Artificial Ground Freezing—On the Soil Deformations during Freeze–Thaw Cycles

: Artificial ground freezing (AGF) has emerged as a prominent treatment method due to its ability to mechanically strengthen the soil while reducing its permeability. However, its implementation has raised concerns about its impact, particularly with respect to frost heave and subsequent thaw-induced displacements. These soil movements can cause subsidence and pose a significant threat to the integrity of surface structures. Overburden pressure plays a crucial role in AGF and determines the amount of heave generated. This paper presents an analysis of the existing literature about soil freezing and thawing. The aim is to offer an understanding of these processes, specifically with regard to their application in AGF. This paper explains the behavior of soil during freezing, with particular emphasis on the influence of overburden pressure. It also investigates frozen soils’ thawing and freeze–thaw (FT) cycles’ long-term effects on soil properties. AGF offers improved soil strength and reduced water permeability, enhancing construction project stability. However, the interplay between the temperature, soil composition, and initial ground conditions during freezing is complex. This thermo-hydro-chemo-mechanical process strengthens the soil and reduces its permeability, but it can also induce frost heave due to water expansion and ice lens formation. Overburden pressure from the overlying soil limits ice lens growth. FT cycles significantly impact soil properties. In fine-grained soils, FT cycles can lead to over-consolidation, while rapid thawing can generate high pore pressures and compromise stability. Importantly, FT acts as a weathering mechanism, influencing soil properties at both the microscopic and macroscopic scales. These cycles can loosen over-consolidated soil, densify normally consolidated soil, and increase overall hydraulic conductivity due to structural changes. They can also weaken the soil’s structure and deteriorate its mechanical performance.


Introduction
Artificial ground freezing (AGF) is a temporary soil treatment method used to create watertight peripheral enclosures during various construction projects.Its field of application concerns a wide range of soft or strongly weathered soils and rocky masses in cases where other temporary consolidation methods would not be suitable, safe enough, or technically feasible.The core principle of AGF revolves around transforming the soil into a frozen state, thereby enhancing its mechanical strength and reducing its hydraulic conductivity compared to its natural state [1][2][3].The technique has a long history dating back to 1862, when it was first used to construct mine shafts in South Wales [2].
A significant challenge associated with AGF lies in accurately predicting the surface deformations arising during the freezing and thawing processes.Frost heave, a phenomenon caused by the volume expansion of water upon freezing, can lead to unexpected upward movements of the soil [4,5].Conversely, during the thawing process, soil particles undergo rearrangement, potentially resulting in thaw settlement, particularly if water drainage is unrestricted [6,7].Upon the completion of a freeze-thaw (FT) cycle, the soil exhibits profound mechanical and physical characteristic changes.Due to FT cycles, the soils often undergo volume change, crack development, loss of shear strength and stiffness, and a change in hydraulic conductivity [8][9][10].
A persistent difficulty lies in accurately predicting the magnitude of these deformations.Often, these predictions underestimate the actual displacements seen in true-scale projects.For example, during the construction of tunnels beneath railroad tracks in Boston, the maximum predicted heave was 114 mm, but some localized areas experienced heave of up to 178 mm [11].Additionally, thaw settlement can be even more significant than frost heave.In 1969, Endo [12] reported a case where the thaw settlement was 10% greater than the preceding frost heave during a subway construction project.These discrepancies between the predicted and observed deformations in AGF projects highlight the limitations of our understanding of the complex mechanisms at play during an FT cycle.True knowledge of AGF requires a thorough investigation into how it affects the fundamental characteristics of soil, including the granulometry, porosity, and mechanical strength.
This review was conducted with the ambition of providing a state-of-the-art overview to understand the complex behavior of soil during both the freezing and the thawing phases of an AGF project.In this context, this paper was organized around four main key areas.The first explores the fundamental thermo-hydro-chemo-mechanical processes governing soil freezing.The second analyzes heave deformations and the approaches developed to predict them.The third emphasizes the importance of considering overburden pressure for safe and effective AGF implementation in deep construction projects.The last part goes over frozen soils' behavior upon thawing.It explores the long-term effects of freeze-thaw cycles on the physical and mechanical properties of soil, which is essential for ensuring long-term project stability.

Definition of Ground Freezing
Upon freezing, the soil becomes a complex four-phase material composed of soil particles, ice crystals, air bubbles, and unfrozen water.Figure 1 illustrates the synthesis of the fundamental freezing process on three distinct scales.Figure 1A provides insight into the dynamics of the soil-water system undergoing freezing.Ice formation can be divided into four zones (after [13] from [3]). Figure 1B is a schematic representation of the soil freezing characteristic curve (SFCC), a soil-specific parameter that is used to characterize the variation of the unfrozen water content as a function of increasing suction [14,15].Studying the evolution of cryogenic suction during freezing helps in understanding the thermodynamics and behavior of the soil by providing information on the water content and temperature changes in the soil during the freezing process and insights into the microscopic processes that occur.The SFCC describes the freezing process of soil in terms of three distinct zones: the boundary effect zone, the transition zone, and the residual unfrozen state zone.Finally, Figure 1C shows the evolution of the unfrozen water and ice phases in fully saturated soil under freezing conditions at the microscopic level.
The form of the different parts of the curves in Figure 1 and their duration is determined by the mineralogical composition of the soil, the grain size, the specific surface area, the surface tensions at the liquid/grain interface, the presence or absence of impurities in the pore water, and the initial water content [3,16,17].

Figure 1.
(A) Schematic representation of the cooling curve for soil water and ice (after [13]).(B) Schematic representation of a typical soil freezing characteristic curve.(C) Saturated soil freezing: microscopic evolution of unfrozen water and ice phases ( [18]).

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In Zone I (Figure 1A), the free pore water does not freeze until the temperature drops to a supercooled temperature-Tsc.This is because the supercooled water is in a metastable equilibrium state until nucleation centers cause an abrupt transformation of free water into ice, marking the beginning of Zone II.Nuclei can be aggregates of water molecules or soil particles.Zone I corresponds to the boundary effect zone on the SFCC (Figure 1B) and stage (1) of Figure 1C.Initially, the pores of the saturated soil are filled with liquid water.During the freezing process, the temperature of the pore water decreases, but due to confinement and interaction with soil particles, its freezing point is lower than that of free water.Therefore, even if the soil temperature reaches 0 °C, the pore water will not freeze.

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In Zone II (Figure 1A), ice formation releases latent heat, causing the temperature to rise from Tsc to Tf, the initial freezing temperature.Tf is close to 0 °C for cohesionless soils with low specific surface area, but the temperature decrease (ΔT) can be as much as 5 °C for fine-grained soils [3].In Zone II, the supercooled water contained in the (A) Schematic representation of the cooling curve for soil water and ice (after [13]).(B) Schematic representation of a typical soil freezing characteristic curve.(C) Saturated soil freezing: microscopic evolution of unfrozen water and ice phases ( [18]).

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In Zone I (Figure 1A), the free pore water does not freeze until the temperature drops to a supercooled temperature-Tsc.This is because the supercooled water is in a metastable equilibrium state until nucleation centers cause an abrupt transformation of free water into ice, marking the beginning of Zone II.Nuclei can be aggregates of water molecules or soil particles.Zone I corresponds to the boundary effect zone on the SFCC (Figure 1B) and stage (1) of Figure 1C.Initially, the pores of the saturated soil are filled with liquid water.During the freezing process, the temperature of the pore water decreases, but due to confinement and interaction with soil particles, its freezing point is lower than that of free water.Therefore, even if the soil temperature reaches 0 • C, the pore water will not freeze.

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In Zone II (Figure 1A), ice formation releases latent heat, causing the temperature to rise from Tsc to Tf, the initial freezing temperature.Tf is close to 0 • C for cohesionless soils with low specific surface area, but the temperature decrease (∆T) can be as much as 5 • C for fine-grained soils [3].In Zone II, the supercooled water contained in the large interconnected pores is isothermally converted into ice.Zone II corresponds to the transition zone on the SFCC (Figure 1B) and stage (2) of Figure 1C.The beginning of the transition zone is marked by the onset of ice nucleation as the temperature continues to decrease.Small ice crystals begin to form in large pores, replacing existing water.The cryogenic suction at which ice nucleation begins is referred to as the ice entry value (IEV).As the ice continues to grow, it will gradually enter smaller pores.For the SFCC, the IEV is the intersection of the linear extent of the initial straight segment of the SFCC and its central zone, which is characterized by a significant decrease in the amount of remaining unfrozen water.From this point on, the water bound to the grains is gradually converted into ice, as shown in the third part (Zone III) of the curve in Figure 1A.

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Zone III corresponds to stage (3) in Figure 1C.Unlike free pore water, the solidification of bound water in soil is not a uniform, constant temperature process due to the influence of capillarity and absorption forces [17].The resulting latent heat slows down the temperature decrease until a limit temperature Te (about −70 • C) is reached.At this point, all the free water and most of the bound water (unfrozen water film adsorbed on soil particles) is frozen.For fine-grained soils with high specific surface areas, a significant amount of unfrozen water may still be present at higher negative temperatures.

