A dynamic soil freezing characteristic curve model for frozen soil

The soil freezing characteristic curve(SFCC)plays a fundamental role in comprehending thermohydraulic behavior and numerical simulation of frozen soil.This study proposes a dynamic model to uniformly express SFCCs amidst varying total water contents throughout the freezing-thawing process.Firstly,a general model is proposed,wherein the unfrozen water content at arbitrary temperature is determined as the lesser of the current total water content and the reference value derived from saturated SFCC.The dynamic performance of this model is verified through test data.Subsequently,in accordance with electric double layer(EDL)theory,the theoretical residual and minimum temperatures in SFCC are calculated to be-14.5℃to-20℃for clay particles and-260℃,respectively.To ensure that the SFCC curve ends at minimum temperature,a correction function is introduced into the general model.Furthermore,a simplified dynamic model is proposed and investigated,necessitating only three parameters inherited from the general model.Additionally,both general and simplified models are evaluated based on a test database and proven to fit the test data exactly across the entire temperature range.Typical recommended parameter values for various types of soils are summarized.Overall,this study provides not only a theoretical basis for most empirical equations but also proposes a new and more general equation to describe the SFCC.

Experimental and numerical interpretation on composite foundation consisting of soil-cement column within warm and ice-rich frozen soil

Affected by climate warming and anthropogenic disturbances, the thermo-mechanical stability of warm and ice-rich frozen ground along the Qinghai-Tibet engineering corridor(QTEC) is continuously decreased, which may delay the construction of major projects in the future. In this study, based on chemical stabilization of warm and icerich frozen ground, the soil-cement column(SCC) for ground improvement was recommended to reinforce the foundations in warm and ice-rich permafrost regions. To explore the validity of countermeasures mentioned above, both the original foundation and the composite foundation consisting of SCC with soil temperature of -1.0℃ were prepared in the laboratory, and then the plate loading tests were carried out. The laboratory investigations indicated that the bearing capacity of composite foundation consisting of SCC was higher than that of original foundation, and the total deformation of original foundation was greater than that of composite foundation, meaning that overall stability of foundation with warm and ice-rich frozen soil can be improved by SCC installation. Meanwhile, a numerical model considering the interface interaction between frozen soil and SCC was established for interpretating the bearing mechanism of composite foundation. The numerical investigations revealed that the SCC within composite foundation was responsible for the more applied load, and the applied load can be delivered to deeper zone in depth due to the SCC installation, which was favorable for improving the bearing characteristic of composite foundation. The investigations provide the valuable guideline for the choice of engineering supporting techniques to major projects within the QTEC.

Mechanical behaviors of warm and ice-rich frozen soil stabilized with sulphoaluminate cement

The warm and ice-rich frozen soil is characterized by high unfrozen water content, low shear strength and large compressibility, which is unreliable to meet the stability requirements of engineering infrastructures and foundations in permafrost regions. In this study, a novel approach for stabilizing the warm and ice-rich frozen soil with sulphoaluminate cement was proposed based on chemical stabilization. The mechanical behaviors of the stabilized soil, such as strength and stress-strain relationship, were investigated through a series of triaxial compression tests conducted at -1.0℃, and the mechanism of strength variations of the stabilized soil was also explained based on scanning electron microscope test. The investigations indicated that the strength of stabilized soil to resist failure has been improved, and the linear Mohr-Coulomb criteria can accurately reflect the shear strength of stabilized soil under various applied confining pressure. The increase in both curing age and cement mixing ratio were favorable to the growth of cohesion and internal friction angle. More importantly, the strength improvement mechanism of the stabilized soil is attributed to the formation of structural skeleton and the generation of cementitious hydration products within itself. Therefore, the investigations conducted in this study provide valuable references for chemical stabilization of warm and ice-rich frozen ground, thereby providing a basis for in-situ ground improvement for reinforcing warm and ice-rich permafrost foundations by soil-cement column installation.

