Unfrozen water model coupling electrolyte solution freezing mechanism and clay electric double layer theory

Abstract

The invention relates to an unfrozen water model coupling an electrolyte solution freezing mechanism and a clay electric double layer theory, which comprises the following steps: S1, collecting a soil sample, and measuring soil humidity and soil specific surface area AS at room temperature; when the clay components in the soil are illite and kaolinite, measuring the specific surface area AS of the soil by using an N2 adsorption method; when the clay component in the soil contains expansive clay, measuring the specific surface area AS of the soil by adopting a liquid adsorption method; taking the measured soil humidity as the initial water content w0; s2, determining a required temperature T; and S3, establishing an unfrozen water content model, and calculating the unfrozen water content wu. The method has the advantages of simple expression, few input parameters, convenience in calculation and deeper theoretical basis.

Description

Technical Field

[0001] The invention relates to the field of natural science and technology in cold and arid regions, and in particular to an unfrozen water model coupling the freezing mechanism of electrolyte solutions and the clay double electrical layer theory. Background Art

[0002] Permafrost around the world is being seriously affected by climate warming, which is manifested in rising ground temperature, melting of permafrost, thickening of active layer and thinning of permafrost thickness (Cheng Guodong, 2019). These changes affect the regional carbon cycle, water cycle, ecology, hydrological environment and the stability of engineering buildings (Wu Qingbai et al., 2021). Frozen soil is defined as a four-phase rock and soil body with a temperature below 0°C and containing ice. A certain amount of unfrozen water is always maintained in frozen soil, which plays a key role in the water, heat and mechanical behavior of the soil (Xu Xiaozu et al., 2010). Therefore, it is of great significance to establish a parameterized model that uses common soil parameters as independent variables and can accurately calculate the unfrozen water content of frozen soil, which is of great significance for simulating regional freeze-thaw cycles and predicting hydrological and ecological processes in frozen soil regions under the background of climate warming.

[0003] Among the physical models used to study the freeze-thaw process of frozen soil, the unfrozen water model is one of the key tools (Niu and Yang, 2006). Although more than 20 unfrozen water models have been developed and some of them have been verified by a large amount of measured data, the formation mechanism of these models and their specific application scope are still not clear enough (Hu et al., 2020). Therefore, researchers often face great challenges when selecting and applying these models. In order to obtain accurate simulation results, it is usually necessary to conduct experiments on the target soil samples before each use to determine the corresponding model parameters (Zhang et al., 2008). In view of this, current research does not lack the number of unfrozen water models, but urgently needs unfrozen water parameterized models whose independent variables are basic soil parameters.

[0004] The unfrozen water content in frozen soil is affected by many factors, including soil texture parameters (such as specific surface area, particle shape, type, content and porosity), electrochemical parameters (such as cation exchange capacity, surface charge density), salt parameters (such as solution composition and concentration), environmental parameters (such as temperature, initial water content) and freeze-thaw history (Xu Xiaozu et al., 2010; Jin et al., 2020). Since soil parameters vary non-uniformly in geographic space, an ideal unfrozen water parameterization model needs to clarify the mechanism of action of each parameter in the freeze-thaw process, so as to ignore parameters with less influence and retain significant parameters. Based on adsorption and capillary action, unfrozen water can be divided into bound water and capillary water. Bound water is a double-layer cation solution on the surface of clay, which is essentially an electrolyte solution (Jin et al., 2023). The double-layer theory can quantitatively calculate the effects of soil texture, salt and electrochemical parameters on the cation concentration on the clay surface, thereby establishing the relationship between these parameters and the unfrozen water content, and is therefore suitable as a parameterization model (Jin et al., 2020). In the research of chemistry and food preservation, scholars have revealed the freezing process of different types of electrolyte solutions through experiments, and analyzed their freezing mechanisms from the perspective of physicochemistry - the difference between hydrogen bonds and ionic bonds (Chen and Steven, 1987; Haghighi et al., 2008; Kim et al., 2008). Although the bound water on the surface of clay particles is essentially an electrolyte solution, existing studies have not yet fully clarified the difference and connection between electrolyte solutions and bound water in the freezing mechanism (Jin et al., 2020). Therefore, it is expected to couple the freezing mechanism of electrolyte solutions to the study of unfrozen water to clarify the freezing characteristics of unfrozen water on the clay surface and provide a physicochemical basis for understanding the freezing mechanism of unfrozen water. Summary of the invention

