A method for generating random particles of coarse aggregate in asphalt concrete based on gradation curves

Abstract

This invention discloses a method for generating random particles of coarse aggregate in asphalt concrete based on a gradation curve. According to the particle size range composition of the gradation curve, random particle polyhedra and a particle backup option library are formed based on geometric transformation. Asphalt mixture particles are quickly added to the particle backup option library to a specified shape based on the gradation curve, thus forming a placement criterion that satisfies the gradation of the asphalt mixture.

Description

Technical Field

[0001] This invention belongs to the field of road engineering asphalt mixture simulation and processing, specifically involving a method for generating random particles of coarse aggregate in asphalt concrete based on gradation curves. Background Technology

[0002] Asphalt mixtures have a complex internal structure, being a multiphase composite material composed of coarse aggregates, fine aggregates, asphalt, and voids. Their micromechanical behavior is a hot topic in road engineering research, with numerical simulation analysis being the primary method employed. A primary challenge in simulation analysis is establishing a numerical model that accurately reflects the internal characteristics of the granular material and its internal features. Currently, the main methods for modeling asphalt mixtures include:

[0003] Traditional numerical models of asphalt mixtures typically involve scanning the surface of the mixture or the cross-section of a cut specimen with a digital camera, then using digital image processing technology to reconstruct the granular material numerical model of the mixture specimen. While this method can produce a digital model with a high degree of similarity to the real specimen, it has the following drawbacks: high experimental requirements, high cost, and inability to meet simulation requirements under certain conditions.

[0004] Direct modeling method: This method simulates asphalt mixtures as homogeneous bodies, which cannot reflect the micromechanical behavior of asphalt mixtures.

[0005] Random particle generation method; this method has achieved considerable results, but it has the following drawbacks: in the aggregate generation algorithm, there may be problems such as parallel or overlapping cutting surfaces; the particle polyhedrons differ to some extent from the actual ones.

[0006] Existing technology: A method for randomly generating numerical models of asphalt mixtures, which reflects the random generation of three-dimensional discrete element numerical models of asphalt mixtures with irregular shapes of coarse aggregates and mineral aggregate gradation, fully reflects the angular characteristics of aggregates while avoiding the problem of parallel or overlapping cutting surfaces.

[0007] The disadvantages of existing technologies are: particle selection is not based on the particle size range of the gradation curve; particle overlap determination is not performed; and particle selection takes a long time.

[0008] This invention generates random particle polyhedra and a particle backup option library based on particle size and geometric transformation; it rapidly adds asphalt mixture particles from the particle backup option library based on gradation curves; and it forms a gradation criterion for asphalt mixtures. Summary of the Invention

[0009] In order to solve the technical problems existing in the background art, the present invention aims to provide a method for generating random particles of coarse aggregate in asphalt concrete based on gradation curve.

[0010] To solve the technical problem, the technical solution of the present invention is as follows:

[0011] A method for generating random particles of coarse aggregate in asphalt concrete based on gradation curves, the method comprising:

[0012] S1: Random particle generation;

[0013] S2: Based on the generated particles, establish a particle backup option library;

[0014] S3: Establish particle delivery rules and deliver particles from the particle backup option library.

[0015] Furthermore, step S1 specifically includes:

[0016] S11: Based on the particle size characteristics, determine the radius of the circumcircle of the triangle formed by the particles, randomly generate the three angles of the triangle, and use the relationship between the triangle and the radius of the circumcircle to calculate the coordinates of points A, B, and C of the plane triangle.

[0017] S12: According to geometric principles, add two points D and E arbitrarily to the outside of the plane triangle to form a convex geometric body;

[0018] S13: Perform a base point transformation on the convex geometry to obtain the convex polygonal geometry after the base point transformation.

[0019] S14: Randomly transform the processed convex polygonal geometry to obtain preliminary single particles;

[0020] S15: Correct the needle-like and flaky particles in the initial single particles to obtain corrected single particles;

[0021] S16: After correction by needle-like particles, particle generation ends, and the coordinates and shape data of the particles are stored.