A rate-dependent constitutive model for saturated frozen soil considering local breakage mechanism

A rate-dependent constitutive model for saturated frozen soil is vital in frozen soil mechanics,especially when simultaneously describing the nonlinearity,dilatancy and strain-softening characteristics.The distribution of the non-uniform strain rate of saturated frozen soil at the meso-scale due to the local icecementation breakage is described by a newly binary-medium-based homogenization equation.Based on the field-equation-based approach of the meso-mechanics theory,the interaction expression of the strain rate at macro-and meso-scale is derived,which can give the strain rate concentration tensor at different crushed degrees.With the thermodynamics and empirical assumption,a breakage ratio in the rate-dependent form is determined.This overcomes the limitations of the existing binary-medium-based models that are difficult to simulate rate-dependent mechanical response.Based on these assumptions,a newly binary-medium-based rate-dependent model is proposed considering both the ice bond breakage and material composition characteristics of saturated frozen soil.The proposed constitutive model has been validated by the test results on frozen soils with different temperatures and strain rates.

Stabilized effects of L-S cement-mixed batter pile composite foundation for existed warm frozen soil subgrade

In permafrost regions with warm frozen soil,subgrade thaw-collapse phenomenon commonly occurs,facing thaw collapse problems of the existed frozen soil subgrade,thus it is difficult to use traditional methods such as active cooling and passive protection technology to stabilize the existed warm frozen soil subgrade.This study derives a novel stabilizer method,a long-short(L-S)cement-mixed batter pile composite foundation to stabilize the existed warm frozen soil subgrade.To solve the thawcollapse problems in warm frozen soil subgrade,high water content and large compressibility characteristics were compared between soft soil and warm frozen soils.Theoretical analysis of heat conduction and numerical simulation of finite element model were used to study the freeze–thaw process and evaluate the stabilized effects of the L-S cement-mixed batter piles on the warm frozen soil foundation of the Qinghai-Tibet Highway.Furthermore,the thaw process and mechanical properties of foundation and piles were analyzed by introducing the hydration heat factor in the thermodynamic control equation.The results indicate that the thawing displacement of the existed warm frozen soil subgrade was reduced owing to the“support”and“grasp”effects of the L-S cement-mixed batter piles on the surrounding soil.The composite ground formed by strengthening the warm frozen ground with batter piles could considerably improve the bearing capacity of the existed warm frozen ground,effectively restrain the deformation of the upper embankment,and improve the strength of the ground.The analysis can provide method for the construction design of cement mixing batter pile foundation in cold regions.

Microstructure and strength features of warm and ice-rich frozen soil treated with high-performance cements

Warm and ice-rich frozen soil(WIRFS) exhibits lower shear strength due to the weak binding forces between soil particles and ice crystals. To enhance the strength of WIRFS, frozen soil was treated separately with Portland, Phosphate, Sulphoaluminate, Portland-Phosphate and PortlandSulphoaluminate cements. After the samples were cured under -1.0°C for 7 days, the microscopic pore distribution characteristics and the macro-mechanical properties of WIRFS were investigated using mercury intrusion porosimetry(MIP), scanning electron microscopy(SEM) and unconfined compressive strength(UCS) tests. To quantitatively analyze the laws of pore-size transformation and the variation of Hausdorff volumetric fractal dimensions for pre-and post-treated WIRFS, the CURVEEXTRACT and Image-Pro Plus(IPP) image analysis system has been developed for analysing SEM images of the soil samples. Statistics of the pore-area dimension and pore-volume dimension were calculated. The results reveal that the cement-based treatment of WIRFS can improve the cementation fill of soil pores and the bond forces between soil particles. There is an evident correlation between the microstructure characteristics and the mechanical properties of the treated WIRFS. As the fractal dimensions of pore-area decrease, the unconfined compressive strength of cement-treated WIRFS increases significantly. In contrast, as the fractal dimensions of pore-volume increases, the unconfined compressive strength decreases remarkably.

