Frost Heave Model Research Articles

Frost heave model and frost heaving force analysis of permafrost tunnel based on segregated ice

Bi-directional freezing occurs when a tunnel portal passes through an active layer in cold region, or when the tunnel passes through permafrost. The surrounding rock of tunnel portal is frozen by air inside of the tunnel and earth surface. The freezing-thawing cycle of permafrost tunnels is frozen by the permafrost and air inside the tunnel. To investigate the frost heave force on the lining of permafrost tunnels, and verify the layered segregation ice in the surrounding rock of these tunnels, a one-dimensional hydrothermal stress model of bi-directional freezing is established, so as to study the evolution law of segregated ice from the surrounding rock in permafrost tunnels based on the theory of hydro-thermal coupling and segregated ice. After that, based on the mechanical theory, a frost-heave elastic mechanical model including secondary lining, freeze–thaw zone, freezing zone and segregated ice is established. The results show that there is layered segregated ice in the surrounding rock after the lining of permafrost tunnel. The annual difference and the annual average temperature have a great influence on the thickness of segregated ice, while the influence of thermal conductivity is relatively small. The thickness of thawing cycle should be less than 5 m, so that the frost heaving force acting on the lining will not be too large. Good water plugging quality can decrease the thickness of segregated ice. The frost-heaving force acting on the lining increases as the thickness of segregated ice increases. When the thickness of segregated ice is 10 cm, the maximum frost heaving force generated on the lining of single-layer segregated ice is 1.39 times that of non-segregated ice. The frost-heaving force caused by the segregated ice should be considered to guarantee the safety of tunnel structure.

Data assimilation of PS-InSAR vertical deformation into a frost heave model to analyze subgrade deformation of high-speed railway in northwest China

Temperature changes may cause irregular soil uplift or thawing settlements in frozen soil areas, potentially affecting the safe operation of High-Speed Railways (HSR). Analyzing and predicting these deformation characteristics is thus critical. However, the conventional forecasting and analysis techniques rarely considered factors such as dynamic parameter variations, uncertainties, and measurement errors, which hinder accurate regional scale forecasting. To bridge this gap, this paper introduces a novel time-series coupling method, which integrates post-processing deformation from Interferometric Synthetic Aperture Radar (InSAR) with a frost heave model (FHM), facilitated by the ensemble Kalman filter (EnKF) assimilation algorithm. We obtained deformation observations along the HSR using Persistent Scatterer InSAR (PS-InSAR) technology in combination with time-series post-processing techniques. Considering the causative factors for deformation, we structured the FHM. By integrating FHM with observational data using the EnKF algorithm achieved an efficient upgrade of the posterior distribution of model parameters. This integration significantly improves the predictive accuracy, it facilitates an efficient update to the posterior distribution of model parameters, leading to enhanced prediction accuracy of our model. Our experimental results indicate that the effectiveness of this approach, with observational data assimilation into FHM reducing the average Root Mean Square Error (RMSE) to a mere 0.247 mm. Concurrently, both the Normalized Reduction Error Index (NER) and the Assimilation Efficiency Factor (EFF) values surpassed 0.60 and 0.84 respectively. These underlines signify a successful update of our model parameters, which in turn elevates the accuracy of future deformation predictions, thereby promising safer railway operations.

Experimental and Numerical Analyses on the Frost Heave Deformation of Reclaimed Gravel from a Tunnel Excavation as a Structural Fill in Cold Mountainous Regions

In cold mountainous regions of China, the construction of highways is challenging, owing to frost damage of weak subgrade soils and the difficulties posed from dealing with waste materials derived from tunnel excavation. In order to address these issues, Wu et al. proposed a new approach of using coarse gravel reclaimed from tunnel excavation as an antifrost structural fill replacing the top layer of frost-susceptible subgrade soils. This approach was validated against the results of field investigations on the highway between Tanchang county and Diebu county (the TDH) in south Gansu Province, northwest China, but only studied the results of the first year. As an environmentally friendly and sustainable ground-treatment method, this strategy merits extensive research and widespread implementation. In this study, the frost-heave deformation of a two-year monitoring period is investigated through a field trial, and a frost-heave model is applied to explore the growth of the ice lens and accomplish the quantitative prediction of frost heave based on experimental measurements. The fine particles of reclaimed gravel sediments from the Lazikou tunnel are found to be resistant to frost. The measured values of the maximum frost heave are significantly lower than the permissible limit of 50 mm specified in the Chinese standards. The reclaimed gravel could significantly reduce frost heave. With a 2 m thick gravel fill, frost heave could be reduced by more than 70% when the groundwater table is located at a depth greater than 3 m. An empirical relationship to predict the frost heave in terms of the gravel fill thickness is proposed. This study presents a safe and sustainable approach focusing on the construction of highways in cold mountainous regions.

