A method for predicting soil water characteristic curve based on solid-liquid interface theory and particle size distribution

Abstract

This invention discloses a method for predicting soil-water characteristic curves based on solid-liquid interface theory and particle size distribution. The method includes the following steps: S1. Experimentally obtaining the particle size distribution, dry density, soil particle density, and saturated water content of natural soil; S2. Determining the mathematical expression of the natural soil particle size distribution; S3. Determining the matrix suction head for each drainage stage of the natural soil; S4. Determining the water content corresponding to the matrix suction head for each drainage stage of the natural soil. Based on solid-liquid interface theory and particle size distribution, this invention considers both adsorption and capillary water retention mechanisms in soil, deriving the relationship between the soil matrix suction head and water content, and providing a calculation formula for the soil-water characteristic curve with parameters of soil particle size distribution, dry density, and soil particle density. The model involved in this invention closely approximates the objective water retention mechanism of soil, and the physical meaning of each parameter is clear and easy to obtain, providing a theoretical basis for soil water retention prediction, soil moisture management optimization, and hydrological model applications.

Description

Technical Field

[0001] This invention relates to a method for predicting soil-water characteristic curves, specifically a method for calculating soil-water characteristic curves based on solid-liquid interface theory and particle size distribution. Background Technology

[0002] Moisture content has numerous effects on soil properties and is an important indicator in engineering, hydrology and meteorology, environmental management, and agricultural science. In engineering activities, changes in soil moisture content cause variations in the strength, permeability, and deformation of unsaturated soils, thus affecting the safety of engineering projects and the stability of structures. It is one of the most important triggering factors for engineering and geological disasters such as pit collapses, slope instability, and landslides. The soil-water characteristic curve (SWCC) is widely considered to represent the relationship between the moisture content (or saturation) and matric suction in unsaturated soils. It can be used to estimate the physical, mechanical, and hydraulic properties of soils, such as shear strength, hydraulic conductivity or permeability coefficient, diffusion coefficient, and adsorption coefficient. Furthermore, it is a fundamental tool for simulating water, temperature, and solute transport in unsaturated soils. Therefore, the SWCC is considered one of the most basic hydraulic properties of unsaturated soils and is crucial for environmental and geotechnical engineering, soil science, and other fields.

[0003] Currently, methods for obtaining SWCC can be broadly categorized into two types. The first type involves directly obtaining SWCC through experiments; these methods are often expensive, demanding, and time-consuming. The second type involves indirectly obtaining SWCC through predictive models; these methods are simpler, faster, and less expensive, and have great potential. Predictive models are mainly divided into empirical models and physical-empirical models. Empirical models primarily use techniques such as multiple regression or neural network analysis to establish a relationship between easily obtainable soil physical and chemical properties, such as soil dry density and the content of sand, silt, clay, and organic matter, and SWCC. Empirical models generally have fitting parameters, and when a sufficient number of fitting parameters are used, they can fit the measured data well. However, the performance of these empirical models strongly depends on the database used for model calibration and testing, and the fitting parameters in the model have no physical meaning. Therefore, many researchers tend to favor physical-empirical models derived from the physical and chemical properties of soil. Physical-empirical models are mainly based on the shape similarity between SWCC and particle size distribution curves, implying a close correlation between pore size distribution and particle size distribution. In the classical physical-empirical model framework, soil particles and pore structure are generalized as spherical particles and cylindrical capillary bundles, respectively. Particle size distribution and pore size distribution are divided into multiple size fractions, corresponding to multiple stages of soil drainage. The matric suction of a certain size fraction can be calculated using the particle-pore size conversion relationship, while the water content can be derived from the cumulative particle size distribution function. Based on this theory, many scholars have proposed their own physical-empirical models. However, current physical-empirical models still have some shortcomings. First, most of the conversion relationships proposed by physical-empirical models are linear relationships with poor adaptability, while research shows that nonlinear relationships are more consistent with the conversion relationship between soil particle size and pore size. More importantly, many of these conversion relationships exhibit mass effects. That is, for the same soil sample, taking different masses will result in different pore sizes after conversion using the pore-particle size conversion relationship, and thus different SWCCs, which is clearly unreasonable. Secondly, the physical-empirical model generalizes the soil pore structure as cylindrical capillary bundles, only considering the contribution of capillary action to water content, while neglecting the influence of adsorbed water formed by adsorption controlled by soil particle surface forces. Existing research shows that soil-water characteristic curves (SWCCs) link water content to matrix suction through adsorption and capillary action, often leading to an underestimation of water content in the high matrix suction range. Although many scholars have subsequently incorporated adsorbed water into the model to improve the underestimation of water content in the high matrix suction range by the physical-empirical model, the effect has been limited, and the explanation of adsorption is still incomplete. Therefore, to overcome the shortcomings of the physical-empirical model and more comprehensively predict soil-water characteristic curves, not only is a nonlinear, mass-independent particle size-pore size relationship needed, but also more sufficient theoretical basis to further explain and quantify adsorption. Summary of the Invention

[0004] The purpose of this invention is to provide a method for calculating soil-water characteristic curves based on solid-liquid interface theory and particle size distribution. This method is referred to as the improved physical-empirical model. Compared to the aforementioned methods for obtaining soil-water characteristic curves, the method described in this invention is simpler to calculate, the model closely approximates the objectively existing water-holding mechanism of soil, and the physical meaning of each parameter is clear and easy to obtain.

