A method and system for generating manifold element meshes for geomechanical analysis

Abstract

This invention proposes a method and system for generating manifold element meshes for geomechanical analysis, belonging to the fields of computational geometry, computer graphics, and geomechanics. The method includes: S1: using a geological volume mesh C as input, selecting a background mesh BKG and defining a mathematical cover; S2: using the background mesh BKG to cut the geological volume mesh C, dividing the geocell into multiple geological volume mesh sub-units (smallcells); S3: constructing a physical cover by analyzing the connectivity of geological volumes within and between each bkgcell in the mathematical cover; S4: extracting and outputting the manifold element mesh from the physical cover. The manifold element mesh generated by this method can be used for geomechanical analysis based on three-dimensional numerical manifold methods while preserving the information of the original volume mesh.

Description

Technical Field

[0001] This invention belongs to the fields of computational geometry, computer graphics, and geomechanics, and specifically relates to a method and system for generating manifold element meshes for geomechanical analysis. Background Technology

[0002] In the field of geomechanics, mechanical analysis of geological bodies is a crucial task. By analyzing the mechanical behavior of geological bodies, we can gain a deeper understanding of the distribution, structural characteristics, and evolutionary history of strata, and predict their responses to natural conditions (such as earthquakes and debris flows) or human activities (such as mining and tunnel excavation). Furthermore, mechanical analysis is particularly important in resource development, especially in the development of oil, natural gas, and mineral resources. It provides a scientific basis for selecting drilling locations and formulating extraction strategies, improving resource extraction efficiency, and enhancing the safety of mining operations.

[0003] In geomechanics, various problems can typically be expressed using ordinary differential equations or partial differential equations. However, due to the characteristics of geological bodies, such as discontinuity, inhomogeneity, and unknown initial states, solving these equations analytically becomes extremely difficult. Therefore, in practical applications, numerical simulations using computers are usually required to obtain numerically accurate solutions. Effective numerical simulations often depend on accurate geological body modeling. Because geological bodies contain numerous faults and strata, geological body meshes are often volume meshes with complex internal properties. These polyhedral meshes can well describe the geometry and properties of geological bodies and can also be used for fluid dynamics calculations. However, due to the varying number of vertices per cell and face in such meshes, it is difficult to perform mechanical analysis directly on these meshes.

[0004] Currently, the mainstream method for solving mechanical problems is the finite element method (FEM). Its basic idea is to discretize the solution domain to obtain a finite number of elements. For a geological body mesh with complete internal geometric data and corresponding attribute data, it is difficult to directly use it for finite element analysis. The common approach is to first extract its framework surfaces (i.e., surface mesh) using software, then further subdivide the interior into tetrahedral or hexahedral finite element meshes, and finally perform finite element static analysis on this mesh. This approach has two problems: first, internal meshing of complex framework surfaces is very complex and time-consuming; second, the finite element mesh obtained through this internal subdivision does not contain the geological body's attributes, which need to be obtained through sampling and interpolation from the original body mesh. This means that the attribute data of the original body mesh is not effectively utilized.

[0005] The Numerical Manifold Method (NMM) is a discontinuous deformation analysis method, which can be seen as an extension of the finite element method. It employs a dual-coverage system combining mathematical and physical coverage, enabling the unified handling of continuous and discontinuous deformation problems. Therefore, the NMM holds great promise in the field of geology. The NMM uses two sets of meshes—a geological volume mesh and a manifold element mesh. If the volume mesh is used as the material mesh to construct the manifold element mesh, the information of the original volume mesh can be preserved on the manifold element mesh, and mechanical calculations can be performed using it. While this method, employing a dual-coverage system combining mathematical and physical coverage, has been widely applied in two dimensions, its application in three dimensions is relatively limited, and most studies are confined to surface meshes. Therefore, how to apply the NMM to three-dimensional volume meshes is a pressing issue. Summary of the Invention

[0006] To address the aforementioned technical problems, this invention provides a method for generating manifold element meshes for geomechanical analysis, comprising the following steps:

[0007] Step S1: Using the geological body mesh C as input, select the background mesh BKG and define the mathematical cover; wherein, the geological body mesh C is composed of multiple geological body mesh units geocell, and the background mesh BKG is composed of multiple background mesh units bkgcell;

[0008] Step S2: Use the background mesh BKG to cut the geological body mesh C, and cut the geocell into multiple geological body mesh sub-units smallcell;

[0009] Step S3: Construct a physical cover by analyzing the connectivity of geological bodies within and between each bkgcell in the mathematical cover;

[0010] Step S4: Extract and output the manifold mesh from the physical overlay.

