Modeling frost heave in freezing soils

A generalized model for secondary frost heave in freezing fine-grained soils is presented. The cryostatic suction effect, which causes an increase in upward water permeation, ice-lens growth during freezing, and, as a consequence, the increase of soil heave, is considered to be the main mechanism of moisture transfer. Although the model in this paper has a number of approaches in common with the model of Fowler and Krantz (1994) it differs in at least several important respects. We recognize the need to determine the distribution of the moisture within the frozen fringe by approximation of the experimental data for the equilibrium unfrozen water content. This distribution is the result of the complicated interaction between water, ice and the mineral skeleton during the freezing process. The generalization of the Clapeyron relation, which is used in the work cited above, only estimates the drop in initial freezing temperature and does not define the connection with the external temperature gradient ∇T, which is responsible for the frost heave process. This very important aspect is discussed in detail in the Introduction to our paper. Another difference is the fact that our solution is based on a dimensionless system of equations. We take into account the ratio Pe/Ste ≠ 1 (where Pe << 1). This approach allows us to obtain both a more general solution as well as analyze frost heave and propagation of the freezing front as they depend upon the convective (Pe) and phase transition (Ste) characteristics (criteria) of the process. The theoretical results derived from our solution of the analysis for fine-grained soils are compared, in good agreement, with experimental investigations and numerical models. A singularity of the solution at the initial point in time is discussed. In this respect the asymptotic solution for short and long times is obtained. The results are compared with both solutions (modeling and asymptotic). The model presented predicts the frost heave and freezing processes in porous media with reasonable accuracy and satisfactorily reflects observed phenomena, and thus can be suitable for engineering practice.     

Frost heave and phase front instability in freezing soils

The main equations and conditions at the phase transition front are presented for a generalized model of secondary frost heave in freezing fine-grained soils. The analytical criterion for the stability/instability of the freezing phase front in porous media is derived. This criterion is obtained for the occurrence of the frost heave process by using the perturbation method in a two-dimensional, coupled heat and mass transfer model. This model assumes that the non-instantaneous crystallization process takes place in the kinetic zone, and that the rate of crystallization is a function of supercooling. This corresponds to the Arrhenius form equation and agrees with experimental investigations. The perturbation analysis of the freezing front shows that the stability criterion depends upon 1) the Stefan and Peclet numbers, 2) a parameter describing the phase transition kinetics and also 3) dimensionless parameters which characterize the frost heave process. Employing Fourier synthesis, actual front shape evolution is calculated. It is seen that the front displays a periodic morphology whose scale is essentially unrelated to that of the initial (starting) perturbation. The effect of the non-instantaneous kinetics on the front shape evolution is described. As is shown in results, the kinetics has a stabilizing effect and, in this case, the perturbations grow more slowly. The theoretical stability/instability conditions as predicted from the derived criterion were found to be in agreement with experimental investigations of the formation of soil cryogenic structure in the freezing process. On the basis of the asymptotic solution the engineering approach for the calculation of the heave rate and maximal frost penetration depth values — main characteristics for design and construction in cold regions, is presented. The good agreement between calculated values and experimental data is observed.     

New ice lens initiation condition for frost heave in fine-grained soils

Frost heave results from ice segregation and ice lens formation and growth as a soil freezes. This formation is initiated by cracking of the soil in the frozen fringe. Therefore, evaluation of the ice lens initiation requires the determination of the crack initiation condition in the frozen fringe. A new fundamental approach is proposed to determine the ice lens initiation condition using the soil freezing characteristics curve (SFCC). It is demonstrated that an ice lens initiates close to the so-called ice-entry value defined using the SFCC. Ice lens initiation conditions for different boundary conditions were determined in a laboratory using the SFCC and were then compared with the ice lens initiation conditions from a one-dimensional open system frost heave tests. The results using the SFCC showed good agreement with the values determined experimentally. It was therefore concluded that the SFCC derived information can be used as an input parameter in existing frost heave models to establish the segregation temperature.     