[0022] Furthermore, step S14 specifically includes:

[0023] After the convex geometry undergoes a base point transformation on the xy plane, the convex geometry is then transformed on the zy or zx plane to obtain the convex polygonal geometry after the base point transformation.

[0024] Further, step S14 specifically includes: selecting a point outside the processed convex geometry for expansion; for a certain face of the geometry, randomly selecting a point outside the face for expansion to generate a tetrahedron; and determining whether to continue expansion based on whether the area of ​​each face of the tetrahedron is greater than a predetermined area. If A... i ≥A max Then this surface will be used as the base surface for expansion until all surfaces satisfy A.i <A max If A is not found, then the expansion stops; where A is not found. max It is a predefined maximum area, related to the particle size, and the maximum number of faces that the particle can expand to is specified as 14. Once all faces satisfying the conditions have expanded, if there exists A... i ≥A max Discard and regenerate new base particles, repeat the process until initial single particles are generated.

[0025] Furthermore, the needle-like and flaky particles in the initial individual particles are corrected, specifically including:

[0026] For any initially expanded single particle, let the radius of the circumcircle of the plane triangle that generates it be R, and the center point be O. Let the vertices that make up the particle be P1, P2...P n ;

[0027] Calculate the distance d between any point on the particle and point O. i If d i If the value is greater than kR, then the vertex of the particle is corrected, where k is a coefficient. When k is between 1.8 and 2.2, the resulting particle shape is more consistent with the actual situation.

[0028] If point P does not satisfy d≤kR, the particle needs to be corrected;

[0029] The specific operation method is as follows: In the initial single particle, a part of the polyhedron with P as the vertex is cut off. The points connected to point P are A, B, C, D, and E. The three points with the shortest line segment to point P are calculated and set as A, B, and C in this case. The midpoints of line segments PA, PB, and PC are taken as A1, B1, and C1. Three points A2, B2, and C2 are randomly selected between line segments PA1, PB1, and PC1. The polyhedron is cut off with plane A2B2C2 to obtain new vertices P1, P2, P3, P4, and P5. At the same time, the triangle planes PBA, PAC, PCD, PDE, and PEB are corrected to P1BAP2, P2ACP3, P3CDP4, P4DEP5, and P5EBP1, which can correct the needle-like particles.

[0030] Furthermore, a granular alternative option library is established, specifically including:

[0031] After determining the particle size distribution curve and the percentage of particle volume in the total volume, calculate the percentage of the total volume of the sum of particle sizes in each range.

[0032] Based on the particle size range, particles of a specified size are randomly generated. The particle volume is calculated, and the cumulative volume of randomly generated particles is recorded. When the cumulative volume of particles within this range exceeds a specified percentage of the total volume, particle generation within that range is stopped. The same process is then repeated for the next particle size range, ultimately generating a particle backup option library for a given particle size distribution curve.

[0033] Furthermore, the particles in the particle backup option library are deployed, specifically including:

[0034] Step 1: Sort the particles in the generated particle backup option library from largest to smallest in size, and release the particles with the largest size first; let the total initial release count be M = 0, the number of single particle releases be DN; the maximum number of releases for a single particle is MAX1, and the maximum total number of releases is MAX2.

[0035] Step 2: Let the number of particles added this time be S. i The radius is R i DN = 0;

[0036] Step 3: Randomly generate delivery point P i Determine whether the particle goes outside the boundary after being placed. If the placement point does not meet the requirements, select another placement point until the requirements are met.

[0037] Step 4: Let any one of the particles that has been placed be S. j L is P i With P j The distance; record the distance R i +R j For particles whose values ​​are greater than kL, store the recorded particle numbers in matrix KS. Since the particle size of polyhedra differs from that of spheres, the coefficient k is taken to be less than 1. This is to ensure that the values ​​in matrix S are consistent with the possible values. i All intersecting particles were selected, and after multiple experiments, k was chosen to be 0.5;

[0038] Step 5: Determine S i Does it conflict with the particles in KS?

[0039] The planar entity that encloses the aggregate is written in the form of an inequality. Any two adjacent aggregates are combined to obtain an inequality. If the inequality is empty, the two aggregates do not conflict; otherwise, the two aggregates have an intersection.

