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.

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.

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.

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.

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.

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.

Seasonally frozen soil effects on the dynamic behavior of highway bridges

Frozen ground is significantly stiffer than unfrozen ground. For bridges supported on deep foundations, bridge stiffness is also measurably higher in winter months. Significant changes due to seasonal freezing in bridge pier boundary conditions require addi- tional detailing in order to ensure a ductile performance of the bridge during a design earthquake event. This paper reports the lat- est results obtained from a project that systematically investigated the effects of seasonally frozen soil on the seismic behavior of highway bridges in cold regions. A bridge was chosen and was monitored to study its seismic performance and assess the impact of seasonally frozen soil on its dynamic properties. A Finite Element （FE） model was created for this bridge to analyze the impact of seasonal frost. It was found that when frost depth reaches 1.2 m, the first transverse modal frequency increases about 200% when compared with the no-frost case. The results show that seasonal frost has a significant impact on the overall dynamic be- havior of bridges supported by pile foundations in cold regions, and that these effects should be accounted for in seismic design.

Study on potential evapotranspiration and wet-dry condition in the seasonal frozen soil region of northern Tibetan Plateau

This study was based on the CEOP/CAMP-Tibet observed data at AWS （Automatic Weather Station） of MS3478 in the seasonal frozen soil region of northern Tibetan Plateau from March 2007 to February 2008. The variation characteristics of PE （potential evapotransph＇ation） were analyzed based on the Penman-Monteith method recommended by FAO （the Food and Agriculture Organization of the United Na- lions）. The contributions of dynamic, thermal and water factors to PE were discussed, and the wet-dry condition of the plateau region was further studied. The results indicated that daily PE was between 0.52 mm and 6.46 mm for the whole year. Monthly PE was over 107 mm from May to September, but decreased to less than 41 mm from November to February. Annual PE was 1,037.8mm. In the summer, thermal PE was significantly more than dynamic PE, but conversely in the winter. Annual variation of thermal PE was of sine wave pattern. In addition, drought and semi-drought climate lasted for a long time while semi-humid climate was short. The effect of water and dynamic factors on PE varied considerably with the seasons. Annual variation of thermal PE was of sine wave pattern.

Variation characteristics of temperature and moisture content of seasonal frozen soil during freezing process in Changchun,China

In China, seasonal frozen soil is widely distributed. The freezing damage of subgrade soil in Jilin Province has been one of major engineering geological problems troubling the safety of road, in which some common damage phenomena, such as frost heave, subsidence deformation and frost boiling, are all caused by water translocation. Aiming at the phenomenon, the changes of moisture content of seasonal frozen soil in Changchun City are mainly studied by long-term field observation and indoor testing of physical properties under different conditions, and then the variation characteristics of moisture content in soil under different compactness and temperature conditions are realized. The results show that the increasing section of moisture content and negative temperature section all lie in O. 0 - 1.0 m of subgrade. Both lowest air and earth temperature occur in January to February, and the most negative temperature ranges from -7℃ to -10℃.

Vibration characteristics of frozen soil under moving track loads

Vibration due to moving traffic loads is an important factor which induces frozen soil damage; this paper analyzed these vibration characteristics of frozen soil foundation under track loads. Firstly, seismic observation array （SOA） technology was applied to monitor the three dimensional dynamic characteristics of frozen soil under movable track load in a per- mafrost region and seasonal frozen soil area. Secondly, a numerical simulation for the response of frozen soil under movable track load was performed based on finite element analysis （FEA）, The results show that dynamic characteristics of frozen soil in perpendicular and parallel direction of the track are obviously different. In the direction perpendicular to the track, the vertical acceleration amplitude had an abrupt increase in the 9-10 m from the track line. In the direction parallel to the track, the acceleration in vertical and horizontal direction had a quick attenuation compared to the other direction. Lastly, various parameters were analyzed for the purpose of controlling the dynamic response of frozen soil and the vibration attenuation in frozen soil layer.

Stress relaxation of warm frozen soil under drained or undrained conditions

To investigate the influence of drainage conditions on stress relaxation characteristics of warm frozen soil, a series of laboratory tests were carried out under drained and undrained conditions. The results indicate that confining pressure obviously influences the relaxation process of warm frozen soil. Under undrained condition, with increase in confining pressure, the critical relaxation du- ration tends to grow as well as instantaneous relaxation. But the relaxation rate is sensitive to confining pressure in the initial stage, and with further development, the effect tends to diminish. Under drained condition, the relaxation rate is greater than that under tmdrained condition in the initial stage but with the development of relaxation, the difference decreases. The volumetric defor- mation of warm frozen clay under drained condition is much larger than that under undrained condition.

A spring-like interface between saturated frozen soil and circular tunnel lining under the moving load in cold regions without considering frost heave

The vibration of underground or buried piping during construction and long-term operation causes secondary disasters,and becomes more complex when tubes are buried in cold regions.The interface between saturated frozen soil and lining is regarded as a thin spring-like layer whose thickness could be negligible.In this paper,the dynamic response of saturated frozen soil is studied in frequency domain by using the Helmholtz composition and Fourier transform to obtain analytical solutions of the radial and axial displacement,as well as expressions of the stiffness coefficient(Kr)and damping coefficient(Cr)of the spring-like interface.Numerical results indicate that Krand Crare related to physical properties of the lining and its surrounding soil,and the coefficients of the springlike model could be changed by adjusting lining parameters to improve structure stability under the same load conditions.Also,the viscoelastic contact surface of the spring-like model is considered to have less effect on the surrounding soil than that when the lining has complete contact with the soil under load.The degree of soil freezing significantly affects the axial and radial displacement of the soil when the interface between lining and unsaturated frozen soil is taken into consideration.

Characterizing Subzero-Temperature Thermal Properties of Seasonally Frozen Soil in Alpine Forest in the Western Sichuan Province, China

Seasonally frozen soil in alpine and subalpine zones in the mountains of Qinghai-Tibetan Plateau is particularly sensitive to global climate change. Therefore, a better understanding of the thermal properties of frozen soil is crucial for predicting the responses of frozen soils to soil warming. In this study, thermal properties of frozen soil with different moisture contents under subzero temperature (0°C - 20°C) in an alpine forest in western Sichuan were analyzed by KD2 Pro in its cooling and heating processes, respectively. Our results reveal that the soil apparent volumetric specific heat capacity (Cv) and apparent thermal conductivity (K) under the same water content show similar response patterns to changing temperature lower than -2°C in both heating and cooling processes. Moreover, ice content of frozen soils can be well predicted by Logistic model in cooling and heating processes. The Cv and K tend to increase along with increasing soil moisture contents. Remarkably, asymptotic characters of the value of Cv and K are at the vicinity of the initial temperature of phase transitions, indicating that both Cv and K are particularly sensitive to changing soil temperature at the range of -2°C to 0°C. Therefore, the widely distributed frozen soil layers with temperature above -2°C in alpine and subalpine zones over Qinghai-Tibetan Plateau are susceptible to the observed climate warming during cold season.

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.

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.

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.

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.