Method for evaluating three-dimensional roughness of natural rock joint surface based on effective weighted area ratio

Abstract

The application discloses a natural rock joint surface three-dimensional roughness evaluation method based on effective weighted area ratio, uses a three-dimensional scanning technology to collect natural rock joint surface three-dimensional point cloud data and carries out pretreatment; carries out grid processing on the three-dimensional point cloud data; connects three sampling points of mutually adjacent joint surface point clouds after the grid processing into triangular microelements; screens out effective microelements; divides effective areas by using connected components; calculates effective average apparent dip angles and areas of each effective area; calculates weighted effective area ratios by summing up the weighted effective area ratios and dividing the sum by the entire three-dimensional joint surface projection area. The effective weighted area ratio not only considers the area of the effective area, but also introduces the sine value of the effective average apparent dip angle as a weighting factor, comprehensively considers the contribution of the area size and the topographic feature to the shear resistance, reflects the shear failure mechanism of the natural rock joint surface, and makes the evaluation result more comprehensive and accurate.

Description

Technical Field

[0001] This application relates to the field of rock mechanics technology, specifically to a three-dimensional roughness evaluation method for natural rock joint surfaces based on the effective weighted area ratio. Background Technology

[0002] Rock joints, as widely present weak structural surfaces in rock masses, play a crucial role in the stability of rock engineering due to their shear strength. The roughness of joint surfaces, as one of the key factors affecting shear strength, has long been a research hotspot.

[0003] Traditional methods for evaluating the roughness of rock joint surfaces often rely on two-dimensional line parameters, such as the Joint Roughness Coefficient (JRC) proposed by Barton. While this method is simple and easy to implement, it is primarily based on subjective visual judgment and cannot fully reflect the three-dimensional morphological characteristics and complexity of the joint surface. Furthermore, the application of the JRC standard profile curve also has certain limitations, as it is difficult to adapt to the diversity of different rock types and joint characteristics, and it also cannot effectively reflect the anisotropy of rock mass roughness.

[0004] In recent years, scholars have begun to explore roughness evaluation methods based on three-dimensional morphological features. These methods utilize three-dimensional scanning technology to acquire three-dimensional point cloud data of joint surfaces and perform three-dimensional reconstruction and morphological parameter analysis. Among them, Grasselli et al. proposed a three-dimensional roughness parameter based on the apparent dip angle distribution using three-dimensional scanning technology and triangulation algorithms, and established a corresponding joint shear strength model. However, the Grasselli roughness parameter overemphasizes the effect of a single maximum apparent dip angle, and the relationship between roughness indices and joint morphology is unclear, indicating shortcomings in reflecting roughness anisotropy and clarifying the relationship between roughness indices and joint morphology. 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 evaluating the three-dimensional roughness of natural rock joint surfaces based on the effective weighted area ratio, including:

[0007] Three-dimensional point cloud data of natural rock joint surfaces were acquired using 3D scanning technology, and the point cloud data was then processed by noise reduction, smoothing, and data compression.

[0008] The spatially unevenly distributed point cloud data is processed into a grid according to a preset sampling interval;

[0009] Based on the Delaunay triangulation algorithm, three sampling points of the joint surface point cloud that are adjacent to each other after meshing are connected to form a triangular micro-element;

[0010] Calculate the apparent tilt angle between the triangular element and the shear reference plane along the shear direction, and select the effective elements;

[0011] Identify the set of interconnected effective micro-elements, and divide the discrete effective micro-elements into several continuous effective regions according to different sets of effective micro-elements;

[0012] Calculate the effective average apparent tilt angle and area of ​​each effective region;

[0013] Calculate the weighted effective area, sum all the weighted effective areas, and compare them with the projected area of ​​the entire three-dimensional joint surface to obtain the effective weighted area ratio.

[0014] In one possible implementation, the use of 3D scanning technology to acquire 3D point cloud data of natural rock joint surfaces, and the subsequent denoising, smoothing, and data compression processing of the point cloud data, includes:

[0015] Select natural rock joint surfaces in the field and use a scanner to scan the three-dimensional point cloud data of the natural rock joint surfaces;

[0016] Then, use the Revo Scan software to crop in the editing interface to initially select the point cloud area of ​​the preset size;

[0017] Further point cloud fusion, detection and deletion of isolated point clouds, and detection and deletion of overlapping and unnecessary data points in the point cloud are performed as needed to obtain optimized point cloud data.