[0005] The objective of this invention is achieved through the following technical solution:

[0006] A method for predicting soil-water characteristic curves based on solid-liquid interface theory and particle size distribution includes the following steps:

[0007] S1. The experiment obtains the particle size distribution, dry density, soil particle density, and saturated water content of natural soil.

[0008] Step S1 includes the following sub-steps:

[0009] S1. Obtain the particle size distribution, dry density, soil particle density, and saturated moisture content of natural soil through experiments. The particle size distribution can be obtained using methods such as sieving or laser particle size analyzers; the dry density can be obtained using methods such as the ring sampler method; the soil particle density can be obtained using methods such as the hydrometer bottle method; and the saturated moisture content is obtained through drying. Convert the mass moisture content obtained by drying to the volumetric moisture content:

[0010] (1)

[0011] In equation (1), This refers to the volumetric moisture content. For mass moisture content, For dry density, This is the density of water.

[0012] S2. Determine the mathematical expression of the particle size distribution of natural soil;

[0013] Step S2 includes the following sub-steps:

[0014] S201. The number of measured particle size distribution points is inconsistent and the curves are discontinuous for different soil types. The logistic growth model for describing particle size distribution, proposed by Liu et al., is used to make the measured particle size distribution continuous, thereby obtaining a mathematical expression for the particle size distribution:

[0015] (2)

[0016] In equation (2), (%) represents particles with a diameter smaller than The cumulative mass percentage of particles (μm) , and These are the fitting parameters. For different soil samples, as long as the measured particle size distribution is obtained, the fitting parameters can be determined. , and The value of .

[0017] S202. To facilitate calculation, after obtaining the mathematical expression of the particle size distribution, the particle size distribution is re-divided into several segments, each representing a different drainage stage of the soil. The specific segments are: 2, 5, 10, 15, 20, 30, 40, 50, 60, 70, 80, 90, 100, 200, 500, 1000, 2000 μm.

[0018] S3. Determine the matrix suction head for each drainage stage of the natural soil;

[0019] Step S3 includes the following sub-steps:

[0020] S301. Assume that soil particles and pore structure are generalized as spherical particles and cylindrical capillary bundles, respectively. The particle size distribution is divided into n particle size units, corresponding to n stages of soil drainage. The soil particles in each particle size unit are arranged in a certain way. The dry density and particle density of the soil sample are applicable to each unit, which means that the sample porosity is also applicable to each unit. Therefore, the porosity fraction of each particle size unit is equal to the particle fraction. According to step S2, the specific stages are 17 segments. During the drainage process, water in large pores is drained first, while water is retained in small pores. For the... For a particle size unit, according to the Yong-Laplace equation, the radius of this unit under mechanical equilibrium is... The total pressure change at the gas-water interface surface of the capillary pores, i.e., matrix suction. for:

[0021] (3)

[0022] In equation (3), For the first Matrix suction (kPa) per particle size unit For the first Pore ​​radius of each particle size unit (cm) The surface tension at the air-water interface at 25℃ is taken as 7.179 × 10⁻⁶. -4 N·cm -1 , The contact angle is 0° during soil drainage.

[0023] S302. Based on the theoretical framework of the physical-empirical model of soil-water characteristic curves, the first... Pore ​​radius of each particle size unit The particle size-pore size conversion relationship can be established by using particle radius. First, we establish the relationship between pore volume and pore radius, expressed in terms of particle number. and pore length The quantitative relationship of pore volume is expressed as follows:

[0024] (4)

[0025] In equation (4), For pore volume, The total volume of the particles. The particle radius (cm) Porosity For the first The number of equivalent spherical particles per particle size unit. Porosity. and particle count The expressions are as follows:

[0026] (5)

[0027] (6)

[0028] In equations (5) and (6), This represents the soil particle density of the soil sample. This represents the dry density of the soil sample. For the first The particle mass fraction of each particle size unit (obtained from the results of particle size distribution segmentation).

[0029] The physical-empirical model assumes that, under ideal conditions, the pore length of a unit is the length of all the soil particles accumulated within that unit, i.e. Therefore, according to equation (4), we know However, due to the non-spherical shape of actual soil particles and the complex tortuous nature of pores, the actual pore length is often longer than the ideal condition. To estimate pore length from a completely new perspective, based on the idea of ​​"virtual" particles proposed by Campos-Guereta et al., a shape factor is defined. This process transforms the particles into "virtual" particles with equal density, ensuring that the volume and mass of the particles and "virtual" particles are equal. At this point, the total volume of the particles... for:

[0030] (7)

[0031] In equation (7), For the first The number of "virtual" equivalent spherical particles corresponding to each particle size unit, at which point the pore length... This can be expressed as the length formed by the "virtual" accumulation of particles, i.e.:

[0032] (8)

[0033] Substituting equation (8) into equation (4), we can obtain the pore volume. for:

[0034] (9)

[0035] The pore radius can be obtained from equation (9). for:

[0036] (10)

[0037] As can be seen from equation (10), the conversion between particle size and pore size is nonlinear and independent of mass. Substituting equation (10) into equation (3), we can obtain the first... Substrate suction in each drainage stage for:

[0038] (11)

[0039] Finally, after transformation, we can obtain the first soil body. Substrate suction head at each drainage stage (cm) is:

[0040] (12)

[0041] In equation (12), The density of water (g·cm³) -3 ), gravitational acceleration (N·g) -1 ).

