Tunnel over-excavation and under-excavation identification and over-excavation and under-excavation amount calculation method based on voxel method

Through the voxel method based on the method, three-dimensional laser scanning and RANSAC algorithm are used to quickly judge and calculate the tunnel super-under-digging amount, solving the problems of slow speed and low accuracy of traditional methods, and achieving efficient and accurate calculation of tunnel super-digging amount.

CN119919473APending Publication Date: 2025-05-02DALIAN UNIV OF TECH

Patent Information

Application Number
CN202411871081.2
Authority / Receiving Office
CN · China
Patent Type
Applications(China)
Current Assignee / Owner
Filing Date
2024-12-18
Publication Date
2025-05-02

AI Technical Summary

Technical Problem

In tunnel engineering, the traditional calculation method for over-under-digging is slow, and marking points are required, which is difficult to adapt to rapidly changing geological conditions, and it is difficult to accurately judge and calculate over-under-digging.

Method used

Using a voxel-based method, the three-dimensional point cloud data of the tunnel is obtained through a three-dimensional laser scanner, and the palm surface and the side wall part of the tunnel are extracted in combination with the RANSAC algorithm to generate a design outline point cloud and register it with the actual point cloud. The super-under-digging area is judged through projection and voxel division and the amount of earth is calculated.

Benefits of technology

It realizes fast and efficient tunnel over-under-digging judgment and quantity calculation, improves work efficiency and calculation accuracy, is suitable for different geological conditions and tunnel shapes, and has wide applicability and cost control effects.

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Abstract

The invention discloses a voxel method-based tunnel over-excavation and under-excavation identification and over-excavation and under-excavation quantity calculation method, and belongs to the field of tunnel intelligent construction and blasting quality evaluation. According to the technical scheme, three-dimensional point cloud of exposed surrounding rock is obtained for noise reduction processing, and RANSCA is used for extracting tunnel face and tunnel side wall surrounding rock parts; generating a design contour point cloud, registering the design contour point cloud with the actual tunnel, and moving to the same coordinate system; projecting the actual point cloud and the design point cloud of the tunnel to the cross section, and converting into points on a plane; connecting the projections of the design point clouds into a closed polygon; judging an over-excavation and under-excavation area; the space is divided into tiny voxels, and the affiliation relation between each voxel and an over-excavation or under-excavation area is judged; the number of voxels in the over-excavation and under-excavation areas is accumulated and multiplied by the volume of a single voxel, and the over-excavation and under-excavation earthwork volume is obtained. The method has the advantages of high efficiency, accuracy, intuition, feasibility, accurate quantification, high adaptability, cost control and the like, the construction quality of tunnel engineering is effectively improved, and the engineering cost is reduced.
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Description

Technical Field

[0001] The present invention belongs to the technical field of intelligent tunnel construction and blasting quality assessment, and relates to a method for intelligently judging over-break and under-break of a tunnel excavated by blasting and calculating the amount of over-break and under-break, and in particular to a method for identifying over-break and under-break of a tunnel and calculating the amount of over-break and under-break based on a voxel method. Background Art

[0002] In tunnel engineering, blasting excavation methods still occupy a relatively important position due to their advantages such as simplicity, low cost and wide applicability. However, the rapidly changing geological conditions during tunnel excavation make it difficult to control the amount of explosives, resulting in over-excavation or under-excavation, which is difficult to meet the actual design outline. The estimation and calculation of over-excavation or under-excavation are particularly important for cost control. The traditional over-excavation and under-excavation method usually uses a total station or level to roughly measure and estimate its volume. This method is slow and requires the setting of landmarks, which is particularly tight for short tunnel excavation periods.

[0003] Laser scanners calculate the distance of objects by emitting lasers and recording the reflection time and reflectivity. Laser scanners can collect dense point clouds of exposed surrounding rock contours, which is particularly simple and practical when applied to the judgment of tunnel over-excavation and under-excavation.

[0004] Patent CN106401643B proposes a method for judging over-break and under-break of a section and a method for calculating the over-break and under-break area, but does not provide a method for calculating the over-break amount (volume). Therefore, a method is needed that can simply and quickly judge and calculate the over-break and under-break amount. The present invention is proposed based on this demand. Summary of the invention

[0005] In order to solve the above technical problems existing in the prior art, the present invention provides a method for identifying tunnel over-break and under-break and calculating the over-break amount based on the voxel method, which can quickly and efficiently judge and calculate the over-break area and over-break amount of the blasting excavated tunnel.

