Near-field dynamics modeling method and system based on rock heterogeneity

Abstract

The invention 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, dividing the target rock sample according to a voronoi Thiessen polygon, and obtaining a plurality of voronoi Thiessen polygon regions; performing material point discrete processing on each voroni Thiessen polygon region to obtain a plurality of corresponding discrete material points; generating a corresponding random joint line segment from each discrete substance point through a Monte-Carlo method, and counting the number of different bonds penetrated by the currently generated random joint line segment; sequentially judging whether the number of different keys penetrated by the generated random joint line segment meets a preset number requirement or not; if yes, the current joint line segment is reserved and counted until the statistical number reaches a set value, and the heterogeneous rock near-field kinetic model containing the random joint line segment is obtained. The invention aims to accurately reflect the actual mechanical property and deformation condition in 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 and 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 the differences in the physical properties of the rock at the macroscopic level. The accumulation of fractures and slips within and between mineral crystals forms the macroscopic mechanical and deformation characteristics of rock materials. At the same time, natural rock materials often contain a large number of joint structural surfaces, and the characteristics of the joints have an important influence on their mechanical properties and deformation. In the current numerical methods for underground engineering excavation simulation, many finite element and discrete element methods have been used to study the stability of surrounding rocks. However, the finite element method is always based on the theory of continuous medium mechanics, and the discrete element method requires more parameters to be determined. At the same time, existing studies often regard rocks as homogeneous bodies in terms of materials, and often conduct research on situations with obvious joint distribution characteristics in terms of structure, ignoring the heterogeneity of rock materials and the randomness of joint structures.

[0003] The existing invention patent with the patent publication number CN118230873A discloses a method, device and storage medium for heterogeneous near-field dynamic simulation of rock material fracture and destruction, which proposes to obtain the mineral composition information and porosity information of the rock respectively according to the X-ray diffraction test and the scanning electron microscope test to perform rock heterogeneity modeling. Although this method relatively restores the heterogeneity of the rock, it does not take into account the random joints that will appear in the rock at a larger engineering scale, as well as the coupling between the rock heterogeneity and the randomness of the joints, and thus cannot simulate the actual mechanical properties and deformation inside 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 the existing peridynamic simulation 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, obtaining a target rock sample, and dividing the target rock sample according to Voronoi Thiessen polygons to obtain a plurality of Voronoi Thiessen polygon regions, wherein the target rock sample includes the composition distribution of the rock material;

[0007] Step 2, discretizing the material points of each voroni Thiessen polygon area to obtain a corresponding plurality of discrete material points, and assigning different attribute labels to the discrete material points with the same coordinates according to the corresponding polygon shape and the rock sample component distribution;

[0008] Step 3, generating corresponding random joint segments for each discrete material point by Monte-Carlo method and counting the number of different bonds passed by the currently generated random joint segments;

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

[0010] Step 5: If the condition is satisfied, the current joint line segment is retained and counted until the number of statistics reaches a set value, thereby obtaining a heterogeneous rock peridynamic model containing random joint line segments;

[0011] Step 6, determining 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:

[0013] Step 11, set the seed of the random number generator to 0, and generate a random number matrix in the interval [0,1), and then multiply it by the preset width and preset height [width, height] to scale it into the specified rectangular area 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] Step 14, constructing the boundary of the Voronoi diagram by connecting perpendicular bisectors between adjacent generated 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 intracrystalline bond of material 1 at both ends of the bond>intracrystalline bond of material 2 at both ends of the bond>intercrystalline bond of material 1 and material 2 respectively at both ends of the bond.

[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 particle, H x It is the near field range.

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

[0026]

[0027] The local damage degree 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, the system comprising a memory and a processor, the memory storing a peridynamic modeling program based on rock heterogeneity, and the processor implementing any of the steps of the peridynamic modeling method based on rock heterogeneity described above 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 peri-field dynamic modeling program based on rock heterogeneity, and the peri-field dynamic modeling program based on rock heterogeneity can be loaded and executed by a processor to implement the steps of the peri-field dynamic 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 adopting Voroni Thiessen polygons, realizes the joint randomness of rock in peridynamics by adopting Monte-Carlo method, realizes the coupling of heterogeneity and joint randomness by iterative judgment, thereby realizing the acquisition of heterogeneous rock peridynamics model, and obtains the local damage degree of target rock based on the heterogeneous rock peridynamics model. This method is different from the classical mechanics theory of finite element which adopts the derivation method, does not have the singularity problem of discontinuity, and is different from the discrete element method which needs to determine multiple micromechanical parameters, thereby simplifying the acquisition process under the condition of rock heterogeneity, and can simulate the actual mechanical properties and deformation inside the rock, thereby realizing wide application. BRIEF DESCRIPTION OF THE DRAWINGS

[0032] Figure 1 It 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 a target rock 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 realization of the purpose, functional features and advantages of the present invention will be further explained in conjunction with embodiments and with reference to the accompanying drawings. DETAILED DESCRIPTION

[0039] It should be understood that the specific embodiments described herein are only used to explain the present invention, and are not used 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 comprises 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] Among them, 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 types and the total number of polygons of the Voronoi Thiessen polygon division, and the proportion of the types of Voronoi Thiessen polygons is determined according to the proportion of the main components. And the Voronoi Thiessen polygon is a method of dividing space into multiple regions, each region is defined by a generation point and contains all points that are closer to the generation point than other generation 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, and then generate a random number matrix in the interval [0,1), and 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 in 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, so as to assign 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 generated points, and then dividing the plane into a plurality of Voronoi polygons by the perpendicular bisectors, and finally obtaining a plurality of 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 component distribution.