[0042] S4. Determine the moisture content corresponding to the matrix suction head at each drainage stage of the natural soil.

[0043] Step S4 includes the following sub-steps:

[0044] S401. Existing research has shown that the soil-water characteristic curve links water content with matrix suction through adsorption and capillary action. Based on this objective fact, water content is divided into adsorbed water content and capillary water content. Then, the... Moisture content at each drainage stage for:

[0045] (13)

[0046] In equation (13), It is the first Moisture content (cm³) at each drainage stage 3 ·cm -3 ), and These represent the water content (cm³) of the adsorbed water during this drainage stage. 3 ·cm -3 ) and capillary water content (cm 3 ·cm -3 ).

[0047] S402. Capillary water content, representing the contribution of capillary action to water content in equation (13). One approach can be derived using a theoretical framework based on a physics-empirical model. Assume soil particles and pore structure are generalized as spherical particles and cylindrical capillary bundles, respectively. The particle size distribution is divided into n particle size units, corresponding to n stages of soil drainage. The soil particles in each particle size unit are arranged in a specific manner. The dry density and particle density of the soil sample are applicable to each unit, meaning the sample void ratio is also applicable to each unit. Therefore, the porosity fraction of each particle size unit is equal to the particle fraction. During drainage, water in large pores drains first, while water remains in small pores. The volumetric water content at each stage can be expressed as the cumulative volume of water-filled pores divided by the total volume, i.e., the capillary water content. This can be expressed as the particle mass fraction accumulated from the smallest particle size to the corresponding particle size:

[0048] (14)

[0049] In equation (14), saturated moisture content For the first Mass fraction of some particles (obtained from the results of particle size distribution segmentation).

[0050] S403. In formula (13), the adsorbed water moisture content represents the contribution of adsorption to the water content. One possibility is that this can be obtained using the Derjaguin-Landau-Verwey-Overbeek (DLVO) theory within the solid-liquid interface theory framework. Tuller, Or, Chang, and other scholars have quantified the contribution of adsorption to water content by examining changes in the thickness of the adsorbed water film during drainage. In their research, the mechanical balance between matrix suction and the water film separation pressure caused by van der Waals forces on soil particle surfaces is the reason for the stable maintenance of the adsorbed water film, and the adsorbed water content... It can be represented as:

[0051] (15)

[0052] In equation (15), and Representing the first The adsorbed water moisture content (cm³) of each drainage stage 3 ·cm -3 ) and capillary water content (cm 3 ·cm -3 ), saturated moisture content These are empirical parameters. For the first The thickness of the adsorbed water film (m) at each drainage stage. The specific surface area of ​​the soil sample (m²) 2 ·kg -1 ), The dry density of the soil sample (kg·m³) -3 ).

[0053] However, existing studies have shown that adsorption is mainly caused by the electric field and van der Waals force field near the solid (soil particles)-liquid (soil pore water) interface. Considering only van der Waals forces is insufficient to fully explain adsorption. Therefore, we consider using the DLVO theory from solid-liquid interface theory to further quantify adsorption. The DLVO theory posits that the forces at the solid-liquid interface are mainly composed of short-range van der Waals forces and long-range double-layer forces, which aligns with existing descriptions of the primary causes of adsorption. When the adsorbed water film remains stable, the matrix suction and the water film separation pressure caused by the combined van der Waals forces and double-layer electrostatic forces reach mechanical equilibrium, as deduced below:

[0054] According to the Kelvin equation, matrix suction at phase equilibrium. Relative vapor pressure above the curved surface ( )related:

[0055] (16)

[0056] In equation (16), It is the gas constant (=8.314 J·K). -1 ·mol -1 ), It is absolute temperature (K). This is the molar volume of water at 25℃ (=1.8×10⁻⁶). -5 m 3 ·mol -1 ), It is relative humidity (%).

[0057] When the adsorbed water film on the surface of soil particles thins under external force, the two interfaces of the water film approach each other, generating separation pressure to balance the external force and thus keep the adsorbed water film stable. The pressure of separation in the water film at equilibrium no longer decreases. ) is also related to related:

[0058] (17)

[0059] By combining equations (16) and (17), we can obtain

[0060] (18)

[0061] According to the DLVO theory, the separation pressure in the water film It equals the sum of the separation pressures caused by both van der Waals forces and double-layer electrostatic forces:

[0062] (19)

[0063] In the formula, It is the separation pressure caused by van der Waals forces. The separation pressure is caused by the electrostatic force of the electric double layer. The specific mathematical expression of these two separation pressure components is as follows:

[0064] (20)

[0065] (twenty one)

[0066] In equations (20) and (21), This is the Hamaker constant; for soil, the effective Hamaker constant is generally taken as -6 × 10⁻⁶. -20 J, It is the relative permittivity of water (78.4 at 25°C). It is the vacuum permittivity (=8.85×10⁻⁶). −12 C 2 ·J −1 ·m −1 ), It is the Boltzmann constant (=1.38×10). −23 J.K. −1 ), It is the elementary charge (=1.60×10⁻⁶). −19 C), It is the electrolyte valence state (taken as 1).