[0011] Beneficial effects:

[0012] 1. Existing technologies typically require preprocessing of the geological body mesh, such as extracting the frame surface and then re-meshing the internal mesh. This process is cumbersome and prone to losing the attribute information within the original mesh. In contrast, this invention directly uses the original geological body mesh as input, fully preserving this attribute information during the construction of the manifold element mesh. Furthermore, because there is an explicit mapping relationship between the manifold element mesh and the geological body mesh, attribute mapping is convenient, allowing subsequent mechanical analysis to fully utilize the original characteristics of the geological body and improving the accuracy and reliability of the analysis results.

[0013] 2. Although numerical manifold methods have been widely used in two dimensions, research in three dimensions is relatively limited and mostly limited to surface meshes. Most implementations use the surface mesh of the geological body as input. However, this invention realizes the direct construction of manifold element meshes on the three-dimensional volume mesh as input, so that numerical manifold methods can be applied to three-dimensional geomechanical analysis. Attached Figure Description

[0014] Figure 1 This is a schematic diagram of a manifold element mesh generation method for geomechanical analysis according to the present invention;

[0015] Figure 2 This is a schematic diagram of a geological body grid.

[0016] Figure 3 This is a schematic diagram of a virtual grid cell;

[0017] Figure 4 This is a diagram illustrating the physical coverage.

[0018] Figure 5A Example 1 shows a schematic diagram of the original geological body grid;

[0019] Figure 5B Example 1 shows a schematic diagram of the fault plane extracted from the manifold element mesh;

[0020] Figure 5C Example 1 shows a schematic diagram of the artificial interface extracted from the manifold mesh;

[0021] Figure 5D Example 1 shows a schematic diagram of the ground plane extracted from the manifold element mesh;

[0022] Figure 6A Example 2 shows a schematic diagram of the original geological body grid;

[0023] Figure 6B Example 2: Schematic diagram of geological body deformation under a background grid with a step size of 50 meters;

[0024] Figure 6C Example 2: Schematic diagram of geological body deformation under a background grid with a step size of 100 meters;

[0025] Figure 6D Example 2: Schematic diagram of geological body deformation under a background grid with a step size of 200 meters;

[0026] Figure 7 This is a structural block diagram of a manifold element mesh generation system for geomechanical analysis according to the present invention. Detailed Implementation

[0027] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the invention. Furthermore, the technical features involved in the various embodiments of this invention described below can be combined with each other as long as they do not conflict with each other.

[0028] Example 1

[0029] like Figure 1 As shown in the figure, an embodiment of the present invention provides a method for generating manifold element meshes for geomechanical analysis, comprising the following steps:

[0030] Step S1: Using the geological body mesh C as input, select the background mesh BKG and define the mathematical cover; wherein, the geological body mesh C is composed of multiple geological body mesh units geocell, and the background mesh BKG is composed of multiple background mesh units bkgcell;

[0031] Step S2: Use the background mesh BKG to cut the geological body mesh C, and cut the geocell into multiple geological body mesh sub-units smallcell;

[0032] Step S3: Construct a physical cover by analyzing the connectivity of geological bodies within and between each bkgcell in the mathematical cover;

[0033] Step S4: Extract and output the manifold mesh from the physical overlay.

[0034] In one embodiment, step S1 above involves selecting a background grid BKG and defining a mathematical overlay using the geological body grid C as input; wherein the geological body grid C is composed of multiple geological body grid cells (geocells), and the background grid BKG is composed of multiple background grid cells (bkgcells); specifically including:

[0035] A three-dimensional regular hexahedral mesh that completely covers the geological body mesh C is selected as the background mesh BKG, where the rotation direction of BKG is arbitrary; the space occupied by the 8 bkgcells with common vertices in BKG is selected as the mathematical cover.

