Drilling and blasting method tunnel surrounding rock flatness calculation method based on three-dimensional point cloud

Abstract

The invention provides a drilling and blasting method tunnel surrounding rock flatness calculation method based on a three-dimensional point cloud, and relates to the technical field of surrounding rock detection.The method comprises the steps that a grid and an orthogonal coordinate system are constructed according to a design datum plane, obtained point cloud data are matched with the design datum plane, mapping of the grid in the point cloud and mapping points of all grid points in the point cloud are obtained, and the mapping points of all the grid points in the point cloud are obtained; the flatness requirement of the design requirement for each grid position is obtained according to the coordinates of the grid points, then the actual flatness state of the tunnel surrounding rock at the corresponding position is obtained according to the coordinates of the mapping points in the point cloud, and the difference of the actual flatness state relative to the flatness requirement is compared and judged, so that the flatness of the position is formed. The situation that the flatness is judged only by looking at the concave-convex condition of a certain position is avoided, and the flatness is measured by judging the deviation degree of the position according to design requirements.

Description

Technical Field

[0001] This invention relates to the field of surrounding rock detection technology, specifically a method for calculating the smoothness of surrounding rock in drill-and-blast tunnels based on three-dimensional point clouds. Background Technology

[0002] During tunnel blasting and excavation, initial support is required for the surrounding rock. The smoothness of the surrounding rock affects the adhesion of the initial support and its stability in later use. Therefore, it is necessary to measure the smoothness of the surrounding rock and formulate corresponding initial support strategies based on the specific smoothness to ensure the performance of the initial support. Drill-and-blast method is a common construction method in the current engineering field, with advantages of convenient construction and high efficiency. However, due to uncontrollable factors, the smoothness of the surrounding rock may be poor, which will cause difficulties for subsequent initial support work. Therefore, it is necessary to accurately assess the smoothness of the surrounding rock at various locations to provide information support and strategic guidance for the initial support process. With the development and advancement of technology, 3D scanning has made significant progress in large-area data measurement. It can simulate the details of the tunnel surface through scanned point cloud data, thereby realizing the measurement of various points in the program system, including but not limited to relative position and coordinates.

[0003] The prior art, disclosed in technical document CN116226957A, provides a method, apparatus, and storage medium for calculating the initial support smoothness of a tunnel based on point clouds. The method includes: embedding pre-processed point cloud data of a scanned segment into a design contour map; obtaining a cross-section of the design contour map based on the axial position of the point cloud, drawing a normal to the design contour on the cross-section, with the normal passing through each point in the point cloud, and recording the distance from the point on the normal to the design contour line; keeping the distance from each point on its normal to the cross-section design contour line constant, unfolding the arc surface of the design contour map into a rectangular surface, and adjusting the point cloud data to calculate the point cloud data to obtain the unfolded map; moving the detection window along a preset detection path, calculating the depth-to-length ratio parameter for each point after each window movement; comparing the maximum depth-to-length ratio parameter after each window movement with a preset threshold to determine whether the detection result of each window is qualified, and determining whether the initial support smoothness of the scanned tunnel segment is qualified.

[0004] Although this method achieves the measurement of tunnel smoothness, the process is complex. Moreover, by unfolding the arc surface into a rectangular surface, the process inevitably causes a change in relative position, resulting in errors. Furthermore, this method does not take into account changes relative to the design reference plane, which can easily cause the measured data to deviate from the actual design value.

[0005] The information disclosed in the background section is only intended to enhance the understanding of the background of this disclosure, and therefore may include information that does not constitute prior art known to those skilled in the art. Summary of the Invention

[0006] The purpose of this invention is to provide a method for calculating the smoothness of the surrounding rock in a drill-and-blast tunnel based on three-dimensional point clouds, so as to solve the problems mentioned in the background art.

[0007] To achieve the above objectives, the present invention provides the following technical solution: A method for calculating the smoothness of surrounding rock in drill-and-blast tunnels based on three-dimensional point clouds, comprising the following steps: Step 1: Obtain the design reference plane of the tunnel, construct an orthogonal coordinate system in the design reference plane, and divide the design reference plane into grids to obtain multiple closely connected grids. Scan the tunnel in the field to obtain point cloud data and match the point cloud data to the design reference plane and the orthogonal coordinate system. Step 2: Obtain the coordinates of grid points in each grid. The grid points include the bottom midpoint, top midpoint, front midpoint, rear midpoint, and grid center point. With the grid center point as the center, construct four reference vectors for this grid based on the top-bottom direction and the front-back direction, respectively. Step 3: Construct rays passing through each grid point, starting from the Z-axis of the orthogonal coordinate system. Obtain the mapping point of each grid point in the point cloud through the rays of each grid point. Construct four mapping vectors in this grid based on the top and bottom directions and the front and back directions, respectively, according to the coordinates of the mapping points. Step 4: Obtain the reference angles of each grid in the top-bottom direction and the front-back direction according to the four reference vectors. Obtain the mapping angles of each grid in the top-bottom direction and the front-back direction according to the four mapping vectors. Correct the mapping angles using the reference angles to obtain the flatness of the center position of each grid.

