A frozen soil unfrozen water parameterization model based on microcosmic freezing characteristics of bound water

Abstract

The present application relates to a frozen soil unfrozen water parameterization model based on the microcosmic freezing characteristics of combined water, which first collects low-salt or salt-free soil samples, measures the soil temperature T , specific surface area A S and soil solution concentration n 0, and limits n 0≤0.05mol / L; then obtains the mass water content of the soil w u The present application clarifies the main causes of unfrozen water in frozen soil by revealing the relationship between the microcosmic freezing characteristics of combined water and the macroscopic freezing characteristics of soil, calculates the unfrozen water content of salt-free and low-salt frozen soil, and provides an innovative research method for the public to intuitively understand the freezing and thawing behavior of frozen soil, the freezing and thawing process of frozen soil regions, and the simulation of hydrology and ecological environment.

Description

TECHNICAL FIELD

[0001] The present application relates to the field of natural science in cold and arid regions, and particularly relates to a frozen soil unfrozen water parameterization model based on combined water micro freezing characteristics. BACKGROUND

[0002] The unfrozen water content of frozen soil fluctuates with the change of environmental temperature, thereby affecting the distribution of regional soil water, solute and ice, and this change further affects the water and heat transport processes in the active layer, resulting in frost heaving and thawing settlement of local soil body (Wen et al., 2012; Cheng et al., 2019). In recent years, climate warming has intensified the changes of 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 and the formation mechanism of unfrozen water, and constructing an unfrozen water parameterization model are the premise of simulating and predicting the changes of climate, ecology and hydrology in cold regions.

[0003] The relationship between unfrozen water content and temperature is called soil freezing characteristic curve (SFCC) ( Figure 1 ). The curve has two characteristics: (1) the unfrozen water content in the main part of the curve changes with temperature in a power exponent; (2) at lower temperatures, the unfrozen water content hardly changes with temperature, which is called residual unfrozen water (Jin et al., 2020). Early semi-empirical models of unfrozen water are mainly fitting expressions of soil characteristic curves. Anderson and Tice (1972) proposed a semi-empirical model of unfrozen water in the form of power exponent by analyzing the relationship between measured unfrozen water content and specific surface area of more than 10 kinds of soil. Xu 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 described the change of the main part of SFCC (the difference between initial water content and residual unfrozen water content) with temperature by an exponential equation.

[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 matric suction and soil moisture ( Figure 1b), which is similar to the soil freezing characteristic curve (SFCC) (Jin et al., 2020; Li et al., 2023). Since the soil matric suction and the pore water pressure can be converted to each other, the Clausius-Clapeyron equation, which describes the relationship between the pore water pressure and the freezing point, can be applied to convert the soil matric suction in the SWCC model to the freezing point of unfrozen water, thus establishing a theoretical model reflecting the relationship between the unfrozen water content and the temperature (Zhou et al., 2018; Wang & Hu, 2023). In summary, both the semi-empirical model of unfrozen water and the theoretical model of unfrozen water apply the two characteristics of the SFCC.

[0005] Since the matric suction (or pore water pressure) in the soil-water characteristic curve is measured by instruments such as tensiometers, it reflects the combined effect of adsorption and capillary action, so there is controversy about the origin 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 the matric suction is influenced by multiple physical factors such as soil texture, structure, water content, salt content, and temperature, it is difficult to determine the independent influence of each factor based on the matric suction, thus making it difficult to clarify the specific effects of these physical quantities on the unfrozen water content (Ying et al., 2021). SUMMARY

[0006] The technical problem to be solved by the present application is to provide a frozen soil unfrozen water parameterization model based on the microcosmic freezing characteristics of bound water.

[0007] To solve the above problems, the frozen soil unfrozen water parameterization model based on the microcosmic freezing characteristics of bound water according to the present application is characterized by: first collecting low-salt or salt-free soil samples, measuring the soil temperature T, specific surface area A S , and soil solution concentration n0, and limiting n0≤0.05 mol / L; then obtaining the mass water content w u of the soil according to the following formula:

[0008]

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

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

[0011] The present application applies the clay double electric layer theory and Henry's law to deduce the micro freezing characteristics of the bound water on the surface of clay particles, and establishes a macro non-frozen water parameterization model based on the micro freezing characteristics of the bound water. By revealing the relationship between the micro freezing characteristics of the bound water and the macro freezing characteristics of the soil, the main causes of the non-frozen water in the frozen soil are clarified, the non-frozen water content of the salt-free and low-salt frozen soil is calculated, and an innovative research method is provided for the public to intuitively understand the freezing and thawing behavior of the frozen soil, the freezing and thawing process of the frozen soil region, and the simulation of the hydrology and ecological environment. BRIEF DESCRIPTION OF DRAWINGS

[0012] The specific embodiments of the present application will be further described in detail below with reference to the accompanying drawings.

