A method for determining the overall attitude of spatial structural surfaces

Abstract

This invention discloses a method for determining the comprehensive attitude of spatial structural surfaces. Rock masses contain numerous discontinuous structural surfaces, such as faults, bedding planes, joints, and fissures. The spatial attitude of these discontinuous surfaces determines the deformation and strength characteristics of the rock mass. For larger structural surfaces such as faults and dikes, in-situ measurements are mainly conducted through exploration adits, outcrops, and boreholes. However, the spatial attitude results obtained from measurements at different locations vary significantly, greatly affecting the judgment of the spatial morphology of the structural surfaces and potential instability modes. To solve the above problems, this invention proposes a method for determining the comprehensive attitude of spatial structural surfaces based on in-situ measurements. This method first fits the spatial morphology of the structural surfaces and divides them into elements using known measurement points and spatial attitudes. Then, it calculates the normal vector of each element and determines the spatial attitude of the structural surface based on the comprehensive normal vector of the elements.

Description

Technical Field

[0001] This invention relates to a method for determining the comprehensive attitude of spatial structural surfaces, belonging to the field of determining the spatial attitude of structural surfaces in geotechnical engineering, and is also applicable to three-dimensional geological modeling data processing. Background Technology

[0002] Rock masses contain numerous discontinuous structural planes (such as faults, bedding planes, joints, and fissures), and the spatial attitude of these discontinuities determines the deformation and strength characteristics of the rock mass. For larger structural planes such as faults and dikes, in-situ measurements are mainly conducted through exploration adits, outcrops, and boreholes. However, the spatial attitude results obtained from measurements at different locations vary significantly, greatly affecting the judgment of the spatial morphology of the structural planes and potential instability modes. Therefore, it is essential to propose a method that can address the uncertainty and stochastic nature of the spatial attitude of structural planes. Summary of the Invention

[0003] The technical problem to be solved by the present invention is to propose a method for determining the comprehensive attitude of a spatial structural surface based on field measurements. First, the spatial morphology of the structural surface is fitted and divided into elements by using known measurement points and spatial attitude. Then, the normal vector of the element is calculated, and the spatial attitude of the structural surface is determined according to the comprehensive normal of the element.

[0004] To solve the above-mentioned technical problems, the technical solution adopted by the present invention is: a method for determining the comprehensive attitude of a spatial structural surface, comprising the following steps:

[0005] S1. On the XOY plane, a two-dimensional mesh is generated according to the research range of the structural surface. Based on the measured spatial attitude and location information of the structural surface at the outcrop, adit and borehole, the elevation of the mesh node is calculated by weighting the distance inversely to obtain the spatial geometry of the structural surface, and the three-dimensional mesh unit of the structural surface is generated.

[0006] S2. Calculate the normal vector of each grid cell of the three-dimensional mesh of the structural surface according to the right-hand screw rule. The normal vector contains the area-related weight function and direction information.

[0007] S3. Calculate the sum of the normal vectors of all mesh elements in the three-dimensional mesh of the structural surface, and calculate the spatial attitude of the structural surface based on the sum of the normal vectors.

[0008] Step S1 includes the following steps:

[0009] S1.1 On the XOY plane, a two-dimensional mesh is generated according to the research scope of the structural surface. The mesh element adopts one or a combination of triangles and quadrilaterals. The following principle is followed when dividing: the mesh element nodes are arranged in counterclockwise order. The triangular mesh element is represented as A = p1p2p3, and the quadrilateral mesh element is represented as A = p1p2p3p4, where p1, p2, p3, and p4 are mesh element nodes.

[0010] S1.2. Based on the measured spatial attitude and location information of the structural surface at the outcrop, adit, and borehole, the elevation of the grid element nodes is calculated using the reciprocal weight of the distance, thus obtaining the spatial geometric point set of the structural surface. The formula for calculating the reciprocal weight of the distance is:

[0011]

[0012] In the formula, n is the number of known points measured at the outcrop, adit, and borehole locations, i is the index number of the known points, and h is the index number of the known points. i Let h be the elevation of a known point i, h be the elevation of a grid node, and d be the elevation of a known point i. i The distance between the grid cell node and the known point i on the XOY plane;

[0013] S1.3. Based on the set of points of the spatial geometric shape of the structural surface obtained in S1.2, perform three-dimensional mesh cell division of the structural surface. In addition to following the mesh cell division principle in S1.1, the following principle should also be followed: the surface normal vector is determined to point outward according to the right-hand screw rule, and the z-coordinate component of the surface normal vector is greater than 0.