A probabilistic-deterministic analysis of one-dimensional ice segregation in a freezing soil column

A deterministic model of frost heave based upon simultaneous analysis of coupled heat and moisture transport is cascaded with a probabilistic model of parameter variations. The multiparameter, deterministic model is based upon submodels of moisture transport, heat transport, and lumped isothermal freezing processes. The probabilistic model is based upon Rosenblueth's method which only requires knowledge of parameter means and their coefficients of variation. The deterministic model is relatively insensitive to thermal parameter variations because the phase change process dominates the thermal regime of a freezing moist soil. The model is sensitive to hydraulic parameters which control the rate mobile liquid water is drawn into the freezing soil region. Four hydraulic parameters were varied within reported and assumed levels of parameter variation for two soils; a frost-susceptible silt and a marginally frost-susceptible dirty gravel for which laboratory data on parameters and frost heave were available. The resulting frost heave variations were fit to a beta distribution and confidence limits of at least 95% were predicted within two sigma bounds. The coefficient of variation of unfrozen hydraulic conductivity primarily determines the coefficient of variation of simulated frost heave. Comparison of these results with two detailed field cases indicates a close comparison with beta distribution parameters.     

Non-equilibrium crystallization in freezing porous media: Numerical solution

The boundary value problem which arises during heat and moisture transfer in freezing fine-grained porous media under phase transition conditions is solved. It is assumed that the phase transition process occurs with finite rate of the water crystallization. So, the non-instantaneous kinetics is considered. Since the problem is significantly nonlinear the numerical method for the solution is applied. For the approximation of the system of differential equations the implicit two-level finite-difference scheme with central differences for space coordinate and one-side differences for time is used. The finite-difference system of equations is solved by “double sweep method.” It was shown the stability of “double sweep method” and solvability of the problem. Based on the correlation analysis, the dimensionless form for the diffusion coefficient as a function of moisture is obtained and used for the modeling. It is shown that the results for the characteristic distributions — temperature and total moisture, obtained in numerical solution, are in a good agreement with experimental investigations. The effect of the main criteria for the considered process — Lewis and Stefan numbers on the temperature, moisture, ice content and total moisture distributions is discussed. Especial attention was paid on the formation of the kinetic zone and its transformation in the course of non-equilibrium freezing. It was shown that the kinetic zone has a width of about 20–40% of the overall dimension of the system. Therefore the simulation of the phase transition zone as an infinitely thin front in freezing process, which is an approach incorporated in most theoretical models, is not suitable for the non-equilibrium water crystallization processes in fine-grained soils, and thereby conforms the validity of the kinetic approach.     

Thermal elasto-plastic computation model for a buried oil pipeline in frozen ground

The 813-mm-diameter China-Russia Crude Oil Pipeline enters northeastern China at Lianyin, Mo'he County, Heilongjiang Province and crosses 441 km of warm discontinuous, sporadic and isolated patches of permafrost and 512 km of seasonally frozen ground before reaching Daqing, China. It is inevitable that the buried pipeline is subject to frost heave and/or thaw settlement when it passes through regions of permafrost and seasonally frozen ground with available moisture. Therefore, stress and deformation analyses of the pipe subject to frost action or thaw settlement are important for the safety, long-term stability and economic feasibility of the buried oil pipeline system. Based on the (empirical) frost heave and/or thaw settlement coefficients, a simple thermal elasto-plastic finite element computation model is put forward for analyzing the stress and strain state of the pipe. The influences of soil temperatures on the soil deformation were considered, but those of the soil deformation on the soil temperatures were ignored in the modelling. Finally, two examples of the application of the computation model are presented, in which the stress and deformation of a pipe exposed to frost heave or thaw settlement is calculated. The results of the frost action computation show that the effective stress on the pipe increases linearly with the frost heave deformation. The largest pipe deformations and stresses may occur when crossing frost mounds due to differential frost heaving. The stress and deformation smooth out from the frost mound. The results of thaw settlement computation show that the pipe stress changes greatly near the interface of thaw settlement zone and no thaw settlement zone, and the thaw settlement has small effect on the stability of oil-pipeline. The computation results show that the oil pipeline design in the permafrost regions should pay more attention on frost heave hazard than thaw settlement hazard.     

