A method for determining a three-dimensional fracture rock mass permeability tensor based on single-direction permeability

Abstract

The application provides a method for determining a three-dimensional fracture rock mass permeability tensor based on one-way permeability, for a fracture developed rock mass, obtaining statistical rules of structural planes of the rock mass, establishing a three-dimensional fracture network model, obtaining two-dimensional trace information of each orthogonal section by using three sets of orthogonal section cutting models, then establishing a theoretical relationship of each direction permeability of the three-dimensional rock mass by using the trace information of each section, and substituting the permeability in a known direction into the theoretical relationship of each direction permeability to obtain the permeability tensor of the fracture rock mass. For a fracture developed and dense rock mass, the application considers the influence of the geometric characteristics of the structural plane on the permeability anisotropy, combines the mathematical properties of the permeability tensor, establishes the relationship of the permeability in each direction in the three-dimensional space, and thus realizes obtaining the permeability tensor reflecting the three-dimensional space permeability of the fracture rock mass when the permeability in a certain direction is known. The method provided by the application is simple in operation and intuitive in structure, and solves the problem that it is difficult to determine the three-dimensional fracture network permeability tensor.

Description

Technical Field

[0001] This invention belongs to the field of water conservancy and hydropower engineering, and relates to a method for determining the permeability tensor of fractured rock masses, and in particular to a method for determining the permeability tensor of three-dimensional fractured rock masses based on unidirectional permeability. Background Technology

[0002] Quantitatively evaluating the permeability of fractured rock masses is an important aspect of water conservancy and hydropower engineering. It can provide technical support for the design of anti-seepage curtains and the prediction of sudden water inrush in hydraulic tunnels. It is also an important input parameter for the analysis of water conservancy and hydropower engineering using the continuous medium method.

[0003] The determination of the permeability tensor in fractured rock masses includes theoretical methods, numerical calculation methods, and field test methods. Theoretical methods have relatively large errors; numerical calculation methods often fail to converge when dealing with complex three-dimensional seepage calculations in fractured rock masses; field test methods obtain the permeability distribution by conducting a large number of pressure water tests, which requires a lot of manpower and resources. Summary of the Invention

[0004] The purpose of this invention is to provide a method for determining the permeability tensor of a three-dimensional fractured rock mass based on unidirectional permeability.

[0005] Therefore, the above-mentioned objective of the present invention is achieved through the following technical solution:

[0006] A method for determining the permeability tensor of a three-dimensional fractured rock mass based on unidirectional permeability, characterized in that the method includes the following steps:

[0007] S1. Through outdoor observation, analyze the development of rock mass structural surfaces in the area to be tested, and obtain the geometric information (geometric statistical regularity parameters) of the rock mass structural surfaces;

[0008] S2. Based on the geometric information of the rock mass structure surface in step S1, a three-dimensional fracture network model is established using numerical software.

[0009] S3. Establish three sets of mutually orthogonal cross sections, cut the three-dimensional fracture network model established in step S2, and the cross sections intersect with the three-dimensional fracture network to form traces;

[0010] S4. Statistical analysis of trace information on each cross section in step S3;

[0011] S5. Based on the trace information of each section in step S4, determine the cross-sectional seepage anisotropy ellipse;

[0012] S6. Based on the anisotropic ellipses of seepage at each cross section obtained in step S5, determine the three-dimensional anisotropic ellipsoid of seepage.

[0013] S7. Substitute the known unidirectional permeability into the three-dimensional spatial anisotropic ellipsoid of seepage determined in step S6 to determine the permeability ellipsoid, thereby obtaining the rock mass permeability tensor.

[0014] While adopting the above technical solutions, the present invention may also adopt or combine the following technical solutions:

[0015] As a preferred technical solution of the present invention: in step S1, the geometric information includes: the number of groups, shape, occurrence, opening, volume density, size, etc. of the rock mass structural planes.

[0016] As a preferred technical solution of the present invention: in step S4, the trace information includes: the number of trace groups, attitude, opening degree, linear density, areal density, trace length, etc.

