Method for correcting permeability coefficient of saturated medium-coarse sand medium

Abstract

The invention discloses a saturated medium-coarse sand medium permeability coefficient correction method, and relates to the technical field of geotechnical engineering and hydraulic engineering, and the saturated medium-coarse sand medium permeability coefficient correction method comprises the following steps: obtaining microstructure parameters of a saturated medium-coarse sand medium through a nondestructive testing technology, the microstructure parameters at least comprising an effective porosity ne, a tortuosity gamma and a pore average diameter dp; the double-path permeability coefficient calibration algorithm comprises the following steps: calculating a permeability coefficient based on a correction formula of the effective porosity ne and the permeability coefficient K; and calculating the permeability coefficient based on theoretical models of the effective porosity ne, the tortuosity gamma and the average pore diameter dp. According to the invention, an empirical calculation model based on effective porosity and a theoretical calculation model fused with tortuosity are constructed to form a dual-path correction algorithm system, so that the calculation precision of the permeability coefficient and the reliability of the algorithm in related engineering scenes are effectively improved; and an innovative algorithm system is provided for medium-coarse sand medium permeability coefficient evaluation in the fields of geotechnical engineering, hydraulic engineering and the like.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of geotechnical engineering and water conservancy engineering, in particular to a saturated medium of medium-coarse sand permeability coefficient correction method. BACKGROUND

[0002] In geotechnical engineering and water conservancy engineering, the accurate evaluation of the permeability coefficient of saturated medium of medium-coarse sand is crucial. It is directly related to the management of groundwater resources, such as in the development of groundwater exploitation plan, the permeability coefficient affects the judgment of groundwater recharge and discharge; for foundation stability analysis, it determines the change of pore water pressure, and then affects the bearing capacity of foundation; in the prediction of pollutant migration, the permeability coefficient is a key parameter to judge the diffusion speed and range of pollutants in groundwater.

[0003] The traditional permeability coefficient calculation method mainly relies on empirical formula and macroscopic experimental data, and is estimated based on parameters such as total porosity. However, this method does not fully consider the complexity and connectivity of the internal pore structure of the medium. The internal pores of medium-coarse sand medium are of different sizes and shapes, and have different connectivity, and the traditional method ignores these factors, resulting in deviation between the evaluation results and the actual situation. For example, in the foundation treatment of some large water conservancy projects, due to inaccurate estimation of the permeability coefficient, it may cause piping and other permeation damage problems, threatening the safety of the project.

[0004] In recent years, non-destructive testing technologies such as X-ray computed tomography (CT) and magnetic resonance imaging (MRI) have developed rapidly. These technologies can obtain three-dimensional images of the internal pores of the medium, analyze the connectivity, shape and distribution characteristics of the pores, and provide more accurate micro parameters for permeability coefficient calculation. However, how to effectively integrate these micro information into the calculation model and establish the quantitative relationship between microstructure and macroscopic permeability performance is still a difficult and hot issue in current research.

[0005] At present, no effective solution has been proposed for the problems in the related art. SUMMARY

[0006] In view of the problems in the related art, the present application proposes a saturated medium of medium-coarse sand permeability coefficient correction method to overcome the above technical problems existing in the prior art.

[0007] The technical scheme of the present application is as follows:

[0008] A saturated medium of medium-coarse sand permeability coefficient correction method, comprising the following steps:

[0009] Obtain the microstructure parameters of the saturated medium of medium-coarse sand by non-destructive testing technology, wherein the microstructure parameters at least include effective porosity n e , tortuosity Γ and pore average diameter d p ;

[0010] The calibration double-path permeability coefficient algorithm, comprising:

[0011] The effective porosity n e The permeability coefficient K is calculated based on the correction formula, which is expressed as:

[0012] n e = 75.1339 + 36.5664lnK;

[0013] wherein n e is the dimensionless effective porosity, the unit of K is m / d, and the applicable object is limited to saturated medium of medium-coarse sand;

[0014] The permeability coefficient is calculated based on the theoretical model of the effective porosity n e , tortuosity Γ and pore average diameter d p , which is expressed as:

[0015]

[0016] wherein the unit of K is m / s, ρ is the density of water (kg / m 3 ), g is the gravitational constant (N / kg), and v is the kinematic viscosity of water (m 2 / s);

[0017] Further, the microstructure parameters of the saturated medium of medium-coarse sand are obtained, comprising the following steps:

[0018] The saturated medium of medium-coarse sand is placed in a non-destructive testing technology for three-dimensional scanning imaging;

[0019] The scanning image is binarized and segmented into solid-liquid two phases using image processing software, the connected pore network is extracted, and the effective porosity n e is calculated;

[0020] The pore connectivity and actual fluid motion path are analyzed, and the tortuosity Γ is calculated;

[0021] The pore average diameter d p is interpreted based on the CT scanning image.

