Construction method and device of breakable particle discrete element numerical model and application of construction method and device

Abstract

The invention provides a construction method and device of a broken particle discrete element numerical model and application of the construction method and device. The method comprises the following steps: constructing N isometric particle contour models based on N real particles; based on the target grading curve and the total number of the particles, constructing a spherical particle set model; replacing each spherical particle model in the spherical particle set model with a breakable model composed of a plurality of polyhedrons one by one; and after all the spherical particle models are replaced by fragmentable models, generating a fragmentable particle material numerical model instruction file, and directly inputting the instruction file into PFC3D in a reading manner to generate a fragmentable particle discrete element numerical model. The breakable particle discrete element numerical model obtained through the construction method has the shape of real particles and is composed of coplanar Voronoi polyhedrons, the size of the model conforms to grading characteristics, and analysis of particle breaking characteristics and the microscomic influence of particle breaking on material macromechanical characteristics is facilitated.

Description

TECHNICAL FIELD

[0001] The present application belongs to the technical field of geotechnical engineering, and particularly relates to a construction method and device of a breakable particle discrete element numerical model and application thereof. BACKGROUND

[0002] Natural particle materials, such as ballast, rockfill, calcareous sand, etc., as a kind of discontinuous, heterogeneous and complex multiphase medium, are widely used in engineering construction. When the external load acting on the particle exceeds the ultimate strength that the particle can bear, the particle breaks. As one of the important characteristics of particle materials, breakage directly leads to the change of particle grading, and has an indiscernible influence on the shear strength, dilatancy, porosity, compaction characteristics, permeability coefficient, etc. of the particle materials.

[0003] Discrete element numerical simulation is a powerful tool for studying the behavior of particle breakage. The discrete element method returns to the essence that granular materials are composed of particles and surrounding voids, and can track the breakage process of particles in real time during loading, which is convenient for analyzing the mesoscopic mechanics mechanism of particle breakage, and therefore has been widely used in the research related to particle breakage. There are two main methods for discrete element simulation of particle breakage: ① particle replacement method, that is, when a particle meets a pre-set breakage criterion, it is considered that the particle breaks, and is replaced by a number of sub-particles with certain topological relationship; ② bonded cell method, that is, the particle is represented as a collection of cells bonded together, and the cell can be a sub-sphere or a polyhedron. Among them, the bonded cell method can reflect the topographic characteristics of the particle, and does not need to assume the particle breakage criterion, so it is more widely used. When the bonded cell method is used to simulate particle breakage, the most commonly used method is to assume that the particle is a collection of a plurality of spherical cells bonded together. However, existing studies have shown that if a coplanar Voronoi polyhedron (an irregular convex polyhedron) is used as a cell, the particle material breakage behavior can be more realistically reflected.

[0004] At present, there is no particle material modeling method that can reflect the true topography and grading curve characteristics of the particle, and can subdivide the particle into a collection of Voronoi cell, which limits the in-depth study of the influence of particle breakage on the macroscopic mechanical properties and microscopic mechanical mechanisms of particle materials. SUMMARY

[0005] The present application aims to provide a method for accurately constructing a breakable particle material discrete element numerical model, to solve the problem that the numerical model of the breakable particle material constructed by the existing numerical simulation method cannot accurately reflect particle breakage, particle topography and grading characteristics, and to further help the design of geotechnical particle materials in the fields of civil engineering such as earth-rock dams, railways, highways and airport runways.

[0006] In a first aspect, the present application provides a construction method of a breakable particle discrete element numerical model, the construction method comprising the following steps: step S10, obtaining initial geometric models of N real particles, obtaining particle outline models with the same equivalent particle diameter based on a preset operation, and the centroid of each particle outline model coincides with the coordinate origin, randomly numbering each particle outline model according to a positive integer 1-N, and exporting each particle outline model in an STL file respectively, the preset operation comprising reconstructing the initial geometric models, and scaling and moving the reconstructed geometric models; step S20, obtaining a target grading curve, constructing a spherical particle set model comprising a plurality of spherical particle models using PFC3D software based on the target grading curve and a predetermined total number of particles, the plurality of spherical particle models in the spherical particle set model being in contact with each other and reaching a static equilibrium state, and the particle diameter of each spherical particle model being M times the actual particle diameter of the particle determined based on the target grading curve, 1.5≤M≤2.0; step S30, replacing each spherical particle model in the spherical particle set model with a breakable model composed of a plurality of polyhedrons one by one, and individually naming each generated breakable particle model and writing it into a same text file, and the outline of the breakable model being obtained from the N particle outline models based on a random principle; step S40, after all the spherical particle models are replaced with the breakable models, generating a breakable particle material numerical model instruction file, directly inputting the instruction file into PFC3D in a read mode, and generating the breakable particle discrete element numerical model.

[0007] In a specific embodiment, the step of replacing any one spherical particle model with a breakable model composed of a plurality of polyhedrons includes: a step S31 of replacing the spherical particle model with the particle contour model generated in the step S10 based on a random principle; a step S32 of generating a plurality of spherical sub-particles in the replaced particle contour model and expanding by using a radius expansion method until a porosity in the replaced particle contour model reaches a preset porosity to obtain a first particle packing model; a step S33 of first converting each spherical sub-particle in the first particle packing model into a coplanar Voronoi polyhedron, then converting the replaced particle contour model into a joint set, cutting the Voronoi polyhedron to generate a plurality of polyhedrons, and deleting the polyhedrons outside the replaced particle contour model to obtain a second particle packing model; and a step S34 of generating a text file of the breakable model for replacing the spherical particle model by performing scaling, translation and export operations on the vertices of each polyhedron in the second particle packing model based on the particle size and spatial coordinates of the replaced spherical particle model, wherein a ratio of the particle size of the replaced spherical particle model to the effective particle size of the breakable model is M times, and the spatial coordinates of the center of the breakable model are the same as the spatial coordinates of the center of the replaced spherical particle model.

