CN109583123B - Method for predicting unsaturated relative permeability coefficient - Google Patents

Method for predicting unsaturated relative permeability coefficient Download PDF

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CN109583123B
CN109583123B CN201811521107.5A CN201811521107A CN109583123B CN 109583123 B CN109583123 B CN 109583123B CN 201811521107 A CN201811521107 A CN 201811521107A CN 109583123 B CN109583123 B CN 109583123B
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陶高梁
匡航
庄心善
胡其志
肖衡林
马强
李丽华
朱志政
万娟
李奕
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Hubei University of Technology
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Abstract

The invention discloses a method for predicting unsaturated relative permeability coefficient, which is characterized in that the measured unsaturated relative permeability coefficient k r Fitting to obtain an index lambda before deformation by combining a relational graph of the suction force psi of the matrix and an unsaturated relative permeability coefficient fractal model II 0 And initial void ratio e before deformation 0 Inlet air value Ψ a0 Obtaining a deformed intake value psi by calculation a Combined with the index after deformation λ = the index before deformation λ 0 At K r In the relationship Ψ, K is the suction force for the low suction force stage less than the inlet value Ψ r -the Ψ -curve is a coincident horizontal line; for high suction phase greater than the inlet value psi, for the original K r - Ψ -line is made parallel to the right direction to predict the unsaturated relative permeability k under arbitrary deformation conditions r . Overcomes the defect that the existing unsaturated relative permeability coefficient fractal model calculates the index lambda through a specific relation 0 The method has the advantages that the application range of the unsaturated relative permeability coefficient model is expanded, and the prediction precision is improved.

Description

Method for predicting unsaturated relative permeability coefficient
Technical Field
The invention relates to the technical field of research on unsaturated soil water-force coupling in geotechnical engineering and the seepage characteristics of soil under deformation conditions, in particular to a method for predicting unsaturated relative permeability coefficient.
Background
The analysis of the unsaturated soil seepage is one of the hot problems of actual engineering research of rock and environment, for example, side slope landslide disaster caused by rainfall, seepage prevention of soil dams, migration of underground soil pollutants and the like all relate to seepage problems, and the unsaturated relative permeability coefficient is a key parameter in the analysis of the unsaturated soil seepage.
The unsaturated relative permeability coefficient can be directly obtained through experiments, but the direct testing method is complex in operation, time-consuming and labor-consuming, and the measurement accuracy and operability of the existing testing instrument are still to be improved. In addition, the unsaturated soil permeability analysis under complex conditions must also be based on a permeability coefficient prediction method, for example, tests cannot meet the measurement requirement of unsaturated relative permeability coefficient under any deformation condition. Therefore, the method for predicting the unsaturated relative permeability coefficient under the deformation condition is significant to research.
At present, in the aspect of predicting the unsaturated relative permeability coefficient by using fractal theory, three types of linear relations between the exponent λ and the fractal dimension D in the unsaturated relative permeability coefficient model are assumed, such as λ =5-D in a Tao & Kong model, λ =9.5-2.5D in a Mualem model, and λ =11-3D in a Burdine model, and in practice, the three relations hardly include all cases. If the index λ is obtained by using these specific relationships, it may be greatly different from the actual measurement situation. Moreover, the application ranges of the three models are different, and the wrong selection of the model also causes a large error.
Disclosure of Invention
The invention aims to provide a simple and high-precision method for predicting unsaturated relative permeability coefficient aiming at the defects of the technology.