[0040] Conflict: Then DN = DN + 1. If N > MAX1, go to step 8; otherwise, go to step 3.

[0041] No conflict: This campaign was successful, campaign point P. i That is, S i The center point;

[0042] Step 6: Record the already deployed particles in sequence in matrix S, record the particle center point in matrix P, and record the particle radius in matrix R;

[0043] Step 7: M = M + DN. If M >= MAX2, end the delivery and return.

[0044] Step 8: Proceed to the next particle delivery.

[0045] Compared with the prior art, the advantages of the present invention are as follows:

[0046] 1. Rapidly forming polyhedral random particles based on gradation curves;

[0047] 2. Quickly add asphalt mixture particles from the option library in descending order of size;

[0048] 3. Based on the corresponding feeding criteria, quickly generate an effective coarse aggregate gradation curve for random particles. Attached Figure Description

[0049] Figure 1 Overall flowchart of the invention;

[0050] Figure 2 A diagram illustrating the correction process in step 1 of this invention;

[0051] Figure 3 Flowchart of step 2 of the present invention for retrieving the spare particle option inventory;

[0052] Figure 4 The diagram shows the effect of the method for generating random particles of coarse aggregate in asphalt concrete based on gradation curves according to the present invention. Detailed Implementation

[0053] The specific implementation of the present invention is described below with reference to embodiments:

[0054] It should be noted that the structures, proportions, sizes, etc. shown in this specification are only used to complement the content disclosed in the specification for those skilled in the art to understand and read, and are not intended to limit the conditions under which the present invention can be implemented. Any modifications to the structure, changes in the proportions, or adjustments to the size, without affecting the effects and objectives that the present invention can produce, should still fall within the scope of the technical content disclosed in the present invention.

[0055] Furthermore, the terms such as "upper," "lower," "left," "right," "middle," and "one" used in this specification are merely for clarity of description and are not intended to limit the scope of the invention. Any changes or adjustments to their relative relationships, without substantially altering the technical content, should also be considered within the scope of the invention.

[0056] Example 1

[0057] A method for generating random particle sizes of coarse aggregate in asphalt concrete based on gradation curves, such as... Figure 1 As shown, it includes the following steps:

[0058] 1. Random particle generation;

[0059] 2. Establish a spare option library for granules;

[0060] 3. Particle placement and rules.

[0061] Step 1) To ensure that the simulated particle shape matches the actual shape, based on geometric meaning and the particle size requirements, a convex geometric body is formed using the simplest triangle rotation transformation. On this basic unit, the edge lines are extended to form particles that conform to the particle size characteristics of asphalt mixtures.

[0062] a) Determining a simple triangle

[0063] Based on the characteristics of the particles, we can first determine the radius of the circumcircle of the triangle, and then randomly generate the three angles of the triangle to determine their values. To control the range of the three angles of the triangle, we can use the semi-equivalence relationship between the triangle and its circumcircle to calculate the coordinates of points A, B, and C of the planar triangle.

[0064] b) Transformation of convex geometry

[0065] According to geometric principles, adding any two points D and E to the outside of the triangular plane will create a convex geometric shape. Based on experience, the resulting particles must meet the requirements of being concave or convex.

[0066] c) Formation of actual particles

[0067] To conform to the actual particle shape in engineering, a base point transformation is performed on the convex geometry. This is planned to be implemented in two steps: first, the base point transformation of the convex geometry is performed on the xy plane; second, the base point transformation of the convex geometry is performed on the zy or zx plane.

[0068] d) Expansion of convex geometric particles

[0069] To ensure the diversity of the resulting mixture particles, the particles are randomly transformed. This is generally achieved by expanding the particles. A point is selected outside the surface for expansion. To conform to the particle size distribution of the mixture, the distance of the selected point from the plane of the convex geometry should be limited. For a certain face of the geometry, a point is randomly selected outside the face to expand and generate a tetrahedron. Whether to continue expansion depends on whether the area of ​​each face of the tetrahedron is greater than the limited area. If A... i ≥A max Then this surface will be used as the base surface for expansion until all surfaces satisfy A. i <A max If A , then the expansion stops.max This is a pre-defined maximum area, related to the particle size. It also specifies a maximum number of faces that the particle can expand to: 14. After all faces meeting the conditions have expanded, if there are still A's within them... i ≥A max If the selected parameters for the base particles are incorrect, they should be discarded and new base particles should be generated. This process should be repeated until a single particle that meets the requirements is generated.

