CN109115664B - Unified unsaturated soil relative permeability coefficient simplified prediction method - Google Patents

Unified unsaturated soil relative permeability coefficient simplified prediction method Download PDF

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CN109115664B
CN109115664B CN201810730592.0A CN201810730592A CN109115664B CN 109115664 B CN109115664 B CN 109115664B CN 201810730592 A CN201810730592 A CN 201810730592A CN 109115664 B CN109115664 B CN 109115664B
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陶高梁
陈阳阳
庄心善
肖衡林
胡其志
万娟
何俊
朱志政
罗晨晨
彭弯
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Hubei University of Technology
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Abstract

The invention discloses a unified simplified prediction method for relative permeability coefficient of unsaturated soil, which combines the existing four classical models of relative permeability coefficient and the existing fractal model of soil-water characteristic curve to provide a unified simplified prediction model for relative permeability coefficient of unsaturated soil and a parameter model value taking method, wherein the measured data of soil-water characteristic curve is measured based on a pressure plate test to obtain the measured matrix suction psi0And measuring the saturation Sr0According to the measured substrate suction psi0And measuring the saturation Sr0And combining a soil-water characteristic curve fractal model to obtain a measurement fractal dimension D through fitting0And measuring the intake value psia0According to the measurement dimension D0Selecting corresponding f (S)r) And will measure the intake air value psia0And f (S)r) And substituting the prediction model to predict the relative permeability coefficient of the unsaturated soil. The defect that the existing classical unsaturated soil permeability coefficient prediction model is only suitable for a certain type of soil is overcome, and the existing classical unsaturated soil permeability coefficient prediction model is unified.

Description

Unified unsaturated soil relative permeability coefficient simplified prediction method
Technical Field
The invention belongs to the technical field of relative permeability coefficients of unsaturated soil in civil engineering and geotechnical engineering, and particularly relates to a unified simplified prediction method for the relative permeability coefficient of unsaturated soil.
Background
The method is used for quantitatively describing the influence rule of the unsaturated soil relative permeability coefficient, is the basis for establishing a soil constitutive model considering the mutual influence of hydraulic and mechanical properties, carrying out researches such as unsaturated soil fluid-solid coupling analysis and the like, and therefore, the establishment of the unsaturated soil relative permeability coefficient simplified prediction model has extremely important significance. The permeability coefficient is a scale index for describing the flowing property of pore water in soil pores, directly reflects the seepage characteristic of the soil, is a basic parameter of the mechanical property of the soil, quantitatively describes the influence rule of unsaturated soil relative to the permeability coefficient, is the basis for establishing a soil constitutive model considering the mutual influence of the hydraulic property and the mechanical property, and carrying out research such as unsaturated soil fluid-solid coupling analysis, and therefore, the method has extremely important significance for establishing a simplified prediction model of the unsaturated soil relative to the permeability coefficient. The structural stability is not negligible in engineering application, and the method is mainly reflected in engineering and daily problems such as slope stability analysis caused by rainfall, roadbed deformation, leakage problem of clay walls and flood dams of earth and rockfill dams, influence of landfill sites and nuclear waste landfill sites on underground water pollution and diffusion, diffusion and migration problems of underground sewage and the like. At present, research models for permeability coefficients mainly include three types, namely an empirical model, a macroscopic model and a statistical model. The empirical model of the permeability coefficient is firstly a model of Richards (1931), and then a semi-empirical semi-theory combined permeability coefficient prediction method is developed, and a large number of corresponding empirical expressions are provided. Empirical models often accurately predict permeability coefficients for a certain type of soil or a certain aspect of permeability problem, but the accuracy of such empirical formulas has not been verified for other problems.
Disclosure of Invention
The invention aims to provide a unified simplified prediction method for the relative permeability coefficient of unsaturated soil aiming at the defects of the technology, overcomes the defect that the existing classical unsaturated soil permeability coefficient prediction model is only suitable for certain type of soil, and unifies the existing classical unsaturated soil permeability coefficient prediction model.