A model of segregation frost heave for saturated soil freezing under overburden pressure

To study the inhibition mechanism of overburden pressure on water migration in freezing soil, the pressure-suction coexistence state of film water is analyzed, and it is found that the main function of ice pressure is to offset and balance the theoretical suction. Under the combined action of ice pressure and theoretical suction, the surface adsorption force that drives water migration is produced. Based on this, the mechanical model of the pressure-suction coexistence state is introduced into the frozen fringe theory, and it is found that as the overburden pressure increases, the surface adsorption force gradually increases, while the total permeability coefficient of the frozen fringe decreases according to a high-order power function. Given this, a theoretical model of segregation frost heave under pressure is established and an explicit equation for the water migration velocity is given. Finally, a frost heave loading test is performed on saturated silt under open-system conditions, and the main parameters of the test process are substituted into the explicit equation for water migration velocity, the results showed that the calculated value of the model is completely consistent with the experimental value, thus verifying the correctness of the model. In summary, the proposed model has important theoretical value and practical significance for improving the existing frost heave theory.

A thermomechanical model for frost heave and subglacial frozen fringe

Ice-infiltrated sediment, or frozen fringe, is responsible for phenomena such as frost heave, ice lenses and metres of debris-rich ice under glaciers. Understanding frozen fringes is important as frost heave is responsible for damaging infrastructure at high latitudes and sediment freeze-on at the base of glaciers can modulate subglacial friction, influencing the rate of global sea level rise. Here we describe the thermomechanics of liquid water flow and freezing in ice-saturated sediments, focusing on the conditions relevant for subglacial environments. The force balance that governs the frozen fringe thickness depends on the weight of the overlying material, the thermomolecular force between ice and sediments across liquid premelted films and the water pressure required by Darcy flow. We combine this mechanical model with an enthalpy method that conserves energy across phase change interfaces on a fixed computational grid. The force balance and enthalpy model together determine the evolution of the frozen fringe thickness and our simulations predict frost heave rates and ice lens spacing. Our model accounts for premelting at ice–sediment contacts, partial ice saturation of the pore space, water flow through the fringe, the thermodynamics of the ice–water–sediment interface and vertical force balance. We explicitly account for the formation of ice lenses, regions of pure ice that cleave the fringe at the depth where the interparticle force vanishes. Our model results allow us to predict the thickness of a frozen fringe and the spacing of ice lenses in subaerial and subglacial sediments.

The mechanics of frost heave with stratigraphic microstructure evolution

Frost heave is a major cause of engineering geology hazards in cold regions, which is mainly the result of frost-heaving pressure due to the non-linear transport-freezing of water in the pore network. However, few studies have fully quantified the contribution of the strata pore-network structure to that pressure and the hazard to cold-region projects under multifactorial effects. Therefore, to address this long-term challenge in cold regions, we pioneered a generic, interdisciplinary, thermal-hydrological-mechanical fractal model for the quantitative study of the effect of strata microstructure on frost heave and hence the assessment of construction risk for engineering geology projects. First, a strata frost heave model based on fractal theory is proposed, with pore fractal dimension, maximum pore diameter, and pore tortuosity fractal dimension used to characterize strata pore density, pore size, and throat complexity, respectively. Secondly, the numerical model is compared with field observations in cold-region projects, and reasonable agreements can be obtained. The results indicate that various fractal parameters have different effects on engineering geology projects in cold regions. The strata displacement changes by 9.7–20.3% as microscopic parameters change. This study contributes to a better understanding of the micro- and macro-interactions of soil in cold regions, as well as a reference for geoengineering stability in cold regions under frost heave conditions.