[0005] The technical problem to be solved by the present invention is to provide an unfrozen water model of coupled electrolyte solution freezing mechanism and clay double layer theory with simple expression, few input parameters and convenient calculation.

[0006] To solve the above problems, the unfrozen water model of the coupled electrolyte solution freezing mechanism and clay double layer theory described in the present invention comprises the following steps:

[0007] S1 collects soil samples and measures soil moisture and soil specific surface area A at room temperature S ;

[0008] When the clay components in the soil are illite and kaolinite, the specific surface area A of the soil is measured using the N2 adsorption method. S ; When the clay component in the soil contains swelling clay, the soil specific surface area A is measured by liquid adsorption method S ;

[0009] The measured soil moisture is taken as the initial water content w0;

[0010] S2 determines the required temperature T;

[0011] S3 establishes the following unfrozen water content model and calculates the unfrozen water content w u :

[0012] w u =w m +Cexp(C0(-T) -b )-D w0≤w bmax ,T≤T d

[0013] w m =ρ bw A S δ×10 -2 =0.03A S ; C = ρ w A s ×10 -2 =0.01A S ; D = ρ w cA s ×10 -2 =0.06A s ;

[0014] w bmax =w m +w wbmax =δρ bw A S 10 -2 +dρ w A S 10 -2 =0.2625A S

[0015] Where: C, D are double layer parameters; a = 2.192, b = -0.14, c = 5.98, T d =-0.263℃,K c =12.5,ρ bw =1.2g / cm 3 , w =1g / cm 3 ; C0=aK c b =3.12; w u , w m , w wbmax and w bmax All are mass moisture content, in %; T, T d Negative temperature.

[0016] The S1 soil is non-saline soil.

[0017] The clay content of the soil is less than 18%, and its specific surface area A S 60.5~6.22g / cm 3 between.

[0018] The T in S2 is between -0.26°C and -20°C.

[0019] Compared with the prior art, the present invention has the following advantages:

[0020] 1. The present invention has a strong theoretical basis. The model combines the freezing mechanism of electrolyte solution and clay double layer theory to improve the freezing mechanism of bound water.

[0021] 2. Through theoretical deduction, the present invention simplifies the final input parameters into the input parameters of temperature (T), specific surface area (A S ), initial water content and double layer parameters (C, D) whose independent variables are specific surface area. Therefore, the expression of the present invention is simple, the input parameters are few (three), the calculation is convenient and has a deep theoretical basis.

[0022] 3. The test using the measured unfrozen water data showed that the model of the present invention can accurately simulate the changes of the unfrozen water content in clay, silt and sand with temperature and initial water content. BRIEF DESCRIPTION OF THE DRAWINGS

[0023] The specific implementation modes of the present invention are further described in detail below in conjunction with the accompanying drawings.

[0024] Figure 1 The present invention shows the location and microstructure of bound water and capillary water in the soil. Among them: a is the microscopic double electric layer structure of bound water; b is the location of bound water and capillary water in the soil; c is the microstructure of surface tension; the cation solution concentration curve is the curve of the change of the cation solution concentration in the diffusion layer with the surface distance; the weakly bound water freezing characteristic curve is the curve of the change of the freezing point of the diffusion layer solution with the surface distance.

[0025] Figure 2 The freezing point of the electrolyte solution changes with concentration (the data in the figure are from the literature Haghighi et al., 2012).

