Method for predicting soil water retention characteristic curve by fusing capillary water and film water

Abstract

The application relates to a soil water retention characteristic curve prediction method combining capillary water and film water, and comprises the following steps: S1, a power function relationship between particle size and pore size is established, and a continuous and complete soil pore size distribution is obtained by combining soil particle size distribution, so that the relationship between the soil pore size distribution and the soil particle size distribution is constructed; S2, a relationship formula of film water and capillary water changing with pore size in a single capillary tube section is established, and a formula for calculating the capillary water volume V c and the adsorbed water volume V a in the single circular pore tube section is constructed; S3, the soil pore system is discretely grouped, and a calculation expression for the soil pore number dN in the radius range of r to r+dr is constructed; S4, the saturation degrees of the capillary water and the film water under any water head height are calculated, and a prediction model of the water retention characteristic curve in the whole water head height range is obtained according to the maximum water head height h max and the minimum water head height h min . The application can effectively capture the water retention characteristics of soil, and the accuracy and applicability are verified.

Description

Technical Field

[0001] This invention relates to a method for predicting soil water holding characteristic curves. More specifically, it relates to a method for predicting soil water holding characteristic curves that integrates the effects of capillary water and film water. Background Technology

[0002] In geotechnical engineering, the complex behavior of unsaturated soils is central to many technical challenges, including soil bearing capacity assessment, consolidation settlement control, and slope stability maintenance. Solving these problems relies on in-depth research into their water-holding characteristics and stress states. The soil-water characteristic curve (SWRC), as a mathematical model quantitatively describing the relationship between matric suction and water content, has become a core tool for characterizing the physical and mechanical properties of unsaturated soils. Methods for directly obtaining SWRC are mainly divided into two categories: field measurement and laboratory measurement. Field real-time SWRC measurements generally suffer from limited measurement range, the need to develop more accurate and convenient calibration methods, potentially high manufacturing costs, and the need for further verification of long-term stability. Laboratory measurement methods, such as the filter paper method, pressure plate method, and saturated salt solution method, also have their own limitations. For example, sample collection and transportation may be disturbed, affecting the accuracy of SWRC data; at the same time, the laboratory environment cannot completely simulate the field environment, including the influence of factors such as temperature, humidity, and vegetation cover.

[0003] Existing indirect SWRC prediction models generally lack universal applicability and are limited to specific soil types. In addition, existing SWRC model studies mainly consider the capillary effect of soil matrix potential, but do not fully consider adsorption, resulting in an overestimation of matrix suction in the low saturation range, making it difficult to obtain a complete SWRC. Summary of the Invention

[0004] The technical problem to be solved by this invention is to provide a method for predicting soil water characteristic curves by using particle size distribution to predict the effects of capillary water and film water. This method solves the cumbersome experimental verification process and complex error analysis problems of directly using pore distribution models to predict soil hydraulic characteristics. Furthermore, it significantly reduces the prediction error of water content in the high matrix suction range, and has better fitting performance and a wider range of applications.

[0005] The technical solution adopted by this invention to solve its technical problem is: to construct a method for predicting soil water holding characteristic curves that integrates the effects of capillary water and film water, comprising the following steps: S1. Establish the power function relationship between particle size and pore size, and obtain a continuous and complete soil pore size distribution by combining soil particle size distribution, thereby constructing the connection between soil pore size distribution and soil particle size distribution; S2. Establish the relationship between film water and capillary water in a single capillary cross-section as a function of pore size, and construct the capillary water volume in a single circular pore tube cross-section.V c and the volume of adsorbed water V a Calculation formula; S3. Discretize and group the soil pore system, and construct a system with a radius between... r to r +d r Number of soil pores within the range (d) N Calculate the expression; S4. Calculate the saturation of capillary water and film water at any given head height, and base this on the maximum head height. h max and minimum head height h min A predictive model for the water-holding characteristic curve across the entire head height range is obtained.

