A method for generating a two-dimensional geometric model of soil-rock mixture with high volume fraction

Abstract

The present invention discloses a method for generating a two-dimensional high-volume-fraction soil-rock mixture geometric model. First, randomly distributed particles of arbitrary shapes are generated according to a grading curve. Then, a Minkowski sum operation is performed on the particles to control the minimum gap between adjacent particles. Then, the overlapping discrete element cluster method is used to achieve the transition from particles to clusters, and the clusters are randomly placed in a certain area. Then, a linear contact model is assigned, and a DEM simulation is performed to separate overlapping clusters, and the initial position, displacement, and rotation of the clusters are recorded. Finally, the model is reconstructed based on the displacement and rotation information. The present invention easily obtains the theoretical maximum volume fraction of arbitrary particle shapes, while solving the boundary distribution problem of particles and the contact problem between particles. In addition, the periodic boundary conditions in the DEM provide a simple implementation method for periodic microstructures, making the generated model more consistent with actual conditions and improving the reliability of subsequent numerical method experimental research results, which has strong application significance.

Description

Technical Field

[0001] The present invention belongs to the technical field of mechanical parameter research of heterogeneous rock and soil materials, and particularly relates to a method for generating a two-dimensional high volume fraction soil-rock mixture material geometric model based on a discrete element method (DEM) for generating material numerical model test blocks. Background Art

[0002] Numerical methods for studying the mechanical parameters of heterogeneous geomaterials (such as concrete and aggregates) have developed rapidly in recent years. These methods can effectively overcome the problems of sampling difficulties, specimen disturbance, large discrete results, and the small test scale compared to the internal structure in real experimental parameter studies. However, numerical methods for studying heterogeneous material parameters still face a major challenge: model establishment. This involves generating a numerical model specimen that meets the requirements of the numerical test based on the internal structural parameters of the aggregate (such as the aggregate gradation and shape in concrete).

[0003] Many scholars have attempted various approaches to model building. Some have used cellular automata models, while others have used two-dimensional random aggregate models to construct geometric models of concrete. Some researchers have also attempted to establish a method for generating three-dimensional particle models. While research in this area has primarily focused on two dimensions, significant progress has been made, enabling the generation of relatively complex particle geometry models. However, current methods for generating two-dimensional high-volume-fraction particle volume models have drawbacks. Generating high-volume-fraction aggregate models is inefficient and time-consuming, and particles are not permitted to be placed on boundaries, which can affect the accuracy of the modeling results. Summary of the Invention

[0004] Purpose of the invention: The purpose of the present invention is a method for generating a two-dimensional high volume fraction soil-rock mixture geometric model. The generated particles can more realistically simulate the shape of aggregate particles, providing a basis for predicting the mechanical properties of particle-reinforced composite materials using numerical simulation methods.

[0005] Technical solution: The present invention provides a method for generating a two-dimensional high volume fraction soil-rock mixture geometric model, which specifically includes the following steps:

[0006] (1) Generate all particles according to grading information;

[0007] (2) Based on the Minkowski sum theory, the particles are extended outward, the processed particle coordinate data are imported into the discrete element software, the particles are replaced by clusters, and the specified domain and boundary conditions are set;

[0008] (3) Perform DEM simulation in the linear contact model and obtain the displacement and rotation of the particles based on the DEM results;

[0009] (4) The final distribution of particles is located based on the initial position coordinates and rotational displacement of the particles. The boundary positioning algorithm is used to screen out the particles located at the boundary, and the same particles are replicated on the boundaries that do not intersect with the boundaries where they are located to generate the final soil-rock mixture geometric model.

[0010] Furthermore, the implementation process of step (1) is as follows:

[0011] The method randomly generates particles with a custom particle size distribution and volume fraction within a preset coordinate area. The randomly generated custom particles are simulated using Monte Carlo simulation. The particles are polygonal in shape and are generated by selecting a custom number of vertices on the circumference with (0,0) as the center, specifying an angle and radius, and connecting them in order. The method randomly generates custom particles by calculating all possible positions according to a specified spacing distance dt before placing a particle. When a particle is placed, the point in the set will be removed and the position will be updated.

