Many types of soils and rock masses show frost-heaving behavior during the freeze-thaw cycles because of temperature variations when they contain water. Generally, frost heaving occurs in the northern hemisphere (cold regions) countries like America, Canada, Russia, and the Nordic regions e.g., Denmark, Finland, Iceland, Norway, Sweden, and Greenland (Brown et al., 1998; Prince et al., 2018) (Figure 1A), and its influence is a problem of national concern since it delays many engineering projects (Taivainen, 1963). The effect of frost heaving causes a lot of damage to geo-structures, such as pipelines (Oswell, 2011), subgrades (Wu et al., 2018), foundations, tunnels, etc.

The prevalence of seasonal freezing and thawing in the northern hemisphere has far-reaching implications with more than half of the northern hemisphere’s land area (Figure 1A) (Prince et al., 2018). Within this vast region, a significant portion, precisely one-quarter as well as 17% of the Earth’s exposed land surface is characterized by permafrost, where the ground remains frozen at or below 0°C for a minimum of two consecutive years (Christiansen et al., 2010; Gruber, 2012; Biskaborn et al., 2019). In China, there is an extensive distribution of frozen soil in the northern climates like Tibet, Xinjiang, and Qinghai, where the temperature is low (below 0°C), large frozen depths, and long durations in the soil throughout two-thirds of the time in a year (Liu et al., 2017). It is reported that engineers working at underground tunnels in these areas in China often observe ice in fractured rock mass at low temperatures, which sometimes causes the fissure volume to expand, resulting in underground instability (Wang et al., 2016b). Permafrost in the Nordic region can be found in lowland areas with marine sediments, palsas, and peat plateaus, and in many mountainous regions at temperatures near 0.8°C (Figure 1B), making it highly responsive to climate variations (Christiansen et al., 2010).

In locations such as Svalbard, northeast Greenland, and the highest mountainous zones throughout the Nordic area, permafrost is slightly colder but still just a few degrees above freezing (Christiansen et al., 2010). Notably, in Finland, the penetration of frost into glacial soils exhibits distinct regional patterns; thus, in the southern part of the country, frost reaches depths of approximately 1.22 m–1.83 m (4–6 ft), while in the northern part, this freezing phenomenon extends much deeper, ranging from 2.13 m to 3.05 m (7–10 ft) which accounts for more frost occurrence in the northern climate of Finland (Taivainen, 1963). As a result, boundary markers often shift from their designated positions due to the upward movement of rocks resulting from the volumetric expansion of ice beneath road beds (Taivainen, 1963).

Extensive research on frost-heaving has been conducted since the early 1990s till date. Taber (1930) and Taber (1929) explored the frost-heaving mechanisms such as the growth of ice lenses in soil. Mu and Ladanyi, (1987) developed models that integrated stress-strain behavior, heat, and mass transport to estimate frost heave. Matsuoka (1990) focused on measuring frost-heaving strains in rocks, observing the influence of surface area on freezing expansion (Huang et al., 2020). Dagli et al. (2018) investigated the role of suction in water migration to the frost front. Wang and Zhou, (2018) emphasized how jointed rock mass properties can affect frost-heaving pressure due to phase changes. Osokin et al. (2000), Rekstad et al. (2013), and Liu et al. (2017) highlighted the importance of freezing and negative temperatures in soil, leading to volume expansion and negative pressure formation in frozen areas.

Frost heaving is primarily affected by factors such as temperature and pressure, and the details of each factor are expressed below. However, it is important to recognize that the study of this phenomenon requires a comprehensive understanding of multiple contributing factors (Lu et al., 2021). The change in volume resulting from the freezing of water and the subsequent melting of ice serves as the fundamental trigger for soil deformation within a freezing-thawing environment. Periodic frozen soil is susceptible to temperature variation (Niu et al., 2017; Niu et al., 2017; Lin et al., 2018), and the cyclic pattern of freezing and thawing of soil significantly affects soil strength. Bouyoucos (1920) studied soil physics and chemistry and discovered that water in the soil freezes at multiple temperatures, not just one. Huixin et al. (2012) pointed out that in a closed system, as the freezing temperature rises, the amount of frost heave and the ratio of frost heave relative to the soil mass water content and dry density also increase. Liu et al. (2017) identified frost heave in coarse-grained soils when specific combinations of clay content (the mass fraction of the particle with a diameter less than 0.075 mm), initial moisture, and temperature occurred in seasonal frozen regions.