[0006] According to the above scheme, in step S1, a three-parameter logic function is used to represent the particle size distribution of the soil, and the expression is as follows: (1) In the formula, R Particle size; w For particles smaller than R The percentage of accumulated soil particles, and 0 <w< 1; a and b For shape parameters, c For generalized exponential parameters, and a >0, b >0, c >0.

[0007] According to the above scheme, assuming the soil pore system is a series of capillaries, and the porosity calculated from the soil particle size and the corresponding pore size is equal to the total soil porosity, then the relationship between soil particle size and pore size can be expressed by a power function as follows: (2) In the formula, r For aperture; A and B These are parameters related to the geometry and physical properties of the soil; According to the above scheme, the soil pore size distribution is expressed as follows: (3) In the formula, v For aperture smaller than r The percentage of cumulative soil particle mass, and 0 < v <1.

[0008] According to the above scheme, in step S2, if the capillaries are arranged from smallest to largest, and the maximum pore radius is... r max The minimum pore radius is r min Then for any given head height h There always exists a corresponding critical pore radius. r c ;when r c > r max At that time, the soil is saturated and the pores are filled with water; when r min < r c < r max When the aperture is larger than r c The pores contain only thin film water, while those smaller than r c The pores contain both capillary water and thin film water; when r c < r min At this time, soil moisture exists only in the form of film water, and capillary water disappears; For capillary water, the resulting capillary matrix suction is closely related to pore characteristics; according to the Young-Laplace equation, the head height generated by capillary action... h With pore radius r The following relationship exists: (4) In the formula, C 1 is the capillary pressure constant, and C 1 = 2 T cos θ ,in T It is surface tension. θ It is the contact angle between soil particles and capillary water.

[0009] According to the above scheme, the water head height generated by adsorption... h With critical pore radius r c The relationship between them is represented by the following formula: (5) In the formula, C 2 represents the adsorption pressure constant; Combining the Poisson-Boltzmann equation and the Gibbs free energy equation, the thickness ratio of the thin film water film is... ω / rRatio of suction characteristic radius r c / r It is directly proportional to the power function, that is: (6) In the formula, α and β These represent the soil's adsorption strength and adsorption capacity, respectively. 0<α< 1, 0<β< 1; In a single circular pore tube cross-section, the capillary water volume V c and film water volume V a They are represented as follows: (7) (8) Combining equation (6), equations (7) to (8) are transformed into: (9) (10).

[0010] According to the above scheme, in step S3, since the pore size and length of the pore tubes in the soil vary significantly, the pore system needs to be discretized and grouped for ease of calculation. The specific grouping method is as follows: (1) Arrange all pores in the soil according to their radius r Divided into n Group; Set aperture range [ r min , r max [and define a set of discrete aperture values] r 0, r 1, ..., r n ,satisfy r min = r 0< r 1< < r n = r max Among them, the first i Group of pores corresponding to the radius range ( r i 1, r i ]; (2) For those belonging to the same aperture group i That is, the radius is r iAll pore tubes, per unit length L 0. Perform equal-length cutting; let the number of unit pore tubes after cutting within this group be . N i Then the total length of this group of pores l i Volume of pore tube per unit length V wi They are represented as follows: (11) (12) (3) Definition and calculation of pore volume for each group: Based on the definition of cumulative pore volume fraction in equation (3), the first group of pore volume is calculated as follows: i Group of pores (corresponding pore size range) r i 1, r i The volume fraction Δ) v i The difference between the cumulative scores at both ends of the interval: (13) If the total pore volume in the soil is V p Then the first i Volume of group pores V i for: (14) (4) According to the principle of volume conservation, the first i Total pore volume V i It should be equal to the sum of the volumes of all pore tubes per unit length within that group: (15) Substituting equations (12) and (14) into equation (15), then the first... i Number of pore tubes N i : (16) When the grouping is infinitely refined (i.e.) n Let Δ r i =( r i r i 1) → 0, then Δ v iIt can be approximated as: Correspondingly, discrete N i Transform into the differential form d under continuous distribution N and discrete radius r i Approaching continuous variables r Therefore, the radius is between r to r +d r Number of pores d within the range N Represented as: (17) In the formula, For cumulative pore volume fraction v For radius r The derivative of .

