Numerical Analysis Method and System for Rock Mass Joint Morphology Feature Model Based on Spatial Delaunay Triangulation

Abstract

The present invention provides a numerical analysis method and system for a rock mass joint morphology feature model based on spatial Delaunay triangulation, which relates to the technical field of rock mass morphology analysis. It includes establishing a coordinate system, collecting point cloud data, performing triangulation division, and processing the point cloud data to generate anisotropic parameters and joint anisotropy coefficients for reflecting anisotropic characteristics. By comprehensively considering the influences of triangulation and quadrilateral division on joint morphology characteristics and anisotropy evaluation, the present invention first divides the triangulation into triangulation A and triangulation B, which can more precisely reflect the characterization quantities of joint morphology characteristics. And based on triangulation A and triangulation B, formulas for triangulation A, triangulation B, and quadrilateral division for reflecting the surface roughness of the joint surface are generated, and various division methods are analyzed to find the optimal division method under different conditions, making the numerical analysis more accurate.

Description

Technical Field

[0001] The present invention relates to the technical field of rock mass morphology analysis, and specifically to a numerical analysis method and system for the morphological characteristics model of rock mass joints based on spatial Delaunay triangulation. Background Technique

[0002] A large number of discontinuous joints are contained in the rock mass structure, and joints are the fundamental reasons for the discontinuity, anisotropy, and inhomogeneity of the rock mass. Therefore, studying the mechanical properties of joints is of great significance for analyzing the instability problem of rock masses. As one of the important factors affecting the shear behavior of joints, the morphological characteristics of joints have a complex surface morphology and great randomness. When using 3D scanning software to analyze the geomorphic features and using 3D parameters to evaluate joints, the first thing to do is to perform mesh triangulation on the digital model of the joints. However, the current triangulation methods are not unified. When analyzing the point cloud data obtained by 3D scanning, the comparison method and the parameter evaluation method are used to evaluate the morphological characteristics of joints. The specific process of evaluating the morphological characteristics of joints by the comparison method is to first extract several 2D contour lines on the joint surface using a 3D scanner, and then evaluate the value of its joint roughness coefficient by comparing with 10 standard contour curves. Although this method is simple to operate, the reliability of the evaluated joint roughness coefficient value is too dependent on personal engineering experience and has great subjectivity. When using the parameter method to evaluate the morphological characteristics of joints, multiple profile lines are usually selected on the joint surface, and then 2D parameters are used to quantitatively evaluate them. The function fitting relationship is used to determine the value of its joint roughness coefficient, and the average value of the joint roughness coefficient values of these profile lines is used as the roughness of the joint. This method has simple data processing, but only considers the morphological characteristics of the selected 2D profile lines, and the geometric surface information revealed is limited, which will lead to the problem of incomplete description of the joint surface characteristics and cannot effectively evaluate the anisotropic morphological characteristics of joints.

[0003] The above information disclosed in the background section is only used to enhance the understanding of the background of the present disclosure, and therefore it may include information that does not constitute the prior art known to those of ordinary skill in the art. Summary of the Invention

[0004] The purpose of the present invention is to provide a numerical analysis method and system for the morphological characteristics model of rock mass joints based on spatial Delaunay triangulation to solve the problems raised in the above background technique.

[0005] To achieve the above purpose, the present invention provides the following technical solutions:

[0006] A numerical analysis method for the morphological characteristics model of rock mass joints based on spatial Delaunay triangulation, the specific steps include:

[0007] S1. Establish a three-dimensional coordinate system and obtain the three-dimensional point cloud data of the target area topography through 3D scanning;

[0008] S2. Triangulate all four adjacent three-dimensional point cloud data into triangles, and perform correlation analysis on all four adjacent three-dimensional point cloud data to generate the center distance R and the circumradius d;

[0009] S3. Divide the triangles with R greater than d into triangulation B, and divide the triangles with R not greater than d into triangulation A;

[0010] S4. Perform correlation analysis on the three-dimensional point cloud data to generate the root mean square gradient and the joint roughness index;

[0011] S5. Based on the integral forms of the root mean square gradient and the joint roughness index, derive the formulas for triangulation A and triangulation B;

[0012] S6. Analyze the formulas of the four adjacent three-dimensional point cloud data with the maximum empty circle as the criterion to generate the quadrilateral meshing parameter formula;

[0013] S7. Perform correlation analysis on the triangulation A, triangulation B, and the quadrilateral meshing parameter formula to generate the anisotropy parameter and the joint anisotropy coefficient;

[0014] S8. Analyze the stability of the meshing method.

