CN113588916B - Method for predicting water accumulation adsorption in expansive soil - Google Patents

Method for predicting water accumulation adsorption in expansive soil Download PDF

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CN113588916B
CN113588916B CN202110779223.2A CN202110779223A CN113588916B CN 113588916 B CN113588916 B CN 113588916B CN 202110779223 A CN202110779223 A CN 202110779223A CN 113588916 B CN113588916 B CN 113588916B
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梁英杰
田沛博
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Abstract

The invention discloses a method for predicting water accumulation adsorption in expansive soil, which comprises the following steps: s1, selecting a water adsorption process in expansive soil as a research object, and determining to perform a water adsorption test on the expansive soil to obtain test data of water accumulated adsorption; s2, establishing a fractal derivative diffusion fluctuation model of expansive soil moisture adsorption according to the material coordinates; s3, deducing a water accumulation adsorption quantity equation in the expansive soil by combining a fractal derivative diffusion fluctuation equation; s4, combining the test data of water accumulation adsorption, and obtaining the order number alpha and the diffusion coefficient D of the time fractal derivative through data fittingmA value of (d), classifying the moisture adsorption process; s5, comparing the parameters alpha and DmSubstituting the water accumulation adsorption quantity equation to predict the water accumulation adsorption process in the expansive soil. The invention improves the accuracy of water accumulation and adsorption in the expansive medium, can effectively predict the evolution process of the groundwater environment problem, and can be used for repairing and treating pollutants in expansive soil and the like.

Description

Method for predicting water accumulation adsorption in expansive soil
Technical Field
The invention relates to environmental hydrodynamics, in particular to a method for predicting water accumulation and adsorption in expansive soil.
Background
The absorption and permeation of rivers to the expansive soil along the bank, the diffusion process of pollutant solutes on the ground surface, the diffusion process of aquifers in the soil, the site selection of refuse landfills and the process of seawater back-flow all relate to the problem of the migration rule of the solutes in complex soil media, and the expansibility of the soil is a common characteristic of most of the soil. The diffusion process of moisture in general soil is relatively complex, and the diffusion process of moisture and solute in general expansive soil can cause soil expansion, thereby influencing the subsequent diffusion process. Thus, the cumulative diffusion process of water and solutes is a non-linear diffusion process on a time scale, related to the order of the fractal derivative of time and the material properties of the soil.
Up to now, a common abnormal diffusion and absorption model is that a porous soil medium is assumed to be a rigid medium, and the diffusion and absorption process comes in and out with the diffusion and absorption process in an actual situation, in the actual absorption process, water is rapidly diffused due to capillary action and a large hydraulic gradient at the beginning, then the water content of soil is gradually increased along with the gradual permeation of water molecules, soil particles are gradually expanded in the diffusion process, and the diffusion process is gradually slowed down. Most studies on absorption have focused on "rigid" porous media, which contradict the properties of real porous media, because real porous media undergo changes in expansion and contraction, and thus do not accurately describe the migration process of water in swelling clay. The methods related to the solute transport problem in the porous medium in the prior art do not relate to convection action in some methods and do not consider spatial scale correlation in some methods. Therefore, the existing diffusion model has the defects.
Disclosure of Invention
The purpose of the invention is as follows: the invention aims to provide a method for predicting water accumulated adsorption in expansive soil.
The technical scheme is as follows: a method of predicting cumulative adsorption of moisture in swelling soil comprising the steps of:
s1, selecting a water adsorption process in certain expansive soil as a research object, and determining to perform a water adsorption test on the water adsorption process to obtain test data of water accumulated adsorption;
s2, establishing a fractal derivative cumulative diffusion model of expansive soil moisture adsorption according to the material coordinates;
s3, combining the fractal derivative diffusion wave equation in the step S2 to deduce an equation of the water accumulated adsorption amount in the expansive soil;
s4, combining the test data of the water accumulation adsorption in the step S1, and obtaining the order number alpha and the diffusion coefficient D of the time fractal derivative in the water accumulation adsorption quantity in the step S3 through data fittingmThe value of (a), classifying the process of water adsorption in expansive soil;
s5, substituting the parameters obtained in the step S4 into the moisture accumulated adsorption amount in the step S3; and predicting the water accumulation adsorption process in the expansive soil according to the water accumulation adsorption quantity equation, and solving the water accumulation adsorption quantity in the expansive soil at any moment.