[0011] According to the above scheme, the method for establishing the water retention characteristic curve (SWRC) prediction model for capillary water and adsorbed water in step S4 is as follows: Capillary water component saturation S c and film water component saturation S a With water head height h The relationship is represented as: (18) (19) In the formula, h max and h min These are the maximum pore sizes under capillary action. r max Minimum aperture r min The corresponding minimum and maximum water head heights; in: (20) (twenty one) (twenty two) (twenty three) (twenty four) The soil water-holding characteristic curve over the entire water head range is represented as follows: (25).

[0012] According to the above scheme, it also includes step S5: fitting the parameters of the prediction model for the water-holding characteristic curve based on the test data of the soil sample. The fitting method includes: First, the parameters in equation (1) are calibrated based on soil particle distribution PSD data. a , b and c Determine whether soil pore distribution PoSD data is available. If so, fit the pore distribution model shown in equation (3) using the soil PoSD data and determine its parameters. A and B Finally, by fitting equations (18) to (25) to the soil-water characteristic curve test data, the parameters of the prediction model are obtained. α , β , C 2. h max and h min .

[0013] According to the above scheme, it also includes step S5: fitting the parameters of the prediction model for the water-holding characteristic curve based on the test data of the soil sample. The fitting method includes: First, the parameters in equation (1) are calibrated based on soil particle distribution PSD data. a、b and c To determine whether soil pore distribution PoSD data is available, if not, combine the soil-water characteristic curve test data with equations (18) to (25) to obtain the parameters of the prediction model. A , B , α , β , C 2. h max and h min .

[0014] The method for predicting soil-water characteristic curves based on the influence of capillary water and film water using particle size distribution, as described in this invention, has the following beneficial effects: 1. This invention analyzes the complex relationship between pores and particles, establishes the connection between soil pore size and particle size using a nonlinear and exponential relationship, divides each capillary into sections, and reassembles them into cylindrical capillary sections arranged in ascending order of size. The PSD is converted into PoSD, thereby obtaining a complete functional relationship of cumulative pore size distribution. The applicability of this function can be derived from the good fitting performance shown by the newly established SWRC model. 2. The newly established SWRC model of this invention is based on the cumulative pore size distribution, takes into account the composition of soil adsorbed water, and uses the microscopic principle to obtain the relationship between the macroscopic adsorbed water film and the pore size. The capillary water and adsorbed water content of each capillary are accumulated to obtain the final relationship between the saturation of capillary water and adsorbed water and the matrix suction. Due to the inclusion of adsorbed water analysis, the model's prediction in the high suction range is closer to the measured value. 3. This invention compares the newly established SWRC model with multiple measured data points of different soil types in the UNSODA database. The comprehensive analysis results show that the data fitted by the new model is closer to the measured data in the database, and the overall fitting degree is higher. Therefore, the newly established model can more accurately predict the soil-water characteristic curves of different soils. Attached Figure Description

[0015] The present invention will be further described below with reference to the accompanying drawings and embodiments. In the accompanying drawings: Figure 1 This is a flowchart of the calculation steps for the soil-water characteristic curve prediction method based on particle size distribution to predict the effects of capillary water and film water, as per the present invention. Figure 2 This is a graph showing the fitting effect of the newly established SWRC model in Embodiment 1 of the present invention on the test data of clay No. 1400 (a); Figure 3 This is a graph showing the fitting effect of the newly established SWRC model in Embodiment 1 of the present invention on the test data of silty loam soil No. 1351 (b). Figure 4 This is a graph showing the fitting effect of the newly established SWRC model in Embodiment 1 of the present invention on the test data of sand (c) No. 1061. Figure 5 This is a graph showing the fitting effect of the newly established SWRC model in Embodiment 2 of the present invention on the test data of clay No. 4680 (a). Figure 6 This is a graph showing the fitting effect of the newly established SWRC model in Embodiment 2 of the present invention on the test data of loam sandy soil No. 3150 (b); Figure 7 This is a fitting effect diagram of the test data of the newly established SWRC model (c) No. 4051 sand in Embodiment 2 of the present invention. Detailed Implementation