[0012] Furthermore, the process of extending the particles outward based on the Minkowski sum theory in step (2) is as follows:

[0013] The thickness offset operation after particle generation is implemented based on the Minkowski sum theory. The Minkowski sum of point sets A and B is determined as:

[0014]

[0015] The thickness offset operation is based on the vertex position coordinates of the particles after placement. By setting different disk radius controls, multiple vertices are added after outward offset, so that the particles have an additional shell. By setting different disk radius, the minimum gap between aggregates can be flexibly controlled.

[0016] Furthermore, the boundary conditions in step (2) include periodic boundaries and rigid boundaries; periodic modeling applies periodic boundary conditions, and when the cluster centroid falls outside the model domain, the cluster is converted back to the other side of the model.

[0017] Furthermore, the implementation process of step (3) is as follows:

[0018] The centroid of the cluster is recorded before DEM packaging. After completing the DEM simulation, the displacement and rotation of each cluster are obtained. The geometric structure of the aggregate is calculated based on the translation and rotation transformations. For the contact of the clusters, a linear model with normal and tangential stiffness is used. The contact forces in the normal and shear directions are:

[0019]

[0020] Where, F i n is the normal contact force, K nis the normal secant contact stiffness, U n is the total normal displacement, n i is the unit normal vector, ΔF i s is the shear stress increment, k s is the shear stiffness, is the shear displacement increment;

[0021] The friction parameter affects the rotation of the clusters and is set to 0 in the simulation; if the clusters are distributed along a certain direction, the rotation of the clusters is fixed.

[0022] Furthermore, the final distribution of the particles in step (4) includes the X, Y coordinates of each vertex of the polygon relative to (0,0) and the vertex order.

[0023] Beneficial effects: Compared with the prior art, the present invention has the following beneficial effects: the present invention greatly improves the upper limit of the volume fraction of the generative model and the generation efficiency, while solving the boundary distribution problem of particles and the contact problem between particles, making the generated model more in line with the actual situation, and can improve the reliability of subsequent numerical method test research results, and has strong application significance. BRIEF DESCRIPTION OF THE DRAWINGS

[0024] Figure 1 is a flow chart of the present invention;

[0025] Figure 2 Schematic diagram for the application of Minkowski and theory;

[0026] Figure 3 This is a demonstration diagram of periodic boundary conditions;

[0027] Figure 4 Schematic diagram of particle position transformation;

[0028] Figure 5 Schematic diagram of the process of generating a model using the method of the present invention, wherein (a) is the initial particle distribution diagram; (b) is the particle-to-cluster distribution diagram; (c) is the DEM simulation result distribution diagram; and (d) is the final particle distribution diagram. DETAILED DESCRIPTION

[0029] The present invention will be further described below with reference to the accompanying drawings.

[0030] The present invention provides a method for generating a two-dimensional high volume fraction soil-rock mixture geometric model, such as Figure 1 As shown, the specific steps include:

[0031] Step 1: Generate all particles according to grading information.

[0032] Randomly generate particles with custom particle gradation and volume fraction within a preset coordinate area. Use Matlab to randomly generate particles with specified gradation and volume fraction using Monte Carlo simulation within a preset 50*100 Cartesian coordinate system area. Monte Carlo simulation is used to randomly generate custom particles. The particle shape is polygonal. The generation method is to use (0,0) as the center of the circle, specify the angle and radius, select a custom number of vertices on the circumference, and connect them in order. The method of randomly generating custom particles is to calculate all possible positions based on the specified spacing distance dt before placing a particle. When a particle is placed, the point in the set will be removed and the possible positions will be updated. This reduces the collision area between the new aggregate and the existing aggregate, and improves the performance of subsequent DEM simulation.