In order to achieve the above purpose, the method for predicting unsaturated relative permeability coefficient designed by the present invention comprises:
1) The initial porosity e before deformation is determined by testing 0 Unsaturated relative permeability coefficient k of soil sample under different substrate suction r Measuring data actually to obtain unsaturated relativeCoefficient of permeability k r A map of substrate suction Ψ; fitting to obtain an index lambda before deformation according to the unsaturated relative permeability coefficient fractal model II 0 And initial void ratio e before deformation 0 Inlet air value Ψ a0 The fractal dimension D is unchanged before and after the deformation of the soil sample, and according to the fact that the index lambda in the unsaturated relative permeability coefficient fractal model II is a coefficient linearly related to the fractal dimension D, the index lambda after the deformation = the index lambda before the deformation 0 ；
Wherein the fractal model II is
Figure GDA0001962731490000021
K r (Ψ) is the relative permeability coefficient for unsaturation, the index λ is the coefficient that is linearly related to the fractal dimension D, Ψ a Psi is the substrate suction, the deformed inlet value;
2) Initial void ratio e before deformation from step 1) 0 K of r The relationship Ψ, K, at a low suction level less than the intake value Ψ r The Ψ -curve is a coincident horizontal line, and K is the value of the suction at a high suction level greater than the intake air value r - Ψ -curve is a set of parallel straight lines; calculating to obtain a deformed air inlet value psi through an air inlet value prediction formula III a Combining the index after deformation in step 1) = the index before deformation λ 0 At K, in r In the relationship Ψ, K is the suction force for the low suction force stage less than the inlet value Ψ r - Ψ -curve is a coincident horizontal line; for high suction stages greater than the inlet value psi, for the original K r -psi straight line is parallel straight line towards right direction, so as to predict unsaturated relative permeability coefficient k under arbitrary deformation condition r ；
Wherein the intake air value prediction formula III is
Figure GDA0001962731490000022
Ψ a0 The initial porosity ratio e before deformation in step 1) 0 Intake value of e 1 For the deformed void ratio, D is the fractal dimension, and D is a fixed value during deformation.
Further, in the step 1), three existing permeability coefficient models and SWCC fractal models are usedType derivation unsaturated relative permeability coefficient fractal model
Figure GDA0001962731490000031
II, the specific derivation process is as follows:
the three permeability coefficient models and the SWCC fractal model are as follows:
Tao&relative permeability coefficient of non-saturation of Kong model
Figure GDA0001962731490000032
Wherein in the formula (1), psi is the substrate suction force, theta r Indicates the residual volume water content, θ s Represents the saturated volume water content, and theta represents the volume water content;
relative permeability coefficient of non-saturation of Mualem model
Figure GDA0001962731490000033
Wherein in the formula (2), psi is the substrate suction force, theta r Indicates the residual volume water content, θ s Showing saturated volume water content, theta showing volume water content, S e Is the effective saturation;
burdine model unsaturated relative permeability coefficient
Figure GDA0001962731490000034
Wherein psi is substrate suction force theta in formula (3) r Indicates the residual volume water content, θ s Showing saturated volume water content, theta showing volume water content, S e Is the effective saturation;
the expression of the SWCC fractal model is expressed by volume water content as follows:
Figure GDA0001962731490000035
in the formula (4), θ is the volume water content, θ s Is saturated volume water content, psi a0 Is the initial void ratio e before deformation 0 Intake value of psiIs the substrate suction, D is the fractal dimension;
phi is more than or equal to phi in formula (4) by adopting SWCC fractal model expression a0 The formula (II) can be obtained by simultaneous derivation of two sides
Figure GDA0001962731490000041
Formula (5) is adopted to respectively derive formula (6), formula (7) and formula (8) for formula (1), formula (2) and formula (3):
Figure GDA0001962731490000042
/>
Figure GDA0001962731490000043
Figure GDA0001962731490000044
unifying fractal form formulas (6), (7) and (8) of unsaturated relative permeability coefficients of the Tao and Kong models, the Mualem models and the Burdine models into a fractal model II
Figure GDA0001962731490000045
The exponent λ in the fractal model II is the coefficient linearly related to the fractal dimension D, in Tao&λ =5-D in Kong model, λ =9.5-2.5D in Mualem model, λ =11-3D in Burdine model; k r (Ψ) is the relative permeability coefficient for unsaturation, Ψ a Psi is the substrate suction for the intake air value after deformation.