[0036] The physical mesh of the model is used to describe the boundaries, internal cross-sections, details, and properties of an object. In this invention, the physical mesh of the model is defined as a geological volume mesh. A geological volume mesh is a mathematical model that discretizes geological bodies in three-dimensional space. It achieves a digital description of geological structures by dividing the geological body into multiple layered units (such as hexahedrons), each unit containing specific geological properties. In this invention, the input geological volume mesh is as follows: Figure 2As shown, the included attribute information includes the type representing the face and the identifier id of the face. These two values ​​combined provide a unique identifier for the face attribute information. Each geological body grid cell has a series of attributes, which can be represented as a series of attribute arrays.

[0037] In one embodiment, step S2 above: using the background mesh BKG to cut the geological body mesh C, the geocell is cut into multiple geological body mesh sub-units smallcell; specifically including:

[0038] Traverse all geocells in the geological body grid C, cut the geocells using BKG, and obtain the geological body inside each BKG cell.

[0039] Since a geological unit may be a spatial polyhedron, this type of polyhedron is not easy to cut directly. And since the three points must lie on a plane, it is necessary to transform its surface into a planar piece through surface triangulation. The specific steps are as follows:

[0040] First, the surface of the geocell is triangulated, transforming the geocell into a surface-triangulated mesh. During the triangulation process, a fixed rule is strictly followed to select the starting triangle from the polygon for recursive triangulation. At the same time, a topology consistency check algorithm is used to ensure the topology consistency of the common surfaces of adjacent geocells.

[0041] Then, a depth-first method is used to cut the mesh, calculate the bounding box size of the mesh, and calculate all interference surfaces in the x-direction that interfere with it, storing them in an array. For each interference surface in the x-direction in the array, Boolean operations from CGAL (Computational Geometry Algorithms Library) are used to calculate the intersection and difference between the interference surface and the mesh. The part of the mesh inside the interference surface in the x-direction is the intersection, and the part outside is the difference between the cut cell and the space represented by the cutting plane. The difference is kept in the loop for further cutting, while the intersection is cut in the y-direction in the same way as described above. Then, the intersection is cut out in the y-direction and cut in the z-direction. The difference is kept in the loop for further cutting. Finally, the intersection obtained after being cut by the z-direction interference surface is the so-called geological body mesh sub-unit smallcell, which must completely belong to a certain background mesh unit. The set of smallcells belonging to the same background mesh unit is the geological body inside that background mesh unit bkgcell.

[0042] In one embodiment, step S3 above: constructing a physical cover by analyzing the connectivity of geological bodies within and between each bkgcell in the mathematical cover; specifically including:

[0043] Traverse the bkgcell to obtain the set of smallcells in the current bkgcell. Based on the connectivity between each smallcell, obtain all connected components within the bkgcell. For each connected component, add a corresponding physical cover to the mathematical cover at the 8 vertices of the bkgcell it belongs to. Construct virtual mesh cells (VCs) to record the tuple relationship between connected components, the bkgcell they belong to, and the 8 introduced physical covers. Based on the connectivity between virtual mesh cells (VCs), merge the physical covers to obtain the final physical cover (PC).