[0008] Furthermore, the design reference surface of this tunnel is obtained. The design reference surface is the theoretical shape required by the tunnel designer. The design reference surface is then divided into a grid, and the logic for the grid division is as follows: An orthogonal coordinate system is constructed with the geometric center point of the tunnel entrance section as the origin, the tunnel extension direction as the positive Z-axis, the horizontal leftward direction as the positive X-axis, and the vertical upward direction as the positive Y-axis. The tunnel section is divided at the origin at equal angles, and the tunnel outline is divided into multiple curved segments. The length of each curved segment corresponds to the height of the grid. The grid length is set along the Z-axis, and the design reference plane is divided into multiple closely connected grids.

[0009] Furthermore, the equipment acquires three-dimensional point cloud data of the surrounding rock of the tunnel, and the point cloud data is denoised, matched to the design reference plane, and matched to an orthogonal coordinate system.

[0010] Furthermore, the coordinates of each grid point in the design reference plane in the orthogonal coordinate system are obtained respectively. The grid points include the bottom midpoint, top midpoint, front midpoint, rear midpoint, and grid center point. The grid center point is the geometric center point of the grid. The division logic of the bottom, top, front, and rear ends is as follows: With the positive Z-axis of the orthogonal coordinate system as the forward direction and the negative Z-axis as the backward direction, in the XY-axis plane, with the origin as the center, the clockwise direction is the top direction and the counterclockwise direction is the bottom direction; Based on the coordinates of the five grid points, four reference vectors are obtained for each grid, namely reference vector I, reference vector II, reference vector III, and reference vector IV, according to the following formula: in, , , , They represent the first Line number The reference vectors I, II, III, and IV of the column grid. , , , and These represent the X-axis coordinates of the center point, bottom midpoint, top midpoint, rear midpoint, and front midpoint of the grid in an orthogonal coordinate system, respectively. , , , and These represent the Y-axis coordinates of the center point, bottom midpoint, top midpoint, rear midpoint, and front midpoint of the grid in an orthogonal coordinate system, respectively. , , , and These represent the Z-axis coordinates of the center point, bottom midpoint, top midpoint, rear midpoint, and front midpoint of the grid in an orthogonal coordinate system, respectively. Retrieve the variable for the number of rows in the grid. , , Indicates the total number of rows in the grid. The column number of the grid is the retrieval variable. , , Indicates the total number of columns in the grid.

[0011] Furthermore, the point cloud is mapped to the design reference plane, and the logic of the mapping is as follows: In a plane perpendicular to the Z-axis, construct rays that start from the Z-axis and pass through the center point of the grid, the bottom midpoint, the top midpoint, the rear midpoint, and the front midpoint, respectively. The points in the point cloud that this ray passes through are the mapping points of the grid points, and are respectively labeled as the grid center point mapping point, bottom midpoint mapping point, top midpoint mapping point, rear midpoint mapping point, and front midpoint mapping point.

[0012] Furthermore, the coordinates of the mapped points of each grid point are obtained. Based on the coordinates of the five mapped points of each grid, four mapping vectors are constructed, namely mapping vector I, mapping vector II, mapping vector III, and mapping vector IV, according to the following formula: in, , , and They represent the first Line number The mapping vectors I, II, III, and IV of the column grid. , , , and These represent the X-axis coordinates of the center point, bottom midpoint, top midpoint, rear midpoint, and front midpoint of the grid in an orthogonal coordinate system, respectively. , , , and These represent the Y-axis coordinates of the center point, bottom midpoint, top midpoint, rear midpoint, and front midpoint of the grid in an orthogonal coordinate system, respectively. , , , and These represent the Z-axis coordinates of the center point, bottom midpoint, top midpoint, rear midpoint, and front midpoint of the grid in an orthogonal coordinate system.

[0013] Furthermore, the four reference vectors and four mapping vectors are standardized respectively to obtain the reference angles of each grid in the top and bottom directions and the front and back directions of the design reference plane, based on the following formula: in, Indicates the first Line number The reference angle between the top and bottom directions of the column grid. Indicates the first Line number The reference angle between the front and rear directions of the column grid. , , and They represent the first Line number The column grid is standardized using reference vectors I, II, III, and IV; The mapping angles of the mapping vectors for each grid cell in the top-bottom and front-back directions are obtained using the following formulas: in, Indicates the first Line number The included angle of the top and bottom directions of the column grid. Indicates the first Line number The included angle of the front and rear directions of the column grid. , , and These represent the standardized mapping vectors I, II, III, and IV, respectively.

[0014] Furthermore, the reference angle of each grid is corrected to the mapped angle to obtain the actual angles of each grid in the top-bottom direction and the front-back direction, based on the following formula: in, Indicates the first Line number The actual included angle between the top and bottom directions of the column grid. Indicates the first Line number The actual included angle between the front and rear directions of the grid; The flatness at the center of each grid is obtained using the following formula: in, Indicates the first Line number The flatness of the center position of the column grid. and Indicates weight, , , ; The flatness of the center position of each grid is summarized and output.

[0015] Compared with the prior art, the beneficial effects of the present invention are: This invention constructs a grid and an orthogonal coordinate system based on a design reference plane. It matches the acquired point cloud data to the design reference plane to obtain the mapping of the grid in the point cloud and the mapping point of each grid point in the point cloud. The coordinates of the grid points are used to obtain the flatness requirements of the design for each grid position. Then, based on the coordinates of the mapping points in the point cloud, the actual flatness of the tunnel surrounding rock at the corresponding position is obtained. The difference between the actual flatness and the flatness requirements is compared and judged to form the flatness of that position. This avoids judging the flatness by looking only at the unevenness of a certain position, but rather combines the design requirements to judge the degree of deviation of the position to achieve the measurement of flatness. Attached Figure Description

[0016] Figure 1 This is a schematic diagram of the overall method flow of the present invention. Detailed Implementation

[0017] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to specific embodiments.

