Frozen soil unfrozen water parameterized model based on combined water microscopic freezing characteristics

Abstract

The invention relates to a frozen soil unfrozen water parameterized model based on combined water microscopic freezing characteristics, which comprises the following steps: firstly, collecting a low-salt or salt-free soil sample, measuring the soil temperature T, the specific surface area AS and the soil solution concentration n0, and limiting n0 to be less than or equal to 0.05 mol / L; and then obtaining the mass water content wu of the soil. According to the method, the content of the unfrozen water in the salt-free and low-salt frozen soil is calculated by revealing the relationship between the microscopic freezing characteristics of the combined water and the macroscopic freezing characteristics of the soil and sorting out the main cause of the unfrozen water in the frozen soil; and an innovative research method is provided for the public to intuitively understand freeze-thaw behaviors of frozen soil, freeze-thaw processes of frozen soil areas and simulation of hydrological and ecological environments.

Description

Technical Field

[0001] The invention relates to the field of natural sciences in cold and arid regions, and in particular to a parameterized model of unfrozen water in frozen soil based on microscopic freezing characteristics of combined water. Background Art

[0002] The unfrozen water content of frozen soil fluctuates with changes in ambient temperature, thus affecting the distribution of regional soil moisture, solutes and ice. This change will further affect the water and heat transfer process in the active layer, leading to frost heave and thaw settlement of local soil bodies (Wen et al., 2012; Cheng Guodong et al., 2019). In recent years, climate warming has exacerbated changes in global permafrost surface temperature, area, active layer thickness and greenhouse gas emissions (Chen et al., 2021; Smith et al., 2022). Therefore, clarifying the freezing characteristics of frozen soil bodies and the formation mechanism of unfrozen water, and constructing a parameterized model of unfrozen water, is a prerequisite for simulating and predicting climate, ecological and hydrological changes in cold regions.

[0003] The relationship between unfrozen water content and temperature is called the soil freezing characteristic curve (SFCC) ( Figure 1 ). The curve has two characteristics: (1) the unfrozen water content in the main body of the curve changes exponentially with temperature; (2) at lower temperatures, the unfrozen water content hardly changes with temperature and is called residual unfrozen water (Jin et al., 2020). The early semi-empirical model of unfrozen water was mainly a fitting expression of the soil characteristic curve. Anderson and Tice (1972) proposed a semi-empirical model of unfrozen water in the form of a power exponential by analyzing the relationship between the measured unfrozen water content and specific surface area of ​​more than 10 kinds of soil. Xu Xiaozu et al. (1985) found that in addition to soil temperature and type, initial water content, bulk density and soil salinity also affect the unfrozen water content in frozen soil, and proposed an unfrozen water model based on "one point" or "two points" on the SFCC curve to predict the entire SFCC. Michalows et al. (1993) and Kozlowski et al. (2007) separated the residual unfrozen water when constructing the unfrozen water model and used an exponential equation to describe the variation of the main part of SFCC (the difference between the initial water content and the residual unfrozen water content) with temperature.

[0004] Similarly, some theoretical models also use these two characteristics of SFCC to describe the freezing characteristics of frozen soil. The soil-water characteristic curve (SWCC) describes the relationship between soil matrix suction and soil moisture ( Figure 1b), whose variation characteristics are similar to the soil freezing characteristic curve (SFCC) (Jin et al., 2020; Li et al., 2023). Since soil matrix suction and pore water pressure can be converted into each other, the Clausius-Clapeyron equation describing the relationship between pore water pressure and freezing point can be used to convert soil matrix suction in the SWCC model into the freezing point of unfrozen water, thereby establishing a theoretical model reflecting the relationship between unfrozen water content and temperature (Zhou et al., 2018; Wang & Hu, 2023). In summary, most semi-empirical models and theoretical models of unfrozen water use the two characteristics of SFCC.

[0005] Since the matrix suction (or pore water pressure) in the soil-water characteristic curve is measured by instruments such as tensiometers, reflecting the combined effects of adsorption and capillary action, there is controversy about the cause of unfrozen water in frozen soil (Li et al., 2023). Scholars attribute the unfrozen water in the main part of the soil freezing characteristic curve to capillary action, adsorption, or a combination of the two. In addition, since matrix suction is affected by multiple physical factors such as soil texture, structure, water content, salinity, and temperature, the unfrozen water model based on matrix suction is difficult to clarify the independent influence of each factor, and thus cannot clarify the specific role of these physical quantities on the unfrozen water content (Ying et al., 2021). Summary of the invention

[0006] The technical problem to be solved by the present invention is to provide an intuitive and simple parameterized model of unfrozen water in frozen soil based on the microscopic freezing characteristics of combined water.

