Method for constructing rock joint surface two-dimensional discrete element model based on point cloud data

Abstract

The application discloses a method for constructing a rock joint surface two-dimensional discrete element model based on point cloud data, collects natural rock joint surface three-dimensional point cloud, carries out denoising and center normalization preprocessing on the three-dimensional point cloud, rotates the three-dimensional point cloud after preprocessing to make it parallel to the Z axis of a three-dimensional coordinate system, and screens the three-dimensional point cloud according to a screening radius; projects the screened three-dimensional cloud onto a set plane to obtain two-dimensional point cloud; establishes a two-dimensional coordinate system, and moves the projected two-dimensional point cloud to the first quadrant of the two-dimensional coordinate system; divides the point cloud in the two-dimensional coordinate system into n parts according to the x range of the point cloud, finds the maximum value and the corresponding x value in each part; and outputs the processed point cloud data in a dxf format which is common to discrete element software. Based on the three-dimensional point cloud data of the joint surface, the point cloud data is preprocessed and screened in a target range, and finally a general discrete element modeling format is generated, the three-dimensional joint surface model is converted into a two-dimensional joint model, and the method is suitable for rock mass mechanical test analysis.

Description

Technical Field

[0001] This application relates to the field of rock mechanics experimental technology, specifically to a method for constructing a two-dimensional discrete element model of rock joint surfaces based on point cloud data. Background Technology

[0002] Rock joint surfaces are key factors affecting the mechanical properties and stability of rock masses, and their geometric morphology and spatial distribution significantly influence the mechanical behavior of the rock mass. With the development of 3D scanning technology, point cloud data has become an important tool for describing the characteristics of rock joint surfaces. However, when building 3D joint surface models based on point cloud data for numerical analysis, the large data volume leads to high computational cost and low efficiency. Therefore, current research is still mainly based on 2D numerical models. However, how to scientifically and rationally convert 3D point cloud data into 2D models is an urgent problem to be solved.

[0003] Currently, existing patents provide methods for establishing three-dimensional discrete element models of jointed rock masses based on point cloud data. For example, Chinese patent CN112784403B discloses a numerical simulation method for establishing a discrete element model of jointed rock masses based on point cloud data. Its main steps are: collecting and preprocessing point clouds on the surface of the jointed rock mass; identifying structural surfaces and calculating their attitude parameters based on the simplified point cloud dataset; performing statistical analysis of the structural surface attitude parameters; inputting all structural surface attitude statistical parameters into fracture modeling software to obtain an initial three-dimensional model of the jointed rock mass; using 3D modeling software to convert the initial three-dimensional model of the jointed rock mass into a file type recognizable by the discrete element numerical analysis software; and inputting the file-type recognizable three-dimensional model into numerical simulation software for numerical analysis to generate the final three-dimensional model of the jointed rock mass.

[0004] While the above method can construct a realistic three-dimensional model of rock, it is not suitable for constructing a two-dimensional joint surface model. Summary of the Invention

[0005] In order to solve the above-mentioned technical problems, this application proposes the following technical solution:

[0006] In a first aspect, embodiments of this application provide a method for constructing a two-dimensional discrete element model of rock joint surfaces based on point cloud data, including:

[0007] A 3D laser scanner was used to scan the rock joint surface from multiple angles to obtain a 3D point cloud of the joint surface.

[0008] The three-dimensional point cloud of the joint surface is denoised and center-normalized to obtain the pre-processed three-dimensional point cloud.

[0009] Rotate the preprocessed 3D point cloud to make it parallel to the Z-axis of the 3D coordinate system;

[0010] Based on the rotated 3D point cloud in the 3D coordinate system x shaft and y The maximum and minimum values ​​on the axis are used to obtain the center of the circle. The filtering radius is set, and the 3D point cloud that is retained within the filtering radius is filtered.

[0011] The filtered 3D point cloud is projected onto a set plane to obtain a 2D point cloud;

[0012] Establish a two-dimensional coordinate system and move the projected two-dimensional point cloud to the first quadrant of the two-dimensional coordinate system;

[0013] For two-dimensional point clouds in the first quadrant, x Sort the values ​​in ascending order, and sort them simultaneously. y To maintain the correspondence, based on the point cloud in the two-dimensional coordinate system x The scope divides it into n Find the portion in each portion. y Maximum value and corresponding x value, n The components constitute the two-dimensional contour coordinates of the joint surface;

[0014] The modeling point cloud is obtained based on the two-dimensional contour coordinates of the joint surface, and then the modeling point cloud data is output in the dxf format commonly used by discrete element software.

