CN110516322B - Method for predicting clay saturation nonlinear permeability coefficient under different hydraulic gradients - Google Patents
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Abstract
The invention belongs to the field of geotechnical engineering, and relates to a method for predicting clay saturation nonlinear permeability coefficient under different hydraulic gradients, which is characterized in that the matrix suction is taken as an index of pore channel scale distribution based on a capillary theory, and a soil-water characteristic curve and a saturation permeability coefficient of the tested clay and a correction coefficient c of the matrix suction and the existence of an initial water head are obtained through a pressure plate instrument and a GDS (gas-liquid chromatography) permeability test; calculating the initial hydraulic gradient of each stage of pore channel based on the c value, and calculating a comprehensive permeability proportionality constant k by utilizing a TK saturated permeability coefficient model c (ii) a Under the condition of known actual hydraulic gradient, whether seepage occurs to pore channels with different sizes is judged, and permeability coefficients of all pore channels with the seepage are added to obtain a soil saturation permeability coefficient under the corresponding actual hydraulic gradient, so that the saturation nonlinear permeability coefficient of the soil under different hydraulic gradients is determined. The invention has important significance for the research of soil nonlinear seepage and initial water head, and can play a scientific guiding role for dam seepage-proofing engineering.
Description
Technical Field
The invention belongs to the field of geotechnical engineering, and relates to a method for predicting a clay saturation nonlinear permeability coefficient, in particular to a method for predicting a clay saturation nonlinear permeability coefficient under different hydraulic gradients.
Background
A Soil-Water Characteristic Curve (SWCC) is a Curve describing the relationship between the suction force of a matrix in unsaturated Soil and the volume Water content or the mass Water content, and the Soil-Water Characteristic Curve can reflect the size and the distribution rule of pores in a Soil body. The permeability coefficient k is also called hydraulic conductivity (hydraulic conductivity), and is an index for comprehensively reflecting the permeability of the soil body, and the accurate determination of the value of the permeability coefficient k has very important significance for permeability calculation. As a result of research by a plurality of scholars in dense clay with strong viscosity, the v-i relation curve of the clay shows nonlinear growth before the seepage is stabilized and does not pass through the origin. This is because the water absorbed by the dense clay has a large viscous resistance, and the penetration can only occur when the hydraulic gradient exceeds the initial hydraulic gradient and overcomes the viscous resistance in the soil body. For the determination of the clay saturation nonlinear permeability coefficient with the initial hydraulic gradient, no systematic prediction method can be established at present.
Therefore, the method for predicting the saturated nonlinear permeability coefficient of the cohesive soil considering the initial water head needs to be researched urgently, but at present, the research in the aspect cannot make great progress. For example, a T-K saturated permeability coefficient model is provided through a microscopic angle by virtue of a ceramic sorghum, a porous great and the like, and although the saturated permeability coefficient of a soil body can be accurately predicted, the initial hydraulic gradient existing in clay is not considered, and the seepage rule in cohesive soil cannot be accurately described. And the relation between the permeability coefficient and the soil body pore is researched by a large number of Xiaoshan clay experiments like Xiekang and the like, and the permeability coefficient under different hydraulic gradients is approximately considered to be a constant. Although it is recognized that the v-i relationship curve of the saturated cohesive soil tends to increase in a non-linear manner under different hydraulic gradients, an accurate and quantitative prediction method cannot be provided, and the initial water head to be considered is only the initial water head corresponding to the maximum pore passage, which is far from sufficient because the pore passages have very wide pore size distribution. Because the soil body comprises magnanimity continuous pore passageway, and the pore passageway is not of uniform size, takes place the order of seepage flow also different: the large pore channel needs a smaller hydraulic gradient for seepage, and the small pore channel is slowly added into seepage along with the increase of the hydraulic gradient. According to the invention, by using a capillary theory, the matrix suction is taken as an index for reflecting the size of a pore channel, namely, a soil-water characteristic curve reflecting the relation between the volume water content and the matrix suction in the original unsaturated soil is taken as an indirect index for reflecting the size of the pore channel of the saturated soil. And superposing the permeability coefficients of the pore channels with the seepage under the actual hydraulic gradient by using a T-K model so as to obtain the saturated nonlinear permeability coefficient.
Disclosure of Invention
In order to solve the technical problems in the background art, the invention provides a prediction method of clay saturation nonlinear permeability coefficient under different hydraulic gradients, which has important significance for the research of nonlinear seepage and initial water head of soil.
