Method for quantifying pre-melting liquid phase fraction of salinized soil in cold region based on multi-mechanism pre-melting theory

Abstract

The invention discloses a method for quantifying a pre-melting liquid phase fraction of salinized soil in a cold region based on a multi-mechanism pre-melting theory. The method comprises the following steps: step 1, correcting a plane pre-melting model and deriving a curvature-related supercooling degree equation; 2, establishing an improved soil particle accumulation model based on a random accumulation theory; 3, quantifying the contribution of a porous matrix interface pre-melting mechanism to the liquid phase fraction; 4, quantifying the contribution of a grain boundary pre-melting mechanism to the liquid phase fraction; 5, quantifying the contribution of a curvature-induced pre-melting mechanism to the liquid phase fraction; 6, determining the total pre-melting liquid phase fraction; and 7, determining solute concentration correction. On the basis of a pre-melting theory, a quantitative model coupling interface pre-melting, grain boundary pre-melting and curvature pre-melting is constructed by combining a particle accumulation mode, a solute segregation effect and an interface force balance mechanism. The method is clear in physical mechanism and definite in physical significance, and can provide a theoretical basis for hydrothermal coupling transport numerical simulation in the freezing and thawing process of the salinized soil in the cold region.

Description

Technical Field

[0001] This invention relates to a method for quantifying the pre-melted liquid phase fraction of cold-region saline soil, specifically a method for quantifying the pre-melted liquid phase fraction of cold-region saline soil based on a multi-mechanism pre-melting theory. Background Technology

[0002] With global warming and the advancement of cold-region engineering projects, a large amount of infrastructure is being built in permafrost areas. The behavior of permafrost when temperatures cross the phase transition point directly determines the stability and safety of these projects. In the initial stage of thawing, permafrost does not undergo a global phase transition. Instead, a quasi-liquid water film at the nanometer to micrometer scale first forms at high curvature locations such as the interface between soil particles and ice, grain boundaries between ice crystals, and sharp corners of pores. This process is called pre-thawing. The proportion of the total volume of quasi-liquid water formed in this stage to the total volume of the medium, i.e., the "pre-thawing liquid phase fraction," is a key initial physical quantity controlling the thermal conductivity, permeability, mechanical strength, and solute transport initiation of permafrost near the phase transition critical point. It is crucial for accurately predicting the thermo-hydraulic-mechanical response of permafrost engineering projects.

[0003] However, existing inventions on the phase change process of permafrost mostly focus on the empirical relationship between macroscopic unfrozen water content and temperature, or only theoretically explore a single pre-melting mechanism under ideal flat interfaces. These methods fail to deeply reveal the microscopic physical landscape of real soil, a complex porous medium, in the initial stage of thawing. Specifically, existing technologies have the following shortcomings: First, they lack a physical description framework for the actual particle packing patterns of soil (from loose to compacted states), making it difficult to construct a geometric model corresponding to the actual pore structure; second, they fail to systematically integrate multiple physical mechanisms such as interface pre-melting, grain boundary pre-melting, and curvature-induced pre-melting (including multiple forms such as particle contact points and grain boundary intersections), and quantitatively calculate their synergistic contribution to the total liquid phase fraction; third, when dealing with saline soils, they do not fully consider the key coupling effect of solute enrichment in the pre-melting layer and its reaction on the pre-melting process. Due to these shortcomings, there is currently a lack of a general method based on rigorous physical principles that can accurately quantify the pre-melted liquid phase fraction of complex cold-region saline soils.

[0004] This invention aims to solve the aforementioned problems. Specifically, it describes the soil microstructure based on an improved random close-packed model, systematically couples multi-mechanism pre-melting theories, and introduces dynamic correction for solute concentration, ultimately establishing a physical model capable of accurately quantifying the pre-melting liquid phase fraction of saline soils in cold regions. This invention will help accurately characterize the physical state of the initial stage of permafrost thawing, providing key theoretical parameters and physical foundations for numerical simulation of engineering in cold regions. Summary of the Invention

[0005] To address the aforementioned issues, this invention discloses a method for quantifying the pre-melted liquid phase fraction of cold-region saline soil based on a multi-mechanism pre-melting theory. Compared to other measurement methods, the method described in this invention is simple to calculate, and the physical meaning of each parameter is clear and easy to obtain.

[0006] The objective of this invention is achieved through the following technical solution:

[0007] A method for quantifying the pre-melted liquid phase fraction of cold-region saline soils based on multi-mechanism pre-melting theory includes the following steps:

[0008] Step 1: Modify the planar pre-melting model and derive the curvature-related undercooling equation;

[0009] Step 1 includes the following sub-steps:

[0010] a. To introduce pre-melting theory into the thawing process of freeze-thaw cycles in cold-region saline soils, the planar pre-melting model was modified, taking into account the curvature of the ice-water interface in the actual soil-water environment, and assuming that the ice crystal has a radius of... By considering the spherical shape, we obtain the expression for supercooling.

[0011] (1)

[0012] In the formula, The radius of curvature of the ice-water interface; The molar density of ice crystals, and The relationship is ; These represent the number of moles of solids, liquids, and impurities in the entire system, respectively. The free energy at the ice-water interface; To balance the melting temperature; The latent heat of phase transition of water molecules is approximately 6.01 kJ / mol under standard conditions. Here, denoted by Hamaker's constant, represents the interaction between the particle surface and the liquid caused by short-range van der Waals forces. This refers to the thickness of the pre-melt layer; It is a relative gas constant; It is the surface charge density; For electron charge, ; The vacuum permittivity, ; is the relative permittivity of the solvent; the relative permittivity of water is approximately 80 at room temperature. The Debye length of a monovalent ion. The unit is 1 / m.

