Soil Freezing Characteristic Curve Research Articles

Measuring soil freezing characteristic curve with thermo‐time domain reflectometry

AbstractThe soil freezing characteristic curve (SFCC) has applications in determining the soil water retention curve (SWRC) and modelling thermal and hydrological processes in cold regions. Accurate measurement of the SFCC in the laboratory has been constrained to the thawing process because of the interference of supercooling during the freezing process. In this study, we introduce a dynamic method based on the technique of thermo‐time domain reflectometry (thermo‐TDR) for measuring the SFCC quickly and accurately. A simple iced‐toothpick approach was used for eliminating supercooling during a freezing experiment. The performance of the thermo‐TDR‐based method was evaluated by comparing the measurements with the equilibration method on two soils of different textures. The results showed that the supercooling phenomena during the freezing process could be eliminated effectively by inserting iced‐toothpicks into the samples at soil freezing point, and both the SFCC (at a freezing rate of 2.5°C h−1) and the soil thawing characteristic curves (STCC) could be determined accurately with the thermo‐TDR‐based method. The thermo‐TDR measured SFCCs agreed well with estimates from the SWRCs, with an average root‐mean square error (RMSE) of 0.02 m3 m−3. The dynamic thermo‐TDR‐based method has the advantages of being easy to operate, time‐saving, and applicable for in situ monitoring of SFCC, and could be used to determine SWRCs indirectly.Highlights The thermo‐TDR method can measure the soil freezing characteristic curve (SFCC) accurately. Supercooling during the freezing process was eliminated by using an iced‐toothpick approach. The slow‐rate dynamic method provided reliable SFCCs as compared with the equilibration method. The thermo‐TDR measured SFCCs could be used to estimate soil water retention curves.

Water retention curve of clayey sands determined from pore structure by using various methods

Besides standard approaches, the soil water retention curve (SWRC) can be estimated either from pore size distribution obtained by mercury intrusion porosimetry or from the soil freezing characteristic curve. These methods are based on simplified laws such as Young-Laplace for capillary suction or ClausiusClapeyron for cryo-suction. These laws might not be valid for clayey sands where the presence of clay particles would induce other water retention mechanisms. This study aims to assess the clay content's effect on the validity of these two methods in determining the SWRC of clayey sands. Clay sands were prepared at different clay contents by mixing pure sand with kaolin clay prior to compaction at the Proctor maximum dry density. Five clay contents (dry mass of clay divided by dry mass of soil) were considered (0, 5, 10, 15, and 20%). The reference SWRC was obtained by standard suction measurements. The results show that SWRCs estimated from mercury intrusion porosimetry and soil freezing characteristic curve are generally in agreement with the reference SWRC. However, the results obtained by the soil freezing characteristic curve are limited in terms of suction range (500 to 5 MPa) which is not appropriate for clayey sands, while those from mercury intrusion porosimetry show significant discrepancy because of the structure heterogeneity obtained by Proctor compaction.

Experimental Study of Soil Water Characteristic Curve for a Clayey Soil Reinforced with Model Geocell for Freezing-Thawing Cycles

The category of geosynthetics includes geocells as a common subclass. As a low-cost, easilyinstalled solution to soil stabilisation problems, geocells are gaining popularity in the field of geotechnical engineering. Assessing and measuring the matric potential of geocell reinforced soil subjected to alternating freezing-thawing cycles depends on understanding the water retention behaviour of the soil. The water retention properties of geocell reinforced soil are influenced by alternate freezing-thawing cycles. For the objective of this study, the thawing soil freezing characteristic curve (SFCC) of a clayey soil with variable numbers of model geocells was determined (0, 1, and 2 number). With the progression of freezingthawing cycles, which dramatically changed the retention behaviour of reinforcing soil, the matric potential was measured using the filter paper method methodology. The thawing SFCC for reinforced soil with model geocell was assessed using the van Genuchten model. For the studied soil with varied numbers of model geocells, the VG model was evaluated for five consecutive freezing-thawing cycles, demonstrating its efficacy in determining the retention behaviour of geocell reinforced soils. The experimental findings showed that the matric potential in SFCC has considerably enhanced due to the presence of model geocell.