Parallel Bar Compressive Strength Model for Pumice Concrete Considering Frost-Heave Stress

Pumice concrete is a lightweight porous building material. Under the continuous low temperature in permafrost regions, the interstitial water of concrete is frozen, which can improve its mechanical properties. In this research, the interstitial water freezing law of pumice concrete is obtained by nuclear magnetic resonance, the frozen-heave stress and compressive strength of pumice concrete under a low-temperature environment are tested, and the relationship among the three is studied. A compressive strength model for pumice concrete considering frost-heave stress is also established using parallel bar theory. Finally, the hydrothermal coupling frost-heave model of concrete is established. Results showed that in the rapid change stage of 0°C to −10°C, the interstitial water with the largest proportion of medium pores (0.1–1 μm) in this temperature range is rapidly frozen and expanded, which makes the frost-heave stress and compressive strength increase rapidly. The frost-heave stress caused by pore-water freezing can be regarded as prestressing force against external load, which is the main reason for the increase in low-temperature compressive strength of pumice concrete. The maximum error between the calculated value of the parallel bar compressive strength model and the experimental value was 7.42%, indicating that the model has good accuracy and certain rationality. The hydrothermal coupling model can reflect the frost-heave process of concrete, and the error between the simulated and experimental values of frost heaving strain was small, which proves that the model has high accuracy.

Classification, deconstruction and evaluation of frost heave models: How modeling methods cause simulation error

Frost heave models are important tools to study engineering damage in cold regions. However, multi-physical-field-coupling and different methods of coupling components bring difficulties to compare the models and to optimize their error sources. Therefore, classifying and deconstructing of different frost heave models and further evaluating them are significant for model development. We reviewed frost heave models for the past 50 years and built frost heave model families to show the classification and inheritance relationships. Then, the models were deconstructed by the thermal–hydraulic framework (THF) and frost heave quantification method (FHQM). Finally, based on simulated and experimental data in cited papers, the model errors caused by different THFs and FHQMs were analyzed. The results show: (a) Present frost heave models can be classified as porosity increase based (P) and ice lens increase based (I) models and they are tending to merge with each other; (b) THFs of P models regarding freezing soil as porous medium are the main reason for water migration error in the region of multi-ice layers, which also results high uncertainty of hydraulic parameters under different simulation conditions; (c) The most used two FHQMs of P models cause error exceeding 20 % because inaccurate relationship between pore strain and frost heave displacement; (d) The errors of THFs and FHQMs offset each other, which will hidden the error sources of the models. This paper can provide a reference for the improvement of frost heave models used in engineering.

A non-local frost heave model based on peridynamics theory

Multitudes of physical phenomena have non-local effects. However, non-local effects are not considered by most soil frost heave models. Peridynamics takes into account non-local interactions, and has not yet been applied in the field of permafrost research. Thus, this study is a preliminary attempt to introduce peridynamics into permafrost research. In this paper, a one-dimensional frost heave model of saturated soils for local theory is established, and then converted to a non-local model of peridynamics. A program of the model is used to verify the model. The comparison between the numerical simulation results and the measured results shows that the model can basically reflect the characteristics of the physical field evolution in the frost heave process of saturated soils. To accelerate the model, the integral term in the mathematical model is deduced into the form of convolution. The modified model can use fast Fourier transform to calculate the convolution term in the model. Compared with the original program, the program accelerated by the fast Fourier transform has a lower memory cost and a higher calculation efficiency.

Frost heave modelling of the sunny-shady slope effect with moisture-heat-mechanical coupling considering solar radiation