[0013] Step 2: Establish an improved soil particle packing model based on the theory of random close packing;

[0014] Step 2 includes the following sub-steps:

[0015] a. Reasonably considering particle packing patterns is crucial for calculating the pre-melted ice liquid phase fraction in soil systems. Two limiting packing patterns are typically considered: the theoretical limits of the loosest packing (SC: Simple Cubic Mound) and the most compact packing (TH: Tetrahedral Mound) of random close packing (RCP). These two packing models are used to determine the maximum and minimum liquid phase volume fractions (the proportion of quasi-liquid water in the interstitial volume). The spherical packing fractions for the two packing patterns are respectively... and The average coordination numbers are respectively and .

[0016] b. Determine the density It is used to reflect the density of a material.

[0017]

[0018] In the formula, For density, It refers to the volume of the solid portion of a material. Total volume. Porosity. Porosity .

[0019] c. Determine the relative density , which is the ratio of the two extreme stacking methods, is used to characterize the looseness of the soil.

[0020] (3)

[0021] In the formula, Density. Porosity is determined based on actual soil conditions. The range of values ​​is To obtain density , .

[0022] d. Determine the number of particles within the loosely packed unit:

[0023] (4)

[0024] In the formula, This refers to the equivalent particle size of soil particles.

[0025] e. Determine the number of particles within a closely packed unit.

[0026] (5)

[0027] In the formula, This refers to the equivalent particle size of soil particles.

[0028] Step 3: Quantify the contribution of the porous matrix interface pre-melting mechanism to the liquid phase fraction;

[0029] Step 3 includes the following sub-steps:

[0030] a. When quantifying the impact of interface pre-melting, consider that the pre-melting layer thickness is much smaller than the matrix particle radius ( ), at this time the Hamaker constant It relates to the matrix material, namely the ice-pre-melted layer-matrix layered system, and uses the corresponding surface charge density. Determine the liquid phase fraction under pre-melting conditions at the interface. :

[0031] (6)

[0032] In the formula, The surface area of ​​matrix particles per unit volume. The fraction representing the stacking of spheres.

[0033] b. Determine the surface area of ​​loosely packed soil per unit volume:

[0034] (7)

[0035] c. Corresponding liquid fraction:

[0036] (8)

[0037] d. Determine the layer area of ​​a compacted soil layer per unit volume:

[0038] (9)

[0039] e. Corresponding liquid fraction:

[0040] (10)

[0041] f. Considering the influence of interfacial pre-melting in actual soil deposition patterns, the expression for the liquid phase fraction is as follows:

[0042]

[0043] (11)

[0044] In the formula, As the shape factor, when the soil particles are perfectly spherical, .

[0045] Step 4: Quantify the contribution of grain boundary pre-melting mechanism to liquid phase fraction;

[0046] Step 4 includes the following sub-steps:

[0047] a. The second contribution to the liquid phase fraction comes from grain-boundary premelting between ice grains. This process involves an ice-premelted layer-ice structure, and its interactions are governed by the grain boundary Hamaker constant. and interface charge density Characterization.

[0048] b. Determine the grain boundary area for pre-melting in simple cubic packing (SC) grain boundaries. Each unit cell contains 4 soil particles connected by ice grain boundaries. Each soil particle contributes 3 independent grain boundaries (because adjacent particles share an interface). The grain boundary area is determined by subtracting the particle cross-sectional area from the cross-sectional area of ​​the square throat:

[0049] (12)

[0050] In the formula, For soil particles, Let be the radius of curvature of the ice-water interface.

[0051] c. Determine the grain boundary area for the pre-fusion of tetrahedral close-packed (TH) grain boundaries. Each unit cell contains 4 soil particles arranged in tetrahedral symmetry, and each particle contributes 8 neck connections (corresponding to grain boundaries). For ease of calculation of the extracted 1 / 6 unit cell model, the total surface area contributed by grain boundaries per unit volume is expressed as:

[0052] (13)

[0053] d. Determine the expression for the liquid phase fraction under the influence of grain boundary pre-melting, taking into account the actual soil deposition pattern:

[0054] (14)

[0055] Step 5: Quantify the contribution of curvature-induced pre-melting mechanism to liquid phase fraction;

[0056] Step 5 includes the following sub-steps:

[0057] a. When the curvature of the ice-liquid interface is large (such as near the contact point of soil particles), the curvature effect will significantly increase the proportion of liquid water. In an idealized matrix model, this type of region manifests as the contact point between two adjacent soil particles, forming a locally high curvature interface, which leads to a decrease in melting point (Gibbs-Thomson effect), thereby inducing the formation of pre-melted liquid water.

[0058] b. Determine the radius of curvature of the ice-water interface:

[0059] (15)

[0060] In the formula, The radius of curvature of the ice-water interface; The molar density of the ice crystals; The free energy at the ice-water interface; To balance the melting temperature; The latent heat of phase transition of water molecules is approximately 6.01 kJ / mol under standard conditions.

