Grating geometric configuration design method based on grain composition and shape characteristics

Abstract

The invention provides a grid geometric configuration design method based on grain grading and shape characteristics, which comprises the following steps: setting the particle size range of gravel particles according to gravel paving requirements, obtaining the shape parameters of gravel particle samples, counting the shape parameters in different particle size ranges, and calculating the shape parameters in different particle size ranges; selecting representative particles in each particle size range according to the distribution range of the shape parameters; the binary image of the representative particles is converted into a real particle form template, and the real particle form template is randomly placed in the rectangular area according to grading data required by gravel material laying; and compacting all the real particle form templates in the rectangular area, reducing the particle sizes of all the real particle form templates in an equal proportion according to the size of the grid, generating a two-dimensional template of the grid, and endowing the grid with a thickness value along a normal vector of a boundary contour of the two-dimensional template to obtain a three-dimensional grid template.

Description

Technical Field

[0001] This invention belongs to the field of civil engineering composite reinforcement materials technology, specifically relating to a grid geometry configuration design method based on particle size distribution and shape characteristics. Background Technology

[0002] Crushed stone is a widely used basic material in civil engineering, commonly found in key structures such as highway and railway subgrade filling, track beds, retaining wall backfill, slope protection, and foundation cushion layers. This type of material is composed of crushed stone particles of different sizes arranged according to design gradation. It provides load-bearing capacity through the interlocking and friction between particles, while also possessing excellent permeability and deformation coordination capabilities.

[0003] However, during long-term service, the combined effects of self-weight stress, environmental erosion, and external loads inevitably cause wear and tear on the edges of crushed stone particles, leading to gradation shift, decreased density, and a significant decline in structural integrity and load-bearing capacity. To suppress the performance degradation of crushed stone structures, the engineering community widely uses geogrids to reinforce roadbeds. The contact surface between the geogrid and the crushed stone particles generates frictional resistance, and the mesh mechanically embeds the particles, restricting their lateral displacement and rotation, and suppressing lateral expansion and shear deformation of the roadbed. In addition, the geogrid forms a tension membrane under tension, distributing the upper load more evenly to the lower foundation, reducing uneven settlement and local stress concentration. These mechanisms work synergistically to significantly improve the integrity, shear strength, and load-bearing capacity of reinforced roadbeds.

[0004] However, existing geogrids generally adopt fixed, uniform pore structures, such as square or triangular ones. This static design ignores the irregular shape and particle size distribution of crushed stone and their impact on the optimal interlocking effect. As a result, the interlocking efficiency is low, standard pores are difficult to form efficient contact with heterogeneous crushed stone, and particle slippage is not sufficiently suppressed. Mismatched pore-particle combinations are prone to local stress increases at the grid ribs or particle edges, accelerating particle breakage and grid damage. Furthermore, it is impossible to customize reinforcement for crushed stone gradation in specific areas or at deterioration stages, limiting the overall reinforcement effect and making it difficult to maximize bearing capacity and service life. Summary of the Invention

[0005] This invention proposes a grid geometry design method based on particle size distribution and shape characteristics, which solves the problem of insufficient geometric adaptability of existing civil grids.

[0006] To address the aforementioned technical problems, this invention provides a grid geometry design method based on particle size distribution and shape characteristics, comprising the following steps: Step S1: Set the particle size range of crushed stone according to the requirements of crushed stone paving, obtain the shape parameters of crushed stone particle samples, statistically analyze the shape parameters in different particle size ranges, and select representative particles for each particle size range based on the distribution range of the shape parameters. Step S2: Convert the binary image of the representative particles into a real particle morphology template, and randomly place the real particle morphology template within the rectangular area according to the gradation data required for crushed stone paving. Step S3: Compact all real particle shape templates within the rectangular area, proportionally reduce the particle size of all real particle shape templates according to the grid size, generate a two-dimensional grid template, assign grid thickness values ​​along the normal vector of the boundary contour of the two-dimensional template, and obtain a three-dimensional grid template.

[0007] Preferably, the step S1 of selecting representative particles for each particle size range includes the following steps: Step S11: Perform a three-dimensional scan on the crushed stone particle sample to obtain the surface mesh model of the crushed stone particle sample; Step S12: Obtain the vertex and face information of each mesh in the surface mesh model, and project the crushed stone particle sample into two dimensions based on the vertex and face information to generate a two-dimensional projection point set; Step S13: Map the projection points in the two-dimensional projection point set to a binary image, and invert the binary image; Step S14: Calculate the shape parameters of the crushed stone particle sample based on the inverted binary image; Step S15: Statistically analyze the particle distribution range and percentage of the shape parameters of the crushed stone particles, fit the normal distribution curve of the shape parameters of the crushed stone in different particle size ranges, and select representative crushed stone particles in each particle size range according to the distribution.