Further, the initial porosity ratio e before deformation is measured through tests in the step 1) 0 Unsaturated relative permeability coefficient k of soil sample under different substrate suction r The actual measurement data comprises the following specific processes: initial void ratio e before deformation by the variable head method 0 Saturated permeability coefficient k of soil sample under different substrate suction s Measuring the initial porosity e before deformation by transient profile method or steady state test method 0 The measured unsaturated permeability coefficient k of the soil sample under different substrate suction forces is calculated by a formula I to obtain the initial pore ratio e before deformation 0 Unsaturated relative permeability coefficient k of soil sample under different substrate suction r Actually measuring data;
k r ＝k/k s Ⅰ
further, the derivation process of the intake value prediction formula iii in step 2) is specifically as follows:
the mass water content is expressed by the proposed SWCC fractal model expression as follows:
Figure GDA0001962731490000051
in equation (9): w represents the mass water content, e is the void ratio, G s Representing relative density of soil particles, Ψ representing substrate suction, Ψ a Representing an air intake value, D being a fractal dimension;
under the condition of converting the soil-water characteristic curve before deformation into the form of mass water content, the soil-water characteristic curve after deformation of psi ≥ psi a at the high suction stage is almost coincident with that before deformation, and when the aperture ratio after deformation is changed into e 1 Then, make horizontal line w = e 1 Gs, to initial pore ratio before deformation e 0 The horizontal coordinate of the intersection point of the soil-water characteristic curve can be approximately regarded as the pore ratio e after deformation 1 Inlet air value psi a1 And calculating on the basis of the formula (9) to obtain a formula III.
Compared with the prior art, the invention has the following advantages: the method for predicting the unsaturated relative permeability coefficient overcomes the defect that the existing unsaturated relative permeability coefficient fractal model calculates the index lambda through a specific relation 0 The application range of the unsaturated relative permeability coefficient model is enlarged, and the prediction precision is improved; the method has extremely important values in the aspects of seepage theory, fluid-solid coupling research, engineering application and the like of unsaturated soil.
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FIG. 1 is a schematic flow chart of a method for predicting unsaturated relative permeability coefficient according to the present invention;
FIG. 2 is a plot of the fit of the initial porosity ratio of 1.012Touchet silt loam fractal dimension D before deformation in the examples.
FIG. 3 is a graph comparing the predicted and measured relative permeability coefficient for Touchet silt loam at different porosity ratios for the examples.
Detailed Description
The invention is described in further detail below with reference to the figures and the specific embodiments.
Deducing an unsaturated relative permeability coefficient fractal model according to the existing three permeability coefficient models and an SWCC fractal model
Figure GDA0001962731490000061
The specific derivation process is as follows:
the three permeability coefficient models and the SWCC fractal model are as follows:
Tao&relative permeability coefficient of non-saturation of Kong model
Figure GDA0001962731490000062
Wherein in the formula (1), psi is the substrate suction force, theta r Indicates the residual volume water content, θ s Represents the saturated volume water content, and theta represents the volume water content;
relative permeability coefficient of non-saturation of Mualem model
Figure GDA0001962731490000063
Wherein in the formula (2), psi is the substrate suction force, theta r Indicates the residual volume water content, θ s The saturated volume water content, theta the volume water content, S e Is the effective saturation;
burdine model unsaturated relative permeability coefficient
Figure GDA0001962731490000064
Wherein psi is substrate suction force theta in formula (3) r Indicates the residual volume water content, θ s Showing saturated volume water content, theta showing volume water content, S e Is the effective saturation;
the expression of the SWCC fractal model is expressed by volume water content as follows:
Figure GDA0001962731490000065
in the formula (4), θ is the volume water content, θ s Is saturated volume water content, psi a0 Is the initial void ratio e before deformation 0 The inlet value psi is the substrate suction and D is the fractal dimension;
phi is more than or equal to phi in formula (4) by adopting SWCC fractal model expression a0 The formula (II) can be obtained by simultaneous derivation of two sides
Figure GDA0001962731490000071
Respectively deriving a formula (6), a formula (7) and a formula (8) from the formula (1), the formula (2) and the formula (3) by adopting a formula (5):
Figure GDA0001962731490000072
Figure GDA0001962731490000073
Figure GDA0001962731490000074
unifying fractal form formulas (6), (7) and (8) of unsaturated relative permeability coefficients of the Tao and Kong models, the Mualem models and the Burdine models into a fractal model II
Figure GDA0001962731490000075
The exponent λ in the fractal model II is the coefficient linearly related to the fractal dimension D, in Tao&λ =5-D in Kong model, λ =9.5-2.5D in Mualem model, λ =11-3D in Burdine model; k is r (Ψ) is the unsaturated relative permeability coefficient, Ψ a Psi is the substrate suction, the intake value after deformation.
