Experiments about working mechanism and mechanical characteristics of the DX model pile foundation under lateral dynamic and static loading were conducted by using a model system of the dynamic frozen soil-pile intera...Experiments about working mechanism and mechanical characteristics of the DX model pile foundation under lateral dynamic and static loading were conducted by using a model system of the dynamic frozen soil-pile interaction. The horizontal displacement-force relationship of the pile head and bending moment distribution along the body in frozen soils of different temperatures were discussed. According to test results, both the horizontal disp!acement-force relationship of the DX pile head and bending moment distribution of the DX pile body are smaller than that of equal-diameter piles under same lateral loads. The piles with different plate positions show different displacements and bending moments. This phenomenon is mainly related to the soil temperature and bearing plates locations. Thus, dynamic response analysis of the pile foundation should be taken into account.展开更多
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 im...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.展开更多
When water between soil particles is frozen, the strength and stiffness behavior of soils significantly change. Thus, nu- merous experimental studies in the laboratory have been carried out to characterize the strengt...When water between soil particles is frozen, the strength and stiffness behavior of soils significantly change. Thus, nu- merous experimental studies in the laboratory have been carried out to characterize the strength and stiffness of frozen soils. The goals of this study are to evaluate the strength characteristics of frozen soils, which underwent confinement in freezing and shearing stages, and to estimate the stiffness variation by shear wave velocity during shear phase. The specimens are prepared in a brass cell by mixing sand and silt with 10% degree of saturation at a relative density of 60%. The applied normal stresses as confining stresses are 5, 10, 25 and 50 kPa. When the temperature of the specimens is lowered up to -5 ~C, direct shear tests are carried out. Furthermore, shear waves are continuously measured through bender elements during shearing stage for the investigation of stiffness change. Test results show that shear strength and stiffness are significantly affected by the confining stress in freezing and shearing phases. This study suggests that the strength and stiffness of frozen soils may be dependent on the confining stresses applied during freezing and shearing.展开更多
To model the creep behavior of frozen soils, three creep stages have to be reasonably described (i.e., primary, secondary and tertiary stages). Based on a series of uniaxial creep test results, three creep models we...To model the creep behavior of frozen soils, three creep stages have to be reasonably described (i.e., primary, secondary and tertiary stages). Based on a series of uniaxial creep test results, three creep models were evaluated. It was shown that hypoplastic creep model has high prediction accuracy for both creep strain and strain rate in a wide stress range. The elementary rheological creep model can only be used for creep strains at low stress levels, because of the restraints of its mathematical construction. For the soft soil creep model, the progressive change from the primary to secondary and tertiary stages cannot be captured at high stress levels. Therefore, the elementary rheological and soft soil creep models can only be used for low stress levels without a tertiary stage; while the hypoplastic creep model is applicable at high stress levels with the three creep stages.展开更多
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 an...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.展开更多
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 de...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.展开更多
The uniform settle caused by the permafrost creep is still the primary problem of engineering construction in cold region.To investigate the creep characteristics of frozen soils mixed with silty clay and coarse-grain...The uniform settle caused by the permafrost creep is still the primary problem of engineering construction in cold region.To investigate the creep characteristics of frozen soils mixed with silty clay and coarse-grained sand,several triaxial creep tests of frozen mixed soils under different conditions(temperature,confining pressure,coarse-grained particle content) were performed,and the effects of the temperature,confining pressure and coarse particle content on the creep characteristics of frozen mixed soils were also analyzed.The results of the experiments indicated that when the confining pressure was low,the specimen exhibited an attenuation creep under a low-stress level(0.4-0.7) and a non-attenuation creep under a high-stress level(0.7-0.9).In contrast,when the confining pressure was high,the specimen had both initial and stable creep stages,but no the accelerated creep stage.The higher the content of coarse grains,the shorter the stable creep stage,and the easier to enter the accelerated creep stage for the specimen.Further,the long-term strength of frozen soils decreased with an increase in the content of coarse grains.Finally,a newly improved Nishihara model was proposed to consider both the hardening effect and damage effect by introducing both the hardening and damage variables,which can model the entire creep process of frozen soils modeled relatively easily.It was found that with the increasing content of coarse particle,both the strengthening and damaged effects in the creep process are reduced。展开更多