[0061] c. Determine the expression for the liquid phase fraction at the contact point. According to the capillary-diffusion-deformation (CDF) theory, a liquid water sac will form at the contact point, and its volume can be expressed in the lowest-order approximation as follows: Utilizing the number density of soil particles and coordination number The liquid phase fraction at the contact point is:

[0062] (16)

[0063] d. Another contribution of curvature-induced premelting comes from the liquid channels at the junction of grain boundaries and matrix particles. When the matrix particle size is much smaller than the linear size of the ice crystals (i.e., When the matrix surface is approximately flat, the cross-sectional area of ​​the liquid channel is:

[0064] (17)

[0065] e. Determine the liquid phase fraction under the SC packing configuration. Each soil particle contains one pore and three ice crystal boundaries, and the total edge length of each ice crystal boundary is equal to the length of the soil particle in contact with it.

[0066]

[0067] f. Determine the liquid phase fraction under the TH packing configuration. Each soil particle contains 8 neck connections (each neck involves 3 particle contacts).

[0068] (19)

[0069] g. Determine the liquid phase fraction occupied by the intersection line between grain boundaries and matrix particles in actual soil accumulation:

[0070] (20)

[0071] h. Curvature-induced premelting forms a liquid vein network at the intersection of multiple grain boundaries, and its contribution to the liquid phase fraction needs to be considered separately. Assuming the ice crystals are cubically packed, the cross-sectional area of ​​a single liquid vein is... Vein line density Defined as the total length of the veins within a unit volume.

[0072] i. Determine the vein linear density under SC deposition. In SC deposition, ice crystals form a grain boundary network within the pores, and the veins are distributed along the contact edges of soil particles. Therefore, the linear density is:

[0073]

[0074] j. Determine the vein linear density under the TH deposition mode. In the TH deposition mode, ice crystal boundaries form arc-shaped veins along the tetrahedral neck (near the soil particle contact point), therefore the linear density is:

[0075]

[0076] k. Determine the liquid phase fraction contributed by grain boundary veins:

[0077]

[0078] Step 6: Determine the total premelted liquid fraction;

[0079] Step 6 includes the following sub-steps:

[0080] a. Determine the total liquid fraction :

[0081]

[0082] This equation is implicit, and its nonlinearity stems from the coupling relationship between the pre-melt layer thickness and temperature, as well as the liquid phase fraction. The impurities themselves affect the distribution of impurities, which in turn feeds back into the pre-melting process. Therefore, the influence of impurities needs to be characterized by molar density and areal density.

[0083] Step 7: Determine the solute concentration correction.

[0084] Step 7 includes the following sub-steps:

[0085] a. Determine the solute concentration. For soils containing a single type of soluble salt, the initial water content and salinity are respectively... and The initial mass ratio of salt to water was... At a given temperature Below, solute concentration for:

[0086]

[0087] In the formula, This represents the actual salt content; This represents the actual moisture content.

[0088] b. To address non-ideal solution effects (such as deviations in NaCl solutions at high concentrations), an effective concentration is introduced. :

[0089]

[0090] In the formula, (mol / L) is the effective molar concentration coefficient, when Tend to hour, tending to The solution tends to be ideally diluted.

[0091] c. Assume that the total amount of solute is conserved during the freeze-thaw process:

[0092]

[0093] In the formula, This represents the initial moisture content.

[0094] d. The effective concentration can be expressed as:

[0095]

[0096] e. Determine the effective impurity surface density:

[0097]

[0098] In the formula, The number of ions per solute molecule, for sodium chloride, .

[0099] f. Determine the dynamically corrected liquid fraction. Because ice has an extremely low segregation coefficient for impurities, the pre-melted liquid becomes enriched with impurities during system cooling and diluted during heating. Assuming that impurities are almost entirely contained in the interstitial water liquid fraction (due to the repulsion of impurities by solid ice), the final expression for the liquid fraction is:

[0100]

[0101] The beneficial effects of this invention are:

[0102] This invention, based on the synergistic effect of multiple mechanisms such as interface pre-melting, grain boundary pre-melting, and curvature-induced pre-melting, constructs a physical model capable of systematically quantifying the pre-melted liquid phase fraction in cold-region saline soils during freeze-thaw cycles, and clarifies the calculation method for the quasi-liquid water volume fraction dominated by pre-melting. This method fully considers the actual soil particle packing structure and pore geometry characteristics, and the physical meaning of each parameter is clear and easily obtained through conventional geotechnical tests or property handbooks. The quantitative framework provided by this invention can provide key theoretical parameters and a physical model foundation for accurately predicting the hydrothermal migration and solute transport behavior of cold-region saline soils near the phase transition critical point, demonstrating significant application value. In addition to the above-mentioned objectives, features, and advantages, this invention also has other objectives, features, and advantages. The invention will now be described in further detail with reference to the accompanying drawings. Attached Figure Description

[0103] Figure 1 This is a schematic diagram of the soil particle accumulation method in this invention.

[0104] Figure 2 This is a schematic diagram of interface pre-fusion and grain boundary pre-fusion under different soil particle packing modes in this invention.

[0105] Figure 3 This is a schematic diagram of curvature-induced pre-fusion in this invention.

[0106] Figure 4 This is a particle size distribution curve of the soil sample in this invention.

[0107] Figure 5 This is a schematic diagram illustrating the variation of liquid phase fraction with radius of curvature in this invention.

[0108] Figure 6 This is a schematic diagram illustrating the effect of total liquid fraction on effective impurity surface density for different soil samples under different initial salt contents in this invention.

[0109] Figure 7 This is a graph showing the prediction results of the model in this invention.

[0110] Figure 8 This is a comparison chart of the measured and predicted pre-melting initiation temperatures of the samples in this invention.