[0008] In a specific embodiment, the step S31 includes: directly generating an integer N' in the range of 1 to N by uniform distribution, extracting an STL file of a real particle contour model corresponding to the name of N', and introducing the PFC3D as a replacement model of the spherical particle model; and generating three dimension angles in the range of 【0, π】 to randomly distribute the orientation of the real particle contour model as the replacement model in space.

[0009] In a specific embodiment, the number of spherical sub-particles generated in the replaced particle contour model in the step S32 is determined by the following steps, including: a step (a) of calculating the volume of each real particle based on the equivalent particle size of each real particle; a step (b) of sorting the volumes of N real particles to obtain a real particle with the smallest volume; a step (c) of calculating a cell volume based on the number of cells to be divided for the real particle with the smallest volume, which is 100; a step (d) of obtaining the number of cells corresponding to the replaced spherical particle model according to the cell number calculation formula based on the volume of the replaced spherical particle model and the cell volume, wherein the number of cells is the ratio of the volume of the replaced spherical particle model to the cell volume; and a step (e) of determining the number of spherical sub-particles generated in the replaced particle contour model based on the number of cells corresponding to the replaced spherical particle model, wherein the number of spherical sub-particles generated in the replaced particle contour model is the same as the number of cells of the replaced spherical particle model.

[0010] In a specific embodiment, the step S32 comprises: step (1), generating a plurality of spherical sub-particles within the replaced particle contour model to obtain an initial filling model; step (2), calculating the sum of the volumes of all spherical sub-particles in the initial filling model V1, and calculating the ratio of V1 to the volume V2 of the particle contour model to obtain a volume ratio; step (3), when the volume ratio is less than a target volume ratio, expanding the radius of each spherical sub-particle by m times to obtain an updated filling model, wherein 1.02≤m≤1.08; step (4), repeating steps (2) and (3) until the volume ratio corresponding to the updated filling model is greater than the target volume ratio to obtain a first particle packing model, and the sum of the target volume ratio and the preset porosity is 1.

[0011] In a specific embodiment, the step of scaling and translating each vertex of the polyhedron in the second particle packing model comprises: step (a), calculating a scaling ratio of each vertex of the polyhedron in the second particle packing model based on the particle size of the replaced spherical particle model and the contour size of the second particle packing model; step (b), regarding all vertices of the polyhedron in the second particle packing model as all vertices of a single polyhedron, and scaling the spatial coordinates of each vertex based on the scaling ratio; step (c), adding the spatial coordinates of the center of the spherical particle model to the scaled spatial coordinates of each vertex to obtain the translated coordinates of each vertex, and moving each vertex according to the translated coordinates of each vertex.

[0012] In a specific embodiment, the step S20 comprises: step S21, obtaining a target grading curve, and determining the number of particles in each particle size group based on the target grading curve and a predetermined total number of particles; step S22, obtaining the particle size value of each particle based on the particle size range value, the number of particles and the uniform distribution principle of each particle size group; step S23, expanding the particle size value of each particle by M times to obtain a target particle size, and generating a plurality of spherical particle models that are not in contact with each other in the PFC3D space of the discrete element software based on the target particle size of each particle to obtain a spherical particle set model in a first state; step S24, generating a wall on the boundary of the spherical particle set model in the first state, and applying an isotropic compression to the center of the set model or applying a gravitational field to the spherical particle models to make the plurality of spherical particle models contact each other and reach a static equilibrium state to obtain a spherical particle set model in a second state.

[0013] In a specific embodiment, the step S10 comprises: step (1), randomly selecting N real particles, the real particles being one of gravel particles, pebble particles or rainflower stone particles, N being a positive integer, and 1≤N≤100; step (2), obtaining an initial geometric model of each real particle by an image method or a three-dimensional scanning method; step (3), reconstructing the initial geometric model of each real particle by a spherical harmonic function analysis method or a quadrilateral face reconstruction network method to obtain N reconstructed geometric models; step (4), scaling each reconstructed geometric model to a preset volume to obtain N particle contour models, and moving a centroid of each particle contour model to a coordinate origin; and step (5), randomly numbering each particle contour model according to a positive integer 1 to N, and exporting each particle contour model in an STL file.

[0014] In a second aspect, the application further provides a device for constructing a breakable particle discrete element numerical model, the device comprising: an obtaining module, configured to obtain initial geometric models of N real particles, obtain N particle contour models with the same equivalent particle diameter based on a preset operation, and move a centroid of each particle contour model to a coordinate origin, randomly number each particle contour model according to a positive integer 1 to N, and export each particle contour model in an STL file, the preset operation comprising reconstructing the initial geometric models, and scaling and moving the reconstructed geometric models; a constructing module, configured to obtain a target grading curve, construct a spherical particle aggregate model comprising a plurality of spherical particle models based on the target grading curve and a predetermined total number of particles using PFC3D software, the plurality of spherical particle models in the spherical particle aggregate model being in contact with each other and reaching a static equilibrium state, a particle diameter of each spherical particle model being M times a real particle diameter determined based on the target grading curve, and 1.5≤M≤2.0; a replacing module, configured to replace each spherical particle model in the spherical particle aggregate model with a breakable model composed of a plurality of polyhedrons one by one, and name each generated breakable particle model individually, and write the breakable particle model into a same text file in sequence, an outline of the breakable model being obtained from the N particle contour models based on a random principle; and a generating module, configured to generate a breakable particle material numerical model instruction file after all the spherical particle models are replaced with the breakable models, directly input the instruction file into PFC3D in a read mode, and generate a breakable particle discrete element numerical model.

[0015] In a third aspect, the application further provides an application of the breakable particle discrete element numerical model constructed by the construction method described above, the application comprising any one of geotechnical tests including triaxial compression tests, direct shear tests and side loading tests.

