## 4 Conclusions  
This paper proposes a semi-empirical prediction model to predict the long-term dynamic resilient modulus of oil shale residue-modified subgrade soil under unsaturated and seasonal permafrost complex conditions. To verify the prediction model, the dynamic load triaxial experiment, with different moisture contents, freeze-thaw cycles, and stress combinations, was conducted for the modified subgrade soil of oil shale waste residue. The following results can be drawn. 1. Based on the analysis of the soil-water characteristic relation curve of modified soil and the principle of effective stress, this paper constructed a suitable \(\chi\) parameter for modified soil to express the contribution ratio of suction to soil element stress. Through observation and discussion of the relationship between the \(\mathrm{M_{R}}\) of oil shale residue-modified soil and the freeze-thaw cycles, the coefficient function describing the ratio of roadbed after a freeze-thaw cycle to the original state was established. These two were incorporated into the \(\mathrm{M_{R}}\) prediction model proposed by AASHTO [3] so that the new prediction model could comprehensively respond to the influence of stress, water content, and matric suction changes. 2. When the freeze-thaw cycle was 0, the fitting coefficient \(\mathrm{R^{2}}\) of the model reached 0.971. Under the conditions of different moisture contents, 89.2% of the statistical samples had a prediction error \(\leq\)10, which shows that the model fitted the test data well and the prediction results were accurate, while the maximum \(\mathrm{R^{2}}\) of the model used as a comparison for the experimental data of the modified soil was 0.404, so it cannot be used for the \(\mathrm{M_{R}}\) prediction of the modified soil. This shows the importance of constructing a specific modified soil resilient modulus prediction model. 3. It was proved by multiple freeze-thaw experiments that the coefficient \(\eta_{n}\) can well fit the decreasing law of the \(\mathrm{M_{R}}\) of oil shale residue-modified soil after freeze-thaw cycles. Figure 5: Error distribution diagram. \begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**F-T Cycles**} & \multicolumn{4}{c}{**Statistical Parameter**} \\ \cline{2-5}  & **Adj. R Square** & **RMSE** & **Significance F** & **The Largest Residual** \\ \hline
1 & 0.961 & 6.54 & \(3.18\times 10^{-6}\) & 10.97 \\
3 & 0.959 & 6.62 & \(3.65\times 10^{-6}\) & 10.85 \\
5 & 0.953 & 6.8 & \(4.19\times 10^{-6}\) & 12.21 \\
7 & 0.951 & 7.15 & \(6.46\times 10^{-6}\) & 11.48 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Regression parameters of predicted and measured values. After applying freeze-thaw cycles, the maximum prediction error of the prediction model increased to 12.21, the R\({}^{2}\) distribution range of different freeze-thaw cycles was 0.95-0.96, and the RMSE of the model was between 6.54 and 7.15. This shows that the coefficient \(\eta_{n}\) can well simulate the change in the M\({}_{\rm R}\) with the increase in the freeze-thaw cycles. The introduction of the coefficient \(\eta_{n}\) had high accuracy for the M\({}_{\rm R}\) prediction after freeze-thaw cycles. In summary, the prediction model proposed in this paper has good applicability to the M\({}_{\rm R}\) prediction of unsaturated oil shale waste-modified soil in seasonally frozen areas. It can provide a reference for the prediction of the long-term resilience modulus of oil shale slag subgrade filling during a road life cycle. Conceptualization, L.H. and X.L. ; methodology, L.H. and X.L. ; software, L.H. ; validation, X.L. ; formal analysis, L.H. ; resources, L.H. ; data curation, X.L. ; writing--original draft preparation, X.L. ; writing--review and editing, L.H. and X.L. ; project administration, L.H. ; funding acquisition, L.H. All authors have read and agreed to the published version of the manuscript. This research was funded by the Science and Technology Project of the Jilin Province Transportation Department, grant number 2017 ZDGC6. Not applicable.