[0033] The area is generally a 50*100 coordinate area. A point is randomly selected from the area, and the coordinates are added to the polygon coordinates to complete the particle placement. After the placement is completed, the information of the internal points of the particle is deleted and no longer participates in the random point selection in the area, thereby improving efficiency.

[0034] Step 2: Based on the Minkowski sum theory, the particles are extended outward, such as Figure 2 As shown, the processed particle coordinate data are imported into the discrete element software, particles are replaced by clusters, and the specified domain and boundary conditions are set.

[0035] Based on the Minkowski sum theory, the thickness offset operation is implemented after the particle is generated, and a shell with a certain thickness is added to its outer surface; the Minkowski sum of point sets A and B is determined as:

[0036]

[0037] By setting different disc radii, you can flexibly control the minimum gap between aggregates. The thickness offset operation is based on the vertex position coordinates of the particles after placement. By setting different disc radii, multiple vertices are added after the outward offset, adding a shell to the particles, preventing the particles from contacting in subsequent calculation results.

[0038] The processed aggregate particle morphology distribution coordinate data is imported into Flac2D; the particles are replaced by discrete element clusters, and the collision detection algorithm is used in the preset periodic boundary structure. After a certain period of calculation, the model presents the particle redistribution result.

[0039] Boundary conditions include periodic boundaries and rigid boundaries; for regional boundary conditions of periodic modeling, when the cluster centroid falls outside the model domain, the cluster is transformed back to the other side of the model, such as Figure 3 shown.

[0040] Step 3: Perform DEM simulation in the linear contact model and obtain the displacement and rotation of the particles based on the DEM results; Figure 4 shown.

[0041] The centroid of the cluster is recorded before DEM packaging; after completing the DEM simulation, the displacement and rotation of each cluster are obtained; the geometric structure of the aggregate is calculated based on the translation and rotation transformation; for the contact of the clusters, a linear model with normal stiffness and tangential stiffness is used. The contact force in the normal and shear directions is:

[0042]

[0043] Where, F i n is the normal contact force, K n is the normal secant contact stiffness, U n is the total normal displacement, n i is the unit normal vector, ΔF i s is the shear stress increment, k s is the shear stiffness, is the shear displacement increment.

[0044] The friction parameter affects the rotation of the clusters and can be set to 0 during simulation. In addition, if the clusters are distributed along a certain direction, the rotation of the clusters is fixed. Once these parameters are set correctly, simulation can be easily performed.

[0045] For cases where aggregates cannot be located at the boundary, a rigid boundary is implemented using the wall in PFC; the domain size should be slightly larger than the specimen to ensure that the aggregates cannot reach the domain boundary; otherwise, the size of the rigid wall should be slightly smaller than the specimen so that the aggregated clusters will be constrained to the specified area.

[0046] Step 4: Locate the final distribution of particles based on their initial position coordinates and rotational displacement. Use the boundary positioning algorithm to screen out particles located at the boundary, and replicate the same particles on the boundaries that do not intersect with their boundaries to generate the final soil-rock mixture material model, as shown in the following example. Figure 5 shown.

[0047] The coordinates and rotation of the redistributed particles were recorded and imported into Matlab. The imported data was used to adjust the position and direction of the particle distribution within the coordinate region. A boundary location algorithm was used to screen out particles located at the boundary and replicate the same particles on non-intersecting boundaries to generate the final soil-rock mixture model.

[0048] The generated model is output as a geometric format file for the corresponding aggregate particles. The geometric format file is a DXF file, which can be used as a template library file for various numerical experiments. Of course, other geometric format files can also be used for other numerical experiments on the corresponding aggregate particles. In other words, the numerical model generated by the present invention is portable; the corresponding numerical model can be obtained by simply importing the corresponding geometric format file during the experiment.