[0014] Step S2 includes the following steps:

[0015] S2.1 If the 3D mesh of the structural surface uses triangular mesh elements, calculate the weighted normal vector of the triangular element:

[0016] m i = (p3-p2)×(p1-p2) (2)

[0017] In the formula, m i p1 is the weighted normal vector of element i; p2 and p3 are the coordinates of the triangle vertices, which are used as vectors during the calculation.

[0018] S2.2 If quadrilateral mesh elements are used for the 3D mesh generation of the structural surface, calculate the combined normal vector of the quadrilateral elements with weighted functions:

[0019]

[0020] In the formula, m i Let p be the weighted normal vector of cell i, j be the vertex index number, and p be the normal vector of cell i. j p represents the coordinates of the current point.j-1 Let p be the coordinates of the previous point. When j = 1, j-1 =4; p j+1 Let p be the coordinates of the next point. When j = 4, j+1 =1.

[0021] Step S3 includes the following steps:

[0022] S3.1 Calculate the combined normal vector of the structural surfaces:

[0023]

[0024] In the formula, m is the composite normal vector of the structural surface; m i Let n be the weighted normal vector of cell i, n be the total number of cells, and i be the cell index number.

[0025] S3.2 Determine the overall attitude of the structural surfaces based on the combined normal vectors of the structural surfaces:

[0026] tendency:

[0027]

[0028] inclination:

[0029]

[0030] In the formula, D d For the tendency; D a The angle of inclination; n x m y m z These are the components of m on the three coordinate axes.

[0031] A computer program for determining the comprehensive attitude of the aforementioned spatial structural surface.

[0032] An information data processing terminal for determining the comprehensive attitude of the aforementioned spatial structural surface.

[0033] A computer-readable storage medium includes instructions that, when executed on a computer, cause the computer to perform the aforementioned method for determining the overall attitude of spatial structural surfaces.

[0034] The beneficial effects of this invention are: it can calculate the comprehensive attitude of complex spatial structural surfaces, providing technical support for the description of structural surface attitude and the judgment of instability modes. Attached Figure Description

[0035] Figure 1 This is a statistical chart of the measurement results of the F2 fault on the slope abutment of a certain water conservancy and hydropower project using the method of the present invention;

[0036] Figure 2This is a fitting and meshing diagram of the F2 fault on the slope abutment of a water conservancy and hydropower project using the method of this invention;

[0037] Figure 3 This is a diagram illustrating the physical meaning of the triangle normal vector calculation formula using the method of this invention;

[0038] Figure 4 This is a schematic diagram of a node information data file (KLIST.lis) using the method of this invention;

[0039] Figure 5 This is a schematic diagram of a line segment information data file (LLIST.lis) using the method of this invention;

[0040] Figure 6 This is a schematic diagram of a unit information data file (AIST.lis) using the method of the present invention;

[0041] Figure 7 This is the corresponding program interface for using the method of this invention. Detailed Implementation

[0042] The present invention will be further illustrated below with specific examples. It should be understood that these examples are for illustrative purposes only and are not intended to limit the scope of the invention. After reading the present invention, any modifications of the present invention in various equivalent forms by those skilled in the art will fall within the scope defined by the appended claims.

[0043] Example:

[0044] Figure 1 The thick line shows the F2 fault, which was exposed by exploration adits and boreholes on the shoulder slope of a dam in a certain water conservancy and hydropower project. The dip angle of F2, exposed by 4 adits and 4 boreholes, ranges from 20° to 39° and the dip direction ranges from 306° to 350°. It is difficult to make an accurate judgment on the spatial attitude of the fault based on such results.

[0045] right Figure 1 The main solutions and effects of the problem shown are described in the following sections:

[0046] S1. On the XOY plane, a two-dimensional mesh is generated based on the research scope of the structural surface. The spatial attitude and location information of the structural surface are obtained from actual measurements at the outcrop, adit, and borehole locations. The elevation of the mesh nodes is calculated using the reciprocal of the distance as a weight, thus obtaining the spatial geometry of the structural surface. Then, a three-dimensional mesh element is generated for the structural surface. The specific steps are as follows:

[0047] S1.1 On the XOY plane, a two-dimensional mesh is generated according to the research scope of the structural surface. The mesh element adopts one or a combination of triangles and quadrilaterals. The following principle is followed when dividing: the mesh element nodes are arranged in counterclockwise order. The triangular mesh element is represented as A = p1p2p3, and the quadrilateral mesh element is represented as A = p1p2p3p4, where p1, p2, p3, and p4 are mesh element nodes.