In order to achieve the purpose, the following scheme is adopted:
a prediction method of clay saturation nonlinear permeability coefficient under different hydraulic gradients is characterized by comprising the following steps: the prediction method of the clay saturation nonlinear permeability coefficient under different hydraulic gradients comprises the following steps:
1) Measuring a soil-water characteristic curve of the soil sample through a pressure plate instrument experiment, dividing the soil-water characteristic curve into n equal parts according to the volume water content, wherein each equal part corresponds to a pore channel with different pore size grades;
2) Based on Young-Laplace equation and the viscous resistance characteristic of viscous soil pores to be overcome by the flow of free water in the soil pores, obtaining the relation between the initial water head and the air intake value, and measuring the initial water head of the soil sample through GDS experiment to obtain the correction coefficient of the air intake value and the osmotic water pressure;
3) The saturated permeability coefficient k of the soil sample under the maximum head pressure is measured through a GDS (gas diffusion system) experiment s According to the relation between the volume water content obtained by the soil-water characteristic curve measured in the step 1) and the initial water head corrected in the step 2), combining a T-K saturated permeability coefficient model, and reversely calculating a comprehensive permeability proportionality constant K c (ii) a The comprehensive permeability proportionality constant k of the soil sample of the same type c Is a constant value;
4) Utilizing the comprehensive permeability proportionality constant k obtained in the step 3) c And calculating the permeability coefficient of each stage of pore channel.
Preferably, the specific implementation manner of step 1) adopted by the invention is as follows: obtaining fitting parameters through a VG three-parameter model by utilizing Matlab software through data points measured by a pressure plate instrument, and bringing the fitting parameters into origin to be fitted to obtain a complete soil-water characteristic curve; on the basis of the actual measurement value of the soil-water characteristic curve with the known specific dry density, the soil-water characteristic curve is measured from the minimum volume water content theta min To the actually measured maximum volume water content theta max Dividing the soil-water characteristic curve into n equal parts; wherein the change in volumetric water content is Δ θ i ＝θ i+1 -θ i (ii) a Its corresponding equivalent substrate suction is psi i ＝(Ψ x +Ψ y ) /2 where Ψ x 、Ψ y Upper and lower limit substrate suction for a certain level of substrate suction; theta i Is the volume water content under the ith hydraulic gradient; theta.theta. i+1 Is the volume water content under the i +1 th hydraulic gradient.
Wherein, the VG three-parameter model is as follows:
in the formula:
Θ is the normalized water content;
S e is the effective saturation;
a. n and m are fitting parameters;
Ψ is the substrate suction.
Preferably, the specific implementation manner of step 2) adopted by the invention is as follows: considering the pore in the soil body as a cylinder, the initial water head is the shear strength tau formed by water in the pore overcoming viscous resistance s The free water in the pores of the cylinder flows, namely the pressure of the upper part and the lower part of the cylinder is compared with the force generated by the shear strength around the cylinder, namely:
τ s ×2πrl＝(P 1 -P 2 )×πr 2 (a)
(a) The formula is modified as follows:
in the formula:
τ s shear strength to overcome viscous drag;
l is the pore height;
r is the pore radius;
Δ P is the initial head;
P 1 、P 2 the pressures of the upper part and the lower part of the pore are respectively;
while the Young-Laplace equation states that:
in the formula:
psi is the substrate suction;
T S is surface tension;
alpha is a contact angle;
r is the pore radius;
combining the formula (b) and the formula (c), wherein the initial water head is inversely proportional to the aperture and has a direct proportion relation with the air inlet value;
P＝c×ψ a (1)
in the formula:
p is the initial head;
Ψ a is the inlet air value corresponding to the dry density;
c is a correction coefficient; wherein
The c value is the same for the same soil sample.
