductivity in fine sandy soil exhibit similar trends, and the near-phase-transition zone temperature interval can be divided into a drastic phase transition zone and a stable phase transition zone. 3. Increases in the thermal conductivity of fine sandy soil mainly occur in the drastic phase transition zone; these increases account for about 60% of the total increase in thermal conductivity across the entire negative temperature region. With the increase in density and total water content, the rate of the increase in thermal conductivity in the drastic phase transition zone gradually decreases. 4. The prediction models based on the MR and RBFNN methods both have a high accuracy, which highlights their engineering application value. The \(R^{2}\), \(MAE\), and \(RSME\) of the RBFNN model in the drastic phase transition zone are 0.991, 0.011, and 0.021, respectively, and are better than those of the MR prediction model. This study can help researchers to understand trends in the thermal conductivity of sandy soils with temperature in the near-phase-transition zone and also provides basic thermal data for the design of the future Qinghai-Tibet expressway. However, it should be noted that the MR fitting formula of thermal conductivity in the near-phase-transition zone is only applicable to fine sandy soil, and when the dry density of the sample is relatively small, there may be large errors in the predicted values in the drastic phase transition zone. In addition, although the RBFNN prediction model has a high accuracy in both the drastic and stable phase transition zones, it is naturally a data-driven method and its prediction accuracy depends on the amount of test data; thus, a certain amount of data are required for engineering designers to utilize it. Conceptualization, J.L. and Y.Z. ([PERSON]); methodology, J.L. and P.L. ; software, H.H. and L.T. ; validation, J.L., Z.L. and Y.Z. ([PERSON]); formal analysis, P.L. and Y.Z. ([PERSON]); investigation, J.L. and P.L. ; resources, Z.L. and Y.Z. ([PERSON]); data curation, J.L. and Y.Z. ([PERSON]); writing--original draft preparation, J.L. ; writing--review and editing, J.L. and Y.Z. ([PERSON]). All authors have read and agreed to the published version of the manuscript. \begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Evaluation**} & \multicolumn{3}{c}{**MR Model**} & \multicolumn{2}{c}{**RBFNN Model**} \\ \cline{2-5}  & **Drastic Phase** & **Stable Phase** & **Drastic Phase** & **Stable Phase** \\  & **Transition Zone** & **Transition Zone** & **Transition Zone** & **Transition Zone** \\ \hline \(P_{\pm 10}\) & 94.8\% & 100\% & 100\% & 100\% \\ \(R^{2}\) & 0.82 & 0.970 & 0.991 & 0.986 \\ MAE & 0.079 & 0.037 & 0.011 & 0.022 \\ RSME & 0.166 & 0.049 & 0.021 & 0.038 \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Comparison of the prediction effect of MR and RBFNN models. **Funding:** This research was funded by the National Science Foundation of China (Grant Nos.