[0008] Preferably, the shape parameter in step S14 includes sphericity, and the expression for calculating the sphericity is: ; In the formula, The sphericity of the crushed stone particles; , These are the length and width of the crushed stone particle sample, respectively.

[0009] Preferably, the shape parameter in step S14 includes roundness, and the expression for calculating the roundness is: ; In the formula, The roundness of the crushed stone particle sample; This represents the number of all corner points in the crushed stone particle sample. For the first The radius of curvature at each corner point; The radius of the largest inscribed circle in the crushed stone particle sample.

[0010] Preferably, the compaction of all real particle morphology templates within the rectangular area in step S3 includes the following steps: assigning weight to all real particle morphology templates within the rectangular area, causing all real particle morphology templates to fall and accumulate, and generating a cover plate above the rectangular area to compact all real particle morphology templates.

[0011] The beneficial effects of the present invention include at least the following: 1. By directly using the two-dimensional image information of crushed stone particles as the aperture boundary, the geometric fit between the grid and the particles is significantly improved, effectively enhancing the interlocking ability and shear resistance. 2. During the hole design stage, the aggregate gradation data from the construction site is incorporated. The hole size and distribution density are precisely adjusted according to proportion and location to achieve a high degree of synergy between the grid structure and the particle size combination. The constraint efficiency for particles of different sizes is significantly improved, and the overall reinforcement effect is better than that of standardized products. Attached Figure Description

[0012] Figure 1 This is a schematic diagram of the method flow according to an embodiment of the present invention; Figure 2 This is a schematic diagram showing the distribution of crushed stone particles generated in an embodiment of the present invention; Figure 3 This is a schematic diagram of the crushed stone template generated according to an embodiment of the present invention; Figure 4 This is a schematic diagram of a three-dimensional grid template generated according to an embodiment of the present invention; Figure 5 This is a partial enlarged view of the three-dimensional grid template generated in an embodiment of the present invention. Detailed Implementation

[0013] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the protection scope of the present invention.

[0014] like Figure 1 As shown, this embodiment of the invention provides a grid geometry design method based on particle size distribution and shape characteristics, including the following steps: Step S1: To establish a geogrid pore shape that accurately matches the crushed stone gradation, representative shape parameters must first be extracted within each particle size range. This step uses Matlab software as the core platform to sequentially complete 3D scanning, 2D projection, image processing, and parameter calculation. Specifically, it includes the following steps: Step S11: Use a 3D scanner to perform high-precision 3D scanning on the crushed stone samples of each particle size range of the target gradation to obtain a surface mesh model in STL format with a triangular mesh; use Matlab to read the STL file, extract the vertex and face information in the surface mesh model, and project the 3D coordinates onto a 2D plane to generate the corresponding 2D projection point set, laying the data foundation for subsequent image processing.

[0015] Step S12: Expand the projection range and normalize the coordinates to the pixel coordinate system under the set image resolution; call the poly2mask function in Matlab to map the two-dimensional projection point set to the initial binary image, remove the noise region, and fill the holes in the target region to obtain a complete and clean binary image; perform an inversion operation on the binary image, that is, the foreground is white and the background is black, to ensure that the target particle region can be accurately identified and used for shape analysis.

[0016] Step S13: Based on the processed binary image, calculate the shape parameters using Matlab software. In this embodiment of the invention, the shape parameters consider two parameters: sphericity and roundness. Calculate sphericity. The expression is: ; In the formula, For the length and width of the crushed stone particles; Calculate roundness The expression is: ; In the formula, This represents the number of all corner points of the crushed stone particles; For the first The radius of curvature at each corner point; The radius of the largest inscribed circle of the crushed stone particles.

[0017] Step S2: To accurately map the crushed stone gradation characteristics in the subsequent grid aperture design, it is necessary to first systematically statistically analyze the shape parameters of different particle size ranges and select the most representative crushed stone particles accordingly. This specifically includes the following steps: Step S21: Group the measured values ​​of sphericity and roundness within each particle size range according to particle size, and statistically analyze the distribution range and percentage of sphericity and roundness in each particle size group; use these statistical data to fit the normal distribution curve formula of sphericity and roundness, and provide a mathematical model for subsequent probability description and interval division.

[0018] Step S22: After completing the fitting, plot the frequency distribution histogram of shape parameters and the corresponding normal distribution curve for each particle size range; by comparing the graphs, clarify the main distribution range of sphericity and roundness and their proportion in the total sample, thereby defining the high probability interval for representative particles.