[0006] To achieve the above object, the present invention provides the following technical solutions:

[0007] A method for identifying tunnel over-break and under-break and calculating over-break and under-break volume based on voxel method, the specific steps are as follows:

[0008] S1. Use a 3D laser scanner to obtain a 3D point cloud of the exposed surrounding rock in the tunnel face area after blasting and excavation and before the initial support;

[0009] S2, performing noise reduction processing on the obtained three-dimensional point cloud, and using the RANSCA algorithm to extract the tunnel face and the surrounding rock parts of the tunnel side wall respectively;

[0010] S3, generating a design contour point cloud according to the design section of the tunnel, registering the design contour point cloud with the actual tunnel, and moving them to the same coordinate system;

[0011] S4. Project the actual point cloud and the design point cloud of the tunnel to the cross section and convert them into points on the plane. Connect the projection of the design point cloud into a closed polygon. Determine the over-excavation and under-excavation area by whether the projection of the actual point cloud is within the polygon;

[0012] S5, dividing the space into tiny cubes, i.e., voxels, and determining the relationship between each voxel and the over-excavation or under-excavation area;

[0013] S6. Accumulate the number of voxels in the over-excavation area and the under-excavation area, and multiply by the volume of a single voxel to obtain the over-excavation and under-excavation earthwork volume.

[0014] Furthermore, the specific steps of step S1 are: after the tunnel is blasted and slag is discharged and before the initial support, the three-dimensional laser scanning equipment is started to scan the exposed surrounding rock layer by layer to obtain the fine three-dimensional point cloud data of its surface. During the scanning process, the equipment is ensured to be stable to reduce the impact of external vibration on data collection.

[0015] Furthermore, the specific steps of step S2 are to preliminarily process the collected three-dimensional point cloud data, remove noise and invalid data, and retain the structural information of the tunnel face and the tunnel side wall to ensure the quality of the point cloud data in subsequent steps. Preferably, the RANSAC algorithm is used to perform plane fitting on the noise-reduced point cloud, and the matching degree between the model and the point cloud is ensured by setting parameters such as the distance threshold and the number of iterations.

[0016] Furthermore, the specific steps of step S3 are to convert the actual point cloud and the designed point cloud data of the tunnel into a unified coordinate system and align them to the positions of the corresponding cross sections to ensure the projection accuracy and comparability of the two sets of data.

[0017] Furthermore, the specific steps of step S4 are to perform cross-sectional projection on the actual point cloud and the design point cloud respectively, simplifying the three-dimensional data into plane points for subsequent geometric analysis. The projected design point cloud is connected in sequence into a closed polygon to ensure that a closed structure without self-intersection and continuity is formed. The projection points of the actual excavation point cloud are traversed, and the ray method is used to determine whether the point is within the polygon. The points within the polygon correspond to the under-excavation area, and vice versa, they correspond to the over-excavation area. The over-excavation area and the point cloud are determined by this method.

[0018] Furthermore, the specific steps of step S5 are to construct a uniform voxel grid in the three-dimensional space around the tunnel, dividing the area into a series of independent tiny cubes. The voxel size is set according to the engineering accuracy requirements to ensure sufficient resolution to detect subtle over-excavation or under-excavation. The actual point cloud and the designed point cloud data are mapped to the voxel grid, and it is identified whether each voxel contains the actual point cloud or the designed point cloud data. The judgment results are marked in the voxel grid, and each voxel is assigned a category label of "over-excavation", "under-excavation", and "whether it contains tunnel point cloud" for subsequent over-excavation and under-excavation calculations.

[0019] Furthermore, the specific steps of step S6 are to accumulate the number of voxels marked with "overbreak" and "underbreak" respectively, and multiply them by the volume of a single voxel to obtain the overbreak and underbreak earthwork volume. There is a problem with using this calculation method, that is, due to the irregularity of the overbreak and underbreak area, the voxels in the edge area will always exceed the edge, even if the voxels are divided small enough. Therefore, a method is adopted to correct some errors. For the voxels in the overbreak and underbreak area containing the tunnel point cloud, they are regarded as the edge of the overbreak and underbreak area, so the calculated volume of the voxel is taken as one-half.