In order to obtain the parameter c, a plurality of groups of parallel samples with the same dry density are prepared, and after the parallel samples are saturated, GDS permeation tests are carried out under different pressure differences; regarding the pressure difference with suddenly increased permeability coefficient as the initial pressure head; at the moment, the initial water head corresponds to the air inlet value of the dry density soil sample, namely the pressure value of the soil body which begins to drain and permeate:
preferably, the specific implementation manner of step 3) adopted by the invention is as follows: the prepared soil sample with certain dry density is saturated by a vacuum pump, and the saturated permeability coefficient k of the sample under the maximum water head pressure is measured by means of a GDS (gas-liquid separation system) experiment s (ii) a The soil-water characteristic curve obtained by VG three-parameter model fitting is inversely calculated by the fitted curve equation under the condition that the equal volume water content is the same, so as to obtain the psi of the substrate suction corresponding to each volume water content x 、Ψ y . . . The substrate suction psi of the upper and lower limit of each stage of substrate suction x 、Ψ y Find out its psi i (ii) a Each different Ψ determined by the T-K model i As an equivalent initial water head of the theory of the corresponding pore seepage in the soil body, correcting the initial water head of the corresponding pore channel seepage in the soil body into an initial water head of a saturated soil body through a formula (1); due to psi a The air intake value of the soil body is used as an index for the soil body to start water drainage, and the initial water head is used as an index for the soil body to start water drainagePore start to be indicative of seepage. According to the formula (c), different pore diameters r correspond to different matrix suction forces Ψ, and therefore, the soil-water characteristic curve can also be used as an index for reflecting the distribution of the soil pore channels, that is, the size of the matrix suction force is regarded as an indirect index of the size of the soil pore channels, and the larger the pore channel is, the smaller the matrix suction force is, and the smaller the pore channel is, the larger the matrix suction force is. From (1) the initial head is proportional to the inlet air value, so the initial head is different for different pore passages. At this time, the formula (1) is changed;
P i ＝c×ψ i (2)
in the formula: p is i Is the initial head relative to the i-stage pore channel;
through a T-K saturated permeability coefficient model, the comprehensive permeability proportionality constant K of the soil sample is obtained c ：
In the formula:
k c is the comprehensive permeability proportionality constant;
k s is the saturation permeability coefficient;
Δθ i is the volume water content change under the ith hydraulic gradient;
Ψ i the equivalent initial water head under the ith level hydraulic gradient is obtained;
j is the jth level gap; j is less than or equal to n.
Preferably, the specific implementation manner of step 4) adopted by the invention is as follows:
correcting the matrix suction force to be water pressure, so that the air inlet value of the soil body starting to drain is an initial water head of seepage in a GDS (gas-liquid separation) seepage test;
by the water pressure formula:
P＝ρgh (4)
in the formula:
p is water pressure;
ρ is the density of water 1 × 10 3 kg/m 3 ；
g is the gravity acceleration of 9.8N/kg;
h is the height from a pressure point to the liquid level, and the height from the pressure point to the liquid level is a water head value;
regulation in darcy's law:
in the formula:
i is hydraulic gradient;
Δ h is head loss;
l is the length of the sample;
according to the formula (c), different substrate suction forces correspond to different pore sizes, that is, the substrate suction force is used as an index reflecting the pore size. From formulas (2), (4) and (5):
obtaining the initial hydraulic gradient of the ith-stage pore channel through the formula (6);
when the actual hydraulic gradient I reaches the hydraulic gradient I of the pore channel of the ith stage (I > 1) i When the i-th stage pore starts to seep. At the moment, the permeability coefficients of all pore channels which actually generate seepage are superposed through a formula (3) of a T-K saturated permeability coefficient model, and when the actual hydraulic gradient is larger, the superposed permeability coefficient is also larger;
when in use
Is provided with
In the formula:
i is the actual hydraulic gradient;
I i an initial hydraulic gradient for the ith stage pore channel;
k si saturation of 1-i-stage pore superposition when hydraulic gradient is iThe permeability coefficient;
k c is the comprehensive permeability proportionality constant;
Ψ i is the equivalent initial head under the ith hydraulic gradient;
Δθ i is the volume water content change under the ith hydraulic gradient;
judging whether the pore channels with different sizes have seepage according to the formula (6), namely, when the actual hydraulic gradient exceeds the initial hydraulic gradient of the pore channel, the seepage occurs in the pore channel of the stage, and combining the formula (7) to obtain the saturation nonlinear permeability coefficient under different hydraulic gradients.