In addition, the initial void ratio e before deformation was obtained by the pressure plate test 0 Measuring soil-water characteristics under the condition, discarding the data of low substrate suction segment with unchanged water content, calculating fractal dimension D by expression lnw ^ (3-D) (-ln ψ), using-ln Ψ as abscissa, and using lnw or lnS r Drawing a scatter diagram serving as a longitudinal coordinate, and then performing straight line fitting on the scatter diagram to obtain a slope of k, wherein the fractal dimension D =3-k;
the soil-water characteristic curves represented by the mass water content of the deformed soil body are distributed in a broom shape, and the soil-water characteristic curves with different initial pore ratios are basically superposed after the air inlet value (please refer to the water conservancy project, volume 6 in 6.2017, volume 48, stage 6, a saturated/unsaturated soil permeation model based on micro-pore channels and application thereof, haoguan and Chongwei]) The expression lnw ℃ (3-D) (-ln ψ) adopts test data coincident after the air intake value when calculating, so that the fractal dimension D calculated by the soil-water characteristic curve under different initial pore ratio conditions is not changed (for a detailed process, refer to step (3) in the patent application claims of Chinese invention with the application number of 2017104197830 and the application date of 2017.06.06); initial void ratio e before deformation 0 Index of time is lambda 0 And if the fractal dimension D is unchanged before and after the deformation of the soil sample and the index lambda in the unsaturated relative permeability coefficient fractal model II is a coefficient linearly related to the fractal dimension D, the index lambda after the deformation = the index lambda before the deformation 0 。
The method for predicting the unsaturated relative permeability coefficient is combined with the specific process shown in fig. 1 as follows:
1) The initial porosity e before deformation is determined by testing 0 Unsaturated relative permeability coefficient k of soil sample under different substrate suction r Measured data, and thenObtaining the unsaturated relative permeability coefficient k r Graph (K) relating to substrate suction Ψ r - Ψ); fitting to obtain an index lambda before deformation according to the unsaturated relative permeability coefficient fractal model II 0 And initial void ratio e before deformation 0 Air intake value Ψ a0 If the index before and after deformation of the soil sample is unchanged, the index after deformation λ = the index before deformation λ 0 ；
Wherein the fractal model II is
Figure GDA0001962731490000081
K r (Ψ) is the relative permeability coefficient for unsaturation, the index λ is the coefficient that is linearly related to the fractal dimension D, Ψ a Psi is the intake value after deformation and the substrate suction force;
2) Initial porosity e before deformation from step 1) 0 K of r The relationship Ψ, K, at a low suction level less than the intake value Ψ r The Ψ -curve is a coincident horizontal line, and K is the suction level during the high suction phase above the inlet value r - Ψ -curve is a set of parallel straight lines; calculating to obtain a deformed intake value psi by an intake value prediction formula III a Combining the index after deformation in step 1) = the index before deformation λ 0 At K, in r In the relationship Ψ, K is the suction force for the low suction stage less than the inlet value Ψ r - Ψ -curve is a coincident horizontal line; for high suction stages greater than the inlet value psi, for the original K r - Ψ -line is made parallel to the right direction to predict the unsaturated relative permeability k under arbitrary deformation conditions r ；
Wherein the intake air value prediction formula III is
Figure GDA0001962731490000091
Ψ a0 As the initial void ratio e before deformation in step 1) 0 Intake value of e 1 D is a fractal dimension which is the porosity ratio after deformation, and D is a fixed value in the deformation process.
