## 2 Materials and Methods  
### Gravel Ballast and Subgrade Soil  
Gravel ballast and subgrade soil were collected in situ from a railroad site in Cheolwon, South Korea. Because the collected gravel ballast had a biased grain distribution during sampling, the distribution of the gravel ballast in situ was modified following KRCS A015 07 [20]. As the specification provides ranges, averaged values were chosen. The collected samples were sieved at 125 mm, 63.5 mm, 25.4 mm, 9.52 mm, 2.5 mm, and 0.15 mm [21] (Figure 1), and the gravel ballast was reconstituted in the following ratios: 63.5-125 mm (30%), 25.4-63.5 mm (23%), 9.52-25.4 mm (3%), 2.5-9.52 mm (14%), and 0.15-2.5 mm (20%). Subgrade soil was used with the original composition. Sieve analysis was conducted for the subgrade soil. The grain-size distributions of the gravel ballast and subgrade soil are shown in Figure 2. Based on a united soil classification system (USCS) [22], the ballast soils consist of \(-40\%\) cobble (for soils retained on a 76.2 mm sieve) and \(-60\%\) GP (for soils passing a 76.2 mm sieve, poorly graded gravel). The subgrade soil was classified as poorly graded sand (SP). The specific gravities of the ballast soil and subgrade soil were 2.67 and 2.70, respectively [23]. The subgrade soil had a maximum dry unit weight of 19.8 kN/m\({}^{3}\) and an optimum water content of 10.3% [24].  
The actual mixed zone between the gravel ballast and subgrade soil was not easy to sample, including various uncertainties. Therefore, artificial mixture was used to simulate soils mixed at the interfacial zone between the ballast and subgrade based on the porosity of gravel ballast. This study focuses on the frost action of gravel ballast as a major material  
Figure 1: Sieved gravel ballast samples. Largest size on top left and smallest one on bottom right.  
Figure 2: Grain size distributions of gravel ballast and subgrade soil.  
mixed with subgrade as a sub-material; therefore, the subgrade soil was added to the gravel ballast soil with a mixing ratio \(M\) (e.g., \(\text{mass}_{\text{subgrade}}/\text{mass}_{\text{total}}\times 100\%\)) of 0%, 5%, 10%, 15%, 20%, and 25%. \(M=25\%\) indicates a mixture consisting of 25% subgrade soil and 75% gravel ballast based on mass percentage. The dry unit weight (\(\gamma_{\text{d}}\)) and porosity (\(n\)) of the ballast-subgrade mixtures were measured using a mold with a diameter of 28 cm and height of 23 cm. Once the dry gravel ballast and subgrade soil were mixed, the mixture was placed into the mold in five layers with vibrations. Then, the steady-state dry unit weight of the mixtures was evaluated. Rather than compaction, only vibrating energy was applied to simulate the mixing due to the dynamic energy during train operation. The measured \(\gamma_{\text{d}}\) and corresponding \(n\) values are shown in Figure 3. The values of \(\gamma_{\text{d}}\) and \(n\) show an inverse relationship. The trends in Figure 3 showed a complex relationship. When \(M\) increases, the compaction efficiency of the mixture increases as the subgrade soils are finer than the gravel ballast. However, the mass of the gravel ballast decreases as \(M\) increases. The coefficients of uniformity and curvature rapidly change with respect to Figure 2. Therefore, \(\gamma_{\text{d}}\)-\(M\) seems to exhibit an extraordinary relationship.