A method for establishing a three-dimensional microstructure model of semi-flexible pavement material by combining triangular meshing and random placement algorithm

Abstract

The application provides a three-dimensional microstructure model establishment method of semi-flexible pavement material combining a triangular network and a random throwing algorithm, and comprises the following steps: step one, generating three-dimensional spheres with different radii which do not interfere with each other in a specified area according to the aggregate gradation of the semi-flexible pavement material; step two, extracting the spherical center coordinates of all the sphere particles to perform triangular network construction; step three, performing segmentation on the obtained triangular network according to the sphere radius ratio, and performing triangular network construction again on the segmentation points and all the sphere centers; step four, extracting the aggregate geometric information in the grid; step five, generating asphalt mortar with random thickness around the aggregate to obtain an asphalt mixture matrix; step six, randomly throwing cement slurry in the voids of the asphalt mixture matrix; step seven, dividing a structured grid in the model area, and mapping the geometric information of the aggregate, asphalt and cement into the grid; and step eight, establishing a finite element model based on the obtained grid to perform mechanical analysis.

Description

Technical Field

[0001] This invention belongs to the field of numerical simulation technology for semi-flexible pavement materials, specifically a method for establishing a three-dimensional microstructure model of semi-flexible pavement materials by combining triangulation and random distribution algorithms. Background Technology

[0002] Semi-flexible pavement materials are multiphase composite materials composed of a large-void asphalt mixture matrix and cement-based grouting material. They combine the advantages of asphalt pavement materials and cement pavement materials, exhibiting excellent rutting resistance and durability. However, semi-flexible pavement materials have a complex composition and are prone to cracking failure under dynamic loading conditions. The failure process and cracking mechanism are not yet fully understood. Traditional research methods treat semi-flexible pavement materials as isotropic homogeneous bodies, but their complex material composition determines their heterogeneity and anisotropy. Therefore, macroscopic studies are insufficient to reflect the true mechanical properties of semi-flexible pavement materials.

[0003] With the development of computer technology, the microstructure of semi-flexible pavement materials can be directly obtained through computer programs, and the geometric information of the aggregate structure can be controlled by custom mathematical and geometric algorithms, making it one of the most promising research methods.

[0004] Random generation technology uses computer programs to generate geometric models with desired gradation, porosity, angularity, and other characteristics in a specified area. It mainly includes random drop methods and their derivative algorithms (random drop falling method, random drop dilation method, etc.), Delaunry triangulation algorithm, Voronoi diagram method, etc.

[0005] The principle of random placement is to generate particles of the required size and shape within a specified area based on geometric positional interference judgments (separate, intersecting, and overlapping). This means that each particle placement requires interference judgment with all previously placed particles. The more complex the particle shape and the higher the placement rate (the ratio of the volume of placed particles to the volume of the placement area), the more computational resources are required. Therefore, traditional random placement methods generally struggle to generate aggregate models with placement rates exceeding 35%. However, in actual engineering, coarse aggregate volume can reach 40% to 50% of the total concrete volume, and the combined volume of all coarse and fine aggregates can reach 60% to 70% of the total volume. Traditional random placement techniques are insufficient to represent the true aggregate structure.

[0006] Finite element method (FEM) computational analysis mainly includes three parts: mesh generation, computation and solution, and result processing. Mesh generation often takes the most time, and its quality plays a decisive role in the effectiveness and accuracy of the model's computational results. Real aggregate shapes are extremely complex. Using simple spheres or ellipsoids to simulate aggregates can improve convergence and accelerate computational efficiency, but it's difficult to simulate their true shape. Using polyhedra to simulate aggregates can relatively realistically reflect the material's microstructure, and their shape can be controlled by adjusting the number of vertices. Simple polyhedral shapes are easy to converge and computationally efficient, but reduce the realism of their shape. Complex polyhedral shapes are more realistic but difficult to converge and computationally slow. This creates a contradiction between the realism of polyhedral representation of aggregates and convergence. Randomly generated polyhedra can produce distorted elements during mesh generation, leading to low computational efficiency and difficulty in convergence during finite element program operations. Summary of the Invention

[0007] To address the aforementioned technical problems and in order to realistically and efficiently simulate the microstructure of semi-flexible pavement materials, this invention proposes a method for establishing a three-dimensional microstructure model of semi-flexible pavement materials that combines triangulation and random distribution algorithms. The model established by this method has the advantages of high computational efficiency and good convergence.

