change of unfrozen water content in pores of rock during freeze-thaw process is one of the key factors affecting its mechanical properties. In this paper, the sandstone is taken as the research object, and the pore water content of rock during freeze-thaw process (20, 0, -2, -4, -6, -10, -15, -10, -6, -4, -2, 0, 20 degrees C) is monitored by low-field nuclear magnetic resonance system (NMR), and the evolution law of unfrozen water content with temperature is analyzed. The influence of the evolution of unfrozen water content on the mechanical properties of rock during freeze-thaw process is also discussed. The research findings show that the pore water in rocks during the freezing-thawing process is significantly influenced by temperature, passing through five stages: supercooling, rapid freezing, slow freezing, slow melting, and accelerated melting. A distinct hysteresis phenomenon is observed in the rock during thawing. At identical temperatures, the unfrozen water content during freezing is notably higher than during thawing. Consequently, the peak intensity and elastic modulus during thawing are significantly greater than during freezing. The relationship between uniaxial compressive strength, rock elastic modulus, and unfrozen water content in freeze-thaw process can be expressed by exponential function. At the beginning of freezing, the change of rock mechanical parameters is mainly affected by the increase of pore ice content and the cementation effect of pore ice on rock particles. With the further decrease of temperature, the thickness of adsorbed water film decreases, and the adsorption capacity increases, so that the integrity between pore ice and rock particles is enhanced, and rock mechanical parameters further change.

In the context of global climate change, changes in unfrozen water content in permafrost significantly impact regional terrestrial plant ecology and engineering stability. Through Differential Scanning Calorimetry (DSC) experiments, this study analyzed the thermal characteristic indicators, including supercooling temperature, freezing temperature, thawing temperature, critical temperature, and phase-transition temperature ranges, for silt loam with varying starting moisture levels throughout the freezing and thawing cycles. With varying starting moisture levels throughout the freezing and thawing cycles, a model describing the connection between soil temperature and variations in unfrozen water content during freeze-thaw cycles was established and corroborated with experimental data. The findings suggest that while freezing, the freezing and supercooling temperatures of unsaturated clay increased with the soil's starting moisture level, while those of saturated clay were less affected by water content. During thawing, the initial thawing temperature of clay was generally below 0 degrees C, and the thawing temperature exhibited a power function relationship with total water content. Model analysis revealed hysteresis effects in the unfrozen water content curve during freeze-thaw cycles. Both the phase-transition temperature range and model parameters were sensitive to temperature changes, indicating that the processes of permafrost freezing and thawing are mainly controlled by ambient temperature changes. The study highlights the stability of the difference between freezing temperature and supercooling temperature in clay during freezing. These results offer a conceptual framework for comprehending the thawing mechanisms of permafrost and analyzing the variations in mechanical properties and terrestrial ecosystems caused by temperature-dependent moisture changes in permafrost.

Soluble salts significantly influence the freezing characteristic parameters of frozen soil. Previous studies have either insufficiently addressed the effect of sodium sulfate on matric suction or not comprehensively revealed the mechanism by which temperature affects matric suction at freezing temperature. In this study, the moisture and suction sensors were used to quantify the freezing temperature (FT), unfrozen water content (UWC), and matric suction (MS) of Ili loess with varying soluble salt contents. The impact of soluble salt content on three freezing characteristic parameters were investigated with the underlying mechanisms revealed. The results indicated that there was an initial decrease in both freezing and supercooling temperatures as the soluble salt content increased. Beyond a soluble salt content of 14 g/kg, an increase in both the freezing and supercooling temperatures was observed. Specimens with different soluble salt contents exhibited distinct UWC, which could be categorized into three stages based on temperature. A crystal precipitation stage was observed beyond the soluble salt content of 14 g/kg. Moreover, the proposed fitting model for UWC by incorporating the soluble salt content into the Gardner model demonstrated high accuracy. The MS can also be divided into three stages with temperature. Notably, specimens with soluble salt contents of 20 and 26 g/kg exhibited nonlinear increases in MS at temperatures of 5 degrees C and 10 degrees C due to crystal precipitation. Furthermore, theoretical calculations indicated the complete precipitation of sodium sulfate during the positive temperature stage.

Permafrost in marine sediments exhibits a lower freezing point and significant unfrozen water content. This paper investigates the role of the soil freezing characteristic curve (SFCC) in permafrost degradation. Three SFCCs, representing thawing-freezing characteristics of soils with varying clay content and salinity, were established based on experiments and existing data. These SFCCs were then applied in numerical analyses to simulate permafrost thawing under various warming scenarios, using measured ground temperatures and permafrost profiles for a site at Longyearbyen in Svalbard (Norway). It is shown that the ground temperature in non-saline permafrost soil increases more rapidly than saline permafrost, due to a greater downward net heat flux to the permafrost in the former case. Conversely, the thawing rate is more pronounced for saline permafrost soil, attributed to its lower freezing point and latent heat consumption. A more nonlinear ice-melting process is observed for permafrost soil with a lower salinity. The temperature rise follows three stages: a constant-rising, a damp-rising, and an accelerated-rising rates. The duration of the damp-rising rate becomes shorter for saline permafrost under a great warming condition. The study underscores the high significance of the soil-freezing characteristic curve for accurate estimations of permafrost degradation.

