Theoretical model of soil freezing permeability coefficient considering ice phase obstruction based on thermodynamic consideration

Abstract

This invention relates to a method for predicting the freezing permeability coefficient of soil based on thermodynamic principles and considering the obstruction of the ice phase, comprising the following steps: (1) Soil thermodynamic calculation to obtain the ice phase volume. (2) Calculation of the hydraulic radius of the frozen soil to obtain the hydraulic radius considering the obstruction of the ice phase. (3) Calculation of the freezing permeability coefficient of the soil sample at different temperatures. This invention is based on thermodynamic theory, considers the obstruction of the ice phase in frozen soil, and establishes a freezing permeability coefficient prediction model. Based on the soil particle size distribution, this invention considers the influence of soil structure on permeability and quantifies the control effect of pore channels on permeability of ice-containing soil at different phase transition temperatures. Considering influencing factors such as particle size distribution, free energy, and void ratio, the influencing factors are clear and have explicit physical meaning, and can be used to calculate and predict the relationship between temperature and permeability coefficient of frozen soil. In summary, this invention can provide a reference for elucidating the permeability mechanism and studying the hydrothermal behavior of water migration and solute transport, deformation, and strength in cold regions.

Description

Technical Field

[0001] This invention relates to the field of geotechnical engineering technology in cold regions, and in particular to a thermodynamic theoretical model based on the permeability coefficient of frozen soil. Background Technology

[0002] The frozen soil permeability coefficient is a crucial parameter characterizing the relationship between temperature and permeability in frozen soil. It is essential for estimating the properties of soil and rock masses in cold regions and forms the basis for analyzing soil moisture transport, solute migration, and water retention in these areas. The frozen soil permeability coefficient has a wide range of applications in both engineering and agriculture. Directly measuring the frozen soil permeability coefficient is extremely time-consuming and labor-intensive; therefore, obtaining it indirectly is a more economical and efficient method. Existing indirect methods are often divided into empirical fitting models and physical concept models. However, empirical fitting models based on experimental data lack sufficient physical meaning, and while physical concept models have sufficient physical meaning, their accuracy is often less than ideal. This can be attributed to the overly idealistic assumptions made by these models regarding the hindering effect of the ice phase, often considering only the hindering factor while neglecting the formation mechanism of the ice phase in the soil system. Therefore, they are insufficient to accurately describe the relationship between temperature and frozen soil permeability coefficient in real soil conditions.

[0003] In summary, given the urgent needs of research development and engineering construction, there is a pressing need to propose a freezing permeability coefficient model with sufficient physical meaning and that can consider the obstruction of the ice phase based on thermodynamics to fill the theoretical gap. In-depth research on the relationship between soil freezing permeability coefficient and temperature will help to further establish a high-precision model and provide a more comprehensive theoretical basis for numerical calculations. Summary of the Invention

[0004] The technical problem to be solved by the present invention is to provide a method for predicting the freezing permeability coefficient by applying thermodynamic theory to consider the ice phase barrier effect in complex soil environments.

[0005] To address the above problems, the soil freezing permeability coefficient prediction method based on thermodynamic principles and considering ice phase resistance, as described in this invention, includes the following steps:

[0006] (1) Perform soil thermodynamic calculations to obtain the ice phase volume;

[0007] (2) Calculate the hydraulic radius of the frozen soil to obtain the hydraulic radius considering the obstruction of the ice phase;

[0008] (3) The freezing permeability coefficient of the soil sample at different temperatures was calculated.

[0009] The Kozeny-Carman equation (KC equation) is commonly used to calculate the permeability coefficient of positively heated soils. The KC equation was first proposed by Kozeny and further developed by Carman as follows:

[0010] (1)

[0011] Where k (m / s) is the freezing permeability coefficient; τ is the tortuosity (dimensionless). ; It is a dimensionless shape constant; e(m) 3 / m 3 SA(m) is the void ratio. 2 / kg) is the specific surface area of ​​the soil; (Pa·s) is the dynamic viscosity of water. The density of water (kg / m³) 3 );

[0012] In the pores of positively heated soil, the flow and infiltration of water can be described by the average hydraulic radius, defined as:

[0013] (2)

[0014] in, (m 2 () is the cross section of the soil through which the flow occurs; (m) is the wetted perimeter; (m) is the actual flow channel length in the soil; (m 3 The total volume of the flow channel can be considered as the total volume of the pores. (m 2 The total surface area of ​​the flow channel can be considered as the surface area of ​​soil particles.