[0070] e) Correction of needle-like particles

[0071] While needle-like and flaky particles constitute a small proportion of actual production, their use in Boolean operations with asphalt models reduces mesh generation efficiency, increases the number of meshes, and further degrades computational efficiency. Therefore, further modifications are needed for needle-like and flaky particles.

[0072] For any expanded particle, let R be the radius of the circumcircle of the plane triangle that generates it, and O be the center point. Let P1, P2...P1 be the vertices that make up the particle. n .

[0073] Calculate the distance d between any point on the particle and point O. i If d i If the value is greater than kR, then the vertex of the particle is corrected. Here, k is a coefficient. Through trial and error analysis, the particle shape obtained when k is between 1.8 and 2.2 is more consistent with the actual situation. In this study, k = 2.0 is chosen.

[0074] like Figure 2 As shown, assuming point P does not satisfy d≤kR, the particles need to be corrected. The specific operation involves truncating a portion of the polyhedron with P as its vertex. Points connected to P are A, B, C, D, and E. The three points with the shortest line segments connecting to P are calculated and denoted as A, B, and C. The midpoints of line segments PA, PB, and PC are selected as A1, B1, and C1. Three points A2, B2, and C2 are randomly chosen between line segments PA1, PB1, and PC1. The polyhedron is truncated using plane A2B2C2. This yields new vertices P1, P2, P3, P4, and P5. Simultaneously, the triangle planes PBA, PAC, PCDPDE, and PEB are corrected to P1BAP2, P2ACP3, P3CDP4, P4DEP5, and P5EBP1. This corrects the needle-like particles, facilitating mesh generation after modeling.

[0075] f) Storing individual particle data

[0076] After the particles are corrected by needle-like particles, particle generation is complete. The coordinates and shape data of the particles then need to be stored. In finite element methods, each point, surface, and volume has corresponding coordinates. For asphalt concrete specimens with numerous particles, it is necessary to establish corresponding data for each particle separately. Therefore, for each particle, it is necessary to store not only the coordinates of its vertices, but also the numbers of the points forming each surface and the numbers of the surfaces forming each volume.

[0077] Step 2) To generate a good library of particle alternatives that takes into account actual gradation, the following tasks must be completed:

[0078] (1) The particle size range in the particle backup option library is sufficient to provide the particle size range within the gradation curve range;

[0079] (2) The particle backup option library should have an efficient access method. During the deployment process, it should be able to quickly and accurately locate the particle size distribution curve and the percentage of particle volume in the total volume, and then calculate the percentage of the total volume of each particle size range. Then, particles of a specified size can be randomly generated based on the particle size range, and the volume of each particle can be calculated and superimposed. When the percentage of the total volume of particles in this range exceeds the specified percentage, the generation of particles in that range is stopped, and the generation of particles in the next range begins. See the box for the specific process. Figure 3 As shown (using AC13 as an example).

[0080] Step 3) Dispensing the pellets includes the following steps:

[0081] g) Particle placement order. Particle placement is the most critical step in the generation of random particle specimens. This not only involves the utilization rate of the generated particle backup option library, but also affects the efficiency of specimen generation.

[0082] During the particle delivery process, the space for the test specimen becomes smaller due to the random delivery. Therefore, the particles are generally delivered from largest to smallest in order to better ensure the utilization rate of the generated particle backup option library.

[0083] h) Conflict Rules. During the deployment process, particles cannot directly conflict with each other (in spatial polyhedra, this means they intersect). Determining whether particles intersect during deployment is crucial for successful deployment because of the large number of particles and the need for frequent checks to determine conflict. In essence, the deployment process is a process of determining particle conflict. Therefore, selecting an effective conflict rule becomes a key element in the efficiency of the entire deployment process. This is based on Ren Shijun's "A Fast Algorithm for Determining Whether a Convex Space Enclosed by Linear Inequalities is Empty".