[0022] Further, the non-destructive testing technology comprises X-ray computed tomography or gamma ray scanning.

[0023] Further, the image processing software comprises at least one of ScanViewer, GOMBladeInspect or Avizo, which is used to extract the connected pore network and exclude isolated pores.

[0024] Further, the effective porosity n eThe volume proportion of the connected pores in the image is calculated by nondestructive testing.

[0025] Further, the tortuosity Gamma is calculated by analyzing the ratio of the movement path length of the fluid inside the medium to the straight length of the medium.

[0026] The beneficial effects of the present application are:

[0027] The saturated medium permeability coefficient correction method discloses a correction algorithm system for the saturated medium permeability coefficient, directly obtains key parameters such as the pore connectivity, effective porosity and tortuosity inside the medium through nondestructive testing technology, and optimizes the traditional permeability coefficient calculation model in combination with physical experimental data. The method adopts the nondestructive testing technology to perform three-dimensional imaging analysis on the saturated medium, accurately extracts the microstructure features of the actual fluid flow path, constructs an empirical calculation model based on the effective porosity and a theoretical calculation model fusing the tortuosity, and forms a double-path correction algorithm system. By comparing the sand column seepage experimental data of the quartz sand and glass bead media, the improvement of the correction algorithm on the error caused by ignoring the pore connectivity and the real movement path of the fluid in the traditional model is verified. The algorithm system reduces the calculation error of the saturated medium permeability coefficient by 10% to 35% compared with the traditional method, effectively improves the calculation accuracy and algorithm reliability of the permeability coefficient in the related engineering scene, and provides an innovative algorithm system for the evaluation of the medium permeability coefficient in the fields of geotechnical engineering and water conservancy engineering. BRIEF DESCRIPTION OF DRAWINGS

[0028] In order to more clearly illustrate the technical solutions in the embodiments of the present application or the prior art, the following will briefly introduce the drawings needed to be used in the embodiments. Obviously, the drawings in the following description are only some embodiments of the present application, and other drawings can be obtained by those skilled in the art without creative labor.

[0029] Figure 1 The figure is a medium particle size distribution curve of a saturated medium permeability coefficient correction method according to an embodiment of the present application; (a) is a glass bead medium particle size distribution curve, and (b) is a quartz sand medium particle size distribution curve;

[0030] Figure 2 The figure is a medium permeability experimental scene of a saturated medium permeability coefficient correction method according to an embodiment of the present application; (c) is a saturated glass bead medium permeability experiment, and (d) is a saturated quartz sand medium permeability experiment;

[0031] Figure 3 The figure is a comparison of effective porosity before the quartz sand medium sand column seepage experiment of a saturated medium permeability coefficient correction method according to an embodiment of the present application;

[0032] Figure 4 It is a glass bead medium sand column seepage experiment before effective porosity comparison chart of a saturated medium-coarse sand medium permeability coefficient correction method according to an embodiment of the application;

[0033] Figure 5 It is a quartz sand medium sand column seepage experiment after effective porosity comparison chart of a saturated medium-coarse sand medium permeability coefficient correction method according to an embodiment of the application;

[0034] Figure 6 It is a glass bead medium sand column seepage experiment after effective porosity comparison chart of a saturated medium-coarse sand medium permeability coefficient correction method according to an embodiment of the application. DETAILED DESCRIPTION

[0035] The technical solutions in the embodiments of the present application will be clearly and completely described below with reference to the drawings in the embodiments of the present application. Obviously, the described embodiments are only a part of the embodiments of the present application, rather than all the embodiments. Based on the embodiments in the present application, all other embodiments obtained by those skilled in the art belong to the scope of protection of the present application.

[0036] According to an embodiment of the present application, a saturated medium-coarse sand medium permeability coefficient correction method is provided.