Further, the test data of the moisture cumulative adsorption obtained in step S1 includes: the value of the cumulative amount of moisture adsorbed as a function of time.
Further, in step S2, the material coordinate m is:
Figure BDA0003155541500000021
wherein z is a normal spatial coordinate in the vertical direction, z0Is the upper limit of the space coordinate, e is the void ratio, and the formula is
Figure BDA0003155541500000022
Figure BDA0003155541500000023
Is the water content ratio, thetalAnd thetasVolume fractions of liquid and solid, respectively;
the fractal derivative diffusion wave equation under the material coordinates is as follows:
Figure BDA0003155541500000024
wherein t is time, 0<Alpha is less than or equal to 2 and is the order of time fractal derivative, DmIs the diffusion coefficient;
the basic solution of the fractal derivative diffusion wave equation in matter coordinates is:
Figure BDA0003155541500000025
further, the accumulated moisture adsorption amount in the swelling soil in step S3 equation i (t) is:
Figure BDA0003155541500000026
wherein, theta0Is an initial water content, thetaiThe water content of the soil surface is shown.
Further, in step S4, the moisture cumulative adsorption quantity equation i (t) is used to describe the test data in step S1, and the most suitable matching parameters in the cumulative adsorption equation are obtained by using the lsqcurvefit command in Matlab software, i.e., the least square method, and the most suitable matching parameters enable the cumulative adsorptionThe mean square error between the attached equation and the accumulated adsorption test data is minimum; the parameters include: order number alpha and diffusion coefficient D of time fractal derivativemThe value of (c).
Further, in step S4, the adsorption processes are classified according to the order α of the time fractal derivative, where α 1< α ≦ 2 represents fast adsorption, α 0< α <1 represents slow adsorption, and α equals 1 represents normal adsorption.
Further, in step S5, the value of the parameter obtained in step S4 is substituted into the equation of the cumulative adsorption amount i (t) of moisture in the expansive soil in step S3 to obtain a complete equation of the cumulative adsorption amount of moisture in the expansive soil, and the cumulative adsorption value of moisture at any time is calculated to realize the long-term evolution process of moisture adsorption in the expansive soil.
The invention principle is as follows: compared with fractional order derivatives, the basic concept of the fractal derivative is mathematically simple in form, is a local operator and is greatly reduced in calculation amount compared with non-local fractional order derivatives. The presently widely used spread gaussian distribution and spread exponential decay, also known as non-debye decay, spread relaxation, can be directly deduced from the fractal derivative model. The statistical mechanical basis is clear, and the method is completely different from the statistical background of the Levy stable distribution of the fractional derivative and the Mittag-Leffler function attenuation. From the aspect of fractal geometry, the dimension of the fractal derivative in space in the spatial definition is the fractal dimension of the fractal body. The fractal derivative can also be regarded as a scale transformation and is directly used for describing a space-time scale dependent system.
Has the advantages that: the method is based on the fact that the water migration process in specific expansive soil media is used as a research object, firstly, substance coordinates are established according to the diffusion characteristics of expansive clay, the expansibility and the adsorbability can be better described through the medium, a fractal derivative accumulation diffusion model is established to obtain test data of a curve of water accumulation adsorption with respect to time, then the analytical solution of the accumulation adsorption model is deduced, relevant fitting parameters of the fractal derivative accumulation adsorption model are determined by combining test conditions and the test data, the water adsorption curve in the expansive soil media is described, the quantitative relation between the model parameters and time or space scale is finally inspected, and the calculation of the water adsorption capacity of the soil at any time is realized according to the corresponding relation between the actual characteristics of the soil and the fractal derivative. The invention verifies the feasibility of the fractal derivative cumulative diffusion model and provides a new theoretical reference for the treatment and restoration of the environmental pollution of the underground water. The invention has wide application prospect, and can be used for pollutant diffusion prediction, evaluation, restoration and the like of expansive soil. Compared with the existing medium diffusion model in soil, the model is more suitable for the actual situation, and the pollutant diffusion process in soil is more accurately described.