In rock mass, as the freezing temperature decreases, the unfrozen water film thickness between the rock and the ice decreases, leading to an increase in disjoining pressure (De Gennes, 1985; Rempel et al., 2001; Huang et al., 2020). Wang and Zhou (2018) explained that under freezing conditions and low temperatures, prolonged rock exposure can lead to significant changes in the deformation and strength characteristics of the fractured rock mass. Penner (1959) stated that structures and roadways built on materials highly susceptible to frost, along with their associated expansion, could heave up to 0.61 m. Brimblecombe et al. (2010) stated that the count of freeze-thaw cycles can be determined based on the assumption that rocks freeze solely when the mean daily temperature drops below −3°C, and thawing only occurs when the mean daily temperature rises above +1°C. Recently, a novel technique has been developed that utilizes meteorological data to analyze the daily maximum and minimum temperatures. This method entails monitoring and quantifying freeze-thaw cycles, which are defined by temperature fluctuations either from above freezing to below 0°C or from below 0°C to above freezing (Al-Omari et al., 2015). Table 1 provides a comprehensive overview of the geographic distribution of frost-heaving geomaterials and addresses their implications from a geotechnical engineering perspective.

Freezing can generate high pressure when water is constrained to prevent expansion. This phenomenon can also affect the physical and mechanical properties of rocks. Taber, (1929) and Taber, (1930) mentioned that under atmospheric pressure, when a definite amount of water is cooled, it freezes at 0°C with an expansion in volume at about 10%. Also, in soils, Beskow, (1991) stated that an increase in load pressure leads to soil consolidation, resulting in the squeezing out of water. When the pressure decreases, the soil tends to expand and under these conditions, there is potential for the soil to suck the water required for the volume increase (Black and Hardenberg, 1991). Tarefder and Ahmad (2015) reported that when water enters the road surface, under the intense action of the wheel load, it causes a higher pressure concentration at the weak joint between the aggregate and the asphalt binder, which accelerates the damage process and leads to permanent deformation.

Based on the analysis made, it is recognized that freeze-thaw cycles (temperature variations) and pressure control rock heave and settlement in the foundation when little or no water-ice phase change is involved. Also, the volumetric expansion of frozen water (ice) and the melting of pore ice cause heave in wet geomaterials, which in turn affect the concrete structure and underground space engineering.

Various types of natural soil and rock masses exhibit a volume expansion behavior. The natural expansive minerals can be divided into two types: i) clay minerals, mainly montmorillonite, illite, or kaolin. Montmorillonite clay will expand significantly as the volume increases, while illite and kaolin clay will have limited expansion. The typical expansive geomaterials which contain montmorillonite are mud rock and bentonite, etc. ii) The other one is the sulphate minerals such as gypsum, anhydrite, calcium thenardite, and anhydrous thenardite. These two types of expansive minerals expand because of the reaction with water.

The expansion mechanism of frost-heaving soil arises from the interaction between three frost actions: water supply, frost-susceptible soil composition, and temperature as the primary factors (Taber, 1930; Penner, 1959; Black and Hardenberg, 1991; Guthrie et al., 2007; Liu et al., 2017). Heaves are more likely to happen in soil with unique textures, such as loam, silt, and clay, which are moisture-retaining.

Freeze-thaw cycles are common in soils due to fluctuating temperatures. When soil layers freeze, pore water movement is transferred from unfrozen areas to negative regions, which leads to the expansion of the soil’s volume and the development of negative pressure (Beskow, 1991; Black and Hardenberg, 1991; Osokin et al., 2000). In these cold regions, pore water crystallizes and forms ice in the pores, sometimes forming ice lenses (Konrad and Morgentern, 1980; Kozlowski and Nartowska, 2013; Schreiber, 2014). This phenomenon can lead to significant frosts and a decrease in the engineering properties of the soil. In cold climates, the cyclic freezing and thawing processes strongly influence the durability and performance of geo-infrastructures (Tian et al., 2019). The physical and mechanical properties of soils, including expansive soils, change significantly due to freeze-thaw cycles (Yang et al., 2021). Freezing and thawing cycles result in a decrease in the soil’s bulk density and penetration resistance (Unger, 1991). The freeze-thaw process induces uneven stresses within the soil, which create cracks, fractures, and joints in most clay soils, leading to a significant increase in permeability (Eigenbrod, 1996; Fouli et al., 2013; Aksakal et al., 2021). However, coarser soils show a slight change in permeability (Eigenbrod, 1996). As shown in Figure 4A (Schreiber, 2014), when the ice expands within the frozen ground, it induces a soil volume increase of 9%, as proposed by the pore water pressure hypothesis. With high soil moisture content, the surrounding regions will continually provide moisture to the frozen area through capillary action.

