A method for modeling three-dimensional microstructure of asphalt mixture

Abstract

The application discloses a kind of asphalt mixture three-dimensional microstructure modeling methods, it is related to pavement material technical field, the three-dimensional aggregate model of this method uses random polyhedron to represent real aggregate particle, introduces rigid body dynamics impulse theory to simulate the process of coarse aggregate particle rearrangement in actual asphalt mixture compaction process, the accumulation structure of coarse aggregate particle formed by this method has stable skeleton support characteristics, overcome the problem ignored by traditional random coarse aggregate generation method, based on asphalt mortar film equal thickness assumption, on the basis of the accumulation structure of coarse aggregate particle, the modeling of asphalt mortar component in asphalt mixture is established, while realizing the modeling of void component in asphalt mixture, finally realizes the three-dimensional modeling of three components of asphalt mixture, this method has important significance in the space distribution of asphalt mixture each component, aggregate particle movement law in compaction process and microscale numerical simulation.

Description

Technical Field

[0001] This invention relates to the field of road material technology, and in particular to a method for three-dimensional microstructure modeling of asphalt mixtures. Background Technology

[0002] Asphalt mixtures are the most commonly used paving materials for highways or urban roads. After long-term use and under traffic loads, asphalt pavements will develop various defects such as high-temperature rutting and low-temperature cracking. The mechanical properties and durability of asphalt mixtures are important factors affecting whether pavement defects occur. Although the macroscopic mechanical properties of asphalt mixtures can be measured through laboratory tests, their internal microscopic physical state cannot be directly obtained through laboratory tests.

[0003] Finite element numerical simulation technology is an important technical means to study the behavior mechanism of materials. At present, representative large-scale commercial finite element software such as ABAQUS, ANSYS and COMSOL Multiphysics have been widely used in numerical simulation calculations of asphalt mixtures at the microscale. As a type of asphalt-based composite material reinforced with coarse aggregate particles, asphalt mixtures need to first establish a relatively reliable three-dimensional microstructure model before numerical simulation.

[0004] Chinese patent CN102768699B discloses a method for accurately reconstructing a microscopic finite element mesh model of heterogeneous materials based on CT images. This method has the following drawbacks: its application in finite element modeling of asphalt mixtures requires obtaining asphalt mixture specimens through indoor molding or on-site core sampling; therefore, it cannot model the three-dimensional microstructure of asphalt mixtures that have been designed but not yet formed. Furthermore, this method relies on CT scanning equipment, thus significantly limiting the size of the asphalt mixture specimens. The cost of CT scanning equipment and scanning a single asphalt mixture specimen is high. Additionally, a series of digital image processing techniques are required to segment the three components of the asphalt mixture in the scanned sample. These drawbacks result in a cumbersome process, high economic costs, and limitations on the size of the asphalt mixture model.

[0005] Chinese patent CN106874600B discloses a method for rapidly generating a two-dimensional random aggregate model of concrete mixed with pebbles and crushed stone. However, this modeling method has low computational efficiency or even fails to generate the final microstructure model when the volume ratio of coarse aggregate is high. This is because when the volume ratio of coarse aggregate is high, newly generated random coarse aggregate particles have a high probability of intersecting with already generated coarse aggregate particles. The newly generated coarse aggregate particles are considered to have failed to generate, and new random coarse aggregate particles are generated again. The newly generated coarse aggregate particles will then intersect with already generated coarse aggregate particles and be judged as failing again. This cycle repeats itself, easily forming an infinite loop, which leads to the failure of modeling the microstructure of the mixture. Therefore, when the volume fraction of coarse aggregate in the entire specimen space is high, this method is inefficient. At the same time, the randomly generated coarse aggregate particles cannot form a stable skeleton structure with each other, so there is still a difference from the actual mixture structure, which will cause errors in the numerical simulation results. Summary of the Invention

[0006] To address the above technical problems, this invention provides a method for modeling the three-dimensional microstructure of asphalt mixtures, comprising the following steps:

[0007] S1. Determine the shape and size of the asphalt mixture specimen to be modeled, establish the boundary of the asphalt mixture specimen, remove the top surface of the boundary of the asphalt mixture specimen, establish the pressure plate of the asphalt mixture specimen, and set the pressure plate directly above the asphalt mixture specimen.