[0020] Beneficial effects of the present invention:

[0021] Compared with the prior art, the method for identifying tunnel over-break and under-break and calculating the over-break amount based on the voxel method of the present invention has the following technical characteristics or beneficial effects:

[0022] (1) Efficient and accurate over-excavation and under-excavation judgment: The 3D point cloud data of the tunnel face area is obtained by a 3D laser scanner, and the plane fitting is performed in combination with the RANSAC algorithm, which can accurately distinguish the tunnel face and the surrounding rock of the tunnel side wall, providing a high-quality data basis for subsequent over-excavation and under-excavation judgment. Compared with traditional total station or level measurement, this method is not only faster, but also does not require the setting of marker points, greatly improving work efficiency.

[0023] (2) Intuitive and easy identification of over-break and under-break areas: By projecting the actual point cloud and the designed point cloud onto the cross section and converting them into points on the plane, it is possible to intuitively determine whether the actual point cloud is within the designed polygon, thereby quickly identifying the over-break and under-break areas. This method makes the judgment of over-break and under-break simple and clear, easy to understand and operate.

[0024] (3) Accurate and quantitative calculation of over-break and under-break volume: The voxel method is used to divide the space into tiny cubes, and the relationship between each voxel and the over-break or under-break area is determined, so as to accurately calculate the over-break and under-break volume. This method not only takes into account the shape and size of the over-break and under-break area, but also reduces the error by correcting the calculated volume of the voxels in the edge area, thereby improving the accuracy of the calculation.

[0025] (4) Strong adaptability: The method of the present invention is applicable to tunnel projects with different geological conditions and tunnel shapes and has wide applicability. At the same time, by adjusting parameters such as voxel size, it can meet the accuracy requirements of different projects, thereby improving the flexibility and practicality of the method.

[0026] (5) Cost control: By accurately calculating and judging the over-excavation and under-excavation areas and the over-excavation and under-excavation amounts, it can provide strong support for the cost control of tunnel projects. It can avoid problems such as material waste and construction delays caused by over-excavation or under-excavation, and reduce project costs.

[0027] The present invention provides a method for identifying tunnel over-break and under-break and calculating the amount of over-break and under-break based on the voxel method. The method has the advantages of high efficiency and accuracy, intuitiveness and ease of operation, precise quantification, strong adaptability and cost control, and is of great significance for improving the construction quality of tunnel projects and reducing project costs. BRIEF DESCRIPTION OF THE DRAWINGS

[0028] In order to more clearly illustrate the technical solutions of the embodiments of the present invention, the present invention will be described in detail below in combination with the accompanying drawings and detailed embodiments. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without creative labor. Among them:

[0029] Figure 1 It is the technical roadmap of the present invention;

[0030] Figure 2 This is the result diagram of the tunnel face fitting in Example 1;

[0031] Figure 3 This is a schematic diagram of the relationship between the position of the point and the polygon determined by the ray method of the present invention;

[0032] Figure 4 This is a diagram showing the over-excavation and under-excavation judgment results of this embodiment;

[0033] Figure 5 Schematic diagram of the voxel classification method of the present invention. DETAILED DESCRIPTION

[0034] In order to make the purpose, technical solution and advantages of the present invention more clearly understood, the present invention is further described in detail below in conjunction with the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the present invention and are not intended to limit the present invention. Figure 1-5The voxel-based tunnel over-excavation and under-excavation identification and over-excavation and under-excavation amount calculation method is further explained, and the technical solutions in the embodiments of the present application are clearly and completely described; obviously, the described embodiments are only part of the embodiments of the present application, not all of the embodiments, and based on the embodiments in the present application, all other embodiments obtained by ordinary technicians in this field without making creative work are within the scope of protection of this application.

[0035] The present invention provides a method for identifying tunnel over-break and under-break and calculating the over-break amount based on voxel method. Figure 1 As shown, the specific steps include:

[0036] S1, use a 3D laser scanner to obtain the 3D point cloud of the exposed surrounding rock in the tunnel face area after blasting excavation and before the initial support.

[0037] S2, the obtained 3D point cloud is subjected to denoising, and the RANSCA algorithm is used to extract the tunnel face and the surrounding rock of the tunnel side wall.