[0015] Further, the three-dimensional coordinate system includes the XOY plane formed by the X-axis and the Y-axis, and the Z-axis perpendicular to the XOY plane and intersecting the X-axis and the Y-axis. The 3D scanning uses three-dimensional laser scanning, and the projection distances of adjacent three-dimensional point cloud data on the XOY plane are the same.

[0016] Further, the triangulation method uses the Delaunay triangulation method. Perform correlation analysis on all four adjacent three-dimensional point cloud data to generate the center distance d and the circumradius R. The formulas are as follows:

[0017] Among them, a, b, and c are the three side lengths of the triangle formed by three of the four adjacent three-dimensional point cloud data, is the coordinate of the circumcenter of the triangle, is the coordinate of the fourth point, S is the area of the triangle. The center distance d is used to reflect the distance between the circumcenter of the triangle and the fourth point, and the circumradius R is used to reflect the size of the circumradius of the triangle.

[0018] Further, perform correlation analysis on the three-dimensional point cloud data to generate the root mean square gradient and the joint roughness index , and the formula is as follows:

[0019]

[0020] Among them, and are respectively the nominal lengths of four adjacent three-dimensional point cloud data along the x-axis and y-axis, is used to represent the area of four adjacent three-dimensional point cloud data projected on the XOY plane, is the actual area of the joint surface, is the projected area of the joint surface on the XOY plane. The root mean square gradient and the joint surface roughness index are both used to reflect the surface roughness.

[0021] Furthermore, based on the integral forms of the root mean square gradient and the joint roughness index, the formulas for triangulation A and triangulation B are derived. The formulas are as follows:

[0022]

[0023] Among them, ;

[0024]

[0025] Among them, ;

[0026] Among them, is the number of point clouds along the x-axis, is the number of point clouds along the y-axis, and are respectively the sampling intervals along the x-axis and y-axis, represents the point cloud coordinates at the i-th point cloud along the x-axis and the j-th point cloud along the y-axis on the XOY plane, and , and , and , , respectively represent the coordinate values of the point cloud at the i-th point cloud along the x-axis and the j-th point cloud along the y-axis on the x-axis and y-axis on the XOY plane;

[0027]

[0028]

[0029]

[0030]

[0031] , , represent the lengths of the three sides of the triangular element under triangulation A, respectively; , , represent the lengths of the three sides of the triangular element under triangulation B, respectively; , represents the semi-perimeter of the triangle;

[0032] Among them, the triangulation A parameters , are used to reflect the roughness of the joint surface of triangulation A, and the B triangulation parameters , are used to reflect the roughness of the joint surface of triangulation B.

[0033] Furthermore, based on the maximum empty circle criterion, all four adjacent three-dimensional point cloud data are analyzed to generate a quadrilateral meshing parameter formula, and the formula is:

[0034]

[0035]

[0036] Among them, , , , represent the lengths of the four sides of the quadrilateral element under quadrilateral meshing, respectively; B and D are the two diagonals of the quadrilateral element under quadrilateral meshing, and the comprehensive triangulation parameters , are both used to reflect the roughness index of the joint surface generated by combining triangulation A and triangulation B.

[0037] Furthermore, a correlation analysis is performed on triangulation A, triangulation B, and the quadrilateral meshing parameter formula to generate the anisotropy parameter K and the joint anisotropy coefficient , and the formula is:

[0038] Among them, represent the three-dimensional topography characterization parameters along the X-axis direction and the Y-axis direction, respectively, = 1 indicates that the joint is isotropic, the smaller the more significant the degree of anisotropic characteristics, DAC is the joint anisotropy coefficient, and the value range of the joint anisotropy coefficient DAC is [0, 1). When DAC = 0, the topography characteristics of the joint are isotropic; and the larger the DAC, the greater the degree of joint anisotropy, and its topography characteristics are more affected by direction.