[0008] S2. Determine the gradation curve, volume fraction of aggregates, and size of fine aggregates for asphalt mixture specimens, and calculate the target volume of each grade of coarse aggregate.

[0009] S3. Randomly generate coarse aggregate particles within the boundary of the asphalt mixture specimen. Once the total volume of each generated coarse aggregate particle equals its own target volume, no new coarse aggregate particles are generated. Store the global coordinates of the centroid of each generated coarse aggregate particle and the local coordinates of its vertices.

[0010] S4. Set the total time for modeling the asphalt mixture, and divide the total time into sub-time steps with equal step sizes, each step size being Δt. Set the pressure plate to move up and down periodically in the vertical direction, and set the minimum height of the pressure plate descent to be equal to the height of the asphalt mixture specimen. Treat all coarse aggregate particles, the boundaries of the asphalt mixture specimen, and the pressure plate as rigid bodies, and calculate the global coordinates of the centroid of the coarse aggregate particles and the local coordinates of the vertices of the coarse aggregate particles after each sub-time step based on the rigid body dynamics collision response in time sequence. Use the coarse aggregate particles after the last sub-time step as the coarse aggregate model of the asphalt mixture specimen.

[0011] S5. Set the void ratio. Using the coarse aggregate model of the asphalt mixture specimen as a reference, expand along the centroid of each coarse aggregate particle with equal thickness. Calculate the remaining volume fraction of the asphalt mixture specimen. Stop expansion when the remaining volume fraction of the asphalt mixture specimen is the same as the void ratio of the asphalt mixture specimen. The expanded area is the asphalt mortar, and the area with the final remaining space of the asphalt mixture specimen is the void.

[0012] The technical solution further defined in this invention is:

[0013] Furthermore, in step S2, the target volume of each grade of coarse aggregate is calculated using the following formula:

[0014]

[0015] Among them, V agg P represents the target volume of coarse aggregate. u P represents the pass rate of the coarse aggregate through the upper limit of the sieve opening. d V represents the passing rate of the coarse aggregate through the lower limit of the sieve opening, and C represents the volume of the specimen. agg This indicates the volume fraction of the aggregate.

[0016] The aforementioned method for modeling the three-dimensional microstructure of asphalt mixtures, in step S3, includes the following steps for the random generation of coarse aggregate particles.

[0017] S3.1 Generate a regular icosahedron. The distance from the vertex of the regular icosahedron to its centroid satisfies the following equation:

[0018]

[0019] In the formula, d 下 d represents the lower limit of the actual coarse aggregate particle sieve opening. 上 This indicates the upper limit of the actual coarse aggregate particle sieve opening, and d represents the distance from the vertex of the icosahedron to its centroid.

[0020] S3.2. Divide each side of the regular icosahedron into two equal parts. Connect the points on one face of the regular icosahedron with straight lines. Set the distance from the points generated by the bisection to the centroid of the regular icosahedron as d. Transform the regular icosahedron into a sphere with edges.

[0021] S3.3. Using each vertex of the prism as the center, randomly fluctuate the coordinates of each vertex to generate new vertices. The distance between the newly generated vertex and the original vertex does not exceed d / 2, forming a concave-convex surface.

[0022] S3.4 Delete all the original vertices, leaving the newly generated vertices, and calculate the convex body of the smallest convex hull formed by the newly generated vertices;

[0023] S3.5. Randomly stretch a convex body in any direction in space. The stretching ratio depends on the slenderness ratio of the coarse aggregate particles to form coarse aggregate particles.

[0024] In the aforementioned method for modeling the three-dimensional microstructure of asphalt mixtures, in step S3, the origin of the local coordinates of the generated coarse aggregate particle vertices is the centroid of the coarse aggregate particle.

[0025] In the aforementioned method for modeling the three-dimensional microstructure of asphalt mixtures, step S4 involves calculating the global coordinates of the centroid of coarse aggregate particles and the local coordinates of their vertices after each sub-time step based on rigid body dynamics collision response. The initial time of the k-th sub-time step is t. k-1 The end time is t. k The calculation of the global coordinates of the centroid of coarse aggregate particles and the local coordinates of their vertices at the k-th sub-time step includes the following steps:

[0026] S4.1 Calculate the change in translational velocity of coarse aggregate particles in the gravitational field;

[0027] △v a =g△t

[0028] Where g represents gravitational acceleration; Δv a This represents the change in the centroidal translational velocity of coarse aggregate particles in a gravitational field.