[0037] The saturated medium-coarse sand medium permeability coefficient correction method according to the embodiment of the present application comprises the following steps:

[0038] Microstructure parameters of the saturated medium-coarse sand medium are obtained by non-destructive testing technology, and the microstructure parameters at least include effective porosity n e , tortuosity Γ and pore average diameter d p ; specifically comprising the following steps:

[0039] The saturated medium-coarse sand medium is placed in the non-destructive testing technology for three-dimensional scanning imaging; wherein the non-destructive testing technology includes X-ray computed tomography or gamma ray scanning.

[0040] The scanning image is binarized and segmented by using image processing software, the connected pore network is extracted, and the effective porosity n e is calculated; wherein the image processing software includes at least one of ScanViewer, GOMBladeInspect or Avizo, which is used to extract the connected pore network and exclude isolated pores.

[0041] The pore connectivity and the actual fluid motion path are analyzed, and the tortuosity Γ is calculated.

[0042] The pore average diameter d p is interpreted based on the CT scanning image.

[0043] The technical solution, effective porosity n e The effective porosity is directly calculated by the volume proportion of the connected pores in the nondestructive testing image, and is physically equivalent to the effective porosity measured by the isotope tracing method or the medium characteristic curve method. The tortuosity Γ is calculated by analyzing the ratio of the movement path length of the fluid in the medium to the linear length of the medium, and is distributed and analyzed in space based on the three-dimensional pore network model.

[0044] According to the empirical formula proposed by Marotz in 1968, the relationship between the effective porosity and the permeability coefficient in the medium is as follows:

[0045] n e = 0.462 + 0.045lnK; (1)

[0046] In the above, n e in formula 1 is defined as the effective porosity (dimensionless), and K is the permeability coefficient (unit: m / s). The theoretical connotation of the concept of effective porosity is the ratio of the connected pore volume in the medium to the total volume of the medium. According to this concept, the connected pores obtained in the nondestructive testing scanning imaging can also be called effective pores.

[0047] Vukovic M and Soro A summarized a series of methods for measuring the effective porosity by measuring the water level in the study area and indoor physical experiments. Common methods for measuring the effective porosity include the isotope tracer method, the empirical relationship formula method for medium particle size distribution, and the medium characteristic curve method. However, from the perspective of the theoretical definition of effective porosity, which is the proportion of the pore volume in the medium that can affect the flow field, the connected pores interpreted by nondestructive testing are the space for water flow in the medium, and the pore wall of the connected pores is the boundary of the micro flow field in the medium. These connected pores form the flow field in the medium, and the definition of effective pores is also the pores in the medium that can affect the seepage in the medium.

[0048] In summary, the present application considers that the connected pores (Connected Pores) are equivalent to the effective pores (Effective Pores) in physical meaning, so the value of the connected porosity (Connective Porosity) should also be equal to the effective porosity (Effective Porosity). In view of the deviation of the experimental results of the multiple medium, the present application proposes to use n erepresents the effective porosity (dimensionless), K is the permeability coefficient (unit: m / d), and the correlation equation is re-fitted based on the data of multiple coarse sand medium experiments of different media types, that is, based on the effective porosity n e The permeability coefficient is calculated using the modified formula of the permeability coefficient K, which is expressed as:

[0049] n e =75.1339+36.5664lnK; (2)

[0050] Because the medium used in the physical experiments of the present invention is saturated medium-coarse sand, its permeability coefficient is mostly around 30m / d. For the convenience of assignment and calculation, the unit of the permeability coefficient K in Formula 2 is set to "m / d", which is different from the unit in Formula 1. Because the medium used in the experiments of the present invention is medium-coarse sand, the scope of application of Formula 2 is limited to expressing the effective porosity n inside the saturated medium-coarse sand medium that can be read through non-destructive testing. e The correlation between the permeability coefficient K (unit: m / d) and the permeability coefficient K (unit: m / d).

[0051] The present invention does not expand the scope of application of Formula 2 as to whether it is applicable to porous media with other particle size ranges or even media with other properties (such as fractured media or unsaturated media).

