Soil Freezing Process Research Articles

Three phase heat and mass transfer model for unsaturated soil freezing process: Part 1 - model development

Abstract A three-phase model capable of predicting the heat transfer and moisture migration for soil freezing process was developed based on the Shen-Chen model and the mechanisms of heat and mass transfer in unsaturated soil freezing. The pre-melted film was taken into consideration, and the relationship between film thickness and soil temperature was used to calculate the liquid water fraction in both frozen zone and freezing fringe. The force that causes the moisture migration was calculated by the sum of several interactive forces and the suction in the pre-melted film was regarded as an interactive force between ice and water. Two kinds of resistance were regarded as a kind of body force related to the water films between the ice grains and soil grains, and a block force instead of gravity was introduced to keep balance with gravity before soil freezing. Lattice Boltzmann method was used in the simulation, and the input variables for the simulation included the size of computational domain, obstacle fraction, liquid water fraction, air fraction and soil porosity. The model is capable of predicting the water content distribution along soil depth and variations in water content and temperature during soil freezing process.

Three phase heat and mass transfer model for unsaturated soil freezing process: Part 2 - model validation

AbstractThis study aims to validate the three-phase heat and mass transfer model developed in the first part (Three phase heat and mass transfer model for unsaturated soil freezing process: Part 1 - model development). Experimental results from studies and experiments were used for the validation. The results showed that the correlation coefficients for the simulated and experimental water contents at different soil depths were between 0.83 and 0.92. The correlation coefficients for the simulated and experimental liquid water contents at different soil temperatures were between 0.95 and 0.99. With these high accuracies, the developed model can be well used to predict the water contents at different soil depths and temperatures.

Development of a frozen soil dielectric constant model and determination of dielectric constant variation during the soil freezing process

We used an interaction model of electromagnetic waves and mixed dielectric in unsaturated soil to develop an electromagnetic wave and mixed dielectric model of frozen soil. The new dielectric constant model was used to investigate the effects of temperature, mass water content (θm), and dry density on the relative dielectric constant (εr) of a yellow clay soil in Harbin, China. Based on frequency domain reflectometry (FDR) sensors under field conditions, the influencing factors were altered during measurements and the corresponding changes in soil εr were recorded for comparison and analysis. The influence of temperature on εr occurs mainly during the phase change period of liquid water in soil, while in the positive temperature range, εr varies only slightly with temperature. The εr increased with θm or dry density when the temperature was above 0 °C, but εr varied little with respect to θm or dry density after the soil froze. The accuracy of the proposed dielectric constant model in frozen soil was validated by comparing actual and predicted εr values.

Analytical solution for the soil freezing process induced by an infinite line sink

One-dimensional soil freezing process induced by an infinite line sink is investigated, a problem that is generally encountered during the application of the artificial ground freezing technique. The special feature of the freezing process of soil is that the amount of liquid water in the soil pores decreases gradually with the soil temperature decreasing, and thus latent heat is continuously released. After approximating the continuous phase change process of the soil with a multi-step phase change process of a polymorphous material, the original problem is transformed to a cylindrical multiphase Stefan problem. Using the similarity transformation technique, an analytical solution for the problem is developed, in which there are coefficients that need to be determined by a group of non-linear equations. A theoretical proof is presented showing that these coefficients can be appropriately determined by the non-linear equations. The computational results of the analytical solution are compared with those of the numerical solution, and the two solutions are in good agreement. The effects of the variation of different parameters on the movement of freezing front are studied. The results show that neglecting the existence of unfrozen water will underestimate the freezing front velocity. The relative error of this underestimation under different conditions is also investigated and discussed. In situations that the unfrozen water content is given as a discrete function of the temperature, the analytical solution can be applied directly, and an illustrative example is presented.

Estimation of the Land Surface Temperature over the Tibetan Plateau by Using Chinese FY-2C Geostationary Satellite Data.