[0044] Physical covers are derived from the division of mathematical covers by geological bodies. Disconnected geological bodies within a mathematical cover belong to different physical covers. In this invention, constructing a physical cover PC requires traversing background grid cells. First, connected components within each background grid cell are found, then connected components between adjacent background grid cells are found. Initially, a physical cover is added to the mathematical cover at each of the eight vertices of the current connected component, resulting in a total of eight physical covers. To facilitate recording these eight physical covers and the geological bodies in each connected component, this invention proposes a new data structure—the virtual grid cell. For each background grid cell, a new virtual grid cell is created for each connected component, and the geological bodies in that connected component, i.e., the set of smallcells, are recorded within this virtual grid cell. Simultaneously, the eight newly added physical covers are recorded at the eight vertices of the virtual grid cell, effectively adding a physical cover PC to each of the eight vertices representing the mathematical cover. Each virtual grid cell records the smallcell number contained within it, as well as the physical cover numbers at the eight vertices. Figure 3 As shown, the left side is a background grid cell completely occupied by geological bodies, but a geological interface creates two connected domains. Therefore, two virtual grid cells are constructed as shown on the right. Geological bodies that are not connected within the background grid cell (bkgcell) are not necessarily disconnected in the mathematical overlay. After the initial physical overlay is constructed, the physical overlays between virtual grid cells are independent. Connected geological bodies that originally belonged to the same mathematical overlay will be assigned to different physical overlays. Therefore, physical overlay grouping and merging are required. The physical overlays (PCs) that need to be merged on adjacent virtual grids are as follows: Figure 4 As shown.

[0045] The specific steps for building physical coverage are as follows:

[0046] First, iterate through all background grid cells (bkgcell), obtain the set of small cells from the current background grid cell (bkgcell), determine the connectivity between each small cell, create a new virtual grid cell for each connected component, and create 8 physical covers for it. The physical cover number and the small cell number in the current connected component are stored in the member variable of the virtual grid cell.

[0047] Then, iterate through the virtual grid cell set of each background grid cell, and determine whether the virtual grid cell set in each virtual grid cell set is connected to the virtual grid cell sets in its adjacent background grid cells in the x, y, and z directions. If they are connected, merge the four sets of physical covers on the common surface and renumber the physical covers. This step yields the virtual grid cells on all background grid cells, and each virtual grid cell contains an internally connected set of smallcells and eight final physical cover numbers.

[0048] In one embodiment, step S4 above: extracting and outputting the manifold element mesh from the physical overlay specifically includes:

[0049] According to the definition of a manifold, which is the intersection of physical covers (PCs), the geological bodies inside the virtual mesh cell (VC) and the eight physical covers covering the geological bodies are extracted to form the manifold mesh. The BKG, VC, PC, and smallcell are output as files for subsequent calculation and analysis.

[0050] For the background grid (BKG), due to its regularity, the background grid can be fully described by its step size and minimum coordinates in three directions, as well as the number of BKG cells in those three directions. Therefore, its attribute information is stored in a separate file in a fixed order. For the indices of all manifolds in each background grid cell (i.e., the indices of the corresponding virtual grid cells), since the number of virtual grid cells derived from a single background grid cell is inconsistent, they are stored in two array files. The first array stores the indices of all manifolds in each background grid cell sequentially, and the second array identifies the start and end indices of the manifold index in each background grid cell within the first array. The physical coverage information of the manifolds and the background grid cell numbering information are also stored separately. The information is also stored in two arrays. For smallcells, each smallcell is serialized and output sequentially. First, the number of triangular facets and the stratum number of the small cell surface are output. Then, the coordinates of the three vertices on each face are output sequentially and stored in one array file. Another array file is used to record the attribute type and id values ​​of each face on each smallcell, as well as the face normal vector information. For the output of smallcells in manifolds, since the number of smallcells in each manifold is not the same, their information is stored in two array files. One array file is used to describe the number of smallcells in each manifold, and the other is used to describe the start and end indices of the smallcells in the first array.

[0051] The following examples demonstrate that the manifold element mesh generated by the method of the present invention contains information about the original geological body mesh and is suitable for geomechanical analysis:

[0052] Example 1: Verify that the manifold element mesh generated by the method of this invention contains information about the original geological body mesh:

[0053] The input original geological body mesh is as follows Figure 5A As shown, Figure 5B , 5C 5D represents the fault plane, artificial interface, and ground plane extracted from the manifold element mesh after constructing the geological body mesh. It can be seen that the information of these interfaces is complete and correct, which shows that the manifold element mesh constructed by the method of the present invention inherits the geometric and attribute information of the original geological body very well.

[0054] Example 2: Verify that the manifold element mesh generated by the method of this invention can be used for geomechanical analysis:

[0055] The input original geological body mesh is as follows Figure 6A As shown in Table 1, the material geometric and mechanical properties of the geological body are as follows.