Stability of the interphase surface in the freezing of moist ground

It is suggested that the formation of ice layers should be regarded as a consequence of a loss of stability of the motion of the freezing front. The kinetics of the freezing process is investigated and a stability criterion is obtained.Notation s(t) coordinate of the moving front - L length of the specimen - k moisture conductivity - W moisture content - heat of phase transition - W_H amount of unfrozen water - q flow of moisture from the melted zone into the frozen zone - v velocity of motion of the front - T_i temperature - Q_i heat flux - _i thermal conductivity - a_i thermal diffusivity (i=1 is the frozen zone and i=2 is the melted zone) - mass transfer coefficient - T_H the initial temperature Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 39, No. 1, pp. 96–101, July, 1980.     

Numerical study on the effect of frost heave prevention with different canal lining structures in seasonally frozen ground regions

Frost heave damage problems in canal linings are a common phenomenon in seasonally frozen ground regions. These problems are regarded as interactions between heat transport and moisture flow processes. To research the influence of frost heave prevention in two types of canal structures in the Ningxia irrigation district of China, a two-dimensional coupled heat transport and moisture flow model was used to analyze temperature characteristics in the traditional canal lining structure and a new type of canal lining structure for frost heave prevention. The simulated results from this numerical model are in agreement with in situ temperature measurements for both canal lining structures. The in situ measurement results show that the new canal lining structure exhibits low seepage, low thermal conductivity, quick drainage speed and less uneven deformation. Therefore, this new canal lining structure is a good choice for frost heave prevention in seasonally frozen ground regions.     

Frost heave and water uptake rates in silty soil subject to variable water table height during freezing

Given a frost-susceptible soil and a sufficiently cold environment, the availability of water is the most influential factor controlling frost heave in pavement structures. In particular, the depth of the water table below the freezing front determines to a large degree the availability of new water that can be imbibed by freezing pavement layers. This research investigated the effect of water table height on the laboratory frost heave behavior of an undisturbed silty soil typical of frost-susceptible pavement subgrades within the jurisdiction of the Swedish National Road Administration. The tested specimen was 590 mm in height, and the water table was varied between 150 and 300 mm above the bottom of the specimen. A test was also conducted in the absence of a water table. The frost penetration rate was maintained at 1.1 mm/hr throughout the testing to facilitate a similar rate of heat extraction for each frost heave test, and the same depth section of the specimen was analyzed for each test. The test results show consistent and measurable reductions in frost heave and water uptake rates with decreasing water table height. However, the frost heave rate declined more slowly than the water uptake rate, leading to increasing ratios of volumetric frost heave to volumetric water uptake. This observation is explained by the intrusion of increasing amounts of air into the frozen zone during tests utilizing lower water tables.     

A two-dimensional frost-heave model for buried pipelines

The rigid-ice model of frost heave is one of the most comprehensive frost-heave models but is restricted to one-dimensional cases in its present form. In this paper, the model is extended to two-dimensional problems. The complete formulation of the partial differential equations governing heat, moisture and ice transport in freezing soils is provided. The equations are subsequently solved using the Galerkin finite element method in space and the finite difference method in time. A computer program is developed for the two-dimensional rigid-ice model. A case of freezing around chilled gas pipeline is solved and the numerical results are compared with experimental values, with good agreement between the two sets of results.     

Numerical analysis of coupled water,heat and stress in saturated freezing soil

Clapeyron equation can be applied in freezing soil to describe the relationship among temperature, water pressure and ice pressure when ice and water coexist in phase equilibrium. The mathematical deduction shows that the driving force that makes the unfrozen water in soil moves from high temperature area to low temperature area is determined by gravity, temperature and pore pressure. Upon proposing the concept of separating void ratio as a judge criterion for the formation of ice lenses, adjusting the hydraulic conductivity to describe the unfrozen water gathering at the front of ice lenses and the growth of ice lens, a mathematical model of coupled water, heat and stress is established. A typical process of coupled water, heat and stress that happens in a saturated freezing soil column is simulated by COMSOL Multiphysics simulation software. The amount of frost heave is calculated, and the result of simulation gives the distribution bar graph of ice lenses and distribution curves of temperature, equivalent water content and pore pressure, and shows how they change.     