[0052] Based on non-destructive testing technology, the pore tortuosity of medium-coarse sand media can also be obtained. Tortuosity is a parameter that can reflect the actual movement distance of water in saturated water-containing media. It also characterizes the spatial expansion and distribution of effective pores in the medium. The hydraulic conductivity characterizes the degree to which water can flow through the medium. Based on the definition of physical theory, there should be a correlation between tortuosity and hydraulic conductivity, because both reflect the permeability of water flow in saturated porous media to a certain extent. In 2015, Ye Tianqi et al. derived the correlation between tortuosity and hydraulic conductivity as follows:

[0053]

[0054] Wherein, K in formula 3 is the permeability coefficient of the medium (unit: m / s), ρ is the water density (unit: kg / m 3 ), g is the gravity constant (unit: N / kg), n is the medium porosity (dimensionless), d_p is the average diameter of the pores within the medium (unit: m), v is the kinematic viscosity of the water (unit: m² / s), and Γ is the tortuosity (dimensionless). Both the density and kinematic viscosity of water are temperature-dependent. The laboratory temperature used during the seepage experiment was substituted to obtain the corresponding values. Porosity and the average pore diameter within the medium can be obtained by interpreting CT scan images of the sand column.

[0055] The measured permeability coefficient value and non-destructive testing data obtained through the saturated medium coarse sand physical seepage experiment summarized in the present application are compared and analyzed. The medium porosity input value in formula 3 is changed from the total porosity to the effective porosity obtained by non-destructive testing or the effective porosity (connected porosity) measured by other measurement methods. It is closer to the true value of the medium permeability coefficient. The corrected saturated medium coarse sand permeability coefficient algorithm, i.e. the theoretical model calculation of the permeability coefficient based on the effective porosity n e , tortuosity Γ and average pore diameter d p , is expressed as:

[0056]

[0057] Wherein, the unit of K is m / s, ρ is the density of water (kg / m 3 ), g is the gravitational constant (N / kg), and v is the kinematic viscosity of water (m 2 / s);

[0058] Wherein, the water density ρ and the kinematic viscosity v are dynamically adjusted according to the laboratory measured temperature of the seepage experiment.

[0059] Specifically, in application, as shown in Figures 1-6 , the accuracy of the correction algorithm is verified by physical experiment, including: comparing the calculation results of the above empirical formula and theoretical model with the measured permeability coefficient value; calculating the deviation amplitude of the traditional model with total porosity input and the correction model with effective porosity input, and verifying the applicability. Specifically as follows:

[0060] Experimental preparation: as shown in Figure 1 , two kinds of quartz sand medium and glass bead medium with the same average particle size, similar particle size distribution and particle size distribution range belonging to medium coarse sand are selected. The organic glass column is filled for subsequent saturated seepage experiment.

[0061] Physical experiment: as shown in Figure 2 , saturated seepage experiment is carried out on the filled quartz sand and glass bead medium sand column. The water head difference at different depths is measured, and the permeability coefficient of the saturated medium at different depths is calculated combined with Darcy's law. The porosity is obtained by weighing method. The experimental data are recorded in table 1 and table 2. Specifically as follows:

[0062] Table 1 effective porosity data table of two kinds of medium sand column before and after experiment unit: %

[0063]

[0064] Table 2 permeability coefficient data table of two kinds of medium sand column before and after experiment unit: m / d

[0065]

[0066] Nondestructive testing and data processing: Two kinds of medium sand columns are placed in the industrial CT device for high-precision imaging. In the Avizo software, the "Axis Connectivity" module is used for pore connectivity analysis, and the unconnected pores are excluded to calculate the connected porosity, i.e. the effective porosity n e The connected porosity of the two kinds of medium sand columns as a whole and each segment is calculated, and the change of the permeability coefficient measured by the physical experiment is compared and analyzed.

[0067] Comparison and verification: the data in Table 2 is substituted into formula 1 to calculate the effective porosity, which is compared with the effective porosity directly read from Table 1 by Avizo, and the results are shown in Figures 3-6 It is found that there is a large gap between the two, indicating that the traditional formula calculation has deviation.