[0026] Figure 3 Schematic diagram of the freezing mechanism of bound water on the surface of clay particles. Where: δ is the thickness of the adsorption layer, d is the thickness of the diffusion layer, x is the surface distance; w m is the content of adsorption layer solution; w wbmax The total weakly bound water content is equal to the diffusion layer solution content; w bmax is the total bound water content, which is the sum of the content of the adsorption layer and the diffusion layer solution; As The specific surface area is equal to the bound water film area; the concentration and freezing point of the diffusion layer cation solution both change with the surface distance.

[0027] Figure 4 It is the concentration curve of the diffusion layer cation solution based on the electric double layer theory (Eq.5) and the fitting expression (Eq.6) of the present invention.

[0028] Figure 5 The figure is a comparison between the parameterized model results of the present invention and the measured data of unfrozen water in frozen soil. DETAILED DESCRIPTION

[0029] The unfrozen water model that couples the freezing mechanism of electrolyte solutions and the clay double layer theory includes the following steps:

[0030] S1 collects soil samples and measures soil moisture and soil specific surface area A at room temperature (20°C) S ;

[0031] When the clay components in the soil are illite and kaolinite, the specific surface area A of the soil is measured using the N2 adsorption method. S When the clay component in the soil contains swelling clay (such as montmorillonite), the liquid adsorption method is used to measure the soil specific surface area A. S ;

[0032] The measured soil moisture is taken as the initial moisture content w0.

[0033] The soil is non-saline soil. The clay content in the soil is less than 18%, and its specific surface area A S 60.5~6.22g / cm 3 between.

[0034] S2 determines the required temperature T, which is between -0.26°C and -20°C.

[0035] S3 establishes the following unfrozen water content model and calculates the unfrozen water content w u :

[0036] w u =w m +Cexp(C0(-T) -b )-D w0≤w bmax ,T≤T d

[0037] w m =ρ bw A S δ×10 -2 =0.03A S ; C = ρ w A s ×10 -2=0.01A S ; D = ρ w cA s ×10 -2 =0.06A s ;

[0038] w bmax =w m +w wbmax =δρ bw A S 10 -2 +dρ w A S 10 -2 =0.2625A S

[0039] Where: C, D are double layer parameters; a = 2.192, b = -0.14, c = 5.98, T d =-0.263℃,K c =12.5,ρ bw =1.2g / cm 3 , w =1g / cm 3 ; C0=aK c b =3.12; w u , w m , w wbmax and w bmax All are mass moisture content, in %; T, T d Negative temperature.

[0040] The specific process is as follows:

[0041] ⑴ The formation mechanism and occurrence form of bound water and capillary water in soil:

[0042] Bound water in soil is a double-layer cationic solution on the surface of clay particles, while capillary water is liquid water in the form of a meniscus due to surface tension and exists between soil pores (Chai et al., 2018; Jin et al., 2023)( Figure 1 b) According to the different forces, the cationic solution can be further divided into an adsorption layer (also known as the Stern layer) and a diffusion layer (also known as the Gouy layer) ( Figure 1a). The adsorption layer is a cationic solution tightly bound to the surface of clay particles. The adsorption force on this layer is the combined force of van der Waals force, valence force and electrostatic force. Therefore, it will not freeze at extremely low temperatures (below -20°C) and is called residual unfrozen water (Jin et al., 2020). The diffusion layer is a loosely distributed cationic solution, which is mainly affected by the electrostatic force of the negative charge on the surface of clay particles. As the distance from the surface increases, the cation concentration in the diffusion layer decreases exponentially ( Figure 1 a), and the content of the diffusion layer solution is significantly higher than that of the adsorption layer (Jin et al., 2020). The surface tension of capillary water originates from the hydrogen bonding force between water molecules (Drewmyers, 2005). On the meniscus, the hydrogen bonds between water molecules form a certain angle, and their combined force constitutes the surface tension pointing to the center of the meniscus ( Figure 1 c). The smaller the radius of the meniscus, the greater the curvature, and the lower the freezing point of capillary water (Chai et al., 2018). In general, bound water and capillary water have completely different formation mechanisms, storage forms, and freezing mechanisms.

