Three-dimensional rock mesoscopic model modeling method based on Voronoi and four-parameter random growth method

Abstract

The invention discloses a three-dimensional rock mesoscopic model modeling method based on Voronoi and a four-parameter random growth method. The three-dimensional rock mesoscopic model modeling method comprises the steps that the shape and size of a rock sample model are determined; determining the composition and content of each mineral and the particle size of mineral particles of the established rock sample model; determining the internal porosity of the built rock sample model; generating a rock mineral particle model based on a Voronoi structure according to the determined components and contents of the minerals and the particle sizes of the mineral particles; according to the determined internal porosity of the model, generating a rock pore model based on a four-parameter random generation algorithm; and according to the rock mineral particle model and the rock pore model, combining the two models into a whole in the same space. According to the method, the discontinuity, heterogeneity and anisotropy characteristics of rock materials can be simulated by establishing the rock three-dimensional mesoscopic finite element model, and mesoscopic mineral particles and native fractures in the rock can be well reflected.

Description

Technical Field

[0001] The present invention relates to the field of numerical simulation of rock mechanics, and particularly to a three-dimensional modeling method for the mesoscopic structure of rocks, specifically a three-dimensional rock mesoscopic model modeling method based on Voronoi and four-parameter stochastic growth method. Background Art

[0002] Rocks in nature are typical discontinuous, inhomogeneous, and anisotropic materials. Rocks generally consist of multiple mineral components, and at the same time, irregular fractures and other joints may be distributed inside, which have a great impact on the mechanical properties of rocks. Therefore, in geotechnical engineering, the mechanical properties of fractured rocks are a key issue. At present, the research on fractured rocks generally uses numerical simulation methods. In the current mainstream finite element modeling, the rock material is usually regarded as a homogeneous material for calculation, ignoring the characteristics of the rock itself, and cannot meet the requirements of three-dimensional rock mesoscopic modeling. Based on this, a modeling method for a three-dimensional rock mesoscopic model based on Voronoi structure and four-parameter stochastic growth method is proposed. Summary of the Invention

[0003] The purpose of the present invention is to provide a modeling method for a three-dimensional model of the mesoscopic structure of rocks, so as to be able to effectively perform finite element modeling of rock materials.

[0004] To achieve the above object, the present invention provides the following technical solutions:

[0005] A three-dimensional modeling method for the mesoscopic structure of rocks, comprising:

[0006] a) Determining the shape and size of the rock specimen model;

[0007] b) Determining the mineral composition, content, and mineral particle size of the built rock specimen model;

[0008] c) Determining the internal porosity of the built rock specimen model;

[0009] d) Generating a rock mineral particle model based on the Voronoi structure according to the determined mineral composition, content, and mineral particle size;

[0010] e) Generating a rock pore model based on a four-parameter random generation algorithm according to the determined internal porosity of the model;

[0011] f) Merging the two models into a whole in the same space according to the rock mineral particle model and the rock pore model.

[0012] Preferably, the specific implementation method of step b) adopted in the present invention is: using a CT device to scan the rock, and obtaining the mineral composition, content and mineral particle size of the pre-selected rock sample by grayscale recognition;

[0013] Preferably, the specific implementation method of step c) adopted in the present invention is: using CT equipment to scan the rock, identify the pores in the rock, and obtain the porosity of the pre-selected rock sample.

[0014] Preferably, the specific implementation method of step d) adopted in the present invention is: using the Voronoi structure to construct the random distribution of mineral particles inside the rock, the mineral composition, content and mineral particle size are determined according to the CT scanning results, and the specific construction steps are as follows:

[0015] ① Generate a specified number of points in a given space in a completely random distribution manner and form a point set, each point in the point set corresponds to the center of a Voronoi polyhedron. When setting the number of Voronoi cells in the point set in the space, assuming that the rock mineral particles are spherical and the corresponding average pore size is d, the number of random points N can be calculated according to the following formula:

[0016]

[0017] Where: V is the size of the space corresponding to the specimen, which here refers to the volume of the foam aluminum specimen.