[0016] To provide a clearer understanding of the technical features, objectives, and effects of the present invention, specific embodiments of the present invention will now be described in detail with reference to the accompanying drawings.

[0017] like Figure 1 As shown, the method for predicting soil water holding characteristic curves that integrates the effects of capillary water and film water in this invention includes the following steps: S1. Establish the power function relationship between particle size and pore size, and obtain a continuous and complete pore size distribution (PoSD) by combining soil particle size distribution (PSD), thereby constructing the connection between soil pore size distribution (PoSD) and particle size distribution (PSD).

[0018] The particle size distribution (PSD) of soil is represented by a three-parameter logic function, as shown in the following expression: (1) In the formula, R Particle size; w For particles smaller than R The percentage of accumulated soil particles, and 0 <w< 1; a and b For shape parameters, c For generalized exponential parameters, and a >0, b >0, c >0.

[0019] Assuming the soil pore system is a series of capillaries, and the porosity calculated from soil particle size and corresponding pore size equals the total soil porosity, then the relationship between soil particle size and pore size can be expressed by a power function: (2) In the formula, r For aperture; A and B These are parameters related to the geometry and physical properties of the soil; Since PSD and PoSD have similar shapes, the soil pore size distribution (PoSD) can be expressed as follows according to equations (1) and (2): (3) In the formula, v For aperture smaller than r The percentage of cumulative soil particle mass, and 0 < v <1.

[0020] S2. Establish the relationship between film water and capillary water in a single capillary cross-section as a function of pore size, and construct the capillary water volume in a single circular pore tube cross-section. V c and the volume of adsorbed water V a Calculation formula.

[0021] If the capillaries are arranged from smallest to largest, and the maximum pore radius is... r max The minimum pore radius is r min Then for any given head heighth There always exists a corresponding critical pore radius. r c .when r c > r max At that time, the soil is saturated and the pores are filled with water; when r min < r c < r max When the aperture is larger than r c The pores contain only thin film water, while those smaller than r c The pores contain both capillary water and thin film water; when r c < r min At this time, soil moisture exists only in the form of film water, and capillary water disappears.

[0022] For capillary water, the resulting capillary matrix suction is closely related to pore characteristics. According to the Young-Laplace equation, the head height generated by capillary action... h With pore radius r The following relationship exists: (4) In the formula, C 1 is the capillary pressure constant, and C 1 = 2 T cos θ ,in T It is surface tension (25) (Take C as 0.072 N / m). θ It is the contact angle between soil particles and capillary water (its value is generally 0).

[0023] Although the matrix suction induced by adsorbed water differs from that of capillary water, the water head height generated by adsorption is still significant. h With critical pore radius r c The relationship between them can still be represented by the method used in equation (4): (5) In the formula, C 2 is the adsorption pressure constant, which is related to the specific surface area of ​​soil particles, mineral type, and ion valence state.

[0024] Combining the Poisson-Boltzmann equation and the Gibbs free energy equation, the water film thickness ratio of the thin film ( ω / r The ratio of the characteristic radius of suction force to ( r c / r The power function of is directly proportional to it, that is: (6) In the formula, α ( 0<α< 1) and β ( 0<β< 1) These represent the soil's adsorption strength and adsorption capacity, respectively.