[0043] ⑵The difference and connection between combined water and electrolyte solution:

[0044] From the above analysis, it can be seen that bound water is essentially an electrolyte solution. The freezing point of the electrolyte solution is lower than 0°C, and the higher the concentration, the lower the freezing point (Chen Meiting et al., 2019). In the solution, the electrolyte exists in the form of anions and cations, and forms hydrated ions with water molecules. The strength of the ionic bond between the ions and water molecules in the hydrated ions is greater than the hydrogen bond between the water molecules (Israelchivili, 2014). Since the ice-water phase transition is essentially the breaking and reorganization of the hydrogen bonds between water molecules, the difference in the strength of ionic bonds and hydrogen bonds makes it difficult for water molecules to leave the ions to form ice crystals. This is why the concentration of the electrolyte solution is lower than 0°C, and the higher the concentration, the lower the freezing point (Zavitsas and Andreas, 2001).

[0045] The difference between bound water and electrolyte solution is:

[0046] Ionic composition: Bound water is a cationic solution on the surface of clay particles, while electrolyte solutions contain both cations and anions.

[0047] Concentration distribution: The cation concentration in bound water decays exponentially with increasing distance from the clay particle surface, indicating that there is osmotic pressure in bound water. However, the concentration of the electrolyte solution in the container is usually uniform, so there is no osmotic pressure.

[0048] Freezing point range: The freezing point range of bound water is between 0℃ and -20℃. When the temperature is below -20℃, the bound water content changes almost unchanged with temperature. In contrast, the freezing point of the electrolyte solution continues to decrease with the increase of concentration, and its minimum freezing point is far below -20℃.

[0049] In summary, the present invention believes that bound water and electrolyte solution have the same freezing mechanism, so the freezing point depression equation of electrolyte solution can be used to describe the freezing process of bound water (Chen Meiting et al., 2019):

[0050] T=-K c ·n (1)

[0051] Where, T (℃) is the freezing point of the electrolyte solution, n (mol / L) is the molar concentration of the electrolyte solution, (K c ) is the freezing point depression coefficient. Although the freezing point depression coefficient varies with the type of solvent and the concentration of the solution, when the electrolyte solution concentration is low or it is a mixed solution, K c Approximately a constant.

[0052] The variation of freezing point of electrolyte solution with concentration is also called freezing characteristic of electrolyte solution. It is an important component of the microscopic freezing characteristic curve of combined water and is used to calculate the variation of freezing point of diffusion layer cation solution with solution concentration. In electrolyte solution, there are significant differences in the hydration interactions between anions, cations and water molecules. Some anions (such as chloride and bromide) interact weakly with water and are considered to have a "weak negative hydration effect". Nuclear magnetic resonance experiments have found that the residence time of water molecules around chloride ions is similar to their residence time in the solvent, resulting in the hydration effect of chloride ions being considered to be zero. Therefore, the interaction between chloride ions and water is significantly weaker than that of alkali metal ions (such as sodium and potassium ions), and its freezing point depression coefficient is mainly determined by cations (Ge et al., 2013). Figure 2 The freezing process of sodium chloride, potassium chloride solutions and their mixed solutions is demonstrated. Between 0°C and -20°C, the relationship between the freezing point and concentration of sodium chloride and potassium chloride solutions is approximately linear, and the freezing point depression coefficient can be regarded as a constant. For the mixed solution of sodium chloride and potassium chloride, the freezing point depression coefficient is much higher than that of the individual sodium chloride and potassium chloride solutions, and increases sharply with the proportion of potassium chloride. Since the interaction between chloride ions and water is significantly weaker than that between sodium ions and potassium ions, the freezing point depression coefficients of sodium chloride, potassium chloride and their mixed solutions are approximately equal to the freezing point depression coefficients of sodium ions, potassium ions and sodium-potassium mixed cation solutions. The bound water in the soil is mainly a mixed cation solution composed of sodium, potassium, magnesium and calcium ions. Based on Figure 2 The freezing characteristics of sodium-potassium mixed solutions indicate that the freezing point depression coefficient of bound water is relatively high and can be regarded as a constant.