[0017] As a preferred technical solution of the present invention: In step S5, the cross-sectional seepage anisotropic ellipse is: an ellipse obtained by fitting a certain permeability as the standard permeability and the square root of the ratio of the permeability in each seepage direction on the cross section to the standard permeability as the radius.

[0018] As a preferred technical solution of the present invention: In step S5, the determination of the anisotropic ellipse of cross-sectional seepage specifically includes the following steps:

[0019] S510. Select a certain seepage direction on the cross section as the standard seepage direction of the cross section, and define the permeability in this direction as the standard permeability of the cross section.

[0020] S520. Based on the geometric statistical information of the cross-section trace, the theoretical ratio of the permeability in the remaining seepage directions of the cross-section to the standard permeability of the cross-section is calculated using the following formula (1), expressed as M. 1f (where f = 2, 3, ..., f):

[0021]

[0022] Among them, M 12 λ represents the ratio of permeability k2 to k1 for any two seepage directions i2 and i1 on the cross section; the subscript can be adjusted according to different situations; J is the number of fracture groups, j refers to the j-th fracture group, j = 1, 2, ..., J; jm It is the linear density along the average normal direction of the j-th fracture group; n jm is the average normal direction of the j-th fracture group; I is the total number of fractures in the j-th fracture group, and i refers to the i-th fracture in the j-th fracture group; n ji The normal direction of the i-th fracture in the j-th fracture group; t j It is the ratio of the hydraulic opening of the j-th fracture group to the hydraulic opening of the 1-th fracture group;

[0023] S530, with the origin of the coordinate axis as the center, and Anisotropic ellipses are drawn along each cross section and each seepage direction with radius, and the corresponding ellipse equations are obtained.

[0024] As a preferred technical solution of the present invention: In step S6, the three-dimensional spatial seepage anisotropic ellipsoid is: an ellipsoid obtained by fitting a certain permeability as the standard permeability and the square root of the ratio of the permeability in each seepage direction in the three-dimensional space to the standard permeability as the radius.

[0025] As a preferred technical solution of the present invention: Step S6, determining the three-dimensional spatial anisotropic ellipsoid of seepage specifically includes the following steps:

[0026] S610. Establish a three-dimensional coordinate system with three sets of mutually orthogonal cross sections as each coordinate plane, wherein the xy plane, xz plane and yz plane coincide with the cross sections respectively;

[0027] S620. Adjust the permeability anisotropic ellipse on each of the three orthogonal sections so that the three anisotropic ellipses have the same standard permeability.

[0028] S630. Convert the permeation anisotropic ellipse of the three orthogonal sections adjusted in step S620 into a general form to obtain the coefficients of each variable.

[0029] S640. Substitute the coefficients of each variable obtained in step S630 into the general equation of the ellipsoid to obtain the three-dimensional spatial seepage anisotropic ellipsoid.

[0030] As a preferred technical solution of the present invention, step S620 specifically includes the following steps:

[0031] S621. For each cross section, establish the original standard permeability k. m Corresponding direction and newly determined standard permeability k n For coplanar sections in the corresponding directions, substitute the geometric information of the traces of the coplanar sections into formula (1) to calculate k. n / k m The theoretical value is denoted as M. mn ;

[0032] S622. The dimensions of the anisotropic ellipse of seepage based on the original standard permeability are enlarged to the original dimensions. times.

[0033] As a preferred technical solution of the present invention, step S7 specifically includes the following steps:

[0034] S701. Establish a known unidirectional permeability k p Corresponding direction and standard permeability k of the anisotropic ellipsoid of seepage in three-dimensional space qFor coplanar sections in the corresponding directions, substitute the geometric information of the traces of the coplanar sections into formula (1) to calculate k. p / k q The theoretical value is denoted as M. qp ;

[0035] S702. Enlarge the dimensions of the three-dimensional anisotropic ellipsoid from step S701 to its original dimensions. By multiplying the permeability of the known direction, a three-dimensional spatial anisotropic ellipsoid of permeability is obtained under the new standard permeability.

[0036] S703. Reduce the size of the three-dimensional spatial anisotropic ellipsoid of the new standard permeability obtained in step S702 to its original size. This yields a osmotic ellipsoid;

[0037] S704. Based on the permeability ellipsoid, determine the three principal permeability values ​​and direction vectors of the permeability tensor.

