## 3 Results  
### Frost Heaving  
#### 3.1.1 Heaving Behavior  
Figure 5 shows the frost heaving for gravel ballast-subgrade soil mixtures with varying mixing ratios and degrees of saturation. Despite the presence of pure gravelly soils, h-M0-S70/80/90 exhibited certain levels of frost heaving (\(h\)) in the presence of pore water (Figure 5a). When \(S\) = 70%, \(-500\) min was required to reach \(h\) at steady state, whereas \(-100\) min and \(-150\) min were required for \(S\) = 80% and 90%, respectively. The ultimate  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Test Type** & \(M\) **[\%]** & \(S\) **[\%]** & **Test Name** \\ \hline \multirow{5}{*}{Frost heaving} & 0 & h-M0-S70/80/90 \\  & 5 & h-M5-S70/80/90 \\  & 10 & h-M10-S70/80/90 \\  & 15 & h-M15-S70/80/90 \\  & 20 & h-M20-S70/80/90 \\  & 25 & h-M25-S70/80/90 \\  & 0 & p-M0-S70/90 \\ Frost heaving & 5 & p-M5-S70/90 \\ pressure & 15 & 70/90 \\  & 25 & p-M25-S70/90 \\ \hline \hline \end{tabular}
\end{table}
Table 2: Details of frost experiments conducted in this study.  
Figure 4: Scheme of frost experiments. Setup for (**a**) frost heaving test and (**b**) frost heaving pressure test.  
\(h\) (\(h_{\rm{ult}}\), \(h\) selected at 20 h) of h-M0-S70 and S80 were similar (\(-0.3\) mm), but that of S90 showed a higher value (\(-0.75\) mm). The behavior of \(h\) over time for h-M0-S70 was different from that for h-M0-S80/90. h-M0-S70 shrank in the initial phase and gradually expanded to \(h_{\rm{ult}}\). However, \(h\) showed a rapid increase in the case of h-M0-S80/90. Water contracts at 4 \({}^{\circ}\)C and expands below 4 \({}^{\circ}\)C [26]. Therefore, it is natural to observe that \(h\) decreases in the initial phase and then increases. However, it seems that the initial freezing mechanism of the gravel ballast differs from that of \(S\). When \(S\) is lower, frost shrinkage occurs, followed by frost heaving, whereas frost heaving occurs immediately when \(S\) is higher. This implies that the formation of ice lenses in the pore network occurs easily and rapidly when \(S\) is high, resulting in prompt frost heaving.  
When \(M\) = 5%, the frost behavior of the mixtures was similar to that when \(M\) = 0% (Figure 5b). h-M5-S70 exhibited frost shrinkage in the initial phase; however, later on, it frost-heaved. The amount of frost shrinkage (approximately \(-0.5\) mm) was higher than the ultimate frost heaving (approximately 0 mm). The amount of \(h_{\rm{ult}}\) were also analogous to that for \(M\) = 0%.  
The frost behavior for \(M\) = 10% was slightly different from those for \(M\) = 0% and 5% (Figure 5c). All cases exhibited frost shrinkage during the initial phase, regardless of \(S\). Frost shrinkage was maximized at \(-200\) min; thereafter, it gradually increased. \(H_{\rm{ult}}\) was observed at \(-400\)-\(600\) min. In this case, 10% of the subgrade soils were mixed with 90% of the gravel ballast. It is inferred that the migration and release of pore fluid in subgrade  
Figure 5: Results of frost heaving tests. (**a**) \(M\) = 0%, (**b**) 5%, (**c**) 10%, (**d**) 15%, (**e**) 20%, and (**f**) 25%.  
soil induces frost shrinkage during initial freezing [19]. Eventually, the mixtures were heated owing to the expansion of ice lenses from the agglomerated pore fluid. Similar behaviors were observed when \(M=15\%\) and \(25\%\) (Figure 5d,e, respectively). At \(M=25\%\), the mixtures exhibited the highest \(h_{\text{ult}}\) (Figure 5f). Interestingly, the frost shrinkage of h-M25-S70 was the lowest in the \(M\) range of 0-25%. The effect of the migrating pore fluid was maximized for the h-M25-S70 specimen.