[0111] Detailed Implementation Instructions

[0112] A method for quantifying the pre-melted liquid phase fraction of cold-region saline soils based on multi-mechanism pre-melting theory includes the following steps:

[0113] Step 1: Modify the planar pre-melting model and derive the curvature-related undercooling equation;

[0114] Step 1 includes the following sub-steps:

[0115] a. To introduce pre-melting theory into the thawing process of freeze-thaw cycles in cold-region saline soils, the planar pre-melting model was modified, taking into account the curvature of the ice-water interface in the actual soil-water environment, and assuming that the ice crystal has a radius of... By considering the spherical shape, we obtain the expression for supercooling.

[0116] (1)

[0117] In the formula, The radius of curvature of the ice-water interface; The molar density of ice crystals, and The relationship is ; These represent the number of moles of solids, liquids, and impurities in the entire system, respectively. The free energy at the ice-water interface; To balance the melting temperature; The latent heat of phase transition of water molecules is approximately 6.01 kJ / mol under standard conditions. Here, denoted by Hamaker's constant, represents the interaction between the particle surface and the liquid caused by short-range van der Waals forces. This refers to the thickness of the pre-melt layer; It is a relative gas constant; It is the surface charge density; For electron charge, ; The vacuum permittivity, ; is the relative permittivity of the solvent; the relative permittivity of water is approximately 80 at room temperature. The Debye length of a monovalent ion. The unit is 1 / m.

[0118] Step 2: Establish an improved soil particle packing model based on the theory of random close packing;

[0119] Step 2 includes the following sub-steps:

[0120] a. Properly considering particle packing patterns is crucial for calculating the pre-melted ice liquid phase fraction in soil systems. For example... Figure 1 The diagram illustrates the soil particle packing patterns described in this invention. It depicts the theoretical limits of two extreme packing patterns: the loosest packing (SC: Simple Cubic Mound) and the random dense packing (RCP), i.e., the tightest packing (TH: Tetrahedral Mound). These two packing models determine the maximum and minimum liquid phase volume fractions (the proportion of quasi-liquid water in the interstitial volume). The spherical packing fractions for the two packing patterns are respectively... and The average coordination numbers are respectively and .

[0121] b. Determine the density It is used to reflect the density of a material.

[0122]

[0123] In the formula, For density, It refers to the volume of the solid portion of a material. Total volume. Porosity. Porosity .

[0124] c. Determine the relative density , which is the ratio of the two extreme stacking methods, is used to characterize the looseness of the soil.

[0125] (3)

[0126] In the formula, Density. Porosity is determined based on actual soil conditions. The range of values ​​is To obtain density , .

[0127] d. Determine the number of particles within the loosely packed unit:

[0128] (4)

[0129] In the formula, This refers to the equivalent particle size of soil particles.

[0130] e. Determine the number of particles within a closely packed unit.

[0131] (5)

[0132] In the formula, This refers to the equivalent particle size of soil particles.

[0133] Step 3: Quantify the contribution of the porous matrix interface pre-melting mechanism to the liquid phase fraction;

[0134] Step 3 includes the following sub-steps:

[0135] a. When quantifying the impact of interface pre-melting, consider that the pre-melting layer thickness is much smaller than the matrix particle radius ( ), at this time the Hamaker constant It relates to the matrix material, namely the ice-pre-melted layer-matrix layered system, and uses the corresponding surface charge density. Determine the liquid phase fraction under pre-melting conditions at the interface. :

[0136] (6)

[0137] In the formula, The surface area of ​​matrix particles per unit volume. The fraction representing the stacking of spheres.

[0138] b. such as Figure 2 The diagram illustrates the interface pre-fusion under different soil particle packing methods described in this invention. It depicts the interface pre-fusion contact methods under SC and TH packing methods. The surface area per unit soil volume for the loose packing method is determined as follows:

[0139] (7)

[0140] c. Corresponding liquid fraction:

[0141] (8)

[0142] d. Determine the layer area of ​​a compacted soil layer per unit volume:

[0143] (9)

[0144] e. Corresponding liquid fraction:

[0145] (10)

[0146] f. Considering the influence of interfacial pre-melting in actual soil deposition patterns, the expression for the liquid phase fraction is as follows:

[0147]

[0148] (11)

[0149] In the formula, As the shape factor, when the soil particles are perfectly spherical, .

[0150] Step 4: Quantify the contribution of grain boundary pre-melting mechanism to liquid phase fraction;

[0151] Step 4 includes the following sub-steps:

[0152] a. such as Figure 2The diagram illustrates grain-boundary premelting under different soil particle packing configurations described in this invention. It depicts the grain-boundary premelting contact mechanisms under SC and TH packing configurations. The second contribution to the liquid phase fraction originates from grain-boundary premelting between ice grains. This process involves an ice-premelted layer-ice structure, and its interaction is governed by the grain boundary Hamaker constant. and interface charge density Characterization.

[0153] b. Determine the grain boundary area for pre-melting in simple cubic packing (SC) grain boundaries. Each unit cell contains 4 soil particles connected by ice grain boundaries. Each soil particle contributes 3 independent grain boundaries (because adjacent particles share an interface). The grain boundary area is determined by subtracting the particle cross-sectional area from the cross-sectional area of ​​the square throat:

[0154] (12)

[0155] In the formula, For soil particles, Let be the radius of curvature of the ice-water interface.