The invention has the advantages that:
the invention provides a method for predicting saturated nonlinear permeability coefficient of clay under different hydraulic gradients, which comprises the steps of taking the suction force of a matrix as an index reflecting the size of a pore channel of a soil body through a capillary theory, namely taking a soil-water characteristic curve in unsaturated soil as an indirect index reflecting the size of the pore channel of the saturated soil, and obtaining the relation between the soil-water characteristic curve and the saturated permeability coefficient of the tested clay and the suction force of the matrix and an initial water head by utilizing a pressure plate instrument test and a GDS (gas diffusion liquid chromatography) penetration test; calculating a comprehensive permeability proportionality constant k by utilizing a TK saturated permeability coefficient model c (ii) a According to k of the test clay c And reversely calculating the soil-water characteristic curve by using a relevant model to obtain the saturated permeability coefficient of the soil, and superposing the saturated permeability coefficient to overcome the initial water head. The invention considers different initial water heads of different microscopic pore channels for seepage, the smaller the pore diameter of the pore channel is, the larger the initial water head required for seepage, and only when the hydraulic gradient exceeds the initial hydraulic gradient of the level of pores, the level of pore channels participate in the seepage and contribute to the permeability coefficient. Because there are the pore passage of magnanimity not of uniform size in the soil body, therefore flood head pressure is big more, promotes its pore passage quantity of participating in the seepage flow just more, and saturation osmotic coefficient just is big more. And then, by means of the deduced proportional relation between the initial water head and the air inlet value, under the action of considering the initial water head, performing clay saturation nonlinear permeability coefficient by using a T-K modelAnd (6) predicting. The method has important significance for the research of the nonlinear seepage of the soil body and the initial water head from the viewpoint of considering the initial water head. The method considers the volume of certain-level pressure discharge water under test as the seepage flow of soil body seepage, takes a soil-water characteristic curve as an indirect index for reflecting the pore size of the soil body, considers the initial water head of clay seepage, predicts the clay saturation nonlinear permeability coefficient under different hydraulic gradients, more completely reflects the seepage rule of the soil body, has pioneering significance for researching the clay saturation permeability coefficient and the initial water head, and can play a scientific guidance role for seepage-proofing projects such as dams and the like.
Drawings
FIG. 1 is a schematic diagram of pore channels for seepage at different initial heads.
FIG. 2 is a chart of clay seepage in Hunan province predicted by the method of the invention.
Detailed Description
The invention discloses a method for predicting a clay saturation nonlinear permeability coefficient under different hydraulic gradients, which has been verified to be reasonable through experimental data and specifically comprises the following steps:
1) Through a pressure plate instrument experiment, measuring a soil-water characteristic curve of a soil sample, dividing the soil-water characteristic curve into n equal parts according to the volume water content, wherein each equal part corresponds to pore channels with different pore size grades:
and (3) obtaining fitting parameters by using Matlab software through data points measured by a pressure plate instrument, and bringing the fitting parameters into origin to fit to obtain a complete soil-water characteristic curve. On the basis of the actual measurement value of the soil-water characteristic curve with the known specific dry density, the soil-water characteristic curve is measured from the minimum volume water content theta min To the actually measured maximum volume water content theta max And dividing the soil-water characteristic curve into n equal parts. Wherein the change in volume water content, delta theta i ＝θ i+1 -θ i (ii) a Its corresponding equivalent substrate suction is psi i ＝(Ψ x +Ψ y ) /2, where Ψ x 、Ψ y The substrate suction is the upper and lower limits of a certain level of substrate suction. Step 1) of dividing the soil-water characteristic curve into n equal parts, so as to mention the change quantity delta theta of the water content 1 ＝Δθ 2 ＝...＝Δθ n 。
2) The initial water head of the soil sample is measured through a GDS experiment, and the correction coefficient of the air intake value and the osmotic water pressure is obtained:
multiple sets of parallel samples of the same dry density were prepared and saturated and set at different pressure differentials for GDS permeation testing. The pressure difference with the sudden increase in permeability coefficient is regarded as the initial pressure head (i.e., the initial head at this time). At the moment, the initial water head corresponds to the air inlet value of the dry density soil sample, namely the pressure value of the soil body which begins to drain and permeate:
P＝c×ψ a (1)
in the formula: p is the initial head; Ψ a Is the inlet air value corresponding to the dry density; and c is a correction coefficient.