[0039] Further, in S8, when collecting three-dimensional point cloud data, different point spacings are set, and the influence of the parameter formulas of triangulation A, triangulation B, and quadrilateral triangulation on the joint spacing is analyzed; the influence of the parameter formulas of triangulation A, triangulation B, and quadrilateral triangulation on the size effect of joints is analyzed; the three-dimensional point cloud data of the target area topography obtained by 3D scanning is printed by a 3D printer to make a joint model, the joint model is cast with a rock-like material, and uniaxial compression and tensile tests are performed on the joint model.

[0040] Further, the point spacings are respectively set to 0.044 mm, 0.25 mm, 0.50 mm, and 1.00 mm. The eigenvalues of the parameter formulas of triangulation A, triangulation B, and quadrilateral triangulation decrease with the increase of the sampling spacing. Among them, the demarcation point between triangulation A and triangulation B is 14 mm; the influence of the parameter formulas of triangulation A, triangulation B, and quadrilateral triangulation on the size effect of joints is analyzed, and the joints show three regularities: positive size effect, negative size effect, and no size effect. The size effects of triangulation A and triangulation B on joints are consistent.

[0041] The present invention also provides a numerical analysis system for the morphological feature model of rock mass joints based on spatial Delaunay triangulation. The analysis system is used to execute the numerical analysis method for the morphological feature model of rock mass joints based on spatial Delaunay triangulation, including:

[0042] A point cloud data acquisition module, which is used to obtain three-dimensional point cloud data of the target area topography by 3D scanning;

[0043] A point cloud data analysis module, which is used to divide triangles according to triangulation for all four adjacent three-dimensional point cloud data, and perform correlation analysis on all four adjacent three-dimensional point cloud data to generate the center distance R and the circumradius d;

[0044] A division module, which is used to divide the triangles with R greater than d into triangulation B, and divide the triangles with R not greater than d into triangulation A;

[0045] A roughness analysis module, which is used to perform correlation analysis on three-dimensional point cloud data to generate the root mean square gradient and the joint roughness index; based on the integral forms of the root mean square gradient and the joint roughness index, the formulas of triangulation A and triangulation B are derived; taking the largest empty circle as the criterion, the formulas of four adjacent three-dimensional point cloud data are analyzed to generate the quadrilateral triangulation parameter formula;

[0046] An anisotropy analysis module, which is used to perform correlation analysis on the parameter formulas of triangulation A, triangulation B, and quadrilateral triangulation to generate anisotropy parameters and joint anisotropy coefficients and verify the applicability and stability of triangulation A and triangulation B.

[0047] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0048] By comprehensively considering the effects of triangular meshing and quadrilateral meshing on the morphological characteristics of joints and anisotropy evaluation, the present invention first divides triangular meshing into triangular meshing A and triangular meshing B, which can more precisely reflect the characterization quantities of joint morphological characteristics. Based on triangular meshing A and triangular meshing B, formulas for triangular meshing A, triangular meshing B, and quadrilateral meshing for reflecting the surface roughness of the joint surface are generated, and anisotropy parameters and joint anisotropy coefficients for reflecting anisotropy characteristics are generated. The stability and applicability of triangular meshing A and triangular meshing B of the present invention are verified, the evaluation criteria are unified, and a more detailed quantitative evaluation of the joint surface is carried out. BRIEF DESCRIPTION OF THE DRAWINGS

[0049] Figure 1 is a schematic diagram of the overall method flow of the present invention;

[0050] Figure 2 is a schematic diagram of the overall system flow of the present invention;

[0051] Figure 3 is a schematic diagram of the influence of the meshing method of the present invention on the joint spacing effect;

[0052] Figure 4 is a schematic diagram of the influence of the meshing method of the present invention on the joint size effect. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0053] In order to make the objectives, technical solutions, and advantages of the present invention clearer and more understandable, the present invention will be further described in detail below in conjunction with specific embodiments.

