Dangerous rock mass three-dimensional modeling method and stability analysis method based on discrete point cloud

Abstract

The invention relates to the technical field of geological disaster prevention and control, and discloses a dangerous rock mass three-dimensional modeling method and stability analysis method based on discrete point clouds, and the method comprises the steps: carrying out the partitioning processing according to the obtained target point cloud data, and obtaining the point clouds of all partitions; performing gridding processing on the point clouds of each partition to obtain grid point clouds which are regularly distributed; performing curved surface construction processing according to the grid point cloud to obtain a surface triangulation network curved surface of the dangerous rock body; acquiring a boundary surface of the dangerous rock mass according to the structural surface information of the dangerous rock mass; and performing fusion processing on the boundary surface of the dangerous rock body and the surface triangulation net curved surface of the dangerous rock body to form a three-dimensional solid model of the geometrically closed dangerous rock body.

Description

Technical Field

[0001] This invention relates to the field of geological disaster prevention and control technology, specifically to a three-dimensional modeling method and stability analysis method for unstable rock masses based on discrete point clouds. Background Technology

[0002] Rockfalls are a frequent geological hazard worldwide, posing a serious threat to engineering construction and the safety of people's lives and property. This is especially true in mountainous areas with vast areas and complex geological conditions, where such disasters occur frequently and have severe consequences. Traditional rockfall surveys rely on manual field investigations, which suffer from low efficiency, high safety risks, and numerous blind spots, making it difficult to comprehensively and accurately obtain the geometric morphology and structural surface distribution characteristics of the rock mass. With the development of non-contact measurement technologies such as oblique photogrammetry and lidar, rockfall surveys have achieved a leap from two-dimensional description to three-dimensional digital representation. This allows for the rapid acquisition of massive amounts of high-precision discrete point cloud data of the rock mass surface, providing a data foundation for three-dimensional modeling and stability analysis of rockfalls. Structural surface identification and geometric parameter extraction based on point cloud data have become important research directions for rockfall hazard prevention and control.

[0003] However, existing 3D modeling techniques for unstable rock masses based on discrete point clouds still face significant bottlenecks. On the one hand, point clouds obtained from oblique photogrammetry are massive, disordered, and irregular in shape. Directly using them for surface reconstruction is susceptible to data redundancy and noise interference, often generating invalid models with voids, intersections, or distorted triangular faces, making it difficult to form accurate and usable unstable rock surfaces. On the other hand, models used for stability calculations and numerical simulations need to meet geometric closure requirements, but existing methods lack effective means to unify and automatically close complex curved surfaces and structural boundary lines, making it impossible to construct 3D solid models that meet engineering analysis needs. Furthermore, traditional stability analysis often relies on simplified 2D models, ignoring the irregularity of the actual shape of the unstable rock mass, leading to discrepancies between calculation results and actual mechanical behavior, making it difficult to support precise prevention and control of unstable rock disasters. Summary of the Invention

[0004] To address the shortcomings of existing technologies, this invention proposes a three-dimensional modeling method and stability analysis method for unstable rock masses based on discrete point clouds, in order to solve the aforementioned technical problems.

[0005] In a first aspect, the present invention provides a method for three-dimensional modeling of unstable rock masses based on discrete point clouds, including: The acquired target point cloud data is partitioned to obtain point clouds for each partition. The point clouds of each partition are processed into grids to obtain regularly distributed grid point clouds; The surface of the dangerous rock mass is obtained by performing surface construction processing based on the grid point cloud; The boundary surface of the unstable rock mass is obtained based on the structural surface information of the unstable rock mass; The boundary surface of the unstable rock mass and the surface triangular mesh of the unstable rock mass are fused together to form a geometrically closed three-dimensional solid model of the unstable rock mass.

[0006] In one embodiment, the step of partitioning the acquired target point cloud data to obtain point clouds for each partition includes: Based on the geometric features of the surface of the unstable rock mass, including the normal direction, curvature, and elevation gradient, the preprocessed point cloud data is divided into multiple geometrically uniform sub-regions. Establish a corresponding local coordinate system for each sub-region, so that the points in each sub-region meet the functional expression requirements corresponding to a single value, and obtain the point cloud of each partition.

[0007] In one embodiment, the step of performing gridding processing on the point clouds of each partition to obtain a regularly distributed grid point cloud includes: Based on the geometric distribution characteristics of different sub-regions, Cartesian coordinate projection or polar coordinate projection is used to map the point cloud in each partition to the corresponding mesh structure; The cells in the grid structure are assigned corresponding values ​​using either nearest neighbor assignment or mean assignment. Cells with missing values ​​are supplemented by neighborhood interpolation to obtain a regularly distributed grid point cloud.

[0008] In one embodiment, the step of performing surface construction processing based on the mesh point cloud to obtain the surface triangular mesh surface of the unstable rock mass includes: Using the grid point cloud as node input, constrained Delaunay triangulation is performed to obtain the surface triangular mesh surface of the unstable rock mass.

[0009] In one embodiment, obtaining the boundary surface of the unstable rock mass based on its structural surface information includes: Obtain information on the distribution, orientation, and length of the structural planes of the unstable rock mass; Based on the attitude parameters of the structural surface, the corresponding plane equation is established; Solve for the spatial plane corresponding to the plane equation and the surface of the unstable rock mass to obtain the intersection line between the two; The intersection line is sampled to obtain a point set; Based on the point set, a triangular mesh model of the boundary surface is constructed using constrained Delaunay triangulation to obtain the boundary surface.

[0010] In one embodiment, the process of fusing the boundary surface of the unstable rock mass and the surface triangular mesh of the unstable rock mass to form a geometrically closed three-dimensional solid model of the unstable rock mass includes: The surface triangular mesh and the boundary surface triangular mesh model are spliced ​​together to obtain the spliced ​​model; Boundary constraints and mesh optimization are applied to the spliced ​​model. Vertices in the common boundary region are matched and retriangulated to eliminate geometric inconsistencies and obtain a geometrically continuous and consistent optimized model. The optimized model is then processed using Boolean operations to eliminate gaps and overlaps, resulting in a geometrically closed three-dimensional solid model of the unstable rock mass.