[0018] It should be noted that, unless otherwise defined, the technical or scientific terms used in this invention should have the ordinary meaning understood by one of ordinary skill in the art to which this invention pertains. The terms "first," "second," and similar terms used in this invention do not indicate any order, quantity, or importance, but are merely used to distinguish different components. Terms such as "comprising" or "including" mean that the element or object preceding the word encompasses the elements or objects listed following the word and their equivalents, without excluding other elements or objects. Terms such as "connected" or "linked" are not limited to physical or mechanical connections, but can include electrical connections, whether direct or indirect. Terms such as "upper," "lower," "left," and "right" are used only to indicate relative positional relationships; when the absolute position of the described object changes, the relative positional relationship may also change accordingly.

[0019] Example: Please see Figure 1The present invention provides a technical solution: A method for calculating the smoothness of surrounding rock in drill-and-blast tunnels based on three-dimensional point clouds, comprising the following steps: Step 1: Obtain the design reference plane of the tunnel, construct an orthogonal coordinate system in the design reference plane, and divide the design reference plane into grids to obtain multiple closely connected grids. Scan the tunnel in the field to obtain point cloud data and match the point cloud data to the design reference plane and the orthogonal coordinate system.

[0020] Step 1 includes the following: Obtain the design reference surface for this tunnel, which is the theoretical shape required by the tunnel designers. Then, divide the design reference surface into a grid, following the logic of the grid division: An orthogonal coordinate system is constructed with the geometric center point of the tunnel entrance section as the origin, the tunnel extension direction as the positive Z-axis, the horizontal leftward direction as the positive X-axis, and the vertical upward direction as the positive Y-axis. The tunnel section is divided at the origin at equal angles, and the tunnel outline is divided into multiple curved segments. The length of each curved segment corresponds to the height of the grid. The grid length is set along the Z-axis, and the design reference plane is divided into multiple closely connected grids.

[0021] By obtaining the design reference surface provided by the tunnel designer and constructing an orthogonal coordinate system with the geometric center point of the tunnel entrance section as the origin, the design reference surface is divided into multiple closely connected grids. This process provides a standardized reference framework for subsequent point cloud data matching and analysis. It ensures that the calculation of the tunnel surrounding rock smoothness is based on the theoretical shape of the design, avoiding errors caused by inconsistent references and laying the foundation for high-precision smoothness analysis. This step, through establishing an orthogonal coordinate system and grid division, provides clear geometric constraints for point cloud data matching, enabling subsequent steps to perform accurate coordinate mapping and vector calculations based on a unified grid system. Simultaneously, the logic of grid division (dividing at equal angles along the tunnel section and setting the grid length along the Z-axis) ensures the systematic and comprehensive nature of the calculation, covering all parts of the tunnel profile.

[0022] The equipment acquires three-dimensional point cloud data of the surrounding rock of the tunnel, removes noise from the point cloud data, matches the point cloud data to the design reference plane, and matches it to an orthogonal coordinate system.

[0023] In a preferred embodiment, during the matching process, the point cloud is filtered using a stereographic filtering method, and then the point cloud data is matched to the design reference plane using orthogonal projection. This includes, but is not limited to, using a fast matching algorithm. The logic for matching the point cloud data to the design reference plane is as follows: the design reference plane and orthogonal coordinate system have been obtained. The design reference plane and orthogonal coordinate system are then input into a 3D display tool for display. The 3D display tool includes, but is not limited to, BIM. 3D display tools are common technical features in this field and will not be elaborated here. Simultaneously, when the point cloud data is input into the 3D display tool and the device scans the point cloud data of the tunnel surrounding rock, the device's position in the real geographic coordinate system needs to be set in advance. The design reference plane and orthogonal coordinate system also have specific positions in the real geographic coordinate system, which can be obtained through the engineering file. Based on the positional relationship between the device, the design reference plane, and the orthogonal coordinate system in the real geographic coordinate system, the relative positions of the three can be determined. Based on the relative positions, the point cloud data is adjusted in the 3D display tool to achieve the matching of the point cloud data to the design reference plane. The adjustment process in the 3D display tool is a common technical feature in this field and will not be elaborated here.

[0024] Three-dimensional point cloud data of the tunnel surrounding rock was acquired using equipment, and noise points were removed from the data through denoising processing. The point cloud data was then matched to the design datum plane and orthogonal coordinate system. This process ensured the accuracy and applicability of the point cloud data. Its practical significance lies in improving the quality of the point cloud data through denoising, making subsequent mapping point calculations more reliable. Matching the point cloud data to the design datum plane and orthogonal coordinate system achieves a direct correspondence between the actual surrounding rock shape and the theoretical design shape, providing a data foundation for subsequent analysis of grid points and mapping points. This step builds upon the results of the design datum plane mesh generation, using the orthogonal coordinate system as a unified reference to accurately locate the point cloud data within the grid. This provides direct data support for obtaining grid point coordinates and constructing datum vectors in step 2, and also lays the foundation for ray mapping in step 3.