[0015] There is a correlation between the average hydraulic radius and the soil void ratio. The void ratio, expressed by the average hydraulic radius, is:

[0016] (3)

[0017] in, (m 3 () represents the volume of soil particles; (kg) represents soil mass; (kg / m 3 ) is the particle density of the soil;

[0018] Substituting equation (3) into equation (1), we obtain the relationship between the hydraulic radius and the freezing permeability as follows:

[0019] (4)

[0020] Where n is the porosity (m) 3 / m 3 ); Let be the shape constant (dimensionless) for the freezing process, which is a function of temperature. a and b are shape factors describing the ice phase within the pores; (Pa·s) is the dynamic viscosity as a function of temperature during the freezing process. , It refers to the dynamic viscosity of free water at the initial freezing temperature. =0.00175 Pa·s;

[0021] In a frozen state, the formation of ice phase hinders the flow of pore water in the soil, reducing the seepage channels in the pores. The hydraulic radius of the frozen soil is then corrected as follows:

[0022] (5)

[0023] in, (m 3 () is the volume of ice; (m 2 () is the surface area of ​​ice; (kg) represents the mass of soil per unit volume; (kg / m 3 ( ) is the dry density of the soil. ; (kg / m 3 ) is the density of ice;

[0024] The tortuosity of the permafrost has also been corrected to:

[0025]

[0026] (6)

[0027] During the freezing process, large pores freeze before small pores. According to the Gibbs-Thomason equation, the relationship between freezing temperature and soil pore radius can be obtained. The relationship is:

[0028] (7)

[0029] in, (K) represents the freezing temperature; (kJ / kg) represents the latent heat of freezing of ice water; (N / m) represents the interfacial tension between ice and water; This is the initial freezing temperature. =273.15K;

[0030] The logistic growth model was fitted to the particle size distribution data:

[0031] (8)

[0032] in, (m) represents the particle size; For particles smaller than The j-th cumulative quality score; A, B, and C are fitting parameters;

[0033] Based on particle size distribution, each particle size (m) corresponds to a unit cell. The equivalent pore length of the particle stack in each unit cell is determined by the pore complexity. The effect of this is that the change in pore length is uniformly reflected in each particle, and the relationship between the changes is expressed as follows:

[0034] (9)

[0035] (10)

[0036] in, The particle size is The number of soil particles; α is an empirical parameter; (kg) represents the mass of the soil sample, which is considered as the mass of soil that affects the freezing process. (kg / m 3 ) represents soil particle density;

[0037] From equations (18) to (19), we get:

[0038] (11)

[0039] aperture With particle size The relationship is:

[0040] (12)

[0041] Therefore:

[0042] (13)

[0043] surface area of ​​ice The following can be expressed using cylindrical pores:

[0044] (14)

[0045] The specific surface area SA of the medium is estimated as follows:

[0046] (15)

[0047] Among them, SA(m) 2 ·g -1 ) is the specific surface area of ​​the medium; (mm) is the geometric mean diameter of the soil medium:

[0048] (16)

[0049] in, , and The percentages (%) of adhesive, powder, and sand particles in the sample are respectively indicated. , and These represent the geometric mean diameters of clay, silt, and sand particles, respectively, with specific values ​​as follows: =0.001mm, =0.026mm and =1.025mm;

[0050] During the ice-water phase transition, the energy change resulting from the formation of ice and water can be calculated using the thermodynamic expression: The change in free energy of 1 mol of water is:

[0051] (17)

[0052] in It is the enthalpy change of the phase transition during the freezing process; T is the temperature (K); It is the entropy change of the ice-water phase transition;

[0053] During the freezing process, an ice phase is formed in the soil pores. Simultaneously, the formation of ice generates volumetric energy. Surface energy Adsorption energy with soil aqueous solution The changes are as follows:

[0054] (18)

[0055] Change in volume free energy caused by ice formation during freezing It can be represented as:

[0056] (19)

[0057] in and The chemical potential changes of ice and water are compared. and (m 3 / mol) represents the molar volume of ice and water; (Pa) represents water pressure and ice pressure. Equivalent to the matrix suction of frozen soil;

[0058] As the freezing process deepens, the ice's interface expands outwards. The surface energy of ice... for:

[0059] (20)

[0060] in (N / m) represents the interfacial tension between ice and water;

[0061] Based on the surface adhesion and wetting theory in physicochemistry, under the influence of dispersion forces, soil particles are covered with a complete film of bound water during the freezing process. The dispersion force is:

[0062] (twenty one)

[0063] Where h is the thickness of the unfrozen adsorbed water film (m); Hamaker's constant (related to dielectric constant) represents the interaction between the particle surface and the liquid due to short-range van der Waals forces, and in soil applications, ;

[0064] The relationship between the unfrozen adsorbed water film h and temperature is as follows:

[0065] (twenty two)

[0066] The change in adsorption energy of soil particles for water molecules is:

[0067] (twenty three)

[0068] in The initial unfrozen water film thickness is approximately obtained by substituting 273.1499K into equation (21); It refers to the quality of the soil that affects freezing. , For soil quality, M is the soil influence coefficient, which is determined by the residual freezing temperature. =263.15K The upper limit of freezing with soil ice phase, i.e., the initial water content Doing is better than getting. .

[0069] This invention, based on thermodynamic theory and considering the hindering effect of ice phase in permafrost, establishes a model for predicting the permeability coefficient of frozen soil. According to soil particle size distribution, this invention fully considers the influence of soil structure on permeability, and quantifies the controlling effect of pore channels on permeability in ice-containing soil at different phase transition temperatures. It fully considers numerous influencing factors such as particle size distribution, free energy, and void ratio; the influencing factors are clear and have explicit physical meaning, and can be used to calculate and predict the relationship between temperature and permeability coefficient in permafrost. In summary, this invention can provide a reference for elucidating the permeability mechanism and studying the hydrothermal behavior of water migration and solute transport, deformation, and strength in cold regions.

[0070] Compared with the prior art, the present invention has the following advantages:

[0071] 1. This invention, based on thermodynamic theory, considers the influence of the complex ice phase barrier effect on permeability in soil. By taking into account the hydraulic radius corrected for the ice phase, and combining the basic physical properties of soil with its particle size distribution, a permeability coefficient model for frozen soil is established. The final model obtained by this invention has void ratio, particle size distribution, and temperature as input parameters for the frozen soil permeability coefficient.

[0072] 2. This invention can be used to analyze and calculate the relationship between temperature and permeability coefficient of frozen soil, fully considering many influencing factors such as void ratio, particle size distribution, and soil composition. The influencing factors are clear and have explicit physical meaning. Attached Figure Description

[0073] The specific embodiments of the present invention will now be described in detail with reference to the accompanying drawings.

[0074] Figure 1 Schematic diagram of soil ice phase barrier effect

[0075] Figure 2 A diagram showing the conversion relationship between soil particle size distribution and soil pore size distribution.

[0076] Figure 3 A comparison chart of the calculated predicted and measured freezing permeability coefficients.

[0077] Detailed Implementation Instructions

[0078] A method for predicting soil freezing permeability coefficient based on thermodynamic principles and considering ice phase obstruction, the model includes the following steps: [Further details omitted]

[0079] (1) Perform soil thermodynamic calculations to obtain the ice phase volume;

[0080] (2) Calculate the hydraulic radius of the frozen soil to obtain the hydraulic radius considering the obstruction of the ice phase;

[0081] (3) The freezing permeability coefficient of the soil sample at different temperatures was calculated.

[0082] Figure 1 This diagram illustrates the hindering effect of soil ice phase transition, showing the flowable channels in the soil pores before and after the phase change, thus describing the hindering effect of ice phase transition. Figure 2 The conversion diagram between soil particle size distribution and soil pore distribution can generally reflect the pore structure of soil through easily obtainable particle size distribution.

[0083] The Kozeny-Carman equation (KC equation) is commonly used to calculate the permeability coefficient of positively heated soils. The KC equation was first proposed by Kozeny and further developed by Carman as follows:

[0084] (1)

[0085] Where k (m / s) is the freezing permeability coefficient; τ is the tortuosity (dimensionless). ; It is a dimensionless shape constant; e(m) 3 / m 3 SA(m) is the void ratio. 2 / kg) is the specific surface area of ​​the soil; (Pa·s) is the dynamic viscosity of water. The density of water (kg / m³) 3 );

[0086] In the pores of positively heated soil, the flow and infiltration of water can be described by the average hydraulic radius, defined as:

[0087] (2)

[0088] in, (m 2 () is the cross section of the soil through which the flow occurs; (m) is the wetted perimeter; (m) is the actual flow channel length in the soil; (m 3 The total volume of the flow channel can be considered as the total volume of the pores. (m 2 The total surface area of ​​the flow channel can be considered as the surface area of ​​soil particles.