[0029] S4.2 Determine whether all coarse aggregate particles intersect or collide with the boundary or pressure plate of the asphalt mixture specimen. If they do not intersect, the changes in the translational velocity and angular velocity of the centroid of the coarse aggregate particles caused by the collision with the boundary or pressure plate of the asphalt mixture specimen are 0. If they intersect, the changes in the translational velocity and angular velocity of the centroid of the coarse aggregate particles are as follows:

[0030]

[0031] Where, △v b and △ω b These represent the changes in the translational velocity and angular velocity of the centroid of the coarse aggregate particles caused by their collision with the boundary or pressure plate of the asphalt mixture specimen; j n denoted by , m represents the normal impulse of the collision surface between the coarse aggregate particles and the boundary or pressure plate of the asphalt mixture specimen; denoted by , m represents the mass of the coarse aggregate particles; denoted by , I represents the moment of inertia of the coarse aggregate particles; denoted by , μ represents the coefficient of sliding friction between the coarse aggregate particles and the boundary or pressure plate of the asphalt mixture specimen; denoted by , r represents the offset of the centroid of the coarse aggregate particles from the point of collision; denoted by , n represents the normal of the boundary or pressure plate of the asphalt mixture specimen, which always points towards the coarse aggregate particles; denoted by , t represents the projection of the velocity of the coarse aggregate particles at the point of collision onto the collision surface, with the direction consistent with the direction of the velocity of the coarse aggregate particles at the point of collision.

[0032] S4.3 Determine whether all coarse aggregate particles collide with each other. If they do not collide, the changes in the translational velocity and angular velocity of the centroid of the coarse aggregate particles caused by the collisions are 0. If they collide, the changes in the translational velocity and angular velocity of the centroid of the coarse aggregate particles caused by the collisions are as follows:

[0033]

[0034] in, and This represents the change in translational velocity and angular velocity of the centroid of the i-th coarse aggregate particle in the two colliding coarse aggregate particles; j n This represents the normal impulse of the collision surface between two coarse aggregate particles; m i I represents the mass of the i-th coarse aggregate particle among the two colliding coarse aggregate particles; i The moment of inertia of the i-th coarse aggregate particle in the two colliding coarse aggregate particles is represented by r. i denoted by μ, which represents the offset of the centroid of the i-th coarse aggregate particle from the point of collision between the two colliding coarse aggregate particles; μ represents the sliding friction coefficient between the coarse aggregate particles; n represents the normal of the collision surface, which always points from the second coarse aggregate particle to the first coarse aggregate particle; t represents the projection of the velocity of the first coarse aggregate particle at the point of collision onto the collision surface, and its direction is consistent with the direction of the velocity of the first coarse aggregate particle at the point of collision.

[0035] S4.4 Calculate the velocity of coarse aggregate particles after the current sub-time step ends, as shown in the following formula.

[0036]

[0037] Where, v(t) k-1 ) and v(t) k ) represent the translation velocities at the initial and final moments of the current sub-time step, respectively; ω(t) k ) and ω(t k-1 ) represent the angular velocities at the initial and final moments of the current sub-time step, respectively;

[0038] S4.5. Calculate the coordinates of the centroid of the coarse aggregate particles after the current time step using Euler's formula, as shown in the following formula.

[0039] p(t k )=p(t k-1 )+v(t k )△t

[0040] Where p(t) k-1 ) and p(t k) represent the global coordinates of the centroid of the coarse aggregate particles at the initial and final times of the current sub-time step, respectively;

[0041] The coordinates of the coarse aggregate particles at the end of the current time step are calculated using the quaternion method, as shown in the following formula. p l (t k )= ω (t k ) p l (t k-1 ) ω (t k ) -1

[0042] in, p l (t k-1 )and p l (t k ) represent the quaternions of the local coordinates of the vertices of coarse aggregate particles at the initial and final times of the current sub-time step, respectively; ω (t k ) represents the angular velocity ω(t) of the coarse aggregate particles. k Quaternions;

[0043] S4.6 Start the calculation for the next time step, using the position and velocity information of the coarse aggregate particles at the end of the previous time step as the initial values ​​for the position and velocity of the coarse aggregate particles in the next time step.