[0025] Combining equations (5) and (6), it can be seen that the increase in matrix suction leads to a decrease in the critical pore radius. r c This decreases, which in turn affects the thickness of the adsorbed water film. ω It gets smaller.

[0026] In a single circular pore tube cross-section, the capillary water volume V c and film water volume V a They are represented as follows: (7) (8) Combining equation (6), equations (7) to (8) are transformed into: (9) (10).

[0027] S3. Discretize and group the soil pore system, and construct a system with a radius between... r to r +d r Number of soil pores within the range (d) N Calculate the expression; Because the pore size and length of pore tubes in soil vary significantly, the pore system needs to be discretized and grouped for ease of calculation. The specific grouping method is as follows: (1) Arrange all pores in the soil according to their radius r Divided into n Group. Set aperture range [ r min , r max [and define a set of discrete aperture values] r 0, r 1, ..., r n ,satisfy r min = r 0< r1< < r n = r max Among them, the first i Group of pores corresponding to the radius range ( r i 1, r i ].

[0028] (2) For those belonging to the same aperture group i (i.e., radius is) r i All pore tubes, per unit length L 0. Perform equal-length cutting. Let the number of unit pore tubes after cutting within this group be . N i Then the total length of this group of pores l i Volume of pore tube per unit length V wi They are represented as follows: (11) (12) 3) Definition and calculation of pore volume for each group: Based on the definition of cumulative pore volume fraction in equation (3), the first group... i Group of pores (corresponding pore size range) r i 1, r i The volume fraction Δ) v i The difference between the cumulative scores at both ends of the interval: (13) If the total pore volume in the soil is V p Then the first i Volume of group pores V i for: (14) (4) According to the principle of volume conservation, the first i Total pore volume V i It should be equal to the sum of the volumes of all pore tubes per unit length within that group: (15) Substituting equations (12) and (14) into equation (15), then the first... i Number of pore tubes Ni : (16) When the grouping is infinitely refined (i.e.) n Let Δ r i =( r i r i 1) → 0, then Δ v i It can be approximated as: Correspondingly, discrete N i Transform into the differential form d under continuous distribution N and discrete radius r i Approaching continuous variables r Therefore, the radius is between r to r +d r Number of pores d within the range N Represented as: (17) In the formula, For cumulative pore volume fraction v For radius r The derivative of .

[0029] S4. Calculate the saturation of capillary water and film water at any given head height, and base this on the maximum head height. h max and minimum head height h min A method for predicting the water-holding characteristic curve (SWRC) across the entire head height range is derived. Specifically: Combining equations (4) to (5), (9) to (10), and (17), capillary water component saturation S c and film water component saturation S a With water head height h The relationship is represented as: (18) (19) In the formula, h max and h min These are the maximum pore sizes under capillary action. rmax Minimum aperture r min The corresponding minimum and maximum water head heights.

[0030] in: (20) (twenty one) (twenty two) (twenty three) (twenty four) The soil water-holding characteristic curve over the entire water head range is represented as follows: (25) S5. Based on the test data of the soil samples, two approaches are used to fit the parameters of the prediction model: The first approach (five parameters): First, based on the soil particle distribution PSD data calibration formula (1), the parameters are... a , b and c， Determine whether soil pore distribution PoSD data is available. If so, fit the pore distribution model shown in equation (3) using the soil PoSD data and determine its parameters. A and B Finally, by fitting equations (18) to (25) to the soil-water characteristic curve test data, the SWRC model parameters are obtained. α , β , C 2. h max and h min .

[0031] The second approach (seven parameters): First, based on the soil particle distribution PSD data calibration formula (1), the parameters are... a、b and c Determine whether soil pore distribution PoSD data is available. If not, combine the soil-water characteristic curve test data to fit equations (18) to (25) to obtain the SWRC model parameters. A , B , α , β , C 2. h max and h min .