This process subsequently contributes to additional ice volume expansion, ultimately leading to frost heaving at the base of the soil. (Guthrie et al., 2007; Liu et al., 2017). The expansion of the frozen water (ice lens) within the soil will exert upward pressure from the penetration limit and induce deformation, which in turn lifts the in-situ frozen soil (Figure 4B) (Schreiber, 2014; Wang and Zhou, 2018). As the temperature gradually decreases over an extended period at a point where the water supply to the lens stops, the frost front drops down until it encounters the saturated soil and creates another ice lens, which creates consecutive volume expansion within the soil (Figure 5) (Schreiber, 2014). The process can continue and cause vulnerability to the infrastructures in the affected area. Consequently, (Alonso et al., 1987; Alonso et al., 1990; Alonso et al., 1999), Adem and Vanapalli (2015), and Lu et al. (2018) and reported the expansion mechanism in expansive soil during freezing at different degrees of saturation in porous materials. Figures 5A,B represent particle types and arrangements in unfrozen expanded clay at higher and lower saturations, respectively.

Clay particles form aggregates that control macropore space, while elementary clay particles regulate the micropore distribution within the aggregates, creating dual porosity. When soil with higher saturation freezes (Figure 5C), the pores between aggregates expand due to the growth of ice lenses, resulting in the compression and rearrangement of soil aggregates. Low-temperature suction forces the water within the aggregate out, which causes drying-induced shrinkage (Lu et al., 2018). This compensatory shrinkage is insufficient to balance the expansion of the growing ice, resulting in an overall increase in soil volume. In contrast, under lower saturation conditions (Figure 5D), the volume expansion of water between the aggregate and ice is contained by the air present in the pores.

In rock mechanics, the presence of joints and fissures significantly affects the geological stability of a rock mass, especially in fractured rock mass, where they play a pivotal role. As the strength of rock is impacted by these discontinuities, the properties of jointed rock are particularly susceptible to the influence of ice within these joints during freezing temperatures (Wang and Zhou, 2018). The frost heave of a rock mass is subject to various factors: temperature, rock frost susceptibility, surrounding rock grade, porosity, and external water supply conditions (Wang et al., 2016a). Joint water in its free state condenses by undergoing a phase change to ice due to negative temperature, exhibiting an expansion coefficient of 9% (Wang et al., 2016a). The water freezing within rock joints initiates a volumetric expansion of the joint filling. This expansion is constrained by the surrounding rock mass, leading to an increase in frost-heaving pressure as a result of the phase transition. If this pressure exceeds the rock mass strength, the jointed rock will fracture and break apart as shown in Figure 6. Given a homogeneous rock medium, the frost heaving ratio is the relationship between volume increment and the original rock volume. This ratio is affected by the 9% volume phase transition process, influencing the rate of frost heave as shown in Eq. 1 (Wang et al., 2016a): η = Δ V V (1) where η is the frost heaving ratio, Δ V is the volume increment of the frost heave, and V is the volume of the original rock.

Additionally, when a rock is exposed to negative temperatures and freezing conditions for a long time, the deformation and intensity properties of the fractured rock mass change greatly. Such occurrences pose threats to constructions such as tunnels, shafts, storage caves, and other infrastructure (Luo et al., 2015; Wang and Zhou, 2018)

In contrast, the above analysis shows that the frost heaving in geomaterials does not promote water flow, causing high hydraulic conductivity. As geomaterials freeze, their porosity decreases and restricts capillary flow. This phenomenon can prevent water ingress from forming ice lenses that cause volume expansion of the geomaterials, resulting in an uplift at the surface. On the contrary, the freeze-thaw process of these natural expansive materials makes it difficult to control water movement in the underground support environment.