[0156] c. Determine the grain boundary area for the pre-fusion of tetrahedral close-packed (TH) grain boundaries. Each unit cell contains 4 soil particles arranged in tetrahedral symmetry, and each particle contributes 8 neck connections (corresponding to grain boundaries). For ease of calculation of the extracted 1 / 6 unit cell model, the total surface area contributed by grain boundaries per unit volume is expressed as:

[0157] (13)

[0158] d. Determine the expression for the liquid phase fraction under the influence of grain boundary pre-melting, taking into account the actual soil deposition pattern:

[0159] (14)

[0160] Step 5: Quantify the contribution of curvature-induced pre-melting mechanism to liquid phase fraction;

[0161] Step 5 includes the following sub-steps:

[0162] a. such as Figure 3 The diagram illustrates the curvature-induced pre-melting process described in this invention. It depicts the pre-melted liquid phase fraction caused at the contact point between two matrix spheres. When the curvature of the ice-liquid interface is large (such as near the contact point of soil particles), the curvature effect significantly increases the proportion of liquid water. In an idealized matrix model, this type of region manifests as the contact point between two adjacent soil particles, forming a locally high-curvature interface, leading to a decrease in melting point (Gibbs-Thomson effect), thereby inducing the formation of pre-melted liquid water.

[0163] b. Determine the radius of curvature of the ice-water interface:

[0164] (15)

[0165] In the formula, The radius of curvature of the ice-water interface; The molar density of the ice crystals; The free energy at the ice-water interface; To balance the melting temperature; The latent heat of phase transition of water molecules is approximately 6.01 kJ / mol under standard conditions.

[0166] c. Determine the expression for the liquid phase fraction at the contact point. According to the capillary-diffusion-deformation (CDF) theory, a liquid water sac will form at the contact point, and its volume can be expressed in the lowest-order approximation as follows: Utilizing the number density of soil particles and coordination number The liquid phase fraction at the contact point is:

[0167] (16)

[0168] d. For example Figure 3 The diagram illustrates the curvature-induced pre-melting of the present invention. It depicts the pre-melted liquid phase fraction caused by the intersection of matrix particles and grain boundaries. Another contribution of curvature-induced pre-melting originates from the liquid channels at the intersection of grain boundaries and matrix particles. When the matrix particle size is much smaller than the linear size of ice crystals (i.e.,...),... When the matrix surface is approximately flat, the cross-sectional area of ​​the liquid channel is:

[0169] (17)

[0170] e. Determine the liquid phase fraction under the SC packing configuration. Each soil particle contains one pore and three ice crystal boundaries, and the total edge length of each ice crystal boundary is equal to the length of the soil particle in contact with it.

[0171]

[0172] f. Determine the liquid phase fraction under the TH packing configuration. Each soil particle contains 8 neck connections (each neck involves 3 particle contacts).

[0173] (19)

[0174] g. Determine the liquid phase fraction occupied by the intersection line between grain boundaries and matrix particles in actual soil accumulation:

[0175] (20)

[0176] h. For example Figure 3 The diagram illustrates the curvature-induced pre-melting of this invention. It depicts the pre-melted liquid phase fraction caused by the liquid veins formed after multiple ice crystals come into contact. Curvature-induced pre-melting forms a liquid vein network at the intersection of multiple grain boundaries, and its contribution to the liquid phase fraction needs to be considered separately. Assuming the ice crystals are arranged in a cubic packing, the cross-sectional area of ​​a single liquid vein is... Vein line density Defined as the total length of the veins within a unit volume.

[0177] i. Determine the vein linear density under SC deposition. In SC deposition, ice crystals form a grain boundary network within the pores, and the veins are distributed along the contact edges of soil particles. Therefore, the linear density is:

[0178]

[0179] j. Determine the vein linear density under the TH deposition mode. In the TH deposition mode, ice crystal boundaries form arc-shaped veins along the tetrahedral neck (near the soil particle contact point), therefore the linear density is:

[0180]

[0181] k. Determine the liquid phase fraction contributed by grain boundary veins:

[0182]

[0183] Step 6: Determine the total premelted liquid fraction;

[0184] Step 6 includes the following sub-steps:

[0185] a. Determine the total liquid fraction :

[0186]

[0187] This equation is implicit, and its nonlinearity stems from the coupling relationship between the pre-melt layer thickness and temperature, as well as the liquid phase fraction. The impurities themselves affect the distribution of impurities, which in turn feeds back into the pre-melting process. Therefore, the influence of impurities needs to be characterized by molar density and areal density.

[0188] Step 7: Determine the solute concentration correction.

[0189] Step 7 includes the following sub-steps:

[0190] a. Determine the solute concentration. For soils containing a single type of soluble salt, the initial water content and salinity are respectively... and The initial mass ratio of salt to water was... At a given temperature Below, solute concentration for:

[0191]

[0192] In the formula, This represents the actual salt content; This represents the actual moisture content.

[0193] b. To address non-ideal solution effects (such as deviations in NaCl solutions at high concentrations), an effective concentration is introduced. :

[0194]

[0195] In the formula, (mol / L) is the effective molar concentration coefficient, when Tend to hour, tending to The solution tends to be ideally diluted.

[0196] c. Assume that the total amount of solute is conserved during the freeze-thaw process:

[0197]

[0198] In the formula, This represents the initial moisture content.

[0199] d. The effective concentration can be expressed as:

[0200]

[0201] e. Determine the effective impurity surface density:

[0202]

[0203] In the formula, The number of ions per solute molecule, for sodium chloride, .