[0067] Substituting equations (19), (20), and (21) into equation (18), we can obtain the first... Adsorbed water film thickness at each drainage stage and matrix suction (or substrate suction head) The relationship between )

[0068] = (twenty two)

[0069] The specific surface area of ​​soil in equation (15) (m 2 ·g -1 It can be obtained from empirical formulas:

[0070] (twenty three)

[0071] (twenty four)

[0072] In equation (24), , and These represent the percentage content of clay, silt, and sand in the soil sample, respectively (which can be obtained from the measured particle size distribution of the soil sample). , and The geometric mean diameters of clay, silt, and sand particles are 0.001 mm, 0.026 mm, and 1.025 mm, respectively.

[0073] Substituting equations (12), (14), (22), (23), and (24) into equation (15) yields the water content of the adsorbed water. .

[0074] S404. The obtained capillary water content and the water content of adsorbed water By adding the results according to formula (13), the substrate suction head can be obtained. moisture content This allows us to obtain the soil-water characteristic curves of the soil.

[0075] The present invention has the following beneficial effects:

[0076] Compared to other methods for obtaining soil-water characteristic curves, this invention starts from the two objectively existing water-holding mechanisms in soil: capillary and adsorption. It considers the physical processes and development trends of these two mechanisms during the change from saturated to dry state. By combining the theoretical framework of a physical-empirical model with DLVO theory, the two water-holding mechanisms are quantified as capillary water and adsorbed water, respectively, resulting in an improved physical-empirical model of the relationship between matrix suction head and water content. The model fully utilizes physical properties such as soil particle size distribution, dry density, and soil particle density. These parameters are easily obtained and have clear physical meanings, enabling a comprehensive, objective, and accurate reflection of the change in soil water content with matrix suction head. Attached Figure Description

[0077] To more clearly illustrate the technical solutions of the embodiments of the present invention, the accompanying drawings used in the description of the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0078] Figure 1 This is a schematic diagram of the soil-water characteristic curve (SWCC).

[0079] Figure 2 Comparison of pore length estimation for particle size unit: (a) ideal condition, (b) condition of the present invention;

[0080] Figure 3 The measured particle size distribution (PSD) of loam 2531 and the corresponding logistic growth model curve are shown.

[0081] Figure 4 This is a graph showing the predicted soil-water characteristic curve based on the theoretical formula of this invention.

[0082] Figure 5 This is a graph showing the prediction error of the soil moisture content using the theoretical formula of this invention. Detailed Implementation

[0083] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0084] A method for predicting soil-water characteristic curves based on solid-liquid interface theory and particle size distribution includes the following steps:

[0085] S1. The experiment obtains the particle size distribution, dry density, soil particle density, and saturated water content of natural soil.

[0086] Step S1 includes the following sub-steps:

[0087] S1. Obtain the particle size distribution, dry density, soil particle density, and saturated moisture content of natural soil through experiments. The particle size distribution can be obtained using methods such as sieving or laser particle size analyzers; the dry density can be obtained using methods such as the ring sampler method; the soil particle density can be obtained using methods such as the hydrometer bottle method; and the saturated moisture content is obtained through drying. Convert the mass moisture content obtained by drying to the volumetric moisture content:

[0088] (1)

[0089] In equation (1), This refers to the volumetric moisture content. For mass moisture content, For dry density, This is the density of water.

[0090] S2. Determine the mathematical expression of the particle size distribution of natural soil;

[0091] Step S2 includes the following sub-steps:

[0092] S201. The number of measured particle size distribution points is inconsistent and the curves are discontinuous for different soil types. The logistic growth model for describing particle size distribution, proposed by Liu et al., is used to make the measured particle size distribution continuous, thereby obtaining a mathematical expression for the particle size distribution:

[0093] (2)

[0094] In equation (2), (%) represents particles with a diameter smaller than The cumulative mass percentage of particles (μm) , and These are the fitting parameters. For different soil samples, as long as the measured particle size distribution is obtained, the fitting parameters can be determined. , and The value of .

[0095] S202. To facilitate calculation, after obtaining the mathematical expression of the particle size distribution, the particle size distribution is re-divided into several segments, each representing a different drainage stage of the soil. The specific segments are: 2, 5, 10, 15, 20, 30, 40, 50, 60, 70, 80, 90, 100, 200, 500, 1000, 2000 μm.

[0096] S3. Determine the matrix suction head for each drainage stage of the natural soil;

[0097] Step S3 includes the following sub-steps:

[0098] S301. Assume that soil particles and pore structure are generalized as spherical particles and cylindrical capillary bundles, respectively. The particle size distribution is divided into n particle size units, corresponding to n stages of soil drainage. The soil particles in each particle size unit are arranged in a certain way. The dry density and particle density of the soil sample are applicable to each unit, which means that the sample porosity is also applicable to each unit. Therefore, the porosity fraction of each particle size unit is equal to the particle fraction. According to step S2, the specific stages are 17 segments. During the drainage process, water in large pores is drained first, while water is retained in small pores. For the... For a particle size unit, according to the Yong-Laplace equation, the radius of this unit under mechanical equilibrium is... The total pressure change at the gas-water interface surface of the capillary pores, i.e., matrix suction. for:

[0099] (3)

[0100] In equation (3), For the first Matrix suction (kPa) per particle size unit For the first Pore ​​radius of each particle size unit (cm) The surface tension at the air-water interface at 25℃ is taken as 7.179 × 10⁻⁶. -4 N·cm -1 , The contact angle is 0° during soil drainage.