The initial porosity e before deformation is determined by testing in step 1) 0 Unsaturated relative permeability coefficient k of soil sample under different substrate suction r Number of measured measurementsThe specific process comprises the following steps: initial void ratio e before deformation by the variable head method 0 And the saturated permeability coefficient k of the soil sample under different matrix suction forces s Measuring the initial porosity e before deformation by transient profile method or steady state test method 0 The measured unsaturated permeability coefficient k of the soil sample under different substrate suction forces is calculated by a formula I to obtain the initial pore ratio e before deformation 0 Unsaturated relative permeability coefficient k of soil sample under different substrate suction r Actually measuring data;
k r ＝k/k s Ⅰ
in step 2), the derivation process of the intake air value prediction formula iii is specifically as follows:
the mass water content is expressed by the proposed SWCC fractal model expression as follows:
Figure GDA0001962731490000092
in equation (9): w represents the mass water content, e is the void ratio, G s Representing relative density of soil particles, Ψ representing substrate suction, Ψ a Representing an air intake value, D being a fractal dimension;
under the condition of converting the soil-water characteristic curve before deformation into the form of mass water content, the soil-water characteristic curve after deformation of psi ≥ psi a at the high suction stage is almost coincident with that before deformation, and when the aperture ratio after deformation is changed into e 1 Then, make horizontal line w = e 1 Gs, to initial pore ratio before deformation e 0 The horizontal coordinate of the intersection point of the soil-water characteristic curve can be approximately regarded as the pore ratio e after deformation 1 Inlet air value psi of time a1 And calculating a formula III on the basis of the formula (9) (see the steps (4) and (5) in the patent application claims of the Chinese invention with the application number of 2017104197830 and the application date of 2017.06.06 in the specific derivation process).
The invention is further described with reference to specific examples.
The soil samples used in the examples are touchhet silt loam remolding soil samples, and the test data are derived from touchhet silt loam test data in the literature "Hydraulic properties of porous media".
Predicting the unsaturated relative permeability coefficient of the soil body under the deformation condition:
the soil sample used in the examples was a Touchet silt loam remolded soil sample, and a soil-water characteristic curve having an initial void ratio of 1.012 before deformation was measured by a pressure plate test.
Firstly, the unsaturated relative permeability coefficient k of the soil sample under different matrix suction forces with the initial pore ratio of 1.012 before deformation is obtained through tests r Measuring data actually to obtain K r Fitting by using an unsaturated relative permeability coefficient fractal model II to obtain an inlet air value psi of 1.012 before deformation a0 And the index lambda before deformation 0 。
Then, calculating the fractal dimension D according to the soil-water characteristic curve test data by respectively using-ln Ψ as the abscissa, ln w or ln S r As ordinate (in this case lnS r ) Drawing a scatter diagram, and then performing straight line fitting on the scatter diagram to obtain a slope k, wherein the fractal dimension D =3-k; because the fractal dimension D is unchanged before and after the deformation of the soil sample, the index lambda is a coefficient linearly related to the fractal dimension D, and the index lambda is unchanged before and after the deformation of the soil sample. The calculated value of the fractal dimension D before deformation was 2.111, the fitting correlation coefficient was 0.99, and the fitting result is shown in fig. 2.
The air intake values were calculated for different porosity ratios of 0.916, 0.815, 0.733, 0.653touch silt loam. Combining the inlet air value psi with the initial aperture ratio of 1.012 before deformation due to the unchanged fractal dimension D before and after deformation a0 And calculating the formula III to obtain air inlet values with different porosity ratios, as shown in the table 1.