[0204] f. Determine the dynamically corrected liquid fraction. Because ice has an extremely low segregation coefficient for impurities, the pre-melted liquid becomes enriched with impurities during system cooling and diluted during heating. Assuming that impurities are almost entirely contained in the interstitial water liquid fraction (due to the repulsion of impurities by solid ice), the final expression for the liquid fraction is:

[0205]

[0206] Verification of pre-melted liquid phase fraction in saline soil:

[0207] This invention indirectly evaluates the accuracy of the pre-melting water volume fraction by combining theoretical derivation and experimental verification: First, based on a pre-melting model with multiple coupled mechanisms, the theoretical pre-melting water volume fraction is calculated. This model integrates key physical processes such as interface pre-fusion, grain boundary pre-fusion, and curvature-induced pre-fusion; it is then converted into effective impurity surface density through a solute segregation model. Then, the theoretical undercooling is solved by combining the undercooling expression (1). Finally, the data was compared and verified with the actual measured data.

[0208] This invention utilizes freeze-thaw experimental data of chloride-treated saline soils from 18 sets of authoritative literature. This dataset covers three typical soil types: sand, silt, and silty clay, and was prepared uniformly under NaCl single-salt conditions. The soil sample porosity ranged from 55.08% to 84.60%, with salt content gradients set at 0.0%, 0.2%, 0.4%, 0.6%, 0.8%, and 1.0%. The above data has been fully measured and verified in previous work, providing a clear and well-defined verification basis for the reliability assessment of this invention. The selected data covers typical working conditions across multiple dimensions, including soil type, saturation, and salt content, demonstrating strong representativeness. Detailed soil sample physical properties are systematically compiled as shown in Table 1, and particle size distribution diagrams are shown below. Figure 4 As shown.

[0209] This invention uses the mean percentage error (MPAE), root mean square error (RMSE), and determination coefficient. Verify the actual predictive performance of the theoretical model:

[0210] (31)

[0211] (32)

[0212] (33)

[0213] In the formula, For measured values, The average of the measured values. These are the model prediction values. The calculation results for the above measurement parameters are shown in Table 2.

[0214] Table 1. Soil sample physical properties and experimental data compilation

[0215]

[0216] Table 2 provides analysis of model prediction errors.

[0217]

[0218] The determination coefficient of the model of this invention The mean square error (RMSE) is approximately 0.9080, the root mean square error (RMSE) is approximately 0.2698K, and the mean percentage error (MPAE) is approximately 0.0900%, demonstrating excellent predictive performance.

[0219] like Figure 2 As shown in (a)-(c), Figure 2 This invention presents schematic diagrams of interface pre-fusion and grain boundary pre-fusion under different soil particle packing configurations. It describes: a) a schematic diagram of soil particle ice-water interface pre-fusion under the loosest contact (SC) packing configuration in the unit model; b) a schematic diagram of soil particle ice-water interface pre-fusion under the tightest contact (TH) packing configuration in both the unit model and the 1 / 6 unit model (extracted for calculation convenience); and c) a grain boundary contact model within the pores of a single spherical soil particle.

[0220] like Figure 3 As shown in (a)-(c), these are schematic diagrams of the curvature-induced pre-fusion described in this invention. They depict: a) a schematic diagram of the contact point between two equal-diameter soil particles and the intersection of matrix particles and grain boundaries; b) a simplified assumption of cubic packing of ice crystals; and c) a schematic diagram of the grain boundary vein model.

[0221] like Figure 4 The figure shows the soil sample particle size distribution curve of the present invention. It describes the selection of the characteristic particle size d50 as the equivalent particle size in this invention.

[0222] like Figure 5 The diagram illustrates the variation of liquid phase fraction with radius of curvature as described in this invention. It depicts the changes in liquid phase fraction with radius of curvature under different mechanisms for three different soil types. It can be seen that for all soil types, the total liquid phase fraction increases significantly but not nonlinearly with increasing radius of curvature. This is especially true in soils with a radius of curvature smaller than approximately [missing information]. The growth in the nanoscale region is particularly rapid, indicating that in regions of extremely high curvature, minute geometric changes can induce the formation of large amounts of liquid water. On the other hand, from the perspective of soil type, the contribution of interfacial pre-fusion is highest in silty clay and lowest in sandy soil, reflecting the enhancing effect of the high specific surface area of ​​clay particles on interfacial pre-fusion. The contributions of grain boundary pre-fusion and grain boundary-matrix interface dissolution are relatively significant in silt and silty clay, consistent with the structural characteristics of higher grain boundary density in fine-grained soils.

[0223] like Figure 6 The diagram illustrates the effect of total liquid fraction on effective impurity surface density for different soil samples under different initial salt contents, as described in this invention. It depicts the effect of different initial salt concentrations. Below, the total liquid phase fraction of the soil during the pre-melting stage With effective impurity surface density The relationship between the changes was observed. In all three soil types, the total liquid fraction decreased with increasing effective impurity surface density, but the rate of decrease (sensitivity) differed significantly. The decrease curve for sandy soil was the flattest, indicating that its liquid fraction was relatively insensitive to changes in impurity concentration. The changes in silt and silty clay were also observed. Follow The levels increased and then decreased sharply, with silty clay showing the largest and fastest decrease. Figure 5 and Figure 6 In the above indirect verification chain of theoretical pre-melted water volume fraction - effective impurity surface density - theoretical supercooling, the inherent consistency and overall trend of the model were preliminarily confirmed.

[0224] like Figure 7 As shown in the diagram, the predicted results of the model described in this invention are analyzed. The predicted temperature data points for the three soil types exhibit different concentration areas. The predicted starting temperature for silty clay is generally relatively low, while the predicted temperature for sandy soil is relatively high, and the predicted value for silt falls between the two. Different samples of the same soil type do not have a single predicted starting temperature value, but rather a range. This dispersion reflects the sample specificity of the same soil type in terms of initial impurity content, which the model responds to by the differences in input parameters (such as initial salinity).