Dynamic behavior of frozen soil under uniaxial strain and stress conditions

The split Hopkinson pressure bar （SHPB） method is used to investigate the dynamic behavior of the artificial frozen soil under the nearly uniaxial strain and uniaxial stress conditions. The tests are conducted at the temperatures of -3 ℃, -8 ℃, -13℃, -17℃, -23℃, and -28℃ and with the strain rates from 900 s^-1 to 1500 s^-1. The nearly uniaxial stress-strain curves exhibit an elastic-plastic behavior, whereas the uniaxial stress-strain curves show a brittle behavior. The compressive strength of the frozen soil exhibits the positive strain rate and negative temperature sensitivity, and the final strain of the frozen soil shows the positive strain under the nearly uniaxial strain is greater rate sensitivity. The strength of the frozen soil than that under the uniaxial stress. After the negative confinement tests, the specimens are compressed, and the visible cracks are not observed. However, the specimens are catastrophically damaged after the uniaxial SHPB tests. A phenomenological model with the thermal sensitivity is established to describe the dynamic behavior of the confined frozen soil.

Development and Validation of a Simple Frozen SoilParameterization Scheme Used for Climate Model

A simple frozen soil parameterization scheme is developed based on NCAR LSM and the effects of re-vised scheme are investigated using Former Soviet Union (FSU) 6 stations measurement data. In the revised model, soil ice content and the energy change in phase change process is considered; the original soil thermal conductivity scheme is replaced by Johanson scheme and the soil thermal and hydraulic properties is modi-fied depending on soil ice content. The comparison of original model with revised model results indicates that the frozen soil scheme can reasonably simulate the energy budget in soil column and the variation of thermal and hydraulic properties as the soil ice content changes. Soil moisture in spring is decreased because of the reduction of infiltration and increment of runoff. Consequently, the partition of heat flux and surface temperature changes correspondingly.

Anomaly feature of seasonal frozen soil variationson the Qinghai-Tibet Plateau

The seasonal frozen soil on the Qinghai-Tibet Plateau has strong response to climate change, and its freezing-thawing process also affects East Asia climate. In this paper, the freezing soil maximum depth of 46 stations covering 1961–1999 on the plateau is analyzed by rotated experience orthogonal function (REOF). The results show that there are four main frozen anomaly regions on the plateau, i.e., the northeastern, southeastern and southern parts of the plateau and Qaidam Basin. The freezing soil depths of the annual anomaly regions in the above representative stations show that there are different changing trends. The main trend, except for the Qaidam Basin, has been decreasing since the 1980s, a sign of the climate warming. Compared with the 1980s, on the average, the maximum soil depth decreased by about 0.02 m, 0.05 m and 0.14 m in the northeastern, southeastern and southern parts of the plateau, but increased by about 0.57 m in the Qaidam Basin during the 1990s. It means there are different responses to climate system in the above areas. The spectrum analysis reveals different change cycles: in higher frequency there is an about 2-year long cycle in Qaidam Basin and southern part of the plateau in the four representative areas whereas in lower frequency there is an about 14-year long cycle in all the four representative areas due to the combined influence of different soil textures and solutes in four areas.

