A method and system for modeling near-field dynamics based on rock heterogeneity

Abstract

The application discloses a near-field dynamics modeling method and system based on rock heterogeneity, and the method comprises the following steps: obtaining a target rock sample, and dividing the target rock sample according to voronoi tessellation polygons to obtain a plurality of voronoi tessellation polygon regions; performing material point discretization processing on each voronoi tessellation polygon region to obtain a plurality of discrete material points corresponding to the voronoi tessellation polygon region; generating corresponding random joint line segments of each discrete material point by using a Monte-Carlo method, and counting the number of different keys through which the generated random joint line segments pass; sequentially judging whether the number of different keys through which the generated random joint line segments pass meets a preset quantity requirement; if yes, the current joint line segment is reserved and counted until the counted quantity reaches a set value, and a near-field dynamics model of the heterogeneity rock containing the random joint line segment is obtained. The application aims to accurately reflect the actual mechanical properties and deformation conditions inside the rock.

Description

Technical Field

[0001] The present invention relates to the field of rock material technology, and in particular to a peridynamic modeling method and system based on rock heterogeneity. Background Art

[0002] As a natural material, rock material is a heterogeneous, discontinuous medium composed of different mineral components. The heterogeneity of the shape and particle size of the mineral components at the microscopic level leads to differences in the physical properties of the rock at the macroscopic level. The accumulation of fractures and slip within and between mineral crystals forms the macroscopic mechanical and deformation characteristics of the rock material. At the same time, natural rock materials often contain a large number of joint structural planes, and the characteristics of the joints have a significant impact on their mechanical properties and deformation. Among the current numerical methods for simulating underground engineering excavation, many finite element and discrete element methods have been used to study the stability of the surrounding rock. However, the finite element method is always based on the theory of continuum mechanics, and the discrete element method requires more parameters to be determined. At the same time, existing studies often regard rock as a homogeneous body in terms of material, and often focus on cases with obvious joint distribution characteristics in terms of structure, ignoring the heterogeneity of rock materials and the randomness of joint structure.

[0003] Patent publication number CN118230873A discloses a method, device, and storage medium for heterogeneous peridynamic simulation of rock material fracture failure. This method proposes modeling rock heterogeneity by obtaining rock mineral composition and porosity information based on X-ray diffraction and scanning electron microscopy experiments, respectively. While this method largely simulates rock heterogeneity, it fails to consider the random joints that can occur at larger engineering scales, as well as the coupling between rock heterogeneity and joint randomness. Consequently, it fails to simulate the actual mechanical properties and deformation within the rock. Summary of the Invention

[0004] The main purpose of the present invention is to provide a peridynamic modeling method and system based on rock heterogeneity, aiming to solve the technical problem that existing peridynamic simulations cannot accurately reflect the actual mechanical properties and deformation inside the rock.

[0005] To achieve the above object, the present invention provides a method for creating a polymer thermal conductivity simulation model, the method comprising the following steps:

[0006] Step 1: Obtain a target rock sample and divide the target rock sample into Voronoi Thiessen polygons to obtain a plurality of Voronoi Thiessen polygon regions. The target rock sample includes the composition distribution of the rock material.

[0007] Step 2: Discretize the material points of each Vorononi Thiessen polygon area to obtain corresponding multiple discrete material points, and assign different attribute labels to the discrete material points with the same coordinates according to the corresponding polygon shape and rock sample composition distribution;

[0008] Step 3: Generate corresponding random joint segments for each discrete material point using the Monte-Carlo method and count the number of different bonds that the currently generated random joint segments pass through;

[0009] Step 4, determining in sequence whether the number of different bonds passed through by the random joint segment generated in step 3 meets a preset quantity requirement;

[0010] Step 5: If the conditions are met, the current joint segments are retained and counted until the number of statistics reaches a set value, thereby obtaining a heterogeneous rock peridynamic model containing random joint segments.

[0011] Step 6: Determine the local damage degree of the target rock sample at a preset spatial position according to the equation of the heterogeneous rock peridynamic model containing random joint segments.