[0054] It should be noted that unless otherwise defined, the technical terms or scientific terms used in the present invention should have the ordinary meanings understood by those with ordinary skills in the field to which the present invention belongs. The "first", "second", and similar terms used in the present invention do not indicate any order, quantity, or importance, but are only used to distinguish different components. Words such as "including" or "comprising" mean that the elements or objects appearing before this word cover the elements or objects listed after this word and their equivalents, without excluding other elements or objects. Words such as "connected" or "linked" are not limited to physical or mechanical connections, but may include electrical connections, whether direct or indirect. "Up", "down", "left", "right", etc. are only used to represent relative positional relationships, and when the absolute position of the object being described changes, the relative positional relationship may also change accordingly.

[0055] Example:

[0056] Please refer to Figures 1-4, the present invention provides a technical solution:

[0057] A numerical analysis method for the morphological feature model of rock mass joints based on spatial Delaunay triangulation, the specific steps include:

[0058] Step 1, establish a three-dimensional coordinate system, and obtain the three-dimensional point cloud data of the target area morphology through 3D scanning;

[0059] In order to perform data analysis on the target area, first establish a three-dimensional coordinate system, and obtain the three-dimensional point cloud data of the target area morphology through 3D scanning. The three-dimensional coordinate system includes the XOY plane formed by the X-axis and the Y-axis, and the Z-axis perpendicular to the XOY plane and intersecting the X-axis and the Y-axis. The 3D scanning uses three-dimensional laser scanning, and the projection distances of adjacent three-dimensional point cloud data on the XOY plane are the same.

[0060] For the convenience of analysis, the point cloud data of the joints is often processed into equally spaced points on the XOY plane, and then the rock mass joints are discretized into micro unit bodies. The morphological features of the rock mass joints are quantitatively characterized by statistical parameters. The common triangulation methods for quantitatively characterizing the joint morphology can be roughly divided into quadrilateral triangulation and triangular triangulation. And the triangular triangulation can be divided into triangular triangulation A and triangular triangulation B.

[0061] To solve the problem of uncertain triangular triangulation, quadrilateral triangulation can be used to replace the two triangular triangulations. This approach reduces the program calculation amount by half, thereby improving the calculation speed. Due to the very complex morphological features of the joints, the four points involved in some quadrilateral unit bodies are not in the same plane. At this time, according to the geometric coordinates of the four points, the least squares method can be used to perform plane fitting on each triangulated quadrilateral unit. This method will cause a distortion problem of the joints. To avoid the distortion problem, based on Delaunay triangulation, Delaunay triangulation is an important technique in computational geometry for dividing a set of points into several triangles in a plane or higher-dimensional space. The present invention analyzes using the following steps:

[0062] Step 2, divide triangles for all four adjacent three-dimensional point cloud data according to triangulation, and perform correlation analysis on all four adjacent three-dimensional point cloud data to generate the center distance R and the circumradius d; the triangulation method uses the Delaunay triangulation method, and perform correlation analysis on all four adjacent three-dimensional point cloud data to generate the center distance d and the circumradius R. The formula is:

[0063] where a, b, and c are the three side lengths of the triangle formed by three of the four adjacent three-dimensional point cloud data, is the coordinate of the circumcenter of the triangle, It is the fourth point coordinate, S is the area of the triangle, the center distance d is used to reflect the distance between the circumcenter of the triangle and the fourth point, and the circumradius R is used to reflect the size of the circumradius of the triangle.

[0064] Step 3: Divide the triangles with R > d into triangulation B, and divide the triangles with R ≤ d into triangulation A;

[0065] If the radius R is greater than or equal to d, it means that the fourth point is inside the circumsphere, and the triangle at this time is not a Delaunay triangle, and "edge swapping" is required, that is, changing from triangulation A to triangulation B. If the radius R is less than d, it means that the fourth point D is outside the circumsphere, and the triangle at this time is a Delaunay triangle, and its triangulation method remains unchanged.

[0066] In order to more comprehensively study whether the spatial Delaunay triangulation affects the joint morphological characteristics, it is necessary to discretize the morphological characteristic parameters based on the spatial Delaunay triangulation.