[0032] Example 1 To visually compare the prediction performance of the two SWRC models, namely the five-parameter and seven-parameter models, goodness of fit (R²) and root mean square error (RMSE) were used as evaluation metrics. These two metrics characterize the degree of agreement between predicted and measured values, with larger R² and smaller RMSE indicating better prediction performance. The specific calculation methods are as follows: (26) (27) Based on continuous verification of pore distribution, the first method of the newly established model adopts a step-by-step strategy for verification: First, the parameters in equation (1) are calibrated based on soil particle distribution PSD data. a , b and c Then, the pore distribution model shown in equation (3) was fitted using soil PoSD data, and its parameters were determined. A and B Finally, by fitting equations (18) to (25) to the soil-water characteristic curve test data, the parameters of the newly established SWRC model are obtained. α , β , C 2. h max and h min .

[0033] To evaluate the accuracy and applicability of the pore distribution model shown in Equation (3), this invention selects soil sample data from the USDA UNSODA Soil Database for verification, including clay No. 1400, silty loam No. 1351, and sandy soil No. 1061.

[0034] As shown in Table 1, the goodness of fit (R²) of the samples is greater than 0.96, and the root mean square error (RMSE) is less than 0.056. This indicates that the newly established SWRC model has excellent interpretability for pore distribution data, and the deviation between the predicted and measured values ​​is extremely small. In summary, this model demonstrates good applicability in characterizing the PoSD of common soil types.

[0035] Table 1 PoSD model fitting parameters

[0036] To verify the rationality of the newly established SWRC model and evaluate the impact of the PoSD model on its predictions, the first method of this invention employs a fixed-parameter method for verification, that is, maintaining the parameters determined by fitting the pore distribution experimental data (PoSD). A and B The parameters remain unchanged. Under this constraint, the number of parameters to be optimized in the newly established SWRC model is reduced to five. α , β, C 2. h max and h min Table 2 details the model parameter values ​​and their goodness of fit obtained using this method. The advantages of this verification method are twofold: firstly, it directly verifies the rationality of the newly established SWRC model; secondly, if a good fit is still achieved under this constraint, it strongly demonstrates the accuracy of the PoSD model and its crucial supporting role in the newly established SWRC model.

[0037] By comparing the predicted curves of the newly established SWRC model with the experimental data, the model performance can be intuitively evaluated. The model shows significant fitting effects on the three sets of soil sample data: the goodness of fit (R²) exceeds 0.975, and the root mean square error (RMSE) is less than 0.021. The overall results show that the SWRC model proposed in this invention exhibits excellent fitting ability and prediction accuracy under the premise of optimizing only four core parameters.

[0038] Table 2. Fitting parameters for the SWRC model (five parameters)

[0039] like Figure 2-4 As shown, the newly established SWRC model fits the test data of different soil types well, including clay, silty loam, and sand. The model demonstrates high accuracy and strong robustness in predicting soil-water characteristic curves for various soil types. This indicates that: 1) the pore distribution model presented in this invention has high accuracy; 2) the entire process of deriving pore distribution from particle distribution and then predicting the newly established SWRC is reasonable and effective.

[0040] Example 2 To verify the particle distribution-based model, the second method of the newly established model adopts a step-by-step strategy: First, the parameters in equation (3) are calibrated based on the particle distribution PSD data. a , b and c Then, by combining the soil-water characteristic curve test data, the parameters of the newly established SWRC model (i.e., equations (18) to (25)) are obtained through fitting. A , B , α , β , C 2. h max and h min .

[0041] As shown in Table 3, the goodness of fit (R²) of the samples is greater than 0.999, and the root mean square error (RMSE) is less than 0.032. This indicates that the newly established SWRC model has excellent interpretability for pore distribution data, and the deviation between the predicted and measured values ​​is extremely small. In summary, this model demonstrates good applicability in characterizing the PoSD of common soil types.