The Numerical Scheme Development of a Simplified Frozen Soil Model

In almost all frozen soil models used currently, three variables of temperature, ice content and moisture content are used as prognostic variables and the rate term, accounting for the contribution of the phase change between water and ice, is shown explicitly in both the energy and mass balance equations. The models must be solved by a numerical method with an iterative process, and the rate term of the phase change needs to be pre-estimated at the beginning in each iteration step. Since the rate term of the phase change in the energy equation is closely related to the release or absorption of the great amount of fusion heat, a small error in the rate term estimation will introduce greater error in the energy balance, which will amplify the error in the temperature calculation and in turn, cause problems for the numerical solution convergence. In this work, in order to first reduce the trouble, the methodology of the variable transformation is applied to a simplified frozen soil model used currently, which leads to new frozen soil scheme used in this work. In the new scheme, the enthalpy and the total water equivalent are used as predictive variables in the governing equations to replace temperature, volumetric soil moisture and ice content used in many current models. By doing so, the rate terms of the phase change are not shown explicitly in both the mass and energy equations and its pre-estimation is avoided. Secondly, in order to solve this new scheme more functionally, the development of the numerical scheme to the new scheme is described and a numerical algorithm appropriate to the numerical scheme is developed. In order to evaluate the new scheme of the frozen soil model and its relevant algorithm, a series of model evaluations are conducted by comparing numerical results from the new model scheme with three observational data sets. The comparisons show that the results from the model are in good agreement with these data sets in both the change trend of variables and their magnitude values, and the new scheme, together with the algorithm, is more efficient and saves more computer time.

A pseudo-coupled numerical approach for stability analysis of frozen soil slopes based on finite element limit analysis method

To simplify the stability analysis of frozen soil slope, a pseudo-coupled numerical approach is developed. In this approach, the coupled heat transfer and water flow in frozen soils are simulated first, and based on the computed thermal-hydro field, the stability of frozen soil slope is evaluated. Although the shear strength for frozen soil is very complicated and is usually represented by a nonlinear MC failure criterion, a simple linear MC yield criterion is utilized. In this method, the internal friction angle is expressed as a function of volumetric ice content and the cohesion is fitted as a simple bilinear expression of Tand volumetric water content. To assess slope stability, the limit analysis is employed in conjunction with the recently developed a-section search algorithm. A frozen soil slope example is used to examine the proposed pseudo-coupled numerical approach, and numerical studies validate its effectiveness. Based on numerical results, it is seen that slope stability may be remarkably influenced by warming air （or grotmd surface） temperature. With increasing ground surface temperature, slope stability indicated by FOS may reduce to 1.0, implying that wanning air temperature could be a trigger of frozen soil slope failure.

Average temperature calculation for straight single-row-piped frozen soil wall

The average temperature of frozen soil wall is an essential parameter in the process of design, construction, and safety manage- ment of artificial ground freezing engineering. It is the basis of calculating frozen soil＇s mechanical parameters, fiarther prediction of bearing capacity and, ultimately, safety evaluation of the frozen soil wall. Regarding the average temperature of sin- gle-row-piped frozen soil wall, this paper summarizes several current calculation methods and their shortcomings. Furthermore, on the basis of Bakholdin＇s analytical solution for the temperature field under straight single-row-piped freezing, two new calcula- tion models, namely, the equivalent trapezoid model and the equivalent triangle model, are proposed. These two approaches are used to calculate the average temperature of a certain cross section which indicates the condition of the whole frozen soil wall. Considering the possible parameter range according to the freezing pipe layout that might be applied in actual construction, this paper compares the average temperatures of frozen soil walls obtained by the equivalent trapezoid method and the equivalent tri- angle method with that obtained by numerical integration of Bakholdin＇s analytical solution. The results show that the discrepancies are extremely small and these two new approaches are better than currently prevailing methods. However, the equivalent triangle method boasts higher accuracy and a simpler formula compared with the equivalent trapezoid method.

Numerical simulation and experimental validation of moisture-heat coupling for saturated frozen soils

In seasonally frozen regions,freezing-and-thawing action is the main cause responsible for the destruction of canals,which is closely linked to the temperature gradient and water transport.To investigate the behaviour of soils under freezing-and-thawing actions,many numerical models have been established that consider the important coupling of moisture transport and temperature evolution;but they contain excessive parameters,some of which are rather difficult to determine.Based on the well-known Harlan's theory,a simple moisture-heat coupling model was recently proposed to quantify the coupled moisture-heat transport performance of soils in terms of the central temperature and porosity.The mathematical module of COMSOL Multiphysics was further employed to solve the governing equations numerically.To validate our model,a thorough experimental scheme was carried out in our lab.The measured temperature distribution was found to be consistent with the predicted results.