[0084] i) Deployment Process. As the deployable space decreases, finding the deployment point for each particle becomes increasingly difficult, requiring more loops in the program. During particle deployment, it's necessary to determine if a particle has exceeded the boundary and if it conflicts with the positions of already deployed particles. If a conflict exists, deployment must be restarted. This paper selects the following steps for deployment:

[0085] (1) The particles in the generated particle backup option library are sorted from largest to smallest in particle size, and the particles with larger particle size are placed first when the particles are placed; let the total number of initial placements be M=0, the number of single particle placements be DN; the maximum number of single particle placements is MAX1, and the maximum number of total placements is MAX2.

[0086] (2) Let the number of particles released this time be S. i The radius is R i DN = 0;

[0087] (3) Randomly generate delivery point P i Determine whether the particle goes outside the boundary after being placed. If the placement point does not meet the requirements, select another placement point until the requirements are met.

[0088] (4) Let any one of the particles that has been placed be S. j L is P i With P j The distance. Record the distance R. i +R j Particle numbers greater than kL are used to establish (since the particle size of polyhedra differs from that of spheres, the coefficient k is taken as less than 1, to ensure S i All possible and intersecting particles were selected. After multiple experiments, 0.5 was chosen, and the recorded particle numbers were stored in matrix KS.

[0089] (5) Determine S i Does it conflict with the particles in KS?

[0090] The planar solid that encloses the aggregate is written in the form of an inequality. Any two adjacent aggregates are combined to obtain an inequality. If the inequality is empty, the two aggregates do not conflict; otherwise, the two aggregates have an intersection.

[0091] Conflict: Then DN = DN + 1. If N > MAX1, go to 8); otherwise, go to 3.

[0092] No conflict: This campaign was successful, campaign point P. i That is, S i The center point;

[0093] 6) Record the already deployed particles in sequence in matrix S, record the particle center point in matrix P, and record the particle radius in matrix R;

[0094] 7) M = M + DN. If M >= MAX2, end the delivery and return.

[0095] 8) Proceed to the next particle delivery.

[0096] The results obtained are as follows Figure 4 As shown.

[0097] The preferred embodiments of the present invention have been described in detail above. However, the present invention is not limited to the above embodiments. Within the scope of knowledge possessed by those skilled in the art, various changes can be made without departing from the spirit of the present invention.

[0098] Many other changes and modifications can be made without departing from the concept and scope of this invention. It should be understood that this invention is not limited to the specific embodiments, and the scope of this invention is defined by the appended claims.

Claims

1. A method for generating random particles of coarse aggregate of asphalt concrete based on a grading curve, characterized by, The method comprises: S1: random particle generation; S2: based on the generated particles, a particle standby option library is established; S3: particle delivery rules are established, and particles in the particle standby option library are delivered; The step S1 specifically comprises: S11: according to the particle size characteristics of the particle, the circumradius of the triangle of the particle is determined, three angles of the triangle are randomly generated, and the coordinates of each point A, B and C of the planar triangle are calculated by using the relationship between the triangle and the circumradius; S12: according to the geometric principle, two points D and E are randomly added outside the planar triangle to form a convex geometric body; S13: base point transformation processing is performed on the convex geometric body to obtain a convex polygonal geometric body after base point transformation processing; S14: the processed convex polygonal geometric body is randomly transformed to obtain a preliminary single particle; S15: the needle-shaped particle in the preliminary single particle is corrected to obtain a corrected single particle; S16: after the needle-shaped particle correction, the particle generation is completed, and the coordinates and shape data of the particle are stored; The particle standby option library is established, and the option library contains all coarse aggregates meeting the number of grading curves, and specifically comprises: After the delivery of the given particle grading curve and the percentage of the particle volume in the total volume is determined, the total volume percentage of each range of particle size is calculated; Particles of a specified range of particle size are randomly generated according to the particle size range, the particle volume is calculated, and the total volume percentage of the cumulative particle volume in the range is accumulated. When the cumulative total volume percentage of the particles in the range exceeds the specified percentage, the generation of the particles in the range is stopped, and the generation of the particles in the next range is performed in the same way. Finally, the particle standby option library of the given particle grading curve is generated.