[0018] In one possible implementation, the step of gridding the spatially unevenly distributed point cloud data according to a preset sampling interval includes:

[0019] Extract the optimized spatially unevenly distributed point cloud data and determine the range of the gridding (x_min, x_max, y_min, y_max);

[0020] Grid points are generated by setting the gridding step size along the X and Y axes according to the preset sampling interval;

[0021] Then, initialize the Z-axis data after meshing and perform interpolation to interpolate the point cloud data into the meshed data;

[0022] Finally, the gridded data is saved.

[0023] In one possible implementation, the calculation of the tilt angle between the triangular infinitesimal element and the shear reference plane along the shear direction, and the selection of effective infinitesimal elements, includes: setting a critical tilt angle as... When the apparent tilt angle θ of the triangular element * Greater than the critical tilt angle Then the triangular infinitesimal element is an effective infinitesimal element, and the apparent tilt angle is an effective apparent tilt angle.

[0024] In one possible implementation, the step of determining a set of interconnected effective infinitesimal elements, and dividing the discrete effective infinitesimal elements into several continuous effective regions according to different sets of effective infinitesimal elements, includes:

[0025] Treating effective infinitesimal elements as nodes, if two effective infinitesimal elements share the same side, then there is a connection between them;

[0026] By traversing all valid infinitesimal elements using the connected component method and examining the connections between them, the set of all interconnected valid infinitesimal elements is identified.

[0027] The originally discrete effective micro-elements will be combined into several continuous effective regions;

[0028] If a valid micro-element that already belongs to a certain valid region is encountered, the two regions are merged using data structures such as disjoint-set data structures until all valid micro-elements have been traversed and assigned to the corresponding valid regions.

[0029] In one possible implementation, the effective average apparent tilt angle and area of ​​each effective region are calculated using the following formula:

[0030]

[0031]

[0032] In the formula: A is the effective average apparent tilt angle of the effective region. ei Let A be the area of ​​the effective region, and n be the number of effective infinitesimal elements in a given effective region; i Let be the area of ​​a certain effective infinitesimal element.

[0033] In one possible implementation, calculating the weighted effective area includes:

[0034] The sine of the effective average apparent tilt angle is selected as the weighting factor;

[0035] Multiplying the effective area by the sine of the effective average apparent tilt angle of the effective area gives the weighted effective area. The calculation formula is as follows:

[0036]

[0037] In the formula: This represents the area of ​​the i-th effective region after weighting.

[0038] In one possible implementation, the effective weighted area ratio is obtained by summing all weighted effective area areas and dividing the sum by the projected area of ​​the entire three-dimensional joint surface. The calculation formula is as follows:

[0039]

[0040] In the formula: A n This represents the projected area of ​​the entire three-dimensional joint surface.

[0041] In the embodiments of this application, joint surface regions that play a key role in the shearing process can be accurately identified. These effective regions are directly related to the shear strength of rock joint surfaces, providing an important reference for assessing the stability and safety of rock masses. The proposed effective weighted area ratio not only considers the area of ​​the effective region but also introduces the sine of the effective average apparent dip angle as a weighting factor. This weighting method comprehensively considers the contribution of region size and morphological characteristics to shear resistance, fully reflecting the shear failure mechanism of natural rock joint surfaces, and has good anisotropy, making the assessment results more comprehensive and accurate. Attached Figure Description

[0042] Figure 1 A flowchart illustrating a method for evaluating the three-dimensional roughness of natural rock joint surfaces based on the effective weighted area ratio, provided for embodiments of this application;

[0043] Figure 2 This is a 3D view of the point cloud data after meshing processing as described in this invention;

[0044] Figure 3 This is a three-dimensional model diagram of the joint surface constructed after the meshing process of this invention.

[0045] Figure 4 This is a schematic diagram of the triangular micro-element described in this invention;

[0046] Figure 5 A schematic diagram of effective micro-elements selected from the joint surfaces of natural rocks;

[0047] Figure 6 This is a radar image showing the variation of the three-dimensional roughness EWAR of natural rock joint surfaces based on the effective weighted area ratio as described in this invention, along with the shear direction. Detailed Implementation

[0048] The present solution will now be described in conjunction with the accompanying drawings and specific embodiments.

[0049] The analysis of the shear mechanism of natural rock joint surfaces in this application is based on the following assumptions: natural rock joint surfaces with no filling materials between the gaps and being mutually conformed under low normal stress. The reason for making the above assumptions is that under low normal stress conditions, it is not easy to break the surface protrusions, and the influence of joint surface roughness on the shear behavior is more significant. The assumption of no filling materials excludes the possible additional resistance or lubrication effect of the filler on the shear process, enabling the study to more directly explore how key factors such as joint surface roughness and contact area change affect the shear strength.