The sunny-shady slope effect on structures in cold regions is significant due to solar radiation, which threatens structural stability. Solar radiation is rarely considered in modelling frost heave, and its effects on the moisture-heat transfer of frozen soil and structural deformation are unclear. Here, a frost heave model with moisture-heat-mechanical coupling, solar radiation and self-shadowing is presented; its accuracy is verified through comparison with field monitoring data of a canal. Then, the coupling development of the moisture-heat transfer, stress-deformation and differential frost heave progression of differently oriented canals are analyzed. Finally, the effects of solar radiation on the soil frost heave and frost damage mechanism of canals with the sunny-shady slope effect are discussed. The freezing depth is shallower and the water content, deformation, and tensile stress are lower for sunny than for shady slopes. As the canal orientation varies from east-west to north–south, the differences in the freezing characteristics decrease to 0, and the frost damage time of shady slopes is gradually delayed; the opposite occurs for sunny slopes. The developments in structural surface temperature, moisture-heat transfer in frozen soil and structural deformation are consistent with solar radiation and air temperature changes, emphasizing solar radiation’s contribution to structure frost heave. The uneven, asynchronous, asymmetrical frost heave and melting deformation of linings in sunny and shady slopes are the causes of canal damage. This model investigates interactions among solar radiation-diurnal temperature-frozen soil-structures and offers a theoretical basis for using solar energy to reduce frost heave in seasonally frozen regions.

Thermal-Hydraulic-Mechanical Coupling Research on Overburden Pressure Mitigated Ice Lens Growth in the Freezing Soil

Frost heave induced ground surface uplift can have a destructive impact on infrastructures when freezing methods are used for underground construction. The complexity of overburden pressure and the coupled heat and mass transport interaction and their relation to different water flow rates make frost heave modelling an interesting but challenging task. A frost heave model describing phase transition and multiphase interactions (liquid-crystal-soil matrix) is presented in this paper and used to investigate the kinetic growth of the ice lens. By introducing water activity determined growth rate of ice crystals, the micro- and mesophysical mechanisms underlying ice lens growth involve ice crystal nucleation, crystallization, phase transition, and water migration in the frozen fringe are explored. This work indicates that the frozen fringe thickness, the ice crystals growth and the cryogenic-suction in the frozen fringe are particularly significant in determining the ice lens growth kinetics (frost heave) under different overburden pressures. The variation in ice lens growth under various overburden pressures appears to be controlled by the water flow path, cryogenic-suction, and permeability of the frozen fringe. This research reveals the kinetic growth of the ice lens, and helps to evaluate and mitigate geological hazards when artificial ground freezing is applied.

A study on frost heave and thaw settlement of soil subjected to cyclic freeze-thaw conditions based on hydro-thermal-mechanical coupling analysis

Frost heave and thaw settlement are the main cause for damaging the engineering structures in the region of seasonally frozen soil. The soil freeze-thaw (FT) deformation is a typical complex result of multiple physical fields and involves the process of water transfer, heat transfer, ice-water phase transition and stress redistribution. While the theory and model of frost heave have been studied for decades, less attention has been paid to the simulation for soil deformation under FT cycles. In this study, coupled equations for water, heat and the deformation of frozen soil are derived based on previous theories and are realized in numerical software. The volumetric water content of the frozen soil in the experiment was tested by nuclear magnetic resonance (NMR) technology, and the obtained data were imported into the model. Experimental soil samples were arranged in improved model equipment, and the temperature and frost heave at different heights of the soil column varied with time. The model validity and applicability based on the hydro-thermal-mechanical coupled equations is verified by comparing the results of both the experiment and numerical simulation. In this research, from the curves of the soil temperature change, water content distribution, water flux occurred at the soil bottom surface, as well as the displacement of frost heave and thaw settlement, and the pore size distribution, the characteristics of the soil subjected to cyclic FT conditions was analyzed. The existed theoretical model cannot well model the soil FT deformation. Therefore, this study may provide references for developing more accurate theoretical models on the soil subjected to FT cycles.

Evolutions of the unfrozen water content of saturated sandstones during freezing process and the freeze-induced damage characteristics