[0016] The application has at least the following beneficial effects:

[0017] The present application provides a kind of construction method of breakable particle discrete element numerical model, the method comprises: step S10, the initial geometric model of N real particles is obtained, the same particle outline model of N equivalent particle size is obtained based on preset operation, and the centroid of each particle outline model coincides with coordinate origin, each particle outline model is randomly numbered according to positive integer 1 ~ N, and is exported with STL file respectively, the preset operation includes reconstructing to initial geometric model, and scaling and moving to the geometric model after reconstruction;Step S20, obtain target grading curve, based on the target grading curve and the total number of particles determined in advance, a spherical particle set model comprising a plurality of spherical particle models is constructed using PFC3D software, the plurality of spherical particle models in the spherical particle set model are in contact with each other and reach static equilibrium state, the particle size of each spherical particle model is M times of the actual particle size of the particle determined based on the target grading curve, 1.5 ≤ M ≤ 2.0;Step S30, replace each spherical particle model in the spherical particle set model with a breakable model composed of a plurality of polyhedrons one by one, and each generated breakable particle model is named separately, and is written into the same text file in succession, the outline of the breakable model is obtained from the N particle outline models based on random principle;Step S40, after all spherical particle models are replaced with breakable models, generate a breakable particle material numerical model instruction file, input the instruction file into PFC3D in a read mode to generate a breakable particle discrete element numerical model;In this way, the breakable particle discrete element numerical model constructed by the construction method provided by the present application has the topography of real particles, is composed of coplanar Voronoi polyhedrons, and the size meets the grading characteristics, and when used for simulating discrete element numerical simulation of geotechnical tests such as triaxial compression test, direct shear test, side limit loading, it is helpful to analyze the particle breakage characteristics and the mesoscopic influence of particle breakage on material macroscopic mechanical properties.

[0018] In addition to the objects, features, and advantages described above, the present application has other objects, features, and advantages. The present application will be further described in detail below with reference to the drawings. BRIEF DESCRIPTION OF DRAWINGS

[0019] Figure 1 The step flow chart of the construction method of breakable particle discrete element numerical model provided by an embodiment of the present application is shown in the figure;

[0020] Figure 2 The process diagram of the particle outline model obtained in step S20 of the present application, Figure 2 (a) in the figure is the geometric model of real particles obtained by scanning real particles, Figure 2 (b) in the figure is the reconstructed geometric model obtained by reconstructing the geometric model of real particles shown in (a), Figure 2 (a)Figure 2 (c) is a step of scaling the reconstructed geometric model to a preset volume and obtaining a particle contour model by moving the center of the mass;

[0021] Figure 3 is a sub-step flow chart of step S20;

[0022] Figure 4 is a step flow chart of replacing any one spherical particle model with a breakable model composed of a plurality of polyhedrons;

[0023] Figure 5 is a process chart of converting a first particle packing model into a second particle packing model, wherein, Figure 5 (a) in the chart is a model chart of the first particle packing model, Figure 5 (b) in the chart is a chart of converting each spherical sub-particle in the first particle packing model into a coplanar Voronoi polyhedron, Figure 5 (c) of the chart is a chart of cutting the Voronoi polyhedron to generate a plurality of polyhedrons, Figure 5 (d) in the chart is a model chart of the second particle packing model;

[0024] Figure 6 is a chart of converting a spherical particle assembly into an irregular breakable particle model;

[0025] Figure 7 is a chart of Figure 6 the consolidation of the irregular breakable particle model shown in FIG. 8;

[0026] Figure 8 is a chart of Figure 6 the breakage effect of the irregular breakable particle model shown in FIG. 8 under two different loads, Figure 8 (a) in the chart is a chart of the breakage effect under a first load, Figure 8 (b) in the chart is a chart of the breakage effect under a second load;

[0027] Figure 9 is a module chart of a construction device of a breakable particle discrete element numerical model provided by another embodiment of the present application. DETAILED DESCRIPTION

[0028] The embodiments of the present application will be described in detail below with reference to the accompanying drawings.

[0029] Referring to Figures 1 to 8 According to a first aspect of the present application, the present application provides a construction method of a breakable particle discrete element numerical model, and the construction method comprises the following steps:

[0030] Step S10, obtaining an initial geometric model of N real particles, obtaining N particle contour models with the same volume based on a preset operation, the centroid of each particle contour model coincides with the coordinate origin, randomly numbering each particle contour model according to a positive integer 1-N, and exporting each particle contour model in an STL file.

[0031] In an optional embodiment, the step S10 comprises:

[0032] Step (1), randomly selecting N real particles, the real particles being one of gravel particles, pebble particles or rain flower stone particles.

[0033] In an optional embodiment, N is a positive integer, and N is between 1 and 100, specifically, 1, 2, 100, etc.

[0034] In an optional embodiment, the selected real particles are limestone gravel particles with an equivalent particle size of about 20 mm.

[0035] Step (2), obtaining an initial geometric model of each real particle by an image method or a three-dimensional scanning method.

[0036] In the present application, the initial geometric model is a three-dimensional model.

[0037] The image method specifically comprises: collecting particle contours by particle close-range shooting technology. First, continuously photographing the particles, rotating the stone by a certain angle after each photographing, rotating and photographing around the horizontal axis from three pitch angle directions, and ensuring that the overlapping rate of adjacent two photos is not less than 60% by controlling the rotation angle of each photographing. Thus, the photos can fully cover the block stone entity. Finally, inputting all the photos of each particle into a computer for three-dimensional reconstruction, and thus the initial geometric model of the rock and soil particle can be obtained.