[0101] S302. Based on the theoretical framework of the physical-empirical model of soil-water characteristic curves, the first... Pore ​​radius of each particle size unit The particle size-pore size conversion relationship can be established by using particle radius. First, we establish the relationship between pore volume and pore radius, expressed in terms of particle number. and pore length The quantitative relationship of pore volume is expressed as follows:

[0102] (4)

[0103] In equation (4), For pore volume, The total volume of the particles. The particle radius (cm) Porosity For the first The number of equivalent spherical particles per particle size unit. Porosity. and particle count The expressions are as follows:

[0104] (5)

[0105] (6)

[0106] In equations (5) and (6), This represents the soil particle density of the soil sample. This represents the dry density of the soil sample. For the first The particle mass fraction of each particle size unit (obtained from the results of particle size distribution segmentation).

[0107] The physical-empirical model assumes that, under ideal conditions, the pore length of a unit is the length of all the soil particles accumulated within that unit, i.e. Therefore, according to equation (4), we know However, due to the non-spherical shape of actual soil particles and the complex tortuous nature of pores, the actual pore length is often longer than the ideal condition. To estimate pore length from a completely new perspective, based on the idea of ​​"virtual" particles proposed by Campos-Guereta et al., a shape factor is defined. This process transforms the particles into "virtual" particles with equal density, ensuring that the volume and mass of the particles and "virtual" particles are equal. At this point, the total volume of the particles... for:

[0108] (7)

[0109] In equation (7), For the first The number of "virtual" equivalent spherical particles corresponding to each particle size unit, at which point the pore length... This can be expressed as the length formed by the "virtual" accumulation of particles, i.e.:

[0110] (8)

[0111] Substituting equation (8) into equation (4), we can obtain the pore volume. for:

[0112] (9)

[0113] The pore radius can be obtained from equation (9). for:

[0114] (10)

[0115] As can be seen from equation (10), the conversion between particle size and pore size is nonlinear and independent of mass. Substituting equation (10) into equation (3), we can obtain the first... Substrate suction in each drainage stage for:

[0116] (11)

[0117] Finally, after transformation, we can obtain the first soil body. Substrate suction head at each drainage stage (cm) is:

[0118] (12)

[0119] In equation (12), The density of water (g·cm³) -3 ), gravitational acceleration (N·g) -1 ).

[0120] S4. Determine the moisture content corresponding to the matrix suction head at each drainage stage of the natural soil.

[0121] Step S4 includes the following sub-steps:

[0122] S401. Existing research has shown that the soil-water characteristic curve links water content with matrix suction through adsorption and capillary action. Based on this objective fact, water content is divided into adsorbed water content and capillary water content. Then, the... Moisture content at each drainage stage for:

[0123] (13)

[0124] In equation (13), It is the first Moisture content (cm³) at each drainage stage 3 ·cm -3 ), and These represent the water content (cm³) of the adsorbed water during this drainage stage. 3 ·cm -3 ) and capillary water content (cm 3 ·cm -3 ).

[0125] S402. Capillary water content, representing the contribution of capillary action to water content in equation (13). One approach can be derived using a theoretical framework based on a physics-empirical model. Assume soil particles and pore structure are generalized as spherical particles and cylindrical capillary bundles, respectively. The particle size distribution is divided into n particle size units, corresponding to n stages of soil drainage. The soil particles in each particle size unit are arranged in a specific manner. The dry density and particle density of the soil sample are applicable to each unit, meaning the sample void ratio is also applicable to each unit. Therefore, the porosity fraction of each particle size unit is equal to the particle fraction. During drainage, water in large pores drains first, while water remains in small pores. The volumetric water content at each stage can be expressed as the cumulative volume of water-filled pores divided by the total volume, i.e., the capillary water content. This can be expressed as the particle mass fraction accumulated from the smallest particle size to the corresponding particle size:

[0126] (14)

[0127] In equation (14), saturated moisture content For the first Mass fraction of some particles (obtained from the results of particle size distribution segmentation).

[0128] S403. In formula (13), the adsorbed water moisture content represents the contribution of adsorption to the water content. One possibility is that this can be obtained using the Derjaguin-Landau-Verwey-Overbeek (DLVO) theory within the solid-liquid interface theory framework. Tuller, Or, Chang, and other scholars have quantified the contribution of adsorption to water content by examining changes in the thickness of the adsorbed water film during drainage. In their research, the mechanical balance between matrix suction and the water film separation pressure caused by van der Waals forces on soil particle surfaces is the reason for the stable maintenance of the adsorbed water film, and the adsorbed water content... It can be represented as:

[0129] (15)

[0130] In equation (15), and Representing the first The adsorbed water moisture content (cm³) of each drainage stage 3 ·cm -3 ) and capillary water content (cm 3 ·cm -3 ), saturated moisture content These are empirical parameters. For the first The thickness of the adsorbed water film (m) at each drainage stage. The specific surface area of ​​the soil sample (m²) 2 ·kg -1 ), The dry density of the soil sample (kg·m³) -3 ).