[0038] S3, generating a design contour point cloud according to the design section of the tunnel, registering the design contour point cloud with the actual tunnel, and moving them to the same coordinate system.

[0039] S4, project the actual point cloud and the design point cloud of the tunnel to the cross section and convert them into points on the plane. Connect the projection of the design point cloud into a closed polygon. Determine the over-excavation and under-excavation area by whether the projection of the actual point cloud is within the polygon.

[0040] S5, dividing the space into tiny cubes, namely voxels, and determining the relationship between each voxel and the over-excavation or under-excavation area.

[0041] S6, accumulating the number of voxels in the over-excavation area and the under-excavation area, and multiplying the number by the volume of a single voxel to obtain the over-excavation and under-excavation earthwork volume.

[0042] Example 1

[0043] After the tunnel is blasted and slag is discharged, and before the initial support, the 3D laser scanning equipment is started to scan the exposed surrounding rock layer by layer to obtain fine 3D point cloud data of its surface. During the scanning process, the equipment is ensured to be stable to reduce the impact of external vibration on data collection.

[0044] The collected 3D point cloud data is preliminarily processed to remove noise and invalid data, while retaining the structural information of the tunnel face and tunnel sidewall to ensure the quality of point cloud data in subsequent steps. Here, manual and filtering methods can be used to remove noise point clouds.

[0045] Preferably, the RANSAC algorithm is used to perform plane fitting on the denoised point cloud, and the matching degree between the model and the point cloud is ensured by setting parameters such as the distance threshold and the number of iterations. The mathematical model of the plane can be expressed as follows:

[0046] ax+by+cz+d=0 (1)

[0047] Among them, (a, b, c) is the normal vector of the plane, and satisfies a 2 +b 2 +c 2 =1. The RANSAC algorithm is used to find the best combination of a, b, c, and d parameters in the point cloud so that the fitted plane can represent the structure of the face. Three non-collinear points p1 (x1, y1, z1), p2 (x2, y2, z2), and p3 (x3, y3, z3) are randomly selected from the denoised point cloud data. A plane can be determined by these three points. Based on the three selected points, the normal vector (a, b, c) of the plane is calculated using the vector cross product:

[0048] v1=(x2-x1,y2-y1,z2-z1) (2)

[0049] v2=(x3-x1,y3-y1,z3-z1) (3)

[0050] (a,b,c)=v1×v2 (4)

[0051] Using the formula and substituting in the coordinates of one of the points (for example, p1), we can solve for d:

[0052] d=-(ax1+by1+cz1) (5)

[0053] For each point p in the point cloud i (x i ,y i ,z i ), calculate its distance d to the fitting plane i , the formula is:

[0054]

[0055] If d i If the distance between the point and the plane is less than the preset distance threshold ε, the point is considered to be consistent with the plane and recorded as an inlier. The number of inliers in the plane fitting is recorded. Repeat the above random sampling, plane fitting and consistency verification process, and execute the set maximum number of iterations N or until the plane with the largest number of inliers is found. Finally, the plane with the largest number of inliers is selected as the best fitting plane. The result of fitting the face in this embodiment is shown in the figure. Figure 2As shown. The choice of ε depends on the thickness of the tunnel face ε>d / 2, and 1 cm is taken in this embodiment. Based on the above steps, the tunnel face point cloud can be fitted and the tunnel face point cloud is temporarily subtracted.

[0056] Furthermore, the designed contour point cloud is projected onto the cross section to obtain the coordinates (m, n) of the projection point of the central axis of the designed tunnel. According to the actual situation and the reference point, the positional relationship between the central axis of the actual tunnel and the emission point of the laser scanner is obtained, and the projection coordinates of the central axis on the cross section are obtained (the coordinate system is the laser point cloud coordinate system). The center point of the designed tunnel point cloud is moved to the central axis to align the designed point cloud with the central axis of the actual excavated tunnel point cloud.