[0038] The three-dimensional scanning method generates an initial geometric model composed of triangular meshes through relative position calibration, particle surface point cloud data acquisition, point cloud three-dimensional modeling, model automatic splicing, and model sharpening processing. Specifically, a three-dimensional white light object scanner is used to acquire the particle contour, and position calibration and setting the number of scans for one rotation of the turntable are required before scanning. Then the particle is placed in the center of the turntable and scanned for one revolution, and then the particle is turned over to expose the part that has not been scanned, and a second scan is performed. After each scan, the point cloud is automatically spliced, and the particle surface is determined to be completely scanned by observing whether there are large holes in the particle. If there are still large holes, continue to adjust the particle shape as in the previous step until the particle contour formed by the point cloud can truly reflect the actual particle shape. Through sharpening processing, a point cloud model is generated, and an initial geometric model composed of triangular meshes is generated.

[0039] In the present application, a Wiiboox Reeyee three-dimensional white light object scanner is used to scan the real particles to obtain the particle contour information, and an initial geometric model consistent with the real shape is generated through point cloud modeling technology and splicing technology. The model surface is composed of a large number of triangular meshes through topological relationship, and is saved as an "STL" format file which is simple in format and widely used.

[0040] Step (3), reconstructing each real particle's initial geometric model through spherical harmonic function analysis method or four-edge face reconstruction network method to obtain N reconstructed geometric models.

[0041] In the present application, the geometric model of the real particle is reconstructed by spherical harmonic analysis method (spherical harmonic function analysis method). The similarity of the reconstructed geometric model and the initial geometric model is determined by the number of triangular meshes and the order of spherical harmonics. The more the number of meshes and the higher the order, the more accurate the reconstructed particle contour model. However, the modeling time will be longer and the discrete element simulation load will be larger.

[0042] Existing studies have shown that when the number of meshes of the reconstructed geometric model is greater than 1280 and the order is greater than 15, the overall shape of the irregular particle can be well represented. In the present application, preferably, the number of triangular meshes is 1500-2000, and the spherical harmonic order is 15.

[0043] In the present embodiment, the number of triangular meshes is 1536 and the order is 15, and the reconstructed geometric model is also saved as an "STL" format file. When the number of meshes of the reconstructed geometric model is 1536 and the spherical harmonic order is 15, the particle contour can be more comprehensively reflected, and the extremely fine concave and convex points in the contour are eliminated, which is helpful for fast modeling and subsequent simulation. Of course, the number of meshes can also be reduced by other methods, such as rhino software, but the contour surface meshes obtained by these methods have high randomness and poor practicability.

[0044] In this step, the particle model can also be reconstructed using the quadrilateral reconstruction network operation built into the Rhino3D modeling software. To ensure computational efficiency, the number of meshes should not be too large, around 2000 is appropriate.

[0045] Step (4): Scale each of the reconstructed geometric models to a preset volume to obtain multiple particle contour models, and move the centroid of each particle contour model to the origin of the coordinate system.

[0046] The scaling factor of the particle contour model = the volume of the initial geometric model / the preset volume.

[0047] In this invention, the equivalent particle size of each particle profile model is 10 mm.

[0048] It is understandable that a coordinate system is established when constructing the contour model, and the coordinate origin mentioned above is the coordinate origin of the coordinate system corresponding to the construction of the contour model.

[0049] Step (5): Randomly number each particle contour model according to positive integers 1 to N, and export them as STL files respectively.

[0050] In this invention, the N particle contour models can be named L1, L2, L3...L... i ...L N .

[0051] In this invention, the STL file stores the geometric information of the particle profile model.

[0052] Please refer to this carefully. Figure 2 , Figure 2 (a) in the figure is the geometric model of the real particle obtained by scanning the real particle. Figure 2 (b) in the text is a pair Figure 2 (a) shows the reconstructed geometric model obtained by reconstructing the geometric model of the real particle. Figure 2 (c) in the figure represents the particle contour model obtained by scaling the reconstructed geometric model to a preset volume and centrifuging it.

[0053] Step S20: Obtain the target gradation curve. Based on the target gradation curve and the predetermined total number of particles, construct a spherical particle assembly model including several spherical particle models using PFC3D software. The several spherical particle models in the spherical particle assembly model are in contact with each other and reach a static equilibrium state. The particle size of each spherical particle model is M times the actual particle size determined based on the target gradation curve, where 1.5≤M≤2.0.

[0054] Please refer to this carefully. Figure 3 In one optional implementation, step S20 includes:

[0055] Step S21, obtaining a target grading curve, and determining the number of particles in each particle size group based on the target grading curve and a predetermined total number of particles.

[0056] In the present application, the predetermined total number of particles is set according to actual conditions or experience, which can be 8 thousand, 10 thousand, 50 thousand, etc.

[0057] For the convenience of understanding, it is assumed that the total number of particles N = 1000, and based on the target grading curve, the percentage of particles less than 10 mm is 20%, the percentage of particles less than 20 mm is 70%, and the percentage of particles less than 30 mm is 100%. Therefore, the number of particles less than 10 mm is 200, the number of particles in the particle size range of 10 mm to 20 mm is 500, and the number of particles in the particle size range of 20 mm to 30 mm is 300.

[0058] Step S22, obtaining the particle size value of each particle based on the particle size range value, the number of particles in each particle size group, and the uniform distribution principle.

[0059] In the present application, the particle size values of the plurality of particles in each particle size group are uniformly distributed.

[0060] For the convenience of understanding, it is assumed that the number of particles in the particle size range of 20 mm to 30 mm is 300, and the number of particles corresponding to each particle size of 21 mm, 22 mm, 23 mm, …, 30 mm is 30.

[0061] Step S23, expanding the particle size value of each particle by M times to obtain a target particle size, and randomly generating a plurality of spherical particle models in a discrete element software PFC3D space based on the target particle size of each particle, to obtain a spherical particle collection model in a first state.

[0062] In the present application, M can be 1.5, 1.6, 1.7, 1.8, 1.9, 2.0, etc.

[0063] In the present application, the particle size of each spherical particle model is determined by the target particle size, the particle sizes of the plurality of spherical particle models have a one-to-one correspondence with the plurality of target particle sizes, and the correspondence is the same, i.e., the particle size of the spherical particle model having the correspondence is equal to the target particle size.