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 distributio...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.展开更多
The freezing of soil containing a liquid is a complex transient heat conduction problem involving phase change and release or absorption of latent heat.Existing efforts have essentially focused on theoretical research...The freezing of soil containing a liquid is a complex transient heat conduction problem involving phase change and release or absorption of latent heat.Existing efforts have essentially focused on theoretical research and numerical simulations.In the present study,the problem is approached from an experimental point of view using the so-called“freezing model test”method.In particular,in order to establish a precise relationship between the model and the prototype,a temperature similarity criterion is derived using the condition of an equal number of Kosovitch.Similarity is also established with respect to other aspects.A similarity criterion for the water field is determined on the basis of relevant partial differential equations.Analogous criteria for the stress field and load are derived using an elastic model.The validity of this approach is experimentally verified.The research results provide a practical and reasonable method for calculating the parameters for preparing model soils.They also constitute a theoretical basis and a technical support for the design and implementation of a water-heat-force similarity coupled framework.展开更多
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 a...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.展开更多
Buildings are always affected by frost heave and thaw settlement in cold regions,even where saline soil is present.This paper describes the triaxial testing results of frozen silty clay with high salt content and exam...Buildings are always affected by frost heave and thaw settlement in cold regions,even where saline soil is present.This paper describes the triaxial testing results of frozen silty clay with high salt content and examines the in-fluence of confining pressure and temperature on its mechanical characteristics.Conventional triaxial compression tests were conducted under different confining pressures(0.5–7.0 MPa)and temperatures(-6℃,-8℃,-10℃,and-12℃).The test results show that when the confining pressure is less than 1 MPa,the frozen saline silty clay is dominated by brittle behavior with the X-shaped dilatancy failure mode.As the confining pressure increases,the sample gradually transitions from brittle to plastic behavior.The strength of frozen saline silty clay rises first and then decreases with increasing confining pressure.The improved Duncan-Chang hyperbolic model can describe the stress-strain relationship of frozen saline silty clay.And the parabolic strength criterion can be used to describe the strength evolution of frozen saline silty clay.The function relation of strength parameters with temperature is obtained by fitting,and the results of the parabolic strength criterion are in good agreement with the experimental results,especially when confining pressure is less than 5 MPa.Therefore,the study has important guiding significance for design and construction when considering high salinity soil as an engineering material in cold regions.展开更多
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 th...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.展开更多
Using a new low-temperature dynamic triaxial apparatus, the influence law of freezing-thawing cycles on clay shear strength is studied. In this research, the concept of correction coefficients of freezing-thawing cycl...Using a new low-temperature dynamic triaxial apparatus, the influence law of freezing-thawing cycles on clay shear strength is studied. In this research, the concept of correction coefficients of freezing-thawing cycles on clay static strength, cohesion and internal friction angles is proposed, and the change patterns, correction curves and regressive formulae of clay static strength, cohesion and internal friction angles under freezing-thawing cycles are given. The test results indicate that with increasing numbers of freezing-thawing cycles, the clay static strength and cohesion decrease exponentially but the internal friction angle increases exponentially. The performance of static strength, cohesion and internal friction angles are different with increasing numbers of freezing-thawing cycles, i.e., the static strength decreases constantly until about 30% of the initial static strength prior to the freezing-thawing cycling and then stays basically stable. After 5-7 freezing-thawing cycles, the cohesion decreases gradually to about 70% of the initial cohesion. The internal friction angle increases about 20% after the first freezing-thawing cycle, then increases gradually close to a stable value which is an increase of about 40% of the internal friction angle. The freezing-thawing process can increase the variation of the density of the soil samples; therefore, strict density discreteness standards of frozen soil sample preparation should be established to ensure the reliability of the test results.展开更多
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...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.展开更多
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 statio...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.展开更多