[0049] The final distribution position information of the particles includes the X, Y coordinates and vertex order of each vertex of the polygon relative to (0,0). The data output by the generated model should include the coordinates of the center of gravity of the multi-sphere and the rotation angle of the vertex relative to the center of gravity. The final particle coordinate calculation method uses the particles to randomly generate coordinates relative to the origin and add them to the corresponding center of gravity coordinates derived after calculation. Then, the coordinates of each vertex after rotation are calculated by the rotation angle. The particle position boundary detection algorithm is used to determine whether the particle is located on the boundary. If so, the particle is translated and cloned to the boundary relative to its boundary to realize the arrangement of boundary particles. There are multiple options for the format of the model output data. The preferred output is a DXF format file, and the generation method is to generate self-compiled code for generating DXF.

[0050] The embodiments of the present invention are described above in conjunction with the accompanying drawings, but the present invention is not limited to the above-mentioned specific implementation methods. The above-mentioned specific implementation methods are merely illustrative and not restrictive. Under the guidance of the present invention, ordinary technicians in this field can also make many forms without departing from the scope of protection of the purpose of the present invention and the claims, which are all protected by the present invention.

Claims

1. A method for generating a two-dimensional high volume fraction soil-rock mixture geometric model, characterized in that: The following steps are involved: (1) Generate all particles according to grading information; (2) Based on the Minkowski sum theory, the particles are extended outward, the processed particle coordinate data are imported into the discrete element software, the particles are replaced by clusters, and the specified domain and boundary conditions are set; (3) Perform DEM simulation in the linear contact model and obtain the displacement and rotation of the particles based on the DEM results; (4) The final distribution of particles is located based on the initial position coordinates and rotational displacement of the particles. The boundary positioning algorithm is used to screen out the particles located at the boundary, and the same particles are replicated on the boundaries that do not intersect with the boundaries where they are located to generate the final soil-rock mixture geometric model; The implementation process of step (3) is as follows: The centroid of the cluster is recorded before DEM packaging. After completing the DEM simulation, the displacement and rotation of each cluster are obtained. The geometric structure of the aggregate is calculated based on the translation and rotation transformations. For the contact of the clusters, a linear model with normal and tangential stiffness is used. The contact forces in the normal and shear directions are: Where, is the normal contact force, K n is the normal secant contact stiffness, U n is the total normal displacement, n i is the unit normal vector, is the shear stress increment, k s is the shear stiffness, is the shear displacement increment; The friction parameter affects the rotation of the clusters and is set to 0 in the simulation; if the clusters are distributed along a certain direction, the rotation of the clusters is fixed.

2. The method for generating a two-dimensional high volume fraction soil-rock mixture geometric model according to claim 1, characterized in that: The implementation process of step (1) is as follows: The method randomly generates particles with a custom particle size distribution and volume fraction within a preset coordinate area. The randomly generated custom particles are simulated using Monte Carlo simulation. The particles are polygonal in shape and are generated by selecting a custom number of vertices on the circumference with (0,0) as the center, specifying an angle and radius, and connecting them in order. The method randomly generates custom particles by calculating all possible positions according to a specified spacing distance dt before placing a particle. When a particle is placed, the point in the set will be removed and the position will be updated.

3. The method for generating a two-dimensional high volume fraction soil-rock mixture geometric model according to claim 1, characterized in that: The process of extending the particles outward based on the Minkowski sum theory in step (2) is as follows: The thickness offset operation after particle generation is implemented based on the Minkowski sum theory. The Minkowski sum of point sets A and B is determined as: The thickness offset operation is based on the vertex position coordinates of the particles after placement. By setting different disk radius controls, multiple vertices are added after outward offset, so that the particles have an additional shell. By setting different disk radius, the minimum gap between aggregates can be flexibly controlled.

4. The method for generating a two-dimensional high volume fraction soil-rock mixture geometric model according to claim 1, characterized in that: The boundary conditions described in step (2) include periodic boundaries and rigid boundaries; periodic modeling applies periodic boundary conditions, and when the cluster centroid falls outside the model domain, the cluster is converted back to the other side of the model.

5. The method for generating a two-dimensional high volume fraction soil-rock mixture geometric model according to claim 1, characterized in that: The final distribution of the particles described in step (4) includes the X, Y coordinates of each vertex of the polygon relative to (0,0) and the vertex order.

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