[0012] Optionally, in step 1, the specific steps of dividing the target rock sample according to Voronoi Thiessen polygons are as follows:

[0013] Step 11, set the seed of the random number generator to 0, and generate a random number matrix in the interval [0,1), then multiply it by the preset width and preset height [width, height] to scale it into the specified rectangular area, so as to achieve a random distribution of a set of generated points in the corresponding rectangular area;

[0014] Step 12, taking each generated point in step 11 as the center of the corresponding Voronoi polygon;

[0015] Step 13, randomly select any point on the target rock plane, calculate the distance from any point to all generated points, and determine the nearest generated point to assign the nearest generated point to the corresponding Voronoi polygon;

[0016] In step 14, the boundary of the Voronoi diagram is constructed by connecting perpendicular bisectors between adjacent generating points to obtain a plurality of Voronoi polygons.

[0017] Optionally, step 2 specifically includes:

[0018] The generated Voronoi Thiessen polygons are discretized into (width / dx, height / dx) discrete material points with a spacing of dx.

[0019] Optionally, when the target rock sample is composed of material 1 and material 2, the attribute marking in step 2 satisfies the following conditions: intracrystalline bond where both ends of the bond are material 1 > intracrystalline bond where both ends of the bond are material 2 > intercrystalline bond where both ends of the bond are material 1 and material 2 respectively.

[0020] Optionally, in step 4, the numbers of intracrystalline bonds through which both ends of the bond are material 1, intracrystalline bonds through which both ends of the bond are material 2, and intercrystalline bonds through which both ends of the bond are material 1 and material 2 are count1, count2, and count12, respectively, and count1≤count2≤count12 is satisfied.

[0021] Optionally, in step 5, the bond force of the bond body through which the satisfied joint line segment passes is set to 0, that is, this part will not provide any force when the resultant force is solved by integration, and finally a heterogeneous rock peridynamic model containing random joint line segments is generated.

[0022] Optionally, in step 5, the equation of the heterogeneous rock peridynamic model containing random joint segments is:

[0023]

[0024] Where: x represents the material point currently being calculated, x′ is any particle in the near field of material point x, f is the bond force between particles x and x′, t is time, ρ is material density, u is displacement, is the acceleration of the particle x at time t, b(x,t) is the density of the external force acting on the material point, H x It is the near field range.

[0025] Optionally, the local damage degree in step 6 can be expressed as:

[0026]

[0027] The degree of local damage ranges from 0 to 1, where 0 indicates no damage and 1 indicates complete damage.

[0028] In addition, in order to achieve the above-mentioned purpose, the present invention also provides a peridynamic modeling system based on rock heterogeneity, which includes a memory and a processor. The memory stores a peridynamic modeling program based on rock heterogeneity, and the processor implements the steps of any of the above-mentioned peridynamic modeling methods based on rock heterogeneity when executing the peridynamic modeling program based on rock heterogeneity.

[0029] In addition, in order to achieve the above-mentioned purpose, the present invention also provides a computer-readable storage medium, which stores a peridynamic modeling program based on rock heterogeneity. The peridynamic modeling program based on rock heterogeneity can be loaded and executed by a processor to implement the steps of the peridynamic modeling method based on rock heterogeneity as described in any of the above items.

[0030] Beneficial effects:

[0031] The present invention realizes the heterogeneity of rock in peridynamics by using Voronoi Thiessen polygons and the randomness of rock joints by using the Monte-Carlo method. It also realizes the coupling of heterogeneity and joint randomness through iterative judgment, thereby obtaining a heterogeneous rock peridynamic model and obtaining the local damage degree of the target rock based on the heterogeneous rock peridynamic model. This method is different from the classical mechanics theory of finite element method that uses a derivation method and does not have the singularity problem of discontinuities. It is also different from the discrete element method that requires the determination of multiple micromechanical parameters, thereby simplifying the acquisition process under rock heterogeneity conditions, and can simulate the actual mechanical properties and deformation inside the rock, thereby realizing wide application. BRIEF DESCRIPTION OF THE DRAWINGS

[0032] Figure 1 This is a flowchart of the first embodiment of the peridynamic modeling method based on rock heterogeneity of the present invention;

[0033] Figure 2 A schematic diagram for determining joint segments in target rocks composed of two materials;

[0034] Figure 3 This is a partially enlarged model diagram of different mineral components of granite used in one embodiment of the present invention;

[0035] Figure 4 for Figure 3 Schematic diagram of the coupling generation results of the heterogeneity and joint randomness of the mesogranite;

[0036] Figure 5 This is a schematic diagram of the shield tunnel excavation model;

[0037] Figure 6 Schematic diagram of the damage results of excavation disturbance simulation.