[0053] ⑶Derivation of unfrozen water model:

[0054] Bound water consists of adsorption layer solution and diffusion layer solution. Since the adsorption layer solution is residual unfrozen water at extremely low temperatures, its content hardly decreases with temperature drop, so the freezing process mainly occurs in the diffusion layer. Unfrozen bound water content (wu ) is equal to the total adsorption layer solution (w m ) and the unfrozen diffusion layer solution (w wb ) and (such as Figure 3 shown):

[0055] w u =w m +w wb (2)

[0056] The solution content in the adsorption layer is equal to the product of the thickness of the adsorption layer and the area of ​​the water film in the adsorption layer. In nature, common clay particles (montmorillonite, illite, kaolinite) are all flat sheets, so the area of ​​the water film in the adsorption layer on the surface of the clay particles is equal to the specific surface area of ​​the clay. m ) can be expressed as the product of specific surface area and adsorption layer thickness (Jin et al., 2020):

[0057] w m =A s δρ bw (%) (3)

[0058] Among them, ρ bw (g / cm 3 ) is the density of the adsorption layer solution, A S is the specific surface area, which depends on the type and content of clay minerals, and δ is the thickness of the adsorption layer.

[0059] When the soil temperature is T, the bound water with a freezing point above T changes to ice, and the bound water with a freezing point below T is unfrozen water. The surface distance (x) corresponding to the freezing point T is equal to the thickness of the unfrozen diffusion layer water film ( Figure 3 ). Therefore, the unfrozen diffusion layer cation solution content (w wb ) is equal to the product of the specific surface area and the surface distance (x):

[0060] w wb =A S xρ w (%) (4)

[0061] Among them, ρ w (g / cm 3 ) is the density of bound water in the diffusion layer.

[0062] According to the double layer theory, the concentration curve of the diffusion layer cation solution is expressed as:

[0063]

[0064] Among them, a is the core dimensionless parameter formed in the derivation process of double layer theory, d is the thickness of the diffusion layer, v is the average valence of the cation, and n0 is the soil solution concentration, representing the soil salt content.

[0065] Since the calculation process of deriving the unfrozen water model using formula (5) is relatively complicated, the present invention fits and obtains an expression of the change of cation concentration with surface distance, which has a simpler mathematical structure:

[0066] x=exp(a·n -b )-c(6)

[0067] Among them, a, b, and c are the double layer parameters in the fitting equation, which determine the shape of the cation solution concentration curve. Formula (6) and formula (5) are both equations describing the concentration of the diffusion layer cation solution, but formula (6) is simpler and more convenient.

[0068] Since the concentration of the cation solution in the diffusion layer on the surface of clay particles decays exponentially with the surface distance, and the freezing point of the cation solution depends on its concentration, the relationship between the freezing point and concentration of the electrolyte solution (Formula 1) and the relationship between the concentration of the cation solution in the diffusion layer and the surface distance (Formula 6) can be obtained:

[0069]

[0070] Since the volume of the unfrozen cationic solution in the diffusion layer is equal to the product of the specific surface area and the surface distance, by combining formula (4) and formula (7) and eliminating the surface distance x, the unfrozen cationic solution content in the diffusion layer corresponding to the freezing point T can be obtained:

[0071] w wb =ρ w A s ×10 -2 exp(aK c b (-T) -b )-ρ w A s c×10 -2 (8)

[0072] Combining equation (2) and equation (8), the unfrozen water model expression is:

[0073] w u =w m +Cexp(C0(-T) -b )-D w0≤w bmax ,T<T d (9)

[0074] Where C = ρ w A s ×10 -2 ; C0=aK cb ; D = ρ w cA s ×10 -2 .