[0025] Step 2: Obtain the coordinates of grid points in each grid. The grid points include the bottom midpoint, top midpoint, front midpoint, rear midpoint, and grid center point. With the grid center point as the center, construct four reference vectors for this grid based on the top-bottom direction and the front-back direction, respectively. Step 2 includes the following: Obtain the coordinates of each grid point in the orthogonal coordinate system in the design reference plane. The grid points include the bottom midpoint, top midpoint, front midpoint, rear midpoint, and grid center point. The grid center point is the geometric center of the grid. The logic for dividing the bottom, top, front, and rear points is as follows: With the positive Z-axis of the orthogonal coordinate system as the forward direction and the negative Z-axis as the backward direction, in the XY-axis plane, with the origin as the center, the clockwise direction is the top direction and the counterclockwise direction is the bottom direction; In a preferred embodiment, each divided grid has four boundaries. There must be two non-adjacent boundaries. The Z-axis coordinate of each point on one boundary is greater than the Z-axis coordinate of each point on the other boundary. The boundary formed by the points with larger Z-axis coordinates is the forward boundary, and the boundary formed by the points with smaller Z-axis coordinates is the backward boundary. Then there must be two other non-adjacent boundaries. Taking the positive direction of the Z-axis as the viewpoint, each of these two boundaries becomes a point. Connect these two points to the Z-axis and form an angle with the positive direction of the X-axis. Determine the size of these two angles. The boundary represented by the point with the larger angle is the top direction boundary, and the boundary represented by the point with the smaller angle is the bottom direction boundary. Based on this, the four boundaries of the grid are defined as forward, backward, top, and bottom directions.

[0026] By obtaining the coordinates of the bottom midpoint, top midpoint, front midpoint, rear midpoint, and center point of each grid in an orthogonal coordinate system, this process provides precise geometric information for the subsequent construction of reference vectors. Through explicit coordinate definitions, the theoretical shape of the design reference surface is refined into quantifiable grid point data, providing specific reference points for flatness calculations and ensuring the accuracy and operability of the analysis. This step utilizes the orthogonal coordinate system and grid division results established in step 1 to directly extract the coordinates of grid points, providing fundamental data for the subsequent calculation of reference vectors. It also provides a comparative reference for obtaining the coordinates of the mapping points in step 3, ensuring a seamless connection between theory and actual data.

[0027] Based on the coordinates of the five grid points, four reference vectors are obtained for each grid, namely reference vector I, reference vector II, reference vector III, and reference vector IV, according to the following formula: in, , , , They represent the first Line number The reference vectors I, II, III, and IV of the column grid. , , , and These represent the X-axis coordinates of the center point, bottom midpoint, top midpoint, rear midpoint, and front midpoint of the grid in an orthogonal coordinate system, respectively. , , , and These represent the Y-axis coordinates of the center point, bottom midpoint, top midpoint, rear midpoint, and front midpoint of the grid in an orthogonal coordinate system, respectively. , , , and These represent the Z-axis coordinates of the center point, bottom midpoint, top midpoint, rear midpoint, and front midpoint of the grid in an orthogonal coordinate system, respectively. Retrieve the variable for the number of rows in the grid. , , Indicates the total number of rows in the grid. The column number of the grid is the retrieval variable. , , Indicates the total number of columns in the grid.

[0028] , , , They represent the first Line number The mapping vectors I, II, III, and IV of the grid reflect the geometric characteristics of the design reference plane in the top-bottom and front-back directions within the grid. Specifically, they represent the spatial displacement direction and distance of the grid center point relative to the bottom midpoint, the top midpoint relative to the grid center point, the grid center point relative to the rear midpoint, and the front midpoint relative to the grid center point. These reference vectors are used in real-world environments to describe the local geometric characteristics of the tunnel design reference plane within each grid, providing a theoretical reference for subsequent comparison with actual surrounding rock point cloud data and addressing the quantitative problem of deviations between theoretical design and actual surface conditions during tunnel construction. Independent variables ( , , (coordinates of the grid center point), ( , , (Coordinates of the midpoint of the bottom end), ( , , (Coordinates of the midpoint of the top) , , (Coordinates of the midpoint of the back end) and ( , , The coordinates of the midpoint of the front end directly determine the magnitude and direction of each reference vector. The dependent variable is related to these independent variables because they calculate the relative positions between grid points through coordinate differences, reflecting the geometric relationship of the design reference surface in the orthogonal coordinate system. Changes in the independent variables directly affect the vector components of the dependent variable. This relationship is manifested as follows: the larger the absolute value of the coordinate difference of the independent variable, the larger the magnitude of the vector. The direction is determined by the sign of the coordinate difference, thus accurately describing the geometric characteristics of the design reference surface within the grid, providing a reliable mathematical basis for subsequent angle calculations and flatness analysis.

[0029] By calculating the coordinate differences between the bottom midpoint, top midpoint, front midpoint, and rear midpoint of each grid and the grid center point, four reference vectors (reference vectors I, II, III, and IV) are constructed. This process provides a mathematical expression for describing the geometric characteristics of the grid in the top-bottom and front-back directions. The local geometric features of the design reference plane in each grid are quantified in vector form, providing a theoretical basis for subsequent angle calculations and flatness analysis, ensuring the standardization and consistency of the calculation process. This step, based on the aforementioned acquisition of grid point coordinates, directly generates reference vectors, providing necessary data support for the calculation of reference angles in step 4. Simultaneously, it forms a theoretical and practical basis for comparison with the construction of the mapping vectors in step 3, promoting the accuracy of flatness assessment.

