## 4 Discussion  
_Level of Frost Having in Different Soil Types According to Degree of Saturation_  
The frost heaving and pressure of the gravel ballast-subgrade soil mixtures were evaluated through laboratory tests. However, these results need to be compared with those for other types of soil to clarify the degree of frost action on gravelly soils. Several previous studies have evaluated frost heaving in various soil types. For a comprehensive evaluation, typical soil types were classified as gravel (>4.75 mm), sand (4.75-0.075 mm), fine (<0.075 mm), silt (0.075-0.02 mm), and clay (<0.02 mm) [22]. The type of soil that forms more than 50% of the total weight of a soil mixture was considered as the major soil type, and the other soil types as minor soil types. Accordingly, five soil types were artificially categorized in this study: (a) _gravel with sand_, (b) _gravel with fine_, (c) _sand with silt_, (d) _silt with clay_, and (e) _clay with silt_. For example, _gravel with sand_ consisted of more than 50% gravelly soils and less than 50% of sandy soils. _Gravel with sand_ included the gravel ballast-subgrade soil mixtures of this study. _Silt with clay_ mainly consisted of silty soils with minor clay soils. Data from the literature were not ready to use [13; 14; 27; 28; 29; 30]; therefore, several assumptions were made while summarizing the literature. For instance, when the water content (\(w\)) was given, the degree of saturation (\(S\)) was calculated using the specific gravity (\(G_{\rm s}\)) and void ratio (\(e\)) (e). \(Se=wG_{\rm s}\)). When \(e\) was not available, \(e\) was derived using the dry unit weight (\(\gamma_{\rm d}\)) (e.g., \(\gamma_{\rm d}=[G_{\rm s}\cdot\gamma_{\rm w}]/[1+e]\), where \(\gamma_{\rm w}\) is the unit weight of water, 1 g/cm\({}^{3}\)) [31]. The summarized data are shown in Figure 9 in terms of the frost heaving ratio \(\eta\). The data on _gravel with fine_ in this study were compared with previous data on this soil mixture [12; 13; 14]. Some studies performed frost tests on subgrade soils (_sand with silt_) [25; 27; 30]. [PERSON] et al. [29] analyzed the frost-heaving behavior of the clayy silt area in northeastern China (_silt with clay_), while others focused on that of clayey soils, including kaolinite and montmorillonite (_clay with silt_) [17; 28; 32; 33]. The values of \(\eta\) varied from zero to more than 10% (Figure 9). _Gravel with sand_ exhibited low values of \(\eta\) in the range of less than 1%, whereas _gravel with fine_ sand had a wider range of \(\eta\) (less than 2%). In fact, the \(\eta\) range of _gravel with fine_ was closely located where those of _gravel with sand_ are plotted. However, the frost heaving of _gravel with sand_ was negligible when \(S\) was less than 55%, but that of _gravel with fine_ sand was \(\eta-1\)% when \(S\) was less than 40%. This observation indicates that additional fines make gravelly soils more prone to frost heaving than sandy soils. Therefore, _gravel with fine_ can be regarded as having a higher frost potential than _gravel with sand_. _Sand with silt_ and _silt with clay_ were located in a similar range of \(\eta\) (e.g., approximately 0.5-2.5%). Silty soil is considered the most frost-susceptible soil owing to its moderate water retention capacity and hydraulic conductivity to form ice lenses [15]. The \(\eta\) of _sand with silt_ and _silt with clay_ were located at \(S=30\)-100%. In addition, _clay with silt_ showed an extremely high \(\eta\) compared to other types of soil. Kaolinite and typical clayey soils generally show \(\eta>5\%\) at S \(>70\%\). Studies have indicated that ice lenses are usually formed by fissuring the clay body, causing excessive heaving of the clay above the ice lenses. One value of \(\eta\) by montmorillonite is located at  
Figure 8: Summary of frost heaving pressure tests. \(\eta=1.3\) at \(S=38\%\)[17]. Montmorillonite has an exceptionally high water retention capacity, which results in low frost heaving [15].