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Zone IV corresponds to the residual zone on the SFCC (Figure 1B) and stage (4) in Figure 1C.As the temperature decreases, once a certain value is reached, most of the pore water has already been converted into ice, and only a small amount of liquid water remains.This water is found as thin films adsorbed on soil particles and can be referred to as the residual unfrozen water content.At this point, the ice phase is continuous while the water phase is not.
The determination of the SFCC often involves solving an inverse problem.This means using a hydro-thermal model and iteratively adjusting its parameters until its response matches data obtained from in situ observations or laboratory tests.However, the present literature also highlights alternative methods for directly measuring the evolution of a porous medium's freezing state as a function of the temperature.Among the most wellknown methods are the following: • Time Domain Reflectometry (TDR): measures the dielectric permittivity of a soil speci- men from the velocity of an electromagnetic wave's propagation and reflection [19,20]; • Nuclear Magnetic Resonance (NMR): provides knowledge about the spatial distribution of hydrogen atoms [21,22]; • Differential Scanning Calorimetry (DSC): measures the variation of the heat fluxes emitted or received by a sample when it is subjected to temperature variations [23]; • Acoustic approaches: rely on the difference between the ultrasonic wave propagation speeds in water and ice [24].
It is worth noting that these techniques do not provide direct measurements.They all rely on certain assumptions and approximations to calibrate the electronic sensors and correlate the obtained data with the water content.
The Clausius-Clapeyron equation (Equation ( 1)) is generally assumed to be applicable in relating suction and temperature by considering the ice phase to be under atmospheric pressure.This assumption has been adopted by several authors, including [14,15,25,26].
where ψ is the suction in m; L is the latent heat of water fusion (L = 334 kJ/kg); g is the gravitational acceleration; T m is the freezing temperature of bulk water; and T is the subzero temperature in kelvin.
Figure 2 illustrates the coupled thermal (T), hydraulic (H), chemical (C), and mechanical (M) phenomena that occur during ground freezing.Globally, forming a solid hydraulic barrier while freezing will decrease the groundwater flow by reducing the permeability of the porous ground structure.From a mechanical perspective, changes in porosity are likely to impact the bulk thermal conductivity, heat capacity, and groundwater flow, thereby influencing the thermal behavior of the AGF process.Conversely, thermal stresses resulting from phase change and density variation could affect the mechanical response of the ground.Porosity variations are directly linked to the permeability of the ground, which in turn influences the groundwater flow.Furthermore, seepage flow under high pressure will induce significant stress and strain on the frozen wall during the AGF process.
Figure 2 illustrates the coupled thermal (T), hydraulic (H), chemical (C), and mechanical (M) phenomena that occur during ground freezing.Globally, forming a solid hydraulic barrier while freezing will decrease the groundwater flow by reducing the permeability of the porous ground structure.From a mechanical perspective, changes in porosity are likely to impact the bulk thermal conductivity, heat capacity, and groundwater flow, thereby influencing the thermal behavior of the AGF process.Conversely, thermal stresses resulting from phase change and density variation could affect the mechanical response of the ground.Porosity variations are directly linked to the permeability of the ground, which in turn influences the groundwater flow.Furthermore, seepage flow under high pressure will induce significant stress and strain on the frozen wall during the AGF process.In practice, the interactions between the different processes occurring during soil freezing are either simplified into two-way couplings: TH, TM, TC, HM, HC, MC; or they can be studied as three-way couplings: the impact of the TH components on the mechanics of the ground, and vice versa; the impact of the TH aspects on salinity, and vice versa; and the influence of the TM modifications on salinity, and vice versa.The examples of TH, THM, and TC couplings will be further detailed hereafter.

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HT coupling In practice, the interactions between the different processes occurring during soil freezing are either simplified into two-way couplings: TH, TM, TC, HM, HC, MC; or they can be studied as three-way couplings: the impact of the TH components on the mechanics of the ground, and vice versa; the impact of the TH aspects on salinity, and vice versa; and the influence of the TM modifications on salinity, and vice versa.The examples of TH, THM, and TC couplings will be further detailed hereafter.

• HT coupling
Water flow is influenced by temperature changes, which can cause changes in the properties of the soil and the pore fluid, such as the dilation or contraction of materials, changes in permeability as water changes phase into ice, and changes in liquid water viscosity.This flow also contributes to heat transfer through convection, further affecting the overall thermal state of the soil.Water flows, on the other hand, can induce convective heat transfer, which significantly impacts the thermal state of the medium.These flows may occur naturally or may be brought about by the ground freezing itself.In the first scenario, if these flows are strong enough, the formation of the frozen barrier can be slowed down or even prevented.The second type of flow is induced by the density difference between ice and liquid water.Due to its density, the freshly produced ice in the pores can expel the liquid pore water to the nearby unfrozen regions, creating a velocity field at the frozen/non-frozen interface.The speed of these flows determines the relative importance of heat transfer by convection compared to conduction [3,17,35].

• HTM coupling
During soil freezing, a complex interplay emerges between mechanical stresses, deformations, and hydraulic properties.Changes in the effective stress and temperature can induce significant soil deformations.Notably, freezing itself alters the soil's mechanical behavior, creating a coupled system where deformations further modulate the thermal and hydraulic properties.Deformations modify the porosity, which in turn directly influences several parameters like the thermal conductivity, heat capacity, saturation degree, permeability, and groundwater flow [3,17,35].Furthermore, overburden pressure significantly influences the heave amount.This pressure influences the ice lens formation and thickness, permeability, frozen fringe thickness, and suction potential, contributing to the overall magnitude of heave experienced during soil freezing [26,33,[36][37][38][39].Further elaboration on the effect of overburden pressure on AGF is provided in Section 4.

• TC coupling
The influence of solutes has been explored by examining their impact on the depression of the freezing point, the alteration of hydraulic conductivity, and their broader influence on concentration-driven flows and heat transfer phenomena [40].The depression of the freezing point by solutes in the pore fluid is a well-established phenomenon, supported by both laboratory experiments and theoretical models developed for various soil and solute types [41][42][43][44].During freezing, solutes are excluded from the ice crystals, concentrating in the remaining liquid phase [40].This concentration effect further depresses the freezing point of the remaining liquid until a solubility limit is reached for the prevailing temperature.At this point, simultaneous solute precipitation and ice crystallization may occur, leading to a decrease in the solute concentration of the remaining liquid.The situation is further complicated by the temperature dependence of the saturation concentration, with lower temperatures promoting faster precipitation, particularly for initially high solute concentrations [40].
Generally, AGF is a complex process that involves multi-scale, multi-physics phenomena involving transient heat transfer, fluid dynamics, and phase changes within a porous medium.Numerous soil properties-thermal (conductivity, heat capacity), chemical (salt and mineral concentration), mechanical (strength, creep, freeze-thaw deformations), and hydraulic (water content, permeability)-simultaneously influence and are influenced by the freezing process.The interdependent nature of all these parameters renders AGF a THCM-coupled process with dual effects: enhancing soil strength and reducing permeability, while simultaneously inducing significant ground deformations, particularly heave [3,28,[30][31][32]34,35].In practice, these interactions are often simplified into two-way or three-way couplings to facilitate analysis.Key examples include the HT (thermal-hydraulic) coupling, where temperature changes influence water flow through variations in permeability and viscosity, and vice versa.THM coupling further incorporates the impact of mechanical stresses and deformations.

Ground Deformations Induced by AGF
Frost heave is driven by two primary mechanisms: the phase change of water into ice and the formation of ice lenses [3].When the temperature falls below the freezing point, pore water freezes into ice.The one-dimensional pore water expansion, H PW , of 9% is driven by frost penetration x(t), considering the volumetric porosity n and saturation degree Sr, as given in Equation (2) [34].
Ice lenses form when liquid pore water migrates through the soil toward the freezing interface due to suction [34].At the microscale, cryogenic suction is explained by premelting dynamics, where intermolecular forces cause the migration of pre-melted fluid to feed ice lens growth [45].In 1989, Dash [46] proposed that the soil and the ice grains reject each other across pre-melted liquid films created by these same intermolecular forces, generating low pressure that attracts surrounding water and causes heave.The extent of the ice lens formation depends on the pore water availability, movement, and freezing duration [47].The susceptibility of soil to frost heave is strongly influenced by its nature.Coarse-grained soils, characterized by larger particles, exhibit minimal frost heave, while fine-grained soils, with their smaller particles, are highly prone to frost heave [5,48].Figure 3 compares the frost heave caused by freezing in different soil types.Silty clays tend to experience the most heave, especially under lower overburden pressure and higher temperature gradients.This is because these fine-grained soils can hold more unfrozen water at sub-zero temperatures, allowing ice lens formation to contribute to heave alongside water phase change.Clay soils, though generally frost-susceptible, may heave less than coarser-grained silts.Conversely, sandy soils, with their lower water content at freezing temperatures, experience minimal heave as freezing is dominated by simple phase changes.