[0089] There is a correlation between the average hydraulic radius and the soil void ratio. The void ratio, expressed by the average hydraulic radius, is:

[0090] (3)

[0091] in, (m 3 () represents the volume of soil particles; (kg) represents soil mass; (kg / m 3 ) is the particle density of the soil;

[0092] Substituting equation (3) into equation (1), we obtain the relationship between the hydraulic radius and the freezing permeability as follows:

[0093] (4)

[0094] Where n is the porosity (m) 3 / m 3 ); Let be the shape constant (dimensionless) for the freezing process, which is a function of temperature. a and b are shape factors describing the ice phase within the pores; (Pa·s) is the dynamic viscosity as a function of temperature during the freezing process. , It refers to the dynamic viscosity of free water at the initial freezing temperature. =0.00175 Pa·s;

[0095] In a frozen state, the formation of ice phase hinders the flow of pore water in the soil, reducing the seepage channels in the pores. The hydraulic radius of the frozen soil is then corrected as follows:

[0096] (5)

[0097] in, (m 3 () is the volume of ice; (m 2 () is the surface area of ​​ice; (kg) represents the mass of soil per unit volume; (kg / m 3 ( ) is the dry density of the soil. ; (kg / m 3 ) is the density of ice;

[0098] The tortuosity of the permafrost has also been corrected to:

[0099]

[0100] (6)

[0101] During the freezing process, large pores freeze before small pores. According to the Gibbs-Thomason equation, the relationship between freezing temperature and soil pore radius can be obtained. The relationship is:

[0102] (7)

[0103] in, (K) represents the freezing temperature; (kJ / kg) represents the latent heat of freezing of ice water; (N / m) represents the interfacial tension between ice and water; This is the initial freezing temperature. =273.15K;

[0104] The logistic growth model was fitted to the particle size distribution data:

[0105] (8)

[0106] in, (m) represents the particle size; For particles smaller than The j-th cumulative quality score; A, B, and C are fitting parameters;

[0107] Based on particle size distribution, each particle size (m) corresponds to a unit cell. The equivalent pore length of the particle stack in each unit cell is determined by the pore complexity. The effect of this is that the change in pore length is uniformly reflected in each particle, and the relationship between the changes is expressed as follows:

[0108] (9)

[0109] (10)

[0110] in, The particle size is The number of soil particles; α is an empirical parameter; (kg) represents the mass of the soil sample, which is considered as the mass of soil that affects the freezing process. (kg / m 3 ) represents soil particle density;

[0111] From equations (18) to (19), we get:

[0112] (11)

[0113] aperture With particle size The relationship is:

[0114] (12)

[0115] Therefore:

[0116] (13)

[0117] surface area of ​​ice The following can be expressed using cylindrical pores:

[0118] (14)

[0119] The specific surface area SA of the medium is estimated as follows:

[0120] (15)

[0121] Among them, SA(m) 2 ·g -1 ) is the specific surface area of ​​the medium; (mm) is the geometric mean diameter of the soil medium:

[0122] (16)

[0123] in, , and The percentages (%) of adhesive, powder, and sand particles in the sample are respectively indicated. , and These represent the geometric mean diameters of clay, silt, and sand particles, respectively, with specific values ​​as follows: =0.001mm, =0.026mm and =1.025mm;

[0124] During the ice-water phase transition, the energy change resulting from the formation of ice and water can be calculated using the thermodynamic expression: The change in free energy of 1 mol of water is:

[0125] (17)

[0126] in It is the enthalpy change of the phase transition during the freezing process; T is the temperature (K); It is the entropy change of the ice-water phase transition;

[0127] During the freezing process, an ice phase is formed in the soil pores. Simultaneously, the formation of ice generates volumetric energy. Surface energy Adsorption energy with soil aqueous solution The changes are related as follows:

[0128] (18)

[0129] Change in volume free energy caused by ice formation during freezing It can be represented as:

[0130] (19)

[0131] in and The chemical potential changes of ice and water are compared. and (m 3 / mol) represents the molar volume of ice and water; (Pa) represents water pressure and ice pressure. Equivalent to the matrix suction of frozen soil;

[0132] As the freezing process deepens, the ice's interface expands outwards. The surface energy of ice... for:

[0133] (20)

[0134] in (N / m) represents the interfacial tension between ice and water;

[0135] Based on the surface adhesion and wetting theory in physicochemistry, under the influence of dispersion forces, soil particles are covered with a complete film of bound water during the freezing process. The dispersion force is:

[0136] (twenty one)