In order to achieve the purpose, the invention designs a unified unsaturated soil relative permeability coefficient simplified prediction method, which comprises the following steps:
1) a unified unsaturated soil relative permeability coefficient simplified prediction model and a parameter model value taking method are provided by combining the existing four relative permeability coefficient classical models and the existing soil-water characteristic curve fractal model:
Figure BDA0001720778210000021
wherein: k is a radical ofr(psi) represents the relative permeability coefficient of unsaturated soil, psiaIs the air intake value, psi is the substrate suction force, SrIs the saturation;
the parameter model value taking method comprises the following steps:
when D is more than or equal to 2.8<At 3, f (S)r) Get Sr 3Or Sr；
When D is more than or equal to 2.6<At 2.8, f (S)r) Get Sr 3；
When D is more than or equal to 2.2<At 2.6, f (S)r) Taking (8-2D/3-D) Sr-(5-D/3-D)Sr 2、Sr 2.5Or Sr 3；
When D is present<At 2.2, f (S)r) Taking (8-2D/3-D) Sr-(5-D/3-D)Sr 2Or Sr 2.5；
2) Based on the measured data of the soil-water characteristic curve measured by the pressure plate test, the suction force psi of the measured substrate is obtained0And measuring the saturation Sr0；
3) According to the measurement of the substrate suction psi in step 2)0And measuring the saturation Sr0Combining with the expression of the soil-water characteristic curve fractal model in the step 1), fitting to obtain a measured fractal dimension D0And measuring the intake value psia0；
4) According to the measurement fractal dimension D obtained by fitting in the step 3)0Selecting corresponding f (S) in step 1)r) And will measureIntake air quantity psia0And f (S)r) Substituting the formula (1) to predict the relative permeability coefficient of unsaturated soil.
Further, in the step 1), a unified simplified prediction model of unsaturated soil relative permeability coefficient is provided by combining the existing four classical models of relative permeability coefficient and the existing fractal model of soil-water characteristic curve, and the concrete process is as follows:
1a) the existing relative permeability coefficient model of unsaturated soil comprises
TK relative permeability coefficient model
Figure BDA0001720778210000031
CCG relative permeability coefficient model
Figure BDA0001720778210000032
Mualem relative permeability coefficient model
Figure BDA0001720778210000033
Burdine relative permeability coefficient model
Figure BDA0001720778210000034
Wherein: srIs saturation, theta is volume water content, thetasRepresents the saturated water content, thetarIndicating minimum volume water content, # as substrate suction
The expression of the existing soil-water characteristic curve fractal model is
Figure BDA0001720778210000035
Wherein: srIs saturation, psiaIs the air intake value,Psi is the substrate suction;
1b) phi is more than or equal to phi in an expression (2) adopting an existing soil-water characteristic curve fractal modelaDerivation is performed, and derivation is performed simultaneously on both sides of equation (2) to obtain:
dx＝dSr＝(D-3)ψa 3-DψD-4dψ (7)
substituting formula (7) into formula (3), formula (4), formula (5) and formula (6) can obtain formula (8), formula (9), formula (10) and formula (11):
Figure BDA0001720778210000036
Krrelative permeability coefficient of unsaturated soil, SrIs saturation, Sr minIs residual saturation, psiaFor air intake value, psi for substrate suction force, psidMaximum substrate suction, D is fractal dimension;
Figure BDA0001720778210000041
Kris relative permeability coefficient of unsaturated soil, phi is porosity, SrIs saturation, Sr minIs residual saturation, psiaFor air intake value, psi for substrate suction force, psidMaximum substrate suction, D is fractal dimension;
Figure BDA0001720778210000042