Ground Deformations Induced by AGF
Frost heave is driven by two primary mechanisms: the phase change of water in and the formation of ice lenses [3].When the temperature falls below the freezing pore water freezes into ice.The one-dimensional pore water expansion, HPW, of driven by frost penetration x(t), considering the volumetric porosity n and saturatio gree Sr, as given in Equation ( 2) [34].

𝐻 𝑡 = 0.09 ⋅ 𝑛 ⋅ 𝑆 ⋅ 𝑥 𝑡
Ice lenses form when liquid pore water migrates through the soil toward the fre interface due to suction [34].At the microscale, cryogenic suction is explained by pre ing dynamics, where intermolecular forces cause the migration of pre-melted fluid t ice lens growth [45].In 1989, Dash [46] proposed that the soil and the ice grains rejec other across pre-melted liquid films created by these same intermolecular forces, ge ing low pressure that attracts surrounding water and causes heave.The extent of t lens formation depends on the pore water availability, movement, and freezing du [47].The susceptibility of soil to frost heave is strongly influenced by its nature.C grained soils, characterized by larger particles, exhibit minimal frost heave, while grained soils, with their smaller particles, are highly prone to frost heave [5,48].Fig compares the frost heave caused by freezing in different soil types.Silty clays tend perience the most heave, especially under lower overburden pressure and higher te ature gradients.This is because these fine-grained soils can hold more unfrozen wa sub-zero temperatures, allowing ice lens formation to contribute to heave alongside phase change.Clay soils, though generally frost-susceptible, may heave less than co grained silts.Conversely, sandy soils, with their lower water content at freezing tem tures, experience minimal heave as freezing is dominated by simple phase changes Three distinctive zones exist upon freezing the soil under a temperature gradie passive frozen zone, the frozen fringe, and the active unfrozen zone [53][54][55][56][57][58].

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Passive frozen zone: This region is ice-bound and experiences ice crystal an formation.Temperature changes are driven by thermal diffusion mediated b presence of ice.Three distinctive zones exist upon freezing the soil under a temperature gradient: the passive frozen zone, the frozen fringe, and the active unfrozen zone [53][54][55][56][57][58].

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Passive frozen zone: This region is ice-bound and experiences ice crystal and lens formation.Temperature changes are driven by thermal diffusion mediated by the presence of ice.

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Frozen fringe: This transition zone marks the interface between the frozen and the unfrozen zone.Here, ice and water coexist in soil pores, and complex processes of ice nucleation, crystallization, and phase transition occur.• Active unfrozen zone: This zone is dominated by thermal diffusion, water migration, suction, and soil consolidation.
A schematic representation of a typical frozen soil profile is illustrated in Figure 4.
• Frozen fringe: This transition zone marks the interface between the frozen and the unfrozen zone.Here, ice and water coexist in soil pores, and complex processes of ice nucleation, crystallization, and phase transition occur.

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Active unfrozen zone: This zone is dominated by thermal diffusion, water migration, suction, and soil consolidation.
A schematic representation of a typical frozen soil profile is illustrated in Figure 4.For a quantitative theory of frost heave to be robust, it must account for two critical aspects: (1) the migration of water from unfrozen regions of the soil to colder zones where it undergoes a phase change to excess ice, and (2) the tendency of this ice to exert tensile forces within the soil matrix and ultimately accumulate as discrete ice lenses that meet specific criteria for ice lens formation [60].Understanding how ice forms as discrete lenses is critical to modeling frost heave in susceptible soils.Researchers in various fields have studied the mechanisms underlying ice lens formation.These criteria can be broadly classified into four groups.

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Total stress criteria: Focuses on pore pressure exceeding a threshold that separates soil particles [53,61].O'Neill and Miller [62] defined this threshold using neutral stress (overburden pressure minus effective stress).

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Tensile strength criteria: Considers overburden pressure and the soil's tensile strength [63,64].Ice lens formation occurs when the ice pressure overcomes the combined resistance.

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Permeability criteria: Emphasizes the role of frozen fringe permeability linked to segregation temperature [16].A new lens forms when reduced permeability restricts water flow to existing lenses.

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Soil freezing characteristic curve criteria: Uses the SFCC to determine ice lens initiation conditions, including the segregation temperature [26].This method identifies the IEV within the SFCC for fine-grained soils.
Theories on frost heave fall under two groups: primary frost heave (traditionally known as capillary models) and secondary frost heave (frozen-fringe models).By treating the soil as an open system, Taber [48] observed that even when the saturating fluid was changed from water to benzene, which contracts when frozen, frost heave still occurred.This indicated that the volume increase during freezing was not just due to in situ water freezing but also involved water movement from unfrozen areas to the frozen zone.This crucial insight led to the development of the capillary theory, the first fundamental explanation of frost heave.Taber [48] also identified key factors governing frost heave: soil For a quantitative theory of frost heave to be robust, it must account for two critical aspects: (1) the migration of water from unfrozen regions of the soil to colder zones where it undergoes a phase change to excess ice, and (2) the tendency of this ice to exert tensile forces within the soil matrix and ultimately accumulate as discrete ice lenses that meet specific criteria for ice lens formation [60].Understanding how ice forms as discrete lenses is critical to modeling frost heave in susceptible soils.Researchers in various fields have studied the mechanisms underlying ice lens formation.These criteria can be broadly classified into four groups.
• Total stress criteria: Focuses on pore pressure exceeding a threshold that separates soil particles [53,61].O'Neill and Miller [62] defined this threshold using neutral stress (overburden pressure minus effective stress).

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Tensile strength criteria: Considers overburden pressure and the soil's tensile strength [63,64].Ice lens formation occurs when the ice pressure overcomes the combined resistance.

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Permeability criteria: Emphasizes the role of frozen fringe permeability linked to segregation temperature [16].A new lens forms when reduced permeability restricts water flow to existing lenses.