[0064] It can be understood that the particle sizes of the N spherical particle models have a one-to-one correspondence with the particle size values of each particle determined based on the target grading curve, and the correspondence is that the particle size of the spherical particle model having the correspondence is M times the particle size of the particle.

[0065] For the convenience of understanding, it is illustrated by example that if the number of particles with a particle size of 25 mm determined in step S20 is 3, when M = 2, the target particle size corresponding to the 3 particles is calculated to be 50 mm, and then in step S23, the generated several spherical particle models include 3 spherical particle models with a particle size of 50 mm.

[0066] Step S24, a wall is generated at the boundary of the spherical particle set model in the first state, and the set model is isotropically compressed to the center of the set model or a gravity field is applied to the spherical particle model, so that the several spherical particle models are in contact with each other and reach a static equilibrium state, and a spherical particle set model in a second state is obtained.

[0067] It can be understood that the spherical particle set model in the second state is the spherical particle set model constructed in step S20.

[0068] It should be noted that when the spherical particle set model is constructed in step S20, the particle size of the spherical particle model is M times the actual particle size of the particle determined based on the target grading curve, so that the particles can overlap in the replacement operation in step S30 below.

[0069] Step S30, each spherical particle model in the spherical particle set model is replaced by a breakable model composed of a plurality of polyhedrons, and each breakable particle model is named separately and written into the same text file, and the outline of the breakable model is obtained from the N particle outline models based on the random principle.

[0070] In the present application, the text file is in txt format, each breakable model is named separately, and the text files of all breakable models are written into the same file. It should be noted that when writing the instruction of the pure text file, the method of continuation is used instead of the method of covering, so as to prevent the previously generated instructions from being covered.

[0071] It should be noted that in the present application, before the current spherical particle model is replaced, all the polyhedrons in the breakable model obtained by the last replacement are deleted.

[0072] Please refer to Figure 4 Optionally, the step of replacing any one spherical particle model with a breakable model composed of a plurality of polyhedrons includes:

[0073] Step S31, based on the random principle, the spherical particle model is replaced by the particle outline model generated in step S10.

[0074] The step S31 includes:

[0075] An integer N' is directly randomly generated by uniformly distributing in 1-N, an STL file corresponding to the real particle profile model of N' name is extracted and introduced into PFC3D as a replacement model of the spherical particle model.

[0076] For the convenience of understanding, an example is given. Assuming that the randomly generated integer N' is 6, the STL file corresponding to the particle profile model of L6 is extracted and introduced.

[0077] The replacement model is used to replace the spherical particle model, and three-dimensional rotation angles are randomly generated in the range of 【0, π】 to randomly distribute the orientation of the real particle profile model as the replacement model in space.

[0078] In the following, the spherical particle model in step S31 is named as the replaced spherical particle model, and the real particle profile model used to replace the spherical particle model is named as the replaced particle profile model, to distinguish other spherical particle models and other particle profile models.

[0079] In step S32, a plurality of spherical sub-particles are generated in the replaced particle profile model, and inflation is performed by using the radius expansion method until the porosity in the replaced particle profile model reaches a preset porosity, to obtain a first particle packing model.

[0080] Optionally, the number of spherical sub-particles generated in the replaced particle profile model in step S32 is determined by the following steps, comprising:

[0081] Step (a), based on the equivalent particle diameter of each real particle, the volume of each real particle is calculated.

[0082] Step (b), the volumes of all real particles are sorted to obtain the real particle with the smallest volume.

[0083] Step (c), based on the fact that the real particle with the smallest volume needs to be divided into 100 cells, the cell volume is calculated.

[0084] Step (d), based on the volume of the replaced spherical particle model and the cell volume, the number of cells corresponding to the replaced spherical particle model is obtained according to the cell number calculation formula, and the number of cells is the ratio of the volume of the replaced spherical particle model to the cell volume.

[0085] The cell number calculation formula is = volume of the replaced spherical particle model / (M*cell volume).

[0086] Step (e) determining the number of generated spherical sub-particles in the replaced particle outline model based on the number of cells corresponding to the replaced spherical particle model, wherein the number of generated spherical sub-particles in the replaced particle outline model is the same as the number of cells of the replaced spherical particle model.

[0087] For the convenience of understanding, it is assumed by way of example that the volume of the smallest real particle is A1, the volume of the cell is A1 / 100, and the volume of the replaced spherical particle model is A2, and the number of cells corresponding to the replaced spherical particle model is A2*100 / A1.

[0088] It can be understood that, in the present application, the replaced particle outline model has a corresponding relationship with the replaced spherical particle model.

[0089] In an alternative embodiment, the preset porosity can be 0.35, 0.4, 0.42, etc., and is set according to actual needs.

[0090] In an alternative embodiment, the step S32 comprises:

[0091] Step (1) generating a plurality of spherical sub-particles in the replaced particle outline model as a boundary to obtain an initial filling model.

[0092] In the present application, the step is specifically: importing the replaced particle outline model into the discrete element software PFC3D and converting it into a wall, and then generating a plurality of spherical sub-particles in the wall based on the number of cells of the replaced spherical particle model and the initial particle diameter of the spherical sub-particles.

[0093] Step (2) calculating the sum V1 of the volumes of all spherical sub-particles in the initial filling model, and calculating the ratio of V1 to the volume V2 of the particle outline model to obtain a volume ratio.

[0094] In this step, the volume of the replaced particle outline model is a known value, the number of sub-particles and the initial particle diameter are known values, then: according to the volume calculation formula of a sphere, the volume of each spherical sub-particle is first calculated, and then the sum of the volumes of all spherical sub-particles is calculated, and the sum of the volumes of all spherical sub-particles V1 is obtained, and the volume of the replaced particle outline model V2 is a known value, and the volume ratio is V1 / V2.