Distribution of the phase front in the freezing of finely-dispersed soils

The process of the freezing of soils is examined with allowance for the migration of moisture in the freezing and thaw zones.Notation , x time and space coordinates - t, W, L dimensionless values of temperature, moisture content, and ice content - c,a, D volumetric heat capacity, diffusivity, and diffusion of moisture - density of the skeleton - W_e equilibrium value of moisture content - enthalpy of phase transformations - _* characteristic time - , gw, , dimensionless values of temperature, moisture content, ice content, and diffusion coefficient of the moisture - Fo Fourier criterion - Ste Stefan number - n empirical constant Indices 0, 1, and 2 pertain to the initial and boundary states Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 56, No. 5, pp. 805–810, May, 1989.     

Sensitivity of a frost heave model to the method of numerical simulation

A unifying numerical method is developed for solution of frost heave in a vertical freezing column of soil. Within one general computer code a single unifying parameter can be preselected to employ the commonly used Galerkin finite element, subdomain weighted residual, or finite difference methods as well as several other methods developed from the Alternation Theorem. Comparing results from the various numerical techniques in the computation of frost heave to measured frost heave in a laboratory column indicates there is little advantage of one numerical technique over another. One numerical technique, the subdomain method, was used to investigate discretization errors. The model is relatively insensitive to spatial discretization but is significantly sensitive to temporal discretization. The primary reason for this is that an updating procedure, rather than a more accurate iterative procedure, is used to evaluate nonlinear parameters that arise in the moisture transport and heat transport equations.     

Direct contact ultrasound assisted freezing of mushroom (Agaricus bisporus): Growth and size distribution of ice crystals

To reduce the size of ice crystals in mushroom (Agaricus bisporus) contact ultrasound (300 W, 20 kHz) was applied during freezing and frozen storage. Stereomicroscopy was used to observe the ice crystal morphology, and DSC and NMR spectroscopy were performed to evaluate the water states in the samples. Results indicated that ultrasound irradiation initiated the nucleation of ice and reduced the mean size of ice crystals during freezing and frozen storage, and therefore improved the frozen product quality compared to the control samples. Most of the ice crystals in the ultrasound assisted frozen (UAF) samples were in the size range of 0–80 microns while that for the control samples were in the size range of 50–180 microns. SEM photos also proved that due to the application of ultrasound, the sizes of the ice crystals was reduced. This micro-scale information on the documentation of ice crystals will assist in understanding the ice crystal growth phenomena in an ultrasound assisted freezing process.     

Modeling of ice formation in porous solids with regard to the description of frost damage

The freezing and thawing of liquid in porous media in connection with the question concerning the frost durability of solid materials is an important subject for discussion in civil engineering. Each construction or body which is in contact with liquid and frozen water is criticized by its resistance to the environment. The durability concerning frost attacks of a building material is affected by its porosity and the pore size distribution. The ice formation is a phenomenon of coupled heat and mass transport in freezing porous media, and is primarily caused by the expansion of ice in connection with hydraulic pressure. The volume increases due to the freezing front inside the porous solid. Taking into account the aforementioned effects in porous materials, a simplified macroscopic model within the framework of the Theory of Porous Media (TPM) for the numerical simulation of initial and boundary value problems of freezing and thawing processes of super saturated porous solids will be presented. The phase change between the ice and the liquid phase is modeled by different real densities of the phases.     

