Method for calculating unsaturated permeability coefficient based on soil-water characteristic curve

Abstract

The invention relates to a method for calculating an unsaturated permeability coefficient based on a soil-water characteristic curve, which comprises the following steps: establishing a soil-water characteristic curve model, setting a pore space in soil as a capillary bundle with non-uniform size by the model, the curve model comprising a Ropin-Rammer particle size distribution model and a void ratio; an unsaturated permeability coefficient model is established, the total permeability coefficient comprises capillary and non-capillary permeability coefficients, the capillary permeability coefficient is determined through an absolute saturation tortuosity constant, and the change of the non-capillary relative permeability coefficient is represented by a continuous differentiable empirical equation; according to the curve model and the unsaturated permeability coefficient model, determining a plurality of unsaturated permeability coefficient combination models, fitting each combination model to obtain a corresponding soil-water characteristic curve, and fitting each combination model into a calibration data set to obtain an optimal absolute saturation tortuosity constant value for evaluating the performance of different combination models; and determining an optimal unsaturated permeability coefficient model according to an evaluation result.

Description

Technical Field

[0001] The present invention relates to the technical field of soil moisture characteristics in unsaturated soil mechanics, and more particularly to a calculation method for an unsaturated permeability coefficient based on a soil-water characteristic curve. Background Art

[0002] The soil-water characteristic curve (SWCC) describes the relationship between soil saturation and matrix suction. It is widely used in the study of shear strength, deformation, and permeability of unsaturated soils. Whether in the construction of large-scale underground projects, the protection of steep slopes, high-fill roadbeds, or the construction of high dams, all involve controlling the seepage, deformation, and stability of unsaturated soils in complex environments. The effective application of unsaturated soil mechanics in engineering practice depends on relatively accurate unsaturated soil models, such as the soil-water characteristic curve and the unsaturated permeability coefficient.

[0003] In related art, to describe the unsaturated permeability coefficient, the SWCC is artificially "split" into capillary and non-capillary components, or the concept of residual moisture content is introduced to characterize soil saturation as effective saturation. The former approach adheres to the physical interpretation, assuming that the capillary permeability coefficient is contributed by the capillary component and the non-capillary permeability coefficient by the non-capillary component. However, the boundary between the capillary and non-capillary components of the SWCC is subject to significant uncertainty. The latter approach treats the effective saturation as a capillary component and substitutes it into the capillary permeability coefficient model. However, the introduction of residual moisture content undoubtedly abandons the study of non-capillary permeability coefficients, and the concept of residual moisture content contradicts the observation that the soil moisture content ultimately reaches zero during oven drying. Using the FX model to fit the SWCC of reshaped moraine soil, the residual saturation obtained was as high as 65%, rendering the residual moisture content parameter meaningless. Related techniques fragment the soil and calculate the membrane water permeability coefficient for each fragment. This method further considers the random distribution and interconnectedness of the fragments within the soil, and combines this with a derived capillary permeability model to obtain the unsaturated permeability coefficient over the entire suction range. While this method ensures a continuous SWCC and uses saturation as a representation, the unsaturated permeability coefficient obtained is a series of discrete data points, limiting its application and requiring model fitting to a smooth, differentiable curve. Summary of the Invention

[0004] To address the above-mentioned shortcomings, an embodiment of the present invention provides a method for calculating the unsaturated permeability coefficient based on the soil-water characteristic curve, comprising: establishing a soil-water characteristic curve model, wherein the soil-water characteristic curve model sets the pore space in the soil as capillary bundles of uneven sizes, and the soil-water characteristic curve model includes a Roshin-Rammle particle size distribution model and a porosity ratio; establishing an unsaturated permeability coefficient model based on the soil-water characteristic curve model, wherein the total permeability coefficient includes the capillary permeability coefficient and the non-capillary permeability coefficient, wherein the capillary permeability coefficient is determined by the absolute saturated tortuosity constant, and the change of the non-capillary relative permeability coefficient in the non-capillary permeability coefficient is represented by a continuously differentiable empirical equation; determining multiple unsaturated permeability coefficient combination models based on the soil-water characteristic curve model and the unsaturated permeability coefficient model, fitting each combination model to obtain a corresponding soil-water characteristic curve, fitting each combination model to a calibration data set to obtain an optimal absolute saturated tortuosity constant value, and applying it to a test data set to evaluate the performance of different combination models; and determining an optimal unsaturated permeability coefficient model based on the evaluation results.

[0005] Optionally, it also includes: verification of the combined model, including the soil-water characteristic curve model with deformation effect.