[0049] The material point discretization process is to discretize the generated Voronoi Thiessen polygon two-dimensional figure into material points, and discretize the rectangle into (width / dx, height / dx) material points with dx as the spacing. The attribute of each point is determined by finding the attribute of the Voronoi Thiessen polygon with the closest distance. A matnum sequence is established to store the attributes of each material point, which can be simply marked with numbers (1, 2, 3) to distinguish the attributes.

[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 rows i and columns 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 polygon discrete material points generated in step 1 contain rock heterogeneity information. Based on the principle of "the same properties of material points with the same coordinates", different attribute labels are given to peridynamic material points with the same coordinates, as well as their basic physical properties, such as density, elastic modulus, critical elongation s0 of the material, etc. Among them, based on the fact that material points will interact with other material points in the form of bonds within their near field range, s is defined as the elongation of the bond, which refers to the ratio of the difference in bond length before and after deformation to the bond length before deformation. The scalar function μ is introduced here to determine whether the bond is broken or not:

[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 realized by Monte-Carlo method. According to the macroscopic statistical law of joints, the center position generally obeys uniform distribution, and the direction angle and length generally obey normal distribution. The specific steps of realizing random joint generation by Monte-Carlo method are as follows:

[0058] Step 31: Generate uniformly distributed random numbers in the interval [0,1] by linear identity method, and its 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 random number ξ that follows a uniform distribution in the interval [p,q] is generated by sampling i and obey the normal distribution N(μ,σ 2 ) 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 intercrystalline under geological action. The rock composed of two main materials is assigned attributes 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, determine in turn whether the number of different keys passed by the random joint segment generated in step 3 meets the preset quantity requirement.

[0066] Step 5: If the condition is satisfied, the current joint line segment is retained and counted until the number of statistics reaches a set value, thereby obtaining a heterogeneous rock peridynamic model containing random joint line segments;

[0067] Take a 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 action range of a material point. For this point, the number of joints passing through the intercrystalline bonds count12 ≥ the number of joints passing through the intracrystalline bonds count1, so the requirement is met.

[0068] Repeat step 4 until a sufficient number of joints are generated that satisfy the coupling of material heterogeneity and joint randomness. Set the bond force of the bond through which the joint line segment passes to 0, that is, this part will not provide any force when the resultant force is solved by integration. Finally, a heterogeneous rock peridynamic model with random joints is generated.

[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. Then 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 particle, H x It is the near field range.

[0072] Step 6, determining 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, and the damage index can be expressed as:

[0074]

[0075] The damage index takes a value between 0 and 1, where 0 indicates no damage and 1 indicates complete damage. The calculation 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, the system 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 methods when executing the peridynamic modeling program based on rock heterogeneity. 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] Furthermore, the present invention provides a computer-readable storage medium storing a peridynamic modeling program based on rock heterogeneity, wherein 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 the above items, and an 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] Further, in order to better illustrate the peridynamic modeling method based on rock heterogeneity of the present invention, the following takes granite as an example 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 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 with shield tunneling, such as Figure 5 The excavation area selected in the figure can also obtain the damage degree around the granite excavation, such as Figure 6 As shown, in the excavation area, affected by the excavation disturbance, the damage is more obvious at the bottom of the excavation chamber, and slight damage also occurs at the original joints in the surrounding rock.

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

[0082] The serial numbers of the above embodiments of the present invention are only for description 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 specification 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 in that: The method comprises the following steps: Step 1, obtaining a target rock sample, and dividing the target rock sample according to Voronoi Thiessen polygons to obtain a plurality of Voronoi Thiessen polygon regions, wherein the target rock sample includes the composition distribution of the rock material; Step 2, discretizing the material points of each voroni Thiessen polygon area to obtain a corresponding plurality of discrete material points, and assigning different attribute labels to the discrete material points with the same coordinates according to the corresponding polygon shape and the rock sample component distribution; Step 3, generating corresponding random joint segments for each discrete material point by Monte-Carlo method and counting the number of different bonds passed by the currently generated random joint segments; Step 4, determining in turn whether the number of different bonds passed through by the random joint line segment generated in step 3 meets the preset quantity requirement; Step 5: If the condition is satisfied, the current joint line segment is retained and counted until the number of statistics reaches a set value, thereby obtaining a heterogeneous rock peridynamic model containing random joint line segments; Step 6, determining 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 the 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), and then multiply it by the preset width and preset height [width, height] to scale it into 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 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 polygon; Step 14, constructing the boundary of the Voronoi diagram by connecting perpendicular bisectors between adjacent generated points to obtain a plurality of Voronoi 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: both ends of the bond are intracrystalline bonds of material 1 > both ends of the bond are intracrystalline bonds of material 2 > both ends of the bond are intercrystalline bonds of 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 both ends are material 1, intracrystalline bonds whose both ends are material 2, and intercrystalline bonds whose both ends are material 1 and material 2 are count1, count2, and count12 respectively, and count1≤count2≤count12 is 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 peridynamic model of heterogeneous rock with random joint segments is: 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 particle, H x 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 in step 6 can be expressed as: The local damage degree ranges from 0 to 1, where 0 indicates no damage and 1 indicates complete damage.

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

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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