[0011] Secondly, this invention provides a method for analyzing the stability of unstable rock masses based on discrete point clouds, including: A three-dimensional solid model of the unstable rock mass is constructed using the aforementioned three-dimensional modeling method; Extract relevant parameters of the unstable rock mass from the three-dimensional solid model of the unstable rock mass; Based on the relevant parameters of the unstable rock mass extracted from the three-dimensional solid model of the unstable rock mass, and combined with stability analysis theory or numerical simulation method, the stability calculation of the unstable rock mass under different working conditions is carried out to obtain the stability coefficient and related calculation data of the unstable rock mass under each working condition. Based on the stability coefficients and related calculation data of the unstable rock mass under each working condition, the stability evaluation results of the unstable rock mass are output.

[0012] In one embodiment, extracting relevant parameters of the unstable rock mass from the three-dimensional solid model of the unstable rock mass includes: The extracted relevant parameters include geometric parameters and physical parameters. The geometric parameters include volume, centroid coordinates, and slip surface area. The physical parameters include self-weight. The stability analysis theory includes limit equilibrium theory. The different working conditions include natural working conditions and rainstorm working conditions.

[0013] In one embodiment, the method further includes: Export the three-dimensional solid model of the unstable rock mass as a universal format file; The general format file is imported into numerical simulation software for mesh generation and mechanical simulation analysis to obtain the stress distribution, deformation characteristics and instability evolution law of the unstable rock mass.

[0014] Thirdly, an electronic device is provided, including a memory and a processor, wherein the memory and the processor are coupled together; The memory is used to store program data, and the processor is used to execute the program data to implement the three-dimensional modeling method for unstable rock masses based on discrete point clouds as described in any one of claims 1 to 6.

[0015] As can be seen from the above technical solution, the beneficial technical effects of the present invention are as follows: The 3D modeling method of this invention effectively transforms massive disordered point clouds into regular lightweight grid point clouds through a divide-and-conquer partitioning strategy, combined with geometric feature-driven point cloud partitioning and adaptive gridding processing of rectangular and polar coordinates. Then, through constrained Delaunay triangulation and structural surface boundary fusion technology, a 3D solid model of a dangerous rock mass without voids and with geometrically closed structure is successfully constructed. This model retains key morphological features such as surface cavities and complex undulations of the dangerous rock mass while significantly reducing the amount of data. The stability analysis method based on this model can accurately extract key parameters such as volume, centroid coordinates, and slip surface area. Combined with limit equilibrium theory or numerical simulation methods, multi-condition stability calculations can be carried out. The results are more consistent with the actual mechanical behavior of the dangerous rock mass, overcoming the limitations of traditional 2D simplified analysis. Furthermore, the model can be exported to a universal format and imported into mainstream numerical simulation software to achieve in-depth analysis of stress distribution, deformation characteristics, and instability evolution laws. Attached Figure Description

[0016] To more clearly illustrate the specific embodiments of the present invention or the technical solutions in the prior art, the accompanying drawings used in the description of the specific embodiments or the prior art will be briefly introduced below. In all the drawings, similar elements or parts are generally identified by similar reference numerals. In the drawings, the elements or parts are not necessarily drawn to scale.

[0017] Figure 1 This is a flowchart of the three-dimensional modeling method and stability analysis method for unstable rock masses based on discrete point clouds, as described in this invention. Figure 2 This is a point cloud zoning map of the dangerous rock surface from the perspective of the cross-section shown in this application. Figure 3 This is a schematic diagram of the dangerous rock surface zoning shown in the top view of this application; Figure 4 This is a gridded diagram in rectangular coordinates shown in this application; Figure 5 This is a gridded diagram in polar coordinates shown in this application; Figure 6 This application shows a diagram using both rectangular and polar coordinates. Figure 7 This application shows a triangular mesh surface diagram of the generated grid point cloud; Figure 8 This application shows the generated surface of the triangular mesh of the grid point cloud in polar coordinates; Figure 9 This application shows the location and characteristics of the dangerous rock area at Dazhakou. Figure 10 This is a preprocessed image of discrete points from an inclined photograph of a dangerous rock, as shown in this application. Figure 11 This is a point cloud zoning map of the dangerous rock surface shown in this application; Figure 12 This is a modeling diagram of the free face of the unstable rock shown in this application; Figure 13 This is a modeling diagram of the top surface of the unstable rock shown in this application; Figure 14 This is a diagram showing the generation of the boundary surface for modeling a dangerous rock mass, as illustrated in this application. Figure 15 This is a modeling diagram of the unstable rock entity shown in this application; Figure 16 This is a diagram illustrating the discussion of the modeling accuracy of unstable rock masses shown in this application; Figure 17 This application shows a calculation diagram of the stability analysis of a dangerous rock based on limit equilibrium. Figure 18 This application shows the construction diagram of the three-dimensional numerical analysis mesh model of the dangerous rock. Figure 19 This is a flowchart illustrating an embodiment of the present invention's method for three-dimensional modeling of unstable rock masses based on discrete point clouds; Figure 20 This is a flowchart illustrating an embodiment of the method for analyzing the stability of unstable rock masses based on discrete point clouds according to the present invention. Figure 21 This is a schematic diagram of a computer-readable storage medium according to an embodiment of the present invention. Detailed Implementation

[0018] The embodiments of the technical solution of the present invention will now be described in detail with reference to the accompanying drawings. These embodiments are merely illustrative of the technical solution of the present invention and are therefore intended to limit the scope of protection of the present invention.

[0019] It should be noted that, unless otherwise stated, the technical or scientific terms used in this application should have the ordinary meaning understood by those skilled in the art. The terms "first," "second," etc., in the specification, claims, and accompanying drawings of this disclosure are used to distinguish similar objects and are not necessarily used to describe a specific order or sequence. It should be understood that such data can be interchanged where appropriate for implementation of the embodiments of this disclosure described herein. Furthermore, the terms "comprising" and "having," and any variations thereof, are intended to cover non-exclusive inclusion. Unless otherwise stated, the term "a plurality of" means two or more. In this disclosure, the character " / " indicates an "or" relationship between the preceding and following objects. For example, A / B means: A or B. The term "and / or" describes an association relationship between objects, indicating that three relationships can exist. For example, A and / or B means: A or B, or, A and B. The term "corresponding" can refer to an association or binding relationship; A corresponding to B means that there is an association or binding relationship between A and B.