Krrelative permeability coefficient of unsaturated soil, SrIs saturation, Sr minIs residual saturation, psiaFor air intake value, psi for substrate suction force, psidMaximum substrate suction, D is fractal dimension;
Figure BDA0001720778210000043
Krrelative permeability coefficient of unsaturated soil, SrIs saturation, Sr minIs residual saturation, psiaFor air intake value, psi for substrate suction force, psidMaximum substrate suction, D is fractal dimension;
and due to psid>>ψaTherefore, neglect (ψ)a/ψd)4-D、(ψa/ψd)5-D、ψa/ψd)8-2DFormula (8), formula (9), formula (10), and formula (11) may be simplified to obtain formula (12), formula (13), formula (14), and formula (15):
Figure BDA0001720778210000044
Figure BDA0001720778210000051
Figure BDA0001720778210000052
Figure BDA0001720778210000053
a unified unsaturated soil relative permeability coefficient simplified prediction model is provided by the formula (12) to the formula (15)
Figure BDA0001720778210000054
KrRelative permeability coefficient of unsaturated soil, SrIs saturation, psiaIs the air intake value, psi is the substrate suction, D is the fractal dimension;
according to the size of the fractal dimension D, f (S)r) Get Sr、(8-2D/3-D)Sr-(5-D/3-D)Sr 2、Sr 2.5Or Sr 3。
Further, in the step 3), the fractal dimension D is measured0And measuring the intake value psia0The fitting method specifically comprises the following steps: based on the measured data of the soil-water characteristic curve, the data of the low matrix suction segment with unchanged water content is discarded, and the-ln psi is used as the abscissa, lnSrAs ordinate, drawing scatter diagram, fitting straight line to obtain slope k, and measuring fractal dimension D03-k; based on the resulting measurement fractal dimension D0Using psi in formula (2)>ψaFitting the measured data of the soil-water characteristic curve to obtain a measured air inlet value psia0。
Compared with the prior art, the invention has the following advantages: the unified simplified prediction method for the relative permeability coefficient of the unsaturated soil is a unified simplified prediction model for the relative permeability coefficient of the unsaturated soil and a parameter model value taking method thereof based on a fractal dimension by utilizing a fractal theory and combining a soil-water characteristic curve fractal model, overcomes the defect that the existing classic prediction model for the permeability coefficient of the unsaturated soil is only suitable for a certain type of soil, unifies the existing classic prediction model for the permeability coefficient of the unsaturated soil, and has extremely important significance for practical engineering application and theoretical research.
Drawings
FIG. 1 is a fractal dimension fitting graph of an example Yolo light clay;
FIG. 2 is a fitting graph of soil-water characteristic curves of the Yolo light clay of the embodiment;
FIG. 3 is a graph illustrating the prediction of unsaturated relative permeability coefficient of Yolo light clay in the example;
FIG. 4 is a plot of the example Gilat loam fractal dimension fit;
FIG. 5 is a graph of a water characteristic curve fit of Gilat loam in example;
FIG. 6 is a graph showing the prediction of unsaturated relative permeability coefficient of Gilat loam in example;
FIG. 7 is a fractal dimension fitting graph of Touchet silt loam in example;
FIG. 8 is a graph of a fitted curve of water characteristics of the Touchet silt loam soil of the example;
FIG. 9 is a graph showing the prediction of unsaturated relative permeability coefficient of Touchet silt loam in example;
FIG. 10 is a Columbia sandy loam fractal dimension fit chart of the example;
FIG. 11 is a plot of a Columbia sandy loam soil water characteristic curve fit of the examples;
FIG. 12 is a diagram showing the prediction of unsaturated relative permeability coefficient of Columbia sandy loam in example.
Detailed Description
The invention is described in further detail below with reference to the figures and the specific embodiments.