[0013] Figure 1 Fig. 1 is a schematic diagram of the soil freezing characteristic curve and the soil-water characteristic curve. Wherein: a is the soil freezing characteristic curve; b is the soil-water characteristic curve.

[0014] Figure 2 Fig. 2 is a schematic diagram of the double electric layer structure of clay.

[0015] Figure 3 Fig. 3 is a curve of the freezing point of NaCl and KCl solution changing with the concentration (a); a curve of the freezing point of NaCl and CaCl2 mixed solution changing with the concentration (b); and a curve of the freezing point of NaCl and MgCl2 mixed solution changing with the concentration (c).

[0016] Figure 4 Fig. 4 is a micro freezing characteristic curve of the bound water in five different types of salt-free soil.

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

[0018] Figure 6 Fig. 6 is the result of the frozen soil non-frozen water parameterization model of the present application. Wherein: a is the Xiqiang hot spring silt; b is the northwest Alaska silt; c is the Xi'an loess; and d is the brown iron ore. DETAILED DESCRIPTION

[0019] A frozen soil non-frozen water parameterization model based on the micro freezing characteristics of the bound water, characterized in that: first, a low-salt or salt-free soil sample is collected, the soil temperature T, the specific surface area A S and the soil solution concentration n0 are measured, and n0≤0.05 mol / L is defined; then the mass water content w of the soil is obtained according to the following formula u :

[0020]

[0021] In the formula, ρb ≈1.05 g·cm -3 For the density of bound water; For the thickness of the diffuse layer; α ≈ -0.895; K c ≈18.5 °C·L·mol -1 ; For the thickness of the adsorbed layer; T d ≈-0.36 °C.

[0022] The specific process is as follows:

[0023] (1) Introduction to the theory of clay double electric layer

[0024] The double electric layer of the bound water on the surface of clay particles is composed of surface negative charge and cation solution (Jin et al., 2023) Figure 2 ). The cation solution can be further divided into adsorbed layer and diffuse layer. The adsorbed layer is the cation solution closely bound to the surface of clay particles. The diffuse layer is the loosely distributed cation solution. With the increase of surface distance, the concentration of diffuse layer cation solution decreases exponentially. In this invention, the adsorbed layer solution is called strong bound water, and the diffuse layer solution is called weak bound water. The calculation process of Stern double electric layer theory is as follows (Olphen, 1977; Shang et al., 1998)

[0025] The total surface charge density (σ) on the surface of clay particles is equal to the sum of the charge density in the adsorbed layer (σ1) and the diffuse layer (σ2):

[0026] σ = σ1+ σ2 (1)

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

[0028]

[0029] Where: N1= 10 19 / m 2 The number of adsorption sites per unit area on the surface of mineral particles; z ≈ 1.8 is the average valence number of cations in soil without or with low salt; F = 9.6487 × 10 4 C / mol is the Faraday constant; N A = 6.02 × 10 23 / mol is the Avogadro constant; ρ ≈ 1 g / cm 3 is the density of cation solution; M ≈ 18 g / mol is the molecular weight of solvent; n0 (mol / L) is the concentration of soil solution; Φ δ(mV) is the Stern potential at the interface between the diffuse layer and the adsorption layer; Ψ = 0 mV is the specific adsorption potential at the surface of the clay particle; T'(K) is the thermodynamic temperature; R = 8.314 J / (mol-K) is the gas constant.

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

[0031]

[0032] where ε ~ 80 is the relative dielectric constant of the diffuse layer solution; ε0= 8.854 x 10 -12 C 2 / (J-m) is the dielectric constant of vacuum; T' = T + 273.15 (K) is the thermodynamic temperature. A dimensionless parameter a, which describes the change in the diffuse layer cation concentration, is generated during the calculations, and its expression is:

[0033]

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

[0035]

[0036] The diffuse layer cation solution concentration (n) as a function of the surface distance (x) is:

[0037]

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

[0039] 2. Henry's law

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

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

[0042] where Kc (℃·L·mol -1 ) is defined as the freezing point depression coefficient, which is used to represent the freezing point temperature that can be reduced by each mole of solute in different solvents.