[0030] Step 3: Construct rays passing through each grid point, starting from the Z-axis of the orthogonal coordinate system. Obtain the mapping point of each grid point in the point cloud through the rays of each grid point. Construct four mapping vectors in this grid based on the top and bottom directions and the front and back directions, respectively, according to the coordinates of the mapping points. Step 3 includes the following: Step 301: Map the point cloud to the design reference plane. The mapping logic is as follows: In a plane perpendicular to the Z-axis, construct rays that start from the Z-axis and pass through the center point of the grid, the bottom midpoint, the top midpoint, the rear midpoint, and the front midpoint, respectively. The points in the point cloud that this ray passes through are the mapping points of the grid points, and are respectively labeled as the grid center point mapping point, bottom midpoint mapping point, top midpoint mapping point, rear midpoint mapping point, and front midpoint mapping point.

[0031] By constructing rays in a plane perpendicular to the Z-axis, starting from the Z-axis and passing through the center point, bottom midpoint, top midpoint, front midpoint, and rear midpoint of the grid, the corresponding mapping points in the point cloud are determined. This process achieves a precise correspondence between the point cloud data and the design reference plane. Through ray mapping, the 3D point cloud data of the actual surrounding rock is associated with the theoretical grid points, quantifying the deviation of the actual surrounding rock surface from the design reference plane, providing crucial actual data for subsequent smoothness analysis. This step utilizes the point cloud data matched to the orthogonal coordinate system and the mesh generation results from step 1 to generate mapping points through ray mapping, providing direct coordinate data for the construction of the mapping vector in step 302, and laying the foundation for the calculation of the mapping angle in step 4, ensuring a smooth transition from theory to practice.

[0032] Step 302: Obtain the coordinates of the mapped points of each grid point. Construct four mapping vectors based on the coordinates of the five mapped points of each grid, namely mapping vector I, mapping vector II, mapping vector III, and mapping vector IV, according to the following formula: in, , , and They represent the first Line number The mapping vectors I, II, III, and IV of the column grid. , , , and These represent the X-axis coordinates of the center point, bottom midpoint, top midpoint, rear midpoint, and front midpoint of the grid in an orthogonal coordinate system, respectively. , , , and These represent the Y-axis coordinates of the center point, bottom midpoint, top midpoint, rear midpoint, and front midpoint of the grid in an orthogonal coordinate system, respectively. , , , and These represent the Z-axis coordinates of the center point, bottom midpoint, top midpoint, rear midpoint, and front midpoint of the grid in an orthogonal coordinate system.

[0033] , , and They represent the first Line number The mapping vectors I, II, III, and IV of the grid reflect the geometric characteristics of the actual tunnel surrounding rock point cloud data in the top-bottom and front-back directions within the grid. Specifically, they represent the spatial displacement direction and distance of the grid center point mapping relative to the bottom, top, rear, and front midpoint mapping points. These mapping vectors are used in the real environment to quantify the local geometric characteristics of the actual surrounding rock surface. Corresponding to the reference vector in step 2, they provide practical data for subsequent angle calculations and smoothness analysis, solving the problem of measuring the deviation between the actual surrounding rock surface and the design reference surface during tunnel construction. Independent variables ( , , (Coordinates of the grid center point mapping point), ( , , (Coordinates of the midpoint of the bottom point) , , (Top midpoint mapping point coordinates), ( , , (Coordinates of the midpoint mapping point) and ( , , The coordinates of the midpoint mapping point directly determine the magnitude and direction of each mapping vector. The dependent variable is related to these independent variables because they calculate the relative positions between mapping points through coordinate differences, reflecting the geometric relationship of the actual surrounding rock surface in the orthogonal coordinate system. Changes in the independent variables directly affect the vector components of the dependent variable. This relationship is manifested as follows: the larger the absolute value of the coordinate difference of the independent variable, the larger the magnitude of the vector. The direction is determined by the sign of the coordinate difference, thus accurately describing the geometric characteristics of the actual surrounding rock surface within the grid. This provides a reliable mathematical basis for the calculation of the mapping angle in step 4 and the comparison with the reference vector, ensuring the accuracy and scientific nature of the flatness assessment.

[0034] By acquiring the coordinates of five mapping points for each grid and calculating four mapping vectors (mapping vectors I, II, III, and IV) based on these coordinates, this process provides a mathematical expression for describing the geometric characteristics of the actual surrounding rock surface. The mapping vectors quantify the local geometric features of the actual surrounding rock in the top-bottom and front-back directions, corresponding to the reference vectors. This provides practical data support for subsequent angle comparisons and smoothness calculations, ensuring the comprehensiveness and accuracy of the analysis. This step follows the mapping point coordinates from step 301, directly generating mapping vectors, providing necessary data for the calculation of the mapping angles in step 4. Simultaneously, it compares with the reference vectors in step 2, quantifying the geometric differences between the theoretical design and the actual surrounding rock.

[0035] Step 4: Obtain the reference angles of each grid in the top-bottom direction and the front-back direction according to the four reference vectors. Obtain the mapping angles of each grid in the top-bottom direction and the front-back direction according to the four mapping vectors. Correct the mapping angles using the reference angles to obtain the flatness of the center position of each grid.