[0068] The determination coefficient R of formula 2 is 0.7002, which verifies its representativeness. The porosity, average pore diameter inside the medium, tortuosity and other parameters are obtained, and the water density p and the motion viscosity coefficient v are determined according to the experimental temperature. The relevant data are substituted into formula 3, the porosity is the total porosity, and formula 4, the porosity is the effective porosity to calculate the permeability coefficient, and the results are recorded in Table 3. Specifically as follows:

[0069] Table 3 Calculation results of sand column permeability coefficient before and after seepage experiment

[0070]

[0071] Comparing the calculated permeability coefficient values in Table 3 with the corresponding measured permeability coefficient values of the two kinds of media in Table 2, it is found that when the porosity input value is the total porosity, the average deviation amplitude of the calculated permeability coefficient value and the measured value is 17.54%, and when the porosity input value is the effective porosity, the average deviation amplitude is 10.23%. It is proved that formula 4 has better adaptability in saturated medium coarse sand medium, and the modified algorithm system of the application can effectively improve the calculation accuracy of the permeability coefficient.

[0072] In summary, by means of the technical scheme of the present application, under the condition that the internal pore connectivity and effective porosity and tortuosity parameters of the saturated medium can be directly obtained by the non-destructive testing technology, a permeability correction algorithm system based on the microstructure parameters is constructed. By combining the connected porosity (physically equivalent to the effective porosity) obtained by non-destructive testing with the tortuosity data, a double-path permeability algorithm system is established, which includes an empirical relationship between the effective porosity and the permeability and an algorithm model that fuses the pore diameter and the tortuosity. Compared with the single algorithm based on the total porosity or indirect empirical parameters (such as the particle size distribution of the medium) in the prior art, the system realizes quantitative calculation from the direct observation data of the fluid migration boundary (pore wall) and the flow field spatial distribution (tortuous path) in the medium, and solves the problem of permeability estimation deviation caused by the neglect of pore connectivity and the actual fluid motion path in the traditional method.

[0073] The above description is merely that of the preferred embodiments of the application, and is not to be taken in a limiting sense, but is made merely for the purpose of disclosure owing to the requirement of the patent law. Those skilled in the art can readily devise numerous other embodiments without departing from the scope of the present disclosure. The present application is intended to cover any and all variations of the present disclosure which come within the scope of the general concept and which fall within customary practice in the art. The description and embodiments are to be regarded as illustrative only, and the true scope of the present disclosure is to be determined by the appended claims.

[0074] It should be understood that the present disclosure is not limited to the precise construction that has been described above and illustrated in the accompanying drawings, and that various modifications and changes can be made without departing from the scope thereof. The scope of the present disclosure is limited only by the appended claims.

Claims

1. A method for correcting the permeability coefficient of saturated medium-coarse sand medium, characterized in that: The following steps are involved: The microstructural parameters of the saturated medium-coarse sand medium are obtained by non-destructive testing technology, wherein the microstructural parameters include at least the effective porosity n e , tortuosity Γ and average pore diameter d p ; Calibrate the dual-path permeability coefficient algorithm, including: Based on the effective porosity n e The permeability coefficient is calculated using the modified formula of the permeability coefficient K, which is expressed as: n e =75.1339+36.5664lnK; Based on the effective porosity n e , tortuosity Γ and average pore diameter d p The theoretical model for calculating the permeability coefficient is expressed as:

2. The method for correcting the permeability coefficient of saturated medium-coarse sand medium according to claim 1, characterized in that: The method of obtaining the microstructure parameters of the saturated medium-coarse sand medium comprises the following steps: The saturated medium-coarse sand medium is placed in a non-destructive testing technology for three-dimensional scanning imaging; Use image processing software to perform binary segmentation of the solid and liquid phases on the scanned image, extract the connected pore network and calculate the effective porosity n e ; Analyze pore connectivity and actual fluid movement path, and calculate tortuosity Γ; Interpretation of the average pore diameter d based on CT scan images p .

3. The method for correcting the permeability coefficient of saturated medium-coarse sand medium according to claim 2, characterized in that: The non-destructive testing technology includes: X-ray computed tomography or gamma ray scanning.

4. The method for correcting the permeability coefficient of saturated medium-coarse sand medium according to claim 3, characterized in that: The image processing software includes at least one of ScanViewer, GOMBladeInspect or Avizo, which is used to extract the connected pore network and exclude isolated pores.

5. The method for correcting the permeability coefficient of saturated medium-coarse sand medium according to claim 4, characterized in that: The effective porosity n e Calculated by the volume fraction of connected pores in non-destructive testing images.

6. The method for correcting the permeability coefficient of saturated medium-coarse sand medium according to claim 5, characterized in that: The tortuosity Γ is calculated by analyzing the ratio of the length of the fluid's movement path inside the medium to the straight length of the medium.

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