[0050] Under the action of low normal stress on the natural rock joint surface, the joint surface failure mainly concentrates on the shear-facing surface of the joint along the shear direction. This is because under the action of the horizontal shear force, the shear-facing surfaces of the mutually conformed joint surfaces are closely pressed against each other, resulting in obvious wear and tear. Due to the shear displacement and material extrusion deformation on the back slope surface, the joint surfaces are separated from each other and do not come into contact. The steeper the joint protrusion, the more serious the wear. The protrusions with a smaller slope generally do not experience wear because the joint protrusions with a larger slope provide a greater shear resistance during the shear process.

[0051] See Figure 1 , the three-dimensional roughness evaluation method of natural rock joint surfaces based on the effective weighted area ratio provided by the embodiment of this application includes:

[0052] S101, use three-dimensional scanning technology to collect three-dimensional point cloud data of the natural rock joint surface, and perform denoising, smoothing processing, and data compression processing on the point cloud data.

[0053] The scanner used in this embodiment is the Revopoint MINI high-precision blue light three-dimensional scanner, which is developed and produced by Xi'an Zhixiang Optoelectronic Technology Co., Ltd. The product technology is binocular blue light, and the single-frame repeat accuracy is 0.02 mm. The point cloud processing software supporting the Revopoint MINI scanner is Revo Scan. First, select a natural rock joint surface in the field and use the Revopoint MINI scanner to scan the three-dimensional point cloud data of the natural rock joint surface. Then, use the Revo Scan software to perform "cropping" in the editing interface to initially select a point cloud area of 100 mm × 100 mm, and further perform operations such as point cloud fusion, detection and deletion of isolated point clouds, and detection and deletion of overlapping and unnecessary data points in the point cloud according to needs to obtain optimized point cloud data.

[0054] S102, perform grid processing on the point cloud data with uneven spatial distribution according to a preset sampling interval.

[0055] Extract the optimized, spatially unevenly distributed point cloud data, determine the gridding range (x_min, x_max, y_min, y_max), and generate grid points by setting the gridding step size along the X and Y axes according to a preset sampling interval. In this embodiment, the sampling interval is 1 mm. Then, initialize the gridded elevation data (i.e., Z-axis data) and perform interpolation to interpolate the point cloud data into the gridded data. This yields a set of point cloud data with a point cloud interval of 1 mm along both the X and Y axes, such as... Figure 2 and Figure 3 As shown. Finally, the gridded data is saved as a txt file.

[0056] S103, based on the Delaunay triangulation algorithm, connects three sampling points of the joint surface point cloud that are adjacent to each other after meshing into a triangular micro-element.

[0057] This embodiment is based on the Delaunay triangulation algorithm, which connects three adjacent sampling points after meshing to form a triangular element. θ is the true tilt angle of the triangular element. * Let be the apparent tilt angle, t be the shear direction, vector n be the outward normal direction of the triangular element, vector n1 be the projection of vector n onto the shear reference plane, vector n0 be the normal vector perpendicular to the shear reference plane, and α be the angle between the dip of the triangular element and the shear direction t. Figure 4 As shown. The formula for calculating the apparent tilt angle of a triangular infinitesimal element is:

[0058] tanθ * = -tanθcasα.

[0059] S104, calculate the apparent tilt angle between the triangular element and the shear reference plane along the shear direction, and select the effective elements.

[0060] This embodiment, based on the shear mechanism of natural rock joint surfaces under low normal stress, sets a critical apparent dip angle. The apparent tilt angle θ of the effective infinitesimal triangle element was selected. * Greater than the critical tilt angle The effective infinitesimal element is identified and marked in red, such as... Figure 5 As shown. Joint surfaces can only come into contact during shearing; the apparent dip angle at this point is the effective apparent dip angle.

[0061] S105, determine the set of interconnected effective micro-elements, and divide the discrete effective micro-elements into several continuous effective regions according to different sets of effective micro-elements.

[0062] In this embodiment, effective infinitesimal elements are treated as nodes. If two effective infinitesimal elements share the same edge (i.e., they have a common edge or vertex), then there is a connection between them. All effective infinitesimal elements are traversed using the connected component method, and their connections are checked to identify all interconnected sets of effective infinitesimal elements. These sets constitute effective regions, and the originally discrete effective infinitesimal elements are combined into several consecutive effective regions. If an effective infinitesimal element already belongs to a certain effective region is encountered, the two regions are merged using data structures such as disjoint-set data structures. This process is repeated until all effective infinitesimal elements have been traversed and assigned to their respective effective regions. These regions differ significantly in size and shape, and the shear resistance they provide also varies.