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FIG. 1 is a flow chart of the method of the present invention;
FIG. 2 is a graph showing the effect of the present invention on the amount of accumulated moisture adsorbed in the black soil.
Detailed Description
The invention is described in detail below with reference to the drawings and specific embodiments so that those skilled in the art can more completely understand the invention. It is to be understood that the present disclosure is only one representative embodiment. It will be apparent that the invention is not limited to any specific structure, function, device and method described herein, but may have other embodiments and the scope of the invention is not limited to the described embodiments.
The method for predicting the water accumulation adsorption in the expansive soil is suitable for the adsorption process in the expansive soil. In this example, the agglomerates of the surface layer of the black soil were selected as the object of study, and the specific method of analysis will be described in detail. It should be noted that the analysis steps of the present invention are not limited to the agglomerates of the subsoil surface layer, nor to the type of swelling material, and similar methods can be used for the absorption and diffusion of other swelling medium materials.
As shown in fig. 1, a method for predicting cumulative adsorption of moisture in swelling soil, comprising the steps of:
s1, selecting a water adsorption process in certain expansive soil as a research object, and determining to perform a water adsorption test on the water adsorption process to obtain test data of water accumulated adsorption; the experimental data obtained included: the value of the cumulative amount of moisture adsorbed as a function of time.
S2, establishing a fractal derivative cumulative diffusion model of expansive soil moisture adsorption according to the material coordinates;
the material coordinate m is:
Figure BDA0003155541500000041
wherein z is a normal spatial coordinate in the vertical direction, z0Is the upper limit of the space coordinate, e is the void ratio, and the formula is
Figure BDA0003155541500000042
Figure BDA0003155541500000043
Is the water content ratio, thetalAnd thetasThe volume fractions of liquid and solid, respectively.
The fractal derivative diffusion wave equation under the material coordinates is as follows:
Figure BDA0003155541500000044
wherein t is time, 0<Alpha is less than or equal to 2 and is the order of time fractal derivative, DmIs the diffusion coefficient;
the basic solution of the fractal derivative diffusion wave equation in matter coordinates is:
Figure BDA0003155541500000045
s3, combining the fractal derivative diffusion wave equation in the step S2 to deduce an equation of the water accumulated adsorption amount in the expansive soil;
the cumulative water adsorption I (t) is given by the equation:
Figure BDA0003155541500000046
wherein, theta0Is an initial water content, thetaiThe water content of the soil surface is shown.
S4, combining the test data of the water accumulation adsorption in the step S1, and obtaining the order number alpha and the diffusion coefficient D of the time fractal derivative in the water accumulation adsorption quantity in the step S3 through data fittingmThe value of (a), classifying the process of water adsorption in expansive soil; specifically, the method comprises the following steps:
describing the test data in the step S1 by adopting an accumulated moisture adsorption quantity I (t) equation, and obtaining the most appropriate matching parameter in the accumulated moisture adsorption quantity I (t) equation by using an lsqcurvefit command in MATLAB software, namely a least square method, wherein the most appropriate matching parameter enables the mean square error between the accumulated adsorption equation and the accumulated adsorption test data to be minimum; the parameters include: order number alpha and diffusion coefficient D of time fractal derivativemThe value of (c).
Classifying the adsorption process according to the order number alpha of the time fractal derivative, wherein alpha is more than 1 and less than or equal to 2 and represents fast adsorption, alpha is more than 0 and less than 1 and represents slow adsorption, and alpha is equal to 1 and represents normal adsorption.
S5, obtaining the parameters (the order number alpha of the time fractal derivative and the diffusion coefficient D) obtained in the step S4mThe value of (d) is substituted into the equation of the moisture cumulative adsorption amount i (t) in step S3; predicting the water accumulation adsorption process in the expansive soil according to the water accumulation adsorption quantity equation; specifically, the method comprises the following steps:
substituting the value of the parameter obtained in the step S4 into the equation of the water accumulated adsorption amount I (t) in the step S3 to obtain a complete equation of the water accumulated adsorption amount in the expansive soil, and calculating the accumulated adsorption value of water at any moment to realize the prediction of the long-term evolution process of water adsorption in the expansive soil.