[0036] Step 4 includes the following: Step 401: Standardize the four reference vectors and four mapping vectors respectively, and obtain the reference angles of each grid in the top and bottom directions and the front and back directions of the design reference plane, based on the following formula: in, Indicates the first Line number The reference angle between the top and bottom directions of the column grid. Indicates the first Line number The reference angle between the front and rear directions of the column grid. , , and They represent the first Line number The column grid is standardized using reference vectors I, II, III, and IV; and They represent the first Line number The reference angles between the grid lines in the top-bottom and front-back directions reflect the geometric angular relationships between the design reference plane and the top-bottom direction (composed of reference vectors I and II) and the front-back direction (composed of reference vectors III and IV) within that grid. These angles are used in real-world environments to quantify the local geometric characteristics of the design reference plane. As a theoretical reference, they provide a basis for subsequent comparisons with the mapped angles of the actual surrounding rock surface, thus solving the problem of standardized description of the geometric features of the theoretically designed surface in tunnel construction. Independent variable , , , The standardized reference vectors I, II, III, and IV determine the cosine of the included angle through their dot product. The dependent variable is related to these independent variables because the included angle is calculated through the dot product, and the magnitude of the dot product directly reflects the angular difference between the two vectors. Standardization ensures that the vector length is 1, eliminating the interference of the magnitude of the vector in the angle calculation. This relationship is manifested as follows: as the dot product value of the independent variable changes from -1 to 1, the included angle of the dependent variable decreases from 180° to 0°. This accurately describes the geometric angular characteristics of the design reference plane within the grid, providing crucial theoretical data for the correction of the actual included angle and the flatness calculation in step 402, ensuring the scientific nature and consistency of the flatness assessment.

[0037] The mapping angles of the mapping vectors for each grid cell in the top-bottom and front-back directions are obtained using the following formulas: in, Indicates the first Line number The included angle of the top and bottom directions of the column grid. Indicates the first Line number The included angle of the front and rear directions of the column grid. , , and These represent the standardized mapping vectors I, II, III, and IV, respectively.

[0038] and They represent the first Line number The included angles of the grid in the top-bottom direction (composed of mapping vectors I and II) and the front-back direction (composed of mapping vectors III and IV) reflect the geometric angular relationships of the actual tunnel surrounding rock surface within the grid. These angles are used in real-world environments to quantify the local geometric characteristics of the actual surrounding rock surface. Corresponding to the reference angles calculated in step 2, they provide crucial data for subsequent comparisons of the geometric deviations between theoretical design and actual surrounding rock, thus solving the quantitative problem of assessing the smoothness of the actual surrounding rock surface during tunnel construction. Independent variable , , , The standardized mapping vectors I, II, III, and IV have their dot product values ​​determining the cosine of the included angle. The dependent variable is related to these independent variables because the included angle is calculated through the dot product. The magnitude of the dot product directly reflects the angular difference between the two mapping vectors. Standardization ensures that the vector length is 1, eliminating the interference of the magnitude on the angle calculation, thus focusing on the directional difference.

[0039] By standardizing the four reference vectors and four mapping vectors, the reference angles and mapping angles of each grid in the top-bottom and front-back directions are calculated. This process provides a quantitative angular index for assessing the geometric deviation between the actual surrounding rock and the design reference surface. Through angle calculation, the geometric differences between the theoretical design and the actual surrounding rock are transformed into comparable angular data, providing a core basis for subsequent flatness correction and comprehensive evaluation, enhancing the scientific rigor and intuitiveness of the analysis. This step utilizes the reference vectors and mapping vectors generated in steps 2 and 3, respectively, to achieve a direct comparison between theoretical and actual geometric characteristics through standardization and angle calculation. This provides crucial data for angle correction and flatness calculation in step 402, ensuring the consistency and accuracy of the analysis process.

[0040] Step 402: Correct the reference angle to the mapped angle for each grid, and obtain the actual angles of each grid in the top-bottom direction and the front-back direction, based on the following formula: in, Indicates the first Line number The actual included angle between the top and bottom directions of the column grid. Indicates the first Line number The actual included angle between the front and rear directions of the grid; and They represent the first Line number The actual angles between the grid lines in the top-bottom and front-back directions reflect the geometric angular deviations of the actual tunnel surrounding rock surface relative to the design reference plane in the corresponding directions. These actual angles are used in real-world environments to quantify the angular differences between the actual surrounding rock surface and the theoretically designed surface, reflecting the actual deviation of the surrounding rock smoothness during tunnel construction. This provides a key indicator for subsequent comprehensive smoothness calculations and solves the problem of accurately measuring the geometric differences between actual and theoretical values ​​in tunnel construction quality assessment. Independent Variable (The included angle between the top and bottom directions) (The reference angle between the top and bottom directions) (The included angle between the front and rear directions) and The reference angle in the front and rear directions directly determines the size of the actual angle. The dependent variable is related to these independent variables because they are calculated by mapping the difference between the angle and the reference angle. The absolute value of the difference reflects the angular deviation between the actual surrounding rock surface and the design reference surface, eliminating the influence of positive and negative directions and focusing on the absolute degree of deviation.

[0041] The flatness at the center of each grid is obtained using the following formula: in, Indicates the first Line number The flatness of the center position of the column grid. and Indicates weight, , , ; As a preferred embodiment and The methods for obtaining it are as follows: in, These represent the magnitudes of reference vectors I, II, III, and IV, respectively.