[0043] The combined 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 solution and two solute mixed solution with concentration change is shown, and the data is from the literature (Alonso et al., 2011). As can be seen from the figure, the freezing point of the electrolyte solution decreases with the increase of the concentration. The curvature of the freezing point change curve is small, and it is more linear. The curvature of the freezing point change curve of single electrolyte is higher than that of mixed solution, indicating that the freezing point depression coefficient is less than that of mixed solution. The proportion of cations in ordinary mineral soil (non-saline soil) can be simply estimated according to the classification standard of saline soil. According to the standard of the United States saline soil laboratory, the soil with more than 15% of exchangeable sodium ions or sodium ion adsorption ratio is defined as alkaline saline soil (Osman, 2018). According to this standard, it can be inferred that the proportion of Na + in ordinary mineral soil is usually less than 15%. Figure 3 The yellow and blue curves in a and 3b show the freezing point change curve of mixed solution with Na + proportion less than 20%. The freezing point depression coefficient of these curves is obviously higher than that 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 The Na + proportion of the mixed solution of sodium chloride and magnesium chloride in c is close to 30%. It also shows similar characteristics. In addition, Henry's law has been applied to the construction of unfrozen water model (Jin Xiao et al., 2019; Jin et al., 2020). In these studies, the freezing point depression coefficient is usually regarded as a constant. In summary, since the soil targeted by the present invention is salt-free and low-salt soil, the concentration of soil solution is low, and the proportion of sodium chloride in the soil is also low, the value of the freezing point depression coefficient (K c ) of salt-free and low-salt soil is taken Figure 3 The average value of the slope of several yellow and blue curves in a, 3b and 3c is about 18.5.

[0044] ⑶ Combined water micro freezing model derivation

[0045] By combining formulas (6) and (7), the freezing point of weakly combined water on the surface of clay particles changes with the surface distance:

[0046]

[0047] In the double-layer theory, the surface distance x represents the location of the cation 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 into ice, and the bound water with a freezing point lower than T remains liquid. Equation (8) can be expressed as the change in the thickness of the unfrozen weakly bound water film with temperature by transformation:

[0048]

[0049] The adsorbed layer is the cation solution tightly bound to the surface of the clay particle. Since the adsorbed layer is subjected to the combined forces of van der Waals force, valence force, and electrostatic force, the thickness of the adsorbed layer (δ) hardly changes with external factors. Scholars generally consider the thickness of the adsorbed layer to be equal to the thickness of a monolayer of water-solvated ions or a bilayer of water-solvated ions (Shanget al., 1994; Jin et al., 2023). This invention adopts the latter, using as the thickness of the adsorbed layer. Since the adsorbed layer solution does not freeze at extremely low temperatures (below -18℃), the freezing process of the double-layer solution mainly occurs in the diffuse layer. At this time, the change in the thickness of the unfrozen bound water film (d b ) with temperature can be expressed as the sum of the thickness of the adsorbed layer (δ) that does not freeze and the thickness of the unfrozen diffuse layer (x):

[0050]

[0051] Equation (10) describes the microscopic freezing characteristics of the bound water on the surface of the clay particle. The boundary temperature that distinguishes between strong and weakly bound water does not have a clear numerical value, and equation (10) uses the setting of Jin et al. (2020) to define the boundary temperature as -18℃.

[0052] ⑷ Derivation of the frozen soil unfrozen water model

[0053] Clay minerals all exhibit a flat and sheet-like shape (Bergaya & Lagaly, 2006), so the content of unfrozen water can be expressed as the product of the specific surface area (A S ) and the thickness of the unfrozen bound water film (d b ):

[0054]

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

[0056] (5) Data

[0057] The data used in this study 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, silt, and clay types. The second category of data is the measured data of unfrozen water of 12 different texture salt-free soils (see Table 2).

[0058] Table 1 Measured physical parameters of five soils

[0059]

[0060] Table 2 Physical parameters of 12 soils

[0061] Soil type Specific surface area (m 2 g -1 )]]> Reference Moling clay 60.5 Xu et al (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) Xinna hot spring silt 40 Tess et al (1985) Xi’an loess 39 Tang et al (2018) Northwest Alaska silt 35 Tess et al (1985) Brown iron ore 26 Anderson & Tice (1972) Low plasticity clay 22.63 Ma et al (2015) Lebanon west gravel 18 Anderson & Tice (1972) Silt 1 16.6 Zhou et al (2020) Silt 2 6.22 Ma et al (2015)

[0062] Note: Xu, D. Z., O'Leary, J. L., & Taylor, A. R. (1985). Soil water potential, unfrozen water content and temperature. Cold Regions Science and Technology, 7(1), 1-12.