[0018] In the random generation process, the minimum distance between any two nucleation points is set to δ. The smaller the minimum distance δ, the smaller the size of the generated rock mineral particles and the denser the distribution. This parameter can reflect the size and distribution density of the particles represented by the generated Voronoi structure. In addition, the parameter irregularity k is defined to characterize the irregularity of the generated model, so as to control the morphological characteristics of the particles.

[0019]

[0020] In the formula, δ 0 When the particle shape is a regular polyhedron, it is the minimum distance between adjacent nucleation points determined by the number of particles and the model size.

[0021]

[0022] Where V is the volume of the Voronoi structure containing N nucleation points.

[0023] ② After randomly generating nucleation points, the adjacent nucleation points are subjected to Delaunay decomposition to obtain the Voronoi polyhedron structure of the region. The specific decomposition process is to first connect any nucleation point with the adjacent point in space, and make a perpendicular bisector for the line between the two points. The Voronoi polyhedron structure can be obtained by connecting the perpendicular bisectors around the nucleation point and removing the redundant parts. Finally, the Voronoi polyhedron structure of all nucleation points in space is generated.

[0024] ③After the Voronoi polyhedron structure is formed, it is necessary to determine the content and position of the mineral particles of different components. The content of each type of mineral particles is determined according to the content of each mineral component of the rock obtained by CT scanning; the position of mineral particles of different components is determined according to a random function, and the order is from low to high according to the component content. When the position of one mineral particle is completely determined, the position of the next mineral particle is determined immediately until all the mineral particles of all components are completed.

[0025] Preferably, the specific implementation method of step e) adopted in the present invention is: using a four-parameter random growth algorithm to generate a three-dimensional rock fracture model, the rock porosity is determined according to the CT scanning result, and the specific construction steps are as follows:

[0026] ① Set the rock fracture part as the growth phase, the rock mineral part as the non-growth phase, and set the fracture growth phase probability as C dd , each node in the grid area will be assigned a random number between 0 and 1. If the random number is less than the distribution probability C dd , then the node becomes the crack growth core, C dd The value of should be smaller than the porosity setting value ε.

[0027] ② According to each given directional growth probability D i , each crack growth core is extended to the adjacent grid nodes in all directions, where i represents the direction, and the three-dimensional structure growth direction becomes 26, that is, i = 26. Similarly, for each newly added crack, a new random number will be assigned to its adjacent grid nodes. If the random number of the adjacent unit in the i direction is less than D i , it will become the growth phase.

[0028] ③ Repeat steps ① and ②. When the crack content in the grid area meets the set porosity ε, the crack growth process ends.

[0029] Preferably, the specific implementation method of step f) adopted in the present invention is: according to the established three-dimensional rock mineral composition model and three-dimensional rock fracture model, the rock fracture model is implanted into the rock mineral composition model through Boolean operation, and the specific construction steps are as follows:

[0030] ①Unify the appearance shape and size of the three-dimensional rock mineral composition model and the three-dimensional rock fracture model.

[0031] ②Combine the two models spatially and remove the overlapping part with the fracture model in the three-dimensional rock mineral composition model through Boolean operation.

[0032] ③Implant the fracture part in the three-dimensional rock fracture model into the rock mineral composition model to form a three-dimensional mesoscopic model of the rock.

[0033] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0034] The purpose of the present invention is to provide a modeling method for a three-dimensional model of the mesoscopic structure of rocks, so as to be able to effectively perform finite element modeling of rock materials. The three-dimensional mesoscopic finite element model of the rock accurately obtains characteristic parameters such as the internal mineral distribution, content, and porosity of the rock according to image processing technologies such as CT scanning, establishes a three-dimensional rock mineral composition model and a three-dimensional rock fracture model, combines the two models through Boolean operation, determines the mineral composition and pores based on CT scanning; controls the morphology of mineral particles based on the number and position of nucleation points; controls the fracture morphology based on the probability of fracture growth direction. By establishing a three-dimensional mesoscopic finite element model of the rock, the discontinuity, inhomogeneity, and anisotropy characteristics of rock-like materials can be simulated, and the internal mesoscopic mineral particles and primary fractures of the rock can be well reflected. Description of the Drawings