2. The method for generating random particles of coarse aggregate of asphalt concrete based on grading curve according to claim 1, characterized in that, The step S14 specifically comprises: After the base point transformation of the convex geometric body on the xy plane, the base point transformation of the convex geometric body on the zy or zx plane is performed to obtain the convex polygonal geometric body after base point transformation processing.

3. The method for generating random particles of coarse aggregate of asphalt concrete based on grading curve according to claim 1, characterized in that, The step S14 specifically comprises: selecting a point outside the convex polyhedral geometry after processing for expansion, for a certain face of the geometry, a point is randomly selected outside the face for expansion to generate a tetrahedron, and it is determined whether to continue expansion according to whether the area of each face of the tetrahedron is greater than a limited area , if yes, the face will be expanded as a base face until all faces satisfy , then the expansion is stopped; wherein is a set maximum area, which is related to the size of the particle diameter, and the maximum number of faces of the particle expansion is set to 14, and when all the faces satisfying the condition are expanded, if , a new base particle is discarded and regenerated, and the cycle is processed until a preliminary single particle is generated.

4. The method for generating random coarse aggregate particles of asphalt concrete based on grading curve according to claim 1, characterized in that, The needle-shaped particle in the preliminary single particle is corrected, specifically comprising: Any of the expanded primary single particles, let the radius of the circumscribed circle of the plane triangle formed by the particle be R, the center point of the circle be O, and each vertex of the particle be denoted as ; Calculate the distance of any point of the particle to point O If Then correct the vertex of the particle, where k is a coefficient, when k takes 1.8-2.2, the particle shape is more in line with the actual situation; If point P does not satisfy , the particle needs to be corrected; The specific operation mode is: in the preliminary single particle, a part of the polyhedron with P as the top point is cut off, and the points connected with P are A, B, C, D and E. The three points with the shortest line segment connected with P are calculated, which are A, B and C. The midpoints of the line segments PA, PB and PC are A1, B1 and C1. Three points A2, B2 and C2 are randomly taken between the line segments PA1, PB1 and PC1. The polyhedron is cut off by the plane A2B2C2 to obtain new top points P1, P2, P3, P4, P5. At the same time, the triangles PBA, PAC, PCD, PDE and PEB are corrected to P1BAP2, P2ACP3, P3CDP4, P4DEP5 and P5EBP1, so that the needle-shaped particle is corrected.

5. The method for generating random coarse aggregate particles of asphalt concrete based on grading curve according to claim 1, characterized in that, The particles in the particle standby option library are delivered, specifically comprising: Step 1: Sort the particles in the generated particle library by size from large to small, and the particles with large size are put first when the particles are put; Set the total initial number of times as M = 0, the single particle put number as DN; The maximum number of single particle put is MAX1, and the total maximum number of put is MAX2; Step 2: Suppose the number of particles put in this time is , the radius is , and DN=0. Step 3: Randomly generate a drop point determines whether the particle drops out of the boundary, and if the drop point does not meet the requirements, the drop point is selected again until the requirements are met. Step 4: Let any one of the pre-placed particles be... L is and Distance; Recording Order The established particle numbers are stored in matrix KS. Since the particle size of polyhedra differs from that of spheres, the coefficient k is set to a value less than 1 to ensure compatibility with... All intersecting particles were selected, and after multiple experiments, k was chosen to be 0.5; Step 5: Determine Whether the particle collides with the KS: The planar entity enclosing the aggregate is written in the form of inequality, and any two adjacent aggregates are combined to obtain an inequality. If the inequality is empty, the two aggregates are not in conflict, otherwise the two aggregates have intersection; Conflict: DN = DN + 1, if N > MAX1, go to step 8, otherwise jump to step 3; No conflict: This time the success of the launch, launch point That is The center point; Step 6: Record the particles that have been put in order in matrix S, record the particle center point in matrix P, and record the particle radius in matrix R; Step 7: M = M + DN, if M >= MAX2, end the put, return; Step 8: Enter the put of the next particle.

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