[0063] Wen, Z., Ma, W., Feng, W., et al. (2012). Experimental study on unfrozen water content and soil matric potential of Qinghai-Xizang silty clay. Environmental Earth Sciences, 66(5), 1467-1476.

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

[0065] Anderson, D. M., & Tice, A. R. (1972). Predicting unfrozen water contents in frozen soils from surface area measurements. Highway Research Record, 393, 12-18.

[0066] Tice, A. R., Oli phant, J. L., & Zhu, Y. L. (1985). Effect of soluble salts on unfrozen water content of Chinese loess at Lanzhou. Journal of Glaciology and Geocryology, (02), 99-109.

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

[0068] Ma, T. T., Wei, C. F., Zhou, J. Z., et al. (2015). Freezing characteristic curve and water retention 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 Unfrozen Water 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 test the unfrozen water model. The unknown input parameters of the bound water microscopic freezing characteristics model (equation 10) include: 1, the diffusion layer thickness d, the parameter a, the freezing point depression coefficient K of bound water c , and the solution freezing point T d at the edge of the double electric layer, which are mainly calculated by the double electric layer theory. d and a are obtained by equations (5) and (6) respectively; the solution freezing point T d at the edge of the double electric layer can be calculated by bringing x = d into equation (8); K c ≈ 18.5, which is obtained according to Figure 3 ​

[0071] ⑹Model validation

[0072] ①Microscopic freezing characteristics of bound water

[0073] Figure 4 The microscopic freezing characteristics of bound water (double layer cation solution, Eq. 10) for five different types of soils are shown. The five soil samples are from a farmland in Texas, USA, and the soil solution concentration is low (n0≈0.005 mol·L -1 , and the average valence of ions in different types of soils is similar (z≈1.8). From the figure, it can be seen that the unfrozen water film thickness of bound water decreases exponentially with temperature, and the microscopic freezing characteristics of different types of soils almost coincide, which indicates that the microscopic freezing characteristics of bound water are independent of soil texture. Therefore, the present invention considers that the microscopic freezing characteristics of bound water in soils with low salinity are very similar, and the microscopic freezing characteristics curves of the five soils can be replaced by an average curve, and 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 characteristics curves of bound water under different soil solution concentrations are shown. The average valence of cations in the curves is 1.8, and the surface charge density is 1.5×10 -5 C / cm 2 , and the solution concentration is low, from 0.005 mol·L -1 to 0.05 mol·L -1 . From the figure, it can be seen that the unfrozen water film thickness of bound water decreases exponentially with temperature. The microscopic freezing characteristics curves of bound water under different soil solution concentrations almost coincide, which indicates that when the soil solution concentration is low, i.e. 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 the five different types of salt-free soil in Table 1 to calculate the microscopic freezing characteristics curves of low-salt soil, which significantly simplifies the calculation process of the unfrozen water model.

[0075] ②Frozen soil unfrozen water model results

[0076] Figure 6 The comparison between the parameterized model of frozen soil unfrozen water and 12 measured unfrozen water contents (Table 2) is shown. From the figure, it can be seen that the calculation results of the parameterized model are basically consistent with the measured unfrozen water contents. However, in some soil samples, there are certain differences between the model results and the measured data. For example, the Xintaoyuan silt and the Northwest Alaska silt ( Figure 6 a and Figure 6 c), the Xi'an loess and the limonite ( Figure 6 b and Figure 6d). Since all the soils are non-saline soils, these differences could be due to the difference in the type of salts in the soils, which results in the change of the freezing point depression coefficient and the micro- freezing characteristics of bound water. Despite these differences, the parameterized models have the same trend as the measured data, and the errors are not significant Figure 6 except for the limonite in d). The difference between the unfrozen water model and the measured data decreases with the increase of clay content, which indicates that the bound water content in clay is higher. Overall, the unfrozen water model has more accurate results and can be used to calculate the unfrozen water content of frozen soil.

Claims

1. A frozen soil unfrozen water parameterization model based on the micro- freezing characteristics of bound water, characterized in that: First, collect low-salt or salt-free soil samples and measure soil temperature T and specific surface area A. S The soil solution concentration n0 is determined, and n0 is limited to ≤ 0.05 mol / L; then the soil mass water content w is obtained according to the following formula. u : where: p b ≈ 1.05 g-cm -3 is the density of the bound water; is the thickness of the diffusion layer; a c ≈ 18.5 °C-L-mol -1 ; is the thickness of the adsorption layer; T d ≈ -0.36 °C.

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