[0035] Figure 1 is a flow chart of a modeling method for a three-dimensional model of the mesoscopic structure of rocks provided by the present invention;

[0036] Figure 2 is a rock specimen diagram to be scanned in the present invention;

[0037] Figure 3 is a diagram of the division of different mineral components of the rock specimen obtained by scanning;

[0038] Figure 4 is a diagram of a three-dimensional rock mineral composition model established based on the Voronoi structure;

[0039] Figure 5 is a diagram of the cubic pixel points of the rock fracture;

[0040] Figure 6 is a diagram of a three-dimensional model of the rock fracture; Detailed Embodiment

[0041] The technical solutions in the embodiments of the present invention will be clearly and completely described below. Obviously, the described embodiments are only a part of the embodiments of the present invention, rather than all embodiments. All other embodiments obtained by those of ordinary skill in the art based on the embodiments of the present invention without creative efforts shall fall within the protection scope of the present invention.

[0042] As Figures 1-6 shown, the present invention provides a modeling method for a three-dimensional rock mesoscopic model based on the Voronoi structure and the four-parameter random growth method. The method includes the following steps:

[0043] ① Obtain the spatial position distribution of mineral components through CT scanning. Taking the Figure 2 rock specimen shown as an example, its main constituent minerals are feldspar, quartz, biotite, etc.

[0044] ② The process of identifying different types of minerals and extracting particle boundary characteristics is based on the basic principle of CT scanning imaging. Since the pixel values of the images obtained for different mineral components are different, and within the same mineral particle, the pixel values are basically the same, different mineral particles can be distinguished by the gray-scale recognition method according to the difference in pixel values. The gray-scale image is a matrix image, and the value of the matrix represents the shade of gray-scale. Process the gray-scale image to draw a gray-scale histogram and perform image segmentation to identify different types of minerals in the image. The discontinuity and similarity of gray-scale values are two bases for image segmentation: utilize the discontinuity of gray-scale values to identify the boundaries of different mineral particles and different types of mineral particles through the sudden change of gray-scale values; utilize the similarity of gray-scale values to distinguish different mineral particles through the spatial region of similar pixel values, as Figure 3 shown. Based on the gray-scale recognition method, rock characteristic parameters such as the mineral distribution, content, and porosity in the CT scan image can be obtained.

[0045] ③ Use the Voronoi structure to construct the random distribution of mineral particles inside the rock. The mineral composition, content, and the particle size of mineral particles are determined according to the CT scan results. The construction steps are as follows:

[0046] a) Generate a specified number of points in a given space in a completely random distribution manner and form a point set. Each point in the point set corresponds to the center of a Voronoi polyhedron. When setting the number of Voronoi cells in the point set in the space, assume that the rock mineral particles are all spherical and the corresponding average pore diameter is d. Then the number of random points N can be calculated according to the following formula:

[0047]

[0048] In the formula: V is the size of the space corresponding to the specimen, which here refers to the volume of the foam aluminum specimen.

[0049] During the random generation process, the minimum distance between any two nucleation points is set as δ. The smaller the minimum distance δ is, the smaller the size of the generated rock mineral particles and the denser the distribution. This parameter can reflect the size of the particles represented by the generated Voronoi structure and the density of the distribution. In addition, by defining the parameter irregularity k to characterize the irregularity of the generated model, the morphological characteristics of the particles can be controlled.

[0050]

[0051] In the formula, δ 0 is the minimum distance between adjacent nucleation points determined according to the number of particle bodies and the model size when the particle shape is a regular polyhedron.

[0052]

[0053] In the formula, V is the volume of the Voronoi structure containing N nucleation points.