[0038] This invention provides a method for determining the permeability tensor of a three-dimensional fractured rock mass based on unidirectional permeability. For a rock mass with well-developed fractures, the method involves obtaining the statistical regularity of the rock mass's structural surfaces, establishing a three-dimensional fracture network model, obtaining two-dimensional trace information of each orthogonal section using a three-set orthogonal section cutting model, establishing the theoretical relationship of permeability in all directions of the three-dimensional rock mass through the trace information of each section, and substituting the permeability in the known direction into the theoretical relationship of permeability in all directions to obtain the permeability tensor of the fractured rock mass.

[0039] The advantages of this invention are as follows: For rock masses with densely developed fractures, considering the influence of the geometric characteristics of structural planes on permeability anisotropy, and combining the mathematical properties of the permeability tensor, a relationship between permeabilities in three-dimensional space is established. This allows for the determination of the permeability tensor of the three-dimensional permeability of the fractured rock mass when the permeability in a certain direction is known. The method provided by this invention is simple to operate and has an intuitive structure, solving the problem of the difficulty in determining the permeability tensor of a three-dimensional fracture network, greatly reducing the workload of field experiments, and thus reducing the manpower and material resources required for engineering projects. Attached Figure Description

[0040] Figure 1 The flowchart illustrates the method for determining the permeability tensor of a three-dimensional fractured rock mass based on unidirectional permeability, as provided in this invention.

[0041] Figure 2 This is a schematic diagram of the three-dimensional fracture network numerical model in an embodiment of the present invention.

[0042] Figure 3 This is a schematic diagram of three sets of mutually orthogonal cross sections cutting through the rock mass in an embodiment of the present invention.

[0043] Figures 4a-4cThese are schematic diagrams of the anisotropic ellipses of seepage at each orthogonal cross-section in the embodiments of the present invention; wherein: Figure 4a A diagram illustrating the anisotropic ellipse of seepage at the xy section; Figure 4b A diagram illustrating the anisotropic ellipse of seepage at the xz section; Figure 4c This is a diagram of anisotropic ellipse seepage at the yz section.

[0044] Figure 5 This is a schematic diagram of the anisotropic ellipsoid of seepage in fractured rock mass in an embodiment of the present invention. Detailed Implementation

[0045] The present invention will be further described below with reference to the accompanying drawings and specific embodiments.

[0046] like Figure 1 As shown, a method for determining the permeability tensor of a three-dimensional fractured rock mass based on unidirectional permeability includes the following steps:

[0047] S1. Analyze the development of rock mass structural surfaces in the test area through outdoor observation to obtain geometric information of the rock mass structural surfaces;

[0048] The statistical regularity of the geometric parameters of the rock strata structure is shown in Table 1. The average opening of each group of fractures is 1e-4m.

[0049] Table 1 Statistical patterns of geometric parameters of rock mass structural surfaces

[0050]

[0051] S2. Based on the geometric information of the rock mass structure surface in step S1, a three-dimensional fracture network model is established using numerical software.

[0052] The three-dimensional fracture network model established by numerical software is as follows: Figure 2 As shown.

[0053] S3. Establish three sets of mutually orthogonal cross sections to cut the three-dimensional fracture network model established in step S2. The cross sections intersect with the three-dimensional fracture network to form traces. A schematic diagram of the three sets of mutually orthogonal cross sections cutting the rock mass is shown below. Figure 3 As shown.

[0054] S4. Statistical information on the traces on each cross section in step S3; the statistical rules of the geometric information of the crack traces on each orthogonal cross section are shown in Table 2.

[0055] Table 2 Statistical patterns of geometric information on crack traces at various orthogonal cross sections.

[0056]

[0057]

[0058] S5. Based on the trace information of each section in step S4, determine the cross-sectional seepage anisotropy ellipse;

[0059] The anisotropic ellipse of seepage is defined as an ellipsoid obtained by fitting a standard permeability to a sphere with a radius equal to the square root of the ratio of the permeability to the standard permeability in each seepage direction in three-dimensional space. In step S5, the permeability ratio of the cross section is calculated using formula (1).