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Soil freezing characteristic curve criteria: Uses the SFCC to determine ice lens initiation conditions, including the segregation temperature [26].This method identifies the IEV within the SFCC for fine-grained soils.
Theories on frost heave fall under two groups: primary frost heave (traditionally known as capillary models) and secondary frost heave (frozen-fringe models).By treating the soil as an open system, Taber [48] observed that even when the saturating fluid was changed from water to benzene, which contracts when frozen, frost heave still occurred.This indicated that the volume increase during freezing was not just due to in situ water freezing but also involved water movement from unfrozen areas to the frozen zone.This crucial insight led to the development of the capillary theory, the first fundamental explanation of frost heave.Taber [48] also identified key factors governing frost heave: soil particle size, available water content, pore space characteristics, and freezing rate.In 1935, Beskow [5] independently offered significant contributions to our understanding of soil freezing.He drew an analogy between soil freezing and drying, emphasizing that both processes involve a change in the water phase (ice formation vs. evaporation) and a reduction in the liquid water content of the soil.This analogy further supported the capillary theory, which is based on two key equations: Clapeyron's equation, which describes the thermodynamic equilibrium for a system of ice and water at specific pressures and temperatures (Equation ( 1)), and the Young-Laplace equation, which relates the pressure difference between ice and water to the curvature of the interface between them.The ability of ice to invade a porous medium is governed by the relative sizes of the ice crystals and the effective pore radius.The size and geometry of the pore act as a template, dictating the maximum attainable radius of the ice crystal.When the ice radius (r) exceeds the effective pore radius (r p ), the ice becomes too large to pass through the pore throat physically.Capillary theory explains the basic mechanism of frost heave, but limitations became apparent in the 1960s and 1970s.While predictions for idealized soils composed of uniform particle size showed good agreement with experimental data, the predicted heave pressures for soils containing a range of particle sizes were significantly lower than experimental observations.In addition, the model could not account for continuous ice formation, where multiple unconnected ice lenses form at the freezing front instead of a single thick lens.These shortcomings led to the development of a new approach, the frozen-fringe model.
The apparent failure of the capillary theory led some researchers [53,65] to argue that frost heave can occur even after ice has formed a frozen fringe by expanding into soil pores.This fringe, a partially frozen zone located between the ice lens and the warmest soil with pore ice (the volume of soil where pore water and pore ice coexist), was introduced in [53].Water from the unfrozen zone moves slowly but continuously toward the ice lens through this low-permeability frozen fringe Figure 5.
freezing.He drew an analogy between soil freezing and drying, emphasizing that both processes involve a change in the water phase (ice formation vs. evaporation) and a reduction in the liquid water content of the soil.This analogy further supported the capillary theory, which is based on two key equations: Clapeyron's equation, which describes the thermodynamic equilibrium for a system of ice and water at specific pressures and temperatures (Equation ( 1)), and the Young-Laplace equation, which relates the pressure difference between ice and water to the curvature of the interface between them.The ability of ice to invade a porous medium is governed by the relative sizes of the ice crystals and the effective pore radius.The size and geometry of the pore act as a template, dictating the maximum attainable radius of the ice crystal.When the ice radius (r) exceeds the effective pore radius (rp), the ice becomes too large to pass through the pore throat physically.Capillary theory explains the basic mechanism of frost heave, but limitations became apparent in the 1960s and 1970s.While predictions for idealized soils composed of uniform particle size showed good agreement with experimental data, the predicted heave pressures for soils containing a range of particle sizes were significantly lower than experimental observations.In addition, the model could not account for continuous ice formation, where multiple unconnected ice lenses form at the freezing front instead of a single thick lens.These shortcomings led to the development of a new approach, the frozenfringe model.
The apparent failure of the capillary theory led some researchers [53,65] to argue that frost heave can occur even after ice has formed a frozen fringe by expanding into soil pores.This fringe, a partially frozen zone located between the ice lens and the warmest soil with pore ice (the volume of soil where pore water and pore ice coexist), was introduced in [53].Water from the unfrozen zone moves slowly but continuously toward the ice lens through this low-permeability frozen fringe Figure 5. Building on the limitations identified in the capillary theory, Miller [66] proposed the ice-rigid model of frost heave in non-colloidal soils.This model assumes that deformations primarily arise from ice lens formation rather than compression or expansion of the soil matrix.The core concept of the ice-rigid model is a continuous, rigid ice body coexisting with pore water within the frozen fringe.The ice in the frozen fringe remains connected to the growing ice lens above.It moves relative to the surrounding soil particles through a process known as regelation (melting and refreezing).O'Neill and Miller [54] further developed the ice-rigid model to predict the ice lens properties and frost heave rate based on environmental factors and ground behavior.Their model focuses on the evolution of ice saturation within the pore space and its impact on permeability.These parameters can be determined through independent laboratory experiments [67,68].Building on the limitations identified in the capillary theory, Miller [66] proposed the ice-rigid model of frost heave in non-colloidal soils.This model assumes that deformations primarily arise from ice lens formation rather than compression or expansion of the soil matrix.The core concept of the ice-rigid model is a continuous, rigid ice body coexisting with pore water within the frozen fringe.The ice in the frozen fringe remains connected to the growing ice lens above.It moves relative to the surrounding soil particles through a process known as regelation (melting and refreezing).O'Neill and Miller [54] further developed the ice-rigid model to predict the ice lens properties and frost heave rate based on environmental factors and ground behavior.Their model focuses on the evolution of ice saturation within the pore space and its impact on permeability.These parameters can be determined through independent laboratory experiments [67,68].
Many researchers have focused on simplifying the model [69][70][71].Sheng et al. [71] updated the governing equations and interpretations of stress expressions to create an operationally simple model (PC-Heave) that can handle parameters such as the ground frost heave rate, freeze-thaw front velocity, and ice volume content, making it useful for field frost heave monitoring.Bronfenbrener and Bronfenbrener [72] presented another generalized model of secondary frost heave in freezing fine-grained soils, recognizing the importance of determining the moisture distribution within the frozen fringe.Shortly after the rigid-ice model, Nixon [73] introduced the separate ice lens theory, which assumes distinct pore ice and ignores regelation movement.This theory evolved into the separate-ice frost heave model with improved ice lens formation criteria.However, both the ice-rigid and separate ice models suffer from a practical limitation: the difficulty of accurately measuring some of the crucial physical and mechanical parameters they rely on, which restricts and limits their application [45].
A more practical approach is the segregation potential model proposed by Konrad and Morgenstern [16].This widely used model estimates a frost heave parameter called the segregation potential (SP), a constant value relating the water intake flux to the temperature gradient.While successful in some cases, the SP model struggles with unstable environments and lacks fundamental soil characteristic parameters.Ji et al. [74] built upon the SP model and water activity criteria to propose a new model for ice lens formation under time-varying temperatures.However, this model requires laboratory data for time-varying temperatures, limiting its field application.Beyond these specific models, researchers like Nishimura et al. [75] and Casini et al. [76] have developed constitutive models that consider the combined effects of thermal, hydraulic, and mechanical processes during frost heave.These models incorporate both frozen and unfrozen soil behaviors, using variables like the ice pressure, water pressure, and total stress.This comprehensive approach allows for a more holistic understanding of the complex interactions that contribute to frost heave in frozen soils.
This section is an overview of the significant contributions that many scientists have made to understand and ultimately modeling frost heave.While it does not cover every model under development, it offers a glimpse of the different approaches being taken to understand frost heave.One critical point that emerges is that most of the existing models of frost heave focus on naturally frozen soils in cold regions.This limitation implies that they do not account for the effects of overburden pressure on the soil during freezing and the resulting heave.

AGF in the Presence of Overburden Pressure
The scarcity of surface space in urban environments often drives construction projects underground, where excavations can reach tens of meters below ground level.At these depths, the weight of the overlying soil layers exerts substantial overburden pressure, which plays a critical role in AGF and significantly influences the magnitude of frost heave.Beskow [5] was perhaps the first to study the influence of stress on soil freezing nearly a century ago.He noticed that external pressures reduced the heave rates of silty soils upon freezing.Subsequent experimental studies have further identified the connection between the applied pressure and various processes such as water migration, suction development, permeability reduction, and segregation temperature [26,38,[77][78][79].Therefore, the presence of overburden pressure alters the mechanical, thermal, and hydraulic response of soil to both freezing and thawing.
Researchers, including Konrad and Morgenstern [38], Xia et al. [56], and Ji et al. [52], have shown that overburden pressure influences the thermal response of soil to freezing by impacting the thickness of the frozen fringe and the value of the segregation temperature, the temperature at which ice lenses form.Experiments conducted by Konrad and Morgenstern [38] showed that increasing overburden pressure results in a thicker frozen fringe and a reduced hydraulic gradient across the fringe, reducing water migration to the ice lens.Further confirmation came from experiments by Xia et al. [56], who used the fluorescent tracer method to track the frozen fringe thickness under various constant vertical stresses.The frozen fringe increased in thickness by up to 5 mm when subjected to 400 kPa axial stress compared to when not subjected to axial stress.The results globally showed a direct correlation between a higher overburden pressure and a thicker frozen fringe (longer flow path for water migration to the ice lens).
The segregation temperature depends on the cooling rate, soil nature, and overburden pressure [38,79,80].The influence of overburden pressure on the segregation temperature of ice lenses was the subject of three different studies by Konrad [81], Azmatch [82], and Ji et al. [52].Both Konrad [81] and Azmatch [82] studied the segregation temperature of Devon silt using different approaches (Clausius-Clapeyron equation and SFCC, respectively) but reached similar conclusions.They found that under comparable conditions of cooling rate and applied pressure, the segregation temperature remained relatively constant.Ji et al. [52] resorted to numerical simulations to study the impact of overburden pressure on the segregation temperature of clay.Their model accounted for phase transition and multiphase interactions to evaluate the kinetic growth of ice lenses.The model investigates the micro-and meso-physical mechanisms behind ice lens growth by introducing the water activity-controlled growth rate of ice crystals.The results of these three studies are illustrated in Figure 6.These results showed that the increase in the overburden pressure leads to a decrease in the temperature of the warmest ice lens.Overall, these studies consistently show a decrease in the segregation temperature as the overburden pressure increases.Therefore, the overburden pressure increases the thickness of the frozen fringe while reducing the segregation temperature of ice lenses.
showed a direct correlation between a higher overburden pressure and a thicker frozen fringe (longer flow path for water migration to the ice lens).
The segregation temperature depends on the cooling rate, soil nature, and overburden pressure [38,79,80].The influence of overburden pressure on the segregation temperature of ice lenses was the subject of three different studies by Konrad [81], Azmatch [82], and Ji et al. [52].Both Konrad [81] and Azmatch [82] studied the segregation temperature of Devon silt using different approaches (Clausius-Clapeyron equation and SFCC, respectively) but reached similar conclusions.They found that under comparable conditions of cooling rate and applied pressure, the segregation temperature remained relatively constant.Ji et al. [52] resorted to numerical simulations to study the impact of overburden pressure on the segregation temperature of clay.Their model accounted for phase transition and multiphase interactions to evaluate the kinetic growth of ice lenses.The model investigates the micro-and meso-physical mechanisms behind ice lens growth by introducing the water activity-controlled growth rate of ice crystals.The results of these three studies are illustrated in Figure 6.These results showed that the increase in the overburden pressure leads to a decrease in the temperature of the warmest ice lens.Overall, these studies consistently show a decrease in the segregation temperature as the overburden pressure increases.Therefore, the overburden pressure increases the thickness of the frozen fringe while reducing the segregation temperature of ice lenses.Studies have shown that overburden pressure also impacts the hydraulic responses of soil to freezing by modifying the external water migration and intake.Zhang et al. [51] observed reduced water absorption in saturated silty clay samples with increasing pressure.This aligns with the previous research of [36,37,50,83] showing less external water intake under higher pressure, potentially mitigating frost heave.Further studies by Lu et al. [83] found that both confining and deviator stresses significantly impact water migration and external water buildup and that higher overburden pressure reduces external water absorption, consequently diminishing frost heave.Studies have shown that overburden pressure also impacts the hydraulic responses of soil to freezing by modifying the external water migration and intake.Zhang et al. [51] observed reduced water absorption in saturated silty clay samples with increasing pressure.This aligns with the previous research of [36,37,50,83] showing less external water intake under higher pressure, potentially mitigating frost heave.Further studies by Lu et al. [83] found that both confining and deviator stresses significantly impact water migration and external water buildup and that higher overburden pressure reduces external water absorption, consequently diminishing frost heave.
The analysis of the available literature on the effect of applied stress on soil freezing leads to the diagram shown in Figure 7.It compares two columns of frozen soil with and without overburden pressure.Globally, overburden pressure tends to increase the thickness of the frozen fringe, lower the segregation temperature, reduce the water migration toward the frost front, and reduce the overall amount of frost heave produced.
The analysis of the available literature on the effect of applied stress on soil freezing leads to the diagram shown in Figure 7.It compares two columns of frozen soil with and without overburden pressure.Globally, overburden pressure tends to increase the thickness of the frozen fringe, lower the segregation temperature, reduce the water migration toward the frost front, and reduce the overall amount of frost heave produced.