[0225] like Figure 8 As shown in (a), this is a comparison chart of the measured and predicted pre-melting initiation temperatures of the samples described in this invention. It illustrates that the mean absolute error (MAE) of each soil sample is at a low level, and the standard error range is small, further statistically verifying the reliability of the model.

[0226] like Figure 8 As shown in (b), the vast majority of data points are closely distributed on both sides of the baseline, intuitively demonstrating a high degree of agreement between the model's predicted values ​​and the measured values. This proves that the model of this invention can be applied to sodium chloride saline soils with different soil types and salinity levels, and shows good predictive performance.

[0227] In summary, the method for quantifying the pre-melted liquid phase fraction of cold-region saline soil obtained by this invention can effectively predict the pre-melted liquid phase fraction of unsaturated saline soil with different salt contents and different soil types. It is feasible to apply the soil pre-melted liquid phase fraction quantification method of this invention to the actual acquisition of the soil pre-melted liquid phase fraction.

Claims

1. A method for quantifying the pre-melted liquid phase fraction of cold-region saline soil based on multi-mechanism pre-melting theory, characterized in that, The following steps are required: Step 1: Modify the planar pre-melting model and derive the curvature-related undercooling equation; Step 2: Establish an improved soil particle packing model based on the theory of random close packing; Step 3: Quantify the contribution of the porous matrix interface pre-melting mechanism to the liquid phase fraction; Step 4: Quantify the contribution of grain boundary pre-melting mechanism to liquid phase fraction; Step 5: Quantify the contribution of curvature-induced pre-melting mechanism to liquid phase fraction; Step 6: Determine the total premelted liquid fraction; Step 7: Determine the solute concentration correction.

2. The method for quantifying the pre-melted liquid phase fraction of cold-region saline soil based on multi-mechanism pre-melting theory according to claim 1, characterized in that: Step 1 includes: a. To introduce pre-melting theory into the thawing process of freeze-thaw cycles in cold-region saline soils, the planar pre-melting model was modified, taking into account the curvature of the ice-water interface in the actual soil-water environment, and assuming that the ice crystal has a radius of... Given a spherical shape, we obtain the expression for supercooling: (1)； In the formula, Let be the radius of curvature of the ice-water interface; The molar density of ice crystals, and The relationship is ; These represent the number of moles of solids, liquids, and impurities in the entire system, respectively. The free energy at the ice-water interface; To balance the melting temperature; The latent heat of phase transition of water molecules is approximately 6.01 kJ / mol under standard conditions. Here, denoted by Hamaker's constant, represents the interaction between the particle surface and the liquid caused by short-range van der Waals forces. This refers to the thickness of the pre-melt layer; It is a relative gas constant; It is the surface charge density; For electron charge, ; The vacuum permittivity, ; is the relative permittivity of the solvent; the relative permittivity of water is approximately 80 at room temperature. The Debye length of a monovalent ion. The unit is 1 / m.

3. The method for quantifying the pre-melted liquid phase fraction of cold-region saline soil based on multi-mechanism pre-melting theory according to claim 1, characterized in that: Step 2 includes: a. Reasonably considering particle packing patterns is crucial for calculating the pre-melted ice liquid phase fraction in soil systems. Two limiting packing patterns are typically considered: the theoretical limits of the loosest packing (SC: Simple Cubic Mound) and the most compact packing (TH: Tetrahedral Mound) of random close packing (RCP). These two packing models are used to determine the maximum and minimum liquid phase volume fractions (the proportion of quasi-liquid water in the interstitial volume). The spherical packing fractions for the two packing patterns are respectively... and The average coordination numbers are respectively and ; b. Determine the density This is used to reflect the density of the material; ； In the formula, For density, It refers to the volume of the solid portion of a material. Total volume. Porosity Porosity ; c. Determine the relative density This is the ratio of the two extreme stacking methods, used to characterize the looseness of the soil; (3)； In the formula, Density. Porosity is determined based on actual soil conditions. The range of values ​​is To obtain the density , ; d. Determine the number of particles within the loosely packed unit: (4)； In the formula, Equivalent particle size of soil particles; e. Determine the number of particles within a closely packed unit; (5)； In the formula, This refers to the equivalent particle size of soil particles.

4. The method based on the pre-melted liquid phase fraction of saline soil according to claim 1, characterized in that: Step 3 includes: a. When quantifying the impact of interface pre-melting, consider that the pre-melting layer thickness is much smaller than the matrix particle radius ( ), at this time the Hamaker constant It relates to the matrix material, namely the ice-pre-melted layer-matrix layered system, and uses the corresponding surface charge density. Determine the liquid phase fraction under pre-melting conditions at the interface. : (6)； In the formula, The surface area of ​​matrix particles per unit volume. The fraction representing the stacking of spheres. b. Determine the surface area of ​​loosely packed soil per unit volume: (7)； c. Corresponding liquid fraction: (8)； d. Determine the layer area of ​​a compacted soil layer per unit volume: (9)； e. Corresponding liquid fraction: (10)； f. Considering the influence of interfacial pre-melting in actual soil deposition patterns, the expression for the liquid phase fraction is as follows: ； (11)； In the formula, As the shape factor, when the soil particles are perfectly spherical, .