[0006] Optionally, the soil-water characteristic curve model satisfies the following formula:

[0007]

[0008] Where a and b are fitting constants related to the particle size distribution; δ is the arrangement characteristic coefficient; μ is the arrangement characteristic index; e0 is the porosity ratio under the reference state; e i is the void ratio under any deformation state.

[0009] Optionally, the total permeability coefficient, the capillary permeability coefficient, and the non-capillary permeability coefficient satisfy the following formula:

[0010] K=K c +K nc ;

[0011] Where K is the total permeability coefficient, m / s; K c and K nc are the capillary permeability coefficient component and the non-capillary permeability coefficient component, m / s.

[0012] Optionally, the capillary permeability coefficient is determined by an absolute saturation tortuosity constant, satisfying the following formula:

[0013]

[0014] Where γ = 50C 2 / ηρg is a constant, at room temperature of 20℃, γ=3.04×10 -2 m 3 / s, γτ s is the absolute saturation tortuosity constant.

[0015] Optionally, the capillary permeability coefficient is determined by an absolute saturation tortuosity constant and also satisfies the following formula:

[0016]

[0017] Optionally, the change of the non-capillary relative permeability coefficient in the non-capillary permeability coefficient is represented by a continuously differentiable empirical equation that satisfies the following formula:

[0018]

[0019] The slope of the non-capillary relative permeability coefficient is -1.5, so η = -1.5; β is the matrix suction parameter.

[0020] Optionally, the non-capillary saturation permeability coefficient K is introduced s,nc , the non-capillary permeability coefficient function satisfies the following formula:

[0021]

[0022] Substitute the above formula into a non-capillary water permeability coefficient model:

[0023] K nc =ωθ m s -1.5 ;

[0024] The expression of non-capillary saturated permeability coefficient is obtained:

[0025]

[0026] Where ω is a constant, equal to 1.35×10 -8 m 5 / 2 s -1 θ m is the matrix suction, which is equal to the volumetric water content of the soil at 10000 kPa; s m >>a,s m Set to 10000kPa.

[0027] Optionally, the optimal unsaturated permeability coefficient model is a RRP-ASCCG model.

[0028] The embodiment of the present invention first proposes reference values of PSD shape parameters under different soil textures to expand the application range of the RRP model; secondly and more importantly, it proposes the use of the absolute saturation tortuosity constant γτ sInstead of the saturated permeability coefficient proportional constant C * A capillary permeability coefficient model was obtained; thirdly, a continuously differentiable non-capillary permeability coefficient model was proposed; fourthly, 24 unsaturated permeability coefficient combination models were established; fifthly, when the SWCC was known, the unsaturated permeability coefficient combination model of the present invention could be directly predicted without any adjustable parameters; finally, the reliability of the model was verified by multiple sets of experimental data. The prediction accuracy of the RRP-ASCCG model of the present invention was the best, with an average error of only 0.3 orders of magnitude, and it could further better predict the unsaturated permeability coefficient considering the deformation effect. BRIEF DESCRIPTION OF THE DRAWINGS

[0029] The following drawings illustrate exemplary embodiments of the present invention by way of example, and the same or similar reference numerals are used in the drawings to represent the same or similar elements. In the drawings:

[0030] Figure 1 A flow chart illustrating a method for calculating an unsaturated hydraulic conductivity based on a soil-water characteristic curve according to an exemplary embodiment of the present invention is shown.

[0031] Figure 2 A schematic diagram showing comparison of prediction effects of different permeability coefficient models according to an exemplary embodiment of the present invention is shown.

[0032] Figure 3 A schematic diagram of a non-capillary water permeability coefficient model according to an exemplary embodiment of the present invention is shown.

[0033] Figure 4 A comparison chart showing the calculated and measured values of SWCC and unsaturated hydraulic conductivity for two of the twelve calibration data sets according to an exemplary embodiment of the present invention is shown.

[0034] Figure 5 The RMSE θ and θ of different model combinations of exemplary embodiments of the present invention fitted to 12 calibration data sets are shown. Box plot.

[0035] Figure 6 The RRP-ASCCG model root mean square error of the exemplary embodiment of the present invention is shown as the parameter τ s Schematic diagram of the changing surface of β and β.

[0036] Figure 7 A schematic diagram showing comparison between predicted and measured values of SWCC and unsaturated hydraulic conductivity for two of the 23 test data sets according to an exemplary embodiment of the present invention is shown.

[0037] Figure 8 The RMSE θ and θ of 23 test data sets of different model combinations of exemplary embodiments of the present invention are shown. Box plot.