During the process of land–atmosphere interaction, one of the essential parameters is the land surface temperature (LST). The LST has high temporal variability, especially in its diurnal cycle, which cannot be acquired by polar-orbiting satellites. Therefore, it is of great practical significance to retrieve LST data using geostationary satellites. According to the data of FengYun 2C (FY-2C) satellite and the measurements from the Enhanced Observing Period (CEOP) of the Asia–Australia Monsoon Project (CAMP) on the Tibetan Plateau (CAMP/Tibet), a regression approach was utilized in this research to optimize the split window algorithm (SWA). The thermal infrared data obtained by the Chinese geostationary satellite FY-2C over the Tibetan Plateau (TP) was used to estimate the hourly LST time series. To decrease the effects of cloud, the 10-day composite hourly LST data were obtained through the approach of maximal value composite (MVC). The derived LST was used to compare with the product of MODIS LST and was also validated by the field observation. The results show that the LST retrieved through the optimized SWA and in situ data has a better consistency (with correlation coefficient (R), mean absolute error (MAE), mean bias (MB), and root mean square error (RMSE) values of 0.987, 1.91 K, 0.83 K and 2.26 K, respectively) than that derived from Becker and Li’s SWA and MODIS LST product, which means that the modified SWA can be applied to achieve plateau-scale LST. The diurnal variation of the LST and the hourly time series of the LST over the Tibetan Plateau were also obtained. The diurnal range of LST was found to be clearly affected by the influence of the thawing and freezing process of soil and the summer monsoon evolution. The comparison between the seasonal and diurnal variations of LST at four typical underlying surfaces over the TP indicate that the variation of LST is closely connected with the underlying surface types as well. The diurnal variation of LST is the smallest at the water (5.12 K), second at the snow and ice (5.45 K), third at the grasslands (19.82 K) and largest at the barren or sparsely vegetated (22.83 K).

МАТЕМАТИЧЕСКАЯ МОДЕЛЬ ПРОМЕРЗАНИЯ ГРУНТА

Дано сравнение двух математических моделей процесса промерзания влажного грунта, насыщенного водным раствором соли. Для математической модели с постоянными коэффициентами в уравнении теплопроводности в двухфазной области показана возможность непрерывного перехода к нулю водонасыщенности на границе, разделяющей двухфазную зону от мерзлой.

Experimental study of the hydro-thermal characteristics and frost heave behavior of a saturated silt within a closed freezing system

Frost heave behavior during soil freezing process is an important issue of concern in cold regions, which is influenced by the hydro-thermal characteristics including the freezing point and water migration. The frost heave is caused by the freeze of water from different sources, i.e. pristine water, migrated water or both; however, it is difficult to identify the contributions of the different water sources to the frost heave, especially for a closed freezing system. Therefore, the calculation method to evaluate the frost heave induced by different water sources still need to be developed. Definitely, freezing experiments under controlled laboratory conditions can help to give a detailed description of the soil freezing process. Therefore, a large-scale one-directional freezing experiment within a closed system was carried out to investigate the hydro-thermal characteristics and frost heave behavior of a saturated silt. The research results showed the effect of the hydro-thermal behavior on the frost heave of the silt within a closed freezing system, and a calculation method was presented to evaluate the frost heaves from pristine water and migrated water, respectively.

Separate-ice frost heave model for one-dimensional soil freezing process

For one-dimensional soil freezing process, a separate-ice frost heave model is established, and the coupled process of heat transfer, fluid flow and stress development is considered in the model. First, a coupled heat–fluid–stress model describing the growth of a single ice lens is developed by extending the coupled heat–fluid model presented by Zhou and Zhou (Can Geotech J 49(6):686–693, 2012). Second, the mechanism for the formation of a new ice lens in the frozen fringe is studied, and we indicate that if the total vertical disjoining pressure at certain place exceeds the sum of the external pressure and the critical pressure, a new ice lens will emerge. By combining the growth model of a single ice lens and the criterion for the formation of a new ice lens, the separate-ice frost heave model is then established. The difference between the separate-ice model and the rigid-ice model is explained, and the relations for different mathematical models which describe the soil freezing process are also discussed. Numerical analysis of the separate-ice model is conducted using the finite volume method. The freezing tests for Devon silt under no external pressure and Xuzhou silty clay under a constant external pressure are applied to verify the computational results. The consistence between the calculation and the observation validates the separate-ice frost heave model.

Exact solution for a two-phase Stefan problem with power-type latent heat

A two-phase Stefan problem with latent heat a general power function of position is investigated. The background of the problem can be found in the soil-freezing process during the application of the artificial ground-freezing technique. After introducing the specific engineering condition, the governing equations of a two-phase Stefan problem are developed. An exact solution for the problem is established using the similarity transformation technique and the theory of the Kummer functions. It is proved that the coefficients in the solution can be appropriately determined if certain inequality is satisfied. Special cases of the solution are discussed, and several solutions reported in the literature are recovered. A similar two-phase Stefan problem involving first type of boundary condition is also introduced and solved. The coefficients in the solution can always be properly determined with no additional requirement. In the end, computational examples of the solution are presented and discussed. The exact solution provides a useful benchmark that can be used for verifying general numerical algorithms of Stefan problems, and it is also advantageous in the context of the inverse problem analysis.