3) The saturated permeability coefficient k of the soil sample under the maximum head pressure is measured through a GDS (gas diffusion system) experiment s According to the step 1), combining a T-K saturated permeability coefficient model, and inversely calculating a comprehensive permeability proportionality constant K c (comprehensive permeability proportionality constant k of said same type of soil sample c As a constant value):
the prepared soil sample with certain dry density is saturated by a vacuum pump, and the saturated permeability coefficient k of the sample under the maximum head pressure is measured by means of a variable head GDS experiment s . Delta theta obtained by aliquoting in step 1) i And Ψ i The comprehensive permeability proportionality constant K of the soil sample is obtained by a T-K saturated permeability coefficient model, namely the formula (3) c ：
In the formula: k is a radical of formula c Is the osmotic proportionality constant; k is a radical of s Is the saturation permeability coefficient; delta theta i Is the volume water content change; psi i Is equivalent substrate suction。
4) Using k obtained in step 3) c And calculating the permeability coefficient of each stage of pore channel. Calculating initial water heads of pore channels with different pore sizes according to psi-theta relation reflected by a soil-water characteristic curve, wherein when the actual hydraulic gradient exceeds the initial water head value, the pore channels of the grade participate in seepage and contribute to the permeability coefficient of the soil body, namely, the permeability coefficients of the pore channels which have seepage under the actual hydraulic gradient can only be superposed when the total permeability coefficient of the soil body is predicted. However, in unsaturated soil, the pores of the soil body also contain air, so that a water-air interface, namely surface tension, exists in the pores to form a meniscus. When the saturated soil is subjected to seepage, only water pressure is applied, so that the meniscus formed by the surface tension does not exist, and the matrix suction force needs to be corrected according to the correction coefficient obtained in the step 2) so as to convert the matrix suction force into the initial water head of the saturated soil seepage. Therefore, a prediction method of the clay saturation nonlinear permeability coefficient under different hydraulic gradients is established by combining a T-K model. And the model is used for calculating and obtaining saturation nonlinear permeability coefficients under different hydraulic gradients, which specifically comprises the following steps:
4.1 Because the air exists in the pores of the soil body in the unsaturated soil to form the shrink film and the shrink film has surface tension, the liquid level of the pores forms a concave liquid level, the pore air pressure and the pore water pressure exist in the pores, the shrink film bears the air pressure which is greater than the pore water pressure, and the pressure difference is the matrix suction force. However, the saturated soil has no pore air pressure, so that the meniscus and the substrate suction force do not exist. Therefore, if the substrate suction force is equivalent to the water pressure, it needs to be corrected. According to the conclusion obtained in the step 2), at the moment, the air inlet value of the soil body starting to drain water is the initial water head of seepage in the GDS seepage test.
By the water pressure formula:
P＝ρgh (4)
in the formula: p is water pressure; ρ is the density of water 1 × 10 3 kg/m 3 (ii) a g is the gravity acceleration of 9.8N/kg; h is the pressure point to liquid level (referred to herein as head value).
Regulation in darcy's law:
in the formula: i is hydraulic gradient; Δ h is head loss; l is the sample length.
The following equations (2), (4) and (5) show:
4.2 The characteristic curve of soil-water obtained by fitting actual measurement points and the formula (c) show that each matrix suction corresponds to a first-stage pore, namely, under the suction of the ith-stage matrix, seepage occurs in the pores from the 1 st to the ith-stage pore, but seepage of the i +1 st stage does not occur, and only when the matrix suction exceeds i, seepage occurs in the soil (as shown in figure 1). Therefore, the initial hydraulic gradient of different pore size levels can be obtained from the formula (6).
4.3 When the analysis of 4.2) can obtain the infiltration of the ith grade pore, the infiltration of the 1 st to the i-1 st grades already occurs, namely when the permeability coefficient of the ith grade pore channel is calculated, the previous pore channel (macroporous channel) is already involved in the infiltration, so to obtain the saturated permeability coefficient under the complete ith grade hydraulic gradient, the permeability coefficients of the pore channels which are already involved in the infiltration are required to be superposed. And obtaining the saturated nonlinear permeability coefficient under different hydraulic gradients through the formulas (3) and (6) of the T-K model.
In the formula: k is a radical of formula si The saturation permeability coefficient of the 1-i grade pore superposition when the hydraulic gradient is i.
The specific implementation mode of the invention is as follows:
firstly, the idea of the invention considering the saturated nonlinear permeability coefficient of the clay under different hydraulic gradients of the initial water head is as follows: for saturated soil, because the pores of the soil are filled with water, at this time, the drainage process in the soil can be understood as the process of soil seepage. Because mass pore channels with different sizes exist in the soil body, the pore channels with different pore diameter grades have different hydraulic gradients to be achieved when permeating, and the pore channels of the grade have the permeating function only when the hydraulic gradient exceeds the initial hydraulic gradient. Therefore, the soil-water characteristic curve can be regarded as an index for indirectly reflecting the pore size of the soil body. However, since there are no concave liquid surface and matrix suction in the pores of the saturated soil, if the soil-water characteristic curve is used as an indirect index for reflecting the pore size of the soil body, the matrix suction needs to be corrected and converted into an initial head (pressure head) corresponding to the matrix suction on the SWCC:
wherein: c is the correction factor Ψ i For equivalent matrix suction, L is the specimen height, I i An initial hydraulic gradient for the ith stage pore channel; ρ is the density of water 1 × 10 3 kg/m 3 (ii) a g is the gravity acceleration of 9.8N/kg
Under the idea, the TK saturation permeability coefficient can be greatly and conveniently calculated:
in the formula: k is a radical of s Is the saturation permeability coefficient; k is a radical of c Is the comprehensive permeability proportionality constant; psi i Equivalent substrate suction; theta i In response to the initial head Ψ i Volumetric water content of (d); wherein, delta theta i ＝θ i+1 -θ i ；
The following is a prediction using the present method in conjunction with a specific embodiment: the soil sample adopted is the Shaoyang red clay in Hunan province, and the basic index is measured.