[0131] However, existing studies have shown that adsorption is mainly caused by the electric field and van der Waals force field near the solid (soil particles)-liquid (soil pore water) interface. Considering only van der Waals forces is insufficient to fully explain adsorption. Therefore, we consider using the DLVO theory from solid-liquid interface theory to further quantify adsorption. The DLVO theory posits that the forces at the solid-liquid interface are mainly composed of short-range van der Waals forces and long-range double-layer forces, which aligns with existing descriptions of the primary causes of adsorption. When the adsorbed water film remains stable, the matrix suction and the water film separation pressure caused by the combined van der Waals forces and double-layer electrostatic forces reach mechanical equilibrium, as deduced below:

[0132] According to the Kelvin equation, matrix suction at phase equilibrium. Relative vapor pressure above the curved surface ( )related:

[0133] (16)

[0134] In equation (16), It is the gas constant (=8.314 J·K). -1 ·mol -1 ), It is absolute temperature (K). This is the molar volume of water at 25℃ (=1.8×10⁻⁶). -5 m 3 ·mol -1 ), It is relative humidity (%).

[0135] When the adsorbed water film on the surface of soil particles thins under external force, the two interfaces of the water film approach each other, generating separation pressure to balance the external force and thus keep the adsorbed water film stable. The pressure of separation in the water film at equilibrium no longer decreases. ) is also related to related:

[0136] (17)

[0137] By combining equations (16) and (17), we can obtain

[0138] (18)

[0139] According to the DLVO theory, the separation pressure in the water film It equals the sum of the separation pressures caused by both van der Waals forces and double-layer electrostatic forces:

[0140] (19)

[0141] In the formula, It is the separation pressure caused by van der Waals forces. The separation pressure is caused by the electrostatic force of the electric double layer. The specific mathematical expression of these two separation pressure components is as follows:

[0142] (20)

[0143] (twenty one)

[0144] In equations (20) and (21), This is the Hamaker constant; for soil, the effective Hamaker constant is generally taken as -6 × 10⁻⁶. -20 J, It is the relative permittivity of water (78.4 at 25°C). It is the vacuum permittivity (=8.85×10⁻⁶). −12 C 2 ·J −1 ·m −1 ), It is the Boltzmann constant (=1.38×10). −23 J.K. −1 ), It is the elementary charge (=1.60×10⁻⁶). −19 C), It is the electrolyte valence state (taken as 1).

[0145] Substituting equations (19), (20), and (21) into equation (18), we can obtain the first... Adsorbed water film thickness at each drainage stage and matrix suction (or substrate suction head) The relationship between )

[0146] = (twenty two)

[0147] The specific surface area of ​​soil in equation (15) (m 2 ·g -1 It can be obtained from empirical formulas:

[0148] (twenty three)

[0149] (twenty four)

[0150] In equation (24), , and These represent the percentage content of clay, silt, and sand in the soil sample, respectively (which can be obtained from the measured particle size distribution of the soil sample). , and The geometric mean diameters of clay, silt, and sand particles are 0.001 mm, 0.026 mm, and 1.025 mm, respectively.

[0151] Substituting equations (12), (14), (22), (23), and (24) into equation (15) yields the water content of the adsorbed water. .

[0152] S404. The obtained capillary water content and the water content of adsorbed water By adding the results according to formula (13), the substrate suction head can be obtained. moisture content This allows us to obtain the soil-water characteristic curves of the soil.

[0153] A specific application of this embodiment is to use three soil samples (clay 2360, loam 2531, and sand 1466) from the USDA Unsaturated Soil Hydraulic Database (UNSODA) to verify the model's predictive performance. The USDA Unsaturated Soil Hydraulic Database contains detailed and clear data records for the measured soil-water characteristic curves, particle size distribution, dry density, soil particle density, and saturated water content of these three soil samples. For example, the various physical properties and particle size distribution of loam 2531 are shown in Tables 1 and 2, respectively.

[0154] Table 1. Physical properties of loam 2531

[0155] 1.46 2.64 0.401 15.80 43.20 41.00

[0156] Table 2. Particle size distribution of loam 2531

[0157] 1 14 5 21 10 30 20 41 50 59 100 72 500 97 1000 99 2000 100

[0158] Depend on Figure 4 It can be observed that as the matrix suction head increases, the SWCC shows a decreasing trend, which is consistent with theoretical expectations. Figure 5 It can be seen that the soil moisture content predicted by the theoretical formula of this invention is close to the experimental measurement value, with most data points within the 10% error line. The predicted values ​​of the theoretical formula and the experimental data can match well. The prediction results of the improved physical-empirical model established in this invention are generally good. Through statistical analysis of the prediction results of the theoretical formula and the experimental measurement values, the following results are obtained: the coefficient of determination R... 2=0.9895, this indicator shows that the theoretical formula prediction results are relatively close to the experimental measurements; Root Mean Square Error (RMSE) = 0.0138, this indicator shows that the theoretical formula prediction results differ from the experimental measurements by an average of 1.38%; Performance Deviation RPD (Standard Deviation SD / RMSE) = 9.8628, which is greater than 3 (RPD > 3 indicates good model performance, and the higher the better), this indicator shows that the model's predictive performance is good. Therefore, the theoretical formula prediction results have small errors and are relatively accurate.