Properties and Behavior of Soil after FT Cycles
Accurate prediction of frost heave and thaw settlement in models and laboratory tests can be challenging.Often, these predictions underestimate the actual displacements seen in true-scale projects.Key questions regarding the thawing of artificially frozen soils center on the influence of AGF on the post-thaw soil properties (granulometry, porosity, mechanical strength, etc.) and the ability to properly predict surface settlement in AGF projects following thawing.

Differences behind the Freezing and Thawing Paths
In AGF, the freezing path is different from the thawing path.During freezing and excavation, suction gradients induce moisture migration from unfrozen soil toward the freezing front [16].Conversely, thawing can lead to excess pore water pressure and subsequent consolidation if drainage is allowed [28].This can lead to thaw settlements that are even greater than the frost heave generated.This can be attributed to several factors.Clays with high plasticity are less prone to frost heave [3].Suction-induced freezing forces alter the soil's fabric [80], increasing the permeability [84,85] and compressibility [86].These suction forces cause over-consolidation of the clay, which, when combined with increased permeability, results in undesirable additional settlement during thawing.
A valuable resource for understanding soil behavior during freeze-thaw cycles is the SFCC.Its shape depends on the soil's nature, initial void ratio, freezing rate, and freezethaw history [26,80].Figure 8 illustrates the characteristic hysteresis behavior of the SFCC.This hysteresis, where freezing and thawing follow different paths, reflects the distinct processes occurring during each phase.Table 1 presents some of the root causes behind this hysteresis phenomenon.

Properties and Behavior of Soil after FT Cycles
Accurate prediction of frost heave and thaw settlement in models and laboratory tests can be challenging.Often, these predictions underestimate the actual displacements seen in true-scale projects.Key questions regarding the thawing of artificially frozen soils center on the influence of AGF on the post-thaw soil properties (granulometry, porosity, mechanical strength, etc.) and the ability to properly predict surface settlement in AGF projects following thawing.

Differences behind the Freezing and Thawing Paths
In AGF, the freezing path is different from the thawing path.During freezing and excavation, suction gradients induce moisture migration from unfrozen soil toward the freezing front [16].Conversely, thawing can lead to excess pore water pressure and subsequent consolidation if drainage is allowed [28].This can lead to thaw settlements that are even greater than the frost heave generated.This can be attributed to several factors.Clays with high plasticity are less prone to frost heave [3].Suction-induced freezing forces alter the soil's fabric [80], increasing the permeability [84,85] and compressibility [86].These suction forces cause over-consolidation of the clay, which, when combined with increased permeability, results in undesirable additional settlement during thawing.
A valuable resource for understanding soil behavior during freeze-thaw cycles is the SFCC.Its shape depends on the soil's nature, initial void ratio, freezing rate, and freezethaw history [26,80].Figure 8 illustrates the characteristic hysteresis behavior of the SFCC.This hysteresis, where freezing and thawing follow different paths, reflects the distinct processes occurring during each phase.Table 1 presents some of the root causes behind this hysteresis phenomenon.
Therefore, the pathways taken by the freezing and thawing processes are fundamentally different.The core reasons for this discrepancy either entail processes that differ during freezing and thawing or involve processes that occur during one process but not the other.Nevertheless, it is still not fully clear why hysteresis occurs in porous media like soils.

Supercooling of pore water
Despite reaching its freezing point, soil pore water does not always freeze.Instead, pore water is kept in the liquid phase until the temperature drops to temperature Tsc, where water super-cools and freezing is initiated by ice nucleation.On the other hand, the thawing branch displays no rapid changes in θu and no superheating phenomena. [87-90

Effect of electrolytes
When soil is frozen, electrolytes are excluded from the ice, increasing the solute concentrations in the remaining pore water.This lowers the freezing point of the remaining pore water and promotes hysteresis. [87-90

Pore geometry
Hysteresis may be linked to the different curvatures of the ice-water contact during freezing and thawing.Crystallization initiates in large pores upon freezing.Comparatively, when soil is thawed, pore ice melting begins in small pores and then advances gradually to larger pores.Hence, for the same amount of unfrozen water, the temperature on the thawing branch is higher than that on the freezing branch.The melting branch is, therefore, underneath the freezing branch, hence the hysteresis. [91,92 Pore blocking: bottleneck effect The bottleneck effect, which is thought to be the principal reason for the hysteresis frequently seen for the air-water phase transition in soils with a broad range of interconnected pores of diverse geometry (different radii), may also contribute to the hysteresis for the ice-water phase transition in the soil.This effect originates from large pores with narrow necks. [87,92

Effect of contact angle
The rising contact angle during soil freezing differs from the retreating contact angle during soil thawing.[93,94 Change in the pore structure Hysteresis may be caused by the thixotropic property and aging conditions that shape pore size distribution.Soil particles usually relocate from their original locations as soil pores expand due to ice development during the freezing process.Consequently, larger pores would be present than before soil freezing.
[93] Table 1.Potential explanations for the hysterical behavior observed in the SFCC.

Mechanism Explanation References
Supercooling of pore water Despite reaching its freezing point, soil pore water does not always freeze.Instead, pore water is kept in the liquid phase until the temperature drops to temperature Tsc, where water super-cools and freezing is initiated by ice nucleation.On the other hand, the thawing branch displays no rapid changes in θ u and no superheating phenomena.
[ [87][88][89][90] Effect of electrolytes When soil is frozen, electrolytes are excluded from the ice, increasing the solute concentrations in the remaining pore water.This lowers the freezing point of the remaining pore water and promotes hysteresis.
[ [87][88][89][90] Pore geometry Hysteresis may be linked to the different curvatures of the ice-water contact during freezing and thawing.Crystallization initiates in large pores upon freezing.Comparatively, when soil is thawed, pore ice melting begins in small pores and then advances gradually to larger pores.Hence, for the same amount of unfrozen water, the temperature on the thawing branch is higher than that on the freezing branch.The melting branch is, therefore, underneath the freezing branch, hence the hysteresis.[91,92] Pore blocking: bottleneck effect The bottleneck effect, which is thought to be the principal reason for the hysteresis frequently seen for the air-water phase transition in soils with a broad range of interconnected pores of diverse geometry (different radii), may also contribute to the hysteresis for the ice-water phase transition in the soil.This effect originates from large pores with narrow necks.[87,92] Effect of contact angle The rising contact angle during soil freezing differs from the retreating contact angle during soil thawing.[93,94] Change in the pore structure Hysteresis may be caused by the thixotropic property and aging conditions that shape pore size distribution.Soil particles usually relocate from their original locations as soil pores expand due to ice development during the freezing process.Consequently, larger pores would be present than before soil freezing. [93] Furthermore, there is a difference between the initial SFCC and subsequent scanning curves.This difference can be attributed to the modification of the soil's properties during the first freeze-thaw (FT) cycle.As illustrated in Figure 8, the initial thawing curve typically falls below the freezing curve due to hysteresis.The specific reasons behind hysteresis can be found in Table 1.Importantly, subsequent freezing and thawing cycles will occur based on the new soil properties and initial water content established after the first FT cycle.While hysteresis will continue to be observed due to the reasons mentioned earlier, it is crucial to acknowledge that this remains a general scheme of the SFCC upon one or many FT cycles.However, to date, the effect of FT cycling on the SFCC is not well-investigated or -understood in the literature.Current research, like the studies by Kozlowski and Nartowska [95] and Ren and Vanapalli [96], suggests that the effect of FT cycles on the SFCC can be statistically insignificant in some cases.Kozlowski and Nartowska [95] investigated the impact of FT cycles on highly plastic bentonites with varying water contents.They subjected these bentonite specimens to repeated cycles of freezing at −90 • C and thawing at 20 • C within a differential scanning calorimeter (DSC), allowing for free expansion.Their analysis focused on the thawing branches of the SFCC during five FT cycles.While they concluded that the FT cycles had a statistically insignificant effect on the bentonite specimens' SFCC, they did not delve into the reasons behind this observation.Interestingly, their study did find that subzero temperatures and the specific soil type significantly influenced the SFCC behavior, which aligns with established knowledge about frozen soils.Ren and Vanapalli [96] explored the effect of FT cycling on the SFCC of five Canadian soils with low to moderate plasticity.They employed the frequency domain reflectometry (FDR) technique to measure the SFCCs and considered up to three FT cycles.Their findings indicated that these FT cycles had no significant impact on the measured SFCC.They primarily attributed this to the destruction of soil structure during the initial saturation process, suggesting that the subsequent FT cycles had minimal influence on the already disrupted structure (and consequently, the SFCC).Globally, the influence of FT cycles on the SFCC remains far from being fully understood.While some studies have observed statistically insignificant effects on the SFCC in certain scenarios, the overall impact of FT cycles appears to be dependent on several factors.These factors likely include the inherent properties of the soil itself, the methods employed during sample preparation, and the number of freeze-thaw cycles experienced.Further research is necessary to better understand the mechanisms at play and identify the specific soil characteristics that influence the response to FT cycles.