[0007] In order to solve the above problems, the present invention discloses a parameterized model of unfrozen water in frozen soil based on the microscopic freezing characteristics of water, which is characterized by first collecting low-salt or salt-free soil samples, measuring soil temperature T, specific surface area A S and soil solution concentration n0, and limit n0≤0.05mol / L; then obtain the mass water content w of the soil according to the following formula u :

[0008]

[0009] Where: b ≈1.05 g cm -3 is the bound water density; is the diffusion layer thickness; α≈-0.895; K c ≈18.5℃·L·mol -1 ; is the adsorption layer thickness; T d ≈-0.36℃.

[0010] Compared with the prior art, the present invention has the following advantages:

[0011] The present invention applies the clay double layer theory and Henry's law to derive the microscopic freezing characteristics of bound water on the surface of clay particles, and accordingly establishes a macroscopic unfrozen water parameterization model based on the microscopic freezing characteristics of bound water. By revealing the relationship between the microscopic freezing characteristics of bound water and the macroscopic freezing characteristics of soil, clarifying the main causes of unfrozen water in frozen soil, and calculating the unfrozen water content of salt-free and low-salt frozen soil, an innovative research method is provided for the public to intuitively understand the freeze-thaw behavior of frozen soil, the freeze-thaw process of frozen soil areas, and the simulation of hydrology and ecological environment. BRIEF DESCRIPTION OF THE DRAWINGS

[0012] The specific implementation modes of the present invention will be further described in detail below in conjunction with the accompanying drawings.

[0013] Figure 1 Schematic diagram of soil freezing characteristic curve and soil-water characteristic curve. Among them: a is soil freezing characteristic curve; b is soil-water characteristic curve.

[0014] Figure 2 Schematic diagram of the double layer structure of clay.

[0015] Figure 3 The freezing point of NaCl and KCl solutions varies with concentration (a); the freezing point of a mixed solution of NaCl and CaCl2 varies with concentration (b); the freezing point of a mixed solution of NaCl and MgCl2 varies with concentration (c).

[0016] Figure 4 Microscopic freezing characteristic curves of bound water in five different types of salt-free soils.

[0017] Figure 5 It is the characteristic curve of micro-freezing of bound water under different soil solution concentrations.

[0018] Figure 6 The results of the parameterized model of frozen soil and unfrozen water in the present invention are shown in Figure 1. Among them, a is Xina hot spring silt; b is northwest Alaska silt; c is Xi'an loess; and d is limonite. DETAILED DESCRIPTION

[0019] A parameterized model of unfrozen water in frozen soil based on the microscopic freezing characteristics of bound water, characterized by: firstly collecting low-salt or salt-free soil samples, measuring soil temperature T, specific surface area A S and soil solution concentration n0, and limit n0≤0.05mol / L; then obtain the mass water content w of the soil according to the following formula u :

[0020]

[0021] Where:b ≈1.05 g cm -3 is the bound water density; is the diffusion layer thickness; α≈-0.895; K c ≈18.5℃·L·mol -1 ; is the adsorption layer thickness; T d ≈-0.36℃.

[0022] The specific process is as follows:

[0023] ⑴ Introduction to clay double layer theory

[0024] The double layer of water bound to the surface of clay particles consists of surface negative charges and cationic solution (Jin et al., 2023) ( Figure 2 ). Cationic solution can be further divided into adsorption layer and diffusion layer. The adsorption layer is a cationic solution tightly bound to the surface of clay particles. The diffusion layer is a loosely distributed cationic solution. As the surface distance increases, the concentration of the cationic solution in the diffusion layer decreases exponentially. In this invention, the adsorption layer solution is called strongly bound water, and the diffusion layer solution is called weakly bound water. The calculation process of Stern's double layer theory is as follows (Olphen, 1977; Shang et al., 1998)

[0025] The total surface charge density (σ) on the surface of a clay particle is equal to the sum of the charge densities in the adsorption layer (σ1) and the diffusion layer (σ2):

[0026] σ=σ1+σ2 (1)

[0027] The charge density (σ1) in the adsorption layer depends on the number of adsorption sites on the clay surface (N1) and the Stern potential (Φ δ ):

[0028]

[0029] Where: N1 = 10 19 / m 2 is the number of adsorption points per unit area on the surface of mineral particles; z≈1.8 is the average valence of cations in salt-free or low-salt soil; F=9.6487×10 4 C / mol is the Faraday constant; N A =6.02×10 23 / mol is Avogadro's constant; ρ≈1g / cm 3 is the density of the cationic solution; M≈18 g / mol is the molecular weight of the solvent; n0 (mol / L) is the concentration of the soil solution; Φ δ(mV) is the Stern potential at the interface between the diffusion layer and the adsorption layer; Ψ = 0 mV is the specific adsorption potential on the surface of the clay particles; T' (K) is the thermodynamic temperature; R = 8.314 J / (mol·K) is the gas constant.