Taking the Hunan clay as an example, the Hunan clay is measured by GDS experiment to be 1.5g/cm 3 The corrected value of the saturation permeability coefficient of the dry density under the pressure of 35kPa at 15 ℃ is 0.0000588612cm/s;
through pressure plate instrument experiment, 1.5g/c is measuredm 3 Soil-water characteristic curve at dry density. 1.5g/cm 3 And (4) obtaining a fitting parameter of the soil-water characteristic curve of the dry density through Matlab according to an actual measured value. Here, for the sake of convenience, the fitting amount is 1.5g/cm 3 The dry density soil-water characteristic curve is divided into 10 equal parts according to the volume water content change quantity obtained by the actually measured maximum volume water content and the actually measured minimum volume water content. Using equation (3) yields:
in the formula: Δ θ = θ 2 -θ 1 ＝0.00988，Ψ i =57kPa, similarly, obtains Δ θ 2 、Δθ 3 ...Δθ 9 K at a pressure of 35kPa s K is calculated to be 0.0000588612cm/s c Is 0.008890543.
Then, the soil-water characteristic curve is naturally divided into 10 equal parts according to the measured value, and the obtained delta theta is obtained i And Ψ i Substituting the formula (3) to obtain the saturation permeability coefficient k of the corresponding pore when each stage is permeated by superposition s ：
In order to better reflect the seepage rule of water in soil, the prepared dry densities are respectively 1.5g/cm 3 A sample of clay from Hunan in dry density was saturated at back pressure for 48 hours in a GDS permeameter. After the saturation was completed, the permeability coefficients of the saturated clay were measured under pressure differences of 2, 4, 6, 8 and 10kPa, respectively (see Table 2). As can be seen from the data in Table 2, for soil samples of different dry densities, the permeability coefficient is very small in the pressure ranges of 2-4kPa and 8-10kPa, and increases steeply in the pressure range of 4-6kPa, so that 6kPa is taken as the initial head of the clay in Hunan. This example uses 1.5g/cm 3 The dry density sample is also used for better reflecting the seepage rule of the soil body. Therefore, the correction coefficient c of the soil body is determined according to the formula (1) through the existing air inlet values with different initial dry densities:
P＝c×ψ a (1)
in the formula: p =6kPa, Ψ a =9.77kPa, calculated to result in c =0.6141.
The saturation permeability coefficient and the corresponding hydraulic gradient of each stage of initial head are shown in table 1:
TABLE 1 saturated permeability coefficient and initial hydraulic gradient (dry density 1.5 g/cm) predicted by this method 3 )
1.5g/cm in GDS permeation test 3 The permeability coefficients of the dry density samples at different pressure differences are given in table 2:
TABLE 2GDS permeation test 1.5g/cm under different pressure differences 3 Permeability coefficient of dry density (× 10) -6 cm/s)
The minimum initial hydraulic gradient of the sample was I =3.061 as determined from the 6kPa initial head obtained by GDS according to equation (6); the hydraulic gradient, the seepage velocity and the seepage condition of the sample obtained by the method are shown in the table 3:
TABLE 3 Hydraulic gradient, seepage velocity and seepage behavior obtained according to the method of the invention
Based on the data, analysis shows that clay does not have seepage when the hydraulic gradient is small, once the clay exceeds a certain value, the seepage begins to occur, but the seepage shows nonlinear change, along with the increase of the hydraulic gradient, the seepage tends to be stable and shows linear increase, and k in the table 1 s I.e. the slope of the v-I relation curve, and the change of the slope can also reflect the seepage rule of the soil body, i.e. the slope has larger change in the seepage stage after overcoming the initial water head, and the soil body seepage is unstable so as to permeateThe coefficient shows nonlinear increase, along with the gradual progress of seepage, the slope change is smaller and smaller, the seepage basically tends to be stable, and the permeability coefficient shows linear increase. The seepage rule of Darcy's law in clay is consistent with the conclusion. FIG. 2 is a graph of the predicted seepage flow of the present invention.