[0015] In one possible implementation, the step of using a 3D laser scanner to scan the rock joint surface in sections from multiple angles to obtain a 3D point cloud of the joint surface includes:

[0016] Clean the natural jointed surface of the rock and affix markers around the target area;

[0017] Then, using a 3D laser scanner, the joint surface is scanned multiple times from different angles to obtain 3D point cloud data of the rock joint surface.

[0018] In one possible implementation, denoising the 3D point cloud of the joint surface includes:

[0019] For each point in the point cloud Calculate its k The formulas for the mean and standard deviation of the distances to the nearest neighbors are as follows:

[0020] Distance mean:

[0021] In the formula, for The first point j The nearest neighbor point, The distance between two points;

[0022] Distance from standard deviation: ;

[0023] Set the standard deviation scaling factor std_ratio, if The average distance to its neighbors is greater than ,but The point is considered an outlier and is deleted.

[0024] In one possible implementation, the normalization process for the center of the three-dimensional point cloud of the joint surface includes:

[0025] The average coordinates of the denoised point cloud, i.e., the geometric center, are calculated using the following formula:

[0026]

[0027] In the formula, N The total number of points in the point cloud. , , For the first i The coordinates of the points;

[0028] Subtract the coordinates of the geometric center from the coordinates of each point using the following formula:

[0029] .

[0030] In one possible implementation, rotating the preprocessed 3D point cloud to align it parallel to the Z-axis of the 3D coordinate system includes:

[0031] Calculate the covariance matrix of the preprocessed point cloud. C The formula is:

[0032]

[0033] In the formula, p i For the first point cloud i One point; N The total number of points;

[0034] Through formula Eigenvalue decomposition of the covariance matrix yields eigenvalues ​​and eigenvectors. It is a diagonal matrix, and the elements on the diagonal are the eigenvalues ​​of the covariance matrix. V This is an eigenvector matrix, where each column is an eigenvector;

[0035] Then, a rotation matrix is ​​constructed from the eigenvectors. ,in, V i The first covariance matrix is ​​the first... i 1 eigenvector;

[0036] Finally, the formula is used. Rotate the point cloud to obtain the normal direction and z A three-dimensional point cloud parallel to the axis, i.e., a three-dimensional point cloud after rotation.

[0037] In one possible implementation, the step of adjusting the rotated 3D point cloud in a 3D coordinate system... x shaft and y The maximum and minimum values ​​on the axis are used to obtain the center of a circle. A filtering radius is set, and the 3D point cloud within that radius is filtered out, including:

[0038] Determine the 3D point cloud after rotation. x The maximum value x_max and the minimum value x_min on the axis, and in y The maximum value y_max and the minimum value y_min on the axis;

[0039] Calculate the coordinates of center_x, which is (x_max + x_min) / 2, and the coordinates of center_y, which is (y_max + y_min) / 2;

[0040] Set the radius R, and then only keep the point cloud inside the circle with (center_x, center_y) as the center and radius R to obtain the filtered 3D point cloud.

[0041] In one possible implementation, projecting the filtered 3D point cloud onto a predetermined plane to obtain a 2D point cloud includes:

[0042] Define the equation of the projection plane as follows Ax + By + Cz + D =0;

[0043] Based on the known points traversed by this plane The plane normal vector Determine the coefficients of the point method and the point method respectively. ;

[0044] Next, calculate any point in the point cloud. The distance to the projection plane is given by the formula: ;

[0045] Next, calculate the coordinates of the projection point on the projection plane using the following formula: This yields a three-dimensional point cloud projected onto a plane.