[0030] The charge density (σ2) of the diffusion layer is expressed as the soil solution concentration (n0) and the Stern potential (Φ δ ) function:

[0031]

[0032] Where: ε≈80 is the relative dielectric constant of the diffusion layer solution; ε0=8.854×10 -12 C 2 / (J·m) is the dielectric constant of vacuum; T′=T+273.15(K) is the thermodynamic temperature. The dimensionless parameter a describing the change of cation concentration in the diffusion layer is generated in the calculation process, and its expression is:

[0033]

[0034] The thickness of the diffusion layer d mainly depends on the type and content of soil salt, that is, the average valence of cations (z) and the concentration of soil solution (n0), and its expression is as follows:

[0035]

[0036] The change of the concentration of the diffusion layer cation solution (n) with the surface distance (x) is:

[0037]

[0038] In the double layer model, most physical quantities are constants. Changes in thermodynamic temperature have little effect on the double layer, so the temperature can be set to 0°C (273.15K). At the same time, the average valence of cations in salt-free and low-salt soils (z≈1.8) is known. Based on the above characteristics, according to equations (1)-(6), the input parameters that need to be measured in the double layer model include surface charge density (σ) and soil solution concentration (n0).

[0039] ⑵ Henry's Law

[0040] Henry's law is an empirical relationship that describes the relationship between the concentration (n) and freezing point (T) of an electrolyte solution. Its equivalent expression can be written as (Banin & Anderson 1974; Fullerton et al., 1994):

[0041] T=-K c n (7)

[0042] Among them, Kc (℃·L·mol -1 ) is defined as the freezing point depression coefficient, which is used to express the freezing point temperature that can be lowered per mole of solute in different solvents.

[0043] Bound water is a mixed solution composed of various cations, mainly including Ca 2+ 、Na + , K + Mg 2+ etc. (Wang Zunqin et al., 1993; Osman, 2018). Figure 3 The freezing point of sodium chloride, potassium chloride, calcium chloride, magnesium chloride solutions and mixed solutions of two solutes varies with concentration. The data comes from the literature (Alonso et al., 2011). As can be seen from the figure, the freezing point of the electrolyte solution decreases with increasing concentration. The curvature of the freezing point change curve is small and tends to change linearly. The curvature of the freezing point change curve of a single electrolyte is higher than that of the mixed solution, indicating that its freezing point depression coefficient is smaller than that of the mixed solution. The proportion of cations in ordinary mineral soils (non-saline soils) can be simply estimated based on the saline soil classification standards. According to the standards of the American Saline Soil Laboratory, soils with a percentage of exchangeable sodium ions or a sodium ion adsorption ratio exceeding 15% are defined as alkaline saline soils (Osman, 2018). Based on this standard, it can be inferred that Na in ordinary mineral soils + The proportion is usually less than 15%. Figure 3 The khaki and cyan curves in a and 3b show the Na + Freezing point variation curves of mixed solutions with a ratio of less than 20%. The freezing point depression coefficients of these curves are significantly higher than those of other mixed solutions and single electrolyte solutions, and the relationship between freezing point and concentration is closer to linear, indicating that the freezing point depression coefficient can be regarded as a constant in this scenario. Figure 3 Na in c + A mixed solution of sodium chloride and magnesium chloride with a ratio close to 30% also exhibits similar characteristics. In addition, Henry's law has been applied to the construction of unfrozen water models (Jin Xiao et al., 2019; Jin et al., 2020). In these studies, the freezing point depression coefficient is generally regarded as a constant. In summary, since the soil targeted by the present invention is salt-free and low-salt soil, the soil solution concentration is low and the proportion of sodium chloride in the soil is also low, the freezing point depression coefficient (K c ) value is taken Figure 3 The average slope of the khaki and cyan curves in a, 3b, and 3c is approximately 18.5.