[0019] Step S23: Based on the high probability distribution area and proportion of shape parameters in each particle size range, extract the crushed stone particles located in that range proportionally as representative samples of that particle size range; these samples will be directly used for geometric mapping and interlocking verification in subsequent pore optimization.

[0020] Step S3: The binarized images of the selected representative crushed stone particles are directly converted into vector graphics files that can be used for subsequent discrete element modeling. These vector graphics files accurately preserve the geometric details of the particle outlines, providing a geometric basis for generating crushed stone particle templates in the next step.

[0021] Step S4: Using discrete element method (DEM) software, generate a crushed stone particle distribution model from the vector image file based on the crushed stone gradation. Select samples proportionally for each particle size range to statistically analyze representative particles within that range, and randomly generate a crushed stone particle model within a specified area. This specifically includes the following steps: Step S41: Organize the crushed stone gradation data, that is, the mass or volume percentage of each particle in each particle size range.

[0022] Step S42: In the discrete element method software, import the vector image files of representative crushed stone materials in each particle size range as real particle morphology templates; each real particle morphology template is geometrically identical to the representative particles in the corresponding particle size range.

[0023] Step S43: According to the predetermined gradation ratio, real particle shape templates of various particle sizes are randomly placed in the set area, and gravity is applied to make them fall naturally and compact them to form a dense accumulation. In order to meet the requirements of the grid rib spacing, the compacted particles are reduced proportionally to ensure that the net distance between particles meets the grid hole spacing required by the design. Finally, a two-dimensional template of a customized geogrid with a specific hole type for this specific crushed stone gradation is obtained.

[0024] Step S5: Export the generated two-dimensional template, stretch it along the normal vector of its boundary contour and assign a preset grid thickness value to construct a three-dimensional customized geogrid hole design model that perfectly matches the specific crushed stone gradation.

[0025] To illustrate the effectiveness of the method provided in this embodiment of the invention, the requirements for special grade ballast in the railway industry standard TB / T 2140-2008 "Railway Crushed Ballast" are taken as an example. Five particle size ranges of 22.4mm, 31.5mm, 40mm, 50mm, and 63mm are selected, with a corresponding quantity ratio of 3:22:40:34:1.

[0026] Prepare three representative ballast vector diagrams for each particle size range in advance, and set the template usage ratio within each particle size range according to the statistical results of shape parameters: 22.4 mm: 0.25:0.4:0.35; 31.5 mm: 0.25∶0.5∶0.25; 40 mm: 0.35: 0.4: 0.25; 50 mm: 0.2: 0.4: 0.4; 63 mm: 0.3: 0.4: 0.3.

[0027] In the discrete element method software, a rectangular area with a length of 1m and a height of 4m is established. Ballast particles are randomly placed according to the overall gradation ratio and the template ratio within each interval, forming a shape as shown above. Figure 2 The initial ballast particle distribution aggregate is shown. Then, all particles are given their own weight and allowed to fall naturally; when the particles accumulate to a height of about 1 m, a cover plate is formed at a height of 1 m and vertical pressure is applied to further compact the ballast, ensuring that the accumulation density matches the actual site conditions.

[0028] After compaction, all particles are scaled down proportionally to achieve a net spacing of 3–6 mm between them, thus obtaining the desired result. Figure 3 The geometric template for premium ballast under two-dimensional conditions is shown.

[0029] By using the normal vector of the boundary contour of the two-dimensional template as the stretching direction and assigning a preset grid thickness value, a grid like this can be constructed. Figure 4 The model shown is a three-dimensional customized grid aperture design model that perfectly matches the gradation of premium ballast.

[0030] Figure 5 This is a partial enlarged view of the three-dimensional grid template generated in an embodiment of the present invention. The design features of multi-curvature adaptive aperture and variable thickness ribs can be clearly observed from the view, demonstrating that the adaptive configuration has good structural integrity and manufacturing feasibility at the microscale.

[0031] This invention proposes a customized geogrid design method that deeply integrates real particle morphology and on-site gradation data. Its core lies in constructing a particle geogrid interlocking system highly adapted to the particle gradation of crushed stone using irregular, multi-scale coupled pore geometry. Compared with traditional fixed-pore geogrids, it has the following advantages: (1) Geometric adaptation and locking performance By directly using the two-dimensional image information of crushed stone particles as the aperture boundary, the geometric fit between the grid and the particles is significantly improved, effectively enhancing the interlocking ability and shear resistance, thereby improving the long-term stability of the structure.