[0060] According to such Figure 3 In the coordinate system shown, the positive x-direction is chosen as the standard permeability for the xy section, the positive x-direction as the standard seepage direction for the xz section, and the positive y-axis direction as the standard seepage direction for the yz plane. The anisotropic ellipse of seepage calculated for each section is shown below. Figures 4a-4c As shown. Among them, Figure 4c The blue ellipse in the middle is the anisotropic ellipse of seepage under the condition that the positive y-axis direction is taken as the standard seepage direction for the yz section.

[0061] S6. Based on the anisotropic ellipses of seepage at each cross section obtained in step S5, determine the three-dimensional anisotropic ellipsoid of seepage.

[0062] In this process, the anisotropic ellipse of seepage at each cross section needs to be converted to the same standard permeability.

[0063] The anisotropic ellipse of seepage at section yz is transformed from having the positive y-axis as the standard seepage direction to having the positive x-axis as the standard seepage direction, resulting in a new form of anisotropic ellipse of seepage, as shown below. Figure 4c As shown in the red ellipse in the middle.

[0064] The mathematical expressions for the seepage anisotropic ellipsoids of the xy, xz, and yz sections are as follows:

[0065]

[0066] The mathematical expression for the three-dimensional spatial seepage anisotropic ellipsoid obtained from the parameter coefficients of the three anisotropic ellipses in formula (2) is as follows:

[0067] x 2 +0.36y 2 +0.38z 2 +0.36xy-1.01xz-0.02yz=1(3)

[0068] The obtained anisotropic ellipsoid of seepage is as follows Figure 5 As shown.

[0069] S7. Substitute the known unidirectional permeability into the three-dimensional spatial anisotropic ellipsoid of seepage determined in step S6 to determine the permeability ellipsoid, thereby obtaining the rock mass permeability tensor.

[0070] The known unidirectional permeability corresponds to the seepage direction in the positive x-axis direction, and its permeability is 1.5e-12m. 2 .

[0071] Substituting the known unidirectional permeability into the anisotropic ellipsoid of the seepage, we obtain the principal permeability coefficients of the permeability tensor. The corresponding direction vector is

[0072] It should be understood that the embodiments are for illustrative purposes only and are not intended to limit the scope of the invention. Furthermore, it should be understood that after reading the description of this invention, those skilled in the art can make various alterations or modifications to the invention, and these equivalent forms also fall within the scope defined by the appended claims.

Claims

1. A method for determining the permeability tensor of a three-dimensional fractured rock mass based on unidirectional permeability, characterized in that: The method includes the following steps: S1. Analyze the development of rock mass structural surfaces in the test area through outdoor observation to obtain geometric information of the rock mass structural surfaces; S2. Based on the geometric information of the rock mass structure surface in step S1, establish a three-dimensional fracture network model; S3. Establish three sets of mutually orthogonal cross sections, cut the three-dimensional fracture network model established in step S2, and the cross sections intersect with the three-dimensional fracture network to form traces; S4. Statistical analysis of trace information on each cross section in step S3; S5. Based on the trace information of each section in step S4, determine the cross-sectional seepage anisotropy ellipse; S6. Based on the anisotropic ellipses of seepage at each cross section obtained in step S5, determine the three-dimensional anisotropic ellipsoid of seepage. S7. Substitute the known unidirectional permeability into the three-dimensional spatial anisotropic ellipsoid of seepage determined in step S6 to determine the permeability ellipsoid, thereby obtaining the rock mass permeability tensor. In step S5, the determination of the anisotropic ellipse of the cross-section seepage specifically includes the following steps: S510. Select a certain seepage direction on the cross section as the standard seepage direction of the cross section, and define the permeability in this direction as the standard permeability of the cross section. S520. Based on the geometric statistical information of the cross-section trace, the theoretical ratio of the permeability in the remaining seepage directions of the cross-section to the standard permeability of the cross-section is calculated using the following formula (1), expressed as M. 1f Where f = 2, 3, ..., F: （1） in, M 12 Represents any two seepage directions on the cross section i 2 and i The penetration rate corresponding to 1 k 2 to k The value of 1, and its subscript, can be adjusted according to different situations; J It is the number of fracture groups. j Refers to the first j Group of fracture groups, j = 1,2,..., J ; λ jm It is the first j Linear density in the average normal direction of each fracture group; n jm It is the first j The average normal direction of the group of fractures; I It is the first j The total number of fractures in a fracture group. i Refers to the first j The first in the group of fractures i Cracks; n ji Refers to the first j The first group of fracture groups i The normal direction of the crack; t j It is the first j The ratio of the hydraulic opening of the first fracture group to the hydraulic opening of the second fracture group; S530, with the origin of the coordinate axis as the center, and Draw an anisotropic ellipse with radius along each cross section and each seepage direction to obtain the corresponding ellipse equation; In step S6, the three-dimensional spatial anisotropic ellipsoid is: an ellipsoid obtained by fitting a certain permeability as the standard permeability and the square root of the ratio of the permeability in each seepage direction in three-dimensional space to the standard permeability as the radius.