[0008] To achieve the above-mentioned technical objectives, the present invention employs the following technical means:

[0009] A method for establishing a three-dimensional microstructure model of semi-flexible pavement materials by combining triangulation and random distribution algorithms includes the following steps:

[0010] Step S1: Randomly place spherical particles within the three-dimensional spatial region Z where aggregate particles are to be generated, including the following steps:

[0011] Step S1.1: Randomly place spherical particles with a diameter of 9.5 to 16 mm in the first batch within the three-dimensional spatial region Z;

[0012] Step S1.2: Randomly place spherical particles with a diameter of 4.75 to 9.5 mm in the second grade within the three-dimensional spatial region Z;

[0013] Step S1.3: Randomly place spherical particles with a diameter of 2.36 to 4.75 mm in the third grade within the three-dimensional spatial region Z;

[0014] Step S1.4: Fill the gaps in the three-dimensional spatial region Z with spherical particles with a diameter of 2mm;

[0015] Step S2: Construct a triangular network using the centers of all the placed spherical particles;

[0016] Step S3: Construct a triangular network using the centers of all the placed spherical particles and the dividing points of the lines connecting the spherical particles;

[0017] Step S4: Extract the vertex information of each aggregate piece;

[0018] Step S5: Generate asphalt mortar of random thickness around the aggregate to obtain the asphalt mixture matrix;

[0019] Step S6: Randomly add cement grout into the voids of the asphalt mixture matrix;

[0020] Step S7: Perform structured mesh generation on the three-dimensional spatial region Z;

[0021] Step S8: Map the aggregate geometry information into the structured mesh;

[0022] Step S9: Establish a finite element model based on the mesh model obtained by mapping and perform mechanical simulation.

[0023] Step S1.1 includes the following sub-steps:

[0024] Step S1.1.1: Generate the radius of spherical particle i: Use a random generation function to randomly generate the radius R within the range of 4.75 to 8 mm. i ;

[0025] Step S1.1.2, Sphere Particle Deployment: Randomly select a point Oi within the three-dimensional spatial region Z as the center of the sphere to be deployed, i.

[0026] Step S1.1.3, Spherical Particle Interference Judgment: If there are no already deployed spherical particles in the three-dimensional space region Z, then deploy spherical particle i directly; if there are already deployed spherical particles in the three-dimensional space region Z, then iterate through all deployed spherical particles. For deployed spherical particle j and the spherical particle i to be deployed, if the distance between the centers of the two spheres Dis(ij) is greater than the sum of the radii R of the two spheres... i +R j If the conditions for feeding are met, aggregate i is fed; otherwise, repeat step S1.1.2 to feed spherical particles i again.

[0027] Step S1.1.4, Judgment of conditions for completion of spherical particle delivery: The total volume of the first batch of spherical particles delivered is V. 1sum The first batch of spherical particles is designed to have a displacement volume of V1. If V sum If the value is ≥V1, then the first batch of spherical particles has been dispensed; otherwise, repeat steps S1.1.1 to S1.1.3.

[0028] Steps S1.2 and S1.3 are the same as steps S1.1.

[0029] Step S1.4 includes the following sub-steps:

[0030] Step S1.4.1: Take points in the x, y, and z directions of the three-dimensional space region Z at intervals of 6mm and establish a point set P to store the three-dimensional coordinates of the selected points;

[0031] Step S1.4.2: Traverse point p in point set P. For point p, traverse all deployed spherical particles. For point p and spherical particle j, if the distance dis(pj) between the center of point p and spherical particle j is greater than the radius Rj of spherical particle j, the deployment condition is met. A spherical filling particle with a radius of 2mm is generated with point p as the center. Otherwise, no filling particle is generated.