[0046] In one possible implementation, establishing a two-dimensional coordinate system and moving the projected two-dimensional point cloud to the first quadrant of the two-dimensional coordinate system includes:

[0047] Define the projection plane and the original 3D coordinate system xoy The direction of the intersection line between the planes is in the two-dimensional coordinate system. x The axis, its basis vectors Normal vector of the projection plane and xoy plane normal vector The result of the cross product;

[0048] Defined relative to the original three-dimensional coordinate system z The axis parallel to the direction is a two-dimensional coordinate system y The axis, its basis vectors (0, 0, 1);

[0049] Through formula Transform the projection points to a two-dimensional coordinate system;

[0050] Finally, all points in the two-dimensional coordinate system x value minus x Minimum value on the axis, y value minus y The minimum value on the axis yields the two-dimensional point cloud in the first quadrant of the two-dimensional coordinate system.

[0051] In one possible implementation, the step of obtaining the modeling point cloud based on the two-dimensional contour coordinates of the joint surface, and then outputting the modeling point cloud data in the DXF format commonly used by discrete element software, includes:

[0052] All points in the two-dimensional profile coordinates of the joint surface in a two-dimensional coordinate system. x value minus x Minimum value on the axis, all y Value minus all points y The average value is used to obtain the modeled point cloud;

[0053] Then, using the Python third-party software library ezdxf, the modeling point cloud data is output in the dxf format commonly used by discrete element software and imported into the discrete element software PFC2D.

[0054] In this embodiment, based on the three-dimensional point cloud data of the joint surface, from the point cloud data preprocessing and the selection of point clouds within the target range to the final generation of the DXF format, which is a common discrete element modeling format, the two-dimensional joint contour and its coordinate values ​​on any required plane are accurately obtained, and the three-dimensional joint surface model is transformed into a two-dimensional joint model, realizing efficient batch processing, which has an important role in promoting the development of the field of rock mechanics testing. Attached Figure Description

[0055] Figure 1 A flowchart illustrating a method for constructing a two-dimensional discrete element model of rock joint surfaces based on point cloud data, provided in an embodiment of this application;

[0056] Figure 2 This is an image of a joint surface in a natural rock.

[0057] Figure 3 for Figure 2 Image of the 3D point cloud of the joint surface;

[0058] Figure 4 To Figure 3 3D image of midpoint cloud after preprocessing and rotation;

[0059] Figure 5 To Figure 3 Top view after preprocessing and rotation of the midpoint cloud;

[0060] Figure 6 To Figure 5 A top view of the filtered point cloud;

[0061] Figure 7 To Figure 6 Point cloud image in the original coordinate system after planar projection of the point cloud;

[0062] Figure 8 For the new coordinate system Figure 7 Midpoint cloud image;

[0063] Figure 9 To Figure 8 Point cloud image after extracting the 2D contour;

[0064] Figure 10 Images of models created after importing the Discrete Element Method (PFC2D) software. Detailed Implementation

[0065] The present solution will now be described in conjunction with the accompanying drawings and specific embodiments.

[0066] See Figure 1 The method for constructing a two-dimensional discrete element model of rock joint surfaces based on point cloud data provided in this embodiment includes:

[0067] S101 uses a 3D laser scanner to scan the rock joint surface from multiple angles to obtain a 3D point cloud of the joint surface.

[0068] See Figure 2 To obtain an image of a natural rock joint surface, the surface is cleaned and markers are placed around the target area. Then, a 3D laser scanner is used to scan the joint surface multiple times from different angles, acquiring 3D point cloud data of the rock joint surface. Figure 3 The image shown is a 3D point cloud image of a joint surface.

[0069] S102, the three-dimensional point cloud of the joint surface is denoised and the center is normalized to obtain the preprocessed three-dimensional point cloud.

[0070] Denoising of the 3D point cloud of joint surfaces includes:

[0071] For each point in the point cloud Calculate the mean and standard deviation of the distances to its 20 nearest neighbors using the following formulas:

[0072] Distance mean:

[0073] In the formula, for The first point j The nearest neighbor point, The distance between two points;

[0074] Distance from standard deviation: ;

[0075] Set the standard deviation scaling factor std_ratio to 1.0. The average distance to its neighbors is greater than ,but The point is considered an outlier and is deleted.

[0076] In this embodiment, the normalization processing of the three-dimensional point cloud center of the joint surface includes:

[0077] The average coordinates of the denoised point cloud, i.e., the geometric center, are calculated using the following formula:

[0078]

[0079] In the formula, N The total number of points in the point cloud. , , For the first i The coordinates of the points;

[0080] Subtract the coordinates of the geometric center from the coordinates of each point using the following formula:

[0081] .