In-situ experiment investigations of hydrothermal process of highway in deep seasonal frozen soil regions of Inner Mongolia, China

To reveal the influencing factors and changing rules for the hydrothermal interaction process of highway subgrade, the field measurements of Shiwei-Labudalin Highway in Inner Mongolia, China was conducted for 3 years, based on which the freezing-thawing rules and water content changing characteristics were analyzed. The main results show the subgrade presents a frequent freezing-thawing alternation, and the water content of subgrade exhibits an obvious seasonal alternation. The subbase has the maximum water content, while the base has the minimum water content. The change of water flux is concentrated in the thawing period and consistent with the change of temperature gradient. The subbase layer has the most active water flux due to the heat absorption and impermeability of pavement that easily causes the water accumulation in this layer. Therefore, the prevention and treatment for the freezing-thawing disease should be started from heat insulation and water resistance.

A non-destructive method to measure the thermal properties of frozen soils during phase transition

Frozen soils cover about 40% of the land surface on the earth and are responsible for the global energybalances affecting the climate. Measurement of the thermal properties of frozen soils during phasetransition is important for analyzing the thermal transport process. Due to the involvement of phasetransition, the thermal properties of frozen soils are rather complex. This paper introduces the uses of amultifunctional instrument that integrates time domain reflectometry （TDR） sensor and thermal pulsetechnology （TPT） to measure the thermal properties of soil during phase transition. With this method,the extent of phase transition （freezing/thawing） was measured with the TDR module; and the correspondingthermal properties were measured with the TPT module. Therefore, the variation of thermalproperties with the extent of freezing/thawing can be obtained. Wet soils were used to demonstrate theperformance of this measurement method. The performance of individual modules was first validatedwith designed experiments. The new sensor was then used to monitor the properties of soils duringfreezingethawing process, from which the freezing/thawing degree and thermal properties weresimultaneously measured. The results are consistent with documented trends of thermal propertiesvariations. 2015 Institute of Rock and Soil Mechanics, Chinese Academy of Sciences. Production and hosting byElsevier B.V. All rights reserved.

A New Model for the Characterization of Frozen Soil and Related Latent Heat Effects for the Improvement of Ground Freezing Techniques and Its Experimental Verification

The correct determination of thermal parameters,such as thermal conductivity and specific heat of soil during freezing,is the most important and basic problem for the construction of an appropriate freezing method.In this study,a calculation model of three stages of soil temperature was established.At the unfrozen and frozen stages,the specific temperatures of dry soil,water,and ice are known.According to the principle of superposition,a calculation model of unfrozen and frozen soils can be established.Informed by a laboratory experiment,the latent heat of the adjacent zone was calculated for the freezing stage based on different water contents in the temperature section.Both the latent and specific heat of water,ice,and particles were calculated via superposition of the weight percentage content.A calculation model of the specific heat of the freezing stage was built,which provides both guidance and theoretical basis for the calculation of the specific heat of frozen soil.

Coupling numerical simulation with remotely sensed information for the study of frozen soil dynamics