[0057] Preferably, cross-sectional projection is performed on the actual point cloud and the design point cloud respectively, and the three-dimensional data is simplified into plane points to facilitate subsequent geometric analysis. The projected design point cloud is connected in sequence into a closed polygon to ensure that a closed structure without self-intersection and continuity is formed. Use the ray method to determine whether a point in the two-dimensional plane is within the irregular polygon POL1. Starting from the point to be determined, a ray is emitted in any direction, and the number of intersections between the ray and the polygon boundary is counted. If the number of intersections is an odd number, the point is inside the polygon; if it is an even number, the point is outside the polygon. Assume that the vertices of the irregular polygon are arranged in clockwise or counterclockwise order, and the vertex coordinates are (x1, y1), (x2, y2),…, (x n ,y n ), where (x n ,y n )=(x1,y1) means the polygon POL1 can be closed and does not intersect with other edges. The point to be judged is P(x,y). A horizontal ray is emitted from point P to the positive direction of the X axis. Traverse each edge of the polygon and set the two endpoints of the edge to (x i ,y i ) and (x i+1 ,y i+1 ), the coordinates of the intersection point Q need to satisfy:

[0058] min(y i ,y i+1 ) <y≤max(y i ,y i+1 ) (7)

[0059] If the intersection point exists, then the x intersect The coordinates are:

[0060]

[0061] If x intersect>x, it means that the ray passes through the edge; otherwise, the ray does not pass through the edge. In the process of traversing all the edges of the polygon, count the number of times the ray crosses the polygon edge. If the number of intersections is an odd number, the point is inside the polygon, otherwise it is outside the polygon. The schematic diagram of the ray method to determine the position relationship between a point and a polygon can be seen Figure 3 .

[0062] Preferably, this method is used to determine whether the excavation point cloud is inside or outside the design contour. If the projection point falls inside the polygon POL1 formed by the projection of the design contour, the point cloud is an under-excavation point cloud, otherwise it is an over-excavation point cloud. The over-excavation and under-excavation judgment results of this embodiment are as follows: Figure 4 As shown, red represents the under-excavation area, blue represents the over-excavation area, and the black point cloud is the design contour point cloud.

[0063] Furthermore, after determining the over-excavation and under-excavation areas, the amount of over-excavation and under-excavation needs to be calculated. Construct a uniform voxel grid in the three-dimensional space around the tunnel, and divide the area into a series of independent tiny cubes. The voxel size is set according to the engineering accuracy requirements to ensure sufficient resolution to detect subtle over-excavation or under-excavation. The size of the voxel is l, in meters, and in this embodiment, l=1e-4. The coordinates of the center point of the voxel are regarded as the coordinates of the voxel, and the excavated tunnel point cloud is divided into sections along the central axis with a width of 100 voxels (2 cm), and the sectioned point cloud is projected onto the cross section. Similarly, the projected points are connected into an irregular polygon POL2. Traverse each voxel and use the method in step S4 to determine the ownership of the voxel. As shown in Figure 5 As shown, let the voxel be V i , there are the following situations:

[0064] (1)V i ∈POL1∩V i ∈POL2, which is neither an overmined nor an undermined area.

[0065] (2) Undercut area.

[0066] (3) Over-excavation area.

[0067] (4) It is neither an overbreak nor an underbreak area.

[0068] These voxels are classified and marked with corresponding labels. At the same time, for voxels that meet conditions (2) and (3), it is determined whether the voxels contain point clouds. The volume calculation method of the over-excavation area is:

[0069] Q over =(N over -N cp )V voxel / 2 (9)

[0070] Q under =(N under -N cp )V voxel / 2 (10)

[0071] Where Q over represents the amount of over-excavation, Q under is the undercut amount, N over , N under Respectively represent the number of voxels of conditions (3) and (2), N cp is the number of voxels that contain points in the point cloud. voxel = l 3 Indicates the volume of voxels. When the voxels are divided into small enough, the over-excavation and under-excavation calculation will be more accurate.

[0072] Through the above steps, the over-excavation and under-excavation areas and the over-excavation and under-excavation amounts of the tunnel can be quickly and accurately determined and calculated.

[0073] The above description is only a preferred specific implementation manner of the present invention, but the protection scope of the present invention is not limited thereto. Any technician familiar with the technical field can make equivalent replacements or changes according to the technical scheme and inventive concept of the present invention within the technical scope disclosed by the present invention, which should be covered by the protection scope of the present invention.