[0082] S103, rotate the preprocessed 3D point cloud to make it parallel to the Z-axis of the 3D coordinate system.

[0083] Calculate the covariance matrix of the preprocessed point cloud. C The formula is:

[0084]

[0085] In the formula, p i For the first point cloud i One point; N The total number of points.

[0086] Secondly, through the formula Eigenvalue decomposition is performed on the covariance matrix to obtain eigenvalues ​​and eigenvectors. In the formula, It is a diagonal matrix, and the elements on the diagonal are the eigenvalues ​​of the covariance matrix. V It is an eigenvector matrix, where each column is an eigenvector.

[0087] Then, a rotation matrix is ​​constructed from the eigenvectors. ,in, V i The first covariance matrix is ​​the first... i 1 eigenvector.

[0088] Finally, through the formula Rotate the point cloud to obtain the normal direction and z Axially parallel 3D point cloud, i.e., a rotated 3D point cloud, see [link / reference]. Figure 4 and Figure 5 The images are a preprocessed point cloud and a rotated 3D view and a top view, respectively.

[0089] S104, based on the rotated 3D point cloud in the 3D coordinate system x shaft and y The maximum and minimum values ​​on the axis are used to obtain the center of the circle. The filtering radius is set, and the 3D point cloud that is retained within the filtering radius is filtered.

[0090] Determine the 3D point cloud after rotation. x The maximum value x_max and the minimum value x_min on the axis, and in y The maximum value y_max and minimum value y_min on the axes are calculated, and the coordinates center_x are calculated as (x_max + x_min) / 2, and the coordinates center_y are calculated as (y_max + y_min) / 2. The radius R is set to 50 mm, and only the point cloud within a circle centered at (center_x, center_y) with a radius of 50 mm is retained, resulting in the filtered 3D point cloud. See [link to relevant documentation]. Figure 6 This is a top view of the filtered point cloud.

[0091] S105 projects the filtered 3D point cloud onto a set plane to obtain a 2D point cloud.

[0092] In this embodiment, the equation of the projection plane is defined as follows: Ax + By + Cz + D =0, based on the known points traversed by the plane. (50, 50, 0), the normal vector of this plane The coefficients are determined by (1, tan(10), 0) and the point normal form, respectively. , , , =-58.81; Next, calculate any point in the point cloud. The distance to the projection plane is given by the formula: Then calculate the coordinates of the projection point on the projection plane, using the formula: This yields a 3D point cloud projected onto a plane, such as... Figure 7 As shown Figure 6 Point cloud image in the original coordinate system after planar projection of the point cloud.

[0093] S106, Establish a two-dimensional coordinate system and move the projected two-dimensional point cloud to the first quadrant of the two-dimensional coordinate system.

[0094] Define the projection plane and the original 3D coordinate system xoy The direction of the intersection line between the planes is in the two-dimensional coordinate system. x The axis, its basis vectors Normal vector of the projection plane and xoy plane normal vector The cross product result; defined relative to the original coordinate system. z The axis parallel to the direction is a two-dimensional coordinate system y The axis, its basis vectors (0, 0, 1). Using the formula... Transform the projection points to a two-dimensional coordinate system. Finally, convert all points in the two-dimensional coordinate system. x value minus x Minimum value on the axis, y value minus y The minimum value on the axis yields a two-dimensional point cloud in the first quadrant of the two-dimensional coordinate system, such as... Figure 8 The figure shows the coordinate system in two dimensions. Figure 7 Midpoint cloud image.

[0095] S107, For the two-dimensional point cloud in the first quadrant, according to... x Sort the values ​​in ascending order, and sort them simultaneously. y To maintain the correspondence, based on the point cloud in the two-dimensional coordinate system x The scope divides it into n Find the portion in each portion. y Maximum value and corresponding x value, n The components constitute the two-dimensional contour coordinates of the joint surface.

[0096] In this embodiment, based on the point cloud in a two-dimensional coordinate system x Divide the range into 100 parts and find the maximum value in each part. and corresponding ,all( , This constitutes the two-dimensional contour coordinates of the joint surface, such as... Figure 9 This is a point cloud image after extracting the 2D contour.