[0095] Step (3) when the volume ratio is less than a target volume ratio, the radius of each spherical sub-particle is enlarged by m times to obtain an updated filling model, wherein 1.02≤m≤1.08.

[0096] Preferably, m is 1.05, that is, when the volume ratio is less than the target volume ratio, the radius of each sub-particle is enlarged by 1.05 times to obtain an updated packing model.

[0097] In the present application, when the preset porosity is 0.35, the target volume ratio is 0.65.

[0098] Step (4), repeating steps (2) and (3) until the updated packing model corresponds to the volume ratio greater than the target volume ratio, obtaining a first particle packing model, and the sum of the target volume ratio and the preset porosity is 1.

[0099] Step S33, first convert each spherical sub-particle in the first particle packing model into a coplanar Voronoi polyhedron, then convert the replaced particle contour model into a joint set, cut the Voronoi polyhedron to generate a plurality of polyhedrons, and delete the polyhedrons outside the replaced particle contour model to obtain a second particle packing model.

[0100] Please refer to Figure 5 , Figure 5 The process diagram for converting the first particle packing model into the second particle packing model, wherein, Figure 5 (a) in the figure is a model diagram of the first particle packing model, Figure 5 (b) in the figure is a diagram of converting each spherical sub-particle in the first particle packing model into a coplanar Voronoi polyhedron, Figure 5 (c) in the figure is a diagram of cutting the Voronoi polyhedron to generate a plurality of polyhedrons, Figure 5 (d) in the figure is a model diagram of the second particle packing model.

[0101] In the present application, converting each spherical sub-particle in the first particle packing model into a coplanar Voronoi polyhedron specifically includes: taking the center of the spherical small particle as a source node (seed) to generate a plurality of coplanar Voronoi polyhedrons, and deleting all spherical sub-particles.

[0102] In the present application, whether the polyhedron is located outside or inside the particle contour model is determined by the ray method, specifically, when the number of intersection points of the ray emitted by the center of the polyhedron with the particle contour model is odd, it is determined that the polyhedron is located inside the particle contour model, and when the number of intersection points of the ray emitted by the center of the polyhedron with the particle contour model is even, it is determined that the polyhedron is located outside the particle contour model.

[0103] Step S34, after scaling, translating and exporting the vertex of each polyhedron in the second particle accumulation model based on the particle size and the spatial coordinates of the replaced spherical particle model, a text file for replacing the breakable model of the spherical particle model is generated, the ratio of the particle size of the replaced spherical particle model to the effective particle size of the breakable model is M times, and the spatial coordinates of the center of the breakable model are the same as the spatial coordinates of the center of the replaced spherical particle model.

[0104] In the present application, the text file is in txt format, and the exporting operation is exporting to a txt text according to the generation instruction of the polyhedron in PFC3D.

[0105] In the present application, the particle size of the replaced spherical particle model is denoted as D1, and the spatial coordinates of the center of the replaced spherical particle model are represented as (X, Y, Z).

[0106] In an alternative embodiment, the step of scaling and translating the vertex of each polyhedron in the second particle accumulation model comprises:

[0107] Step (a), based on the particle size of the replaced spherical particle model and the contour size of the second particle accumulation model, calculating the scaling ratio of the vertex of each polyhedron in the second particle accumulation model.

[0108] In the present application, the contour size of the second particle accumulation model is the contour size of the replaced particle contour model.

[0109] The calculation formula of the scaling ratio R of the vertex is: the particle size of the replaced spherical particle model / (M×the particle size of the replaced particle contour model).

[0110] In the present application, the particle size of the replaced particle contour model is denoted as D2, then R=D1 / (M×D2).

[0111] Step (b), regarding all the vertices of the polyhedrons in the second particle accumulation model as all the vertices of a single polyhedron, scaling the spatial coordinates of each vertex based on the scaling ratio.

[0112] It should be noted that in the present application, all the vertices of the polyhedrons in the second particle accumulation model can be generated into a polyhedron by the convex hull function built in the discrete element platform.

[0113] For the convenience of understanding, an example is given, assuming that the coordinates of the vertex are represented as (X1, Y1, Z1), then after scaling the spatial coordinates of the vertex, the coordinates of the vertex can be represented as (R×X1, R×Y1, R×Z1).

[0114] Step (c), the space coordinates of each vertex after scaling are added to the space coordinates of the center of the spherical particle model to obtain the coordinates of each vertex after translation, and each vertex is moved according to the coordinates of each vertex after translation.

[0115] When the space coordinates of the center of the spherical particle model are (X, Y, Z), based on the above examples, the vertex coordinates of the vertex translated to (R×X1, R×Y1, R×Z1) are (R×X1+X, R×Y1+Y, R×Z1+Z).

[0116] Step S40, after all the spherical particle models are replaced by breakable models, a breakable particle material numerical model instruction file is generated, and the instruction file is directly input into PFC3D in a read mode to generate a breakable particle discrete element numerical model.

[0117] In the present application, all the breakable models are breakable models with the same profile as the real particles, and are not replaced by breakable models.

[0118] In the present application, the text files of all the breakable models are directly input into PFC3D in a read mode, and the breakable particle discrete element numerical model is generated. Since a breakable particle material numerical model is usually composed of hundreds of thousands or even millions of polyhedrons, the number of instruction lines is extremely large, and the text is often over 100 megabytes. Therefore, the optimal way to import the discrete element platform PFC3D is to directly call read instead of opening and then executing, to prevent the platform from crashing due to a too large file.

[0119] In the present application, the breakable particle model constructed in step S40 has the topography of the real particles, is composed of coplanar Voronoi polyhedrons, and has controllable size, which is used for simulating the discrete element numerical simulation of geotechnical tests such as triaxial compression test, direct shear test, and side limit loading, and is helpful for analyzing the particle breakage characteristics and the mesoscopic influence of particle breakage on the macroscopic mechanical properties of materials.