[0159] In summary, the calculation method described in this invention has wide applicability, clear physical meaning, and high calculation accuracy, and can meet the prediction requirements of soil water characteristic curves.

[0160] The preferred embodiments of the present invention disclosed above are merely illustrative of the invention. These preferred embodiments do not exhaustively describe all details, nor do they limit the invention to the specific implementations described. Clearly, many modifications and variations can be made based on the content of this specification. This specification selects and specifically describes these embodiments to better explain the principles and practical applications of the invention, thereby enabling those skilled in the art to better understand and utilize the invention. The invention is limited only by the claims and their full scope and equivalents.

Claims

1. A soil water characteristic curve prediction method based on solid-liquid interface theory and particle size distribution, characterized in that: Includes the following steps: S1. The experiment obtains the particle size distribution, dry density, soil particle density, and saturated water content of natural soil. S2. Determine the mathematical expression of the particle size distribution of natural soil; S3. Determine the matrix suction head for each drainage stage of the natural soil. Assume the soil particles and pore structure are generalized as spherical particles and cylindrical capillary bundles, respectively. The particle size distribution is divided into n particle size units, corresponding to the n stages of soil drainage. The soil particles in each particle size unit are arranged in a specific manner, and the porosity fraction is equal to the particle fraction in each particle size unit. According to step S2, the specific stages are divided into 17 segments. Substrate suction head at each drainage stage (cm) is: (12) In equation (12), For the first Matrix suction (kPa) per particle size unit The density of water (g·cm³) -3 ), gravitational acceleration (N·g) -1 ), Porosity The surface tension of the air-water interface at 25°C (N·cm) -1 ), For the first Unit particle radius (cm) For shape factor; S4. Determine the moisture content corresponding to the matrix suction head at each drainage stage of the natural soil; step S4 includes: S401. If the moisture content is divided into adsorbed water moisture content and capillary water moisture content, then the... Moisture content at each drainage stage for: (13) In equation (13), It is the first Moisture content (cm³) at each drainage stage 3 ·cm -3 ), and These represent the water content (cm³) of the adsorbed water during this drainage stage. 3 ·cm -3 ) and capillary water content (cm 3 ·cm -3 ); S402. Capillary water content, representing the contribution of capillary action to water content in equation (13). According to a theoretical framework based on a physics-empirical model, during the drainage process, water in large pores is discharged first, while water is retained in small pores. The volumetric water content at each stage can be expressed as the cumulative volume of water-filled pores divided by the total volume, i.e., capillary water content. This can be expressed as the particle mass fraction accumulated from the smallest particle size to the corresponding particle size: (14) In equation (14), saturated moisture content For the first The mass fraction of some particles is obtained based on the segmented results of particle size distribution. S403. In formula (13), the adsorbed water moisture content represents the contribution of adsorption to the water content. One finding, derived from the Derjaguin-Landau-Verwey-Overbeek (DLVO) theory within the solid-liquid interface framework, is that the mechanical equilibrium between matrix suction and the water film separation pressure caused by van der Waals forces on soil particle surfaces is the reason for the stable maintenance of the adsorbed water film. The adsorbed water content... It can be represented as: (15) In equation (15), and Representing the first The adsorbed water moisture content (cm³) of each drainage stage 3 ·cm -3 ) and capillary water content (cm 3 ·cm -3 ), saturated moisture content, These are empirical parameters. For the first The thickness of the adsorbed water film (m) at each drainage stage. The specific surface area of ​​the soil sample (m²) 2 ·kg -1 ), The dry density of the soil sample (kg·m³) -3 ); When the adsorbed water film remains stable, the matrix suction and the water film separation pressure caused by van der Waals forces and double-layer electrostatic forces reach mechanical equilibrium, as shown in the following derivation: According to the Kelvin equation, matrix suction at phase equilibrium. Relative steam pressure above the curved surface related: (16) In equation (16), This is the gas constant, taken as 8.314 J·K. -1 ·mol -1 ; It is absolute temperature (K); This is the molar volume of water at 25℃, taken as 1.8 × 10⁻⁶. -5 m 3 ·mol -1 ; It is relative humidity (%); When the adsorbed water film on the surface of soil particles thins under external force, the two interfaces of the water film approach each other, generating separation pressure to balance the external force and thus keep the adsorbed water film stable. The pressure of separation in the water film at equilibrium no longer decreases. also with related: (17) By combining equations (16) and (17), we can obtain (18) According to the DLVO theory, the separation pressure in the water film is equal to the sum of the separation pressures caused by both van der Waals forces and double-layer electrostatic forces: (19) In the formula, It is the separation pressure caused by van der Waals forces. The separation pressure is caused by the electrostatic force of the electric double layer. The specific mathematical expression of these two separation pressure components is as follows: (20) (21) In equations (20) and (21), This is the Hamaker constant; for soil, the effective Hamaker constant is generally taken as -6 × 10⁻⁶. -20 J; It is the relative permittivity of water, which is 78.4 at 25°C; It is the vacuum permittivity, taken as 8.85 × 10⁻⁶. −12 C 2 ·J −1 ·m −1 ; This is the Boltzmann constant, taken as 1.38 × 10⁻⁶. −23 J.K. −1 ; It is the elementary charge, taken as 1.60 × 10⁻⁶. −19 C; It is the valence state of the electrolyte, so we take it as 1; Substituting equations (19), (20), and (21) into equation (18), we can obtain the first... Adsorbed water film thickness at each drainage stage and matrix suction Or substrate suction head Relationship: = (22) The specific surface area of the soil in formula (15) (m 2 ·g -1 ) can be obtained from an empirical formula: (23) (24) In equation (24), , and These represent the percentage content of clay, silt, and sand in the soil sample, respectively, and can be obtained by measuring the particle size distribution of the soil sample. , and The geometric mean diameters of clay particles, silt particles, and sand particles are 0.001 mm, 0.026 mm, and 1.025 mm, respectively. Substituting the formula (12) in step S3 into the formula (15) with the formula (14), (22), (23) and (24) in step S4, the water content of the adsorbed water can be obtained ; S404. The obtained capillary water content and the water content of adsorbed water By adding the results according to formula (13), the substrate suction head can be obtained. moisture content This allows us to obtain the soil-water characteristic curves of the soil.