Simulating cold-region hydrology in an intensively drained agricultural watershed in Manitoba, Canada, using the Cold Regions Hydrological Model

Abstract. Etrophication and flooding are perennial problems in agricultural watersheds of the northern Great Plains. A high proportion of annual runoff and nutrient transport occurs with snowmelt in this region. Extensive surface drainage modification, frozen soils, and frequent backwater or ice-damming impacts on flow measurement represent unique challenges to accurately modelling watershed-scale hydrological processes. A physically based, non-calibrated model created using the Cold Regions Hydrological Modelling platform (CRHM) was parameterized to simulate hydrological processes within a low slope, clay soil, and intensively surface drained agricultural watershed. These characteristics are common to most tributaries of the Red River of the north. Analysis of the observed water level records for the study watershed (La Salle River) indicates that ice cover and backwater issues at time of peak flow may impact the accuracy of both modelled and measured streamflows, highlighting the value of evaluating a non-calibrated model in this environment. Simulations best matched the streamflow record in years when peak and annual discharges were equal to or above the medians of 6.7 m3 s−1 and 1.25 × 107 m3, respectively, with an average Nash–Sutcliffe efficiency (NSE) of 0.76. Simulation of low-flow years (below the medians) was more challenging (average NSE < 0), with simulated discharge overestimated by 90 % on average. This result indicates the need for improved understanding of hydrological response in the watershed under drier conditions. Simulation during dry years was improved when infiltration was allowed prior to soil thaw, indicating the potential importance of preferential flow. Representation of in-channel dynamics and travel time under the flooded or ice-jam conditions should also receive attention in further model development efforts. Despite the complexities of the study watershed, simulations of flow for average to high-flow years and other components of the water balance were robust (snow water equivalency (SWE) and soil moisture). A sensitivity analysis of the flow routing model suggests a need for improved understanding of watershed functions under both dry and flooded conditions due to dynamic routing conditions, but overall CRHM is appropriate for simulation of hydrological processes in agricultural watersheds of the Red River. Falsifications of snow sublimation, snow transport, and infiltration to frozen soil processes in the validated base model indicate that these processes were very influential in stream discharge generation.

Frost-heaving pressure in geotechnical engineering materials during freezing process

Energy and resources including coal, oil, and gas are in demand all over the world. Because these resources near the earth’s surface have been exploited for many years, the extraction depth has increased. As mining shafts in the coal extraction process become deeper, especially in western China, an artificial freezing method is used and is concentrated in the fractured rock mass. The frost-heaving pressure (FHP) is directly related to the degree of damage of the fractured rock mass. This paper is focused on FHP during the freezing process, with emphasis on the frost-heaving phenomenon in engineering materials. A review of the frost phenomenon in the geotechnical engineering literature indicates that: (1) During the soil freezing process, the ice content that is influenced by unfrozen water and the freezing rate are the determining factors of FHP; (2) During the freezing process of rock and other porous media, the resulting cracks should be considered because the FHP may damage the crack structure; (3) The FHP in a joint rock mass is analyzed by the joint deformation in field and experimental tests and can be simulated by the equivalent expansion method including water migration and joint deformation.

Effect of hydro-thermal behavior on the frost heave of a saturated silty clay under different applied pressures

Abstract Civil engineering buildings are often damaged by frost heave of ground soils in cold regions. The hydro-thermal behavior is a key factor in determining frost heave of soils during freezing process. Moreover, the frost heave is also strongly affected by overburden pressure and external water source. Here, a series of one-directional freezing experiments with a water supply under different applied pressures were carried out to study the effect of hydro-thermal behavior on the frost heave of a saturated silty clay. Four different pressures were applied on the top of each soil sample, respectively, i.e. 50, 150, 300 and 500 kPa. The experimental results indicate that the frost heave of the supplied water is the main component of the total deformation for each soil sample with a water supply. However, the increased applied pressure can restrict water migration, and reduce frost heave during soil freezing process. Furthermore, for the saturated silty clay under different applied pressures, only when the advance rate of the freezing front drops to a critical value, the water intake begins. The start time of the water intake is also delayed with the increased applied pressure. Besides, the shut-off pressure of the saturated silty clay, at which no water flow into or out of the soil sample, is obtained based on the relationship between the critical advance rate of freezing front and the applied pressure.