Example (b):
(1) this example analyses experimental data using the swelling soil adsorption process before the infiltration process reached stability. In expanded earth columns, the infiltration choke occurs below a significantly softer earth layer, rather than at the surface. And the permeation does not reach a constant rate due to the change in the hydraulic characteristics of the throttling valve over time. Therefore, before the water flow reaches the stability, a set of data about the moisture accumulation adsorption process of the expansive black soil can be obtained. Specific test data are shown in table 1.
TABLE 1 swelling Black soil moisture accumulation adsorption test data
Figure BDA0003155541500000051
A group of expansive soil infiltration tests are set in the tests, and the used expansive soil is black soil surface layer aggregate. The soil used in this test was 0.5-1.0mm of black soil surface layer aggregate, collected from the wheat sample plot of the northwest wheat research institute, and had a depth of 0-10 cm. It contains 1.4% organic carbon and 64% clay. The water content and volume weight are measured by dual-source gamma ray attenuation, the pore water pressure passes through a single tensiometer-sensor system, and the soil temperature passes through a single thermistor-bridge system. The empty column was first scanned at the sensor contact height with americium-241 and cesium-137 rays. Uniform packing of the columns is achieved by slowly pouring air-dried soil into the columns at a constant rate and tapping the columns on the surface of the rising soil. The gamma ray scanning was again performed on a 50cm dry soil column, and the initial volume weight and water content were calculated. The marriott bottle was set to a water level of 3.5 cm above the soil, allowing for expansion. The gamma ray beam is set 3cm below the soil surface. The infiltration test uses the technique of Collis-George and Laryea (1971) to continuously record mariotte vial readings and the location of the wetting front, and insert a tensiometer as the wetting front advances. Barometer readings are taken every hour to correct the output of the absolute pressure sensor. Gamma ray attenuation measurements are taken at wet and dry portions of the column, and at locations above the initial soil surface, which are moving upward due to expansion.
When the wetting front reaches the bottom of the column, the flow is measured, and when the outflow is equal to the inflow, the test is terminated. When the column is in "steady state", final gamma ray attenuation, tensiometer and thermistor readings are taken. A column of 5.09 cm diameter and 90 cm long plexiglass was used in the test, and the structure was similar to that of the column. The infiltration measurements were performed in the same manner as the soil column, with the tensiometer element inserted behind the wetting front as infiltration proceeded. Pore water pressure measurements were made in both fine and coarse sand, and a tension gauge was inserted near the grain boundaries. The test was terminated when capillary streaking occurred at the bottom of the column and steady state flow was reached. In the infiltration test, the infiltration time of the water in the soil ranges from 0 to 5 hours. In the test process, the water content and the volume weight in the soil column are calculated by gamma ray absorption data, and the pore water pressure is calculated by the output of a sensor. Thus, the cumulative adsorption curve of the permeated water over time can be obtained before the water flow reaches a steady state.
(2) Establishing a fractal derivative diffusion fluctuation model of water adsorption of expansive soil according to the substance coordinates;
the material coordinate m is:
Figure BDA0003155541500000061
wherein z is a normal spatial coordinate in the vertical direction, z0Is the upper limit of the space coordinate, e is the void ratio, and the formula is
Figure BDA0003155541500000062
Figure BDA0003155541500000063
Is the water content ratio, thetalAnd thetasThe volume fractions of liquid and solid, respectively.
The fractal derivative diffusion wave equation under the corresponding material coordinates is as follows:
Figure BDA0003155541500000064
wherein t is time, 0<Alpha is less than or equal to 2 and is the order of time fractal derivative, DmIs the diffusion coefficient;
the basic solution of the fractal derivative diffusion wave equation is:
Figure BDA0003155541500000071
(3) combining the fractal derivative diffusion fluctuation equation and the basic solution thereof in the step (2) to deduce an equation of the water accumulated adsorption capacity in the expansive soil;
the cumulative water adsorption I (t) is given by the equation:
Figure BDA0003155541500000072
wherein, theta0Is an initial water content, thetaiThe water content of the soil surface is shown.
(4) Combining the test data of water accumulation adsorption in the step (1), and applying an lsqcurvefit (least square method) command in MATLAB software to obtain the most appropriate matching parameter in a creep equation, wherein the mean square error is 0.0306, and the value of the parameter is as follows: alpha is 0.873<1, indicating that the diffusion of moisture in such swelling soils is slow. In addition, by diffusion coefficient Dm＝43.12cm2The swelling capacity of the soil can be described as/h.