[0042] Table 3 PoSD model fitting parameters

[0043] Table 3 presents the parameter results of fitting the newly established SWRC model to three different soil data sets in the UNSODA database. In the three validated UNSODA soil samples, the newly established SWRC model exhibited extremely high accuracy: the goodness of fit (R²) was greater than 0.998, and the root mean square error (RMSE) was less than 0.004. These results demonstrate that the newly established SWRC model not only has high prediction accuracy but also good applicability and robustness to different soil types.

[0044] Table 3 Fitting parameters of the newly established SWRC model (seven parameters)

[0045] like Figure 5-7 As shown, the newly established SWRC model fits the test data of various soil types well, including clay, loamy sand, and sand. This indicates that even if the model is fitted directly from the SWRC test data, the newly established model has good applicability and effectiveness for different soil types throughout the entire matrix suction range.

[0046] The embodiments of the present invention have been described above with reference to the accompanying drawings. However, the present invention is not limited to the specific embodiments described above. The specific embodiments described above are merely illustrative and not restrictive. Those skilled in the art can make many other forms under the guidance of the present invention without departing from the spirit and scope of the claims. All of these forms are within the protection scope of the present invention.

Claims

1. A method for predicting soil water holding characteristic curves by integrating the effects of capillary water and film water, characterized in that, Includes the following steps: S1. Establish the power function relationship between particle size and pore size, and obtain a continuous and complete soil pore size distribution by combining soil particle size distribution, thereby constructing the connection between soil pore size distribution and soil particle size distribution; In step S1, a three-parameter logic function is used to represent the particle size distribution of the soil, as shown in the following expression: （1） In the formula, R Particle size; w For particles smaller than R The percentage of accumulated soil particles, and 0 <w< 1; a and b For shape parameters, c For generalized exponential parameters, and a >0, b >0, c >0; Assuming the soil pore system is a series of capillaries, and the porosity calculated from soil particle size and corresponding pore size equals the total soil porosity, then the relationship between soil particle size and pore size can be expressed by a power function: （2） In the formula, r For aperture; A and B These are parameters related to the geometry and physical properties of the soil; Soil pore size distribution is represented as follows: （3） In the formula, v For aperture smaller than r The percentage of cumulative soil particle mass, and 0 < v <1; S2. Establish the relationship between film water and capillary water in a single capillary cross-section as a function of pore size, and construct the capillary water volume in a single circular pore tube cross-section. V c and the volume of adsorbed water V a Calculation formula; In step S2, if the capillaries are arranged from smallest to largest, and the maximum pore radius is... r max The minimum pore radius is r min Then for any given head height h There always exists a corresponding critical pore radius. r c ;when r c > r max At that time, the soil is saturated and the pores are filled with water; when r min < r c < r max When the aperture is larger than r c The pores contain only thin film water, while those smaller than r c The pores contain both capillary water and thin film water; when r c < r min At this time, soil moisture exists only in the form of film water, and capillary water disappears; For capillary water, the capillary matrix suction it induces is closely related to the pore characteristics; According to the Young-Laplace equation, the head height generated by capillary action... h With pore radius r The following relationship exists: （4） In the formula, C 1 is the capillary pressure constant, and C 1 = 2 T cos θ ,in T It is surface tension. θ The contact angle between soil particles and capillary water; Water head height generated by adsorption h With critical pore radius r c The relationship between them is represented by the following formula: （5） In the formula, C 2 represents the adsorption pressure constant; Combining the Poisson-Boltzmann equation and the Gibbs free energy equation, the thickness ratio of the thin film water film is... ω / r Ratio of suction characteristic radius r c / r It is directly proportional to the power function, that is: （6） In the formula, α and β These represent the soil's adsorption strength and adsorption capacity, respectively. 0<α< 1, 0<β< 1; In a single circular pore tube cross-section, the capillary water volume V c and film water volume V a They are represented as follows: （7） （8） in L 0 represents the unit length of the equal-length cut of the pore tube; Combining equation (6), equations (7) to (8) are transformed into: （9） （10）； S3. Discretize and group the soil pore system, and construct a system with a radius between... r to r +d r Number of soil pores within the range (d) N Calculate the expression; In step S3, since the pore size and length of the pore tubes in the soil vary significantly, the pore system needs to be discretized and grouped for ease of calculation. The specific grouping method is as follows: (1) Arrange all pores in the soil according to their radius r Divided into n Group; Set aperture range [ r min , r max [and define a set of discrete aperture values] r 0, r 1, ..., r n ,satisfy r min = r 0< r 1< < r n = r max , among which, the i Group of pores corresponding to the radius range ( r i 1, r i ]; (2) For those belonging to the same aperture group i That is, the radius is r i All pore tubes, per unit length L 0. Perform equal-length cutting; let the number of unit pore tubes after cutting within this group be . N i Then the total length of this group of pores l i Volume of pore tube per unit length V wi They are represented as follows: （11） （12） (3) Definition and calculation of pore volume for each group: Based on the definition of cumulative pore volume fraction in equation (3), the first group of pore volume is calculated as follows: i Group of pores (corresponding pore size range) r i 1, r i The volume fraction Δ) v i The difference between the cumulative scores at both ends of the interval: （13） If the total pore volume in the soil is V p Then the first i Volume of group pores V i for: （14） (4) According to the principle of volume conservation, the first i Total pore volume V i It should be equal to the sum of the volumes of all pore tubes per unit length within that group: （15） Substituting equations (12) and (14) into equation (15), then the first... i Number of pore tubes N i : （16） When the grouping is infinitely refined (i.e.) n Let Δ r i =( r i r i 1) → 0, then Δ v i It can be approximated as: Correspondingly, discrete N i Transform into the differential form d under continuous distribution N and discrete radius r i Approaching continuous variables r Therefore, the radius is between r To r +d r Number of pores d within the range N Represented as: （17） In the formula, For cumulative pore volume fraction v For radius r The derivative; S4. Calculate the saturation of capillary water and film water at any given head height, and base this on the maximum head height. h max and minimum head height h min A predictive model for the water-holding characteristic curve across the entire head height range is obtained.