A unified unsaturated soil relative permeability coefficient simplified prediction method comprises the following steps:
1) a unified unsaturated soil relative permeability coefficient simplified prediction model and a parameter model value taking method are provided by combining the existing four relative permeability coefficient classical models and the existing soil-water characteristic curve fractal model:
Figure BDA0001720778210000061
wherein: k is a radical ofr(psi) represents the relative permeability coefficient of unsaturated soil, psiaIs the air intake value, psi is the substrate suction force, SrIs the saturation;
the parameter model value taking method comprises the following steps:
when D is more than or equal to 2.8<At 3, f (S)r) Get Sr 3Or Sr；
When D is more than or equal to 2.6<At 2.8, f (S)r) Get Sr 3；
When D is more than or equal to 2.2<At 2.6, f (S)r) Taking (8-2D/3-D) Sr-(5-D/3-D)Sr 2、Sr 2.5Or Sr 3；
When D is present<At 2.2, f (S)r) Taking (8-2D/3-D) Sr-(5-D/3-D)Sr 2Or Sr 2.5；
In the above formula, "-" is a minus sign
A unified unsaturated soil relative permeability coefficient simplified prediction model is provided by combining the existing four relative permeability coefficient classical models and the existing soil-water characteristic curve fractal model, and the concrete process is as follows:
1a) the existing relative permeability coefficient model of unsaturated soil comprises
TK relative permeability coefficient model
Figure BDA0001720778210000071
CCG relative permeability coefficient model
Figure BDA0001720778210000072
Mualem relative permeability coefficient model
Figure BDA0001720778210000073
Burdine relative permeability coefficient model
Figure BDA0001720778210000074
Wherein: srIs saturation, theta is volume water content, thetasRepresents the saturated water content, thetarIndicating minimum volume water content, # as substrate suction
The expression of the existing soil-water characteristic curve fractal model is
Figure BDA0001720778210000075
Wherein: srIs saturation, psiaIs the air intake value and psi is the substrate suction force;
1b) for convenient calculation, the phi is more than or equal to phi in the expression (2) of the existing soil-water characteristic curve fractal modelaDerivation is performed, and derivation is performed simultaneously on both sides of equation (2) to obtain:
dx＝dSr＝(D-3)ψa 3-DψD-4dψ (7)
substituting formula (7) into formula (3), formula (4), formula (5) and formula (6) can obtain formula (8), formula (9), formula (10) and formula (11):
Figure BDA0001720778210000076
Krrelative permeability coefficient of unsaturated soil, SrIs saturation, Sr minIs residual saturation, psiaFor air intake value, psi for substrate suction force, psidMaximum substrate suction, D is fractal dimension;
Figure BDA0001720778210000081
Kris relative permeability coefficient of unsaturated soil, phi is porosity, SrIs saturation, Sr minIs residual saturation, psiaFor air intake value, psi for substrate suction force, psidMaximum substrate suction, D is fractal dimension;
Figure BDA0001720778210000082
Krrelative permeability coefficient of unsaturated soil, SrIs saturation, Sr minIs residual saturation, psiaFor air intake value, psi for substrate suction force, psidMaximum substrate suction, D is fractal dimension;
Figure BDA0001720778210000083
Krrelative permeability coefficient of unsaturated soil, SrIs saturation, Sr minIs residual saturation, psiaIs the intake value and psi is the matrixSuction, psidMaximum substrate suction, D is fractal dimension;
and due to psid>>ψaTherefore, neglect (ψ)a/ψd)4-D、(ψa/ψd)5-D、ψa/ψd)8-2DFormula (8), formula (9), formula (10), and formula (11) may be simplified to obtain formula (12), formula (13), formula (14), and formula (15):
Figure BDA0001720778210000091
Figure BDA0001720778210000092
Figure BDA0001720778210000093
Figure BDA0001720778210000094
a unified unsaturated soil relative permeability coefficient simplified prediction model is provided by the formula (12) to the formula (15)
Figure BDA0001720778210000095
KrRelative permeability coefficient of unsaturated soil, SrIs saturation, psiaIs the air intake value, psi is the substrate suction, D is the fractal dimension;
according to the size of the fractal dimension D, f (S)r) Get Sr、(8-2D/3-D)Sr-(5-D/3-D)Sr 2、Sr 2.5Or Sr 3；
2) Based on the measured data of the soil-water characteristic curve measured by the pressure plate test, the suction force psi of the measured substrate is obtained0And measuring the degree of saturationSr0；
3) According to the measurement of the substrate suction psi in step 2)0And measuring the saturation Sr0Combining with the expression of the soil-water characteristic curve fractal model in the step 1), fitting to obtain a measured fractal dimension D0And measuring the intake value psia0；
Measurement of fractal dimension D0And measuring the intake value psia0The fitting method specifically comprises the following steps: based on the measured data of the soil-water characteristic curve, the data of the low matrix suction segment with unchanged water content is discarded, and the-ln psi is used as the abscissa, lnSrAs ordinate, drawing scatter diagram, fitting straight line to obtain slope k, and measuring fractal dimension D03-k; based on the resulting measurement fractal dimension D0Using psi in formula (2)>ψaFitting the measured data of the soil-water characteristic curve to obtain a measured air inlet value psia0；
4) According to the measurement fractal dimension D obtained by fitting in the step 3)0Selecting corresponding f (S) in step 1)r) And will measure the intake air value psia0And f (S)r) Substituting the formula (1) to predict the relative permeability coefficient of unsaturated soil.