Claims (5)
1. A prediction method of clay saturation nonlinear permeability coefficient under different hydraulic gradients is characterized by comprising the following steps: the prediction method of the saturation nonlinear permeability coefficient of the clay under different hydraulic gradients comprises the following steps:
1) Measuring a soil-water characteristic curve of the soil sample through a pressure plate instrument experiment, dividing the soil-water characteristic curve into n equal parts according to the volume water content, wherein each equal part corresponds to a pore channel with different pore size grades;
2) Based on a Young-Laplace equation and the viscous resistance characteristic of viscous soil pores to be overcome by the flow of free water in the soil pores, obtaining the relation between an initial water head and an air inlet value, measuring the initial water head of a soil sample through a GDS (gas diffusion spectroscopy) experiment, and obtaining a correction coefficient of the air inlet value and osmotic water pressure;
3) Through GDS experiment, the saturated permeability coefficient k of the soil sample under the maximum water head pressure is measured s According to the relation between the volume water content obtained by the soil-water characteristic curve measured in the step 1) and the initial water head corrected in the step 2), combining with a T-K saturated permeability coefficient model, and inversely calculating a comprehensive permeability proportionality constant K c (ii) a Comprehensive permeability proportionality constant k of soil sample of same type c Is a constant value;
4) Utilizing the comprehensive permeability proportionality constant k obtained in the step 3) c And calculating the permeability coefficient of each stage of pore channel.
2. The method for predicting the saturation nonlinear permeability coefficient of the clay under different hydraulic gradients as recited in claim 1, wherein: the specific implementation mode of the step 1) is as follows: obtaining a fitting parameter through a VG three-parameter model by utilizing Matlab software through a data point measured by a pressure plate instrument, and bringing the fitting parameter into origin for fitting to obtain a complete soil-water characteristic curve; at a known specific dry density soil-water characteristicOn the basis of the measured value of the characteristic curve, the soil-water characteristic curve is measured from the minimum volume water content theta min To the actually measured maximum volume water content theta max Dividing a soil-water characteristic curve into n equal parts; wherein the change in volumetric water content is Δ θ i ＝θ i+1 -θ i (ii) a Its corresponding equivalent substrate suction force is Ψ i ＝(Ψ x +Ψ y ) /2, where Ψ x 、Ψ y The substrate suction is the upper and lower limit of a certain level of substrate suction; theta.theta. i Is the volume water content under the ith hydraulic gradient; theta.theta. i+1 Is the volume water content under the i +1 th level hydraulic gradient;
wherein, the VG three-parameter model is as follows:
in the formula:
Θ is the normalized water content;
S e is the effective saturation;
a. n and m are fitting parameters;
Ψ is the substrate suction.
3. The method for predicting the saturation nonlinear permeability coefficient of the clay under different hydraulic gradients as recited in claim 2, wherein: the specific implementation mode of the step 2) is as follows: the pore space in the soil body is regarded as a cylinder, and the initial water head is the shear strength tau formed by water in the pore space overcoming viscous resistance s The free water in the pores of the cylinder needs to flow, namely the pressure at the upper part and the lower part of the cylinder is compared with the force generated by the shear strength around the cylinder, namely:
τ s ×2πrl＝(P 1 -P 2 )×πr 2 (a)
(a) The formula is transformed into:
in the formula:
τ s shear strength to overcome viscous drag;
l is the pore height;
r is the pore radius;
Δ P is the initial head;
P 1 、P 2 the pressures of the upper part and the lower part of the pore are respectively;
while the Young-Laplace equation states that:
in the formula:
Ψ is the substrate suction;
T S is surface tension;
alpha is a contact angle;
r is the pore radius;
combining the formula (b) and the formula (c), wherein the initial water head is inversely proportional to the pore diameter and has a direct proportion relation with the air inlet value;
P＝c×ψ a (1)
in the formula:
p is the initial head;
Ψ a is the air intake value corresponding to the dry density;
c is a correction coefficient; wherein
C values are the same for the same soil samples;
in order to obtain the parameter c, a plurality of groups of parallel samples with the same dry density are prepared, and after the parallel samples are saturated, GDS permeation tests are carried out under different pressure differences; and taking the pressure difference with the suddenly increased permeability coefficient as an initial pressure head, wherein the initial pressure head corresponds to the air inlet value of the dry density soil sample, namely the pressure value of the beginning drainage and permeation of the soil body.