[0067] Commonly used morphological characteristic parameters include root mean square gradient and joint roughness index.

[0068] Step 4: Conduct a correlation analysis on the three-dimensional point cloud data to generate the root mean square gradient and joint roughness index;

[0069] Conduct a correlation analysis on the three-dimensional point cloud data to generate the root mean square gradient and joint roughness index , and the formulas are as follows:

[0070]

[0071] Among them, and are the nominal lengths of four adjacent three-dimensional point cloud data along the x-axis and y-axis respectively, is used to represent the area of the projection of four adjacent three-dimensional point cloud data on the XOY plane, is the actual area of the joint surface, is the projected area of the joint surface on the XOY plane. Both the root mean square gradient and the joint surface roughness index are used to reflect the surface roughness.

[0072] Step 5: Given that the spatial Delaunay triangulation is a combination of triangulation A and triangulation B, based on the integral forms of the root mean square gradient and joint roughness index, derive the formulas for triangulation A and triangulation B;

[0073] Based on the integral forms of the root mean square gradient and joint roughness index, derive the formulas for triangulation A and triangulation B, and the formulas are as follows:

[0074]

[0075] Among them, ;

[0076]

[0077] Among them, ;

[0078] Among them, is the number of point clouds along the x-axis, is the number of point clouds along the y-axis, and are the sampling intervals along the x-axis and the y-axis respectively, represents the point cloud coordinates at the i-th point cloud along the x-axis and the j-th point cloud along the y-axis on the XOY plane, and , and , and , , respectively represent the coordinate values of the point cloud on the x-axis and the y-axis at the i-th point cloud along the x-axis and the j-th point cloud along the y-axis on the XOY plane;

[0079]

[0080]

[0081]

[0082]

[0083] , , respectively represent the lengths of the three sides of the triangular microelement under the triangular mesh A; , , respectively represent the lengths of the three sides of the triangular microelement under the triangular mesh B; , represents the semi-perimeter of the triangle;

[0084] Among them, among them, the triangular mesh A parameters , are used to reflect the roughness of the joint surface of the triangular mesh A, and the triangular mesh B parameters , are used to reflect the roughness of the joint surface of the triangular mesh B.

[0085] Step 6: Taking the largest empty circle as the criterion, select appropriate meshing methods for different quadrilateral elements, so as to calculate the parameter values of the spatial Delaunay mesh. To facilitate the comparison of the effects of different meshing methods on the joint morphological characteristics, generate the quadrilateral meshing parameter formula;

[0086] Taking the largest empty circle as the criterion, analyze all four adjacent three-dimensional point cloud data, and generate the quadrilateral meshing parameter formula. The formula is as follows:

[0087]

[0088]

[0089] Among them, , , , respectively represent the lengths of the four sides of the quadrilateral microelement under quadrilateral meshing; B and D are the two diagonals of the quadrilateral microelement under quadrilateral meshing. The comprehensive triangulation parameters 、 are both used to reflect the roughness index of the joint surface comprehensively generated by combining triangulation A and triangulation B.

[0090] To quantitatively characterize the influence of the above meshing methods on the anisotropic characteristics of the same joint, the present invention adopts the following steps for analysis:

[0091] Step 7: Conduct a correlation analysis on triangulation A, triangulation B, and the quadrilateral meshing parameter formula to generate anisotropic parameters and joint anisotropic coefficients.

[0092] Conduct a correlation analysis on triangulation A, triangulation B, and the quadrilateral meshing parameter formula to generate anisotropic parameter K and joint anisotropic coefficient , and the formula is as follows:

[0093] Among them, respectively represent the three-dimensional morphology characterization parameters along the X-axis direction and the Y-axis direction, represents the joint surface characteristics measured along the X-axis direction, such as the width, spacing or other relevant parameters of the joint, represents the corresponding characteristics measured along the Y-axis direction, When The smaller the degree of anisotropic features, the larger the value of DAC, where DAC is the joint anisotropy coefficient. The value range of the joint anisotropy coefficient DAC is [0, 1). When DAC = 0, the morphological features of the joint are isotropic; and the larger the DAC, the greater the degree of joint anisotropy, and its morphological features are more affected by the direction. By analyzing the collected data, the K value of triangulation A and triangulation B is 0.75.