Editorial: Special Issue on Smart and Green Infrastructures with Optimum Life Cycle Solutions

Editorial: Special Issue on Smart and Green Infrastructures with Optimum Life Cycle Solutions

Thermal-hydro-mechanical coupled analysis of unsaturated frost susceptible soils

Damage caused by frost heave leads to costly maintenance in cold regions, like Hokkaido, Japan. Therefore, the study of the frost mechanism with experimental and numerical methods has been of great interest. Numerous models have been developed to describe the freezing process of saturated soil, which differs from the partially saturated conditions in the field. In fact, most subsurface soils are unsaturated. The freezing process of partially saturated soils is more complex than saturated soils, as the governing equations show strongly nonlinear characteristics. This study proposes a thermo-hydro-mechanical coupled model considering the heat transfer, water infiltration, and deformation of partially saturated soil to reproduce the freezing process of partially saturated frost susceptible soils distributed in Hokkaido. This model better considers the water-ice phase change and soil freezing characteristic curve (SFCC) during freezing under field conditions. The results from the multiphysics simulations agree well with the frost heave and water migration data from frost heave tests of Touryo soil and Fujinomori soil. In addition, this study discussed the influence of the various factors on frost heave amount, including temperature gradients, overburden pressures, water supply conditions, cooling rates, and initial saturation. The simulation results indicate that the frost heave ratio is proportional to the initial degree of saturation and is inversely proportional to the cooling rate and overburden pressure.Moreover, simulation under the open system generates much more frost heave than under the closed system. Finally, the main features of the proposed model are revealed by simulating a closed-system frost heave test. The simulation results indicate that the proposed model adequately captures the coupling characteristics of water and ice redistribution, temperature development, hydraulic conductivity, and suction in the freezing process. Together with the decreased hydraulic conductivity, the increased suction controls the water flow in the freezing zone. The inflow water driven by cryogenic suction gradient feeds the ice formation, leads to a rapid increase in total water content, expanding the voids that exceed the initial porosity and contributing to the frost heave.

Predicting the soil freezing characteristic curve of the expansive soil with double porosity accounting for hydraulic effects

Based on the similarity between the drying-wetting process and freezing-thawing process in the soil, a physically based equation predicting the soil freezing characteristic curve (SFCC) can be formulated combining the generalized Clapeyron equation. In this paper, by introducing the weighing factors in two scales of pore sizes, the physically based equation for single-porosity soil is extended for double-porosity soil, with the ability in well characterizing the bimodality of the SFCC. A systematic approach formulating the SFCC of the expansive soil is presented accounting for the pore size distribution and its evolution in two scenarios of the hydraulic conditions. Good agreements can be found between model predictions and experimental data for both scenarios. The effects of hydraulic condition on the pore structure of an expansive soil, as well as the consequences of the evolved pore structure on the SFCC, are emphasized and quantified. In addition, the framework presented herein demonstrates how an initially bimodal SFCC evolves into a unimodal shape along hydration and provides the theoretical SFCCs at different levels of saturation, which contributes to modelling the water-heat transfer in the freezing process of the unsaturated expansive soil.

A repository of measured soil freezing characteristic curves: 1921 to 2021

Abstract. Soil freeze–thaw processes play a fundamental role in the hydrology, geomorphology, ecology, thermodynamics, and soil chemistry of cold regions' landscapes. In understanding these processes, the temperature of the soil is used as a proxy to represent the partitioning of soil ice and water content via a soil freezing characteristic curve (SFCC). This mathematical construct relates the soil ice content to a specific temperature for a particular soil. SFCCs depend on many factors, including soil properties (e.g., porosity and composition), soil pore water pressure, dissolved salts, (hysteresis in) freezing/thawing point depression, and the degree of saturation, all of which can be site-specific and time-varying characteristics. SFCCs have been measured using various methods for diverse soils since 1921, but, to date, these data have not been broadly compared. This is in part because they had not previously been compiled in a single dataset. The dataset presented in this publication includes SFCC data digitized or received from authors, and it includes both historic and modern studies. The data are stored in an open-source repository, and an R package is available to facilitate their use. Aggregating the data has pointed out some data gaps, namely that there are few studies on coarse soils and comparably few in situ measurements of SFCCs in mountainous environments. It is hoped that this dataset (https://doi.org/10.5281/zenodo.5592825; Devoie et al., 2022a) will aid in the development of SFCC theory and improve SFCC approximations in soil freeze–thaw modelling activities.