[0075] ⑷ Calculation method of data and double layer parameters:

[0076] The data of the present invention are divided into two categories: The first category of data: microscopic physical quantities of five common mineral soils (see Table 1) (Dobson et al., 1985). These soil samples cover typical sand, silt and clay types, and are mainly used to calculate the double layer parameters in the unfrozen water parameterization model. The second category of data: includes the measured data of unfrozen water of 10 soils with different textures. These data are obtained by nuclear magnetic resonance (NMR) method and are used to verify the unfrozen water content of the parameterized model. The specific surface area of ​​these 10 types of soil samples ranges from 6 to 60.5 m 2 / g, covering soils with medium and low clay content. The specific surface area of ​​these soils is mainly determined by nitrogen adsorption. It should be noted that for expansive clay or soils containing montmorillonite, the specific surface area needs to be measured by liquid adsorption. The classification of soil samples is based on the classification system of the United States Department of Agriculture, which is as follows: soil particles with a diameter greater than 0.05 mm are sand; soil particles with a diameter between 0.002 mm and 0.05 mm are silt; soil particles with a diameter less than 0.002 mm are clay.

[0077] Table 1 Soil physical properties and double layer parameters

[0078]

[0079] Note: Parameters a, b, c are derived from the fitting of the results of formula (5); n d and T d They are The cation concentration and freezing point at Substituting into formula (5) we can get n d The value of n d and K c (≈12.5) into formula (1) to obtain T d The value of .

[0080] ⑸ Double layer theory calculation process:

[0081] The parameters in Table 1 are divided into two categories: 1) measured soil data, including the content of clay, silt and sand in the soil, soil solution concentration and surface charge density; 2) double layer parameters, including α, d, a, b, c, n d , T d The calculation process of the double layer parameters is as follows (the calculation formula and process are from the reference Shang et al., 1994).

[0082] The total negative charge (σ) on the surface of clay particles is equal to the sum of the adsorption layer charge (σ1) and the diffusion layer charge (σ2):

[0083] σ = σ1 + σ2 (10)

[0084] The charge in the adsorption layer can be obtained by approximate statistical treatment of the number of cationic adsorption sites and the adsorption force, and the expression is as follows:

[0085]

[0086] Among them, N1≈10 19 pcs / m 2 is the number of adsorption sites per square meter on the surface of clay particles; z≈1.8 is the average valence of cations in the five soil diffusion layers in Table 1; F=9.6487×10 4 C / mol is the Ferrari constant; N A =6.02×10 23 / mol is Avogadro's constant; ρ≈1000Kg / m 3 is the density of the solvent; M≈0.018kg / mol is the molar mass of the solvent; n0 is the concentration of the soil solution (mol / m 3 , values ​​are shown in Table 1); Φ δ is the Stern potential (mV) at the interface between the diffusion layer and the adsorption layer; Ψ = 0 is the specific adsorption potential on the surface of the clay particle; T' = 273.15 K is the thermodynamic temperature; R = 8.314 J / (mol·K) is the gas constant.

[0087] The charge in the diffusion layer (σ2) can be expressed as the product of the soil solution concentration (n0) and the Stern potential (Φ δ ) are related by the following exponential relationship:

[0088]

[0089] Where ε = 80 is the average dielectric constant of the diffusion layer solution. ε0 = 8.854 × 10 -12 C 2 / (J·m) is the dielectric constant of vacuum.

[0090] The unknown input parameters in formulas (10), (11), and (12) are the surface charge density (σ) and the soil solution concentration (n0). Therefore, the surface charge density (σ) and the soil solution concentration (n0) in Table 1 are substituted into formulas (1), (2), and (3) to obtain the Stern potential (Φ δ ).

[0091] The thickness of the diffusion layer (d) is expressed as:

[0092]

[0093] The thickness of the diffusion layer (d) can be directly calculated based on the soil solution concentration (n0).

[0094] The core dimensionless parameter a in the expression of diffusion layer ion concentration is expressed as:

[0095]

[0096] The Stern potential (Φ δ ) into formula (14) to obtain the parameter α, and by substituting the parameter α into formula (5) we can obtain the curve of the change of the cationic solution concentration in the diffusion layer with the surface distance.