[0120] It should be noted that the construction method provided by the present application is also applicable to the modeling of two-dimensional breakable particle models.

[0121] Please refer to Figures 6 to 8 , Figure 6 for the conversion of a spherical particle assembly into an irregular breakable particle model diagram; Figure 7 for Figure 6 the consolidation diagram of the irregular breakable particle model shown in FIG. 8; Figure 8 for Figure 6 the breakage effect diagram of the irregular breakable particle model under two different loads, Figure 8 wherein (a) is the breakage effect diagram under the first load, Figure 8 (b) is the breakage effect under the second load.

[0122] It should be noted that Figure 6 The spherical particle assembly in the step S20 is a spherical particle assembly model constructed in the step S20, Figure 6 The irregular breakable particle model in the step S40 is a breakable particle discrete element numerical model constructed in the step S40.

[0123] It should be noted that Figure 9 The second load is greater than the first load.

[0124] Please refer to Figure 9 According to a second aspect of the present application, the present application further provides a construction device 100 of a breakable particle discrete element numerical model, the construction device comprising: an acquisition module 101, configured to acquire initial geometric models of N real particles, obtain particle outline models with the same equivalent particle diameter based on a preset operation, and the center of each particle outline model coincides with the coordinate origin, randomly number each particle outline model according to a positive integer 1~N, and export each particle outline model in an STL file respectively, the preset operation comprising reconstructing the initial geometric models, and scaling and moving the reconstructed geometric models; a construction module 102, configured to acquire a target grading curve, construct a spherical particle assembly model comprising a plurality of spherical particle models by using PFC3D software based on the target grading curve and a predetermined total number of particles, the plurality of spherical particle models in the spherical particle assembly model are in contact with each other and reach a static equilibrium state, and the particle diameter of each spherical particle model is M times of the actual particle diameter of the particle determined based on the target grading curve, 1.5≤M≤2.0; a replacement module 103, configured to replace each spherical particle model in the spherical particle assembly model with a breakable model composed of a plurality of polyhedrons one by one, and each generated breakable particle model is named separately and written into a same text file successively, and the outline of the breakable model is acquired from the N particle outline models based on a random principle; and a generation module 104, configured to generate a breakable particle material numerical model instruction file after all the spherical particle models are replaced with the breakable models, input the instruction file into PFC3D in a read mode, and generate a breakable particle discrete element numerical model.

[0125] Those skilled in the art can clearly understand that, for the convenience and brevity of description, the working process of the construction device described above can refer to the content in the foregoing method embodiments, which will not be described herein.

[0126] According to a third aspect of the present application, the present application further provides an application of the breakable particle discrete element numerical model constructed by the construction method described above, the application comprising any one of geotechnical tests including triaxial compression test, direct shear test and side loading test.

[0127] The above is further detailed description of the present application in combination with specific preferred embodiments, and cannot be deemed as limitation of the specific implementation of the present application to these descriptions. For those skilled in the art to which the present application belongs, without departing from the concept of the present application, a number of simple deductions and substitutions can be made, and all of them shall be deemed as falling within the protection scope of the present application.

Claims

1. A method for constructing a discrete element numerical model of breakable particles, characterized in that, The construction method includes the following steps: Step S10: Obtain the initial geometric model of N real particles, and obtain N particle outline models with the same equivalent particle size based on preset operations. The centroid of each particle outline model coincides with the origin of the coordinate system. Randomly number each particle outline model according to positive integers 1 to N, and export them as STL files respectively. The preset operations include reconstructing the initial geometric model and scaling and moving the reconstructed geometric model. Step S20: Obtain the target gradation curve. Based on the target gradation curve and the predetermined total number of particles, use PFC3D software to construct a spherical particle assembly model that includes several spherical particle models. The several spherical particle models in the spherical particle assembly model are in contact with each other and reach a state of static equilibrium. The particle size of each spherical particle model is M times the actual particle size determined based on the target gradation curve, where 1.5≤M≤2.

0. Step S30: Replace each spherical particle model in the spherical particle set model with a breakable model composed of multiple polyhedra, and name each generated breakable particle model separately and write it into the same text file. The outline of the breakable model is obtained from N particle outline models based on a random principle. Step S40: After all spherical particle models are replaced with breakable models, a numerical model instruction file for breakable particle materials is generated. The instruction file is then directly input into PFC3D in a read-only manner to generate a discrete element numerical model of breakable particles.

2. The method for constructing a discrete element numerical model of breakable particles according to claim 1, characterized in that, The steps to replace any spherical particle model with a breakable model composed of multiple polyhedra include: Step S31: Based on the principle of randomness, replace the spherical particle model with the particle contour model generated in step S10; Step S32: Generate multiple spherical sub-particles in the replaced particle profile model, and expand them using the radius expansion method until the porosity in the replaced particle profile model reaches the preset porosity, thus obtaining the first particle packing model. Step S33: First, convert each spherical sub-particle in the first particle packing model into a coplanar Voronoi polyhedron. Then, convert the replaced particle outline model into a joint group, cut the Voronoi polyhedron one by one to generate multiple polyhedra, and then delete the polyhedra outside the replaced particle outline model to obtain the second particle packing model. Step S34: Based on the particle size and spatial coordinates of the replaced spherical particle model, after scaling, translating and exporting the vertices of each polyhedron in the second particle packing model, a text file for a breakable model to replace the spherical particle model is generated. The ratio of the particle size of the replaced spherical particle model to the effective particle size of the breakable model is M times, and the spatial coordinates of the centroid of the breakable model are the same as the spatial coordinates of the center of the replaced spherical particle model.

3. The method for constructing a discrete element numerical model of breakable particles according to claim 2, characterized in that, Step S31 includes: By randomly generating integers N' directly and uniformly distributed between 1 and N, the STL file of the real particle contour model corresponding to the name N' is extracted and imported into PFC3D as a replacement model for the spherical particle model. The spherical particle model is replaced with the replacement model, and three dimensional rotations are randomly generated within the range of [0, π], so that the orientation of the real particle contour model, which is the replacement model, is randomly distributed in space.

