## 4 Conclusions  
In this work, the matrix suction test of unsaturated clay under different dry densities and different freeze-thaw cycles was carried out, and the change law of characteristic parameters of SWCC of unsaturated clay was analyzed. The variation characteristics of an SWCC is best explained when combined with a microstructure. The accurate prediction of the SWCC of unsaturated clay under the action of freeze-thaw cycles is realized by fitting the soil-water characteristic parameters. The following conclusions are drawn:  
1. The results of the aspiration test of low-liquid-limit silty clay matric at different densities indicate that a SWCC with high density soil SWCC has higher AEV and residual water content and lower saturated moisture content. In the transition section, the high-density soil sample has a lower moisture-loss rate under the same suction than the low-density soil sample. The high-density soil samples have smaller pores and better water retention; while their porosity is lower than that of low-density soils, the water content in saturated pores is smaller than that in low-density soils. 2. The characteristic parameters of a SWCC are negatively correlated with the number of F-T cycles. With the increase in the number of F-T cycles, the saturated water content and desorption rate of the transition section began to gradually increase. For the test soil samples, the AEV, residual moisture content and water holding capacity began to decrease. The sensitivity of the water in the pores to suction is increased, and became more susceptible to suction and began to dissipate. The first F-T cycle has the most severe effect on the characteristic parameters and then gradually decreases. This change is no longer obvious between five to seven F-T cycles. 3. The results of the SEM revealed that the original pore structure of the soil sample became looser. The plate-like overall structure of the soil sample gradually ruptured, and the crack gradually developed in the soil sample. In detail, the F-T cycles increase the large and medium pores in the soil and reduce the small pores. Overall, the porosity and average pore size of the soil sample are increased. This result explains the mechanism of the SWCC changes after the F-T cycles. 4. The characteristic parameters of a SWCC under different F-T cycles were fitted by a mathematical formula. The relationship between the characteristic parameters and the number of F-T cycles was established to predict the SWCC after n F-T cycles. Taking the correlation coefficient as the criterion, R\({}^{2}\) is all above 0.98, which indicates that the fitting accuracy is outstanding. In summary, the variation characteristics of a SWCC of unsaturated clay considering the freezing-thawing cycles are studied in this paper, which provides a reference for the related application of soil-based engineering in seasonally frozen regions. 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 Jilin Province Transportation Department, grant number 2017 ZDGC6. Not applicable. \begin{table}
\begin{tabular}{c c c c c c c c c c c c c} \hline \hline \multirow{2}{*}{\(\rho\)} & \multicolumn{4}{c}{**1.73 g/cm\({}^{3}\)**} & \multicolumn{4}{c}{**1.67 g/cm\({}^{3}\)**} & \multicolumn{4}{c}{**1.61 g/cm\({}^{3}\)**} \\ \cline{2-13}  & \(\theta_{s}\) & \(\theta_{r}\) & \(\psi_{b}\) & \(s_{1}\) & \(\theta_{s}\) & \(\theta_{r}\) & \(\psi_{b}\) & \(s_{1}\) & \(\theta_{s}\) & \(\theta_{r}\) & \(\psi_{b}\) & \(s_{1}\) \\ \hline R\({}^{2}\) & 0.992 & 0.989 & 0.997 & 0.987 & 0.994 & 0.991 & 0.988 & 0.993 & 0.997 & 0.991 & 0.998 & 0.985 \\ \hline \hline \end{tabular}
\end{table}