[0032] Step S2 includes the following sub-steps:

[0033] Step S2.1: Extract the centers of all deployed spherical particles to establish a discrete point set D1;

[0034] Step S2.2: Perform triangulation on the discrete point set D1 to divide the three-dimensional spatial region Z into a set of non-overlapping, continuous tetrahedrals T1.

[0035] Step S3 includes the following sub-steps:

[0036] Step S3.1: Based on the triangular network constructed in step S2, each edge in the triangular network is divided, and the position of the dividing point is determined according to the ratio of the radii of the two spheres it connects.

[0037] Step S3.2: Extract the center of all the deployed spherical particles and the segmentation points obtained in step S3.1 to establish a discrete point set D2;

[0038] Step S3.3: Perform triangulation on the discrete point set D2 to divide the three-dimensional spatial region Z into a set of non-overlapping, continuous tetrahedrals T2.

[0039] Step S4 includes the following sub-steps:

[0040] Step S4.1: Calculate the centroid positions of all tetrahedra in tetrahedron set T2;

[0041] Step S4.2: Extract tetrahedrons belonging to aggregate: Traverse all tetrahedrons in tetrahedron set T2. For the centroid Ci of tetrahedron i, traverse all the placed spherical particles. If the distance Dis(ij) between the centroid Ci of tetrahedron i and the centroid Oj of spherical particle j is less than the radius of spherical particle j, then tetrahedron i belongs to aggregate j. Extract the triangular faces corresponding to the vertices of tetrahedron i that have the same coordinates as the center of the spherical particle and include them in the face set Fj of aggregate j.

[0042] Step S5 includes the following sub-steps:

[0043] Step S5.1, Aggregate Geometric Information Calculation: Calculate the centroid coordinates based on the vertex information of each aggregate, and then calculate the distance d between each vertex and the centroid. i ;

[0044] Step S5.2, Asphalt Mortar Generation: Traverse each aggregate. For a given aggregate, multiply the distance between each vertex and the centroid of the aggregate by a coefficient k greater than 1 to obtain the vertices of the asphalt mortar polyhedron.

[0045] Step S5.3: Combine all asphalt mortar polyhedra and remove the aggregate portion to obtain asphalt mortar. Then combine the asphalt mortar with the aggregate to obtain the asphalt mixture matrix.

[0046] Step S6 includes the following sub-steps:

[0047] Step S6.1: Randomly generate the centroid coordinates of the cement grout polyhedron: Randomly generate point P within the three-dimensional space region Z of the model. If point P is within the asphalt mortar polyhedron, then regenerate point P; otherwise, calculate the minimum distance dmin between point P and all asphalt mortar polyhedra, and set a distance d0 as the judgment value for whether the gap size meets the placement conditions. If dmin is greater than the set value d0, then point P meets the placement conditions; otherwise, regenerate point P.

[0048] Step S6.2: Generate cement slurry polyhedron: Using each point where cement slurry is to be generated as the center of the sphere, randomly generate n radii Rj and angles Aj, and generate n vertices based on the centroid, radius and angle to form a cement slurry polyhedron.

[0049] Step S7 includes the following sub-steps:

[0050] Step S7.1, Segmentation Point Layout: Layout equally spaced segmentation points with a spacing of s0 on all boundaries of the three-dimensional space region Z of the model;

[0051] Step S7.2, Model Space Segmentation: Connect the corresponding segmentation points on different boundaries to obtain segmentation lines, connect the corresponding segmentation lines to obtain segmentation surfaces, and divide the three-dimensional space region Z into regular hexahedral elements of equal size and regular structure to establish the element set L;

[0052] Step S7.3, Model Nodes, Element Numbers, includes the following sub-steps:

[0053] Step S7.3.1, Node Numbering: Number the nodes in the model space sequentially according to the ascending order of their x, y, z coordinate values, starting from 1.

[0054] Step S7.3.2, Element Numbering: The elements in the model space are numbered sequentially from 1 in ascending order of the x, y, and z coordinate values of the element centroids.

[0055] Step S7.3.3, Element-Node Matching: Record the node numbers included in each element.

