## 1 Introduction  
A ballast in railroad tracks is a component that fixes ties (or sleepers) in a specific position and distributes the loads transmitted from the ties to the subgrade. Ballasts are classified into two types: gravel ballast and concrete ballast (or slab ballast). Minor types such as sand, Moorum, slag, etc. are not discussed in this study [1]. The typical design of gravel and concrete ballasts and their pros and cons of each are summarized in Table 1. A gravel ballast is a ballast constructed by pouring gravels, while concrete ballast is made of prefabricated concrete blocks and cement mortar. At the initial era of railroad construction, gravel ballast was the major format in railroad construction due to its easy and economical constructability [2]. The stability of the gravel-ballasted track is secured by friction between the gravels, and the impact and vibration are absorbed through the elasticity of the ballast. However, concrete ballasts became popular in the world due to the frequent maintenance of gravel ballasts due to changes in track geometry, material deterioration, etc. [3, 4]. Concrete ballast is a more advanced form than a gravel ballast due to its better engineering properties, maintenance, etc. despite the expensive initial construction cost [5]. Advanced railroad countries (France, Germany, Japan, China, etc.) are using concrete ballasts for new or expanded high-speed railroads. In South Korea, concrete ballasts have been used since 2005. Although recently constructed concrete ballasts are superior, the problem is that most existing railroads are still gravel ballasts. One of the problems with gravel ballasts is the frost heaving in cold regions. In South Korea, [PERSON] et al. [6] reported that the number of sites showing frost heaving was 129 with a \(-4\) km distance in 2009, while [PERSON] et al. [7] stated 190 with a \(-8\) km distance in 2011. To countermeasure the frost heaving on gravel ballasts, several approaches are attempted, such as the replacement of gravels, usingcalcium chloride, improving drainage, etc. Those maintenance costs are enormous. The frost potential of gravels is known to be low due to the high drainage capacity. However, it depends on the situation. For example, the subgrade, which is susceptible to freezing and thawing, can be mixed with gravel ballast during train operation, and then the mixture becomes vulnerable to frost damage. Most sites with frost having found mud pumping in summer. Mud pumping is the upward movement of subgrade soils to the gravel ballast surface. Subgrade soils during the rainy season are liquefied and easily move to the surface through gravel ballast. The subgrade soil-gravel ballast mixture brings a decrease in the void ratio, and correspondingly hydraulic conductivity, and eventually poor drainage, which turns out that the mixture is susceptible to frost heaving [8,9]. Therefore, the interfacial zone between the gravel ballast and the subgrade is the place where the frost action develops. The interfacial zone is generally unsaturated, as the gravels have high permeability [10]. There are some studies that observe the action of frost on gravel soils with fines [11, 12, 13, 14]; however, few studies were conducted to evaluate the action of frost on gravel ballast-subgrade soil mixtures under unsaturated conditions. Frost occurs when the following conditions are coincident: temperature is below 0 \({}^{\circ}\)C; there is the presence of water from groundwater or undrained water; and the soils can retain pore water [15]. Frost action has been studied in terms of frost heaving and frost heaving-induced pressure (frost heaving pressure) [16]. Frost heaving is highly dependent on the soil size. Soils more than 0.1 mm (e.g., more than sand) are unlikely to experience frost heaving due to high permeability. Soils with grain sizes of 0.05-0.1 mm (e.g., fine sands) start heaving, and those with grain sizes of 0.002-0.05 mm (e.g., silt) present the most heaving.