[0020] A complete unstable rock mass consists of exposed surfaces and boundary surfaces formed by structural planes. Therefore, constructing a complete 3D model of an unstable rock mass requires establishing its outer surface (usually curved) and the boundary surfaces controlled by structural planes (usually planes), and then forming a complete and closed 3D solid through the closed combination of curved and plane surfaces. Only by constructing a geometrically closed 3D solid can the volume, centroid, gravity, and contact relationship with surrounding rock masses of the unstable rock mass be accurately calculated, supporting further complex force analyses such as mechanical and stability analyses. Although oblique photogrammetry can acquire high-precision surface point cloud data, this data is usually disordered and massive, making it difficult to directly use it to construct a closed and void-free 3D model. Therefore, lightweighting and regularization of point clouds become key steps in achieving high-precision modeling. To achieve the transformation from massive disordered point clouds to lightweight solid models, this invention provides a 3D modeling method for unstable rock masses based on discrete point clouds.

[0021] like Figures 1 to 8 , Figure 19 As shown, the 3D modeling method for unstable rock masses based on discrete point clouds includes: Acquire relevant data on the unstable rock mass and preprocess it to obtain preprocessed point cloud data; Specifically, surveying and mapping.

[0022] Conduct on-site geological surveys to obtain key parameters such as the distribution of fissures, the orientation of boundary surfaces, and the depth of fissures in the unstable rock mass; combine oblique photography or lidar technology to collect point cloud data of the unstable rock surface to further interpret the fissure surface and boundary information.

[0023] Step S110: Perform partitioning processing on the acquired target point cloud data to obtain point clouds for each partition; Step S120: Perform gridding processing on the point cloud of each partition to obtain a regularly distributed grid point cloud; Specifically, point cloud lightweighting and rule-based processing.

[0024] Based on the surface morphological characteristics of the unstable rock (such as concavity and curvature variations), the region is segmented, and each region is processed into a grid, thereby transforming the original disordered point cloud into a regularly distributed grid point cloud. This process significantly reduces the amount of data and improves data regularity while preserving the main geometric features, laying the foundation for subsequent surface construction.

[0025] Step S130: Perform surface construction processing based on the mesh point cloud to obtain the surface triangular mesh surface of the unstable rock mass; Step S140: Obtain the boundary surface of the unstable rock mass based on the structural surface information of the unstable rock mass; Specifically, robust surface model generation.

[0026] Based on the gridded point cloud, a Delaunay triangular mesh surface is constructed. Because the input data has been optimized, this step efficiently generates a high-quality, void-free continuous triangular mesh surface, accurately representing the complex surface morphology of the unstable rock mass.

[0027] Step S150: The boundary surface and the surface triangular mesh of the unstable rock mass are fused to form a geometrically closed three-dimensional solid model of the unstable rock mass.

[0028] Specifically, the entity closure of multi-source boundary fusion.

[0029] Based on boundary surface information obtained from geological surveys and point cloud interpretation, a boundary model of the unstable rock mass is established. The existing surface triangular mesh model is then fused with the boundary surface, and a geometrically closed three-dimensional unstable rock mass solid model is generated through surface-to-plane stitching and Boolean operations.

[0030] In one embodiment, relevant data on the unstable rock mass is acquired and preprocessed to obtain preprocessed point cloud data, including: Conduct on-site geological surveys to obtain information on the distribution, occurrence, and extension length of the structural planes of the unstable rock mass; Point cloud data is obtained by collecting and processing data on the surface of the unstable rock mass using oblique photography or lidar technology. Open-source software was used to perform outlier filtering and preliminary lightweighting operations on the collected point cloud data, removing non-rock noise points such as vegetation to obtain clean point cloud data.

[0031] Specifically, the core objective of this step is to obtain clean and reliable point cloud data and structural surface information to lay the foundation for subsequent modeling. The implementation process is as follows: Conduct on-site geological surveys and use professional geological survey tools and observation methods to comprehensively record key information such as the distribution of structural surfaces, occurrence parameters (dip and dip angle), and extension length of the unstable rock mass. This information directly determines the accuracy of subsequent boundary surface generation.

[0032] Point cloud data is acquired using non-contact measurement techniques: Depending on the topographic conditions of the unstable rock mass and the observation requirements, either oblique photogrammetry or lidar technology, or a combination thereof, is selected. Both technologies can quickly acquire massive amounts of high-precision discrete point cloud data of the rock mass surface. Oblique photogrammetry is suitable for rapid data acquisition of large-scale unstable rock masses, while lidar technology has advantages in capturing high-precision details.

[0033] Point cloud preprocessing: Open-source software (such as CloudCompare) is used to process the collected raw point cloud data. First, outlier filtering is performed. Through the interactive analysis function of the software, outliers caused by equipment errors and environmental interference are identified and removed. Then, preliminary lightweight processing is performed to reduce data redundancy. Finally, non-rock noise points such as vegetation and buildings are removed to obtain clean and interference-free point cloud data.

[0034] In one embodiment, the acquired target point cloud data is partitioned to obtain point clouds for each partition, including: Based on the geometric features of the surface of the unstable rock mass, including the normal direction, curvature, and elevation gradient, the preprocessed point cloud data is divided into multiple geometrically uniform sub-regions. Establish a corresponding local coordinate system for each sub-region, so that the points in each sub-region meet the functional expression requirements corresponding to a single value, and obtain the point cloud of each partition.

[0035] Specifically, based on the geometric features of the unstable rock mass surface, the original point cloud is segmented into regions. This step aims to divide the complex overall point cloud into several sub-regions with relatively simple and uniform geometric features, providing a foundation for subsequent local refinement processing. The partitioning is mainly based on three key geometric features: normal vector direction, curvature, and elevation gradient. These parameters can effectively distinguish different geomorphic units, such as flat rock walls, protruding rock eaves, recessed cavities, and undulating fracture surfaces. By merging adjacent point clouds with similar geometric features into the same category, the original overall point cloud is ultimately divided into several point cloud subsets.