Influence of fines content and degree of saturation on the freezing deformation characteristics of unsaturated soils

In this study, a series of one-dimensional freezing deformation tests were conducted within a closed system to evaluate the influence of fines content and initial water content on the frost susceptibility of soils. Also, the pulsed nuclear magnetic resonance (P-NMR) method was adopted to investigate the pore water distribution and deformation mechanism of freezing soils. Results show that as soil temperature decreases, pore water freezes in two stages: the capillary (or free) water freezes first, followed by certain amounts of adsorbed water turned into pore ice. Soil specimens with higher fines content usually have higher unfrozen water content due to the more abundant adsorbed water from fine particles. The initial water content influences the soil-freezing characteristic curve significantly when the fines content is relatively high (e.g., FC = 50%), while this influence becomes negligible with lower fines content. In addition, the freezing deformation properties of soil within a closed system are affected by the initial water content. A higher degree of saturation (e.g., Sr > 0.5) results in frost heave, and a lower degree of saturation (e.g., Sr < 0.4) results in frost shrinkage. In fact, there is a critical degree of saturation (between 0.4 and 0.5) that separates soil's properties of frost heave and frost shrinkage. Frost heave or frost shrinkage of soil depends on which of the two, freezing of pore water or thinning of adsorbed water (i.e., dehydration), is predominant.

Heat, water and vapor coupled migration in loess under uniaxial freezing condition

Water vapor migration induces frost damage to airport runways and highways in loess areas. In this study, the freezing point, soil-freezing characteristic curve (SFCC) and soil-water characteristic curve (SWCC) of Xining loess were measured. While the temperature and water profiles of loess columns under three temperature gradients were obtained by uniaxial freezing tests. Results show that the freezing point of loess is positively correlated with water content in the range of 2.6%–34%, which was well fitted by the Boltzmann function. Unfrozen water content declines more pronounced with temperature at higher water contents and power functions were fitted for SFCC. At higher water contents or lower cold-end temperatures, water migration in soil column is more significant. The above functions were introduced to the non-isothermal heat-water-vapor coupled migration model and numerically implemented in COMSOL Multiphysics. It was verified by comparing with uniaxial freezing test data. Under a given temperature gradient, the lower the freezing point, the smaller the frozen depth, the more insignificant the liquid water migration, and the lower volume fraction of ice. Vapor migration is less affected by freezing point but by vapor density and flux.

An algorithmic framework for computational estimation of soil freezing characteristic curves

AbstractMany numerical models for simulating freezing and thawing phenomena of soil have been developed due to emerging geotechnical issues in cold regions. In particular, coupled thermo‐hydro‐mechanical (THM) analysis is used to evaluate complicated deformation, thermal, and moisture transport behavior of freezing–thawing soils. This study proposes a soil‐freezing characteristic curve (SFCC) that is robust and adaptive with various computational frameworks, including the THM approach. The proposed SFCC can also account for different soil types by incorporating the particle size distribution. Here an automatic regression scheme is adopted to update the SFCC associated with deformation and thermal changes. In addition, a smoothing algorithm is adopted to prevent a sharp change of the SFCC due to phase transition between the liquid water and crystal ice. Based on experimental works in the literature, the applicability of our model is demonstrated when the initial water contents and soil particle distribution differ. We further investigate the performance of the proposed SFCC as a constitutive model within a simplified THM framework. Our results show that the proposed model captures the desired behavior of different soil types in the freezing process, such as freezing temperature depreciation, the effect of compaction, and mechanical loading on unfrozen water content.

The Prediction of the Soil Freezing Characteristic Curve Using the Soil Water Characteristic Curve

The Prediction of the Soil Freezing Characteristic Curve Using the Soil Water Characteristic Curve

Influence of bimodal structure on the soil freezing characteristic curve in expansive soils

The bimodal structure in expansive soils that refers to the bimodality of the pore size distribution significantly affects the soil freezing characteristic curve (SFCC). In this paper, the artificial samples with different bimodal structures are prepared by mixing Qinghai-Tibet silty clay and bentonite in different proportions. The influence of the bimodal structure on the SFCC of the samples was studied by the mercury intrusion porosimetry test, the nuclear magnetic resonance (NMR) test and the freezing-point test. The results show that the freezing stage of the SFCC in bimodal soils consists of a rapid-drop part related to freezing of macropore water and a slow-drop part related to freezing of micropore water. As the specific surface area increases, the proportion of the rapid-drop part decreases whereas the slow-drop part increases. On the temperature-time curve, the duration of the isothermal stage and the freezing point decrease with the rising specific surface area. Based on the experimental results, we established a novel SFCC function derived from the theory of pore size distribution by extending the lognormal distribution to consider bimodality. The SFCC function can fit the measured data of the SFCC well.