[0048] S1.2. Based on the measured spatial attitude and location information of the structural surface at the outcrop, adit, and borehole, the elevation of the grid element nodes is calculated using the reciprocal weight of the distance, thus obtaining the spatial geometric point set of the structural surface. The formula for calculating the reciprocal weight of the distance is:

[0049]

[0050] In the formula, n is the number of known points measured at the outcrop, adit, and borehole locations, i is the index number of the known points, and h is the index number of the known points. i Let h be the elevation of a known point i, h be the elevation of a grid node, and d be the elevation of a known point i. i The distance between the grid cell node and the known point i on the XOY plane;

[0051] S1.3. Based on the set of points of the spatial geometric shape of the structural surface obtained in S1.2, perform three-dimensional mesh cell division of the structural surface. In addition to following the mesh cell division principle in S1.1, the following principle should also be followed: the surface normal vector is determined to point outward according to the right-hand screw rule, and the z-coordinate component of the surface normal vector is greater than 0.

[0052] Using the method of this invention, on the XOY plane... Figure 1 The range and measured point information are used to generate mesh element nodes. In this example, there are 4382 element nodes. A three-dimensional mesh of the structural surface is generated using the measured points as constraints. In this example, 8495 triangular elements and 19 quadrilateral elements are generated. The mesh element nodes meet the following requirements: 1) Nodes are arranged in counter-clockwise order (triangles are A = p1p2p3, quadrilaterals are A = p1p2p3p4, p1, p2, p3, and p4 are mesh nodes); 2) The surface normal vector is determined to point outwards according to the right-hand screw rule (the z-coordinate component of the surface normal vector is greater than 0). Figure 2 As shown.

[0053] S2: Calculate the normal vector of each mesh element in the 3D mesh of the structural surface according to the right-hand screw rule. The normal vector contains the area-related weight function and direction information. The main steps are as follows:

[0054] S2.1 Calculate the weighted normal vectors of 8495 triangular elements according to equation (2).

[0055] m i= (p3-p2)×(p1-p2) (2)

[0056] In the formula m i p1, p2, and p3 are the weighted normal vectors of element i; p1, p2, and p3 are the coordinates of the triangle vertices, used as vectors during calculation, with the physical meaning as follows: Figure 3 As shown.

[0057] S2.2 Calculate the combined normal vector of the weighted function of the 19 quadrilateral elements according to equation (3).

[0058]

[0059] In the formula m i Let p be the weighted normal vector of cell i, j be the vertex index number, and p be the normal vector of cell i. j p represents the coordinates of the current point. j-1 Let p be the coordinates of the previous point. When j = 1, j-1 =4; p j+1 Let p be the coordinates of the next point. When j = 4, j+1 =1;

[0060] S3: Calculate the sum of the normal vectors of all mesh elements in the 3D mesh of the structural plane, and calculate the spatial attitude of the structural plane based on the sum of the normal vectors. The specific steps are as follows:

[0061] S3.1 Calculate the composite normal vector of the structural surface according to equation (4):

[0062]

[0063] In the formula, m is the composite normal vector of the structural surface; n is the total number of elements; and i is the element index number.

[0064] S3.2 Determine the overall attitude of the structural surfaces based on the overall normal vector of the structural surfaces.

[0065] tendency:

[0066]

[0067] inclination:

[0068]

[0069] In the formula D d For the tendency; D a The angle of inclination; m x m y m z These are the components of m on the three coordinate axes.

[0070] Calculation results: F2 composite attitude dip: 317.35°, dip angle: 23.48°

[0071] To determine the overall attitude of structural planes, a computer program was developed, such as... Figure 7 As shown, the input node and cell information are respectively as follows: Figure 4 , Figure 5 , Figure 6 As shown.

[0072] In the above embodiments, implementation can be achieved, in whole or in part, through software, hardware, firmware, or any combination thereof. When implemented, in whole or in part, as a computer program product, the computer program product includes one or more computer instructions. When the computer program instructions are loaded or executed on a computer, all or part of the processes or functions described in the embodiments of the present invention are generated. The computer can be a general-purpose computer, a special-purpose computer, a computer network, or other programmable device. The computer instructions can be stored in a computer-readable storage medium or transmitted from one computer-readable storage medium to another. For example, the computer instructions can be transmitted from one website, computer, server, or data center to another website, computer, server, or data center via wired (e.g., coaxial cable, fiber optic, digital subscriber line (DSL)) or wireless (e.g., infrared, wireless, microwave, etc.) means. The computer-readable storage medium can be any available medium that a computer can access or a data storage device such as a server or data center that integrates one or more available media. The available medium can be a magnetic medium (e.g., floppy disk, hard disk, magnetic tape), an optical medium (e.g., DVD), or a semiconductor medium (e.g., a solid-state drive (SSD)).