4. The method for constructing a discrete element numerical model of breakable particles according to claim 2, characterized in that, The number of spherical sub-particles generated in the replaced particle profile model in step S32 is determined by the following steps, including: Step (a): Calculate the volume of each real particle based on its equivalent particle size; Step (b): Sort the volumes of the N real particles and obtain the real particle with the smallest volume; Step (c): Based on the fact that the smallest real particle needs to be divided into 100 cells, the cell volume is calculated. Step (d): Based on the volume of the replaced spherical particle model and the cell volume, obtain the cell number corresponding to the replaced spherical particle model according to the cell number calculation formula, wherein the cell number is the ratio of the volume of the replaced spherical particle model to the cell volume. Step (e): Determine the number of spherical sub-particles generated in the replaced particle profile model based on the number of cells corresponding to the replaced spherical particle model, wherein the number of spherical sub-particles generated in the replaced particle profile model is the same as the number of cells in the replaced spherical particle model.

5. The method for constructing a discrete element numerical model of breakable particles according to claim 4, characterized in that, Step S32 includes: Step (1): Using the replaced particle outline model as the boundary, generate multiple spherical sub-particles within the replaced particle outline model to obtain the initial filling model. Step (2): Calculate the sum of the volumes V1 of all spherical sub-particles in the initial filling model, and calculate the ratio of V1 to the volume V2 of the particle outline model to obtain the volume ratio value. Step (3): When the volume ratio is less than the target volume ratio, the radius of each spherical sub-particle is increased by a factor of m to obtain an updated filling model, where 1.02≤m≤1.08; Step (4): Repeat steps (2) and (3) until the updated filling model corresponds to a volume ratio greater than the target volume ratio, and obtain the first particle packing model, wherein the sum of the target volume ratio and the preset porosity is 1.

6. The method for constructing a discrete element numerical model of breakable particles according to claim 2, characterized in that, The steps of scaling and translating the vertices of each polyhedron in the second particle stacking model include: Step (a): Based on the particle size of the replaced spherical particle model and the outline size of the second particle packing model, calculate the scaling ratio of the vertices of each polyhedron in the second particle packing model; Step (b): Treat all the vertices of all the polyhedra in the second particle stacking model as all the vertices of a single polyhedron, and scale the spatial coordinates of each vertex based on the scaling ratio. Step (c): Add the spatial coordinates of the center of the spherical particle model to the scaled spatial coordinates of each vertex to obtain the translated coordinates of each vertex, and move each vertex according to the translated coordinates of each vertex.

7. The method for constructing a discrete element numerical model of breakable particles according to any one of claims 1 to 6, characterized in that, Step S20 includes: Step S21: Obtain the target gradation curve, and determine the number of particles in each particle size group based on the target gradation curve and the predetermined total number of particles. Step S22: Based on the particle size range, number of particles, and uniform distribution principle of each particle size group, obtain the particle size value of each particle; Step S23: Expand the particle size value of each particle by M times to obtain the target particle size. Based on the target particle size of each particle, randomly generate several non-contact spherical particle models in the space of the discrete element software PFC3D to obtain a spherical particle set model in the first state. Step S24: Generate a wall at the boundary of the spherical particle assembly model in the first state. Compress the wall isotropically toward the center of the assembly model or apply a gravitational field to the spherical particle model so that several spherical particle models come into contact with each other and reach a static equilibrium state, thus obtaining the spherical particle assembly model in the second state.

8. The method for constructing a discrete element numerical model of breakable particles according to any one of claims 1 to 6, characterized in that, Step S10 includes: Step (1): Randomly select N real particles, which are one of crushed stone particles, pebble particles or agate particles, where N is a positive integer and 1≤N≤100; Step (2): Obtain the initial geometric model of each real particle using image processing or 3D scanning. Step (3): Reconstruct the initial geometric model of each real particle using the spherical harmonic function analysis method or the quadrilateral reconstruction network method to obtain N reconstructed geometric models; Step (4): Scale each of the reconstructed geometric models to a preset volume to obtain N particle contour models, and move the centroid of each particle contour model to the origin of the coordinate system. Step (5): Randomly number each particle contour model according to positive integers 1 to N, and export them as STL files respectively.

9. A device for constructing a discrete element numerical model of breakable particles, characterized in that, The construction apparatus includes: The acquisition module is used to acquire the initial geometric models of N real particles, obtain N particle outline models with the same equivalent particle size based on preset operations, and the centroid of each particle outline model coincides with the origin of the coordinate system. Each particle outline model is randomly numbered according to positive integers 1 to N, and exported as an STL file. The preset operations include reconstructing the initial geometric model and scaling and moving the reconstructed geometric model. A construction module is used to obtain the target gradation curve. Based on the target gradation curve and the predetermined total number of particles, a spherical particle assembly model including several spherical particle models is constructed using PFC3D software. The several spherical particle models in the spherical particle assembly model are in contact with each other and reach a state of static equilibrium. The particle size of each spherical particle model is M times the actual particle size determined based on the target gradation curve, where 1.5≤M≤2.

0. The replacement module is used to replace each spherical particle model in the spherical particle set model with a breakable model composed of multiple polyhedra. Each generated breakable particle model is named separately and written to the same text file. The outline of the breakable model is obtained from N particle outline models based on a random principle. The generation module is used to generate a numerical model instruction file for breakable particle materials after all spherical particle models have been replaced with breakable models. The instruction file is then directly input into PFC3D in a read-only manner to generate a discrete element numerical model of breakable particles.

10. The application of the discrete element numerical model of breakable particles constructed by the construction method according to any one of claims 1 to 8, characterized in that, The application includes simulation of any type of geotechnical test, including triaxial compression test, direct shear test, and lateral confinement loading test.

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