[0056] Step S7.3.4, Element Centroid Coordinate Calculation: Calculate the centroid coordinates of each element in the structured grid sequentially.

[0057] The aforementioned Step S8 includes the following sub-steps:

[0058] Step S8.1, Aggregate Inscribed Sphere Mapping: Traverse the element set L. For element i, traverse all aggregates. For element i and aggregate j, when the distance Dis(ij) between the centroid of element i and the center of the inscribed sphere of aggregate j is less than the radius of the inscribed sphere of aggregate j, this element is an aggregate element. Remove the element number from the element set L and add it to the aggregate element set S.

[0059] Step S8.2, Aggregate Circumscribed Sphere Mapping: Traverse the element set L. For element i, traverse all aggregates. For element i and aggregate j, when the distance Dis(ij) between the centroid of element i and the center of the circumscribed sphere of aggregate j is greater than the radius of the circumscribed sphere of aggregate j, this element belongs to the binder unit. Remove the element number from the element set L and add it to the binder unit set A.

[0060] Step S8.3, Aggregate Boundary Mapping, includes the following steps:

[0061] Step S8.3.1, Aggregate Volume Calculation: Traverse all aggregates and calculate the volume Vi of aggregate i sequentially.

[0062] Step S8.3.2, Element-Aggregate Boundary Judgment: Traverse the element set L. For element i, traverse all aggregates. Calculate the volume Vk of the tetrahedron formed by the centroid of element i and the faces of aggregate j respectively, and sum the volumes Vk to obtain the volume Vi2 of the combined body of element i and aggregate j. If Vi < Vi2, this element belongs to the aggregate unit. Remove the element number from the element set L and add it to the set S.

[0063] Beneficial Effects:

[0064] The method for establishing a three-dimensional mesoscopic structure model of semi-flexible pavement materials in the present invention, which combines the triangular mesh generation and random placement algorithms, has the following main advantages compared with the existing random placement method:

[0065] First, the present invention can conveniently and quickly control the aggregate gradation and void ratio of the generated mesoscopic structure model of semi-flexible pavement materials by adjusting the parameters in the program, with high generation efficiency and stable effects.

[0066] Secondly, the aggregate volume ratio generated by this invention, that is, the proportion of aggregate to the total volume of concrete, can reach 60-70%, which is close to the aggregate volume ratio in actual production. It can accurately simulate the real mixture and can be used to guide the design and performance optimization of semi-flexible pavement materials in actual production.

[0067] Third, the present invention uses a mesh mapping algorithm to establish a mesh model of the microstructure of semi-flexible pavement material. The finite element model established based on this mesh model has good mesh quality, high computational efficiency, and good convergence. Attached Figure Description

[0068] Figure 1 This is a flowchart of the method of the present invention;

[0069] Figure 2 A schematic diagram of the generated random sphere particle structure;

[0070] Figure 3 A schematic diagram of a triangular network constructed using the centers of all the deployed spherical particles;

[0071] Figure 4 A schematic diagram for generating split points in a triangular mesh;

[0072] Figure 5 To construct a triangular network using the centers of all the deployed spherical particles and the dividing points of the lines connecting the spherical particles;

[0073] Figure 6a This is a perspective view of the three-dimensional geometric structure of the aggregate.

[0074] Figure 6b This is a front view of the three-dimensional geometric structure of the aggregate;

[0075] Figure 7a A perspective view of the three-dimensional geometric structure of the aggregate after boundary cutting;

[0076] Figure 7b A front view of the three-dimensional geometric structure of the aggregate after boundary cutting;

[0077] Figure 8 A schematic diagram of the structured mesh used to divide the model region;

[0078] Figure 9a This is a perspective view of the three-dimensional geometric model of the aggregate.

[0079] Figure 9b An oblique view of the three-dimensional mesh model of the aggregate;

[0080] Figure 10 This is a two-dimensional schematic diagram of randomly applied cement slurry.

[0081] Figure 11The element is obtained by mapping cement paste into a structured mesh;

[0082] Figure 12a A slant view of a three-dimensional finite element model of a three-point bending tension beam;

[0083] Figure 12b This is a front view of the three-dimensional finite element model of a three-point bending tension beam;

[0084] Figure 13 A comparison of load-displacement curves from three-point bending tension beam tests and simulations;

[0085] Figure 14 This is a model diagram of a three-point bending tension beam after loading.