[0038] Figure 9 A comparison chart showing the predicted and measured values of SWCC and unsaturated hydraulic conductivity of two soil samples according to an exemplary embodiment of the present invention is shown. DETAILED DESCRIPTION

[0039] In order to better explain the present invention and facilitate understanding, the present invention is described in detail below through specific implementation methods in conjunction with the accompanying drawings.

[0040] In the present invention, the term "and / or" is intended to cover all possible combinations and subcombinations of the listed elements, including any one, any subcombination, or all of the elements listed individually, without necessarily excluding other elements. Unless otherwise specified, the terms "first," "second," and the like are used to describe various elements without intending to limit the positional relationship, temporal relationship, or importance relationship of these elements. Such terms are only used to distinguish one element from another. Unless otherwise specified, the directions or positional relationships indicated by the terms "front, back, up, down, left, right," and the like are generally based on the directions or positional relationships shown in the accompanying drawings, and are only for the convenience and simplification of description, and should not be understood as limiting the scope of protection of the present invention.

[0041] The embodiment of the present invention first proposes reference values of PSD shape parameters under different soil textures to expand the application range of the RRP model; secondly, it proposes to use the absolute saturation tortuosity constant γτ s Instead of the saturated permeability coefficient proportional constant C * A capillary permeability coefficient model was obtained, and a continuously differentiable non-capillary permeability coefficient model was proposed, and 24 unsaturated permeability coefficient combination models were established; finally, the reliability of the model was verified through multiple sets of experimental data.

[0042] like Figure 1 As shown, S102: establishing a soil-water characteristic curve model, wherein the soil-water characteristic curve model sets the pore space in the soil as a capillary bundle of uneven size, and the soil-water characteristic curve model includes a Roshin-Rammle particle size distribution model and a porosity ratio.

[0043] SWCC model with unified PSD shape parameters. The study found that the relationship between particle size and pore size of sandy soil is linear step-like distribution in double logarithmic coordinates, while clay soil is linear distribution. Combined with the Young-Laplace equation (C = 2T s cosθ), the Roshin-Rammle particle size distribution model and porosity ratio were introduced to establish a physical empirical model of SWCC (RRP model), which satisfies the following formula:

[0044]

[0045] Where a and b are fitting constants related to the particle size distribution; δ is the arrangement characteristic coefficient; μ is the arrangement characteristic index; e0 is the porosity ratio under the reference state; e i is the void ratio under any deformation state.

[0046] S104: Establish an unsaturated permeability coefficient model based on the soil-water characteristic curve model, wherein the total permeability coefficient includes the capillary permeability coefficient and the non-capillary permeability coefficient, wherein the capillary permeability coefficient is the product of the relative permeability coefficient and the saturated permeability coefficient, and the change of the non-capillary relative permeability coefficient in the non-capillary permeability coefficient is represented by a continuously differentiable empirical equation.

[0047] The establishment of unsaturated permeability coefficient model includes permeability coefficient model establishment, model discussion, model parameters, and model verification. The permeability coefficient model establishment includes the establishment of capillary permeability coefficient model and the establishment of non-capillary permeability coefficient model.

[0048] The total permeability coefficient can be expressed as the sum of the capillary permeability coefficient and the non-capillary permeability coefficient (the embodiment of the present invention does not consider the steam water permeability coefficient):

[0049] K=K c +K nc ;(3)

[0050] Where: K is the total permeability coefficient, m / s; K c and K nc are the capillary permeability coefficient component and the non-capillary permeability coefficient component, m / s.

[0051] In related technologies, the capillary permeability coefficient is obtained from the relative permeability coefficient and the saturated permeability coefficient:

[0052] K c =K s K rc ; (4)

[0053] Where: K s is the saturated permeability coefficient, m / s; K rc is the relative permeability coefficient.

[0054] Starting from the concept of tortuous and interconnected pore spaces, for example, the following Mua model:

[0055]

[0056] Where: λ = 0.5, is the bending connectivity factor.

[0057] The common unsaturated permeability coefficient prediction models still have the following problems: first, they only consider the capillary permeability coefficient and ignore the study of non-capillary permeability coefficient; second, the saturated permeability coefficient is required for conversion; finally, the direct prediction of the unsaturated permeability coefficient has large errors and is difficult to reflect the actual situation.

[0058] Because the saturated permeability coefficient is highly uncertain or even missing, the present invention directly predicts the unsaturated permeability coefficient from the SWCC, rather than using the relative permeability coefficient and converting it to the saturated permeability coefficient. This approach aims to derive a universally applicable unsaturated permeability coefficient model, eliminating the need for unsaturated permeability measurement and allowing it to be calculated directly from the SWCC. This model is based on the commonly used relative permeability coefficient model. In some embodiments, the Mua model is selected for illustration because it is the most widely used and has good applicability.