[0073] The embodiments described above are only used to illustrate the technical ideas and features of the present invention. Their purpose is to enable those skilled in the art to understand the content of the present invention and implement it accordingly. The patent scope of the present invention should not be limited by these embodiments. That is, any equivalent changes or modifications made in accordance with the spirit disclosed in the present invention still fall within the patent scope of the present invention.

Claims

1. A method for determining the comprehensive attitude of a spatial structural surface, characterized in that, Includes the following steps: S1. On the XOY plane, a two-dimensional mesh is generated based on the research scope of the structural surface. The spatial attitude and location information of the structural surface are obtained from actual measurements at the outcrop, adit, and borehole locations. The elevation of the mesh nodes is calculated using the reciprocal of the distance as a weight, resulting in the spatial geometry of the structural surface. Then, a three-dimensional mesh is generated for the structural surface. Specifically, the steps include: S1.1 On the XOY plane, a two-dimensional mesh is generated according to the research scope of the structural surface. The mesh element adopts one or a combination of triangles and quadrilaterals. The following principle is followed when dividing: the mesh element nodes are arranged in counterclockwise order. The triangular mesh element is represented as A = p1p2p3, and the quadrilateral mesh element is represented as A = p1p2p3p4, where p1, p2, p3, and p4 are mesh element nodes. S1.

2. Based on the measured spatial attitude and location information of the structural surface at the outcrop, adit, and borehole, the elevation of the grid element nodes is calculated using the reciprocal weight of the distance, thus obtaining the spatial geometric point set of the structural surface. The formula for calculating the reciprocal weight of the distance is: In the formula, n is the number of known points measured at the outcrop, adit, and borehole locations, i is the index number of the known points, and h is the index number of the known points. i Let h be the elevation of a known point i, h be the elevation of a grid node, and d be the elevation of a known point i. i The distance between the grid cell node and the known point i on the XOY plane; S1.

3. Based on the spatial geometric point set of the structural surface obtained in S1.2, perform three-dimensional mesh cell division of the structural surface. In addition to following the mesh cell division principle in S1.1, the following principle should also be followed: the surface normal vector should be determined to point outward according to the right-hand screw rule, and the z-coordinate component of the surface normal vector should be greater than 0. S2. Calculate the normal vector of each grid cell of the three-dimensional mesh of the structural surface according to the right-hand screw rule. The normal vector contains the area-related weight function and direction information. S3. Calculate the sum of the normal vectors of all mesh elements in the three-dimensional mesh of the structural surface, and calculate the spatial attitude of the structural surface based on the sum of the normal vectors.

2. The method for determining the comprehensive attitude of spatial structural surfaces according to claim 1, characterized in that, Step S2 includes the following steps: S2.1 If the 3D mesh of the structural surface uses triangular mesh elements, calculate the weighted normal vector of the triangular element: m i =(p3-p2)×(p1-p2) (2) In the formula, m i p1 is the weighted normal vector of element i; p2 and p3 are the coordinates of the triangle vertices, which are used as vectors during the calculation. S2.2 If quadrilateral mesh elements are used for the 3D mesh generation of the structural surface, calculate the combined normal vector of the quadrilateral elements with weighted functions: In the formula, m i Let p be the weighted normal vector of cell i, j be the vertex index number, and p be the normal vector of cell i. j p represents the coordinates of the current point. j-1 Let p be the coordinates of the previous point. When j = 1, j-1 =4; p j+1 Let p be the coordinates of the next point. When j = 4, j+1 =1.

3. The method for determining the comprehensive attitude of spatial structural surfaces according to claim 2, characterized in that, Step S3 includes the following steps: S3.1 Calculate the combined normal vector of the structural surfaces: In the formula, m is the composite normal vector of the structural surface; m i Let n be the weighted normal vector of cell i, n be the total number of cells, and i be the cell index number. S3.2 Determine the overall attitude of the structural surfaces based on the combined normal vectors of the structural surfaces: tendency: inclination: In the formula, D d For the tendency; D a The angle of inclination; m x m y m z These are the components of m on the three coordinate axes.

4. An information data processing terminal for implementing the method for determining the comprehensive attitude of spatial structural surfaces as described in any one of claims 1-3.

5. A computer-readable storage medium comprising instructions, when executed on a computer, causing the computer to perform the method for determining the comprehensive attitude of a spatial structure surface as described in any one of claims 1-3.

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