# Artificial Neural Network-Based Model for Prediction of Frost Heave Behavior of Silty Soil Specimen
## 1 Introduction  
Hundreds of thousands of people in Alaska, Canada, Russia, and Greenland live on permafrost, a type of soil that covers nearly 24% of the northern hemisphere [1]. Frost heave and thawing actions are key issues in permafrost regions that can cause various engineering problems, such as the progressive lifting of sewer pipelines, subsidence of buildings, cracking of road surfaces, and damage to ground infrastructure structures or geological repository systems (Figure 1). Recently, we have seen that natural freeze-thaw cycles from season to season can also cause significant subsidence problems for buildings or underground structures, even in non-permafrost areas. The sequence of subsidence events caused by the frost heave and thawing cycle is depicted in Figure 2, which shows a homogeneous fine-grained soil column subjected to one-sided natural freezing from top-down. To analyze and predict this phenomenon, it is necessary to understand the complex thermal-hydro-mechanical (THM) coupling that occurs during the freezing process. The preconditions for frost heave action in frozen soil are as follows [2,3]: (a) the soil is potentially subject to frost heave action, (b) a sufficient supply of water, the material source for frost heave in soils, is available, and (c) the thermal conditions must be suitable to cause the freezing front to move at a sufficiently slow rate to allow for water migration. In general, frozen soils comprise three zones: a frozen zone, a frozen fringe, and an unfrozen zone (Figure 3). The boundary between the frozen fringe and the unfrozen zone is called the freezing front, which is related to the 0 \({}^{\circ}\)C (273.15 K) isotherm [2]. When freezing begins in the frozen zone, the freezing front propagates to the unfrozen zone, resulting inan expansion in volume due to the phase change of the pore water behind the frozen fringe. Water subsequently moves into the freezing front to compensate for the water loss due to the phase change, forming a periodic ice layer referred to an ice lens [2; 3; 4; 5]. The continuous growth of the ice lens ultimately causes a significant amount of frost heave. Early research on the subject involved various experimental investigations aimed at understanding the frost heave action mechanism at various scales [6; 7; 8; 9]. Such investigations covered small-scale column-freezing tests [6], large-scale tests [7], and long-term field-scale monitoring [8; 9]. Afterwards, several numerical simulation studies based on heat and mass transfer in porous media were conducted to evaluate frost heave. Initially, such simulation models used empirical equations [10; 11; 12; 13; 14]. [PERSON] and [PERSON] [11] proposed the segregation potential (SP\({}_{0}\)) theory, which explains the correlation between the temperature gradient (gradT) and the water flux in the frozen fringe according to the coefficient SP\({}_{0}\). Subsequently, [PERSON] and [PERSON] [14] proposed a thermodynamic model that treated soil as an incompressible material to derive new standards for ice lens formation. [PERSON] et al. [15] developed an elasto-plastic mechanical constitutive equation for frozen soil using SP\({}_{0}\) to efficiently describe the complex THM phenomena of frozen soil. [PERSON] et al. [16] proposed a practical method that expands the one-dimensional frost heave equation (Takashi's equation) into multi-dimensional situations. Afterwards, a new approach was proposed to account for the fluid flow due to the temperature gradient. This approach estimated cryogenic suction using the interfacial tension between ice and fluid. Several studies used the Clausius-Clapeyron equation,  
Figure 1: Uneven permafrost thawing underneath a building foundation in Kangerlussuaq. (Reprinted with permission from ref. [17]. (photo by: [PERSON])). Figure 2: The sequence of subsidence events caused by frost heave and thawing (Reproduced from [18]). which determines the ice-water pressure at phase equilibrium, to calculate cryogenic suction and perform THM analysis [19; 20; 21; 22; 23; 24].