[0059] Based on the Mua model, the saturated permeability coefficient and the pore distribution function have the following relationship:

[0060]

[0061] Where: R max is the maximum pore radius of the soil sample, R mi0 is the minimum pore radius of the soil sample, and f(r) is the pore distribution function.

[0062] The volumetric water content θ can be characterized by the pore distribution function f(r):

[0063]

[0064] Substituting formula (7) into formula (6), the saturated permeability coefficient can be characterized by the volume water content:

[0065]

[0066] Where: θ r is the residual moisture content, which is set to 0 (based on the shortcomings of using the residual moisture content concept).

[0067] Substituting formulas (5) and (6) into formula (4), the capillary permeability coefficient expression can be obtained:

[0068]

[0069] Where: C * is the proportional constant of the saturated permeability coefficient and can be regarded as a constant.

[0070] Considering the porous medium as a bundle of parallel capillaries of different sizes, the unsaturated permeability coefficient can be expressed as: summing the flux of each water-filled capillary under unit gradient, dividing by the sum of the cross-sectional areas of all capillaries, and then correcting the result by the macroscopic capillary water content:

[0071]

[0072] Where: ρ is the density of water, kg / m 3 ; g is the acceleration due to gravity, m / s 2 ; η is the fluid viscosity coefficient, Ns / m 2 .

[0073] It is worth noting that the seepage of porous media is also affected by the tortuosity of the capillary channel in a strict sense. The tortuosity describes the path length l of a single capillary. p The effect of a distance longer than the direct projection distance l through the soil, tortuosity, is expressed as:

[0074] τ=(l / l p ) 2 ; (11)

[0075] Where: 0<τ<1, compared with the seepage in parallel capillary bundles, it will lead to a decrease in local permeability coefficient and hydraulic gradient.

[0076] Capillary flow is affected not only by tortuosity in the strict sense, but also by other additional effects, such as pore roughness, irregular pore geometry and blocked capillaries, resulting in the tortuosity coefficient not being a constant but a function of water content. The tortuosity coefficient τ is expressed as the saturated tortuosity coefficient τ s and relative tortuosity coefficient τ r When the soil sample is saturated, τ r =1, when the soil sample is completely dry, τ r =0, refer to the processing method of Mua model

[0077]

[0078] Where: τ s is a constant, different soils have different τ s The purpose of this invention is to obtain a universally applicable soil-independent τ s and general values of λ to achieve direct prediction of the unsaturated permeability coefficient.

[0079] Substituting formula (12) into formula (10) yields:

[0080]

[0081] Where: γ=50C 2 / ηρg is a constant, at room temperature of 20℃, γ=3.04×10 -2 m 3 s -1 ,γτ s is the absolute saturation tortuosity constant.

[0082] Comparing and analyzing formulas (9) and (13), by defining C * =γτ s , and substituting it into formula (9), we can obtain the capillary permeability coefficient model of the embodiment of the present invention:

[0083]

[0084] The tortuosity and local correction coefficient are related not only to the degree of saturation but also to the geometry of the soil pores. It is proposed to characterize them using the average radius of the pores filled with water and the average pore radius of the soil. The capillary seepage path length also has similar characteristics. The present invention uses the same method to improve the model (Formula (14)) to obtain a further improved capillary permeability coefficient model of the embodiment of the present invention:

[0085]

[0086] The SWCC model is a well-established and widely used method for predicting the unsaturated permeability of soils. However, for soils with a wide pore distribution (cohesive soils), existing capillary bundle permeability models exhibit an unrealistically steep drop when approaching saturation. By introducing the concept of critical pore radius (i.e., critical matrix suction and critical saturation) into the capillary bundle model, the permeability is approximated with a finite slope when approaching saturation, while maintaining smoothness and continuous differentiability:

[0087]

[0088] Where: s t is the critical matrix suction, S t is the saturation at critical matrix suction.

[0089] The present invention adopts the critical matrix suction to be set to 0.6kPa to improve the deficiency of the model in predicting when the model is close to saturation. Silty loam is selected for illustration. Figure 2 As shown in the figure, the permeability coefficient prediction model uses formula (15) and the matching formula (16) respectively, and SWCC uses the RRP model. It can be found that: both models can match the measured data of capillary permeability coefficient well (only fitting the capillary permeability part), but the modified model can eliminate the error of formula (15) when the permeability coefficient drops sharply when approaching saturation. Figure 2RRP model parameters: θ s =0.515, a=0.024, b=1.111, δ1=1194, δ3=10 3.71 , μ=-0.886, α=435.5, n=10 -2.65 , m = 439.9; permeability coefficient model parameter value: τ s =0.024,λ=0.133.