A new integral model for predicting the hydraulic conductivity of saturated frozen soil

Hydraulic conductivity of frozen soil is indispensable for describing water flow process in freezing soils. However, this conductivity is difficult to measure in the laboratory. So, the objective of this study is to propose a simple and smooth hydraulic conductivity model for saturated frozen soil based on the soil freezing characteristic curve (SFCC). Considering that the volume of pore water approximately represents the pore volume, the distribution of effective pore radii changed as a function of temperature was determined by combining the SFCC and the Gibbs–Thomson equation. Based on the distribution of effective pore radii, Hagen-Poiseuille equation, Darcy’s law, relative hydraulic conductivity and tortuosity, a simple and smooth hydraulic conductivity model for saturated frozen soil based on the SFCC was proposed. To illustrate the model performance, eight existing experimental cases were analyzed. The results showed that predictions considering the three different tortuosity formulations were in good agreement with the tested data; the results were worse when not considering the tortuosity and the results were best when considering the tortuosity τF=B/rb2. Moreover, the predictive modeling power was related to the tortuosity function. Furthermore, the model was further compared with the previous models, the results of which showed the better performance of the proposed model. The model is quite simple and timesaving to use when the SFCC and the saturated hydraulic conductivity are available. This result provides a new idea for developing the hydraulic conductivity model of saturated frozen soil.

A Model for the Soil Freezing Characteristic Curve That Represents the Dominant Role of Salt Exclusion

AbstractThe phenomenon of freezing point depression in frozen soils results in the co‐existence of ice and liquid water in soil pores at temperatures below 273.15 K (0°C), and is thought to have two causes: (a) capillary and adsorption effects, where the phase transition relationship is modified due to soil‐air‐water‐ice interactions, and (b) solute effects, where the presence of salts lowers the freezing temperature. The soil freezing characteristic curve (SFC) characterizes the relationship between liquid water content and temperature in frozen soils. Most hydrological models represent the SFC using only capillary and adsorption effects with a relationship known as the Generalized Clapeyron Equation (GCE). In this study, we develop and test a salt exclusion model for characterizing the SFC, comparing this with the GCE‐based model and a combined salt‐GCE effect model. We test these models against measured SFCs in laboratory and field experiments with diverse soil textures and salinities. We consistently found that the GCE‐based models under‐predicted freezing‐point depression. We were able to match the observations with the salt exclusion model and the combined model, suggesting that salinity is a dominant control on the SFC in real soils that always contain solutes. In modeling applications where the salinity is unknown, the soil bulk solute concentration can be treated as a single fitting parameter. Improved characterization of the SFC may result in improvements in coupled mass‐heat transport models for simulating hydrological processes in cold regions, particularly the hydraulic properties of frozen soils and the hydraulic head in frozen soils that drives cryosuction.

Quantification and division of unfrozen water content during the freezing process and the influence of soil properties by low-field nuclear magnetic resonance

In this study, a low-field nuclear magnetic resonance (NMR) apparatus with the ability to adjust sample temperatures was used to measure the unfrozen water content of frozen soils sampled from the Qinghai-Tibet Plateau. Based on low-field NMR theory, two cutoff values were proposed to quantitatively identify three types of unfrozen water (bulk, capillary, and bound water) in the frozen soils. The influences of soil properties (the clay content, particle size distribution, and clay mineral content) on these three different types of unfrozen water during the soil freezing process were analyzed. The results showed that the soil-freezing characteristic curve of unfrozen water could be divided into three stages, namely, the unfrozen, the rapid-drop, and the residual stages. In the rapid-drop stage, the unfrozen bound water content increases gradually with the increasing clay or clay mineral content, and at a certain temperature, the unfrozen capillary water content increases as the sand and silt content increases. A published power function model is then used to fit the measured data in this study. We found that the single parameter related to soil properties in this model could not sufficiently reflect the influence of clay mineral content or clay content on unfrozen water content.

Implications of measurement metrics on soil freezing curves: A simulation of freeze–thaw hysteresis

AbstractSoil freeze–thaw events have important implications for water resources, flood risk, land productivity, and climate change. A property of these phenomena is the relationship between unfrozen water content and sub‐freezing temperature, known as the soil freezing characteristic curve (SFC). It is documented that this relationship exhibits hysteretic behaviour when frozen soil thaws, leading to the definition of the soil thawing characteristic curve (STC). Although explanations have been given for SFC/STC hysteresis, the effect that ‘scale’ – particularly ‘measurement scale’ – may have on these curves has received little attention. The most commonly used measurement scale metric is the ‘support’, which is the spatial (or temporal) unit within which the measured variable is integrated or soil volume sampled. We show (a) measurement support can influence the range and shape of the SFC and (b) hysteresis can be attributed, in part, to the support and location of the measurements comprising the SFC/STC. We simulated lab measured temperature, volumetric water content (VWC), and permittivity from soil samples undergoing freeze–thaw transitions using Hydrus‐1D and a modified Dobson permittivity model. To assess the effect of measurement support and location on SFC/STC, we masked the simulated temperature and VWC/permittivity extent to match the instrument's support and location. By creating a detailed simulation of the intra‐ and inter‐support variability associated with the penetration of a freezing front, we demonstrate how measurement support and location can influence the temperature range over which water freezing events are captured. We show it is possible to simulate hysteresis in homogenous media with purely geometric considerations, suggesting that SFC/STC hysteresis may be more of an apparent phenomenon than mechanistically real. Lastly, we develop an understanding of how the location and support of soil temperature and VWC/permittivity measurements influence the temperature range over which water freezing events are captured.