Stress Path during a Freeze-Thaw Cycle
In 1977, Chamberlain and Blouin [97] proposed a framework for understanding the stress paths of soil during a freeze-thaw cycle.They presented a theoretical illustration of the thaw consolidation process in a typical clay soil (Figure 9).It is assumed that the soil is initially saturated and normally consolidated to point "a" on the virgin consolidation curve.
The framework considers the total stress path (abc) representing the soil's void ratio change during FT.As the soil freezes in an open system (point a), the void ratio increases due to phase change and water migration (point b).Upon thawing, the void ratio decreases as the ice melts (point c).
The effective stress path identifies how the soil strengthens during freezing and weakens during thawing.During freezing, the suction behind the freezing front increases effective stress, leading to over-consolidation (point b ′ ).Three scenarios are considered for the effective stress path during thawing:

•
Slow thawing (b ′ -c): This scenario represents a situation where drainage and adsorption can keep pace with the thawing rate.The effective stress path follows b ′ -c, reaching equilibrium with no excess pore pressure at point c.

•
Moderate thawing rate (b ′ -c ′ -c): This intermediate scenario occurs when the drainage and adsorption rates are slightly slower than the thawing rate.The soil swells upon thawing, generating excess pore pressure and a significant increase in the volume change (point c ′ ).As the excess pore pressure dissipates, the soil consolidates further to point c.

•
Rapid thawing with minimal drainage/adsorption (b ′ -c ′′ -c): In this case, thawing is very fast, leading to minimal drainage or adsorption.The excess pore pressure can approach the applied stress, causing the effective stress to drop near zero (b ′ -c ′′ ).Over time, this pressure dissipates and the effective stress returns to the applied stress value (point c).
Despite the variations in the effective stress paths, all the freeze-thaw cycles in finegrained soils ultimately lead to over-consolidation.During slow thawing, the generated water drains efficiently, resulting in minimal excess pore pressure and settlement as the soil drains the water (point c).However, rapid thawing can lead to significant excess pore pressure (point c ′ or c ′′ ), compromising the soil stability by reducing the bearing capacity and potentially causing severe differential settlements.
the effective stress path during thawing:

•
Slow thawing (b′-c): This scenario represents a situation where drainage and adsorption can keep pace with the thawing rate.The effective stress path follows b′-c, reaching equilibrium with no excess pore pressure at point c.

•
Moderate thawing rate (b′-c′-c): This intermediate scenario occurs when the drainage and adsorption rates are slightly slower than the thawing rate.The soil swells upon thawing, generating excess pore pressure and a significant increase in the volume change (point c′).As the excess pore pressure dissipates, the soil consolidates further to point c.

•
Rapid thawing with minimal drainage/adsorption (b′-c″-c): In this case, thawing is very fast, leading to minimal drainage or adsorption.The excess pore pressure can approach the applied stress, causing the effective stress to drop near zero (b′-c″).Over time, this pressure dissipates and the effective stress returns to the applied stress value (point c).
Despite the variations in the effective stress paths, all the freeze-thaw cycles in finegrained soils ultimately lead to over-consolidation.During slow thawing, the generated water drains efficiently, resulting in minimal excess pore pressure and settlement as the soil drains the water (point c).However, rapid thawing can lead to significant excess pore pressure (point c′ or c″), compromising the soil stability by reducing the bearing capacity and potentially causing severe differential settlements.[97]).

Modifications in Soil Properties after a Freeze-Thaw Cycle
Throughout a freeze-thaw cycle, the soil undergoes continuous changes.During freezing, ice can develop in different forms, ranging from particle coatings to lenses between soil layers.Upon thawing, the melted water necessitates a new equilibrium void ratio for the soil structure under existing overburden pressure.Freeze-thaw cycles significantly alter the soil properties, including the density, grain size distribution, hydraulic conductivity, strength, compressibility, stiffness, and bearing capacity [8,85,[98][99][100][101][102][103].

Modifications in Soil Properties after a Freeze-Thaw Cycle
Throughout a freeze-thaw cycle, the soil undergoes continuous changes.During freezing, ice can develop in different forms, ranging from particle coatings to lenses between soil layers.Upon thawing, the melted water necessitates a new equilibrium void ratio for the soil structure under existing overburden pressure.Freeze-thaw cycles significantly alter the soil properties, including the density, grain size distribution, hydraulic conductivity, strength, compressibility, stiffness, and bearing capacity [8,85,[98][99][100][101][102][103].
Understanding these changes is crucial for AGF projects, as the soil will inevitably experience one complete FT cycle during its lifespan.Research on FT cycles offers comprehension of the associated degradation mechanisms.Notably, the first FT cycle often exerts the most significant impact on the soil [98,104].This knowledge is essential for the accurate assessment and control of deformations associated with AGF.

•
Soil structure and porosity Over the past few decades, there has been a considerable amount of research conducted on how the soil microstructure changes due to FT cycles.These cycles can alter the size and shape of soil particles, promoting fragmentation of coarse grains (quartz, feldspar, etc.) and aggregation of clay and silt particles.This, in turn, significantly impacts the soil structure and overall properties [6,8,85,102,105].Zhai et al. [105] investigated the effect of FT cycles on the grain size distribution.Four representative soils from the Qinghai-Tibet Plateau (Adamic earth, Qinghai-Tibet silty red clay, Lanzhou Loess, and Haidong Loess) were subjected to 0, 3, 6, 9, 50, and 100 FT cycles.The results, shown in Figure 10, revealed that FT cycles can significantly alter the initial particle size distribution (PSD), consequently impacting the soil type, structure, and various properties like the water content, porosity, permeability, and density.It is important to acknowledge that the transition in soil type based solely on the PSD (e.g., silt to clay) may not fully capture the changes in the chemical and physical nature of the soil grains themselves.
Understanding these changes is crucial for AGF projects, as the soil will inevitably experience one complete FT cycle during its lifespan.Research on FT cycles offers comprehension of the associated degradation mechanisms.Notably, the first FT cycle often exerts the most significant impact on the soil [98,104].This knowledge is essential for the accurate assessment and control of deformations associated with AGF.

•
Soil structure and porosity Over the past few decades, there has been a considerable amount of research conducted on how the soil microstructure changes due to FT cycles.These cycles can alter the size and shape of soil particles, promoting fragmentation of coarse grains (quartz, feldspar, etc.) and aggregation of clay and silt particles.This, in turn, significantly impacts the soil structure and overall properties [6,8,85,102,105].Zhai et al. [105] investigated the effect of FT cycles on the grain size distribution.Four representative soils from the Qinghai-Tibet Plateau (Adamic earth, Qinghai-Tibet silty red clay, Lanzhou Loess, and Haidong Loess) were subjected to 0, 3, 6, 9, 50, and 100 FT cycles.The results, shown in Figure 10, revealed that FT cycles can significantly alter the initial particle size distribution (PSD), consequently impacting the soil type, structure, and various properties like the water content, porosity, permeability, and density.It is important to acknowledge that the transition in soil type based solely on the PSD (e.g., silt to clay) may not fully capture the changes in the chemical and physical nature of the soil grains themselves.The impact of FT cycles on the soil microstructure extends to its pore structure.Zhang and Cui [106] investigated the impact of one FT cycle on the microscopic pore structure of Shanghai grey silty clay using Mercury Intrusion Porosimetry (MIP) tests.Their results revealed a 6.0% increase in the final mercury intrusion volume and a 30.64% increase in the most probable pore size after the FT cycle.These findings suggest that the FT cycle can lead to an enlargement of the microscopic pore structures within the silty clay.An et al. [103] employed Nuclear Magnetic Resonance Imaging (NMRI) to assess the microstructural changes induced by AGF upon a single FT cycle in undisturbed granite residual soils (GRSs).The study revealed a decrease in the pore volume of the micropores and an increase in the pore volume of the macro-pores after FT, signifying a significant alteration in the overall PSD of GRSs.Based on the PSD curves, the authors concluded that the FT cycle induced by AGF led to an increase in macropore volume, a slight decrease in micropore volume, and a net increase in overall porosity of approximately 11.1%.Both studies provide compelling evidence that an FT cycle significantly impacts the microscopic pore structure of soils, generally leading to an enlargement of pores and an increase in overall porosity.