[0086] Figure 15 The image shows the horizontal stress contour of the three-point bending tension beam model after loading. Detailed Implementation

[0087] The present invention will now be described in further detail with reference to the accompanying drawings and embodiments.

[0088] A method for establishing a three-dimensional microstructure model of semi-flexible pavement materials by combining triangular mesh construction and random drop algorithm is proposed. The first objective is to solve the problem of generating the three-dimensional geometric structure of aggregates.

[0089] The technical solution to achieve the first objective of this invention is as follows: Python programming statements inherently possess a rich and powerful database, enabling comprehensive data processing capabilities. Furthermore, Python offers advantages such as portability, scalability, interpretability, object-oriented programming, and flexible memory management. Its embeddability is sensitive, convenient, and fast, allowing direct integration into Abaqus simulation software to build models. Therefore, it is possible to write custom Python language algorithms to define aggregate particle size, shape, and gradation parameters, generating the three-dimensional geometric structure of the aggregate.

[0090] Python statements can be used to define the geometric parameters of aggregates. The volume ratio of three aggregate grades is defined programmatically as 0.74:0.26:0, with the designed loading volume of the first grade of spherical particles being 27720 mm². 3 The design volume for the second-stage spherical particles is 10080 mm². 3 The design volume for the third tier of spherical particles was 0, resulting in the generation of 18 first-tier spherical particles, 48 ​​second-tier spherical particles, 0 third-tier spherical particles, and 200 filler spherical particles. This invention utilizes Python to generate spherical particles of different diameters, such as... Figure 2 As shown.

[0091] Import the third-party library scipy in Python. Figure 2 The triangulation of the point set formed by the center of the sphere yields a triangular mesh, as shown below. Figure 3 As shown.

[0092] right Figure 3 The edges of the triangular mesh are divided, and the method for determining the dividing points is as follows: Figure 4 As shown, there are two relationships in spherical particles: disjoint and tangent. Spheres P1 and P2 are disjoint, with radii R1 and R2 respectively. Determine a point A such that:

[0093]

[0094] If spheres P1 and P3 are tangent, then a point B, the point of tangency between the two circles, is determined such that:

[0095]

[0096] After inserting split points into all edges of the triangular mesh, the newly generated split points and the centers of the previous circular particles are used as a discrete point set to perform triangulation again, resulting in a triangular mesh as shown below. Figure 5 As shown.

[0097] The oblique and front views of the aggregate geometry extracted by this invention are as follows: Figure 6a and Figure 6b As shown, a spatial region of 60mm*35mm*30mm is used as the model area. The aggregate portion outside the model area is removed, and the resulting aggregate structure outside the removed boundary is as follows. Figure 7a and Figure 7b As shown.

[0098] The second objective of this invention is to map the micro-geometry of semi-flexible pavement materials onto a regular hexahedral mesh.

[0099] The technical solution to achieve the second objective of this invention is: firstly, asphalt mortar is generated on the basis of the already generated aggregate geometry, and then cement slurry is added;

[0100] Calculate the centroid coordinates based on the vertex information of each aggregate, then calculate the distance between each vertex and the centroid. Iterate through all aggregates. For a given aggregate, multiply the distances between each vertex and the centroid by a coefficient greater than 1 to obtain the vertices of the asphalt mortar polyhedron. Merge all asphalt mortar polyhedra and remove the aggregate portions to obtain the asphalt mortar. Finally, combine the asphalt mortar with the aggregate to obtain the asphalt mixture matrix. Figure 10 As shown;

[0101] A point is randomly generated within the voids of the mixture within the model space region. Cement paste is then generated with this point as its centroid. Figure 10 As shown, the dashed line represents the cement slurry that has been added.

[0102] Then the model region is divided into regular hexahedral elements with a side length of 1mm, such as Figure 8As shown.