To study the influence of temperature and water content on ultrasonic wave velocity and to establish the relationship between ultrasonic wave velocity and frozen silty clay strength, ultrasonic tests were conducted to...To study the influence of temperature and water content on ultrasonic wave velocity and to establish the relationship between ultrasonic wave velocity and frozen silty clay strength, ultrasonic tests were conducted to frozen silty clay by using RSM-SY5(T) nonmetal supersonic test meter, and the tensile strength and compressive strength of silty clay were measured under various negative temperatures. Test and analysis results indicate that, ultrasonic wave velocity rapidly changes in the temperature range of-1 ℃ to -5 ℃. Ultrasonic wave velocity increased with an increase of water content until the water content reached the critical water content, while decreased with an increase of water content after the water content exceeded the critical water content. This study showed that there was strong positive correlation between the ul- trasonic wave velocity and the frozen soil strength. As ultrasonic wave velocity increased, either tensile strength or com- pressive strength increased. Based on the experimental data, the relationship between ultrasonic wave velocity and frozen silty clay strength was obtained through regression analysis. It was found that the ultrasonic test technique can be used to test frozen soils and lay the foundation for the determination of frozen soil strength.展开更多
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 s...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.展开更多
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 t...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.展开更多
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 unde...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.展开更多
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 ...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.展开更多
基金supported by the Fundamental Research Funds for the Central Universities of China (Grant No.2011JBM269)the State Key Development Programof Basic Research of China (973 Project No.2012CB026104)the College Students Technology Innovation Experiment project in Beijing Jiaotong University
文摘Experiments about working mechanism and mechanical characteristics of the DX model pile foundation under lateral dynamic and static loading were conducted by using a model system of the dynamic frozen soil-pile interaction. The horizontal displacement-force relationship of the pile head and bending moment distribution along the body in frozen soils of different temperatures were discussed. According to test results, both the horizontal disp!acement-force relationship of the DX pile head and bending moment distribution of the DX pile body are smaller than that of equal-diameter piles under same lateral loads. The piles with different plate positions show different displacements and bending moments. This phenomenon is mainly related to the soil temperature and bearing plates locations. Thus, dynamic response analysis of the pile foundation should be taken into account.
文摘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.
基金supported by a gran (13IFIP-B06700801) from Plant Research Program funded by Korea Agency for Infrastructure Technolo gy Advancement
文摘When water between soil particles is frozen, the strength and stiffness behavior of soils significantly change. Thus, nu- merous experimental studies in the laboratory have been carried out to characterize the strength and stiffness of frozen soils. The goals of this study are to evaluate the strength characteristics of frozen soils, which underwent confinement in freezing and shearing stages, and to estimate the stiffness variation by shear wave velocity during shear phase. The specimens are prepared in a brass cell by mixing sand and silt with 10% degree of saturation at a relative density of 60%. The applied normal stresses as confining stresses are 5, 10, 25 and 50 kPa. When the temperature of the specimens is lowered up to -5 ~C, direct shear tests are carried out. Furthermore, shear waves are continuously measured through bender elements during shearing stage for the investigation of stiffness change. Test results show that shear strength and stiffness are significantly affected by the confining stress in freezing and shearing phases. This study suggests that the strength and stiffness of frozen soils may be dependent on the confining stresses applied during freezing and shearing.
基金supported in part by the National Natural Science Foundation of China (No. 41201064 and No. 41172253)the National Key Basic Research (973) Program of China (Grant No. 2012CB026106)
文摘To model the creep behavior of frozen soils, three creep stages have to be reasonably described (i.e., primary, secondary and tertiary stages). Based on a series of uniaxial creep test results, three creep models were evaluated. It was shown that hypoplastic creep model has high prediction accuracy for both creep strain and strain rate in a wide stress range. The elementary rheological creep model can only be used for creep strains at low stress levels, because of the restraints of its mathematical construction. For the soft soil creep model, the progressive change from the primary to secondary and tertiary stages cannot be captured at high stress levels. Therefore, the elementary rheological and soft soil creep models can only be used for low stress levels without a tertiary stage; while the hypoplastic creep model is applicable at high stress levels with the three creep stages.
基金supported by the National Natural Science Foundation of China (No. 41471062, No. 41971085, No. 41971086)。
文摘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.
基金supported by the National Natural Science Foundation of China (No. 41471062, No. 41971085, No. 41971086)。
文摘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.