The primary mechanism of freeze-thaw damage in cemented structures is described by both the hydraulic pressure theory and the osmotic pressure theory, and both mechanisms are attributed to concrete deterioration (Powers, 1949; Powers, 1975; Hudec, 1991; Pigeon et al., 1996; Valenza and Scherer, 2007; Zeng et al., 2010; Dabas et al., 2021; Guo et al., 2022).

According to Powers and Darcy’s law, the hydraulic pressure theory explains the effects of low temperatures on concrete (Powers, 1949; Powers, 1975). When concrete is exposed to low temperatures, the outer layer of the concrete freezes first. This freezing causes the liquid water within the concrete to migrate through capillary pores due to the volume differences between ice and liquid water. Precisely, ice occupies a greater volume than liquid water, creating a differential pressure that drives the migration (Valenza and Scherer, 2007; Dabas et al., 2021; Guo et al., 2022). As the temperature continues to drop, the volume of ice within the concrete increases. This increase in ice volume compresses the remaining liquid water, generating significant compressive stress in the pores of the concrete. Simultaneously, ice expansion induces tensile stress in the concrete matrix (Guo et al., 2022) (Figure 9A). If the tensile stress exceeds the ultimate tensile strength of the concrete, microcracks begin to generate (Zeng et al., 2010). These microcracks generated can compromise the structural integrity of the concrete which can lead to long-term durability issues. In spite of the knowledge addressed by the hydraulic pressure theory, it does not fully explain certain phenomena. For instance, it does not account for the expansion observed in ordinary concrete during freezing or the behavior of non-expansive liquids when they freeze (Rønning, 2001; Yu et al., 2017).

Studies have discussed the osmotic pressure theory, which involves specific salt ions in concrete (Powers, 1949; Powers et al., 1953; Powers, 1975; Hudec, 1991; Valenza and Scherer, 2007). According to this theory, the complex pore structure of concrete results in varied migration rates of ions and water which leads to the development of osmotic pressure and interior damage. When unfrozen water transitions to ice, osmotic pressure is generated because the vapor pressure of liquid water becomes higher than that of ice (Figure 9B). This pressure is directly related to the concentration of the solution; as the concentration increases, so does the osmotic pressure. Conversely, the amount of ice formation has an inverse relationship with osmotic pressure, with the pressure value being highest at a specific concentration of the solution (Washburn, 1921; Guo et al., 2022). Basically, osmotic pressure theory emphasizes that the migration and distribution of salt ions and water within the porous structure of concrete can generate significant internal pressure during freeze-thaw cycles. This can cause damage such as microcracks, especially in areas where the solution concentration is at maximum coupling values (Figure 9B).

To mitigate cracking in concrete due to freeze-thaw cycles, an effective method will be to reduce hydrostatic pressure by decreasing the spacing between pores. This may be accomplished through the use of air-entraining agents, which introduce tiny air bubbles into the concrete mix. These air bubbles create additional space in the concrete that can accommodate the expanding ice, thereby reducing the overall pressure and preventing damage. For instance, in regular concrete, the pressure exerted by the freezing water causes the concrete to expand in volume. Nevertheless, in air-entrained concrete, the presence of micro-pores created by the air-entraining agents allows the ice to form within these spaces, leading to a contraction rather than expansion (Sun and Scherer, 2010).

Concrete deterioration occurs due to sulfate ions reacting with hydrated cement composites in pore solution, leading to expansion and corrosion in geo-infrastructure (Figure 10), and this reaction forms expansion phases like gypsum and ettringite, as well as corrosion types such as calcium alumina, magnesium sulfate complex, and carbon-sulfur calcium silica stone corrosion (Al-Dulaijan et al., 2003; Mamun and Bindiganavile, 2011; Min et al., 2019; Othman et al., 2020; Zhang et al., 2021; Tian et al., 2023). Sulfate attack in concrete is affected by the availability of sulfate ions, moisture content, temperature fluctuations, and exposure duration.

Basically, sulfate attack in concrete involves physical and chemical reactions (Chen et al., 2020). In the physical reaction, sulfate ions penetrate concrete pores, causing crystallization-induced expansion, leading to internal cracking, which can generate tensile stress and lead to progressive loss of mechanical strength (Tulliani et al., 2002; Oualit and Jauberthie, 2019; Brekailo et al., 2023). The deterioration process originates from two main sources: internal and external attacks. The internal attack results from sulfate within the concrete itself, while external sources include various environmental factors like soils, groundwater, transport fluids, river water, seawater, coastal areas, and acid rain (Neville, 2004; Zhao et al., 2020).