(5) Substituting the parameters obtained in the step (4) into the equation of the water accumulated adsorption quantity in the step (3); according to the water accumulated adsorption quantity equation, the water accumulated adsorption quantity in the expansive soil at any moment can be calculated, and the solution of the long-term evolution process of the water adsorption in the expansive soil is realized.
In the embodiment, MATLAB software is used for drawing a change comparison curve of I-t of an integer order and a fractal derivative, and the comparison shows that the fractal derivative model has a good effect, and the increase of the accumulative adsorption water content of the expansive black soil with respect to time is visually described as shown in FIG. 2. From the results, the fractal derivative model has an advantage in predicting the water accumulation adsorption in swelling soil.

Claims (5)

1. A method for predicting cumulative adsorption of moisture in swelling soil, comprising the steps of:
s1, selecting a water adsorption process in certain expansive soil as a research object, and determining to perform a water adsorption test on the water adsorption process to obtain test data of water accumulated adsorption;
s2, establishing a fractal derivative cumulative diffusion model of expansive soil moisture adsorption according to the material coordinates;
the material coordinate m is:
Figure FDA0003533921040000011
wherein z is a normal spatial coordinate in the vertical direction, z0Is the upper limit of the space coordinate, e is the void ratio, and the formula is
Figure FDA0003533921040000012
Is the water content ratio, thetalAnd thetasVolume fractions of liquid and solid, respectively;
the fractal derivative diffusion wave equation under the material coordinates is as follows:
Figure FDA0003533921040000013
wherein t is time, alpha is more than 0 and less than or equal to 2, D is the order of time fractal derivativemIs the diffusion coefficient;
the basic solution of the fractal derivative diffusion wave equation in matter coordinates is:
Figure FDA0003533921040000014
s3, combining the fractal derivative diffusion wave equation in the step S2 to deduce an equation of the water accumulated adsorption amount in the expansive soil;
the accumulated adsorption amount of water in the swelling soil equation I (t) is as follows:
Figure FDA0003533921040000015
wherein, theta0Is an initial water content, thetaiThe water content of the soil surface;
s4, combining with the water in the step S1The order alpha and diffusion coefficient D of the time fractal derivative in the water accumulation adsorption quantity equation of the step S3 are obtained through data fitting according to the test data of the accumulated adsorptionmThe value of (a), classifying the process of water adsorption in expansive soil;
s5, substituting the parameters obtained in the step S4 into the moisture accumulated adsorption quantity equation in the step S3; and predicting the water accumulation adsorption process in the expansive soil according to the water accumulation adsorption quantity equation, and solving the water accumulation adsorption quantity in the expansive soil at any moment.
2. The method of claim 1, wherein the test data of water cumulative adsorption obtained in step S1 comprises: the value of the cumulative amount of moisture adsorbed as a function of time.
3. The method of claim 1, wherein in step S4, the equation of cumulative water adsorption amount i (t) is used to describe the test data in step S1, and the most suitable matching parameters in the cumulative adsorption equation are obtained by using the lsqcurvefit command in Matlab software, i.e. least square method, and the most suitable matching parameters minimize the mean square error between the cumulative adsorption equation and the cumulative adsorption test data; the parameters include: order number alpha and diffusion coefficient D of time fractal derivativemThe value of (c).
4. The method of claim 1, wherein in step S4, the adsorption process is classified according to the order α of the time-fractal derivative, wherein α > 1 ≦ 2 indicates fast adsorption, α > 0 ≦ 1 indicates slow adsorption, and α equals 1 indicates normal adsorption.
5. The method for predicting the cumulative adsorption of moisture in expansive soil as claimed in claim 1, wherein the value of the parameter obtained in step S4 is substituted into the equation of the cumulative adsorption amount of moisture i (t) in expansive soil in step S3 in step S5 to obtain the equation of the cumulative adsorption amount of moisture in complete expansive soil, and the cumulative adsorption value of moisture at any time is calculated to realize the long-term evolution process of moisture adsorption in expansive soil.
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