[0090] Existing unsaturated hydraulic conductivity models, such as Equation (5), only consider capillary flow and ignore non-capillary flow processes. However, thin film water on the surface of soil particles also contributes to the hydraulic conductivity. Existing studies only measure the hydraulic conductivity dominated by capillary flow, resulting in a lack of data on the non-capillary flow. Therefore, accurate prediction of the non-capillary hydraulic conductivity is particularly important.

[0091] This is done by incorporating the correlation to a simple non-capillary water permeability model:

[0092] K nc =ωθ m s -1.5 ; (17)

[0093] Where: ω is a constant, equal to 1.35×10-8m 5 / 2 / s;θ m It is the volumetric moisture content of the soil when the matrix suction is equal to 10000 kPa.

[0094] In order to overcome the defect of non-smooth and non-differentiable at the segmentation point, the present invention proposes a continuously differentiable empirical equation to represent the change of non-capillary relative permeability coefficient:

[0095]

[0096] The slope of the non-capillary relative permeability coefficient is -1.5, so η = -1.5; β is the matrix suction parameter.

[0097] When the matrix suction is less than β, the decrease in soil moisture content is mainly caused by capillary water discharge; when the matrix suction is greater than β, the decrease in soil moisture content is mainly caused by film water discharge. Therefore, the matrix suction is in the upper and lower range close to β, which is the transition zone between capillary and non-capillary permeability coefficients. Since film water will not leave the soil before capillary water is discharged, the value of β should be greater than the air intake suction value. For simplicity, the present invention sets β to the matrix suction value corresponding to the SWCC saturation equal to 0.5. Please note: At this time, β should not be strictly interpreted in a physical sense, but should be interpreted as a shape parameter of the permeability coefficient. Introduce the non-capillary saturated permeability coefficient K in formula (18) s,nc , and the non-capillary permeability coefficient function is obtained:

[0098]

[0099] The non-capillary permeability coefficient model in formula (17) is only valid in the range where non-capillary water is dominant, so only the linear decrease part in formula (19) is considered. Combining formulas (17) and (19), the expression for the non-capillary saturated permeability coefficient is obtained:

[0100]

[0101] Where s m >>a,s m Set to 10000kPa.

[0102] Substituting formula (20) into formula (19), a new non-capillary permeability coefficient model is obtained:

[0103]

[0104] The new non-capillary water permeability coefficient model is as follows Figure 3 As shown. Combining formulas (17)-(19) and (21), it is only necessary to calibrate the universally applicable τ s and λ, the unsaturated permeability coefficient can be directly predicted based on the SWCC.

[0105] This invention directly predicts the unsaturated permeability coefficient based on the SWCC. Notably, the fundamental assumption underlying the SWCC model is that the pore space in the soil is simplified as bundles of capillaries of varying sizes. Essentially, this method assumes all water in the soil is capillary water, allowing for direct integration with existing capillary permeability coefficient models. This eliminates the need for artificial "fragmentation" of the SWCC or the introduction of erroneous residual moisture content concepts, ensuring an accurate description of the SWCC.

[0106] For the non-capillary permeability coefficient, when the matrix suction is small, since the non-capillary water will not decrease before the capillary water, the decrease in soil water content is mainly caused by the discharge of capillary water, which is consistent with our hypothesis and can better fit the capillary permeability coefficient, such as Figure 3 However, when the matrix suction increases further, the reduction of soil water content is gradually controlled by non-capillary water. However, the present invention still assumes this part as capillary bundles, that is, the adsorbed water is assumed to be capillary water, as shown in Figure 3 As shown, the permeability of the soil will be seriously underestimated. To solve this problem, the present invention adds a non-capillary water permeability coefficient model to the capillary water permeability coefficient model to improve the model's shortcomings in describing the permeability characteristics of soil under high suction conditions. The summary of the unsaturated permeability coefficient model is shown in Table 1. Note that S in formulas (22)-(25) r It is saturation, not capillary component saturation or effective saturation.

[0107] Table 1 Summary of unsaturated permeability coefficient models

[0108]

[0109]

[0110] Note: In the AS model, parameter γ'=20.4m 3 s -1 ; Substitute formula (18) into the above four models for replacement, and the resulting four new models are collectively referred to as improved models, abbreviated as: ASMua model, ASCCG model, ASBur model and ASAS model; For convenience, this article refers to formulas (22)-(25) as traditional models.