[0103] After dividing the model region into elements, the geometry of aggregates, asphalt, and cement is mapped onto the divided mesh, such as... Figure 9a , 9b These are the aggregate geometry and the structure mapped onto the mesh, respectively.

[0104] The third objective of this invention is to establish a finite element model based on the mapped mesh to simulate a three-point bending tension beam test.

[0105] The technical solution to achieve the third objective of this invention is: to establish a finite element model of a three-point bending tension beam test based on the mesh obtained by mapping, such as... Figure 10 As shown, the 60mm area in the middle of the model represents the microstructure of the concrete, while the gray homogeneous areas on both sides represent the macrostructure homogeneous bodies of the concrete. The white semi-circular components represent the upper indenter and the lower support, which are established using rigid bodies. Rigid body constraints are established between these components and the reference point and the elements near the beam model. The lower left support restricts translation in the X, Y, and Z directions and rotation in the X and Y directions, allowing it to rotate around the Z direction (depth direction) during the beam's bending and tensile deformation. The lower right support restricts translation in the Y and Z directions and rotation in the X and Y directions, forming a simply supported system with the left support, and allowing it to rotate around the Z direction (depth direction) during the beam's bending and tensile deformation. The top indenter applies a displacement load. Since the loading time in the explicit analysis of the finite element simulation differs from the concept of natural time in the real world, it is only necessary to maintain the loading process as a quasi-static process during the simulation (inertial force is not dominant in the actual beam bending and tensile test) and control the kinetic energy to a certain low proportion to effectively simulate the real loading process. In the model, the solid elements are all 8-node linear reduced integral solid elements (C3D8R), and the cohesive elements are all 8-node 3D cohesive elements (COH3D8).

[0106] The load-displacement curves of the model and the load-displacement curves of the experiment are as follows: Figure 11 As shown, the simulated curve matches the experimental curve.

[0107] Figures 12a-12b and Figure 13 The figures shown are the deformation diagram and the horizontal stress cloud diagram of the beam under compression. It can be seen that the model established by this invention can effectively simulate the mechanical properties of materials.

Claims

1. A method for establishing a three-dimensional microstructure model of semi-flexible pavement materials by combining triangulation and random distribution algorithms, characterized in that, Includes the following steps: Step S1: Randomly place spherical particles within the three-dimensional spatial region Z where aggregate particles are to be generated, including the following steps: Step S1.1: Randomly place spherical particles with a diameter of 9.5 to 16 mm in the first batch within the three-dimensional spatial region Z; Step S1.2: Randomly place spherical particles with a diameter of 4.75 to 9.5 mm in the second grade within the three-dimensional spatial region Z; Step S1.3: Randomly place spherical particles with a diameter of 2.36 to 4.75 mm in the third grade within the three-dimensional spatial region Z; Step S1.4: Fill the gaps in the three-dimensional spatial region Z with spherical particles with a diameter of 2mm; Step S2: Construct a triangular network using the centers of all the placed spherical particles; Step S3: Construct a triangular network using the centers of all the placed spherical particles and the dividing points of the lines connecting the spherical particles; Step S4: Extract the vertex information of each aggregate piece; Step S5: Generate asphalt mortar of random thickness around the aggregate to obtain the asphalt mixture matrix; Step S6: Randomly add cement grout into the voids of the asphalt mixture matrix; Step S7: Perform structured mesh generation on the three-dimensional spatial region Z; Step S8: Map the aggregate geometry information into the structured mesh; Step S9: Establish a finite element model based on the mesh model obtained by mapping and perform mechanical simulation.