Permafrost carbon could produce a positive climate feedback. Until now, the ecosystem carbon budgets in the permafrost regions remain uncertain. Moreover, the frequently used models have some limitations especially regarding to the freeze-thaw process. Herein, we improved the IBIS model by incorporating an unfrozen water scheme and by specifying the parameters to estimate the present and future carbon budget of different land cover types (desert steppe, steppe, meadow, and wet meadow) in the permafrost regions. Incorporating an unfrozen water scheme reduced the mean errors in the soil temperature and soil water content by 25.2%, and the specifying leaf area parameters reduced the errors in the net primary productivity (NPP) by 79.9%. Further, the simulation results showed that steppes are carbon sources (39.16 gC/m(2)/a) and the meadows are carbon sinks (-63.42 gC/m(2)/a ). Under the climate warming scenarios of RCP 2.6, RCP 6.0, and RCP 8.5, the desert steppe and alpine steppe would assimilated more carbon, while the meadow and wet meadow were projected to shift from carbon sinks to carbon sources in 2071-2100, implying that the land cover type plays an important role in simulating the source/sink effects of permafrost ecosystem carbon in the IBIS model. The results highlight the importance of unfrozen water to the soil hydrothermal regime and specific leaf area for the growth of alpine vegetation, and present new insights on the difference of the responses of various permafrost ecosystems to climate warming.

The investigation into the complex mechanical properties of frozen calcareous clay under multi-factor interaction holds significant importance for the reliability and durability of engineering in cold regions. This study investigates the strength properties of frozen calcareous clay under different interaction levels by designing a four-factor, four-level orthogonal test that incorporates temperature, confining pressure, dry density, and water content. The study aimed to assess the sensitivity of each factor to failure stress, and establish an intrinsic model based on the Duncan-Chang model considering temperature, confining pressure, and water content. The results indicated that the stress-strain curves exhibit strain-hardening characteristics across various interaction levels. These curves can be divided into elastic and elastic-plastic phases, with the slope of the elastic phase and the stress value at the inflection point increasing with decreasing temperature and increasing confining pressure. When the confining pressure is maintained constant, the failure stress is negatively correlated with temperature. When the temperature is maintained constant, the failure stress is positively correlated with confining pressure. Sensitivity analysis shows that the influence of each factor on failure stress is as follows: temperature > confining pressure > dry density > water content. Additionally, the influence of temperature and confining pressure on failure stress is markedly greater than that of water content and dry density. The evolution of unfrozen water content follows three stages: sharp reduction, rapid reduction, and slow reduction. Verification against experimental data confirmed that the modified constitutive model effectively reflects the stress-strain relationship of frozen calcareous clay under the interaction of multiple factors.

Unfrozen water content (UWC) plays a critical role in determining the thermal, hydraulic, and mechanical properties of frozen soils. Existing empirical, semi-empirical, and theoretical models for UWC estimation have limitations in terms of accuracy as well as generalizability. To address these challenges, the present study explored the application of six machine learning techniques to predict UWC in frozen soils: Random Forest (RF), eXtreme Gradient Boosting (XGBoost), Light Gradient Boosting Machine (LightGBM), K-Nearest Neighbors (KNN), Support Vector Regression (SVR), and Backpropagation Neural Network (BPNN). Considering the UWC hysteresis phenomenon between the freezing and thawing processes, experimental UWC data collected from the literature were separated into two sub-datasets: freezing branch dataset (FBD) and thawing branch dataset (TBD). Based on that, a comprehensive framework integrating Bayesian optimization and 10-fold crossvalidation was established to optimize the six models' hyperparameters and to evaluate their performance. The results highlighted significant variations in the predictive capability among the six machine learning models, with ensemble methods (i.e., RF, XGBoost, LightGBM) generally demonstrating superior accuracy. Feature importance analysis, robustness checks, and uncertainty quantification further elucidated the strengths and limitations of each model. The present study provides profound insights into the selection and application of machine learning models for accurately modeling the properties of frozen soils for cold regions science and engineering.

The unfrozen water content is crucial to soil's physical and mechanical properties. Soils on the Qinghai-Tibet Plateau are frequently subjected to freeze-thaw (F-T) cycles. The quantitative relationship between F-T effects and the unfrozen water content of soils requires further investigation. This study employs a nuclear magnetic resonance (NMR) scanner with a temperature-control module to measure the unfrozen water content of silty clay during multiple F-T cycles. The soil freezing characteristic curves (SFCC) of silty clay are derived from the T2 (transverse relaxation time) distribution curves based on NMR measurements. Two distinct T2 cutoff values are used to classify three types of water in soils: bound water, capillary water, and bulk water. The impact of F-T cycles on the evolution of unfrozen water content as temperatures decrease has been analyzed. The testing results indicate that the SFCC of silty clay can be segmented into three stages: super-cooling, fast-declining, and stable. As the number of F-T cycles increases, capillary water content decreases while bulk water content increases during the super-cooling stage. The damage coefficient, derived from pore volume measurements, increases sharply during the first four F-T cycles before stabilizing gradually. Additionally, there is a negative linear correlation between the damage coefficient and the initial capillary water content, and a positive linear correlation with the initial bulk water content. This study offers valuable insights for the quantitative analysis of unfrozen water content in seasonally frozen regions and serves as an essential guide for geotechnical construction projects in cold areas.