Water serves as a carrier that allows sulfate ions to infiltrate the concrete matrix over time. This infiltration is further heightened by wetting and drying cycles, which can occur naturally or as a result of environmental conditions such as temperature and water table fluctuations. At higher temperatures, water travels at a faster rate along with sulfate ions, which accelerates the chemical reaction between the sulfate and the hydration products of the cement (Ikumi and Segura, 2019; Chen et al., 2020; Zhu et al., 2023). This acceleration causes swellable compounds to form more quickly and increases the rate of deterioration. This reaction results in the formation of expansive compounds such as gypsum and ettringite (Ikumi and Segura, 2019; Chen et al., 2020). These compounds exert pressure within the concrete matrix, causing internal cracking, expansion, and ultimately deterioration of the concrete structure. However, areas with warmer climates may experience a more rapid progression of sulfate attack than colder environments where temperatures are lower and reactions proceed more slowly.

During sulfate attack, particularly assuming sodium sulfate N a 2 S O 4 as the sulfate source, the following chemical reactions (Zuo et al., 2012; Ikumi and Segura, 2019).

Gypsum formation C S H 2 : when sulfate intrudes into concrete, it reacts with the concrete hydration products, such as calcium hydroxide C H and calcium silicate hydrate C S H ) to form C S H 2 (Zhu et al., 2023). The chemical reaction formula as shown in Eq. 2 (Al-samawi and Zhu, 2020): N a 2 S O 4 + C H   → C S H 2 + N a 2 S i O 4 (2)

Ettringite formation C 6 A S 3 H 2 : when gypsum reacts with calcium aluminate phases, such as Monosulfate C 4 A S H 12 , Tricalcium aluminate C 3 A ), Hydrogarnetto C 3 A H 6 etc. in concrete components, the reaction will result in the formation of ettringite (Zhu et al., 2023). The chemical reactions formula as presented in Eq. 3 (Al-samawi et al., 2023): 3 C S H 2 + C 3 A H 6 + 2 O H   → C 2 A S 4 H 32 (3)

The reaction process of these compounds causes concrete expansion, and microcrack formation, and facilitates the entry of harmful ions, accelerating concrete damage.

Frost heaving, a critical geotechnical concern in cold regions, causes structures built on geomaterials to uplift due to freezing temperatures. It alters soil and rock properties by impacting load-bearing capacity, weakening their strength integrity. This poses a serious threat to both surface and underground geo-infrastructures like tunnels, foundations, pipelines, roads, etc., and, however, necessitates a profound understanding of accurate design and mitigation for geotechnical considerations and engineering practices. Table 3 provides a comprehensive summary of the freeze-thaw cycle effects on expansion materials, highlighting their factors and implications in geotechnical engineering.

Further, in cold weather, especially during negative temperatures, the expansion of ice within fractures acts like a stabilizing agent that binds the fractured rock mass together and enhances its stability as well as any structure adjacent to or within it. This phenomenon is often referred to as frost wedging. In the context of underground openings such as tunnels or mines, the presence of ice filling the fractures can provide additional support and reinforcement to the surrounding rock mass. It helps maintain the structural integrity of the openings and minimize the risk of collapses or instability. In frost-susceptible soils, natural rubber latex (NRL) can significantly improve durability against the adverse effects of wetting and drying (w-d) cycles in cement-stabilized soil, particularly when subjected to cyclic tensile loads (Udomchai et al., 2021; Hoy et al., 2023). The NRL forms films that infiltrate and fill the pores and microcracks within the soil-cement matrix. This infiltration not only strengthens the bond between soil particles and cement but also enhances the overall durability of the geo-infrastructure. By preventing the propagation of microcracks and reducing permeability, these NRL films provide a robust barrier against freeze-thaw cycles (Udomchai et al., 2021; Hoy et al., 2023). It is important to note that this stability enhancement is particularly significant during cold seasons when freezing occurs. However, during warmer seasons or when the ice melts, rock mass maintenance and monitoring are crucial to ensure continued stability.

Natural expansive geomaterials with high shrink-swell potential play a crucial role in geotechnical engineering. These materials exhibit unique properties that can significantly affect infrastructure stability and environmental concerns. Therefore, this section discusses the significance and implications of clay minerals and sulfate minerals in geotechnical engineering, drawing upon relevant research and findings.