[0036] Specifically, such as Figure 2 As shown in (a), in the global coordinate system In the middle, for one Points on a plane There are two corresponding z-values ​​(corresponding to the top and bottom surfaces of the unstable rock mass, respectively), making it impossible to construct a definite single surface based on the point cloud. If the coordinate system is transformed into a local coordinate system... Then at this time in this local area Every point on the plane It corresponds to only one z-value, thus satisfying the conditions for function surface modeling. For example... Figure 2 As shown in (b), the global coordinate system is transformed with only one coordinate transformation. Transform to local coordinate system Even then, it may still be impossible to make the entire surface of the unstable rock mass meet the requirements of the function representation. In this case, based on the geometric characteristics of the unstable rock mass, it can be divided into three sub-regions, N1, N2, and N3, and modeled separately. Figure 2 (b) shows the three local coordinate systems , , This enables a one-point-one-value functional expression within each partition, thereby supporting subsequent partition surface modeling.

[0037] For the N2 region mentioned above, viewed from above along the AA' section, its geometry may exhibit various forms, such as... Figure 3 As shown. Figure 3 (a) is a single convex shape; Figure 3 (b) It contains two convex shapes and one concave shape; Figure 3 (c) has multiple concave shapes. For example... Figure 3 As shown in (a), when the cross-section is only convex, the region satisfies the condition "one point corresponds to one z value" on the corresponding plane; if the cross-section contains one or more concave shapes (such as...), Figure 3 (b) and (c) may not meet this condition. In this case, further zoning is required based on the surface morphology of the dangerous rock. For example... Figure 3 (b) It can be divided into three sub-partitions: S1, S2, and S3. For example... Figure 3 (c) It can be divided into four sub-regions: S1, S2, S3, and S4. By establishing an independent local coordinate system for each sub-region, the functional expression requirement of "a point on the plane corresponds to a unique z-value" can be re-satisfied within each region.

[0038] In one embodiment, the point cloud of each partition is processed into a grid to obtain a regularly distributed grid point cloud, including: Based on the geometric distribution characteristics of different sub-regions, Cartesian coordinate projection or polar coordinate projection is used to map the point cloud in each partition to the corresponding mesh structure; Assign corresponding values ​​to cells in the grid structure using either nearest neighbor assignment or mean assignment; Cells with missing values ​​are supplemented by neighborhood interpolation to obtain a regularly distributed grid point cloud.

[0039] Specifically, rasterization is essentially a resampling process designed to transform a large and irregularly distributed point cloud into a dataset defined by a fixed-resolution grid, thereby significantly reducing the data volume. After region segmentation, rasterization is performed independently on each partition. This step maps the disordered point cloud within each partition to a regular 3D grid structure, achieving data regularization and lightweighting. This paper employs two projection methods to implement this process: Cartesian coordinate projection and polar coordinate projection.

[0040] In rectangular coordinate projection, such as Figure 4 As shown, for each partition or Calculate an optimal local projection plane, whose normal vector is generally taken as the average of the normal vectors of all points within the partition. Project the 3D point cloud in the partition perpendicularly onto this plane, thus transforming the 3D surface reconstruction problem into a mesh generation problem in a 2D plane.

[0041] In a two-dimensional projection plane, a regular grid (lattice) with a set resolution (e.g., 0.5 m × 0.5 m) is defined.

[0042] For each cell, an elevation value needs to be assigned. Common methods include nearest neighbor assignment and mean assignment: the nearest neighbor method assigns the elevation of the nearest projection point to the cell's center; the mean method searches all projection points within the cell's neighborhood and calculates a weighted average or interpolation based on their elevations. For cells with empty values ​​due to uneven point cloud density or occlusion, they can be marked first and then filled using neighborhood interpolation to ensure grid continuity. In practice, since point clouds acquired by oblique photogrammetry or LiDAR are usually high-density, empty values ​​are generally rare during the gridding process.

[0043] In a Cartesian coordinate system, if a local coordinate system and the origin are defined, then the values ​​of the grid interpolation points are: (1) In the formula: The number of points falling into the cell. The first point that falls into the cell in the local coordinate system value, This represents the value of the cell in the local coordinate system after it has been rasterized.

[0044] In polar coordinates, such as Figure 5 If a local coordinate system and origin coordinates are set, then the values ​​of the grid interpolation points are: (2) In the formula: This is the distance from the origin in the local coordinate system to the first point that falls into the cell. This represents the value of the cell in the local coordinate system after it has been rasterized.

[0045] For example Figure 6 (a) shows the point cloud on the surface of the unstable rock, which can be divided into four sub-regions based on its geometric characteristics, labeled S1, S2, S3, and S4. Based on the point cloud morphology characteristics of each region, S1 and S4 are processed using rectangular coordinate projection for rasterization, while S2 and S3 are processed using polar coordinate projection, as shown below. Figure 6 (b). The result after gridding is as follows: Figure 6 As shown in (c), the original massive and messy point cloud is transformed into a lightweight and regular grid point cloud, providing a regular and efficient data foundation for subsequent 3D modeling.

[0046] The degree of lightweighting is directly controlled by the mesh resolution: the higher the resolution, the richer the geometric details preserved, but the data volume increases accordingly; conversely, reducing the resolution can reduce the data volume, but it will also lose some morphological features. Therefore, in practical applications, the mesh resolution can be flexibly set according to specific needs to achieve a reasonable balance between detail preservation and data efficiency.

[0047] In one embodiment, surface construction processing is performed based on the mesh point cloud to obtain the surface triangular mesh surface of the unstable rock mass, including: Using the grid point cloud as node input, constrained Delaunay triangulation is performed to obtain the surface triangular mesh surface of the unstable rock mass.