[0137] Where h is the thickness of the unfrozen adsorbed water film (m); Hamaker's constant (related to dielectric constant) represents the interaction between the particle surface and the liquid due to short-range van der Waals forces, and in soil applications, ;

[0138] The relationship between the unfrozen adsorbed water film h and temperature is as follows:

[0139] (twenty two)

[0140] The change in adsorption energy of soil particles for water molecules is:

[0141] (twenty three)

[0142] in The initial unfrozen water film thickness is approximately obtained by substituting 273.1499K into equation (21); It refers to the quality of the soil that affects freezing. , For soil quality, M is the soil influence coefficient, which is determined by the residual freezing temperature. =263.15K The upper limit of freezing with soil ice phase, i.e., the initial water content Doing is better than getting. ;

[0143] Model result validation:

[0144] The data used in this study to verify the freezing permeability coefficient includes four groups of soil samples obtained from experiments conducted by different researchers, including silt, silty loam, and sandy loam. Detailed physical parameters of the soil samples are shown in Table 1. In summary, the data used in this study covers a wide range of operating conditions and is highly representative.

[0145] Table 1. Detailed physical parameters of the four soil samples

[0146] Soil sample type <![CDATA[Dry density ρ d (g / cm 3 )]]> <![CDATA[Void ratio e (m 3 / m 3 )]]> <![CDATA[Porosity n (m 3 / m 3 )]]> <![CDATA[Particle density ρ s (g / cm 3 )]]> powder clay 1.63 1.22 0.55 3.62 silt 1.35 0.96 0.49 2.65 Sandy loam soil 1.66 0.38 0.60 2.65 silty soil 1.86 0.30 0.43 2.65

[0147] The data in the table above encompasses various soil types and is highly representative. Using the prediction method of this invention, the freezing permeability coefficient can be obtained by inputting the sample parameters. As a theoretical model, the calculation results of this invention demonstrate high reliability for samples of different soil types.

[0148] In summary, the calculation method described in this invention not only has wide applicability and clear physical meaning, but also boasts high model accuracy, meeting the prediction requirements for most soil freezing permeability coefficients. Finally, it should be noted that the above embodiments are merely illustrative of the technical solutions of this invention and not intended to limit it. Although the invention has been described in detail with reference to preferred embodiments, those skilled in the art should understand that modifications or equivalent substitutions can be made to the technical solutions of this invention without departing from the spirit and scope of the invention, and all such modifications and substitutions should be covered within the scope of the claims of this invention.

Claims

1. A method for predicting soil freezing permeability coefficient based on thermodynamic principles and considering ice phase resistance. The method includes the following steps: [The method is characterized by] including the following steps: (1) Perform soil thermodynamic calculations to obtain the ice phase volume; (2) Calculate the hydraulic radius of the frozen soil to obtain the hydraulic radius considering the obstruction of the ice phase; (3) The freezing permeability coefficient of the soil sample at different temperatures was calculated.