The precise determination of unfrozen water content is of great significance to understand the freezing process of pore water and reveal the freeze-induced damage mechanism for frozen rock mass. In this study, low field nuclear magnetic resonance (LF-NMR) tests were conducted on five types of frozen sandstone samples. The changes in the T2 distribution and unfrozen water content (including unfrozen bound water content and unfrozen movable water content) were obtained and then analyzed. The experimental results indicate that there is little unfrozen movable water exists in the sandstone sample at the temperature of -5 °C and lower, whereas the amount of the unfrozen bound water is slowly decreased during the freezing process. The pore size distribution largely dominates the speed of water-ice phase transition and the total ice volume in the sandstone samples. A larger equivalent average pore radius (rm) leads to a higher speed of water-ice phase transition. The freeze-induced strains of the frozen sandstones were theoretically calculated based on a frost heave model. It is indicated that the freezing strain increases rapidly in the temperature range of 0 °C to -10 °C, while tends to be stable with further decreasing the temperature. Owing to the different pore size distributions, the movable water induces more substantial freezing strain than the bound water in terms of the Wuding sandstone and Linyi sandstone having an rm larger than 1.6 μs. However, it is exactly inverted for the other three sandstones including the Tengchong sandstone, Luzhou sandstone and Zigong sandstone with much smaller rm. The study provides a reasonable method for quantifying the unfrozen water content and freeze-induced strain in frozen rock, as well as important guidance for the design and construction of rock engineering in cold regions.

Thermal-hydraulic-mechanical coupling behavior and frost heave mitigation in freezing soil

Frost heave induced by artificial freezing can be destructive to infrastructure. The fundamental physicochemical mechanisms behind frost heave involve mainly the coupled thermal-hydraulic-mechanical (THM) behavior, ice-water phase transition, and heat and fluid flow in porous media. Taking the soil skeleton, pore ice, and pore water as independent bodies to conduct the mechanical analysis, we clarify the physical meaning of the effective stress principle of frozen soil with consideration of the multiphase interactions (ice-water-mineral) and further improve the coupled heat and fluid flow equations. Taking into account the coupled THM mechanism in freezing soils, a discrete ice lenses based model for frost heave is established with focus on segregation and growth of the ice lens. Upon validation of the frost heave model, an intermittent freezing method is applied to investigate mitigation of frost heave. Numerical results show that the intermittent freezing can significantly mitigate frost heave and inhibit the potential frost susceptibility of freezing soil. Our research reveals that the narrowing of the frozen fringe induced by the upward movement of the freezing front is the main reason for the slower growth of the ice lens. The THM behavior and heat and fluid flow based frost heave model enable a better understanding of the geomechanical properties of freezing soil and physical mechanism of frost heave mitigation in porous media (soil).

Evaluation of frost heave in clay soils

Frost heaving in clayey soils with a low coefficient of permeability raises a lot of questions regarding the cryosuction, surface tension forces, and accompanying phase transfer of water. The freeze-thaw laboratory test results were considered in this work in terms of temperature and volumetric parameters change, dry density, and water mass transfer. The article presents a model for calculating the mass transfer of water (vapour) in the gas state under the influence of cryogenic forces. Findings include the improved understanding of the heat and mass transfer phenomenon during the unidirectional freezing of soils in an open system. Most of the tests for engineering properties registered a slight reduction in relation to strength, cohesion, and angle of internal friction. However, there was a significant increase in the coefficient of permeability after the freeze-thaw cycles with initially dense compacted soil samples, which was due to loosening and moistening of the soil samples during the heave at sub-zero temperatures. The conceptual model for frost heave in soils was developed based on the vapour mass transfer. There was presented algorithm of vapour flow calculation in unsaturated soils using fundamental thermodynamic equations.

Modelling frost heave in unsaturated coarse-grained soils

Coarse-grained soils were considered not susceptible to frost heave. However, substantial frost heave has been observed in unsaturated coarse fills in high-speed railway embankments. Recent experimental results in the literature show that vapour transfer has a considerable influence on the frost heaving of coarse-grained soil. However, vapour transfer has rarely been considered in modelling frost heave. This study presents a new frost heave model that considers vapour transfer and its contribution to ice formation. An updated computer program (PCHeave) is developed to account for the vapour transfer in unsaturated coarse-grained soils, where the rigid ice theory is applied to initiate ice lens formation in the frozen fringe. The results of the proposed model are compared with laboratory test results, which show reasonable agreement. The frost heave data monitored in 2013–2014 along the embankment of the Harbin–Dalian Passenger Dedicated Railway are also used to validate the proposed model. The prediction of the model agrees well with the measured results of frost heave and frost depth. This indicates that the proposed model can reasonably reflect the process of frost heave caused by vapour transfer in unsaturated coarse-grained soils.