Importance of vapor flow in unsaturated freezing soil: a numerical study

The role of vapor flow in unsaturated freezing soils is unclear, and usually ignored when analyzing water migration. Indeed, vapor flow is seldom considered in geotechnical design. On the other hand, frost heave damages were recently observed in a cold and arid region in China, where the groundwater table is about 20m deep, and cannot be explained using the classical frost heave theory which focuses on the coupled flow of heat and liquid water. This paper presents a new approach for modeling moisture and heat movement in unsaturated freezing soils, in which the phase change of evaporation, condensation of vapor flow are taken into account. The method enables numerically stable solutions with energy and mass conservation. The performance of the proposed model was evaluated by a series of laboratory freezing experiments, which involve a 60cm long soil column subjected to different initial conditions and boundary temperatures. It is shown that the proposed model is capable of effectively simulating the freezing process of an unsaturated soil. The vapor flux is shown to be significant, especially at the end stage where the freezing process is stabilized. Parametric analysis was carried out to clarify the role of vapor in moisture migration. The results show that vapor flow apparently contributes to ice formation and generally accounts for more than 10% of total water flux. The percentage of vapor flux in total flux (vapor flux ratio) positively relates to temperature gradient and freezing depth, but negatively relates to initial water content. Relations between vapor flux ratio and hydraulic parameters are less clear.

Soil freezing–thawing characteristics and snowmelt infiltration in Cryalfs of Alberta, Canada

Soil freeze–thaw processes and snowmelt infiltration significantly influence the hydrological cycle and ecosystem productivity in cold, semi-arid areas. In this study, 5years (2008–2013) of soil moisture, temperature (0–100-cm depth) and meteorological data monitored at the Breton Plots, University of Alberta was used to understand the soil freezing–thawing phenomena and snowmelt infiltration under natural boundary conditions. The field data demonstrated that the timing of snowpack accumulation and soil wetness prior to freezing govern the winter soil thermal regime. Deep frost (≥50cm) was found in years of late snow accumulation and dry fall soil conditions while shallow frost occurred in years of early snow accumulation and wet fall soil conditions. In addition, air-filled porosity of the top 10cm and the soil water storage of the top 30cm measured in the fall are the main factors governing soil water storage change following spring snowmelt. Furthermore, soil freezing and thawing curves (SFTCs, expressed in the form of TDR-measured relative permittivity/water content vs temperature) were introduced to facilitate the understanding of the freeze–thaw processes under field conditions. The field measured SFTC is different from soil freezing characteristic (SFC, TDR-measured relative permittivity/water content vs temperature) measured in lab conditions (e.g., constant total soil water content and near-thermal equilibrium) because of changing total soil water content under field conditions from snowmelt infiltration or frost-induced water redistribution and transient temperature conditions. The mechanisms for SFTC/SFC are explained and the differences between lab and the field SFTC/SFC are compared and discussed. This study and the use of SFTC could improve our understanding of the frozen soil processes and snowmelt infiltration in field conditions.

Exact solution for Stefan problem with general power-type latent heat using Kummer function

A one-phase Stefan problem in which the latent heat is a power function of position with a positive exponent is investigated. The Stefan problem involves a nonlinear boundary condition of the second type. The physical rational of the problem can be found in the context of both the shoreline movement and the soil freezing process. An exact solution is constructed using the similarity transformation technique and the theory of the Kummer functions. The existence and the uniqueness of the solution are proved. Computational examples of the solution provide useful data for verifying general numerical algorithms of Stefan problems. In the end, the solution for a similar Stefan problem involving a nonlinear boundary condition of the first type is also presented.