•
Density and Void Ratio Freeze-thaw cycles have contrasting effects on soil density (Figure 11).Loose soils tend to densify following FT exposure.This can be due to the formation of ice lenses during freezing, which causes an initial volume increase.Upon thawing, the ice melts, and the soil matrix consolidates, resulting in a denser state characterized by a lower void ratio [104].Conversely, dense soils may experience a net loosening effect from FT cycles.While freezing can lead to a temporary volume increase due to ice formation, thawing typically results in some consolidation.However, due to the inherent difficulty of soil particles returning to their exact pre-freezing positions, the void ratio of initially dense soil generally increases after FT cycles.This translates to a net increase in soil volume and a decrease in density, signifying a looser soil structure [104].
the most probable pore size after the FT cycle.These findings suggest that the FT cycle can lead to an enlargement of the microscopic pore structures within the silty clay.An et al. [103] employed Nuclear Magnetic Resonance Imaging (NMRI) to assess the microstructural changes induced by AGF upon a single FT cycle in undisturbed granite residual soils (GRSs).The study revealed a decrease in the pore volume of the micropores and an increase in the pore volume of the macro-pores after FT, signifying a significant alteration in the overall PSD of GRSs.Based on the PSD curves, the authors concluded that the FT cycle induced by AGF led to an increase in macropore volume, a slight decrease in micropore volume, and a net increase in overall porosity of approximately 11.1%.Both studies provide compelling evidence that an FT cycle significantly impacts the microscopic pore structure of soils, generally leading to an enlargement of pores and an increase in overall porosity.

•
Density and Void Ratio Freeze-thaw cycles have contrasting effects on soil density (Figure 11).Loose soils tend to densify following FT exposure.This can be due to the formation of ice lenses during freezing, which causes an initial volume increase.Upon thawing, the ice melts, and the soil matrix consolidates, resulting in a denser state characterized by a lower void ratio [104].Conversely, dense soils may experience a net loosening effect from FT cycles.While freezing can lead to a temporary volume increase due to ice formation, thawing typically results in some consolidation.However, due to the inherent difficulty of soil particles returning to their exact pre-freezing positions, the void ratio of initially dense soil generally increases after FT cycles.This translates to a net increase in soil volume and a decrease in density, signifying a looser soil structure [104].
Notably, the most significant changes in soil density occur within the first few FT cycles [98,107].Beyond a certain number of cycles (Nres), a residual void ratio (eres) is established and further FT exposure has minimal impact on density [104,108].

Crack formation
Both freezing and thawing processes can contribute to crack formation.During freezing, three main factors are at play: increased pore volume due to water phase change, formation and growth of ice lenses, and shrinkage caused by negative pore pressure near the freezing front [100].The behavior during thawing depends on the soil type (cohesive vs. frictional) and conditions like the water availability and overburden pressure.In clay soils, ice-filled cracks may not fully reseal due to intrinsic strength (cohesion), leading to Notably, the most significant changes in soil density occur within the first few FT cycles [98,107].Beyond a certain number of cycles (N res ), a residual void ratio (e res ) is established and further FT exposure has minimal impact on density [104,108].

• Crack formation
Both freezing and thawing processes can contribute to crack formation.During freezing, three main factors are at play: increased pore volume due to water phase change, formation and growth of ice lenses, and shrinkage caused by negative pore pressure near the freezing front [100].The behavior during thawing depends on the soil type (cohesive vs. frictional) and conditions like the water availability and overburden pressure.In clay soils, ice-filled cracks may not fully reseal due to intrinsic strength (cohesion), leading to additional fissures upon thawing.In coarse-grained soils, cracks formed during freezing can be sealed by particle movement during thawing.
Freeze-thaw cycles significantly impact the permeability of fine-grained soils.Studies consistently report significant changes in the permeability of fine-grained soils subjected to FT [85,98,100,104,107].Clays experience the most substantial increases in permeability, often exceeding two orders of magnitude.Some studies report even higher increases.Silts generally exhibit smaller permeability changes compared to clays.Dense silty tills (low initial void ratio) show a slight increase in permeability after FT, while loose tills (high initial void ratio) experience a decrease.The changes in the permeability of soils after FT are attributed to two main reasons.The first is related to the emergence of polygonal shrinkage microcracks and the formation of larger pores after the thawing of ice lenses.The second is associated with the movement of fine particles out of the large pores during FT [85].The mechanism controlling the process depends on the soil type.
Overburden pressure is a key player in the definition of the permeability of frozenthawed soils.While shrinkage cracks and ice lenses may develop during freezing and increase hydraulic conductivity, the overburden pressure exerted on the soil can seal the fissures and lower the hydraulic conductivity.Tests on thawed and unfrozen Wisconsin glacial clays by Othman and Benson [98] indicated that the degree of the permeability change can be reduced by isotropic loading.The presence of pressure can seal the cracks created by freeze-thaw.Maintaining stress during freeze-thaw had a significant effect, and 70 kPa was sufficient to stop the increase in permeability (Figure 12).However, Viklander [104] emphasized that the test procedure (flexible vs. rigid wall permeameter), temperature gradient (1D or 3D freezing), scale effect, hydraulic gradient, and water conditions (closed or open system) affect this influence.can be sealed by particle movement during thawing.
Freeze-thaw cycles significantly impact the permeability of fine-grained soils.Studies consistently report significant changes in the permeability of fine-grained soils subjected to FT [85,98,100,104,107].Clays experience the most substantial increases in permeability, often exceeding two orders of magnitude.Some studies report even higher increases.Silts generally exhibit smaller permeability changes compared to clays.Dense silty tills (low initial void ratio) show a slight increase in permeability after FT, while loose tills (high initial void ratio) experience a decrease.The changes in the permeability of soils after FT are attributed to two main reasons.The first is related to the emergence of polygonal shrinkage microcracks and the formation of larger pores after the thawing of ice lenses.The second is associated with the movement of fine particles out of the large pores during FT [85].The mechanism controlling the process depends on the soil type.
Overburden pressure is a key player in the definition of the permeability of frozenthawed soils.While shrinkage cracks and ice lenses may develop during freezing and increase hydraulic conductivity, the overburden pressure exerted on the soil can seal the fissures and lower the hydraulic conductivity.Tests on thawed and unfrozen Wisconsin glacial clays by Othman and Benson [98] indicated that the degree of the permeability change can be reduced by isotropic loading.The presence of pressure can seal the cracks created by freeze-thaw.Maintaining stress during freeze-thaw had a significant effect, and 70 kPa was sufficient to stop the increase in permeability (Figure 12).However, Viklander [104] emphasized that the test procedure (flexible vs. rigid wall permeameter), temperature gradient (1D or 3D freezing), scale effect, hydraulic gradient, and water conditions (closed or open system) affect this influence.

Influence of FT Cycles on the Mechanical Properties of Soil
FT cycles significantly impact the mechanical behavior of soils.These cycles alter several key parameters, like the stress-strain relationship and shear strength parameters.

Stress-strain relationship
Studies show that FT cycles can significantly impact the stress-strain properties of various soil types, including fine-grained sands, clays, residual soils, and saline soils [101,103,[109][110][111][112].These studies generally reveal a common pattern: before FT, the stressstrain curve of soil samples exhibits strain softening, while after FT, it shows a strain

Influence of FT Cycles on the Mechanical Properties of Soil
FT cycles significantly impact the mechanical behavior of soils.These cycles alter several key parameters, like the stress-strain relationship and shear strength parameters.