The invention is further described with reference to specific examples below:
the soil samples used in this example were Yolo light clay, Gilat loam, touch silt loam and Columbia sandy loam. Firstly, calculating and measuring fractal dimension D according to actually measured data of soil-water characteristic curve0The calculated measurement fractal dimension D0The correlation coefficient R is shown in fig. 1, 4, 7, and 10. Analyzing and fitting the expression of the existing soil-water characteristic curve model to obtain a measured air inlet value psia0As shown in fig. 2, 5, 8 and 11. Finally, the unified unsaturated soil relative permeability coefficient simplified prediction model formula (1) provided by the invention is utilized to predict the unsaturated soil relative permeability coefficients of different soil samples, as shown in fig. 3, fig. 6, fig. 9 and fig. 12, the actual measurement standard permeability coefficient is obtained by combining the actual measurement standard fractal dimension and the actual measurement standard air inlet value of the table 1, and the predicted value of the relative permeability coefficient is closer to the actual measurement standard permeability coefficient value, which shows that the invention is used for predicting the unsaturated soil relative permeability coefficient of different soil samplesThe unified prediction model of the relative permeability coefficient of the unsaturated soil is reliable and has obvious prediction effect.
TABLE 1 actual measurement standard air intake values and actual measurement standard fractal dimensions of different soil bodies
Figure BDA0001720778210000101
The currently published model for predicting the relative permeability coefficient of unsaturated soil is mainly directed at a single soil body or the same soil body, the calculation results of different prediction models of the same soil body are possibly greatly different, the applicability of the model is not clarified, and the model needs to be further analyzed. The prediction method of the invention utilizes the fractal theory and combines a soil-water characteristic curve fractal model to provide a unified unsaturated soil relative permeability coefficient simplified prediction model based on fractal dimension and a parameter model value taking method thereof, overcomes the defect that the existing classical unsaturated soil permeability coefficient prediction model is only suitable for certain type of soil, unifies the existing classical unsaturated soil permeability coefficient prediction model, and has extremely important significance for practical engineering application and theoretical research.

Claims (2)

1. A unified unsaturated soil relative permeability coefficient simplified prediction method is characterized in that: the prediction method comprises the following steps:
1) a unified unsaturated soil relative permeability coefficient simplified prediction model and a parameter model value taking method are provided by combining the existing four relative permeability coefficient classical models and the existing soil-water characteristic curve fractal model:
Figure FDA0002703419220000011
wherein: kr(psi) represents the relative permeability coefficient of unsaturated soil, psiaIs the air intake value, psi is the substrate suction force, SrIs the saturation;
the parameter D is a fractal dimension, and a model value taking method comprises the following steps:
when D is more than or equal to 2.8<At 3, f (S)r) Get Sr 3Or Sr；
When D is more than or equal to 2.6<At 2.8, f (S)r) Get Sr 3；
When D is more than or equal to 2.2<At 2.6, f (S)r) Taking (8-2D/3-D) Sr-(5-D/3-D)Sr 2、Sr 2.5Or Sr 3；
When D is present<At 2.2, f (S)r) Taking (8-2D/3-D) Sr-(5-D/3-D)Sr 2Or Sr 2.5；
2) Based on the measured data of the soil-water characteristic curve measured by the pressure plate test, the suction force psi of the measured substrate is obtained0And measuring the saturation Sr0；
3) According to the measurement of the substrate suction psi in step 2)0And measuring the saturation Sr0Combining with the expression of the soil-water characteristic curve fractal model in the step 1), fitting to obtain a measured fractal dimension D0And measuring the intake value psia0；