[0038] The purpose, features and advantages of the present invention will be further described with reference to the accompanying drawings and in conjunction with the embodiments. DETAILED DESCRIPTION

[0039] It should be understood that the specific embodiments described herein are only used to explain the present invention and are not intended to limit the present invention.

[0040] like Figure 1-6 As shown, the present invention provides an embodiment of a peridynamic modeling method based on rock heterogeneity, wherein Figure 1 As shown, the method includes the following steps:

[0041] Step 1: Obtain a target rock sample and divide the target rock sample according to Voronoi Thiessen polygons to obtain multiple Voronoi Thiessen polygon regions.

[0042] The heterogeneous material of the target rock sample is determined by the main components of the rock material and the required accuracy to determine the number of Voronoi Thiessen polygon types and the total number of polygons. The proportion of the main components determines the proportion of the Voronoi Thiessen polygon types. Furthermore, Voronoi Thiessen polygons are a method for dividing space into multiple regions. Each region is defined by a generating point and contains all points closer to that generating point than other generating points.

[0043] Furthermore, the specific steps for generating Voronoi Thiessen polygons are as follows:

[0044] Step 11: First, set the seed of the random number generator to 0 to ensure that the random numbers generated each time the code is run are the same. Then, generate a random number matrix in the interval [0,1). Then multiply it by the specified width and height [width,height] to scale it to the specified rectangular area, so as to achieve a random distribution of a set of generated points within the specified rectangular area.

[0045] Step 12, taking each generated point in step 11 as the center of the corresponding Voronoi polygon;

[0046] Step 13, randomly select any point on the target rock plane that is not a generation point, calculate the distance from the arbitrary point to all generation points, and determine the nearest generation point, thereby assigning the nearest generation point to the corresponding Voronoi polygon;

[0047] Step 14, constructing the boundary of the Voronoi diagram by connecting the perpendicular bisectors between adjacent generating points, and then dividing the plane into multiple Voronoi polygons by the perpendicular bisectors, and finally obtaining multiple Voronoi polygons.

[0048] Step 2: Discretize the material points of each voroni Thiessen polygon area to obtain the corresponding multiple discrete material points, and assign different attribute labels to the discrete material points with the same coordinates according to the corresponding polygon shape and rock sample composition distribution.

[0049] The material point discretization process involves discretizing the generated Voronoi Thiessen polygons into material points. The rectangle is discretized into (width / dx, height / dx) material points with a spacing of dx. The properties of each point are determined by comparing it to the properties of the nearest Voronoi Thiessen polygon. A matnum array is created to store the properties of each material point, which can be simply labeled with numbers (1, 2, 3) to distinguish them.

[0050] Generally, the region is defined according to the simulation size and shape, and the continuous material is discretized into a set of peridynamic material points with a spacing dx. For example, the coordinates of the material points in row i and column j are generated as follows:

[0051] The horizontal coordinate coordx = (-1.0 × width / 2.0) + (dx / 2.0) + (i-1) × dx

[0052] Coordination = (-1.0 × height / 2.0) + (dx / 2.0) + (j-1) × dx

[0053] The Voronoi Thiessen polygons generated in step 1 contain information about rock heterogeneity. Based on the principle of "same properties for points with the same coordinates", different attribute labels are assigned to peridynamic points with the same coordinates, as well as their basic physical properties, such as density, elastic modulus, and critical elongation s0 of the material. Since a point interacts with other points in its near field in the form of a bond, s is defined as the elongation of the bond, which is the ratio of the difference in bond length before and after deformation to the bond length before deformation. A scalar function μ is introduced to determine whether a bond is broken:

[0054]

[0055] In the above formula, if the bond elongation is greater than the critical elongation s0, the bond will be irreversibly broken. The critical elongation s0 of the bond is generated according to the following rules: (1) Intracrystalline bond: The material points at both ends of the bond have the same properties, then the critical elongation of the intracrystalline bond = the critical elongation of the material point material; (2) Intercrystalline bond: The material points at both ends of the bond have different properties (such as the critical elongation s0 of material 1) 01 and the critical elongation s of material 2 02 ), then the critical elongation of the intercrystalline bond s0=s 012 =1 / 2×(s 01 +s 02 ).

[0056] Step 3: Generate corresponding random joint segments for each discrete material point through the Monte-Carlo method and count the number of different bonds that the currently generated random joint segments pass through.

[0057] The random joint automatic generation algorithm is implemented using the Monte-Carlo method. According to the macroscopic statistical laws of joints, their center positions generally follow a uniform distribution, and their orientation angles and lengths generally follow a normal distribution. The specific steps for implementing random joint generation using the Monte-Carlo method are as follows:

[0058] Step 31: Generate uniformly distributed random numbers in the interval [0,1] using the linear equivalent method. The recursive formula is:

[0059]

[0060] Where: M is the modulus, modM means the remainder of the modulus; a is the multiplier; c is the increment; x0 is the initial value; r n is a random number uniformly distributed in the interval [0,1]. The selection of the above parameters follows the criteria given by Kunth (1969): (1) x0 is any non-negative integer; (2) a satisfies: a(mod8)=5, (3) c is an odd number, and

[0061] Step 32: Using the uniform random number generated in step 31, a sampling method is used to generate a random number ξ that obeys a uniform distribution in the interval [p,q] i and obey the normal distribution N(μ,σ 2 )'s random number η i .

[0062] ξ i =(pq)r i +q;

[0063]

[0064] Furthermore, according to the principles of step 31 and step 32, each discrete material point is first generated into a connected joint segment, and the number of different bonds passed through the currently generated joint segment is counted. The critical elongation of the bond is related to the difficulty of the bond breaking. When other conditions are the same, the smaller the critical elongation, the easier the bond is to break. Therefore, the total number of different bonds passing through the rock mass should decrease with the increase of the critical elongation s0 of the bond, thereby reflecting the characteristic that the rock is more likely to break along the intergranular under geological action. The rock composed of two main materials is assigned properties through calculation in step 32 to obtain: intracrystalline bond s 01 (Both ends of the bond are material 1) > intracrystalline bond s 02 (Both ends of the bond are material 2) > intercrystalline bond s 012 (The materials at both ends of the bond are material 1 and material 2 respectively).

[0065] Step 4, determining in turn whether the number of different bonds passed through by the random joint segment generated in step 3 meets the preset quantity requirement.

[0066] Step 5: If the conditions are met, the current joint segments are retained and counted until the number of statistics reaches a set value, thereby obtaining a heterogeneous rock peridynamic model containing random joint segments.

[0067] Take the rock composed of two main materials as an example, where the number of joints passing through three different bonds is count1, count2, and count12 respectively. After the joint is generated, count1≤count2≤count12 must be satisfied. Figure 2 As shown, taking the near-field radius dx as an example, the dotted line is the range of action of a material point. For this point, the number of joints passing through intercrystalline bonds count12 ≥ the number of joints passing through intracrystalline bonds count1, so the requirement is met.

[0068] Repeat step 4 until a sufficient number of joints are generated that satisfy the coupling between material heterogeneity and joint randomness. Set the bond force through the bond segments that satisfy the coupling conditions to zero, meaning that this section will not contribute to the force when integrating to solve for the resultant force. This ultimately generates a heterogeneous rock peridynamic model containing random joints.

[0069] Specifically, let x represent the material point currently being calculated, and x′ be any material point in the near field of material point x. The motion equation of the peridynamic material point is:

[0070]

[0071] Where: f is the bond force between particles x and x′, t is time, ρ is material density, u is displacement, is the acceleration of the particle x at time t, b(x,t) is the density of the external force acting on the material point, H x It is the near field range.