TABLE 1
Figure GDA0001962731490000101
Finally, based on K before deformation with an initial porosity ratio of 1.012 r - Ψ -map, incorporating the calculated deformed intake values Ψ a The index lambda before and after deformation of the soil sample is constant, then K is r -a- Ψ -relationship diagram wherein,for low suction phases less than the inlet value, K r -the Ψ -curve is a coincident horizontal line; for high suction stage greater than air inlet value, for original K r - Ψ -line is made as a parallel line in the right direction. So as to predict the unsaturated relative permeability coefficient k under any deformation condition r 。
Actually measuring the unsaturated relative permeability coefficient of the soil body under the deformation condition:
measuring the saturated permeability coefficient k of the soil sample under the same pore state and different substrate suction forces by a variable water head method s Measuring the unsaturated permeability coefficient k of the soil sample under the same pore state and different matrix suction by using a transient section method or a steady-state test method, and further calculating (k) r ＝k/k s ) Obtaining the unsaturated relative permeability coefficient k of the soil sample under the same pore state and different substrate suction forces r . Repeatedly testing before and after the soil sample is deformed, and drawing the obtained measured data through origin software to obtain K under different pore ratios r - Ψ -relationship graph.
The comparison graph of the prediction result of the unsaturated relative permeability coefficient and the measured value is shown in fig. 3 and is basically overlapped, which shows that the prediction method of the invention is accurate.
The method for predicting the unsaturated relative permeability coefficient overcomes the defect that the existing unsaturated relative permeability coefficient fractal model passes through a specific relation (Tao)&λ =5-D in Kong model, λ =9.5-2.5D in Mualem model, λ =11-3D in Burdine model) to calculate the index λ £ m 0 The application range of the unsaturated relative permeability coefficient model is enlarged, and the prediction precision is improved; the method is simple, convenient, quick and effective, and the rationality of the method is verified based on unsaturated relative permeability coefficient test data of the deformed soil; the method has extremely important values in the aspects of seepage theory, fluid-solid coupling research, engineering application and the like of unsaturated soil.

Claims (2)

1. A method of predicting unsaturated relative permeability coefficients, characterized by: the prediction method comprises the following steps:
1) The initial porosity e before deformation is determined by testing 0 Different substrate suctionUnsaturated relative permeability coefficient k of lower soil sample r Data are actually measured, and then the unsaturated relative permeability coefficient k is obtained r A map of substrate suction Ψ; fitting to obtain an index lambda before deformation according to the unsaturated relative permeability coefficient fractal model II 0 And initial void ratio e before deformation 0 Inlet air value Ψ a0 The fractal dimension D is unchanged before and after the deformation of the soil sample, and according to the fact that the index lambda in the unsaturated relative permeability coefficient fractal model II is a coefficient linearly related to the fractal dimension D, the index lambda after the deformation = the index lambda before the deformation 0 ；
Wherein the fractal model II is
Figure FDA0003979961620000011
K r (Ψ) is the relative permeability coefficient for unsaturation, the index λ is the coefficient that is linearly related to the fractal dimension D, Ψ a Psi is the intake value after deformation and the substrate suction force;
2) Initial void ratio e before deformation from step 1) 0 K of r The relationship Ψ, K, at a low suction level less than the intake value Ψ r The Ψ -curve is a coincident horizontal line, and K is the value of the suction at a high suction level greater than the intake air value r - Ψ -curve is a set of parallel straight lines; calculating to obtain a deformed intake value psi by an intake value prediction formula III a Combining the index λ after deformation in step 1) = the index λ before deformation 0 At K r In the relationship Ψ, K is the suction force for the low suction stage less than the inlet value Ψ r - Ψ -curve is a coincident horizontal line; for high suction phase greater than the inlet value psi, for the original K r - Ψ -line is made parallel to the right direction to predict the unsaturated relative permeability k under arbitrary deformation conditions r ；
Wherein the intake air value prediction formula III is
Figure FDA0003979961620000012