基金the funding of the Autonomous Research Topic of the State Key Laboratory of Frozen Soil Engineering,Chinese Academy of Sciences (Nos.Y951061401)the Science and Technology Project of Yalong River Hydropower Development Company (YLLHK-LHA-2019006)the National Natural Science Foundation of China (NSFC) (Grant number 41771066)。
文摘The uniform settle caused by the permafrost creep is still the primary problem of engineering construction in cold region.To investigate the creep characteristics of frozen soils mixed with silty clay and coarse-grained sand,several triaxial creep tests of frozen mixed soils under different conditions(temperature,confining pressure,coarse-grained particle content) were performed,and the effects of the temperature,confining pressure and coarse particle content on the creep characteristics of frozen mixed soils were also analyzed.The results of the experiments indicated that when the confining pressure was low,the specimen exhibited an attenuation creep under a low-stress level(0.4-0.7) and a non-attenuation creep under a high-stress level(0.7-0.9).In contrast,when the confining pressure was high,the specimen had both initial and stable creep stages,but no the accelerated creep stage.The higher the content of coarse grains,the shorter the stable creep stage,and the easier to enter the accelerated creep stage for the specimen.Further,the long-term strength of frozen soils decreased with an increase in the content of coarse grains.Finally,a newly improved Nishihara model was proposed to consider both the hardening effect and damage effect by introducing both the hardening and damage variables,which can model the entire creep process of frozen soils modeled relatively easily.It was found that with the increasing content of coarse particle,both the strengthening and damaged effects in the creep process are reduced。
文摘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.
基金the National Natural Science Foundation of China(Grant No.41877251)Research and Practice Project of Higher Education Teaching Reform in Henan Province,China(Grant No.2019SJGLX463)。
文摘The freezing of soil containing a liquid is a complex transient heat conduction problem involving phase change and release or absorption of latent heat.Existing efforts have essentially focused on theoretical research and numerical simulations.In the present study,the problem is approached from an experimental point of view using the so-called“freezing model test”method.In particular,in order to establish a precise relationship between the model and the prototype,a temperature similarity criterion is derived using the condition of an equal number of Kosovitch.Similarity is also established with respect to other aspects.A similarity criterion for the water field is determined on the basis of relevant partial differential equations.Analogous criteria for the stress field and load are derived using an elastic model.The validity of this approach is experimentally verified.The research results provide a practical and reasonable method for calculating the parameters for preparing model soils.They also constitute a theoretical basis and a technical support for the design and implementation of a water-heat-force similarity coupled framework.
基金supported by the National Natural Science Foundation of China(Grant No.41971086)Natural Science Foundation of Shanxi Province(Grant No.2023-JC-QN-0626,2022JQ-467).
文摘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.
基金the financial support provided by China’s Second Tibetan Plateau Scientific Expedition and Research (No. 2019QZKK0905)the National Natural Science Foundation of China (No. 41371090)the State Key Laboratory for Geomechanics and Deep Underground Engineering,China University of Mining and Technology (No. SKLGDUEK1904)
文摘Buildings are always affected by frost heave and thaw settlement in cold regions,even where saline soil is present.This paper describes the triaxial testing results of frozen silty clay with high salt content and examines the in-fluence of confining pressure and temperature on its mechanical characteristics.Conventional triaxial compression tests were conducted under different confining pressures(0.5–7.0 MPa)and temperatures(-6℃,-8℃,-10℃,and-12℃).The test results show that when the confining pressure is less than 1 MPa,the frozen saline silty clay is dominated by brittle behavior with the X-shaped dilatancy failure mode.As the confining pressure increases,the sample gradually transitions from brittle to plastic behavior.The strength of frozen saline silty clay rises first and then decreases with increasing confining pressure.The improved Duncan-Chang hyperbolic model can describe the stress-strain relationship of frozen saline silty clay.And the parabolic strength criterion can be used to describe the strength evolution of frozen saline silty clay.The function relation of strength parameters with temperature is obtained by fitting,and the results of the parabolic strength criterion are in good agreement with the experimental results,especially when confining pressure is less than 5 MPa.Therefore,the study has important guiding significance for design and construction when considering high salinity soil as an engineering material in cold regions.