2. The method for predicting soil freezing permeability coefficient based on thermodynamic principles and considering ice phase resistance as described in claim 1, characterized in that: The Kozeny-Carman equation (KC equation) is commonly used to calculate the permeability coefficient of positively heated soils. The KC equation was first proposed by Kozeny and further developed by Carman as follows: (1) Where k (m / s) is the freezing permeability coefficient; τ is the tortuosity (dimensionless). ; It is a dimensionless shape constant; e(m) 3 / m 3 SA(m) is the void ratio. 2 / kg) is the specific surface area of ​​the soil; (Pa·s) is the dynamic viscosity of water. The density of water (kg / m³) 3 ); In the pores of positively heated soil, the flow and infiltration of water can be described by the average hydraulic radius, defined as: (2) in, (m 2 () is the cross section of the soil through which the flow occurs; (m) is the wetted perimeter; (m) is the actual flow channel length in the soil; (m 3 The total volume of the flow channel can be considered as the total volume of the pores. (m 2 The total surface area of ​​the flow channel can be considered as the surface area of ​​soil particles. There is a correlation between the average hydraulic radius and the soil void ratio. The void ratio, expressed by the average hydraulic radius, is: (3) in, (m 3 () represents the volume of soil particles; (kg) represents soil mass; (kg / m 3 ) is the particle density of the soil; Substituting equation (3) into equation (1), we obtain the relationship between the hydraulic radius and the freezing permeability as follows: (4) Where n is the porosity (m) 3 / m 3 ); Let be the shape constant (dimensionless) for the freezing process, which is a function of temperature. a and b are shape factors describing the ice phase within the pores; (Pa·s) is the dynamic viscosity as a function of temperature during the freezing process. , It refers to the dynamic viscosity of free water at the initial freezing temperature. =0.00175 Pa·s; In a frozen state, the formation of ice phase hinders the flow of pore water in the soil, reducing the seepage channels in the pores. The hydraulic radius of the frozen soil is then corrected as follows: (5) in, (m 3 () is the volume of ice; (m 2 () is the surface area of ​​ice; (kg) represents the mass of soil per unit volume; (kg / m 3 ( ) is the dry density of the soil. ; (kg / m 3 ) is the density of ice; The tortuosity of the permafrost has also been corrected to: (6) During the freezing process, large pores freeze before small pores. According to the Gibbs-Thomason equation, the relationship between freezing temperature and soil pore radius can be obtained. The relationship is: (7) in, (K) represents the freezing temperature; (kJ / kg) represents the latent heat of freezing of ice water; (N / m) represents the interfacial tension between ice and water; This is the initial freezing temperature. =273.15K; The logistic growth model was fitted to the particle size distribution data: (8) in, (m) represents the particle size; For particle size smaller The j-th cumulative quality score; A, B, and C are fitting parameters; Based on particle size distribution, each particle size (m) corresponds to a unit cell. The equivalent pore length of the particle stack in each unit cell is determined by the pore complexity. The effect of this is that the change in pore length is uniformly reflected in each particle, and the relationship between the changes is expressed as follows: (9) (10) in, The particle size is The number of soil particles; α is an empirical parameter; (kg) represents the mass of the soil sample, which is considered as the mass of soil that affects the freezing process. (kg / m 3 () represents soil particle density; From equations (18) to (19), we get: (11) aperture With particle size The relationship is: (12) Therefore: (13) surface area of ​​ice This can be represented by a cylindrical pore as follows: (14) The specific surface area SA of the medium is estimated as follows: (15) Wherein, SA(m) 2 ·g -1 ) is the specific surface area of ​​the medium; (mm) is the geometric mean diameter of the soil medium: (16) in, , and The percentages (%) of adhesive, powder, and sand particles in the sample are respectively. , and These represent the geometric mean diameters of clay, silt, and sand particles, respectively, with specific values ​​as follows: =0.001mm, =0.026mm and =1.025mm; During the ice-water phase transition, the energy change resulting from the formation of ice and water can be calculated using the thermodynamic expression: The change in free energy of 1 mol of water is: (17) in It is the enthalpy change of the phase transition during the freezing process; T is the temperature (K); It is the entropy change during the phase transition of ice and water; During the freezing process, an ice phase is formed in the soil pores. Simultaneously, the formation of ice generates volumetric energy. Surface energy Adsorption energy with soil aqueous solution The changes are as follows: (18) Change in volume free energy caused by ice formation during freezing It can be represented as: (19) in and The chemical potential changes of ice and water are compared. and (m 3 / mol) represents the molar volume of ice and water; (Pa) represents water pressure and ice pressure. Equivalent to the matrix suction of frozen soil; As the freezing process deepens, the ice's interface expands outwards. The surface energy of ice... for: (20) in (N / m) represents the interfacial tension between ice and water; Based on the surface adhesion and wetting theory in physicochemistry, under the influence of dispersion forces, soil particles are covered with a complete film of bound water during the freezing process. The dispersion force is: (21) Where h is the thickness of the unfrozen adsorbed water film (m); Hamaker's constant (related to dielectric constant) represents the interaction between the particle surface and the liquid due to short-range van der Waals forces, and in soil applications, ; The relationship between the unfrozen adsorbed water film h and temperature is as follows: (22) The change in adsorption energy of soil particles for water molecules is: (23) in The initial unfrozen water film thickness is approximately obtained by substituting 273.1499K into equation (21); It refers to the quality of the soil that affects freezing. , For soil quality, M is the soil influence coefficient, which is determined by the residual freezing temperature. =263.15K The upper limit of freezing with soil ice phase, i.e., the initial water content Doing is better than getting. .

3. The method for predicting soil freezing permeability coefficient based on thermodynamic principles and considering ice phase resistance as described in claim 2, characterized in that: Based on the hydraulic radius derived from thermodynamics, the resistance of ice to the infiltration process of frozen soil can be described, and the freezing permeability coefficient at the corresponding temperature can be obtained, thus obtaining a freezing permeability coefficient prediction model.

Images