2. The method for predicting soil water holding characteristic curves by integrating capillary water and film water effects according to claim 1, characterized in that, In step S4, the method for establishing the water retention characteristic curve (SWRC) prediction model for capillary water and adsorbed water is as follows: Capillary water component saturation S c and film water component saturation S a With water head height h The relationship is represented as: (18) (19) In the formula, h max and h min These are the maximum pore sizes under capillary action. r max Minimum aperture r min The corresponding maximum and minimum water head heights; in: （20） （21） （22） (23) （24） The soil water-holding characteristic curve over the entire water head range is represented as follows: （25）。 3. The method for predicting soil water holding characteristic curves by integrating capillary water and film water effects according to claim 2, characterized in that, It also includes step S5, which involves fitting the parameters of the prediction model for the water-holding characteristic curve based on the test data of the soil sample. The fitting methods include: First, the parameters in equation (1) are calibrated based on soil particle distribution PSD data. a , b and c Determine whether soil pore distribution PoSD data is available. If so, fit the pore distribution model shown in equation (3) using the soil PoSD data and determine its parameters. A and B Finally, by fitting equations (18) to (25) to the soil-water characteristic curve test data, the parameters of the prediction model are obtained. α , β , C 2. h max and h min .

4. The method for predicting soil water holding characteristic curves by integrating capillary water and film water effects according to claim 3, characterized in that, It also includes step S5, which involves fitting the parameters of the prediction model for the water-holding characteristic curve based on the test data of the soil sample. The fitting methods include: First, the parameters in equation (1) are calibrated based on soil particle distribution PSD data. a、b and c To determine whether soil pore distribution PoSD data is available, if not, combine the soil-water characteristic curve test data with equations (18) to (25) to obtain the parameters of the prediction model. A , B , α , β , C 2. h max and h min .

Images