[0094] Step 8: Analyze the stability of the triangulation method.

[0095] The spacing of the point clouds extracted on the joint surface is not uniform. The measurement of joint morphological features is affected by the point spacing and has an interval effect. When collecting three-dimensional point cloud data, different point spacings are set to analyze the influence of triangulation A, triangulation B, and the quadrilateral triangulation parameter formula on the joint spacing; analyze the influence of triangulation A, triangulation B, and the quadrilateral triangulation parameter formula on the size effect of the joint; the statistical parameters decrease as the sampling interval increases, and the attenuation amplitude gradually increases.

[0096] The three-dimensional point cloud data of the target area morphology obtained by 3D scanning is used to print a joint model through a 3D printer. The joint model is cast with a rock-like material, and uniaxial compression and tensile tests are performed on the joint model.

[0097] Refer to Figure 3 , the point spacings are set to 0.044 mm, 0.25 mm, 0.50 mm, and 1.00 mm respectively. The eigenvalues of triangulation A, triangulation B, and the quadrilateral triangulation parameter formula decrease as the sampling spacing increases. Among them, the demarcation point between triangulation A and triangulation B is at 14 mm; it shows that the spatial Delaunay triangulation has a more stable spacing effect.

[0098] Refer to Figure 4 , analyze the influence of triangulation A, triangulation B, and the quadrilateral triangulation parameter formula on the size effect of the joint. Among them, the joint shows three regularities: positive size effect, negative size effect, and no size effect. Triangulation A and triangulation B have the same effect on the joint size effect.

[0099] Thus, the stability and applicability of triangulation A and triangulation B can be verified.

[0100] Refer to Figure 2 , the present invention also provides a numerical analysis system for the morphological features model of rock mass joints based on spatial Delaunay triangulation. The analysis system is used to execute the numerical analysis method for the morphological features model of rock mass joints based on spatial Delaunay triangulation, including:

[0101] A point cloud data acquisition module, which is used to obtain three-dimensional point cloud data of the target area morphology through 3D scanning;

[0102] A point cloud data analysis module, configured to triangulate all four adjacent three-dimensional point cloud data, perform correlation analysis on all four adjacent three-dimensional point cloud data, and generate a center distance R and a circumradius d;

[0103] A partitioning module, configured to partition the triangles with R greater than d into triangulation B, and partition the triangles with R not greater than d into triangulation A;

[0104] A roughness analysis module, configured to perform correlation analysis on three-dimensional point cloud data to generate a root mean square gradient and a joint roughness index; based on the integral forms of the root mean square gradient and the joint roughness index, derive the formulas for triangulation A and triangulation B; analyze the formulas of the four adjacent three-dimensional point cloud data based on the maximum empty circle criterion to generate a quadrilateral partitioning parameter formula;

[0105] An anisotropy analysis module, configured to perform correlation analysis on triangulation A, triangulation B, and the quadrilateral partitioning parameter formula to generate an anisotropy parameter and a joint anisotropy coefficient, and analyze the stability of the partitioning method.

[0106] The above formulas are all dimensionless and take their numerical calculations. The formulas are obtained by collecting a large amount of data for software simulation to obtain a formula closest to the actual situation. The preset parameters in the formulas are set by those skilled in the art according to the actual situation.

[0107] The above embodiments can be implemented in whole or in part by software, hardware, firmware, or any other combination. When implemented using software, the above embodiments can be implemented in whole or in part in the form of a computer program product. Those skilled in the art can realize that the units and algorithm steps of each example described in combination with the embodiments disclosed herein can be implemented by electronic hardware, or by a combination of computer software and electronic hardware. Whether these functions are executed by hardware or software methods depends on the specific application and design constraints of the technical solution.

[0108] The units described as separate components may or may not be physically separated, and the components shown as units may or may not be physical units. They can be located in one place or distributed to multiple network units. Some or all of the units can be selected according to actual needs to achieve the purpose of the solution of this embodiment.