Use of neutron activation analysis for evaluating the efficiency of water treatment to remove heavy metal ions by zone freezing

The efficiency of zone freezing for potable water treatment to remove inorganic impurities was examined. The content of impurities in model solutions before and after zone freezing was evaluated by neutron activation analysis with the formation of ⁵⁶Mn, ^116m In, and ¹⁹⁸Au radionuclides. The zone freezing procedure is the most efficient at low ice front velocities (no greater than 0.15 cm h⁻¹).     

The adsorbed film controversy

Adsorption force fields that (i) decay with distance and (ii) act preferentially on liquid water relative to ice should cause “ordinary” water and ice to behave in a manner often perceived as incompatible with expected behavior, especially when viewed from outside the force field. This illusion, its relationship to freezing temperature and to the mechanism of frost heave, is demonstrated using a simple example in which earth and its gravitational field interact with water and ice.     

A new structure to control frost boiling and frost heave of embankments in cold regions

Frost boiling and frost heave are the main factors that cause road damage in cold regions. A new kind of embankment structure, which consists of geotextile, crushed-rock layer and geomembrane, was designed and investigated both in the laboratory and at the field of Budongquan located at Qinghai–Tibet Plateau. Comparison tests were conducted at the same time. The key of the new structure is the porous crushed-rock layer which has smaller thermal conductivity with function of drainage and blocking of moisture migration induced by freezing. Both the laboratory and field research results show that the frost penetration and thawing depths of the new structural embankment are much smaller than those of the coarse-grained soil embankment. Also, the new embankment structure has lower water content in the upper layer and smaller frost heave and thawing settlement than the latter does. In addition, it has good drainage effect. Water coming from the road surface can be drained away from the embankment through the porous crushed-rock layer. All these states that the new structure consisting of the porous crushed-rock layer is superior in frost damage mitigation to the normal structure used in cold regions.     

The influence of freeze–thaw cycles on the unconfined compressive strength of fiber-reinforced clay

Freeze–thaw cycling is a weathering process that frequently occurs in cold climates. In the freeze state, thermodynamic conditions at temperatures just below 0 °C result in the translocation of water and ice. Consequently, the engineering properties of soils such as permeability, water content, stress–strain behavior, failure strength, elastic modulus, cohesion, and friction angle may be changed. Former studies have been focused on changes in physical and mechanical properties of soil due to freeze–thaw cycles. In this paper, the effect of freeze–thaw cycles on the compressive strength of fiber-reinforced clay is investigated. For this purpose, kaolinite clay reinforced by steel and polypropylene fibers is compacted in a laboratory and exposed to a maximum of 10 closed-system freezing and thawing cycles. The unconfined compressive strength of reinforced and unreinforced specimens is then determined. The results of the study show that for the soil investigated, the increase in the number of freeze–thaw cycles results in the decrease of unconfined compressive strength of clay samples by 20–25%. Moreover, inclusion of fiber in clay samples increases the unconfined compressive strength of soil and decreases the frost heave. Furthermore, the results of the study indicate that fiber addition does not decrease the soil strength against freeze–thaw cycles. Moreover, the study shows that the addition of 3% polypropylene fibers results in the increase of unconfined compressive strength of the soil before and after applying freeze–thaw cycles by 60% to 160% and decrease of frost heave by 70%.     

Effect of hydrophobic surface treatment on freeze-thaw durability of concrete

The effect of surface treatment using silanes on the frost durability is investigated on both laboratory and field specimens in an accelerated laboratory test. Measurements include moisture uptake during the pre-saturation and F-T stages, cumulative mass loss and internal bulk cracking under frost salt/water exposure. It is found silane treatment substantially reduces surface scaling, but cannot prevent bulk moisture uptake or the occurrence of the internal frost damage when concrete is insufficiently air entrained. Salt scaling is dominated by the capillary suction process in the thin surface region under freezing which can be curtailed by the pore lining effect from silanes creating a hydrophobic barrier to the ingress of external liquid. This in turn suppresses ice growth in the surface region, evidenced by the complete elimination of sub-freezing dilation in a length-change measurement of small-scale concrete specimens with surface treatment. However, internal frost damage is controlled by the universal degree of pore saturation which in turn is dependent on the bulk moisture uptake.