5. The method for quantifying the pre-melted liquid phase fraction of cold-region saline soil based on multi-mechanism pre-melting theory according to claim 1, characterized in that: Step 4 includes: a. The second contribution to the liquid phase fraction comes from grain-boundary premelting between ice grains. This process involves an ice-premelted layer-ice structure, and its interactions are governed by the grain boundary Hamaker constant. and interface charge density Characterization, b. Determine the grain boundary area for pre-melting in simple cubic packing (SC) grain boundaries. Each unit cell contains 4 soil particles connected by ice grain boundaries. Each soil particle contributes 3 independent grain boundaries (because adjacent particles share an interface). The grain boundary area is determined by subtracting the particle cross-sectional area from the cross-sectional area of ​​the square throat: (12)； In the formula, For soil particles, Let be the radius of curvature of the ice-water interface. c. Determine the grain boundary area for the pre-fusion of tetrahedral close-packed (TH) grain boundaries. Each unit cell contains 4 soil particles arranged in tetrahedral symmetry, and each particle contributes 8 neck connections (corresponding to grain boundaries). For ease of calculation of the extracted 1 / 6 unit cell model, the total surface area contributed by grain boundaries per unit volume is expressed as: (13)； d. Determine the expression for the liquid phase fraction under the influence of grain boundary pre-melting, taking into account the actual soil deposition pattern: (14)。 6. The method for quantifying the pre-melted liquid phase fraction of cold-region saline soil based on multi-mechanism pre-melting theory according to claim 1, characterized in that: Step 5 includes: a. When the curvature of the ice-liquid interface is large (such as near the contact point of soil particles), the curvature effect will significantly increase the proportion of liquid water. In an idealized matrix model, this type of region manifests as the contact point between two adjacent soil particles, forming a locally high curvature interface, leading to a decrease in melting point (Gibbs-Thomson effect), thereby inducing the formation of pre-melted liquid water; b. Determine the radius of curvature of the ice-water interface: (15)； In the formula, Let be the radius of curvature of the ice-water interface; The molar density of ice crystals; The free energy at the ice-water interface; To balance the melting temperature; The latent heat of phase transition of water molecules is approximately 6.01 kJ / mol under standard conditions. c. Determine the expression for the liquid phase fraction at the contact point. According to the capillary-diffusion-deformation (CDF) theory, a liquid water sac will form at the contact point, and its volume can be expressed in the lowest-order approximation as follows: Utilizing the number density of soil particles and coordination number The liquid phase fraction at the contact point is: (16)； d. Another contribution of curvature-induced premelting comes from the liquid channels at the junction of grain boundaries and matrix particles. When the matrix particle size is much smaller than the linear size of the ice crystals (i.e., When the matrix surface is approximately flat, the cross-sectional area of ​​the liquid channel is: (17)； e. Determine the liquid phase fraction under SC deposition. Each soil particle contains one pore and three ice crystal boundaries, and the total edge length of each ice crystal boundary is equal to the length of the soil particle in contact with it; ； f. Determine the liquid phase fraction under the TH packing configuration. Each soil particle contains 8 neck connections (each neck involves 3 particle contacts); (19)； g. Determine the liquid phase fraction occupied by the intersection line between grain boundaries and matrix particles in actual soil accumulation: (20)； h. Curvature-induced premelting forms a liquid vein network at the intersection of multiple grain boundaries, and its contribution to the liquid phase fraction needs to be considered separately. Assuming the ice crystals are cubically packed, the cross-sectional area of ​​a single liquid vein is... Vein line density Defined as the total length of the veins per unit volume; i. Determine the vein linear density under SC deposition. In SC deposition, ice crystals form a grain boundary network within the pores, and the veins are distributed along the contact edges of soil particles. Therefore, the linear density is: ； j. Determine the vein linear density under the TH deposition mode. In the TH deposition mode, ice crystal boundaries form arc-shaped veins along the tetrahedral neck (near the soil particle contact point), therefore the linear density is: ； k. Determine the liquid phase fraction contributed by grain boundary veins: 。 7. The method for quantifying the pre-melted liquid phase fraction of cold-region saline soil based on multi-mechanism pre-melting theory according to claim 1, characterized in that: Step 6 includes: a. Determine the total liquid fraction : ； This equation is implicit, and its nonlinearity stems from the coupling relationship between the pre-melt layer thickness and temperature, as well as the liquid phase fraction. The impurities themselves affect the distribution of impurities, which in turn feeds back into the pre-melting process. Therefore, the influence of impurities needs to be characterized by molar density and areal density.

8. The method for quantifying the pre-melted liquid phase fraction of cold-region saline soil based on multi-mechanism pre-melting theory according to claim 1, characterized in that: Step 7 includes: a. Determine the solute concentration. For soils containing a single type of soluble salt, the initial water content and salinity are respectively... and The initial mass ratio of salt to water was... At a given temperature Below, solute concentration for: ； In the formula, This represents the actual salt content. This represents the actual moisture content. b. To address non-ideal solution effects (such as deviations in NaCl solutions at high concentrations), an effective concentration is introduced. : ； In the formula, (mol / L) is the effective molar concentration coefficient, when Tend to hour, tending to The solution tends to be ideally diluted; c. Assume that the total amount of solute is conserved during the freeze-thaw process: ； In the formula, This represents the initial moisture content. d. The effective concentration can be expressed as: ； e. Determine the effective impurity surface density: ； In the formula, The number of ions per solute molecule, for sodium chloride, ; f. Determine the dynamically corrected liquid fraction. Because ice has an extremely low segregation coefficient for impurities, the pre-melted liquid becomes enriched with impurities during system cooling and diluted during heating. Assuming that impurities are almost entirely contained in the interstitial water liquid fraction (due to the repulsion of impurities by solid ice), the final expression for the liquid fraction is: 。

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