[0054] b) After randomly generating nucleation points, Delaunay triangulation is performed on adjacent nucleation points to obtain the Voronoi polyhedron structure of the region. The specific triangulation process is to first connect any nucleation point with adjacent points in space, and make a perpendicular bisecting plane for the connection between two points. Connect the perpendicular bisecting planes around the nucleation point and remove the redundant parts to obtain the Voronoi polyhedron structure. Finally, the Voronoi polyhedron structures of all nucleation points in space are generated in this way.

[0055] c) After the Voronoi polyhedron structure is formed, it is necessary to determine the content and position of mineral particles of different components. The content of various mineral particles is determined according to the content of each mineral component of the rock obtained by CT scanning; the positions of mineral particles of different components are determined according to a random function, and the order is from low to high according to the component content. When the positions of all mineral particles of one component are determined, the positions of the next mineral component are immediately determined until all components of mineral particles are completed, as Figure 4 shown.

[0056] ④ Using the four-parameter random growth algorithm, a three-dimensional rock fracture model is generated. The rock porosity is determined according to the CT scan results. The construction steps are as follows:

[0057] a) Set the rock fracture part as the growth phase and the rock mineral part as the non-growth phase. The growth pixel points are as Figure 5 shown. Set the fracture growth phase probability as C dd , and random numbers between 0 and 1 will be assigned to each node in the grid area. If the random number is less than the distribution probability C dd , then this node becomes the fracture growth core, Cdd Its value should be less than the porosity set value ε.

[0058] b) According to each given directional growth probability D i , each fracture growth nucleus is extended to adjacent grid nodes in all directions, where i represents the direction, and the three-dimensional structure growth direction becomes 26, that is, i = 26. Similarly, for each newly added fracture, a new random number will be assigned to its adjacent grid nodes. If the random number of the adjacent cell in the i direction is less than D i , it will become the growth phase.

[0059] c) Repeat steps a) and b). When the fracture content in the grid area meets the set porosity ε, the fracture growth process ends, as Figure 6 shown.

[0060] ⑤ According to the established three-dimensional rock mineral composition model and three-dimensional rock fracture model, through Boolean operation, implant the rock fracture model into the rock mineral composition model. The construction steps are as follows:

[0061] a) Unify the appearance shape and size of the three-dimensional rock mineral composition model and the three-dimensional rock fracture model.

[0062] b) Combine the two models in space. Through Boolean operation, remove the overlapping part with the fracture model in the three-dimensional rock mineral composition model.

[0063] c) Implant the fracture part in the three-dimensional rock fracture model into the rock mineral composition model to form a three-dimensional mesoscopic model of the rock.

[0064] Although the embodiments of the present invention have been described, for those of ordinary skill in the art, it can be understood that various changes, modifications, substitutions, and variations can be made to these embodiments without departing from the principles and spirit of the present invention. The scope of the present invention is defined by the appended claims and their equivalents.

Claims

1. A three-dimensional rock mesoscopic modeling method based on Voronoi and four-parameter random growth method, characterized in that: include: a) Determine the shape and size of the rock sample model; b) Determine the mineral composition, content and mineral particle size of the constructed rock sample model; c) Determine the internal porosity of the constructed rock sample model; d) generating a rock mineral particle model based on the Voronoi structure according to the determined mineral components, contents and mineral particle sizes; e) generating a rock pore model based on a four-parameter random generation algorithm according to the determined internal porosity of the rock sample model; f) Based on the rock mineral particle model and the rock pore model, the two models are combined into a whole in the same space.

2. The three-dimensional rock mesoscopic modeling method based on Voronoi and four-parameter random growth method according to claim 1 is characterized in that: The specific implementation method of step b) is: use CT equipment to scan the rock, and obtain the mineral composition, content and mineral particle size of the pre-selected rock sample through grayscale recognition.

3. The three-dimensional rock mesoscopic modeling method based on Voronoi and four-parameter random growth method according to claim 1 is characterized in that: The specific implementation method of step c) is: use CT equipment to scan the rock, identify the pores in the rock, and obtain the porosity of the pre-selected rock sample.