2. The method according to claim 1, characterized in that: Step S1 includes: S1. The particle size distribution, dry density, soil particle density, and saturated moisture content of natural soil were obtained through experiments. The particle size distribution could be obtained by sieving or laser particle size analyzer; the dry density could be obtained by ring sampler method; the soil particle density could be obtained by hydrostatic bottle method; and the saturated moisture content was obtained by drying method. The mass moisture content obtained by drying method was then converted to volumetric moisture content as follows: (1) In formula (1), is the volumetric water content, is the mass water content, is the dry density, is the water density.

3. The method according to claim 1, characterized in that: Step S2 includes: S201. The number of measured particle size distribution points is inconsistent and the curves are discontinuous for different soil types. A logical growth model describing particle size distribution is adopted to make the measured particle size distribution continuous, thereby obtaining a mathematical expression of the particle size distribution: (2) In equation (2), (%) represents particles with a diameter smaller than The cumulative mass percentage of particles (μm) , and These are the fitting parameters. For different soil samples, as long as the measured particle size distribution is obtained, the fitting parameters can be determined. , and The value; S202. To facilitate calculation, after obtaining the mathematical expression of the particle size distribution, the particle size distribution is re-divided into several segments, each representing a different drainage stage of the soil. The specific segments are: 2, 5, 10, 15, 20, 30, 40, 50, 60, 70, 80, 90, 100, 200, 500, 1000, 2000 μm.

4. The method according to claim 1, characterized in that: Step S3 includes: S301. During the drainage process, water from large pores is discharged first, while water remains in small pores. For the first... For a particle size unit, according to the Yong-Laplace equation, the radius of this unit under mechanical equilibrium is... The total pressure change at the gas-water interface surface of the capillary pores, i.e., matrix suction. for: (3) In equation (3), For the first Matrix suction (kPa) per particle size unit For the first Pore ​​radius of each particle size unit (cm) The surface tension at the air-water interface at 25℃ is taken as 7.179 × 10⁻⁶. -4 N·cm -1 , The contact angle is 0° during soil drainage. S302. Based on the theoretical framework of the physical-empirical model of soil-water characteristic curves, the first... Pore ​​radius of each particle size unit The particle size-pore size conversion relationship can be established by using particle radius. First, we establish the relationship between pore volume and pore radius, expressed in terms of particle number. and pore length The quantitative relationship of pore volume is expressed as follows: (4) In formula (4), is the pore volume, is the total particle volume, is the particle radius (cm), is the pore ratio, is the number of equivalent sphere particles in the th particle size unit, the pore ratio and the particle number are expressed as follows, respectively: (5) (6) In equations (5) and (6), This represents the soil particle density of the soil sample. This represents the dry density of the soil sample. For the first The particle mass fraction of each particle size unit is obtained based on the segmented results of particle size distribution. The physical-empirical model assumes that, under ideal conditions, the pore length of a unit is the length of all the soil particles accumulated within that unit, i.e. Therefore, according to equation (4), we know However, because actual soil particles are not spherical and pores are complexly tortuous, the actual pore length is often longer than the ideal situation. To estimate pore length from a completely new perspective, we define a shape factor based on the concept of "virtual" particles. This process transforms the particles into "virtual" particles with equal density, ensuring that the volume and mass of the particles and "virtual" particles are equal. At this point, the total volume of the particles... for: (7) In equation (7), For the first The number of "virtual" equivalent spherical particles corresponding to each particle size unit, at which point the pore length... This can be expressed as the length formed by the "virtual" accumulation of particles, i.e.: (8) Substituting equation (8) into equation (4), we can obtain the pore volume. for: (9) The pore radius can be obtained from equation (9). for: (10) As can be seen from equation (10), the conversion between particle size and pore size is nonlinear and independent of mass. Substituting equation (10) into equation (3), we can obtain the first... Substrate suction in each drainage stage for: (11) Finally, after transformation, we can obtain the first soil body. Substrate suction head at each drainage stage (cm) is: (12) In equation (12), The density of water (g·cm³) -3 ), gravitational acceleration (N·g) -1 ).

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