2. The method for establishing a three-dimensional microstructure model of semi-flexible pavement materials combining triangular mesh construction and random placement algorithm as described in claim 1, characterized in that, Step S1.1 includes the following sub-steps: Step S1.1.1: Generate the radius of spherical particle i: Use a random generation function to randomly generate the radius R within the range of 4.75 to 8 mm. i ; Step S1.1.2, Sphere Particle Deployment: Randomly select a point Oi within the three-dimensional spatial region Z as the center of the sphere to be deployed, i. Step S1.1.3, Spherical Particle Interference Judgment: If there are no already deployed spherical particles in the three-dimensional space region Z, then deploy spherical particle i directly; if there are already deployed spherical particles in the three-dimensional space region Z, then iterate through all deployed spherical particles. For deployed spherical particle j and the spherical particle i to be deployed, if the distance between the centers of the two spheres Dis(ij) is greater than the sum of the radii R of the two spheres... i +R j If the conditions for feeding are met, aggregate i is fed; otherwise, repeat step S1.1.2 to feed spherical particles i again. Step S1.1.4, Judgment of conditions for completion of spherical particle delivery: The total volume of the first batch of spherical particles delivered is V. 1sum The first batch of spherical particles is designed to have a displacement volume of V1. If V sum If the value is ≥V1, then the first batch of spherical particles has been dispensed; otherwise, repeat steps S1.1.1 to S1.1.

3. Steps S1.2 and S1.3 are the same as steps S1.

1.

3. The method for establishing a three-dimensional microstructure model of semi-flexible pavement materials combining triangular mesh construction and random placement algorithm as described in claim 1, characterized in that, Step S1.4 includes the following sub-steps: Step S1.4.1: Take points in the x, y, and z directions of the three-dimensional space region Z at intervals of 6mm and establish a point set P to store the three-dimensional coordinates of the selected points; Step S1.4.2: Traverse point p in point set P. For point p, traverse all deployed spherical particles. For point p and spherical particle j, if the distance dis(pj) between the center of point p and spherical particle j is greater than the radius Rj of spherical particle j, the deployment condition is met. A spherical filling particle with a radius of 2mm is generated with point p as the center. Otherwise, no filling particle is generated.

4. The method for establishing a three-dimensional microstructure model of semi-flexible pavement materials combining triangular mesh construction and random placement algorithm as described in claim 1, characterized in that, Step S2 includes the following sub-steps: Step S2.1: Extract the centers of all deployed spherical particles to establish a discrete point set D1; Step S2.2: Perform triangulation on the discrete point set D1 to divide the three-dimensional spatial region Z into a set of non-overlapping, continuous tetrahedrals T1.

5. The method for establishing a three-dimensional microstructure model of semi-flexible pavement materials combining triangular mesh construction and random placement algorithm according to claim 1, characterized in that, Step S3 includes the following sub-steps: Step S3.1: Based on the triangular network constructed in step S2, each edge in the triangular network is divided, and the position of the dividing point is determined according to the ratio of the radii of the two spheres it connects. Step S3.2: Extract the center of all the deployed spherical particles and the segmentation points obtained in step S3.1 to establish a discrete point set D2; Step S3.3: Perform triangulation on the discrete point set D2 to divide the three-dimensional spatial region Z into a set of non-overlapping, continuous tetrahedrals T2.

6. The method for establishing a three-dimensional microstructure model of semi-flexible pavement materials combining triangular mesh construction and random placement algorithm according to claim 1, characterized in that, Step S4 includes the following sub-steps: Step S4.1: Calculate the centroid positions of all tetrahedra in tetrahedron set T2; Step S4.2: Extract tetrahedrons belonging to aggregate: Traverse all tetrahedrons in tetrahedron set T2. For the centroid Ci of tetrahedron i, traverse all the placed spherical particles. If the distance Dis(ij) between the centroid Ci of tetrahedron i and the centroid Oj of spherical particle j is less than the radius of spherical particle j, then tetrahedron i belongs to aggregate j. Extract the triangular faces corresponding to the vertices of tetrahedron i that have the same coordinates as the center of the spherical particle and include them in the face set Fj of aggregate j.

7. The method for establishing a three-dimensional microstructure model of semi-flexible pavement materials combining triangular mesh construction and random placement algorithm according to claim 1, characterized in that, Step S5 includes the following sub-steps: Step S5.1, Aggregate Geometric Information Calculation: Calculate the centroid coordinates based on the vertex information of each aggregate, and then calculate the distance d between each vertex and the centroid. i ; Step S5.2, Asphalt Mortar Generation: Traverse each aggregate. For a given aggregate, multiply the distance between each vertex and the centroid of the aggregate by a coefficient k greater than 1 to obtain the vertices of the asphalt mortar polyhedron. Step S5.3: Combine all asphalt mortar polyhedra and remove the aggregate portion to obtain asphalt mortar. Then combine the asphalt mortar with the aggregate to obtain the asphalt mixture matrix.