[0056] Table 1. Material geometric and mechanical properties of geological bodies

[0057]

[0058] When constructing the manifold element mesh, experiments were conducted using background meshes with step sizes of 50 meters, 100 meters, and 200 meters in the x, y, and z directions, respectively. The two sides of the model in the x direction were fixed, and the natural falling under gravity was observed. By default, the two sides of the interface are in fixed contact during static analysis.

[0059] The deformation diagrams of geological bodies under background grids with step lengths of 50 meters, 100 meters, and 200 meters are shown below. Figure 6B , Figure 6C and Figure 6D As shown in the figure above, it can be seen that under different background grid step sizes, static analysis of the same intact geological body under the same mechanical scenario shows that the overall displacement falls downwards and the displacement shape is roughly the same. Furthermore, it was observed that no intrusion or fracture occurred in the material mass surrounding the geological body interface, a phenomenon consistent with mechanical laws. Further, the specific experimental data for the three experiments at different step sizes are shown in Table 2. As the step size is halved each time, the displacement range between different step sizes gradually decreases, indicating that the displacement results do indeed converge as the step size decreases. Since the model's work area is 4000 meters... 2800 meters The displacement is 1240.4 meters, therefore the difference between the displacements at different time lengths in Table 2 is acceptable, which shows that the manifold element mesh generated by the method of the present invention is applicable to real geological bodies.

[0060] Table 2 Experimental data under different pace lengths

[0061]

[0062] Example 2

[0063] like Figure 7 As shown, this embodiment of the invention provides a manifold element mesh generation system for geomechanical analysis, comprising the following modules:

[0064] Construct a background mesh and mathematical overlay module 51 to define the background mesh specifications, position, and rotation direction;

[0065] The geological body mesh cutting module 52 is used to cut the geological body mesh C using the background mesh BKG, cutting the geocell of the geological body mesh C into multiple geological body mesh sub-units smallcell, and assigning them to the corresponding background mesh unit bkgcell.

[0066] A physical cover module 53 is constructed to analyze the connectivity of geological bodies within and between each bkgcell in the mathematical cover, and to construct the physical cover.

[0067] The manifold mesh module 54 is used to extract and output the manifold mesh from the physical overlay.

[0068] A manifold element mesh generation device for geomechanical analysis includes one or more electronic devices, wherein the one or more electronic devices are used to implement the manifold element mesh generation method, system and device for geomechanical analysis.

[0069] An electronic device includes: one or more processors; and a memory for storing one or more programs, wherein when the one or more programs are executed by the one or more processors, the one or more processors cause the one or more processors to implement a manifold element mesh generation method, system, and apparatus for geomechanical analysis.

[0070] A computer-readable storage medium having executable instructions stored thereon, which, when executed by a processor, cause the processor to implement a manifold element mesh generation method, system, and apparatus for geomechanical analysis.

[0071] A non-transitory computer-readable storage medium storing a computer program that, when executed by a processor, implements a manifold element mesh generation method, system, and apparatus for geomechanical analysis.

[0072] The above description is merely a specific embodiment of the present invention, enabling those skilled in the art to understand or implement this application. Various modifications to these embodiments will be readily apparent to those skilled in the art, and the general principles defined herein may be implemented in other embodiments without departing from the spirit or scope of this application. Therefore, the present invention is not to be limited to the embodiments shown herein, but is to be accorded the widest scope consistent with the principles and novel features claimed herein.

Claims

1. A method for generating manifold element meshes for geomechanical analysis, characterized in that, include: Step S1: Using the geological body mesh C as input, select the background mesh BKG and define the mathematical cover; wherein, the geological body mesh C is composed of multiple geological body mesh units geocell, and the background mesh BKG is composed of multiple background mesh units bkgcell; Step S2: Use the background mesh BKG to cut the geological body mesh C, and cut the geocell into multiple geological body mesh sub-units smallcell; Step S3: Construct a physical cover by analyzing the connectivity of geological bodies within and between each bkgcell in the mathematical cover, specifically including: Traverse the bkgcell to obtain the set of smallcells in the current bkgcell. Based on the connectivity between each smallcell, obtain all connected components within the bkgcell. Each connected component adds a corresponding physical cover to the mathematical cover at the 8 vertices of its bkgcell. Construct virtual mesh units (VCs) to record the tuple relationship between connected components, their respective bkgcells, and the 8 introduced physical covers. Based on the connectivity between virtual mesh units (VCs), merge the physical covers to obtain the final physical cover (PC). Step S4: Extract and output the manifold element mesh in the physical cover. Since there is an explicit mapping relationship between the manifold element mesh and the geological body mesh during the construction of the manifold element mesh, the manifold element mesh completely retains all its attribute information from the geological body mesh, which facilitates attribute mapping.