[0048] Specifically, this paper employs the constrained Delaunay angle subdivision method to construct the surface of the unstable rock mass. Based on the aforementioned gridding process, each partition outputs a regularly distributed 2.5D grid point cloud in the local coordinate system. In the Cartesian coordinate system, each... Coordinates correspond to unique Value; in polar coordinates, each The coordinates correspond to unique Values. Such regular point clouds can be directly used as node input for constrained Delaunay triangulation. Because the point set possesses regularity and order, algorithms such as Bowyer-Watson can effectively avoid common problems in traditional scattered point cloud triangulation, such as triangle intersections and elongated cells, thereby generating higher-quality, better-shaped triangular meshes.

[0049] The specific process is as follows: Figure 7 and Figure 8 As shown: For the grid point cloud in the Cartesian coordinate system, it is first projected onto a two-dimensional plane in the local coordinate system, then a planar Delaunay triangulation is constructed, and finally the triangulation is mapped back to three-dimensional space to restore the triangular model of the unstable rock mass surface, as shown. Figure 7 For point clouds in polar coordinates, they are first projected onto a cylindrical surface of a specified radius, then unfolded into a two-dimensional plane and triangulated to generate a triangular mesh. This mesh is then mapped back to the cylindrical surface and the original three-dimensional coordinate system, thus completing surface reconstruction. Figure 8 This method significantly improves the efficiency and stability of triangulation construction based on grid point clouds. After triangulation of each partition, a set of continuously optimized triangulated mesh surfaces is generated. S 1, S 2,…, Sn Together, they form a complete surface model of the unstable rock mass.

[0050] In one embodiment, obtaining the boundary surface of the unstable rock mass based on its structural surface information includes: Obtain information on the distribution, orientation, and length of the structural planes of the unstable rock mass; Based on the attitude parameters of the structural surfaces, the corresponding plane equations are established; Solve for the spatial plane corresponding to the plane equation and the surface of the unstable rock mass to obtain the intersection line between the two; The intersection line is sampled to obtain a point set; Based on the point set, a triangular mesh model of the boundary surface is constructed using constrained Delaunay triangulation to obtain the boundary surface.

[0051] Specifically, a dangerous rock mass can be geometrically viewed as an isolated rock block formed by different structural planes cutting through the rock mass. Therefore, based on the completed surface modeling of the dangerous rock mass, it is necessary to further mathematically describe the boundary surfaces formed by the structural planes according to their boundary conditions, thereby fully constructing the three-dimensional geometric shape of the dangerous rock mass in space.

[0052] The boundary surface of the unstable rock determined by the structural plane can be considered as a plane in space. According to spatial geometry theory, any spatial plane can be uniquely determined by its normal vector and a certain fixed point on the plane. Let the dip direction of this plane be... Inclination angle is Then its unit normal vector can be expressed as If the coordinates of a point on this plane Then the equation of the plane can be expressed as follows: (3) Based on the aforementioned plane equations, the intersection lines between multiple boundary planes, as well as the intersection lines between each plane and the existing unstable rock surface model, can be further solved. By sampling these intersection lines, the point set on the boundary surface is obtained, and the Delaunay triangulation method is used to construct a planar triangular mesh model of the boundary surface, thereby completing the boundary representation of the three-dimensional solid model of the unstable rock mass.

[0053] In one embodiment, the boundary surface of the unstable rock mass and the surface triangular mesh of the unstable rock mass are fused to form a geometrically closed three-dimensional solid model of the unstable rock mass, including: The surface triangular mesh and the boundary surface triangular mesh model are spliced ​​together to obtain the spliced ​​model; Boundary constraints and mesh optimization are applied to the spliced ​​model. Vertices in the common boundary region are matched and retriangulated to eliminate geometric inconsistencies and obtain a geometrically continuous and consistent optimized model. Boolean operations are used to eliminate gaps and overlaps in the optimized model, forming a geometrically closed three-dimensional solid model of the unstable rock mass.

[0054] Specifically, the independently constructed boundary surface triangular mesh models are integrated with the unstable rock surface triangular mesh model to form a seamless closed 3D solid model. Since the triangular meshes of each zone may overlap or have gaps at adjacent boundaries, boundary constraints and mesh optimization algorithms are introduced to match and retriangulate the vertices of common boundary regions to eliminate geometric inconsistencies and ensure continuity and smooth transitions between surfaces. Finally, all processed triangular meshes are merged into a unified and complete 3D model of the unstable rock mass. This model combines high accuracy with lightweight design: it significantly reduces the amount of data while preserving key geometric features.

[0055] like Figures 9-18 As shown, application examples: The Dazhakou dangerous cliff is located in Lizhi Subdistrict, Fuling District, Chongqing, China. Situated in a low mountain and hilly area, it specifically develops on a steep cliff at the top of a sloping hillside. Below the dangerous cliff is a major transportation route with residential areas along the way. In the event of instability and collapse, it would pose a serious threat to the lives and property of residents and the safety of passing vehicles.

[0056] The lithology of this area is mainly Upper Triassic Jialingjiang Formation limestone, with a dip of 75°∠18°. The unstable rock mass W1 is located at the leading edge of a steep cliff, with a top elevation of 324.0–326.0 m, a bottom elevation of 281.0–284.5 m, a top width of 16.20 m, a bottom width of 18.30 m, and a thickness of 3–8.5 m. The unstable rock mass has a quadrangular prism shape, as shown in the figure. Fracturing is well-developed at the rear edge of the unstable rock mass, with the main fracture at the rear edge approximately 12.7 m long, having an opening of 20–200 cm and a visible depth of 2–20 m. The left-side fracture L1 dips... The crack has a dip angle of approximately 90° and is nearly vertical, with a length of about 12m. The crack opening ranges from 12 to 35cm, and the visible depth is 4m. The right-side crack L2 dips... The rock mass has a dip angle of approximately 90° and is nearly vertical, with a length of about 10m, an opening of 12-25cm, and a visible depth of 5m. The failure mode of this unstable rock mass is sliding, with the potential sliding surface at the bottom along the weak surface L3 of the rock strata, and its dip angle being 75°∠18°.