[0032] (2) Gradation coordination and reinforcement efficiency By incorporating the aggregate gradation data from the construction site during the aperture design phase, the aperture size and distribution density are precisely adjusted according to proportion and location, achieving a high degree of synergy between the grid structure and the particle size combination. This significantly improves the constraint efficiency for particles of different sizes, and the overall reinforcement effect is superior to standardized products.

[0033] (3) Delaying degradation and extending lifespan Irregular aperture shapes excel in limiting ballast slippage, breakage, and rearrangement. They can effectively alleviate stress concentration within the crushed stone layer under localized loads, suppress uneven deformation and displacement accumulation between particles, thereby delaying structural deterioration, improving the overall mechanical stability and deformation coordination of the layer, and helping to extend the service life of crushed stone layers for roads, site foundations, etc.

[0034] (4) Resource conservation Compared to existing standard grilles, customized designs avoid material waste caused by dimensional redundancy, improving resource utilization while ensuring reinforcement performance.

[0035] In summary, the adaptive geometric configuration driven by particle size distribution and shape features in this embodiment of the invention provides reliable technical support for improving the stability, deformation resistance and service life of crushed stone structural layers, and effectively overcomes the limitations of traditional grids in terms of geometric matching and constraint performance.

[0036] The technical features of the above embodiments can be combined arbitrarily. For the sake of brevity, not all possible combinations of the technical features in the above embodiments are described; only preferred embodiments of the present invention are illustrated. The descriptions are relatively specific and detailed, but they should not be construed as limiting the scope of the present invention. As long as the combination of these technical features does not contradict each other, it should be considered within the scope of this specification.

[0037] It should be noted that those skilled in the art can make various modifications and improvements without departing from the inventive concept, and these all fall within the scope of protection of this invention. Therefore, the scope of protection of this invention should be determined by the appended claims.

Claims

1. A grid geometry design method based on particle size distribution and shape characteristics, characterized in that, Includes the following steps: Step S1: Set the particle size range of crushed stone according to the requirements of crushed stone paving, obtain the shape parameters of crushed stone particle samples, statistically analyze the shape parameters in different particle size ranges, and select representative particles for each particle size range based on the distribution range of the shape parameters. Step S2: Convert the binary image of the representative particles into a real particle morphology template, and randomly place the real particle morphology template within the rectangular area according to the gradation data required for crushed stone paving. Step S3: Compact all real particle shape templates within the rectangular area, proportionally reduce the particle size of all real particle shape templates according to the grid size, generate a two-dimensional grid template, assign grid thickness values ​​along the normal vector of the boundary contour of the two-dimensional template, and obtain a three-dimensional grid template.

2. The grid geometry design method based on particle size distribution and shape characteristics according to claim 1, characterized in that: Step S1, which involves selecting representative particles for each particle size range, includes the following steps: Step S11: Perform a three-dimensional scan on the crushed stone particle sample to obtain the surface mesh model of the crushed stone particle sample; Step S12: Obtain the vertex and face information of each mesh in the surface mesh model, and project the crushed stone particle sample into two dimensions based on the vertex and face information to generate a two-dimensional projection point set; Step S13: Map the projection points in the two-dimensional projection point set to a binary image, and invert the binary image; Step S14: Calculate the shape parameters of the crushed stone particle sample based on the inverted binary image; Step S15: Statistically analyze the particle distribution range and percentage of the shape parameters of the crushed stone particles, fit the normal distribution curve of the shape parameters of the crushed stone in different particle size ranges, and select representative crushed stone particles in each particle size range according to the distribution.

3. The grid geometry design method based on particle size distribution and shape characteristics according to claim 2, characterized in that: The shape parameter mentioned in step S14 includes sphericity, and the expression for calculating the sphericity is: ； In the formula, The sphericity of the crushed stone particles; , These are the length and width of the crushed stone particle sample, respectively.

4. The grid geometry design method based on particle size distribution and shape characteristics according to claim 2, characterized in that: The shape parameter mentioned in step S14 includes roundness, and the expression for calculating the roundness is: ； In the formula, The roundness of the crushed stone particle sample; This represents the number of all corner points in the crushed stone particle sample. For the first The radius of curvature at each corner point; The radius of the largest inscribed circle in the crushed stone particle sample.

5. The grid geometry design method based on particle size distribution and shape characteristics according to claim 1, characterized in that: The compaction of all real particle morphology templates within the rectangular area in step S3 includes the following steps: assigning weight to all real particle morphology templates within the rectangular area, causing all real particle morphology templates to fall and accumulate, and generating a cover plate above the rectangular area to compact all real particle morphology templates.

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