[0042] The flatness of the center position of each grid is summarized and output.

[0043] Indicates the first Line number The flatness at the center of the grid reflects the degree of comprehensive geometric deviation of the actual surface of the tunnel surrounding rock relative to the design reference plane within that grid. This flatness index is used in real-world environments to comprehensively evaluate the flatness of the tunnel surrounding rock surface. By combining deviations in the top-bottom and front-back directions, it provides a direct indicator for quantifying construction quality, solving the problem of how to scientifically measure the flatness of the surrounding rock surface during tunnel construction, and providing a basis for engineering quality control and optimization. (The actual angle between the top and bottom directions) (The actual angle between the front and rear directions) and weights and (satisfy The weight directly determines the degree of flatness. and The contribution ratio of the two directions to the flatness is adjusted according to engineering requirements, reflecting the impact of deviations in different directions on the overall flatness. When When the value increases, it indicates a greater deviation in the direction of the top and bottom, multiplied by the weight. Later The contribution increased; similarly, The increase will also be through Increase the flatness value. This magnitude variation is reflected in: or The higher the value, the smoother the surface. The larger the value, the greater the deviation of the surrounding rock surface within the grid, indicating greater unevenness, while the weight... and The allocation adjusts the relative impact of the two directional deviations on flatness, thereby accurately describing the flatness of the grid center position. This provides a scientific mathematical basis for the final summarization and output of flatness results, ensuring the reliability and engineering applicability of the evaluation results.

[0044] By comparing the reference angle of each grid with the mapped angle, the actual angle is calculated, and the flatness at the center of each grid is calculated using weights. The results are then summarized and output, completing a comprehensive assessment of the flatness of the tunnel surrounding rock. Angle correction eliminates the systematic deviation between theoretical design and actual surrounding rock. By combining weights and comprehensively considering the geometric characteristics of the top and bottom directions and the front and rear directions, an index that intuitively reflects the flatness of the surrounding rock surface is generated, providing a reliable basis for evaluating tunnel construction quality. This step follows the angle data from step 401, generating the final flatness index through correction and weighted calculations. This completes the entire process from point cloud data acquisition to flatness assessment, and the output results can be directly used in engineering practice, providing data support for subsequent construction optimization and quality control.

[0045] The above formulas are all dimensionless calculations. The formulas are derived from software simulations based on a large amount of collected data to obtain the most recent real-world results. The preset parameters in the formulas are set by those skilled in the art according to the actual situation.

[0046] The above embodiments can be implemented, in whole or in part, by software, hardware, firmware, or any other combination thereof. When implemented in software, the above embodiments can be implemented, in whole or in part, as a computer program product. Those skilled in the art will recognize that the units and algorithm steps of the various examples described in conjunction with the embodiments disclosed herein can be implemented by electronic hardware, or a combination of computer software and electronic hardware. Whether these functions are implemented in hardware or software depends on the specific application and design constraints of the technical solution.

[0047] The units described as separate components may or may not be physically separate. The components shown as units may or may not be physical units; they may be located in one place or distributed across multiple network units. Some or all of the units can be selected to achieve the purpose of this embodiment, depending on actual needs.

[0048] The above description is merely a specific embodiment of this application, but the scope of protection of this application is not limited thereto. Any changes 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 scope of protection of this application.

Claims

1. A three-dimensional point cloud-based calculation method for the flatness of surrounding rock in a drill-and-blast tunnel, characterized in that, The specific steps include: Step 1: Obtain the design reference surface of the tunnel, construct an orthogonal coordinate system in the design reference surface, and divide the design reference surface into a plurality of closely connected grids, obtain point cloud data by actually scanning the tunnel, and match the point cloud data to the design reference surface and the orthogonal coordinate system; Step 2: Obtain the coordinates of the grid points in each grid, including the bottom midpoint, top midpoint, front midpoint, rear midpoint and grid center point, and construct four reference vectors in the top-bottom direction and front-rear direction of the grid based on the grid center point as the center; Step 3: Construct a ray passing through each grid point with the Z-axis of the orthogonal coordinate system as the starting point, obtain the mapping points of each grid point in the point cloud through the ray passing through each grid point, and construct four mapping vectors in the top-bottom direction and front-rear direction of the grid based on the coordinates of the mapping points; Step 4: Obtain the reference angles of each grid in the top-bottom direction and front-rear direction based on the four reference vectors, obtain the mapping angles of each grid in the top-bottom direction and front-rear direction based on the four mapping vectors, and correct the mapping angles based on the reference angles to obtain the flatness of the center position of each grid.

2. The three-dimensional point cloud-based tunnel surrounding rock flatness calculation method according to claim 1, characterized in that: Obtain the design reference surface of the tunnel, which is the theoretical shape required by the tunnel design party, divide the design reference surface into grids, and the logic of the grid division is as follows: The geometric center point of the tunnel entrance section is taken as the coordinate origin, the tunnel extension direction is taken as the positive direction of the Z-axis, the horizontal left direction is taken as the positive direction of the X-axis, and the vertical upward direction is taken as the positive direction of the Y-axis to construct an orthogonal coordinate system, the tunnel section is divided at the coordinate origin according to equal angles, the tunnel profile is divided into a plurality of curve segments, the length of each curve segment corresponds to the height of the grid, the grid length is set along the Z-axis direction, and the design reference surface is divided into a plurality of closely connected grids.