[0097] S108, the modeling point cloud is obtained based on the two-dimensional contour coordinates of the joint surface, and then the modeling point cloud data is output in the dxf format commonly used by discrete element software.

[0098] All points in the two-dimensional profile coordinates of the joint surface in a two-dimensional coordinate system. x value minus x Minimum value on the axis, all y Value minus all points y The average value is used to obtain the modeled point cloud. Then, the Python third-party software library ezdxf is used to output the modeled point cloud data into the dxf format, which is common to discrete element method (DEM) software, and import it into the DEM software PFC2D. See [link to documentation]. Figure 10 The image is for modeling, where 1 represents a particle and 2 represents a two-dimensional joint.

[0099] In this application embodiment, "at least one" refers to one or more, and "more than one" refers to two or more. "And / or" describes the relationship between related objects, indicating that three relationships can exist. For example, A and / or B can represent the existence of A alone, the simultaneous existence of A and B, or the existence of B alone. A and B can be singular or plural. The character " / " generally indicates that the preceding and following related objects have an "or" relationship. "At least one of the following" and similar expressions refer to any combination of these items, including any combination of single or plural items. For example, at least one of a, b, and c can represent: a, b, c, ab, ac, bc, or abc, where a, b, and c can be single or multiple.

[0100] The above description is merely a specific embodiment of this application. Any variations or substitutions that can be easily conceived by those skilled in the art within the scope of the technology disclosed in this application should be included within the protection scope of this application. The protection scope of this application should be determined by the protection scope of the claims.

Claims

1. A method for constructing a two-dimensional discrete element model of rock joint surfaces based on point cloud data, characterized in that, include: A 3D laser scanner was used to scan the rock joint surface from multiple angles to obtain a 3D point cloud of the joint surface. The three-dimensional point cloud of the joint surface is denoised and center-normalized to obtain the pre-processed three-dimensional point cloud. Rotate the preprocessed 3D point cloud to make it parallel to the Z-axis of the 3D coordinate system; Based on the rotated 3D point cloud in the 3D coordinate system x shaft and y The maximum and minimum values ​​on the axis are used to obtain the center of the circle. The filtering radius is set, and the 3D point cloud that is retained within the filtering radius is filtered. The filtered 3D point cloud is projected onto a set plane to obtain a 2D point cloud; Establish a two-dimensional coordinate system and move the projected two-dimensional point cloud to the first quadrant of the two-dimensional coordinate system; For two-dimensional point clouds in the first quadrant, x Sort the values ​​in ascending order, and sort them simultaneously. y To maintain the correspondence, based on the point cloud in the two-dimensional coordinate system x The scope divides it into n Find the portion in each portion. y Maximum value and corresponding x value, n The components constitute the two-dimensional contour coordinates of the joint surface; The modeling point cloud is obtained based on the two-dimensional contour coordinates of the joint surface, and then the modeling point cloud data is output in the dxf format commonly used by discrete element software.

2. The method for constructing a two-dimensional discrete element model of rock joint surfaces based on point cloud data according to claim 1, characterized in that, The method of using a 3D laser scanner to scan the rock joint surface from multiple angles to obtain a 3D point cloud of the joint surface includes: Clean the natural jointed surface of the rock and affix markers around the target area; Then, using a 3D laser scanner, the joint surface is scanned multiple times from different angles to obtain 3D point cloud data of the rock joint surface.

3. The method for constructing a two-dimensional discrete element model of rock joint surfaces based on point cloud data according to claim 1, characterized in that, Denoising of the 3D point cloud of joint surfaces includes: For each point in the point cloud Calculate its k The formulas for the mean and standard deviation of the distances to the nearest neighbors are as follows: Distance mean: In the formula, for The first point j The nearest neighbor point, The distance between two points; Distance from standard deviation: ; Set the standard deviation scaling factor std_ratio, if The average distance to its neighbors is greater than ,but The point is considered an outlier and is deleted.