[0057] On-site geological surveys and UAV oblique photogrammetry were conducted on the unstable rock mass. The on-site survey obtained key boundary condition information such as fracture distribution, attitude, spatial location, and extension length of the unstable rock mass. Multi-view image data of the unstable rock surface were acquired using a UAV oblique photogrammetry system, and a 3D real-world model and surface point cloud of the study area were generated based on this. On this basis, point cloud data within the main body of the unstable rock mass were extracted and processed using CloudCompare software to remove noisy point clouds such as vegetation, ultimately obtaining a clean and complete point cloud of the unstable rock mass in the overall coordinate system, such as... Figure 10 As shown.

[0058] Through interactive observation and geometric feature analysis of the unstable rock mass, the Dazhakou unstable rock mass was vertically divided into two regions, N1 and N2. For example... Figure 11 As shown in (a), region N1 is modeled using a rectangular coordinate system, with its positive Z-axis pointing vertically upwards; region N2, on the other hand, is modeled using a local coordinate system, with its positive Z-axis pointing horizontally towards the outward normal to the surface of the unstable rock. Viewing region N2 from a top-down perspective... Figure 11 (b) can be further divided into a sub-region S1. Based on the geometric distribution characteristics of the point cloud in region S1, polar coordinate projection is selected for gridding processing. The boundary of the polar coordinate projection is determined by the boundary surface formed by the fracture surfaces on both sides of the unstable rock mass. The origin of the coordinates is set at the intersection of the two fracture surfaces, with spatial coordinates of (104.10, 3280389.39, 254.0). The polar angle scanning range is set to a starting angle of 30° and an ending angle of 130°, thus completely covering the region S1.

[0059] The sampling parameters for polar coordinate gridding were set as follows: vertical spacing of 1 m and angular interval of 2°. The gridding result is as follows. Figure 12 (a) (Top-down view) and Figure 12 (b) (side view) shows the surface model of the triangular network of unstable rocks constructed based on this grid point cloud. Figure 12 As shown in (c), it can be seen that after processing by the method in this paper, the amount of data in the grid point cloud is significantly reduced, while the morphology and geometric features of the unstable rock mass are well preserved.

[0060] For the area above the unstable rock face, a rectangular coordinate system was used for grid sampling, with a spacing of 1 m along both the horizontal x and y directions. To ensure the integrity of the boundary geometry, the boundary lines were also resampled with higher density to avoid loss of contour information. The processed point cloud and corresponding triangular mesh model are shown below. Figure 13 As shown.

[0061] Based on on-site geological surveys and oblique photogrammetry analysis, the attitude parameters of the left boundary L1, right boundary L2, and bottom slip surface L3 of the unstable rock were obtained (as shown in Table 1). Plane equations for L1, L2, and L3 were established according to formula (3), and point sampling was performed on each boundary surface using point cloud data of the unstable rock surface. Based on this, a planar triangulation model enclosed by L1, L2, L3, and the bottom boundary of the model (Z = 250 m) was constructed using the Delaunay triangulation method, as shown in Table 1. Figure 14 As shown.

[0062] Table 1. Fitting data for fracture surface modeling

[0063] By combining the above steps, the construction of all curved and planar models, including the surface, top, left and right side boundaries, and bottom of the unstable rock, has been completed. These curved and planar models will then be combined and enclosed to form a... Figure 15 (a) shows a three-dimensional solid model of the unstable rock mass. Further, a Boolean cut operation is performed on this solid model using the bottom slip surface L3 to obtain a structural model showing the separation of the unstable rock mass from the underlying bedrock, as shown below. Figure 15 As shown in (b), this model accurately reproduces the surface morphology of the dangerous rock mass (such as detailed features like cavities) while fully preserving the geometric structure of its two side boundaries and bottom slip surface, thus achieving a high-precision representation of the geometric morphology of the dangerous rock mass.

[0064] like Figures 9-18 , Figure 20 The embodiment shown provides a method for analyzing the stability of unstable rock masses based on discrete point clouds, including: Step S210: Construct a three-dimensional solid model of the unstable rock mass using the three-dimensional modeling method; Specifically, the aforementioned method for 3D modeling of unstable rock masses based on discrete point clouds is employed, encompassing data preprocessing, partitioning, gridding, surface construction, boundary surface generation, and fusion closure. This process yields a geometrically closed, parameter-extractable 3D solid model of the unstable rock mass. This model provides a precise geometric and physical basis for stability analysis.

[0065] Step S220: Extract relevant parameters of the unstable rock mass from the three-dimensional solid model of the unstable rock mass; Specifically, based on the completed 3D solid model, relevant parameters are automatically extracted using a model parameter extraction algorithm: Geometric parameters: These include key parameters such as the volume of the unstable rock mass, the coordinates of its centroid, and the area of ​​the slip surface. These parameters directly affect the accuracy of stability calculations.

[0066] Physical parameters: Primarily the self-weight of the unstable rock mass, calculated from its volume and density (determined based on lithology). All extracted parameters undergo accuracy verification to ensure consistency with the actual unstable rock mass conditions.

[0067] Step S230: Based on the extraction of relevant parameters of the unstable rock mass from the three-dimensional solid model of the unstable rock mass, and combined with stability analysis theory or numerical simulation method, carry out stability calculation of the unstable rock mass under different working conditions, and obtain the stability coefficient and related calculation data of the unstable rock mass under each working condition. Specifically, the choice of analysis method depends on the failure mode of the unstable rock mass (e.g., sliding or overturning). Stability analysis theory or numerical simulation method should be selected accordingly. Limit equilibrium theory is suitable for conventional stability calculations, while numerical simulation methods are suitable for in-depth analysis of complex stress conditions.

[0068] Working conditions: Considering the actual stress environment of the unstable rock mass, different analysis working conditions are set, mainly including natural working conditions (no special external force interference) and rainstorm working conditions (water filling of the rear edge fissures, increasing water pressure). The water filling height of the fissures needs to be determined in conjunction with the actual rainfall situation for the rainstorm working condition.

[0069] Stability calculation: Substitute the extracted parameters into the corresponding analysis model or numerical simulation software to calculate the stability coefficient of the unstable rock mass under different working conditions. The magnitude of the stability coefficient directly reflects the stability state of the unstable rock mass.

[0070] Step S240: Based on the stability coefficient of the unstable rock mass under each working condition and related calculation data, output the stability evaluation results of the unstable rock mass.