The warming climate in high-latitude permafrost regions is leading to permafrost degradation. Estimating seismic wave velocities in permafrost could help predict the geomechanical properties of permafrost and provide information to plan and design resilient civil infrastructure in cold regions. This paper evaluates the performance of seven models when predicting the seismic wave velocities of permafrost statistically; these models are the time-average, Zimmerman and King, Minshull et al., weighted equation, three-phase, Biot-Gassmann theory modified by Lee (BGTL), and Dou et al. models. The data used in the evaluation are from published laboratory and in situ data, which includes 369 data points for joint P and S wave velocities from nine publications and 943 unfrozen water content data points from 12 publications. The unfrozen water content that is used in these models is determined from a modified Dall'Amico's model that is proposed, which is evaluated against six existing unfrozen water content models based on soil temperature. This paper finds that saturated nonsaline permafrost generally shares similar linear trends between the P and S wave velocities, regardless of soil type, porosity, grain size, and temperature. Fitting all existing data, an empirical linear relationship is derived between the P and S wave velocities. Among the seven models evaluated, the Minshull et al. and BGTL models are the most accurate when predicting the seismic velocities of permafrost. Unfrozen water content and seismic wave velocity models are valuable tools for quantitatively predicting permafrost dynamics and degradation, with practical applications in various engineering areas with permafrost environments. As permafrost thaws due to rising temperatures, these models could be used to guide the quantitative interpretation of geophysical changes in subsurface conditions, assess the potential for ground instability, and predict future permafrost degradation. Unfrozen water content models are used to predict the percentage of unfrozen water within permafrost, which links the changes with permafrost temperature. Unfrozen water content models of permafrost are essential when assessing permafrost thaw, thermal performance, heat transfer processes in permafrost, and the effect of civil infrastructure on permafrost (Chen et al.,). The seismic wave velocity models could help engineers assess the subsurface conditions in permafrost areas; this assessment is crucial for environmental and seismic monitoring, land use planning, infrastructure design and construction, and natural resources exploration.

The relationship between unfrozen water content and temperature, called as soil freezing characteristic curve (SFCC), is of importance for hydrologic, engineering, environmental issues related to frozen soil. The SFCC of saline soil is essentially a result of phase equilibrium of pore solution, which is similar but not identical to that of bulk solution. However, there is still a vacancy of study on the phase equilibrium of pore solution in frozen soil. In this study, image transformation was used to establish the relationship of phase equilibrium between bulk solution and pore solution, with four introduced parameters. Then, the new model of SFCC for saline soil was proposed based on the equivalent state of bulk solution with Pitzer model and SFCC of nonsaline soil. The model was validated by the experimental data from published articles and showed good performance in calculating SFCC of saline soils regardless of soil type, phase transition path, and soil initial water-salt condition, and some advantages when compared to other three models. All the four introduced parameters have clear physical meanings and their relationships with soil type and initial salt concentration were discussed. Finally, the evolution of phase diagram from bulk solution to pore solution at icing stage was figured out. Further studies are needed for their relationship at salt crystallization stage. Shifting the research perspective from unfrozen water content to pore solution, this study gives a new approach to research of freezing characteristic of saline soil and could promote hydrological and engineering research in cold regions. The freezing temperature of pure water declines in soil like in solution. There is a reason to believe that the chemical equilibrium of pore solution differs from that of bulk solution. The chemical equilibrium of pore solution, to a certain extent, determines the amount of unfrozen water content, which affects the thermal, hydraulic and mechanical properties of soil. Two phase transition stages have been found in some saline soils with high salt content, which does not appear in nonsaline soils. The relationship of chemical equilibrium between pore solution and bulk solution is the vital interface to apply mature results of chemical characteristics of bulk solution into research of freezing characteristic of saline soils. However, it is still ambiguous for most researchers ignore the soil matrix effect on chemical equilibrium of pore solution. This paper used the transformation of phase diagram from pore solution to bulk solution, sounds like coordinate conversion, to establish their relationship and proposed an intuitive model to calculate the unfrozen water content of saline soil with equivalent state of bulk solution. The performance of the proposed model is good for various saline soils. This study provides an interesting perspective for frozen soil research. A soil freezing characteristic curve (SFCC) model for saline soil is proposed with the equivalent bulk solution and SFCC of nonsaline soil Good performance of the new model at predicting SFCC of saline soil both in ice-eutectic and crystallization-eutectic paths The evolution of phase diagram at icing stage from bulk solution to pore solution is discovered with the proposed model