4. The three-dimensional rock mesoscopic modeling method based on Voronoi and four-parameter random growth method according to claim 1 is characterized in that: The specific implementation method of step d) is: using the Voronoi structure to construct the random distribution of mineral particles inside the rock, the mineral composition, content and mineral particle size are determined according to the CT scanning results, and the specific construction steps are as follows: ① Generate a specified number of points in a completely random distribution in a given space and form a point set, each point in which corresponds to the center of a Voronoi polyhedron; when setting the number of Voronoi cells in the point set in the space, assuming that the rock mineral particles are spherical and the corresponding average pore size is d, the number of random points N is calculated according to the following formula: Where: V is the size of the space corresponding to the specimen, which refers to the volume of the foam aluminum specimen; In the random generation process, the minimum distance between any two nucleation points is set to δ. The smaller the minimum distance δ is, the smaller the size of the generated rock mineral particles is and the denser the distribution is. This parameter can reflect the size of the particles represented by the generated Voronoi structure and the density of their distribution. In addition, the parameter irregularity k is defined to characterize the irregularity of the generated model, so as to control the morphological characteristics of the particles. Where δ0 is the minimum distance between adjacent nucleation points determined by the number of particles and model size when the particle shape is a regular polyhedron; Where V is the volume of the Voronoi structure containing N nucleation points; ② After randomly generating nucleation points, the adjacent nucleation points are subjected to Delaunay partitioning to obtain the Voronoi polyhedron structure of the region. The specific partitioning process is to first connect any nucleation point with the adjacent point in space, and make a perpendicular bisector for the line between the two points. The Voronoi polyhedron structure can be obtained by connecting the perpendicular bisectors around the nucleation point and removing the redundant parts. Finally, the Voronoi polyhedron structure of all nucleation points in space is generated. ③After the Voronoi polyhedron structure is formed, it is necessary to determine the content and position of the mineral particles of different components; the content of each type of mineral particles is determined according to the content of each mineral component of the rock obtained by CT scanning; the position of mineral particles of different components is determined according to a random function, and the order is from low to high according to the component content. When the position of one mineral particle is determined, the position of the next mineral particle is determined immediately until all the mineral particles of all components are completed.

5. The three-dimensional rock mesoscopic modeling method based on Voronoi and four-parameter random growth method according to claim 1 is characterized in that: The specific implementation method of step e) is: using a four-parameter random growth algorithm to generate a three-dimensional rock fracture model, the rock porosity is determined according to the CT scanning results, and the specific construction steps are as follows: ① Set the rock fracture part as the growth phase, the rock mineral part as the non-growth phase, and set the fracture growth phase probability as C dd , each node in the grid area will be assigned a random number between 0 and 1. If the random number is less than the distribution probability C dd , then the node becomes the crack growth core, C dd The value of should be smaller than the porosity setting value ε; ② According to each given directional growth probability D i , each crack growth core is extended to the adjacent grid nodes in all directions, where i represents the direction, and the three-dimensional structure growth direction becomes 26, i.e., i=26; Similarly, for each newly added crack, a new random number will be assigned to its adjacent grid nodes; if the random number of the adjacent cells in the i direction is less than D i , it will become the growth phase; ③ Repeat steps ① and ②. When the crack content in the grid area meets the set porosity ε, the crack growth process ends.

6. The three-dimensional rock mesoscopic modeling method based on Voronoi and four-parameter random growth method according to claim 1 is characterized in that: The specific implementation method of step f) is: according to the established three-dimensional rock mineral composition model and three-dimensional rock fracture model, the rock fracture model is implanted into the rock mineral composition model through Boolean operation. The specific construction steps are as follows: ① Unify the appearance shape and size of the 3D rock mineral composition model and the 3D rock fracture model; ② Combine the two models in space and remove the overlapping parts with the fracture model in the three-dimensional rock mineral composition model through Boolean operation; ③Implant the fracture part in the three-dimensional rock fracture model into the rock mineral composition model to form a three-dimensional rock microscopic model.

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