8. The method for establishing a three-dimensional microstructure model of semi-flexible pavement materials combining triangular mesh construction and random placement algorithm according to claim 3, characterized in that, Step S6 includes the following sub-steps: Step S6.1: Randomly generate the centroid coordinates of the cement grout polyhedron: Randomly generate point P within the three-dimensional space region Z of the model. If point P is within the asphalt mortar polyhedron, then regenerate point P. Otherwise, calculate the minimum distance dmin between point P and all asphalt mortar polyhedra, and set a distance d0 as the judgment value for whether the gap size meets the placement conditions. If dmin is greater than the set value d0, then point P meets the placement conditions; otherwise, regenerate point P. Step S6.2: Generate cement slurry polyhedron: Using each point where cement slurry is to be generated as the center of the sphere, randomly generate n radii Rj and angles Aj, and generate n vertices based on the centroid, radius and angle to form a cement slurry polyhedron.

9. The method for establishing a three-dimensional microstructure model of semi-flexible pavement materials combining triangular mesh construction and random placement algorithm according to claim 3, characterized in that, Step S7 includes the following sub-steps: Step S7.1, Segmentation Point Layout: Layout equally spaced segmentation points with a spacing of s0 on all boundaries of the three-dimensional space region Z of the model; Step S7.2, Model Space Segmentation: Connect the corresponding segmentation points on different boundaries to obtain segmentation lines, connect the corresponding segmentation lines to obtain segmentation surfaces, and divide the three-dimensional space region Z into regular hexahedral elements of equal size and regular structure to establish the element set L; Step S7.3, Model Nodes, Element Numbers, includes the following sub-steps: Step S7.3.1, Node Numbering: Number the nodes in the model space sequentially according to the ascending order of their x, y, z coordinate values, starting from 1. Step S7.3.2, Element Numbering: Number the elements in the model space sequentially according to the x, y, z coordinate values ​​of the element centroid in ascending order, starting from 1; Step S7.3.3, Element and Node Matching: Record the node numbers contained in each element; Step S7.3.4, Calculation of centroid coordinates of each element: Calculate the centroid coordinates of each element in the structured mesh in sequence.

10. The method for establishing a three-dimensional microstructure model of semi-flexible pavement materials combining triangular mesh construction and random placement algorithm according to claim 9, characterized in that, Step S8 includes the following sub-steps: Step S8.1, Mapping of the inscribed spheres of the aggregates: Traverse the unit set L. For unit i, traverse all the aggregates. For unit i and aggregate j, when the distance Dis(ij) between the centroid of unit i and the center of the inscribed sphere of aggregate j is less than the radius of the inscribed sphere of aggregate j, this unit is an aggregate unit. Remove the unit number from the unit set L and add it to the aggregate unit set S. Step S8.2, Mapping of the circumscribed spheres of the aggregates: Traverse the unit set L. For unit i, traverse all the aggregates. For unit i and aggregate j, when the distance Dis(ij) between the centroid of unit i and the center of the circumscribed sphere of aggregate j is greater than the radius of the circumscribed sphere of aggregate j, this unit belongs to the binder unit. Remove the unit number from the unit set L and add it to the binder unit set A. Step S8.3, Aggregate boundary mapping, including the following steps: Step S8.3.1, Calculation of the volume of the aggregates: Traverse all the aggregates and calculate the volume Vi of aggregate i in sequence. Step S8.3.2, Judgment of the boundary between the unit and the aggregate: Traverse the unit set L. For unit i, traverse all the aggregates. Calculate the volume Vk of the tetrahedron formed by the centroid of unit i and the faces of aggregate j respectively. Sum the volumes Vk to obtain the volume Vi2 of the combined body of unit i and aggregate j. If Vi < Vi2, this unit belongs to the aggregate unit. Remove the unit number from the unit set L and add it to the set S.

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