3. The three-dimensional point cloud-based tunnel surrounding rock flatness calculation method according to claim 2, characterized in that: Obtain three-dimensional point cloud data of the tunnel surrounding rock through the device, denoise the point cloud data, and match the point cloud data to the design reference surface and the orthogonal coordinate system.

4. The three-dimensional point cloud-based tunnel surrounding rock flatness calculation method according to claim 3, characterized in that: Obtain the coordinates of each grid point in the design reference surface in the orthogonal coordinate system, including the bottom midpoint, top midpoint, front midpoint, rear midpoint and grid center point, the grid center point is the geometric center point of the grid, and the division logic of the bottom, top, front and rear is as follows: The positive direction of the Z-axis of the orthogonal coordinate system is forward, the negative direction of the Z-axis is rearward, the origin is taken as the center in the XY-axis plane, the clockwise direction is taken as the top direction, and the counterclockwise direction is taken as the bottom direction; Obtain four reference vectors of each grid based on the coordinates of the five grid points, including reference vector I, reference vector II, reference vector III and reference vector IV, and the formula is as follows: wherein, , , , respectively represent the reference vector I, the reference vector II, the reference vector III and the reference vector IV of the grid of the row and the column, respectively represent the X-axis coordinate of the grid center point, the bottom end midpoint, the top end midpoint, the rear end midpoint and the front end midpoint of the grid in the orthogonal coordinate system, , , , and respectively represent the Y-axis coordinate of the grid center point, the bottom end midpoint, the top end midpoint, the rear end midpoint and the front end midpoint of the grid in the orthogonal coordinate system, , , , and respectively represent the Z-axis coordinate of the grid center point, the bottom end midpoint, the top end midpoint, the rear end midpoint and the front end midpoint of the grid in the orthogonal coordinate system, , , , and respectively represent the Z-axis coordinate of the grid center point, the bottom end midpoint, the top end midpoint, the rear end midpoint and the front end midpoint of the grid in the orthogonal coordinate system, is a row search variable of the grid, , , represents the total number of rows of the grid, is a column search variable of the grid, , , represents the total number of columns of the grid.​ 5. The three-dimensional point cloud-based tunnel surrounding rock flatness calculation method according to claim 4, characterized in that: Map the point cloud to the design reference surface, and the mapping logic is as follows: In the plane perpendicular to the Z axis, the rays passing through the grid center point, the bottom end midpoint, the top end midpoint, the rear end midpoint and the front end midpoint are respectively constructed with the Z axis as the starting point. The points in the point cloud through which the rays pass are the mapping points of the grid points, which are respectively marked as the grid center point mapping point, the bottom end midpoint mapping point, the top end midpoint mapping point, the rear end midpoint mapping point and the front end midpoint mapping point.

6. The three-dimensional point cloud-based tunnel surrounding rock flatness calculation method according to claim 5, characterized in that: The coordinates of the mapping points of the grid points of each grid are respectively obtained, and four mapping vectors are constructed according to the coordinates of the five mapping points of each grid, which are respectively mapping vector I, mapping vector II, mapping vector III and mapping vector IV, and the formula is as follows: in, , , and They represent the first Line number The mapping vectors I, II, III, and IV of the column grid. , , , and These represent the X-axis coordinates of the center point, bottom midpoint, top midpoint, rear midpoint, and front midpoint of the grid in an orthogonal coordinate system, respectively. , , , and These represent the Y-axis coordinates of the center point, bottom midpoint, top midpoint, rear midpoint, and front midpoint of the grid in an orthogonal coordinate system, respectively. , , , and These represent the Z-axis coordinates of the center point, bottom midpoint, top midpoint, rear midpoint, and front midpoint of the grid in an orthogonal coordinate system.

7. The three-dimensional point cloud-based tunnel surrounding rock flatness calculation method according to claim 6, characterized in that: The four reference vectors and the four mapping vectors are respectively normalized, and the reference angles of each grid in the top-bottom direction and the front-rear direction of the design reference surface are respectively obtained, and the formula is as follows: wherein, represents the reference angle of the top-bottom direction of the grid in the first row and the first column, represents the reference angle of the front-back direction of the grid in the first row and the first column, , , and respectively represent the reference vector I, the reference vector II, the reference vector III and the reference vector IV of the grid in the first row and the first column after standardization; The mapping angles of the mapping vectors of each grid in the top-bottom direction and the front-rear direction are respectively obtained, and the formula is as follows: wherein, represents the mapping angle of the top-bottom direction of the grid in the first row and the first column, represents the mapping angle of the front-back direction of the grid in the first row and the first column, , , and represent the normalized mapping vector I, mapping vector II, mapping vector III and mapping vector IV, respectively.

8. The three-dimensional point cloud-based tunnel surrounding rock flatness calculation method according to claim 7, characterized in that: The reference angles of each grid are corrected to the mapping angles to obtain the actual angles of each grid in the top-bottom direction and the front-rear direction, and the formula is as follows: wherein, represents the actual angle of the top-bottom direction of the grid in the first row and the first column, represents the actual angle of the front-back direction of the grid in the first row and the first column; The flatness of the center position of each grid is obtained, and the formula is as follows: wherein, represents the first row and the column grid center position, and represents the weight, , , ; The flatness of the center position of each grid is summarized and output.

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