[0111] S106: Determine multiple unsaturated permeability coefficient combination models based on the soil-water characteristic curve model and the unsaturated permeability coefficient model, fit each combination model to obtain a corresponding soil-water characteristic curve, and fit each combination model to a calibration data set to obtain an optimal value to evaluate the performance of different combination models.

[0112] S108: Determine an optimal unsaturated permeability coefficient model based on the evaluation results.

[0113] The three SWCC models were combined with the eight unsaturated permeability coefficient models obtained in Table 1 to obtain a total of 24 unsaturated permeability coefficient combination models. First, the corresponding SWCC was fitted for each combination; then, each combination was fitted to the calibration data set to obtain the τ with the minimum root mean square error. s and λ values; finally, the optimal τ s The and λ values are used in the corresponding unsaturated hydraulic conductivity prediction models to evaluate the performance of different combination models and finally obtain the optimal unsaturated hydraulic conductivity prediction model.

[0114] To obtain the saturation tortuosity τ s With the general value of the bending connectivity factor λ, the present invention uses 12 calibration data sets used in the related art, and the texture and coding of the selected soil samples are shown in Table 2.

[0115] Figure 4 The SWCC and unsaturated hydraulic conductivity of two soil samples from the 12 calibration data sets in Table 2 are shown, and the model fitting parameters are shown in Table 3. The present invention selects the ASCCG combination model for illustration because it performs best in predicting the unsaturated hydraulic conductivity. The numbers in the lower left corner of the figure represent the RMSEθ and Depend on Figure 4As can be seen from (b) and (d), for the capillary permeability component, both the RRP and FX combined models are well suited to describe the water content. The differences between the models are minimal and difficult to distinguish on the graph because they largely overlap. The VG combined model, however, exhibits a larger error. However, for the non-capillary permeability component, differences emerge between the RRP and FX combined models. This is because the non-capillary permeability is an absolute prediction without any adjustable fitting parameters and is closely related to the water content corresponding to the SWCC at s = 10,000 kPa, as shown in Figure 1. Figure 4 As shown in (a) and (c), different SWCC models calculate different water contents in the medium and high matric suction range.

[0116] Table 2 Calculation of saturation curvature τ s Calibration dataset with curved connectivity factor λ

[0117]

[0118] Table 3 Model calculation parameters for 2 of the 12 calibration data sets

[0119]

[0120] Figure 5 The RMSEθ for the 12 calibration datasets and 24 combined models is shown. The distribution of the RRP model shows the best fitting accuracy, with a median of 0.0033. The corresponding RRP combination model also exhibits superior performance in fitting the unsaturated permeability coefficient, as shown in Table 4. The FX combination model performs second, and the VG combination model performs worst. Furthermore, because the improved model proposed in this paper aligns the functional expressions of the ASMua and ASAS models, their fitting accuracy is comparable. When the unsaturated permeability coefficient is available, the combination of the Mua, CCG, ASMua, and ASAS models among the FX and RRP models is more recommended.

[0121] Figure 6 The total root mean square error of the RRP-ASCCG model is given as the parameter τ s and β changing surface, it can be seen from the figure that when When β = 0.4, The best fitting effect is shown in Table 5. The best fitting parameters of all combination models are shown in Table 5. It can be seen that the ASCCG model has the best fitting effect in all combinations. The value is the lowest, and the improved model of unsaturated permeability coefficient proposed in this invention The values are lower than those of the traditional model, indicating that the improved model has better performance.

[0122] Table 4 24 combination models of 12 calibration datasets median

[0123]

[0124] Table 5 Minimum total root mean square error and optimal parameters of different model combinations fitted to 12 calibration data sets

[0125]

[0126] To test the combined model's predictive effectiveness for unsaturated hydraulic conductivity, we selected 23 test datasets used in related art. The soil sample textures and codes are shown in Table 6, and detailed soil information is available in the original literature. The optimal fitting parameters (see Table 5) were substituted into the SWCCs of the 23 test datasets to directly predict the unsaturated hydraulic conductivity.

[0127] The present invention still selects the ASCCG combination model for explanation, such as Figure 7 As shown in Figure 7, the water holding capacity data and unsaturated hydraulic conductivity data of two soil samples in the 23 test data sets, and the model parameters are shown in Table 7. As can be seen from the figure, the RRP and FX combination model still shows better prediction performance than the VG combination model.