[0063] S106, calculate the effective average apparent tilt angle and area of ​​each effective region.

[0064] Calculate the effective average apparent tilt angle for each effective region. and area A ei The calculation formula is:

[0065]

[0066]

[0067] In the formula: n is the number of effective infinitesimal elements in a certain effective region; A i Let be the area of ​​a certain effective infinitesimal element.

[0068] S107, calculate the weighted effective area and sum all the weighted effective areas and compare them with the projected area of ​​the entire three-dimensional joint surface to obtain the effective weighted area ratio.

[0069] Select effective average tilt angle The sine value is used as a weighting factor to determine the effective area A. ei Multiply by the effective mean apparent tilt angle of the effective region The sine value of the weighted effective area is calculated using the following formula:

[0070]

[0071] In the formula: A ei Let i be the area of ​​the i-th valid region; This represents the area of ​​the i-th effective region after weighting.

[0072] When the effective mean tilt angle When approaching 0°, Since the effective area is close to 0, the weighted area is also close to 0. Even if the effective area is large, the apparent tilt angle is too small, so almost no infinitesimal elements can participate in the shear process, thus failing to provide significant shear resistance. When the effective average apparent tilt angle... When approaching 90°, When the weighted area approaches 1, it is close to the effective area itself, indicating that the region can fully utilize its area advantage during shearing and provide greater shear resistance. Furthermore, by introducing... Such a weighting function can effectively reduce the dominant role of the maximum apparent dip angle in solely determining shear strength, and combine the apparent dip angle with the area of ​​the region for comprehensive consideration.

[0073] Finally, the sum of all weighted effective area areas is divided by the projected area of ​​the entire three-dimensional joint surface. The percentage form of this ratio is the Effective Weighted Area Ratio (EWAR), and its calculation formula is as follows:

[0074]

[0075] In the formula: A n The total projected area of ​​the three-dimensional joint surface; Let be the area of ​​the i-th weighted effective region.

[0076] When calculating EWAR, the overall three-dimensional joint surface projection area A is selected. n The denominator is based on the fact that, under low normal stress, the shear strength of rock joints is mainly affected by the morphological characteristics of the shear face. The total projected area A of the three-dimensional joint surface... n The projected area of ​​the joint surface onto the shear reference plane accurately captures the morphological characteristics of the shear face, thus accurately assessing its contribution to shear behavior. In contrast, the actual area of ​​the three-dimensional joint surface contains all the information of both the shear face and the back slope surface. This introduces unnecessary interference when assessing shear strength under low normal stress, because the back slope surface does not directly provide shear strength during shearing.

[0077] Furthermore, to illustrate the good anisotropy of EWAR, this embodiment selected 16 shear directions (0° to 360°, with one shear direction taken at every 22.5° interval), calculated the values ​​of EWAR along the 16 shear directions, and plotted a radar chart of the variation of the natural rock joint surface roughness parameter EWAR with shear direction based on the calculation results, as shown below. Figure 6 As shown in the figure. The results indicate that the roughness of natural rock joint surfaces characterized by EWAR exhibits good anisotropy.

[0078] In summary, this embodiment:

[0079] By combining high-precision 3D scanning technology and the Delaunay triangulation algorithm, accurate quantification of the 3D roughness of rock joint surfaces can be achieved. This not only overcomes the limitations of traditional 2D measurement methods but also ensures the accuracy and reliability of the measurement data through meshing and data optimization.

[0080] Based on the connected component method, this embodiment can accurately identify joint surface regions that play a key role in the shearing process. These effective regions are directly related to the shear strength of rock joint surfaces, providing important reference for assessing the stability and safety of rock masses, and offering new ideas and methods for research in the field of rock mechanics.

[0081] The Effective Weighted Area Ratio (EWAR) proposed in this embodiment not only considers the area of ​​the effective region but also introduces the sine of the effective average apparent dip angle as a weighting factor. This weighting method comprehensively considers the contribution of region size and morphological features to shear resistance, fully reflects the shear failure mechanism of natural rock joint surfaces, and has good anisotropy, making the evaluation results more comprehensive and accurate.

[0082] This embodiment, based on high-precision 3D scanning and Python programming, can quickly calculate EWAR values ​​under different shearing directions and sampling accuracies, significantly improving data processing efficiency and point cloud data utilization.

[0083] 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 are in 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.