Investigation on frost heave of saturated–unsaturated soils

Frost heave is a process of coupled heat–water–mechanics, which refers to heat transfer, water migration, water–ice phase change, deformation, etc. The mechanism of the frost heave for saturated–unsaturated soils was investigated to establish a frost heave model. As the freezing continues, for saturated soils, because all pores are filled with pore water, the total increased volume due to water migration and water crystallization will separate soil particles and induce frost heave. For unsaturated soils, because of the existence of unsaturated pores, volume expansion generates by water and vapor migration and water–ice transition will firstly fill into the unsaturated pores until a critical state is reached. After that, further increased volume will separate soil particles and induce frost heave. Therefore, effective strain ratio was introduced to establish the relationship between frost heave strain of unsaturated soils and the fields of moisture and temperature. Tests were carried out for silty soil. Then, based on the inverse theory, a simplified criterion was proposed to determine the effective strain ratio, and the effective strain ratio was back-calculated according to the test results. Finally, an innovative universal frost heave model for saturated–unsaturated soils was proposed.

A frost heave model of unsaturated coarse-grained soil considering vapour transfer

Substantial frost heave has been observed in coarse fills in high-speed railway embankments. These coarse fills have low fine contents and very low water content. The groundwater table is located below the coarse fills. The coarse fills were considered not susceptible to frost heave. Recent experimental results in the literature showed that vapour transfer has a considerable influence on the frost heaving of unsaturated coarse-grained soil. But vapour transfer has been rarely considered in the modelling of frost heave. This study presents a new frost heave model with considering vapour transfer and its contribution to ice formation. The rigid ice theory is applied to initiate an ice lens formation in the frozen fringe. An updated computer programme PCHeave is developed by considering the vapour transfer. The results of the proposed model are compared with laboratory test results, which show reasonable agreement. The prediction of the model agrees well with the measured frost heave and frost depth, which indicates that the proposed model can reasonably reflects the process of frost heave in unsaturated coarse soil.

Frost heave and thaw consolidation modelling. Part 1: A water flux function for frost heaving

Although much effort has been made to develop various frost heave models in the past decades, a simple yet versatile model is still needed for engineering applications. This paper presents a method to estimate frost heave in frozen soil using a macroscopic water flux function that extends the segregation potential to make it applicable for both steady state and transient freezing and thawing states. The formation of an individual ice lens is modelled by combining previously developed stress and strain criteria. The water flux function, which includes various factors in accordance with the porosity rate function, can describe the growth of both new and old ice lenses. More importantly, every component of the water flux function is physically explained by the theory of pre-melting dynamics, where all the influencing factors are traced back to their impacts on the ice volume distribution. The performance of the model is demonstrated via simulations of one-dimensional freezing and thawing processes after the model is validated by a specific case from previous literature. Although adequate data are not available for a stricter experimental verification of the model, it is observed that the simulations predict the general course of events together with significant specific features that were identified in previous experimental studies.

Ice lens induced interfacial hydraulic resistance in frost heave

Frost heave and ice lens cause the failure of engineerings and change the soil structure in cold regions. It is known that the water migrates from the unfrozen zone to feed the ice lens, but the mechanism of water migration in the vicinity of the ice lens is not well understood. In this study, the water migration at the interface between the ice lens and soil particles is theoretically investigated. Pore water flows from the soil pores to the unfrozen film between the ice lens and soil particles to expands the integral ice lens. The kinetics of the microscopic flow in the unfrozen film produces the hydraulic resistance at the macroscopic interface between ice lens and soil particles. Based on the global mechanical equilibrium at the ice-water interface, the rate of frost heave is derived for freezing soils with and without a frozen fringe. An expression for the neutral stress in the frozen fringe is developed to predict the initiation of new ice lenses with considering the effect of anisotropic stress of ice. The impacts of overburden pressure, temperature gradient, and interfacial hydraulic resistance on the rate of frost heave are discussed. In a relatively thick frozen fringe, the interfacial hydraulic resistance is insignificant compared to the hydraulic resistance of frozen fringe. However, if the thickness of frozen fringe is less than a critical value the interfacial hydraulic resistance will play a dominant role in the frost heave. This research is expected to facilitate the improvement of frost heave models, studying the influence of the interfacial hydraulic resistance on the characteristic of frost heave with and without a frozen fringe.