Ψ a0 The initial porosity ratio e before deformation in step 1) 0 Intake value of e 1 The porosity ratio after deformation, D is a fractal dimension, and D is a fixed value in the deformation process;
in the step 1), a non-saturated relative permeability coefficient fractal model is deduced according to the three existing permeability coefficient models and the SWCC fractal model
Figure FDA0003979961620000021
The specific derivation process is as follows:
the three permeability coefficient models and the SWCC fractal model are as follows:
Tao&relative permeability coefficient of non-saturation of Kong model
Figure FDA0003979961620000022
Wherein psi is substrate suction force theta in formula (1) r Indicates the residual volume water content, θ s Represents the saturated volume water content, and theta represents the volume water content;
relative permeability coefficient of non-saturation of Mualem model
Figure FDA0003979961620000023
Wherein in the formula (2), psi is the substrate suction force, theta r Indicates the residual volume water content, θ s The saturated volume water content, theta the volume water content, S e Is the effective saturation;
burdine model unsaturated relative permeability coefficient
Figure FDA0003979961620000024
Wherein in the formula (3), psi is the substrate suction force, theta r Indicates the residual volume water content, θ s The saturated volume water content, theta the volume water content, S e Is the effective saturation;
the expression of the SWCC fractal model is expressed by volume water content as follows:
Figure FDA0003979961620000025
in the formula (4), θ is the volume water content, θ s Is saturated volume water content, psi a0 Is the initial void ratio e before deformation 0 The inlet value psi is the substrate suction and D is the fractal dimension;
phi is more than or equal to phi in formula (4) by adopting SWCC fractal model expression a0 The formula (II) can be obtained by simultaneous derivation of two sides
Figure FDA0003979961620000031
Formula (5) is adopted to respectively derive formula (6), formula (7) and formula (8) for formula (1), formula (2) and formula (3):
Figure FDA0003979961620000032
Figure FDA0003979961620000033
Figure FDA0003979961620000034
unifying fractal formulas (6), (7) and (8) of unsaturated relative permeability coefficients of the Tao and Kong models, the Mualem models and the Burdine models into a fractal model II
Figure FDA0003979961620000035
The exponent λ in the fractal model II is the coefficient linearly related to the fractal dimension D, in Tao&λ =5-D in Kong model, λ =9.5-2.5D in Mualem model, λ =11-3D in Burdine model; k r (Ψ) is the unsaturated relative permeability coefficient, Ψ a Psi is the substrate suction, the deformed inlet value;
the derivation process of the intake value prediction formula III in the step 2) is specifically as follows:
the mass water content is expressed by the proposed SWCC fractal model expression as follows:
Figure FDA0003979961620000036
in equation (9): w represents the mass water content, e is the void ratio, G s Representing relative density of soil particles, Ψ representing substrate suction, Ψ a Representing an air intake value, D being a fractal dimension;
under the condition of converting the soil-water characteristic curve before deformation into the form of mass water content, the soil-water characteristic curve after deformation of psi ≥ psi a at the high suction stage is almost coincident with that before deformation, and when the aperture ratio after deformation is changed into e 1 Then, make horizontal line w = e 1 Gs, to initial pore ratio before deformation e 0 The horizontal coordinate of the intersection point of the soil-water characteristic curve can be approximately regarded as the pore ratio e after deformation 1 Inlet air value psi a1 And calculating on the basis of the formula (9) to obtain a formula III.
2. The method of predicting unsaturated relative permeability coefficient according to claim 1, wherein: the initial porosity e before deformation is measured by test in the step 1) 0 Unsaturated relative permeability coefficient k of soil sample under different substrate suction r The actual measurement data comprises the following specific processes: initial void ratio e before deformation by the variable head method 0 Saturated permeability coefficient k of soil sample under different substrate suction s Measuring the initial porosity e before deformation by transient profile method or steady state test method 0 Measuring the unsaturated permeability coefficient k of the soil sample under different substrate suction forces, and calculating to obtain the initial porosity ratio e before deformation through formula I 0 Unsaturated relative permeability coefficient k of soil sample under different substrate suction r Actually measuring data;
k r ＝k/k s Ⅰ。
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