[0109] The above is only a specific implementation manner of the present application, but the protection scope of the present application is not limited thereto. Any person skilled in the art can easily think of changes or substitutions within the technical scope disclosed in the present application, and all should be covered within the protection scope of the present application.

Claims

1. Numerical analysis method for rock joint morphology feature model based on spatial Delaunay triangulation, characterized in that, The specific steps include: S1. Establish a three-dimensional coordinate system and obtain the three-dimensional point cloud data of the target area topography through 3D scanning; S2. Triangulate all four adjacent three-dimensional point cloud data into triangles, and perform correlation analysis on all four adjacent three-dimensional point cloud data to generate the center distance R and the circumradius d; S3. Divide the triangles with R greater than d into triangulation B, and divide the triangles with R not greater than d into triangulation A; S4. Perform correlation analysis on the three-dimensional point cloud data to generate the root mean square gradient and the joint roughness index; S5. Based on the integral forms of the root mean square gradient and the joint roughness index, derive the formulas for triangulation A and triangulation B; S6. Analyze the formulas of all four adjacent three-dimensional point cloud data based on the maximum empty circle criterion to generate the quadrilateral subdivision parameter formula; S7. Perform correlation analysis on triangulation A, triangulation B, and the quadrilateral subdivision parameter formula to generate the anisotropy parameter and the joint anisotropy coefficient; S8. Analyze the stability of the subdivision method; Based on the integral forms of the root mean square gradient and the joint roughness index, derive the formulas for triangulation A and triangulation B. The formulas are as follows: Among them, ； Among them, ; Among them, is the number of point clouds along the x-axis, is the number of point clouds along the y-axis, and are the sampling intervals along the x-axis and the y-axis respectively, represents the point cloud coordinates at the i-th point cloud along the x-axis and the j-th point cloud along the y-axis on the XOY plane, and , and , and , 、 respectively represent the coordinate values of the point cloud on the x-axis and the coordinate values on the y-axis at the i-th point cloud along the x-axis and the j-th point cloud along the y-axis on the XOY plane; , , respectively represent the lengths of the three sides of the triangular element under triangulation A; , , respectively represent the lengths of the three sides of the triangular element under triangulation B; , represents the semi - perimeter of the triangle; Among them, the triangular meshing A parameter , is used to reflect the roughness of the joint surface of the triangular meshing A, and the B triangular meshing parameter , is used to reflect the roughness of the joint surface of the triangular meshing B; Analyze all four adjacent three-dimensional point cloud data based on the maximum empty circle criterion to generate the quadrilateral subdivision parameter formula. The formula is as follows: Among them, , , , respectively represent the lengths of the four sides of the quadrilateral element under quadrilateral subdivision; B and D are respectively the two opposite angles of the quadrilateral element under quadrilateral subdivision. The comprehensive triangulation parameters 、 are both used to reflect the roughness index of the joint surface comprehensively generated by combining triangulation A and triangulation B.

2. The numerical analysis method for the rock mass joint morphology feature model based on spatial Delaunay triangulation according to claim 1, characterized in that: The three-dimensional coordinate system includes the XOY plane formed by the X-axis and the Y-axis, and the Z-axis perpendicular to the XOY plane and intersecting with the X-axis and the Y-axis. The 3D scanning uses three-dimensional laser scanning, and the projection distances of adjacent three-dimensional point cloud data on the XOY plane are the same.

3. The numerical analysis method for the rock joint morphology feature model based on spatial Delaunay triangulation according to claim 2, wherein: The triangulation method uses the Delaunay triangulation method. Perform correlation analysis on all four adjacent three-dimensional point cloud data to generate the center distance d and the circumradius R. The formulas are as follows: Among them, a, b, and c are the three side lengths of a triangle formed by three of four adjacent three-dimensional point cloud data, is the coordinate of the circumcenter of the triangle, is the coordinate of the fourth point, S is the area of the triangle, the center distance d is used to reflect the distance between the circumcenter of the triangle and the fourth point, and the circumradius R is used to reflect the size of the circumradius of the triangle.