4. The method for constructing a two-dimensional discrete element model of rock joint surfaces based on point cloud data according to claim 3, characterized in that, The normalization process for the center of the three-dimensional point cloud of the joint surface includes: The average coordinates of the denoised point cloud, i.e., the geometric center, are calculated using the following formula: In the formula, N The total number of points in the point cloud. , , For the first i The coordinates of the points; Subtract the geometric center coordinates from the coordinates of each point in the denoised point cloud using the following formula: 。 5. The method for constructing a two-dimensional discrete element model of rock joint surfaces based on point cloud data according to claim 1, characterized in that, Rotating the preprocessed 3D point cloud to make it parallel to the Z-axis of the 3D coordinate system includes: Calculate the covariance matrix of the preprocessed point cloud. C The formula is: In the formula, p i For the first point cloud i One point; N The total number of points; Through formula Eigenvalue decomposition of the covariance matrix yields eigenvalues ​​and eigenvectors. It is a diagonal matrix, and the elements on the diagonal are the eigenvalues ​​of the covariance matrix. V This is an eigenvector matrix, where each column is an eigenvector; Then, a rotation matrix is ​​constructed from the eigenvectors. ,in, V i The first covariance matrix is ​​the first... i 1 eigenvector; Finally, the formula is used. Rotate the point cloud to obtain the normal direction and z A three-dimensional point cloud parallel to the axis, i.e., a three-dimensional point cloud after rotation.

6. The method for constructing a two-dimensional discrete element model of rock joint surfaces based on point cloud data according to claim 5, characterized in that, The method based on the rotated 3D point cloud in the 3D coordinate system x shaft and y The maximum and minimum values ​​on the axis are used to obtain the center of a circle. A filtering radius is set, and the 3D point cloud within that radius is filtered out, including: Determine the 3D point cloud after rotation. x The maximum value x_max and the minimum value x_min on the axis, and in y The maximum value y_max and the minimum value y_min on the axis; Calculate the coordinates of center_x, which is (x_max + x_min) / 2, and the coordinates of center_y, which is (y_max + y_min) / 2; Set the radius R, and then only keep the point cloud inside the circle with (center_x, center_y) as the center and radius R to obtain the filtered 3D point cloud.

7. The method for constructing a two-dimensional discrete element model of rock joint surfaces based on point cloud data according to claim 1, characterized in that, The step of projecting the filtered 3D point cloud onto a set plane to obtain a 2D point cloud includes: Define the equation of the projection plane as follows Ax + By + Cz + D =0; Based on the known points traversed by this plane The plane normal vector Determine the coefficients of the point method and the point method respectively. ; Next, calculate any point in the point cloud. The distance to the projection plane is given by the formula: ; Next, calculate the coordinates of the projection point on the projection plane using the following formula: This yields a three-dimensional point cloud projected onto a plane.

8. The method for constructing a two-dimensional discrete element model of rock joint surfaces based on point cloud data according to claim 7, characterized in that, The step of establishing a two-dimensional coordinate system and moving the projected two-dimensional point cloud to the first quadrant of the two-dimensional coordinate system includes: Define the projection plane and the original 3D coordinate system xoy The direction of the intersection line between the planes is in the two-dimensional coordinate system. x The axis, its basis vectors Normal vector of the projection plane and xoy plane normal vector The result of the cross product; Defined relative to the original three-dimensional coordinate system z The axis parallel to the direction is a two-dimensional coordinate system y The axis, its basis vectors (0, 0, 1); Through formula Transform the projection points to a two-dimensional coordinate system; Finally, all points in the two-dimensional coordinate system x value minus x Minimum value on the axis, y value minus y The minimum value on the axis yields the two-dimensional point cloud in the first quadrant of the two-dimensional coordinate system.

9. The method for constructing a two-dimensional discrete element model of rock joint surfaces based on point cloud data according to claim 1, characterized in that, The process involves obtaining a modeling point cloud based on the two-dimensional contour coordinates of the joint surface, and then outputting the modeling point cloud data in the DXF format commonly used by discrete element software, including: All points in the two-dimensional profile coordinates of the joint surface in a two-dimensional coordinate system. x value minus x Minimum value on the axis, all y Value minus all points y The average value is used to obtain the modeled point cloud; Then, using the Python third-party software library ezdxf, the modeling point cloud data is output in the dxf format commonly used by discrete element software and imported into the discrete element software PFC2D.

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