[0044] ⑶Combined with the derivation of water micro-freezing model

[0045] Combining equations (6) and (7) yields the following equation:

[0046]

[0047] In the double layer theory, the surface distance x represents the position of the cationic solution, and its value is equal to the thickness of the unfrozen weakly bound water film. When the soil temperature is T, the bound water with a freezing point higher than T changes to ice, and the bound water with a freezing point lower than T remains in liquid state. Formula (8) can be expressed as the change of the unfrozen weakly bound water film thickness with temperature by deformation:

[0048]

[0049] The adsorption layer is a cationic solution tightly bound to the surface of clay particles. Since the adsorption force on the adsorption layer is the combined force of van der Waals force, valence force and electrostatic force, the thickness of the adsorption layer (δ) hardly changes with external factors. Scholars generally believe that the thickness of the adsorption layer is equal to the monolayer hydrated ion or double layer hydrated ions The thickness of the film is (Shang et al., 1994; Jin et al., 2023), and the present invention adopts the latter. As the adsorption layer thickness. Since the adsorption layer solution will not freeze at extremely low temperatures (below -18 ° C), the freezing process of the double layer solution mainly occurs in the diffusion layer. At this time, the unfrozen bound water film thickness (d b ) can be expressed as the sum of the thickness of the adsorption layer (δ) that never freezes and the thickness of the diffusion layer (x) that does not freeze as the temperature changes:

[0050]

[0051] Formula (10) describes the microscopic freezing characteristics of bound water on the surface of clay particles. There is no clear value for the boundary temperature that distinguishes strongly bound water from weakly bound water. Formula (10) uses the setting of Jin et al. (2020) and defines the boundary temperature as -18°C.

[0052] (4) Derivation of frozen soil unfrozen water model

[0053] Clay minerals are flat sheets (Bergaya & Lagaly, 2006), so the unfrozen water content can be expressed as specific surface area (A S ) and the thickness of the unfrozen combined water film (d b )product:

[0054]

[0055] The unit calculation process on the right side of formula (11) is as follows: is the mass water content. Therefore, the right side of the equation needs to be multiplied by 10 -2, so that both sides of the equation have the same unit magnitude. b ≈1.05 g cm -3 is the bound water density, is the adsorption layer thickness. n0≤0.05mol·L -1 ,α≈-0.895, It is the average value of the five soils in Table 1.

[0056] ⑸Data

[0057] The data used in the present invention are divided into two categories. The first category of data includes the microscopic physical parameters of five common mineral soils (see Table 1), which are derived from Dobson et al. (1985). The soil samples involved represent typical sandy soil, silt soil and clay types. The second category of data is the measured data of unfrozen water in 12 salt-free soils of different textures (see Table 2).

[0058] Table 1 Measured physical parameters of 5 kinds of soil

[0059]

[0060] Table 2 Physical parameters of 12 kinds of soil

[0061] Soil Type <![CDATA[Specific surface area (m 2 g -1 )]]> References Moling Clay 60.5 Xu Juezu (1985) Silty clay 1 52 Wen et al. (2012) Silty clay 2 52 Chai et al. (2018) Dow Field Silty Clay 50 Anderson & Tice (1972) Xina Hot Spring Powder 40 Theis et al. (1985) Xi'an Loess 39 Tang et al (2018) Northwest Alaska Silt 35 Theis et al. (1985) Limonite 26 Anderson & Tice (1972) Low plastic clay 22.63 Ma Tiantian et al. (2015) West Lebanon Gravel 18 Anderson & Tice (1972) Powder 1 16.6 Zhou et al. (2020) Powder 2 6.22 Ma Tiantian et al. (2015)

[0062] Note: Xu Dunzu, Olivier JL, Taylor AR (1985). Soil water potential, unfrozen water content and temperature. Glaciology and Geocryology, 7(1), 1-12.

[0063] Wen, Z., Ma, W., Feng, W., et al. (2012). Experimental study 0n unfrozenwater content and soil matric potential 0f Qinghai-Xizang siltyclay. Environmental Earth Sciences, 66(5), 1467-1476.

[0064] Chai, M., Zhang, J., Zhang, H., Mu, Y., Sun, G., & Yin, Z. (2018). A method forcalculating unfrozen water content of silty clay with consideration of freezing point. Applied Clay Science, 161, 474-481.

[0065] Anderson, DM, & Tice, AR (1972). Predicting unfrozen water contents infrozen soils from surface area measurements. Highway Research Record, 393, 12-18.

[0066] Theis AR, Olifont JL, Zhu Yuanlin. (1985). Effects of soluble salts on the unfrozen water content of the Lanzhou loess in China. Glaciology and Geocryology, (02), 99-109.

[0067] Tang,L.,Wang,K.,Jin,L.,Yang,G.,Jia,H.,&Taoum,A.(2018).A resistivitymodel for testing unfrozen water content of frozen soil.Cold Regions Science and Technology,153,55-63.