[0097] (6) Concentration curve of cation solution in diffusion layer:

[0098] Figure 4 The diffusion layer cation solution concentration curves of five different types of soils calculated based on the double layer theory and fitting expressions are shown. The results show that the cation solution concentration changes exponentially with the distance from the surface of the soil particles. The results of the fitting equation (Equation 6) are highly consistent with the theoretical formula (Equation 5), and the correlation coefficients are both up to 0.999. This shows that the fitting expression is almost completely consistent with the theoretical prediction when describing the change of cation concentration with surface distance. Combined with the data analysis of Table 1, it is found that the values ​​of the fitting parameters (a, b, c) of the five soils are very close and have very low dependence on soil texture. The cation solution concentration curves of different soil types are almost the same, which shows that the diffusion layer parameters are consistent between different soil textures. Therefore, a set of average parameter values ​​can effectively represent the cation solution concentration curves of different types of soils.

[0099] In summary, the fitting formula can accurately replace the theoretical formula to describe the concentration curve of the diffusion layer cation solution in different soil textures. This discovery not only simplifies the complexity of the model, but also enhances its applicability under different soil conditions.

[0100] ⑺ Unfrozen water parameterization model:

[0101] Substituting the average values ​​of the double layer parameters in Table 1 into the parameterized model (9) yields the parameterized expression:

[0102] w u =w m +Cexp(C0(-T) -b )-D w0≤w bmax ,T<-0.26℃ (15)

[0103] Among them, K c=12.5According to the fitting result of the measured unfrozen water content, a=2.192, b=-0.14, c=5.98, T d =-0.263℃,K c =12.5,ρ bw =1.2g / cm 3 , w =1g / cm 3 、w m =ρ bw A S δ×10 -2 =0.03A S , C = ρ w A s ×10 -2 =0.01A S 、C0=aK c b =3.12, D = ρ w cA s ×10 -2 =0.06A s 、w bmax =w m +w wbmax =δρ bw A S 10 -2 +dρ w A S 10 -2 =0.2625A S .

[0104] ⑻Model results:

[0105] Table 2 gives the measured specific surface areas and model physical quantities of 12 soil samples. The soil samples include sand, silt, loess and clay, with specific surface areas ranging from 6.22 to 60.5 m 2 / g, with a maximum clay content of 18%. The measured unfrozen water content of these samples ( Figure 5 ) is used to test the unfrozen water model.

[0106] Table 2 Soil physical parameters

[0107]

[0108] Note: A S is the specific surface area, w0 is the initial water content, w m is the residual water content, w bmax is the maximum bound water content.

[0109] Xu Xiaozu, Olivier JL, & Taylor AR (1985). Soil water potential, unfrozen water content and temperature. Glaciology and Geocryology, 7(1), 1-12.

[0110] Wen,Z.,Ma,W.,Feng,W.,Deng,Y.,Wang,D.,Fan,Z.,&Zhou,C.Experimental study on unfrozen water content and soil matric potential of Qinghai-Tibetansilty clay[J].Environmental earth sciences, 2012, 66(5),1467-1476.

[0111] Chai,M.,Zhang,J.,Zhang,H.,Mu,Y.,Sun,G.,&Yin,Z..Amethod forcalculating unfrozen water content of silty clay with consideration offreezing point[J].Applied Clay Science,2018,161,474-481.

[0112] Anderson, DM, & Tice, AR (1972). Predicting unfrozen water contents infrozen soils from surface area measurements. Highway Research Record, 393.

[0113] AR Theis, JL Oliphant, & Zhu Yuanlin. (1985). Effects of soluble salts on the unfrozen water content of the Lanzhou loess in China. Glaciology and Geocryology, (02), 99-109.

[0114] Ma Tiantian, Wei Changfu, Zhou Jiazuo, et al. Freezing characteristic curve and water holding characteristics of soil[J]. Chinese Journal of Geotechnical Engineering, 2015(S1):6.

[0115] Zhou,J.,Meng,X.,Wei,C.,&Pei,W.Unified soil freezing characteristic for variably saturated and saline soils[J].Water Resources Research,2020,56(7).