[0128] like Figure 8 As shown, the RMSEθ and Box plots. All combined models The medians are shown in Table 8. The medians are 0.4424 and 0.3249 respectively, while the median of the RRP-ASCCG model combined with the more accurate SWCC is only 0.3078. This also indirectly reflects that a more accurate SWCC is more conducive to the prediction of unsaturated hydraulic conductivity. Among all the combined models, the RRP-ASCCG model is not only The median performance is the best, and the prediction accuracy also shows the smallest error range, with an error range of only 0.2264-0.3974. The optimal prediction model (FX-Mua model) proposed based on the calibration data set and the test data set is The median is 0.40, and the error range of the prediction accuracy is about 0.2567-0.4853. Compared with the FX-Mua model, the RRP-ASCCG model proposed in this invention has a 23% improvement in prediction accuracy and a smaller error range.

[0129] Table 6 Test data set of unsaturated permeability coefficient

[0130]

[0131] Table 7 Model calculation parameters for 2 of the 23 test datasets

[0132]

[0133] Table 8 24 combination models of 23 test data sets and the median of RMSEθ of the three SWCC models

[0134]

[0135] Unsaturated permeability coefficient considering deformation effect. Based on the recently proposed SWCC model considering deformation effect, as shown in formulas (1) and (2). They are respectively substituted into the unsaturated permeability coefficient model proposed in the present invention and compared with the common VG and FX models. The present invention selects the main drying and unsaturated permeability coefficient experiments carried out on Columbia sandy loam and Touchet silty loam using relevant technologies. The present invention selects the optimal model: RRP-ASCCG model for illustration. Figure 9 The water holding data and unsaturated hydraulic conductivity data of Columbia sandy loam and Touchet silt loam are shown respectively. The model parameters are shown in Table 9. The SWCC model parameters are calibrated by any two water holding data at different constant porosity ratios, as shown in Table 9. Figure 9 (a) and (c) are solid lines. Figure 9 As can be seen from (a) and (c), the RRP model considering the influence of different porosity ratios can better describe the water holding characteristics of soil. Figure 9 As shown in (b) and (d), the predicted values of the RRP-ASCCG model are in good agreement with the measured values of the unsaturated permeability coefficient, indicating that the model can be used to predict the unsaturated permeability coefficient considering the deformation effect. As shown in Table 10, the RMSEθ and the predicted accuracy of the unsaturated permeability coefficient considering the deformation effect are significantly better than those of the traditional model. The RRP-ASCCG model is the best among all the combined models in terms of both the prediction accuracy of SWCC and the prediction accuracy of the unsaturated permeability coefficient. This once again shows that the accurate description of SWCC is conducive to a more accurate prediction of the unsaturated permeability coefficient.

[0136] Table 9 Calculation parameters of Columbia sandy loam and Touchet sand model

[0137]

[0138] Table 10 Total of two soil samples and RMSEθ

[0139]

[0140] The unsaturated permeability coefficient is key to describing the seepage, mechanics, and coupled processes of unsaturated soils. Obtaining reliable data to parameterize models is crucial, but selecting the appropriate unsaturated permeability coefficient is equally important. Based on the proposed SWCC model, this paper proposes 24 unsaturated permeability coefficient models and uses extensive experimental data to verify the correctness and rationality of the proposed models.

[0141] The present invention adopts the generally applicable saturation tortuosity τ s The capillary permeability coefficient is predicted from the SWCC with the tortuosity connectivity factor λ. A continuously differentiable empirical equation is proposed to predict the non-capillary permeability coefficient from the SWCC. The two are superimposed to obtain a prediction model for the unsaturated permeability coefficient. Eight unsaturated permeability coefficient models are proposed and combined with three SWCC models to obtain 24 combination models. The optimal saturated tortuosity τ is determined for each combination model. s The unsaturated permeability coefficient was then predicted by combining the bend connectivity factor λ and the RRP-ASCCG combined model. The results show that the RRP-ASCCG combined model has the best prediction accuracy among all combined models, both for the soil-water characteristic curve and the unsaturated permeability coefficient. This research provides a theoretical basis for describing the seepage, mechanics, and coupled processes of unsaturated soils.

[0142] The embodiment of the present invention first proposes reference values of PSD shape parameters under different soil textures to expand the application range of the RRP model; secondly and more importantly, it proposes the use of the absolute saturation tortuosity constant γτ s The capillary permeability coefficient model is obtained by replacing the saturated permeability coefficient proportional constant C*. Third, a continuously differentiable non-capillary permeability coefficient model is proposed. Fourth, 24 unsaturated permeability coefficient combination models are established. Fifth, when the SWCC is known, the unsaturated permeability coefficient combination model of the present invention can be directly predicted without any adjustable parameters. Finally, the reliability of the model is verified by multiple sets of experimental data. The RRP-ASCCG model of the present invention has the best prediction accuracy, with an average error of only 0.3 orders of magnitude, and can further better predict the unsaturated permeability coefficient considering deformation effects. The embodiments of the present invention provide a reliable solution to the problem of missing unsaturated permeability coefficient data.