[0068] Ma Tiantian, Wei Changfu, Zhou Jiazuo, et al. (2015). Freezing characteristic curve and water holding characteristics of soil. Chinese Journal of Geotechnical Engineering, 37(S1), 172-177.

[0069] Zhou,J.,Wei,C.,Lai,Y.,Wei,H.,&Tian,H.(2020).Application of the Generalized Clapeyron Equation to Freezing Point Depression and UnfrozenWater Content.Water Resources Research, 54(11),9412-9431.

[0070] The first type of data is used to calculate the microscopic freezing characteristics of bound water. The second type of data is used to verify the unfrozen water model. The unknown input parameters of the bound water microscopic freezing characteristics model (Formula 10) include: 1. The diffusion layer thickness d, the parameter α, the bound water freezing point depression coefficient K c , and the freezing point T of the solution at the edge of the double layer d , these parameters are mainly calculated by double layer theory. d and α are obtained by formula (5) and (6) respectively; Substituting x = d into formula (8) can calculate the freezing point T of the solution at the edge of the double layer d ; K c ≈18.5, based on Figure 3 Judgment is drawn.

[0071] ⑹Model verification

[0072] ① Combined with the microscopic freezing characteristics of water

[0073] Figure 4 The microscopic freezing characteristic curves of bound water (double-layer cation solution, formula 10) of five different types of soil are shown. The five soil samples were from farmland in Texas, USA, and the soil solution concentration was low (n0≈0.005mol·L -1 ), the average valence of ions in different types of soil is similar (z≈1.8). As can be seen from the figure, the thickness of the unfrozen water film of bound water changes exponentially with the decrease of temperature, and the microscopic freezing characteristic curves of different types of soils almost overlap, which shows that the microscopic freezing characteristics of bound water are independent of soil texture. Therefore, the present invention believes that the microscopic freezing characteristics of bound water in soils with low salinity are very similar, and the microscopic freezing characteristic curves of five types of soils can be replaced by an average curve. The factor affecting the microscopic freezing characteristics of soil bound water is the soil salt content rather than the soil texture.

[0074] Figure 5 The microscopic freezing characteristic curves of bound water under different soil solution concentrations are shown. The average valence of cations in the curve is 1.8, and the surface charge density is 1.5×10 -5 C / cm 2 , the solution concentration is low, from 0.005mol·L -1 To 0.05 mol·L -1 . It can be seen from the figure that the thickness of the unfrozen water film of bound water changes exponentially with decreasing temperature. The microscopic freezing characteristic curves of bound water under different soil solution concentrations almost overlap, which indicates that when the soil solution concentration is low, that is, the salt content in the soil is low, the microscopic freezing characteristics of bound water are independent of the soil salt content. Based on the above characteristics, the present invention can use the average values ​​of the double layer parameters of five different types of salt-free soils in Table 1 to calculate the microscopic freezing characteristic curve of low-salt soil, which significantly simplifies the calculation process of the unfrozen water model.

[0075] ② Results of frozen soil and unfrozen water model

[0076] Figure 6 The comparison between the parameterized model of unfrozen water in frozen soil and 12 measured unfrozen water contents (Table 2) is shown. As can be seen from the figure, the calculated results of the parameterized model are basically consistent with the measured unfrozen water contents. However, in some soil samples, there are some differences between the model results and the measured data. For example, the Xi Na Hot Spring Silt and Northwest Alaska Silt ( Figure 6 a and Figure 6 c) Xi'an loess and limonite ( Figure 6 b and Figure 6d). Since these soils are all non-saline soils, these differences may be due to differences in the types of salts in the soil, which leads to changes in the freezing point depression coefficient and the microscopic freezing characteristics of bound water. Despite these differences, the parameterized model and the measured data have exactly the same trend, and the error is not significant ( Figure 6 d). The difference between the unfrozen water model and the measured data decreases with the increase of clay content, indicating that the bound water content in clay is higher. In general, the unfrozen water model has more accurate results and can be used to calculate the unfrozen water content of frozen soil.

Claims

1. A parameterized model of unfrozen water in frozen soil based on the microscopic freezing characteristics of bound water, characterized by: First, collect low-salt or salt-free soil samples and measure soil temperature T, specific surface area A S and soil solution concentration n0, and limit n0≤0.05mol / L; then obtain the mass water content w of the soil according to the following formula u : Where: b ≈1.05 g cm -3 is the bound water density; is the diffusion layer thickness; α≈-0.895; K c ≈18.5℃·L·mol -1 ; is the adsorption layer thickness; T d ≈-0.36℃.

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