The acquisition of spatial-temporal information of frozen soil is fundamental for the study of frozen soil dynamics and its feedback to climate change in cold regions.With advancement of remote sensing and better understanding of frozen soil dynamics,discrimination of freeze and thaw status of surface soil based on passive microwave remote sensing and numerical simulation of frozen soil processes under water and heat transfer principles provides valuable means for regional and global frozen soil dynamic monitoring and systematic spatial-temporal responses to global change.However,as an important data source of frozen soil processes,remotely sensed information has not yet been fully utilized in the numerical simulation of frozen soil processes.Although great progress has been made in remote sensing and frozen soil physics,yet few frozen soil research has been done on the application of remotely sensed information in association with the numerical model for frozen soil process studies.In the present study,a distributed numerical model for frozen soil dynamic studies based on coupled water-heat transferring theory in association with remotely sensed frozen soil datasets was developed.In order to reduce the uncertainty of the simulation,the remotely sensed frozen soil information was used to monitor and modify relevant parameters in the process of model simulation.The remotely sensed information and numerically simulated spatial-temporal frozen soil processes were validated by in-situ field observations in cold regions near the town of Naqu on the East-Central Tibetan Plateau.The results suggest that the overall accuracy of the algorithm for discriminating freeze and thaw status of surface soil based on passive microwave remote sensing was more than 95%.These results provided an accurate initial freeze and thaw status of surface soil for coupling and calibrating the numerical model of this study.The numerically simulated frozen soil processes demonstrated good performance of the distributed numerical model based on the coupled water-heat transferring theory.The relatively larger uncertainties of the numerical model were found in alternating periods between freezing and thawing of surface soil.The average accuracy increased by about 5%after integrating remotely sensed information on the surface soil.The simulation accuracy was significantly improved,especially in transition periods between freezing and thawing of the surface soil.

Experimental study of the dynamic behavior of high-grade highway-subgrade soil in a seasonally frozen area

Regarding the freezing damage of high-grade highway subgrade in seasonally frozen area,the thesis explores the effect on the dynamic behavior of subgrade soil under freeze–thaw cycles and draws the change law of parameters(including dynamic strength,dynamic cohesion,and internal friction angle;and dynamic elastic modulus)of high-grade highway-subgrade soil with the number of freeze–thaw cycles.It aims to provide the reference for operation and maintenance of a high-grade highway.Conclusions:(1)Dynamic strength tends to decline evidently after freeze–thaw cycles,with 60%~70%decline after three cycles,and remains stable after five to seven cycles.(2)With the number of freeze–thaw cycles increasing,the internal friction angle fluctuates within a certain range without an obvious change law,only presenting the tendency of dropping off.The dynamic cohesion declines obviously,about 20%~40%after seven freeze–thaw cycles,and then tends to be stable.(3)With the number of freeze-thaw cycles increasing,the dynamic elastic modulus and maximum dynamic elastic modulus are inclined to decrease distinctly.After five freeze–thaw cycles,the former declines 30%~40%and then remains stable.Meanwhile,the latter falls 20%~40%.

Characterization of frozen soil-cement mixture for berm construction in cold regions

Lagoon berms in western Alaska are difficult to design and build due to limited resources, high cost of construction and materials, and warm permafrost conditions. This paper explores methods to treat locally available frozen materials and use them for berm construction. The goal is to find an optimized mix ratio for cement and additives that can be effective in increasing the strength and decreasing the thaw settlement of an ice-rich frozen silty soil. Soil of similar type and ice content to the permafrost found at a project site in Eek, Alaska is prepared in a cold room. The frozen soil is pulverized and cement, additives and fibers are added to the samples for enhancing shear strength and controlling thaw settlement. Thaw settlement and direct shear tests are performed to assess strength and settlement characteristics. This paper presents a sample preparation method, data from thaw settlement and direct shear tests, and analyses of the test results and preliminary conclusions.

Numerical Simulation of Heat Transfer Characteristics of Horizontal Ground Heat Exchanger in Frozen Soil Layer

A simplified numerical model of heat transfer characteristics of horizontal ground heat exchanger (GHE) in the frozen soil layer is presented and the steady-state distribution of temperature field is simulated. Numerical results show that the frozen depth mainly depends on the soil′s moisture content and ambient temperature. The heat transfer loss of horizontal GHE tends to grow with the increase of the soil′s moisture content and the decrease of ambient temperature. Backfilled materials with optimal thermal conductivity can reduce the thermal loss effectively in the frozen soil. The applicability of the Chinese national standard “Technical Code for Ground Source Heat Pump (GB 50366-2005)” is verified. For a ground source heat pump project, the feasible layout of horizontal GHE should be determined based on the integration of the soil′s structure, backfilled materials, weather data, and economic analysis.