Comparison of freezing and hydration characteristics for porous media

AbstractThe processes of freezing–thawing and hydration–dissociation change the content of liquid water that coexists with ice or hydrate in porous media, such as frozen soils and hydrate‐bearing sediments, changing their physicomechanical properties. In this study, a generalized phase equilibrium equation is presented for both frozen soils and hydrate‐bearing sediments by considering the capillary and osmotic pressures. The liquid water content is related to temperature depression, plotted as the soil freezing characteristic curve (SFCC) or the soil hydration characteristic curve (SHCC), by combining the generalized phase equilibrium equation and the soil‐water characteristic curve (SWCC). From the SFCC or the SHCC, the phase equilibrium surface can be calculated in the space of temperature, pressure, and liquid water content. The proposed generalized phase equilibrium equation and the model of SFCC and SHCC can help to estimate the physicomechanical properties that depend on the fraction of the liquid or solid phase in porous media. Finally, the SHCC is employed to analyze the dissociation of hydrate‐bearing sediments using various methods.

A mathematic model for the soil freezing characteristic curve: the roles of adsorption and capillarity

The relationship between the unfrozen water content in frozen soil and negative temperature is defined as the soil freezing characteristic curve (SFCC). The SFCC plays a crucial role in understanding the hydrothermal migration, frost heaving and constitutive relations of frozen soil. The mechanism of the SFCC is less understood, especially in the low-temperature range. Considering the adsorption and capillary action between soil particles and the ice interface, a new SFCC model for saturated frozen soil is proposed from the pore scale. The predicted results of the model show that the unfrozen water content gradually decreases with the increasing particle radius at the same temperature. The SFCC of monodisperse silica microspheres and quartz sand samples were tested based on nuclear magnetic resonance technology. The experimental results were compared with the mathematical model, which showed that the new SFCC model is in good agreement with the experimental results. The new model has a clear physical meaning and can provide a theoretical basis for understanding the phase change process in frozen soils, which is of great significance to the application of the proposed model.

Unified Soil Freezing Characteristic for Variably‐Saturated Saline Soils

AbstractFreezing and thawing of soil have a significant impact on the thermal‐hydrological processes in cold regions. Freezing point and unfrozen water content are key variables characterizing the freezing and thawing of soil. The testing results show that unfrozen water content is independent of initial water content in nonsaline silt, based on which a unified model for a soil freezing characteristic curve (SFCC) is presented. The SFCC describes the relationship between unfrozen water content and temperature for variably‐saturated saline soils. It is also demonstrated that the SFCC can describe the variation of soil freezing point with respect to water content and salt concentration. The SFCC model is validated by comparing the experimental data to the calculated result for unfrozen water content and freezing point in a variety of conditions. When the initial water content varies in saline soil, the SFCC changes with constant initial salt concentration, but it remains unchanged with constant gravimetric salt content. The SFCC model can be adopted in the simulation of thermal‐hydrological processes in arid and saline lands and coastal regions. Finally, an example of thermal‐hydrological processes was simulated with the new SFCC model to show the application of the presented model.

Influence of plasticity on unfrozen water content of frozen soils as determined by nuclear magnetic resonance

The mechanical properties of frozen soils are closely related to the unfrozen water content. It has been generally recognized that the unfrozen water content varies with plasticity of soils, while the quantitative relationship between the plastic index and the unfrozen water content is yet to be further examined. This paper takes soil samples with different plasticity as study objects, which are prepared from two typical soil materials, i.e., the Chinese ISO standard sand and bentonite. Nuclear magnetic resonance (NMR) is used to measure the unfrozen water content of soil samples under different temperatures. Test results show that there are three stages in the soil-freezing characteristic curve (SFCC), i.e., the super-cooling stage, the rapid-drop stage and the stable stage. With the increase of the plasticity index, the super-cooling stage is less significant, while the curve in the rapid-drop stage becomes gentler. In the stable stage, the unfrozen water content is barely affected by plasticity. A piecewise function consisting of a linear formula and a power formula is then proposed to describe the SFCC, where the formula parameters are functions of the plastic index. It is found that the unfrozen water content calculated by the proposed formula agrees with the measured results.