[0072] Step 6: Determine the local damage degree of the target rock sample at a preset spatial position according to the equation of the heterogeneous rock peridynamic model containing random joint segments.

[0073] Specifically, the integral of the number of bond breaks per unit volume represents the local damage degree of the material at the current spatial position. The damage index can be expressed as:

[0074]

[0075] The damage index ranges from 0 to 1, with 0 indicating no damage and 1 indicating complete damage. Calculations can be performed by applying boundary conditions and constraints, such as force loading and velocity loading, to the established model.

[0076] In addition, the present invention also provides a peridynamic modeling system based on rock heterogeneity, which includes a memory and a processor. The memory stores a peridynamic modeling program based on rock heterogeneity. When the processor executes the peridynamic modeling program based on rock heterogeneity, the steps of any of the above methods are implemented. The embodiment of the peridynamic modeling system based on rock heterogeneity is basically the same as the above method and will not be described in detail here.

[0077] In addition, the present invention also provides a computer-readable storage medium, which stores a peridynamic modeling program based on rock heterogeneity. The peridynamic modeling program based on rock heterogeneity can be loaded and executed by a processor to implement the steps of the peridynamic modeling method based on rock heterogeneity as described in any of the above items. The embodiment of the peridynamic modeling system based on rock heterogeneity is basically the same as the above method and will not be described in detail here.

[0078] Furthermore, in order to better illustrate the peridynamic modeling method based on rock heterogeneity of the present invention, the following is an example of granite for corresponding explanation, wherein the main components of granite are mica, quartz, and feldspar, accounting for 30%, 30%, and 40%, and the granite is divided into Voronoi Thiessen polygons to obtain the following specific Figure 3 The Voronoi Thiessen polygon area is shown.

[0079] Furthermore, the granite is discretized into material points, and the corresponding random joint segments are generated by the Monte-Carlo method for each discrete material point, and the number of different bonds passed by the currently generated random joint segments is counted, and the following is obtained: Figure 4 The results of the coupling generation of granite heterogeneity and joint randomness are shown, where the critical elongation of the bonds satisfies mica>feldspar>quartz, and the number of joint-crossing bonds satisfies: mica-mica ≤ mica-feldspar ≤ mica-quartz ≤ feldspar-feldspar ≤ feldspar-quartz ≤ quartz-quartz.

[0080] Furthermore, the granite is treated by shield tunneling, e.g. Figure 5 The excavation area selected in the and the damage degree around the granite excavation can be obtained, such as Figure 6 As shown in the figure, the excavation area is affected by the excavation disturbance, the damage is more obvious at the bottom of the excavation chamber, and the original joints in the surrounding rock also have slight damage.

[0081] It should be noted that, in this document, the terms "comprises," "includes," or any other variations thereof are intended to encompass non-exclusive inclusion, such that a process, method, article, or system comprising a series of elements includes not only those elements but also other elements not explicitly listed, or elements inherent to such process, method, article, or system. In the absence of further limitations, an element defined by the phrase "comprising a ..." does not exclude the presence of other identical elements in the process, method, article, or system comprising the element.

[0082] The serial numbers of the above embodiments of the present invention are for description only and do not represent the advantages or disadvantages of the embodiments.

[0083] The above are only preferred embodiments of the present invention and are not intended to limit the patent scope of the present invention. Any equivalent structure or equivalent process transformation made using the contents of the present invention description and drawings, or directly or indirectly applied in other related technical fields, are also included in the patent protection scope of the present invention.

Claims

1. A peridynamic modeling method based on rock heterogeneity, characterized by: The method comprises the following steps: Step 1: Obtain a target rock sample and divide the target rock sample into Voronoi Thiessen polygons to obtain a plurality of Voronoi Thiessen polygon regions. The target rock sample includes the composition distribution of the rock material. Step 2: Discretize the material points of each Vorononi Thiessen polygon area to obtain corresponding multiple discrete material points, and assign different attribute labels to the discrete material points with the same coordinates according to the corresponding polygon shape and rock sample composition distribution; Step 3: Generate corresponding random joint segments for each discrete material point using the Monte-Carlo method and count the number of different bonds that the currently generated random joint segments pass through; Step 4, determining in sequence whether the number of different bonds passed through by the random joint segment generated in step 3 meets a preset quantity requirement; Step 5: If the conditions are met, the current joint segments are retained and counted until the number of statistics reaches a set value, thereby obtaining a heterogeneous rock peridynamic model containing random joint segments. Step 6: Determine the local damage degree of the target rock sample at a preset spatial position according to the equation of the heterogeneous rock peridynamic model containing random joint segments.