Claims

1. A method for identifying tunnel over-break and under-break and calculating over-break and under-break based on voxel method, characterized in that: Here are the steps: S1. Use a 3D laser scanner to obtain a 3D point cloud of the exposed surrounding rock in the tunnel face area after blasting and excavation and before the initial support; S2, performing noise reduction processing on the obtained three-dimensional point cloud, and using the RANSCA algorithm to extract the tunnel face and the surrounding rock parts of the tunnel side wall respectively; S3, generating a design contour point cloud according to the design section of the tunnel, registering the design contour point cloud with the actual tunnel, and moving them to the same coordinate system; S4, projecting the actual point cloud and the design point cloud of the tunnel onto the cross section and converting them into points on the plane; connecting the projection of the design point cloud into a closed polygon; judging the over-excavation and under-excavation areas by whether the projection of the actual point cloud is within the polygon; S5, dividing the space into tiny voxels, and determining the relationship between each voxel and the over-excavation or under-excavation area; S6. Accumulate the number of voxels in the over-excavation area and the under-excavation area, and multiply by the volume of a single voxel to obtain the over-excavation and under-excavation earthwork volume.

2. The method for identifying tunnel over-break and under-break and calculating over-break and under-break based on voxel method according to claim 1, characterized in that: The specific steps of step S1 are: after blasting and slag removal in the tunnel and before the initial support, start the three-dimensional laser scanning equipment to scan the exposed surrounding rock layer by layer to obtain fine three-dimensional point cloud data of its surface.

3. The method for identifying tunnel over-break and under-break and calculating over-break and under-break based on voxel method according to claim 1, characterized in that: The specific steps of step S2 are: preliminarily processing the collected three-dimensional point cloud data, removing noise and invalid data, and retaining the structural information of the tunnel face and the tunnel side wall to ensure the quality of the point cloud data in subsequent steps.

4. The method for identifying tunnel over-break and under-break and calculating over-break and under-break based on voxel method as claimed in claim 3, characterized in that: The RANSAC algorithm is used to perform plane fitting on the denoised point cloud, and the matching degree between the model and the point cloud is ensured by setting the distance threshold and the number of iterations.

5. The method for identifying tunnel over-break and under-break and calculating over-break and under-break based on voxel method according to claim 1, characterized in that: The specific steps of step S3 are: converting the actual point cloud and design point cloud data of the tunnel into a unified coordinate system and aligning them to the positions of the corresponding cross sections to ensure the projection accuracy and comparability of the two sets of data.

6. The method for identifying tunnel over-break and under-break and calculating over-break and under-break based on voxel method according to claim 1, characterized in that: The specific steps of step S4 are: performing cross-sectional projection on the actual point cloud and the design point cloud respectively, simplifying the three-dimensional data into plane points, so as to facilitate subsequent geometric analysis; connecting the projected design point clouds into closed polygons in sequence, ensuring that a closed structure without self-intersection and continuous is formed; Traverse the projection points of the actual excavation point cloud and use the ray method to determine whether the point is within the polygon; the point within the polygon corresponds to the under-excavation area, otherwise it corresponds to the over-excavation area; this method is used to determine the over-excavation area and the point cloud.

7. The method for identifying tunnel over-break and under-break and calculating over-break and under-break based on voxel method according to claim 1, characterized in that: The specific steps of step S5 are as follows: construct a uniform voxel grid in the three-dimensional space around the tunnel, dividing the area into a series of independent tiny cubes; set the voxel size according to the engineering accuracy requirements to ensure sufficient resolution to detect subtle over-excavation or under-excavation; map the actual point cloud and the designed point cloud data to the voxel grid, and identify whether each voxel contains the actual point cloud or the designed point cloud data; mark the judgment result to the voxel grid, and assign each voxel a category label of "over-excavation", "under-excavation", and "whether it contains tunnel point cloud" for subsequent over-excavation and under-excavation calculations.

8. The method for identifying tunnel over-break and under-break and calculating over-break and under-break based on voxel method according to claim 1, characterized in that: The specific steps of step S6 are to accumulate the number of voxels marked with "overbreak" and "underbreak" respectively, and multiply them by the volume of a single voxel to obtain the overbreak and underbreak earthwork volume.

9. The method for identifying tunnel over-break and under-break and calculating over-break and under-break based on voxel method according to claim 8, characterized in that: The voxels in the over-undercut area of ​​the tunnel point cloud are regarded as the edge of the over-undercut area, and the calculated volume of the voxel is taken as one-half.

Citation Information

Patent Citations

  • Tunnel over-under-excavation detection method based on laser point cloud

    CN106401643B

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