[0071] Specifically, based on the stability coefficients calculated from stability analysis and related data, a stability evaluation report for the unstable rock mass is generated. The report must clearly define the stability level, potential instability risk, and key influencing factors of the unstable rock mass under different working conditions, providing a direct basis for the design of rock mass disaster prevention and control.

[0072] Model format conversion: Export the constructed 3D solid model to a common format file such as STL, ensuring that the format is compatible with mainstream numerical simulation software.

[0073] Mechanical simulation analysis: Import the exported general-format file into numerical simulation software such as ANSYS, Abaqus, FLAC3D, or 3DEC. After completing operations such as mesh generation and mechanical parameter assignment (e.g., cohesion, internal friction angle) in the software, perform mechanical simulation analysis to obtain the stress distribution characteristics, deformation laws, and instability evolution process of the unstable rock mass, providing more comprehensive technical support for in-depth evaluation of the stability of the unstable rock mass and optimization of prevention and control schemes.

[0074] In one embodiment, extracting relevant parameters of the unstable rock mass from a three-dimensional solid model of the unstable rock mass includes: The extracted relevant parameters include geometric parameters and physical parameters. Geometric parameters include volume, centroid coordinates, and slip surface area, while physical parameters include self-weight. The stability analysis theory includes limit equilibrium theory. Different working conditions include natural working conditions and rainstorm working conditions.

[0075] In one embodiment, the method further includes: Export the 3D solid model of the unstable rock mass as a universal format file; Import the common format file into numerical simulation software for mesh generation and mechanical simulation analysis to obtain the stress distribution, deformation characteristics and instability evolution law of the unstable rock mass.

[0076] Specifically, the geometric accuracy of the 3D model of the unstable rock mass is directly affected by the sampling parameters of the gridded point cloud. To compare the modeling effects under different parameters, Figure 16(a) The sampling parameters used are a vertical spacing of 1 m and an angular interval of 2°; Figure 16 (b) uses a denser vertical spacing of 0.5 m and an angular interval of 1°. A comparison shows that... Figure 16 In region (1) of (b), the model boundary exhibits significantly better performance. Figure 16 (a) is more refined; while in region (2), Figure 16 (b) The surface texture is also more detailed, preserving more local details. The results show that the finer the sampling parameters, the stronger the model's ability to reproduce geometric features, but the corresponding data volume also increases significantly. Therefore, in practical applications, a balance should be struck between model accuracy and computational efficiency based on specific task requirements, and the mesh resolution should be set reasonably.

[0077] Based on the three-dimensional solid model of the unstable rock mass, its key geometric parameters such as volume, center of gravity, and base area can be accurately extracted, providing a reliable basis for stability analysis calculations. As shown in Table 2, the actual volume of the unstable rock mass in this case is 1979.43 m³. 3 The bottom sliding surface area is 97.28 m². 2 .

[0078] Without 3D modeling technology, the volume of a dangerous rock mass is typically estimated based on on-site measurements of its length, width, and height, approximating a rectangular shape. In this example, based on on-site survey data: the top elevation ranges from 324.0 to 326.0 m, the bottom elevation from 281.0 to 284.5 m, and the estimated average height is 42.25 m; the top and bottom widths are 16.20 m and 18.30 m respectively, with an average width of 17.25 m; the thickness ranges from 3 to 8.5 m, with an average thickness of 5.75 m. Therefore, the estimated volume is 17.25 × 5.75 × 42.25 ≈ 4190 m³. 3 The results differ significantly from those obtained from 3D modeling.

[0079] In the practice of rockfall prevention and control engineering, due to the inaccuracy of traditional methods in dimensional measurement and the inherent limitations of rectangular approximation models, the volume estimation results often deviate significantly from the actual values, sometimes by several times or even orders of magnitude. This can easily lead to insufficient design basis for prevention and control engineering, affecting the safety and economy of the project.

[0080] Table 2 Information Extraction Based on 3D Geological Model

[0081] In this case, based on Figure 17 (a) The three-dimensional model is shown, and its typical cross-section is extracted as follows: Figure 17As shown in (b), three-dimensional stability analysis and two-dimensional stability analysis based on this profile were conducted. The three-dimensional stability calculation adopted the formula for calculating the stability of sliding unstable rocks proposed in the technical literature (Equations (5) to (7)), while the two-dimensional calculation adopted the limit equilibrium method formula (Equation (4)). The calculation results show that under natural conditions, the three-dimensional stability coefficient is 1.454, while the two-dimensional calculation result is 1.29; under heavy rain conditions (the water filling height of the rear edge fracture is 5.1 m), the three-dimensional stability coefficient is 1.316, while the two-dimensional calculation result is 1.09. It can be seen that there is a significant difference between the two-dimensional and three-dimensional calculation results.

[0082] Because the shapes of unstable rocks in nature are generally irregular, they are often not suitable for analysis using simplified two-dimensional models. Therefore, traditional two-dimensional stability calculation methods have significant limitations, while calculations using three-dimensional models can more accurately reflect actual mechanical behavior and have greater engineering applicability.

[0083] (4) (5) (6) (7) In the formula: The stability coefficient of the unstable rock; The self-weight of the unstable rock mass (kN / m); The height of water filling the trailing edge fissure (m); The fracture water pressure is (kN / m). ; This represents the horizontal component of the seismic force (kN / m). This represents the vertical component of the seismic force (kN / m). The inclination angle (º) of the contact surface between the unstable rock mass and the base; Slip cohesion (kPa); Slip friction angle (º); The slip length is in meters (m). The pressure of the slip surface water (kN / m) .

[0084] Furthermore, the three-dimensional geological model of the unstable rock mass constructed in this paper can be exported as a common three-dimensional format file such as STL, facilitating its import into three-dimensional modeling and visualization software such as Rhino and 3DMAX for subsequent applications. It also supports direct import into numerical simulation platforms such as ANSYS, Abaqus, FLAC3D, and 3DEC. Within these platforms, further mesh generation and mechanical simulation can be performed, allowing for in-depth analysis of the stress distribution, deformation characteristics, and instability evolution of the unstable rock mass. As an example, this paper imports the three-dimensional geological model of the Dazhakou unstable rock mass into FLAC3D and performs meshing processing; the resulting numerical model is shown below. Figure 18 As shown.