2. The peridynamic modeling method based on rock heterogeneity according to claim 1, characterized in that: In step 1, the specific steps of dividing the target rock sample according to Voronoi Thiessen polygons are as follows: Step 11: Set the seed of the random number generator to 0 and generate a random number matrix in the interval [0, 1). Then, multiply it by the preset width and height [width, height] and scale it to the specified rectangular area to achieve a random distribution of a set of generated points in the corresponding rectangular area. Step 12, taking each generated point in step 11 as the center of the corresponding Voronoi Thiessen polygon; Step 13, randomly select any point on the target rock plane, calculate the distance from any point to all generated points, and determine the nearest generated point to assign the nearest generated point to the corresponding Voronoi Thiessen polygon; In step 14, the boundary of the Voronoi Thiessen diagram is constructed by connecting perpendicular bisectors between adjacent generated points to obtain a plurality of Voronoi Thiessen polygons.

3. The peridynamic modeling method based on rock heterogeneity according to claim 2, characterized in that: Step 2 specifically includes: The generated Voronoi Thiessen polygons are discretized into (width / dx, height / dx) discrete material points with a spacing of dx.

4. The peridynamic modeling method based on rock heterogeneity according to claim 1, characterized in that: When the target rock sample is composed of material 1 and material 2, the attribute markings in step 2 satisfy the following conditions: intracrystalline bond where both ends of the bond are material 1 > intracrystalline bond where both ends of the bond are material 2 > intercrystalline bond where both ends of the bond are material 1 and material 2 respectively.

5. The peridynamic modeling method based on rock heterogeneity according to claim 4, characterized in that: In step 4, the numbers of intracrystalline bonds whose end materials are both material 1, intracrystalline bonds whose end materials are both material 2, and intercrystalline bonds whose end materials are both material 1 and material 2 are count1, count2, and count12 respectively, and count1≤count2≤count12 are satisfied.

6. The peridynamic modeling method based on rock heterogeneity according to claim 5, characterized in that: In step 5, the bond force of the bond body through which the satisfied joint line segment passes is set to 0, that is, this part will not provide any force when the resultant force is solved by integration, and finally a heterogeneous rock peridynamic model containing random joint line segments is generated.

7. The peridynamic modeling method based on rock heterogeneity according to any one of claims 1 to 6, characterized in that: In step 5, the equation of the heterogeneous rock peridynamic model with random joint segments is: ； Where: represents the material point currently being calculated, Material point Any particle in the near field, It is a point mass and The bond strength between For time, is the material density, is the displacement, For point mass exist The acceleration of time, is the density of the external force acting on the material point, It is the near field range.

8. The peridynamic modeling method based on rock heterogeneity according to claim 7, characterized in that: The local damage degree of the material point in step 6 can be expressed as: ； The local damage degree is between 0 and 1, where 0 means no damage and 1 means complete damage. is a scalar function, For time, Represents the material point currently being calculated.

9. A peridynamic modeling system based on rock heterogeneity, characterized by: The system includes a memory and a processor, wherein the memory stores a peridynamic modeling program based on rock heterogeneity, and when the processor executes the peridynamic modeling program based on rock heterogeneity, the steps of the peridynamic modeling method based on rock heterogeneity according to any one of claims 1 to 8 are implemented.

10. A computer-readable storage medium, characterized in that The computer-readable storage medium stores a peridynamic modeling program based on rock heterogeneity, and the peridynamic modeling program based on rock heterogeneity can be loaded and executed by a processor to implement the steps of the peridynamic modeling method based on rock heterogeneity as described in any one of claims 1 to 8.

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