4) According to the measurement fractal dimension D obtained by fitting in the step 3)0Selecting corresponding f (S) in step 1)r) And will measure the intake air value psia0And f (S)r) Substituting the formula (1) to predict the relative permeability coefficient of the unsaturated soil;
a unified unsaturated soil relative permeability coefficient simplified prediction model is provided by combining the existing four relative permeability coefficient classical models and the existing soil-water characteristic curve fractal model, and the concrete process is as follows:
1a) the existing relative permeability coefficient model of unsaturated soil comprises
TK relative permeability coefficient model
Figure FDA0002703419220000021
CCG relative permeability coefficient model
Figure FDA0002703419220000022
Mualem relative permeability coefficient model
Figure FDA0002703419220000023
Burdine relative permeability coefficient model
Figure FDA0002703419220000024
Wherein: krRelative permeability coefficient of unsaturated soil, SrIs saturation, theta is volume water content, thetasRepresents the saturated water content, thetarIndicating minimum volume water content, # as substrate suction
The expression of the existing soil-water characteristic curve fractal model is
Figure FDA0002703419220000025
Wherein: krRelative permeability coefficient of unsaturated soil, SrIs saturation, psiaIs the air intake value and psi is the substrate suction force;
1b) phi is more than or equal to phi in an expression (2) adopting an existing soil-water characteristic curve fractal modelaDerivation is performed, and derivation is performed simultaneously on both sides of equation (2) to obtain:
dx＝dSr＝(D-3)ψa 3-DψD-4dψ (7)
substituting formula (7) into formula (3), formula (4), formula (5) and formula (6) can obtain formula (8), formula (9), formula (10) and formula (11):
Figure FDA0002703419220000026
Kris a relative permeability system of unsaturated soilNumber, SrIs saturation, Sr minIs residual saturation, psiaFor air intake value, psi for substrate suction force, psidMaximum substrate suction, D is fractal dimension;
Figure FDA0002703419220000031
Kris relative permeability coefficient of unsaturated soil, phi is porosity, SrIs saturation, Sr minIs residual saturation, psiaFor air intake value, psi for substrate suction force, psidMaximum substrate suction, D is fractal dimension;
Figure FDA0002703419220000032
Krrelative permeability coefficient of unsaturated soil, SrIs saturation, Sr minIs residual saturation, psiaFor air intake value, psi for substrate suction force, psidMaximum substrate suction, D is fractal dimension;
Figure FDA0002703419220000033
Krrelative permeability coefficient of unsaturated soil, SrIs saturation, Sr minIs residual saturation, psiaFor air intake value, psi for substrate suction force, psidMaximum substrate suction, D is fractal dimension;
and due to psid>>ψaTherefore, neglect (ψ)a/ψd)4-D、(ψa/ψd)5-D、ψa/ψd)8-2DFormula (8), formula (9), formula (10), and formula (11) may be simplified to obtain formula (12), formula (13), formula (14), and formula (15):
Figure FDA0002703419220000034
Figure FDA0002703419220000041
Figure FDA0002703419220000042
Figure FDA0002703419220000043
a unified unsaturated soil relative permeability coefficient simplified prediction model is provided by the formula (12) to the formula (15)
Figure FDA0002703419220000044
KrRelative permeability coefficient of unsaturated soil, SrIs saturation, psiaIs the air intake value, psi is the substrate suction, D is the fractal dimension;
according to the size of the fractal dimension D, f (S)r) Get Sr、(8-2D/3-D)Sr-(5-D/3-D)Sr 2、Sr 2.5Or Sr 3。
2. The unified simplified prediction method for the relative permeability coefficient of unsaturated soil according to claim 1, wherein: in said step 3), the fractal dimension D is measured0And measuring the intake value psia0The fitting method specifically comprises the following steps: based on the measured data of the soil-water characteristic curve, the data of the low matrix suction segment with unchanged water content is discarded, and the-ln psi is used as the abscissa, lnSrAs ordinate, drawing scatter diagram, fitting straight line to obtain slope k, and measuring fractal dimension D03-k; based on the resulting measurement fractal dimension D0By the formula(2) Middle psi>ψaFitting the measured data of the soil-water characteristic curve to obtain a measured air inlet value psia0。
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