2. The method for determining the permeability tensor of a three-dimensional fractured rock mass based on unidirectional permeability according to claim 1, characterized in that: In step S1, the geometric information includes: the number of rock mass structural planes, their shape, attitude, aperture, volume density, and size.

3. The method for determining the permeability tensor of a three-dimensional fractured rock mass based on unidirectional permeability according to claim 1, characterized in that: In step S4, the trace information includes: number of trace groups, attitude, opening degree, linear density, areal density, and trace length.

4. The method for determining the permeability tensor of a three-dimensional fractured rock mass based on unidirectional permeability according to claim 1, characterized in that: In step S5, the cross-sectional anisotropic ellipse is an ellipse obtained by fitting a certain permeability as the standard permeability and using the square root of the ratio of the permeability in each seepage direction on the cross-section to the standard permeability as the radius.

5. The method for determining the permeability tensor of a three-dimensional fractured rock mass based on unidirectional permeability according to claim 1, characterized in that: Step S6, determining the three-dimensional spatial anisotropic ellipsoid of seepage specifically includes the following steps: S610. Establish a three-dimensional coordinate system with three sets of mutually orthogonal cross sections as each coordinate plane, wherein the xy plane, xz plane and yz plane coincide with the cross sections respectively; S620. Adjust the permeability anisotropic ellipse on each of the three orthogonal sections so that the three anisotropic ellipses have the same standard permeability. S630. Convert the permeation anisotropic ellipse of the three orthogonal sections adjusted in step S620 into a general form to obtain the coefficients of each variable. S640. Substitute the coefficients of each variable obtained in step S630 into the general equation of the ellipsoid to obtain the three-dimensional spatial seepage anisotropic ellipsoid.

6. The method for determining the permeability tensor of a three-dimensional fractured rock mass based on unidirectional permeability according to claim 5, characterized in that: Step S620 specifically includes the following steps: S621. For each cross section, establish the original standard permeability k. m Corresponding direction and newly determined standard permeability k n The coplanar cross sections in the corresponding directions are used to calculate k based on the geometric information of the traces of the coplanar cross sections. n / k m The theoretical value is denoted as M. mn ; S622. The dimensions of the anisotropic ellipse of seepage based on the original standard permeability are enlarged to the original dimensions. times.

7. The method for determining the permeability tensor of a three-dimensional fractured rock mass based on unidirectional permeability according to claim 1, characterized in that: Step S7 specifically includes the following steps: S701, Establishing a known unidirectional permeability k p Corresponding direction and standard permeability of the anisotropic ellipsoid of seepage in three-dimensional space k q The coplanar cross sections in the corresponding directions are used to calculate k based on the geometric information of the traces of the coplanar cross sections. p / k q The theoretical value is denoted as M. qp ; S702. Enlarge the dimensions of the three-dimensional anisotropic ellipsoid from step S701 to its original dimensions. By multiplying the permeability of the known direction, a three-dimensional spatial anisotropic ellipsoid of permeability is obtained under the new standard permeability. S703. Reduce the size of the three-dimensional spatial anisotropic ellipsoid of the new standard permeability obtained in step S702 to its original size. Thus, a osmotic ellipsoid is obtained; S704. Based on the permeability ellipsoid, determine the three principal permeability values ​​and direction vectors of the permeability tensor.

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