[0085] To implement the three-dimensional modeling method for unstable rock masses based on discrete point clouds described in the above embodiments, this application proposes another electronic device, which can be found in the following details. Figure 21 , Figure 21 This is a schematic diagram of the structure of an embodiment of the electronic device provided in this application.

[0086] Electronic device 700 includes memory 701 and processor 702, wherein memory 701 and processor 702 are coupled together.

[0087] The memory 701 is used to store program data, and the processor 702 is used to execute the program data to implement the three-dimensional modeling method of dangerous rock mass based on discrete point cloud in the above embodiment.

[0088] In this embodiment, processor 702 can also be referred to as CPU (Central Processing Unit). Processor 702 may be an integrated circuit chip with signal processing capabilities. Processor 702 can also be a general-purpose processor, digital signal processor, application-specific integrated circuit, field-programmable gate array or other programmable logic device, discrete gate or transistor logic device, or discrete hardware component. The general-purpose processor can be a microprocessor, or processor 702 can be any conventional processor.

[0089] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, and not to limit them; although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some or all of the technical features; and these modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the scope of the technical solutions of the embodiments of the present invention, and they should all be covered within the scope of the claims and specification of the present invention.

Claims

1. A three-dimensional modeling method for unstable rock masses based on discrete point clouds, characterized in that, include: The acquired target point cloud data is partitioned to obtain point clouds for each partition. The point clouds of each partition are processed into grids to obtain regularly distributed grid point clouds; The surface of the dangerous rock mass is obtained by performing surface construction processing based on the grid point cloud; The boundary surface of the unstable rock mass is obtained based on the structural surface information of the unstable rock mass; The boundary surface of the unstable rock mass and the surface triangular mesh of the unstable rock mass are fused together to form a geometrically closed three-dimensional solid model of the unstable rock mass.

2. The method according to claim 1, characterized in that, The step of partitioning the acquired target point cloud data to obtain point clouds for each partition includes: Based on the geometric features of the surface of the unstable rock mass, including the normal direction, curvature, and elevation gradient, the preprocessed point cloud data is divided into multiple geometrically uniform sub-regions. Establish a corresponding local coordinate system for each sub-region, so that the points in each sub-region meet the functional expression requirements corresponding to a single value, and obtain the point cloud of each partition.

3. The method according to claim 1, characterized in that, The step of performing gridded processing on the point clouds of each partition to obtain a regularly distributed grid point cloud includes: Based on the geometric distribution characteristics of different sub-regions, Cartesian coordinate projection or polar coordinate projection is used to map the point cloud in each partition to the corresponding mesh structure; The cells in the grid structure are assigned corresponding values ​​using either nearest neighbor assignment or mean assignment. Cells with missing values ​​are supplemented by neighborhood interpolation to obtain a regularly distributed grid point cloud.

4. The method according to claim 1, characterized in that, The process of constructing a surface based on the mesh point cloud to obtain the surface triangular mesh surface of the unstable rock mass includes: Using the grid point cloud as node input, constrained Delaunay triangulation is performed to obtain the surface triangular mesh surface of the unstable rock mass.

5. The method according to claim 1, characterized in that, The step of obtaining the boundary surface of the unstable rock mass based on its structural surface information includes: Obtain information on the distribution, orientation, and length of the structural planes of the unstable rock mass; Based on the attitude parameters of the structural surface, the corresponding plane equation is established; Solve for the spatial plane corresponding to the plane equation and the surface of the unstable rock mass to obtain the intersection line between the two; The intersection line is sampled to obtain a point set; Based on the point set, a triangular mesh model of the boundary surface is constructed using constrained Delaunay triangulation to obtain the boundary surface.

6. The method according to claim 1, characterized in that, The process of fusing the boundary surface of the unstable rock mass and the surface triangular mesh of the unstable rock mass to form a geometrically closed three-dimensional solid model of the unstable rock mass includes: The surface triangular mesh and the boundary surface triangular mesh model are spliced ​​together to obtain the spliced ​​model; Boundary constraints and mesh optimization are applied to the spliced ​​model. Vertices in the common boundary region are matched and retriangulated to eliminate geometric inconsistencies and obtain a geometrically continuous and consistent optimized model. The optimized model is then processed using Boolean operations to eliminate gaps and overlaps, resulting in a geometrically closed three-dimensional solid model of the unstable rock mass.

7. A method for analyzing the stability of unstable rock masses based on discrete point clouds, characterized in that, include: A three-dimensional solid model of the unstable rock mass is constructed using the aforementioned three-dimensional modeling method; Extract relevant parameters of the unstable rock mass from the three-dimensional solid model of the unstable rock mass; Based on the relevant parameters of the unstable rock mass extracted from the three-dimensional solid model of the unstable rock mass, and combined with stability analysis theory or numerical simulation method, the stability calculation of the unstable rock mass under different working conditions is carried out to obtain the stability coefficient and related calculation data of the unstable rock mass under each working condition. Based on the stability coefficients and related calculation data of the unstable rock mass under each working condition, the stability evaluation results of the unstable rock mass are output.

8. The method according to claim 7, characterized in that, The extraction of relevant parameters of the unstable rock mass from the three-dimensional solid model of the unstable rock mass includes: The extracted relevant parameters include geometric parameters and physical parameters. The geometric parameters include volume, centroid coordinates, and slip surface area. The physical parameters include self-weight. The stability analysis theory includes limit equilibrium theory. The different working conditions include natural working conditions and rainstorm working conditions.

9. The method according to claim 7, characterized in that, The method further includes: Export the three-dimensional solid model of the unstable rock mass as a universal format file; The general format file is imported into numerical simulation software for mesh generation and mechanical simulation analysis to obtain the stress distribution, deformation characteristics and instability evolution law of the unstable rock mass.

10. An electronic device, characterized in that, Includes memory and processor, wherein the memory and processor are coupled; The memory is used to store program data, and the processor is used to execute the program data to implement the three-dimensional modeling method for unstable rock masses based on discrete point clouds as described in any one of claims 1 to 6.

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