[0143] It will be understood that the present invention is described by way of some embodiments, and it will be appreciated by those skilled in the art that various changes or equivalent substitutions may be made to these features and embodiments without departing from the spirit and scope of the present invention. In addition, under the teachings of the present invention, these features and embodiments may be modified to adapt to specific circumstances and materials without departing from the spirit and scope of the present invention. Therefore, the present invention is not limited to the specific embodiments disclosed herein, and all embodiments falling within the scope of the claims of this application are intended to be protected by the present invention.

Claims

1. A method for calculating the unsaturated permeability coefficient based on the soil-water characteristic curve, characterized in that: include: Establishing a soil-water characteristic curve model, wherein the soil-water characteristic curve model assumes the pore space in the soil as a capillary bundle of uneven size, including a Roshin-Rammle particle size distribution model and a porosity ratio; An unsaturated permeability coefficient model is established based on the soil-water characteristic curve model, wherein the total permeability coefficient includes the capillary permeability coefficient and the non-capillary permeability coefficient, wherein the capillary permeability coefficient is determined by the absolute saturated tortuosity constant, and the change of the non-capillary relative permeability coefficient in the non-capillary permeability coefficient is expressed by a continuously differentiable empirical equation; Determining multiple unsaturated permeability coefficient combination models based on the soil-water characteristic curve model and the unsaturated permeability coefficient model, fitting each combination model to obtain a corresponding soil-water characteristic curve, fitting each combination model to a calibration data set to obtain an optimal absolute saturated tortuosity constant value, and applying the optimal value to a test data set to evaluate the performance of different combination models; An optimal unsaturated permeability coefficient model is determined according to the evaluation results.

2. The calculation method of the unsaturated permeability coefficient based on the soil-water characteristic curve according to claim 1 is characterized in that: Also includes: Validation of the combined model including the soil-water characteristic curve model with deformation effects.

3. The calculation method of the unsaturated permeability coefficient based on the soil-water characteristic curve according to claim 2 is characterized in that: The soil-water characteristic curve model satisfies the following formula: Where a and b are fitting constants related to the particle size distribution; δ is the arrangement characteristic coefficient; μ is the arrangement characteristic index; e0 is the porosity ratio under the reference state; e i is the void ratio under any deformation state.

4. The method for calculating the unsaturated permeability coefficient based on the soil-water characteristic curve according to claim 3, characterized in that: The total permeability coefficient, capillary permeability coefficient and non-capillary permeability coefficient satisfy the following formula: K=K c +K nc ; Where K is the total permeability coefficient, m / s; K c and K nc are the capillary permeability coefficient component and the non-capillary permeability coefficient component, m / s.

5. The method for calculating the unsaturated permeability coefficient based on the soil-water characteristic curve according to claim 4, characterized in that: The capillary permeability coefficient is determined by the absolute saturation tortuosity constant and satisfies the following formula: Where γ = 50C 2 / ηρg is a constant, at room temperature of 20℃, γ=3.04×10 -2 m 3 / s, γτ s is the absolute saturation tortuosity constant.

6. The method for calculating the unsaturated permeability coefficient based on the soil-water characteristic curve according to claim 5, characterized in that: The capillary permeability coefficient is determined by the absolute saturation tortuosity constant and also satisfies the following formula:

7. The method for calculating the unsaturated permeability coefficient based on the soil-water characteristic curve according to claim 6, characterized in that: The change of the non-capillary relative permeability coefficient in the non-capillary permeability coefficient is expressed by a continuously differentiable empirical equation, which satisfies the following formula: The slope of the non-capillary relative permeability coefficient is -1.5, so η = -1.5; β is the matrix suction parameter.

8. The method for calculating the unsaturated permeability coefficient based on the soil-water characteristic curve according to claim 7, characterized in that: Introducing the non-capillary saturated permeability coefficient K s,nc , the non-capillary permeability coefficient function satisfies the following formula: Substitute the above formula into a non-capillary water permeability coefficient model: K nc =ωθ m s -1.5 ; The expression of non-capillary saturated permeability coefficient is obtained: Where ω is a constant, equal to 1.35×10 -8 m 5 / 2 s -1 θ m is the matrix suction, which is equal to the volumetric water content of the soil at 10000 kPa; s m >>a,s m Set to 10000kPa.

9. The method for calculating the unsaturated permeability coefficient based on the soil-water characteristic curve according to claim 8, characterized in that: The optimal unsaturated permeability coefficient model is the RRP-ASCCG model.

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