Coupled cellular automata for frozen soil processes

Abstract. Heat and water movement in variably saturated freezing soils is a strongly coupled phenomenon. The coupling is a result of the effects of sub-zero temperature on soil water potential, heat carried by water moving under pressure gradients, and dependency of soil thermal and hydraulic properties on soil water content. This study presents a one-dimensional cellular automata (direct solving) model to simulate coupled heat and water transport with phase change in variably saturated soils. The model is based on first-order mass and energy conservation principles. The water and energy fluxes are calculated using first-order empirical forms of Buckingham–Darcy's law and Fourier's heat law respectively. The liquid–ice phase change is handled by integrating along an experimentally determined soil freezing curve (unfrozen water content and temperature relationship) obviating the use of the apparent heat capacity term. This approach highlights a further subtle form of coupling in which heat carried by water perturbs the water content–temperature equilibrium and exchange energy flux is used to maintain the equilibrium rather than affect the temperature change. The model is successfully tested against analytical and experimental solutions. Setting up a highly non-linear coupled soil physics problem with a physically based approach provides intuitive insights into an otherwise complex phenomenon.

Atmosphere-Cryosphere Coupled Model for Regional Climate Applications

There have been significant advances in our understanding of the climate system, but two major problems still exist in modeling atmospheric response during cold seasons: (a) lack of detailed physical description of snow and frozen soil in the land-surface schemes and (b) insufficient understanding of regional climate response from the cryosphere. A multilayer snow land-surface model based on the conservations of heat and water substance inside the soil and snow is coupled to an atmospheric RCM, to investigate the effect of snow, snowmelt, and soil frost on the atmosphere during cold seasons. The coupled RCM shows much improvement in moisture and temperature simulation for March-April of 1997 compared to simple parameterizations used in GCMs. The importance of such processes in RCM simulation is more pronounced in mid-to-high latitudes during the transition period (winter–spring) affected by changes in surface energy and the hydrological cycle. The effect of including cryosphere physics through snow-albedo feedback mechanism changes the meridional temperature gradients and in turn changes the location of weather systems passing over the region. The implications from our study suggest that, to reduce the uncertainties and better assess the impacts of climate change, RCM simulations should include the detailed snow and frozen soil processes.

Research on Moisture Migration Experiment of Seasonally Frozen Zone Saline Soil

Saline soil is widely distributed in Jilin seasonally frozen zone. Many engineering hazards are associated closely related to moisture migration with freezing-thawing cycles. Soil salinization in the region is mainly due to migration of soil moisture and salinity caused by the temperature gradient with soil freezing process in this area. Adopt self-developed experiment instrument for measuring the freezing experiments of saline soil in Sanzhigou. Constract and analyze the transformation of moisture content and soluble salt before and after the freeze, and quantify the moisture and salinity substance migration in the freezing process.

A distributed scheme developed for eco-hydrological modeling in the upper Heihe River

Modeling the hydrological processes at catchment scale requires a flexible distributed scheme to represent the catchment topography, river network and vegetation pattern. This study has developed a distributed scheme for eco-hydrological simulation in the upper Heihe River. Based on a 1 km × 1 km grid system, the study catchment is divided into 461 sub-catchments, whose main streams form the streamflow pathway. Furthermore, a 1 km grid is represented by a number of topographically similar “hillslope-valley” systems, and the hillslope is the basic unit of the eco-hydrological simulation. This model is tested with a simplified hydrological simulation focusing on soil-water dynamics and streamflow routing. Based on a 12-year simulation from 2001 to 2012, it is found that variability in hydrological behavior is closely associated with climatic and landscape conditions especially vegetation types. The subsurface and groundwater flows dominate the total river runoff. This implies that the soil freezing and thawing process would significantly influence the runoff generation in the upper Heihe basin. Furthermore, the runoff components and water balance characteristics vary among different vegetation types, showing the importance of coupling the vegetation pattern into catchment hydrological simulation. This paper also discusses the model improvement to be done in future study.

A moving-pump model for water migration in unsaturated freezing soil

This paper presents a new approach for simulating the water migration in freezing soils, in which the pore water migration and heat transfer are characterized using an imaginary pump attached with a small imaginary reservoir. The pump moves with the freezing front as temperature decreases, sucks the liquid water from the unfrozen zone and then stores it in the frozen zone. The reservoir is used to gather the sucked water and store it in the form of pore ice through phase change. Explicit governing equations are developed for describing the water migration, crystallization and/or heat transfer in the soil, the pump and the reservoir. The proposed model is numerically implemented into a commercial code. Compared to the previous approaches used to simulate the soil freezing processes, application of the new approach avoids remeshing and recalculating the moving boundaries, and this feature can drastically simplify the numerical implementation of the theoretical model. The new approach is used to analyze the one-dimensional freezing process in soils. The simulated results are compared with the experimental data available in the literature and the simulations based on other approaches, showing that the new approach is capable of effectively simulating the freezing process of soils.