• Stress-strain relationship
Studies show that FT cycles can significantly impact the stress-strain properties of various soil types, including fine-grained sands, clays, residual soils, and saline soils [101,103,[109][110][111][112].These studies generally reveal a common pattern: before FT, the stress-strain curve of soil samples exhibits strain softening, while after FT, it shows a strain hardening tendency.For example, Leroueil et al. [109] investigated the mechanical behavior of nine Champlain Sea clays before and after one FT cycle using consolidated isotropic undrained triaxial tests.The results showed a clear change in behavior.The intact clays displayed a peak stress at around 1% strain followed by strain softening.In contrast, the frozen-thawed clays exhibited no peak stress and significantly lower stiffness.Notably, at a strain of 0.5%, the undrained modulus of the frozen-thawed clays was only 20-40% of that of the intact clays.Similar findings were reported by An et al. [103] for granite residual soils.They attributed the significant reduction in peak stress after FT to the pressure exerted by ice lens development.This pressure promotes the soil's friability, leading to lower peak stress when the sample undergoes significant deformation.Liu et al. [113] carried out unconsolidated and undrained (UU) triaxial tests on silty sand samples that were subjected to varying numbers of FT cycles at a constant axial strain rate and three different confining pressures (100,200, and 300 kPa).The results indicated a transition in the stress-strain curve from a weak strain-softening type to a strain-hardening type after FT cycles, particularly under low confining pressures.Both the unfrozen and thawed silty sand samples exhibited strain-hardening behavior at higher confining pressures.Liu et al.'s [113] results differ from those reported by Wang et al. [114], who found that thawed clay displayed strain-softening behavior under low confining pressure and strain-hardening behavior under higher confining pressure.The discrepancies in these findings are likely attributable to the use of different soil types in the experiments, potentially leading to variations in the critical confining pressures at which the stress-strain behavior transitions from softening to hardening.

• Shear strength parameters
Freeze-thaw cycles have a significant effect on the shear strength of soil.Cohesion generally decreases with more cycles, as soils become less cohesive and more porous.An et al. [103] reported a reduction of 15.7% in the cohesion of granite residual soils after one FT cycle, while Han et al. [101] observed a similar decrease in saline soil.This cohesion decrease can be associated with the loss of contact between soil particles following the emergence of cracks due to FT.
The impact of FT cycles on the friction angle is less conclusive.Han et al. [101] observed a slight increase in the friction angle for saline soil during initial FT cycles, but a decrease after many cycles followed this.They attributed the increase in the angle of friction after the first 10 cycles to the bonding effect of salt crystals.
It is important to acknowledge that various factors beyond temperature and salinity can influence the response of soil to FT cycles.For instance, Yao et al. [115] reported an unexpected increase in cohesion for certain fine-grained soils after FT cycles.Their findings highlight the potential influence of the initial soil density on the response to freeze-thaw.They observed that depending on the initial soil density, FT cycles could cause particle connections to become stronger or weaker, increasing or decreasing the apparent cohesion.Interestingly, while FT cycles enhanced the apparent friction angle of the soil regardless of the initial dry unit weight, they decreased the apparent cohesion of the samples prepared at a lower density (16.0 kN/m 3 ) and increased it for those prepared at a higher density (18.3 kN/m 3 ).
Freeze-thaw is a weathering process that has major effects on the mechanical and physical properties of soil at both the microscopic and macroscopic scales.An FT cycle tends to densify loose soil, decreasing its void ratio, and loosen dense soil, increasing its void ratio.Regardless of the void ratio changes, frozen-thawed soil will increase the hydraulic conductivity due to crack development and changes in structure and porosity.FT cycles have also been proven to damage the structure of soils and deteriorate their mechanical performance (peak strength, shear strength, etc.).Damage brought on by freeze-thaw cycles can appear as differential soil heave or settlement that hinders the stability of aboveground or underground structures.These damages originate from thermal and hydraulic deformations induced by the soil's temperature variations, the freezing of pore water, and the migration of unfrozen water within the pore network.

Conclusions
This paper presented the relationship between AGF and its subsequent effects on soil properties.The core findings highlight the highly complex nature of AGF, revealing both its benefits and its potential drawbacks.
• AGF improves soil mechanics and reduces water permeability, creating a more stable environment for construction projects.However, unfrozen water can persist at subzero temperatures and migrate in certain soils, forming ice lenses.• The success of AGF relies on understanding the complex interplay between factors like the temperature, soil composition, and initial ground conditions, which all influence the freezing process.This intricate thermo-hydro-chemo-mechanical process strengthens soil and decreases permeability but can also induce deformations due to water expansion and ice lens formation.

•
Frost heave, the upward movement of the ground surface caused by freezing water, has two main contributors: phase change and ice lens formation.

•
Overburden pressure, the weight of overlying soil, affects freezing progression and limits ice lens growth by reducing the water flow and lowering the temperature at which ice lenses form.

•
Freeze-thaw cycles significantly impact soil properties.In fine-grained soils, FT cycles can lead to over-consolidation, but rapid thawing risks generating high pore pressures and compromising stability.• The freeze-thaw process by itself acts as a form of weathering that influences the me- chanical and physical properties of soil at both the microscopic and macroscopic levels.Notably, FT cycles can loosen dense soil, densify loose soil, and increase the overall hydraulic conductivity due to structural changes within the soil matrix.Additionally, these cycles can weaken the soil structure and deteriorate its mechanical performance.
This review opens up important prospects for furthering our understanding of the complex interactions between the stress, thermal, hydraulic, and mechanical processes underlying frost heave.While significant progress has been made in understanding the influence of overburden pressure on soil freezing, substantial knowledge gaps remain, particularly in the context of large-scale urban AGF applications.A key challenge is the limited experimental data on soil freezing under high stress.Most existing studies rarely explore pressures exceeding 500 kPa, which is not representative of the overburden pressures encountered in urban environments.To address this, future research should focus on developing experimental methods that can simulate the effects of higher overburden pressure on soil freezing behavior while accounting for the presence of a thermal gradient.Moreover, investigating the long-term effects of overburden pressure on soil properties and assessing frost heave mitigation strategies under different ground conditions are crucial areas to be explored in the future.
From a numerical point of view, despite the significant advancements that have been made in the modeling of AGF, it is still far from complete.Capturing the intricate interplay between the soil properties and the multiphysics processes (thermal, hydraulic, mechanical, and chemical) during freezing remains a challenge.Existing models often rely on simplifications or limited couplings and struggle to represent in situ complexities like variations in temperatures, water flows, and external stresses.Furthermore, the validation of the developed model is often faced with limited, high-quality field data.To bridge the gap between complex models and practical applications, future efforts should focus on developing user-friendly, computationally efficient models that can capture the highly coupled and complex nature of AGF projects.

Figure 1 .
Figure 1.(A) Schematic representation of the cooling curve for soil water and ice (after [13]).(B) Schematic representation of a typical soil freezing characteristic curve.(C) Saturated soil freezing: microscopic evolution of unfrozen water and ice phases ([18]).

Figure 2 .
Figure 2. Coupled thermal, hydraulic, chemical, and mechanical phenomena during the freezing of a porous medium.

Figure 2 .
Figure 2. Coupled thermal, hydraulic, chemical, and mechanical phenomena during the freezing of a porous medium.

Figure 3 .
Figure 3.A summary of the relationship between heave deformations and applied stress based on soil types from four distinct studies (Ming et al. and Sheng et al. [49,50], Zhang et al. [51], Ji et al. [52]).

Figure 4 .
Figure 4. Schematic representation of a frozen soil profile and the processes that govern freezing-Tf: freezing temperature of water; and Ts: segregation temperature (at the base of the ice lens) [59].

Figure 4 .
Figure 4. Schematic representation of a frozen soil profile and the processes that govern freezing-Tf: freezing temperature of water; and Ts: segregation temperature (at the base of the ice lens) [59].

Figure 5 .
Figure 5.A schematic diagram (not to scale) of the frozen fringe [59].

Figure 5 .
Figure 5.A schematic diagram (not to scale) of the frozen fringe [59].

Figure 7 .
Figure 7.A schematic diagram of a frozen soil profile with and without overburden pressure [59].

Figure 7 .
Figure 7.A schematic diagram of a frozen soil profile with and without overburden pressure [59].

Figure 8 .
Figure 8. Schematic representation of a typical soil freezing characteristic curve.

Figure 8 .
Figure 8. Schematic representation of a typical soil freezing characteristic curve.

Figure 9 .
Figure 9. Schematic illustration of the thaw consolidation process during an FT cycle of a typical clay (after[97]).

Figure 9 .
Figure 9. Schematic illustration of the thaw consolidation process during an FT cycle of a typical clay (after [97]).

Figure 10 .
Figure 10.Variation of the sand, silt, and clay fractions as a function of increasing FT cycles [102].Figure 10.Variation of the sand, silt, and clay fractions as a function of increasing FT cycles [102].

Figure 10 .
Figure 10.Variation of the sand, silt, and clay fractions as a function of increasing FT cycles [102].Figure 10.Variation of the sand, silt, and clay fractions as a function of increasing FT cycles [102].

Figure 11 .
Figure 11.Microstructural and volume changes of a fine-grained till after several FT cycles [104].

Figure 11 .
Figure 11.Microstructural and volume changes of a fine-grained till after several FT cycles [104].

Figure 12 .
Figure 12.Hydraulic permeability of Wisconsin glacial clay as a function of the overburden pressure for unfrozen and post-thawed (5 FT cycles) samples [98].

Figure 12 .
Figure 12.Hydraulic permeability of Wisconsin glacial clay as a function of the overburden pressure for unfrozen and post-thawed (5 FT cycles) samples [98].

Table 1 .
Potential explanations for the hysterical behavior observed in the SFCC.