4. The numerical analysis method for the rock joint morphology feature model based on spatial Delaunay triangulation according to claim 3, wherein: Perform correlation analysis on 3D point cloud data to generate the root mean square gradient , and the joint roughness coefficient . The formula used is as follows: Among them, and are the nominal lengths of four adjacent three-dimensional point cloud data along the x-axis and y-axis respectively, is used to represent the area of four adjacent three-dimensional point cloud data projected on the XOY plane, is the actual area of the joint surface, is the projected area of the joint surface on the XOY plane. The root mean square gradient and the joint surface roughness index are both used to reflect the surface roughness.

5. The numerical analysis method for the rock mass joint morphology feature model based on spatial Delaunay triangulation according to claim 1, characterized in that: Perform a correlation analysis on the triangulation A, triangulation B, and the parameter formula of quadrilateral triangulation to generate the anisotropic parameter K and the joint anisotropy coefficient , and the formula used is: Among them, respectively represent three-dimensional topography characterization parameters in the X-axis direction and the Y-axis direction. When it is equal to 1, it means that the joints are isotropic. The smaller it is, the greater the degree of anisotropic characteristics. DAC is the joint anisotropy coefficient, and the value range of the joint anisotropy coefficient DAC is [0, 1). When DAC = 0, the topography characteristics of the joints are isotropic.

6. The numerical analysis method for the rock mass joint morphology feature model based on spatial Delaunay triangulation according to claim 1, characterized in that: In S8, when collecting the three-dimensional point cloud data, set different point spacings, analyze the influence of triangulation A, triangulation B, and the quadrilateral subdivision parameter formula on the joint spacing; analyze the influence of triangulation A, triangulation B, and the quadrilateral subdivision parameter formula on the size effect of the joint; print and produce a joint model by 3D printing the three-dimensional point cloud data of the target area topography obtained by 3D scanning, pour the joint model with a rock-like material, and perform uniaxial compression and tensile tests on the joint model.

7. The numerical analysis method for the rock mass joint morphology feature model based on spatial Delaunay triangulation according to claim 6, wherein: The point spacings are set to 0.044 mm, 0.25 mm, 0.50 mm, and 1.00 mm respectively. The eigenvalues of triangulation A, triangulation B, and the quadrilateral subdivision parameter formula decrease with the increase of the sampling spacing. Among them, the demarcation point between triangulation A and triangulation B is at 14 mm; it shows that the spatial Delaunay triangulation has a more stable spacing effect; analyze the influence of triangulation A, triangulation B, and the quadrilateral subdivision parameter formula on the size effect of the joint. Among them, the joint shows three regularities: positive size effect, negative size effect, and no size effect. The size effects of triangulation A and triangulation B on the joint are the same.

8. Numerical analysis system for the morphological feature model of rock mass joints based on spatial Delaunay triangulation, the analysis system is used to execute the numerical analysis method for the morphological feature model of rock mass joints based on spatial Delaunay triangulation as claimed in claim 1, characterized in that, Including: A point cloud data acquisition module for obtaining the three-dimensional point cloud data of the target area topography through 3D scanning; A point cloud data analysis module, which is used to divide all four adjacent three-dimensional point cloud data into triangles according to triangulation, and perform correlation analysis on all four adjacent three-dimensional point cloud data to generate the center distance R and the circumradius d; A division module, which is used to divide the triangles with R greater than d into triangulation B, and divide the triangles with R not greater than d into triangulation A; A roughness analysis module, which is used to perform correlation analysis on three-dimensional point cloud data to generate the root mean square gradient and the joint roughness coefficient; based on the integral forms of the root mean square gradient and the joint roughness coefficient, derive the formulas for triangulation A and triangulation B; taking the maximum empty circle as the criterion, analyze the formulas of four adjacent three-dimensional point cloud data to generate the quadrilateral division parameter formula; An anisotropy analysis module, which is used to perform correlation analysis on triangulation A, triangulation B, and the quadrilateral division parameter formula to generate the anisotropy parameter and the joint anisotropy coefficient and analyze the stability of the division method.

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