2. The manifold element mesh generation method for geomechanical analysis according to claim 1, characterized in that, Step S1: Using the geological body mesh C as input, select the background mesh BKG and define mathematical coverage; wherein, the geological body mesh C is composed of multiple geological body mesh units (geocells), and the background mesh BKG is composed of multiple background mesh units (bkgcells); specifically including: A three-dimensional regular hexahedral mesh that completely covers the geological body mesh C is selected as the background mesh BKG, wherein the rotation direction of BKG is arbitrary; the space occupied by the 8 bkgcells with common vertices in BKG is selected as the mathematical cover.

3. The manifold element mesh generation method for geomechanical analysis according to claim 2, characterized in that, Step S2: Use the background mesh BKG to cut the geological body mesh C, and cut the geocell into multiple geological body mesh sub-units smallcell; Specifically, it includes: Traverse all geocells in the geological body grid C, cut the geocells using BKG, and obtain the geological body inside each BKG cell.

4. The manifold element mesh generation method for geomechanical analysis according to claim 3, characterized in that, Step S4: Extracting and outputting the manifold element mesh from the physical overlay specifically includes: According to the definition of a manifold, which is the intersection of physical covers (PCs), the geological bodies inside the VC and the eight physical covers covering the geological bodies are extracted to form the manifold mesh. The BKG, VC, PC and smallcell are output as files for subsequent calculation and analysis.

5. A manifold element mesh generation system for geomechanical analysis, characterized in that, Includes the following modules: Construct background mesh and mathematical overlay modules to define the background mesh specifications, location, and rotation direction; The geological body mesh cutting module is used to cut the geological body mesh C using the background mesh BKG, cutting the geocell of the geological body mesh C into multiple geological body mesh sub-units smallcell, and assigning them to the corresponding background mesh unit bkgcell; The physical cover construction module is used to analyze the connectivity of geological bodies within and between each bkgcell in the mathematical cover, and to construct the physical cover, specifically including: Traverse the bkgcell to obtain the set of smallcells in the current bkgcell. Based on the connectivity between each smallcell, obtain all connected components within the bkgcell. Each connected component adds a corresponding physical cover to the mathematical cover at the 8 vertices of its bkgcell. Construct virtual mesh units (VCs) to record the tuple relationship between connected components, their respective bkgcells, and the 8 introduced physical covers. Based on the connectivity between virtual mesh units (VCs), merge the physical covers to obtain the final physical cover (PC). The manifold mesh acquisition module is used to extract and output manifold meshes from physical overlays. Since there is an explicit mapping relationship between manifold meshes and geological body meshes during the construction of manifold meshes, the manifold meshes completely retain all attribute information from the geological body meshes, which facilitates attribute mapping.

6. A manifold element mesh generation device for geomechanical analysis, characterized in that, It includes one or more electronic devices, wherein the one or more electronic devices are used to implement the method of any one of claims 1 to 4.

7. An electronic device, characterized in that, include: One or more processors; A memory for storing one or more programs, wherein when the one or more programs are executed by the one or more processors, the one or more processors cause the one or more processors to implement the method of any one of claims 1 to 4.

8. A computer-readable storage medium, characterized in that, It stores executable instructions that, when executed by a processor, cause the processor to implement the method described in any one of claims 1 to 4.

9. A non-transitory computer-readable storage medium, characterized in that, It stores a computer program that, when executed by a processor, implements the steps of the method as described in any one of claims 1 to 4.

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