4. The method for predicting saturation nonlinear permeability coefficient of clay under different hydraulic gradients as claimed in claim 3The method is characterized in that: the specific implementation manner of the step 3) is as follows: the prepared soil sample with certain dry density is saturated by a vacuum pump, and the saturated permeability coefficient k under the maximum head pressure is measured by means of a GDS (gas diffusion system) experiment s (ii) a Fitting the soil-water characteristic curve obtained by the VG three-parameter model, and under the condition that the equal volume water content is the same, calculating out psi of the substrate suction force corresponding to each volume water content by the back calculation of the fitted curve equation x 、Ψ y 8230where the suction force Ψ is determined by the upper and lower boundary of the suction force for each stage x 、Ψ y Find out its psi i (ii) a Each different Ψ determined by the T-K model i As an equivalent initial water head of a corresponding pore seepage theory in the soil body, correcting the initial water head of the corresponding pore seepage in the soil body into an initial water head of a saturated soil body through a formula (1); due to psi a The water drainage method comprises the following steps of (1) taking an air inlet value of a soil body as an index of starting water drainage of the soil body, and taking an initial water head as an index of starting seepage of pores; according to the formula (c), different pore diameters r correspond to different matrix suction forces psi, so that a soil-water characteristic curve is used as an index for reflecting the distribution of soil body pore channels, namely the size of the matrix suction force is regarded as an indirect index of the size of the soil body pore channels, and the larger the pore channels are, the smaller the matrix suction force is, the smaller the pore channels are, the larger the matrix suction force is; the initial water head is directly proportional to the air inlet value from (1), so that the initial water heads for different pore passages are different, and then the formula (1) is changed;
P i ＝c×ψ i (2)
obtaining the comprehensive permeability proportionality constant K of the soil sample through a T-K saturated permeability coefficient model c ：
In the formula:
k c is the comprehensive permeability proportionality constant;
k s is the saturation permeability coefficient;
Δθ i the volume water content change under the ith hydraulic gradient is shown;
Ψ i the equivalent initial water head under the ith hydraulic gradient is obtained;
j is the jth level gap; j is less than or equal to n.
5. The method for predicting the saturation nonlinear permeability coefficient of clay under different hydraulic gradients as recited in claim 4, wherein: the specific implementation manner of the step 4) is as follows:
4.1 Correcting the matrix suction force to be water pressure, so that the air inlet value of the soil body for starting to drain is the initial water head of seepage in the GDS seepage test;
from the water pressure formula:
P＝ρgh (4)
in the formula:
p is water pressure;
ρ is the density of water 1 × 10 3 kg/m 3 ；
g is the gravity acceleration of 9.8N/kg;
h is the height from a pressure point to the liquid level, and the height from the pressure point to the liquid level is a water head value;
regulation in darcy's law:
in the formula:
i is hydraulic gradient;
Δ h is head loss;
l is the length of the sample;
through the formula (c), different substrate suction forces correspond to pore channels with different sizes, namely the substrate suction force is used as an index for reflecting the size of the pore channels; the following equations (2), (4) and (5) show:
4.2 Obtaining the initial hydraulic gradient of the i-th stage pore channel by the formula (6);
4.3 When the actual hydraulic gradient I reaches the ithStage (I > 1) pore channel hydraulic gradient I i When the flow is in the ith-level pore, seepage begins to occur; at the moment, the permeability coefficients of all pore channels which actually generate seepage are superposed through a formula (3) of a T-K saturated permeability coefficient model, and when the actual hydraulic gradient is larger, the superposed permeability coefficient is also larger;
when in use
Is provided with
In the formula:
i is the actual hydraulic gradient;
k si the cumulative permeability coefficient is the permeability coefficient of the 1-I grade pore channel which generates seepage when the hydraulic gradient is I;
k c is the comprehensive permeability proportionality constant;
Ψ i is the equivalent initial head under the ith hydraulic gradient;
Δθ i is the volume water content change under the ith hydraulic gradient;
4.4 Judging whether the pore channels with different sizes have seepage according to the formula (6), namely, when the actual hydraulic gradient exceeds the initial hydraulic gradient of the pore channel, the seepage of the pore channel of the stage occurs, and combining the formula (7) to obtain the saturation nonlinear permeability coefficient under different hydraulic gradients.
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| CN113916746B (en) * | 2021-10-14 | 2023-08-04 | 深圳大学 | Unsaturated stratum infiltration analysis method based on cellular automaton |
| CN114034621B (en) * | 2021-11-09 | 2023-07-07 | 中国电建集团成都勘测设计研究院有限公司 | Soil body permeability coefficient acquisition method and device and model construction method |
| CN114324103B (en) * | 2021-12-15 | 2023-12-12 | 宿迁学院 | Method for measuring permeability coefficient of saturated clay body |
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