基金supported by the National Natural Science Foundation of China (No.11172251)the Open Fund of State Key Laboratory of Frozen Soil Engineering (No.SKLFSE201001)the Fundamental Research Funds for the Central Universities (No.SWJTU09CX069)
文摘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.
基金Scientific Research Fund of Institute of Engineering Mechanics,China Earthquake Administration under Grant No.2018D12National Natural Science Foundation of Heilongjiang Province under Grant No.E 2016045+1 种基金National Natural Science Foundation of China under Grant No.5137816451508140
文摘Using a new low-temperature dynamic triaxial apparatus, the influence law of freezing-thawing cycles on clay shear strength is studied. In this research, the concept of correction coefficients of freezing-thawing cycles on clay static strength, cohesion and internal friction angles is proposed, and the change patterns, correction curves and regressive formulae of clay static strength, cohesion and internal friction angles under freezing-thawing cycles are given. The test results indicate that with increasing numbers of freezing-thawing cycles, the clay static strength and cohesion decrease exponentially but the internal friction angle increases exponentially. The performance of static strength, cohesion and internal friction angles are different with increasing numbers of freezing-thawing cycles, i.e., the static strength decreases constantly until about 30% of the initial static strength prior to the freezing-thawing cycling and then stays basically stable. After 5-7 freezing-thawing cycles, the cohesion decreases gradually to about 70% of the initial cohesion. The internal friction angle increases about 20% after the first freezing-thawing cycle, then increases gradually close to a stable value which is an increase of about 40% of the internal friction angle. The freezing-thawing process can increase the variation of the density of the soil samples; therefore, strict density discreteness standards of frozen soil sample preparation should be established to ensure the reliability of the test results.
基金the National Natural Science Foun-dation of China under Grant Nos. 40575043 and 40605024as well as 40730952the National Basic Research Program of China under Grant No. 2009CB421405The Innovation Project of the Chinese Academy of Sci-ences (Grant No. KZCX2-YW-220)
文摘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.
基金Key project of CAS, No.KZCX1-10-07 Key project of Cold and Arid Regions Environmental and Engineering Research Institute, CAS, No.CX210097 NSFC No.49805006.
文摘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.
基金supported by the National Natural Science Foundation of China (No.41271080 and No.41230630)the Western Project Program of the Chinese Academy of Sciences(KZCX2-XB3-19)the open fund of Qinghai Research and Observation Base, Key Laboratory of Highway Construction and Maintenance Technology in Permafrost Region Ministry of Transport, PRC (2012-12-4)
文摘To study the influence of temperature and water content on ultrasonic wave velocity and to establish the relationship between ultrasonic wave velocity and frozen silty clay strength, ultrasonic tests were conducted to frozen silty clay by using RSM-SY5(T) nonmetal supersonic test meter, and the tensile strength and compressive strength of silty clay were measured under various negative temperatures. Test and analysis results indicate that, ultrasonic wave velocity rapidly changes in the temperature range of-1 ℃ to -5 ℃. Ultrasonic wave velocity increased with an increase of water content until the water content reached the critical water content, while decreased with an increase of water content after the water content exceeded the critical water content. This study showed that there was strong positive correlation between the ul- trasonic wave velocity and the frozen soil strength. As ultrasonic wave velocity increased, either tensile strength or com- pressive strength increased. Based on the experimental data, the relationship between ultrasonic wave velocity and frozen silty clay strength was obtained through regression analysis. It was found that the ultrasonic test technique can be used to test frozen soils and lay the foundation for the determination of frozen soil strength.
基金supported by the National Natural Science Foundation of China (No. 50578120)the National High Technology Research and Development Program of China (863 Program) (No. 2006AA11Z118)
文摘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.
基金supported in part by the Scientific Research Foundation for the 973 Program of China (No. 2012CB026104)Research Fund of Young Teachers for the Doctoral Program of Higher Education of China (No. 20110009120020)the Fundamental Research Funds of the Central Universities (No. 2013JBM059)
文摘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.
基金This work was supported by the National Key R&D Program of(Grant No.2016YFA0602302).
文摘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.
基金This work was supported by the National Natural Science Foundation of China(No.41472253)the Key project of Natural Science Foundation of Tianjin City(No.6JCZDJC39000).
文摘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.