[0116] Tang L,Wang K,Jin L,et al.Aresistivity model for testing unfrozenwater content of frozen soil[J].Cold Regions Science and Technology,2018,153:55-63.

[0117] Figure 5 The comparison between the parameterized model and the measured unfrozen water content of 12 soil samples is presented. The results show that the parameterized model results are consistent with the measured unfrozen water content of the 10 soil samples. However, some soil samples (e.g. Figure 5 e,h,k,i), there are some differences between the model results and the measured data. For example, Figure 5 e and Figure 5 In the silt sample in g, the model's predicted values ​​in the range of 0 to -20 °C are slightly higher than the measured data; Figure 5 h. Figure 5 k and Figure 5 In the soil sample i, the model results are lower than the measured data. These differences may be caused by factors such as soil salinity and cation exchange capacity, but the specific reasons are not clear. Despite these differences, the correlation coefficients between the model and the measured data are all higher than 0.9, and the correlation coefficient increases with the increase of clay content. This shows that the parameterized model can accurately simulate the freeze-thaw process of soil.

[0118] It should be pointed out that the unfrozen water content is different when the soil sample is first frozen and thawed, but this difference is significantly reduced after multiple freeze-thaw cycles. Since natural soil has undergone countless freeze-thaw cycles, the difference between freezing and thawing can be ignored in practical applications, which significantly simplifies the model. The root mean square error does not change significantly with soil texture changes, which means that the unfrozen water content is the largest when it is close to 0 degrees Celsius. Therefore, the difference between the measured and model results of the unfrozen water content close to 0 degrees Celsius determines the size of the root mean square error. This also shows that the model has a large error when it is close to 0 degrees Celsius. The parameterized model depends on three types of input parameters: temperature, soil specific surface area, and double layer parameters, while factors such as soil salinity, cation exchange capacity, and surface charge density affect the model results by affecting the concentration curve of the diffusion layer cation solution. However, the parameterized model regards these factors as constants, which significantly simplifies the model expression.

[0119] In summary, the parameterized model only needs to input three parameters (soil temperature, specific surface area, and initial water content) to calculate the unfrozen water content of frozen soil, and the model results are good, indicating that the present invention is feasible.

Claims

1. The unfrozen water model that couples the freezing mechanism of electrolyte solution and clay double layer theory includes the following steps: S1 collects soil samples and measures soil moisture and soil specific surface area A at room temperature S ; When the clay components in the soil are illite and kaolinite, the specific surface area A of the soil is measured using the N2 adsorption method. S ; When the clay component in the soil contains swelling clay, the soil specific surface area A is measured by liquid adsorption method S ; The measured soil moisture is taken as the initial water content w0; S2 determines the required temperature T; S3 establishes the following unfrozen water content model and calculates the unfrozen water content w u : w u =w m +Cexp(C0(-T) -b )-D w0≤w bmax ,T≤T d w m =ρ bw A S d×10 -2 =0.03A S ;C=ρ w A s ×10 -2 =0.01A S ;D=ρ w cA s ×10 -2 =0.06A s ; w bmax =w m +w wbmax =dr bw A S ·10 -2 +dp w A S ·10 -2 =0.2625A S Where: C, D are double layer parameters; a = 2.192, b = -0.14, c = 5.98, T d =-0.263℃,K c =12.5,ρ bw =1.2g / cm 3 , w =1g / cm 3 ; C0=aK c b =3.12; w u , w m , w wbmax and w bmax All are mass moisture content, in %; T, T d Negative temperature.

2. The unfrozen water model of coupling electrolyte solution freezing mechanism and clay double layer theory as claimed in claim 1, characterized in that: The S1 soil is non-saline soil.

3. The unfrozen water model of coupling electrolyte solution freezing mechanism and clay double layer theory as claimed in claim 2, characterized in that: The clay content of the soil is less than 18%, and its specific surface area A S 60.5~6.22g / cm 3 between.

4. The unfrozen water model of coupling electrolyte solution freezing mechanism and clay double layer theory as claimed in claim 1, characterized in that: The T in S2 is between -0.26°C and -20°C.

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