[0084] 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 evaluating the three-dimensional roughness of natural rock joint surfaces based on effective weighted area ratio, characterized in that, include: Three-dimensional point cloud data of natural rock joint surfaces were acquired using 3D scanning technology, and the point cloud data was then processed by noise reduction, smoothing, and data compression. The spatially unevenly distributed point cloud data is processed into a grid according to a preset sampling interval; Based on the Delaunay triangulation algorithm, three sampling points of the joint surface point cloud that are adjacent to each other after meshing are connected to form a triangular micro-element; Calculate the apparent tilt angle between the triangular element and the shear reference plane along the shear direction, and select the effective elements; Identify the set of interconnected effective micro-elements, and divide the discrete effective micro-elements into several continuous effective regions according to different sets of effective micro-elements; Calculate the effective average apparent tilt angle and area of ​​each effective region; The effective area after weighting is calculated, and the sum of all the effective areas after weighting is calculated and compared with the projected area of ​​the entire three-dimensional joint surface to obtain the effective weighted area ratio. The three-dimensional roughness of the natural rock joint surface is evaluated based on the effective weighted area ratio. The calculation of the weighted effective area includes: The sine of the effective average apparent tilt angle is selected as the weighting factor; Multiplying the effective area by the sine of the effective average apparent tilt angle of the effective area gives the weighted effective area. The calculation formula is as follows: In the formula: For the weighted first i The area of ​​each effective region The area of ​​the effective region, The effective average apparent tilt angle of the effective area; The effective weighted area ratio is obtained by summing all weighted effective area areas and dividing the sum by the projected area of ​​the entire three-dimensional joint surface. The calculation formula is as follows: In the formula: A n This represents the projected area of ​​the entire three-dimensional joint surface.

2. The method for evaluating the three-dimensional roughness of natural rock joint surfaces based on the effective weighted area ratio according to claim 1, characterized in that, The process of acquiring three-dimensional point cloud data of natural rock joint surfaces using three-dimensional scanning technology, and then performing noise reduction, smoothing, and data compression on the point cloud data, includes: Select natural rock joint surfaces in the field and use a scanner to scan the three-dimensional point cloud data of the natural rock joint surfaces; Then, use the Revo Scan software to crop in the editing interface to initially select the point cloud area of ​​the preset size; Further point cloud fusion, detection and deletion of isolated point clouds, and detection and deletion of overlapping and unnecessary data points in the point cloud are performed as needed to obtain optimized point cloud data.

3. The method for evaluating the three-dimensional roughness of natural rock joint surfaces based on effective weighted area ratio according to claim 1, characterized in that, The step of performing gridding processing on spatially unevenly distributed point cloud data according to a preset sampling interval includes: Extract the optimized spatially unevenly distributed point cloud data and determine the range of gridding (x_min, x_max, y_min, y_max). Grid points are generated by setting the gridding step size along the X and Y axes according to the preset sampling interval; Then, initialize the Z-axis data after meshing and perform interpolation to interpolate the point cloud data into the meshed data; Finally, the gridded data is saved.

4. The method for evaluating the three-dimensional roughness of natural rock joint surfaces based on the effective weighted area ratio according to claim 1, characterized in that, The calculation of the tilt angle between the triangular element and the shear reference plane along the shear direction, and the selection of effective elements, includes: setting a critical tilt angle as... ∈[0°, 90°], when the apparent tilt angle of the triangular element is... Greater than the critical tilt angle Then the triangular infinitesimal element is an effective infinitesimal element, and the apparent tilt angle is an effective apparent tilt angle. .

5. The method for evaluating the three-dimensional roughness of natural rock joint surfaces based on the effective weighted area ratio according to claim 4, characterized in that, The process involves identifying a set of interconnected effective infinitesimal elements, and then dividing the discrete effective infinitesimal elements into several continuous effective regions based on these different sets, including: Treating effective infinitesimal elements as nodes, if two effective infinitesimal elements share the same side, then there is a connection between them; By traversing all valid infinitesimal elements using the connected component method and examining the connections between them, the set of all interconnected valid infinitesimal elements is identified. The originally discrete effective micro-elements will be combined into several continuous effective regions; If a valid micro-element that already belongs to a certain valid region is encountered, the two regions are merged using a disjoint-set data structure until all valid micro-elements have been traversed and assigned to their respective valid regions.

6. The method for evaluating the three-dimensional roughness of natural rock joint surfaces based on the effective weighted area ratio according to claim 5, characterized in that, The effective average apparent tilt angle and area of ​​each effective region are calculated using the following formula: In the formula: The effective average apparent tilt angle of the effective area. Let n be the area of ​​the effective region, and n be the number of effective infinitesimal elements in a certain effective region. Let be the area of ​​a certain effective infinitesimal element.

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