[0044] In the aforementioned method for modeling the three-dimensional microstructure of asphalt mixtures, step S4.2, the solution for the normal impulse of the boundary or pressure plate collision surface between coarse aggregate particles and the asphalt mixture specimen is as follows:

[0045]

[0046] In the formula, e represents the coefficient of restitution, which represents the energy loss during the collision process between coarse aggregate particles and the boundary or pressure plate of the asphalt mixture specimen, and v p This indicates the translational velocity of coarse aggregate particles at the point of impact.

[0047] In the aforementioned method for modeling the three-dimensional microstructure of asphalt mixtures, step S4.3, the solution for the normal impulse of the collision surface of two coarse aggregate particles is as follows:

[0048]

[0049] Where e represents the coefficient of restitution, which represents the energy loss during the collision process between coarse aggregate particles, and v p1 and v p2These represent the translational velocities of the first and second coarse aggregate particles at the point of collision, respectively.

[0050] The beneficial effects of this invention are:

[0051] This invention simulates the rearrangement of coarse aggregate particles during the actual compaction of asphalt mixtures. The resulting coarse aggregate particle packing structure exhibits stable skeletal support characteristics, closely matching the actual packing structure of coarse aggregate particles in asphalt mixtures, thus overcoming the problems neglected by traditional random coarse aggregate generation methods. Based on the assumption of equal thickness of the asphalt mortar film, modeling of the asphalt mortar component in the asphalt mixture is achieved, along with modeling of the void component. Ultimately, a three-dimensional model of the three components of the asphalt mixture is realized. The three-dimensional model of the asphalt mixture established using this modeling method can be applied to numerical simulation calculations at the microscale of asphalt mixtures, providing a possibility for studying and predicting the mechanical and thermal properties of asphalt mixtures. Furthermore, this modeling method also provides an important technical means for optimizing pavement material design methods by utilizing the spatial distribution of each component of the asphalt mixture. Attached Figure Description

[0052] Figure 1 This is a flowchart illustrating the three-dimensional modeling of asphalt mixtures in an embodiment of the present invention;

[0053] Figure 2 This is a model diagram of the Marshall specimen boundary and pressure plate in an embodiment of the present invention;

[0054] Figure 3 This is a diagram illustrating the generation process of a single aggregate particle in an embodiment of the present invention.

[0055] Figure 4 This is a schematic diagram of randomly generated coarse aggregate particles in an embodiment of the present invention;

[0056] Figure 5 This is a schematic diagram showing the change in distance from the pressure plate to the top surface of the specimen within one cycle in an embodiment of the present invention;

[0057] Figure 6 This is a schematic diagram of the coarse aggregate particle distribution of the asphalt mixture at time 0s in an embodiment of the present invention.

[0058] Figure 7 This is a schematic diagram of the coarse aggregate particles of the asphalt mixture at 200s in an embodiment of the present invention;

[0059] Figure 8 This is a cross-sectional schematic diagram of the coarse aggregate particle thickness expansion process in an embodiment of the present invention;

[0060] Figure 9 This is a schematic diagram of the void space distribution of the final asphalt mixture in an embodiment of the present invention;

[0061] Figure 10 This is a schematic diagram showing the void distribution of the final asphalt mixture and the void distribution of the CT scan specimen in an embodiment of the present invention. Detailed Implementation

[0062] This embodiment provides a method for modeling the three-dimensional microstructure of asphalt mixtures, taking the three-dimensional modeling process of standard Marshall specimens of asphalt mixtures as an example. Figure 1 As shown, it includes the following steps

[0063] S1. Determine the shape and size of the asphalt mixture specimen for modeling. The standard Marshall specimen for asphalt mixture is cylindrical with a diameter of 101.6 mm and a height of 63.5 mm. Establish the boundary of the asphalt mixture Marshall specimen, remove the top surface of the boundary, and establish the pressure plate of the asphalt mixture Marshall specimen, as shown below. Figure 2 As shown, the pressure plate is placed directly above the asphalt mixture Marshall specimen, and the distance between the pressure plate and the top surface of the asphalt mixture Marshall specimen is 1 cm.

[0064] S2. Determine the gradation curve, volume fraction of aggregates, and size of fine aggregates for asphalt mixture specimens, and calculate the target volume of each grade of coarse aggregate.

[0065] The asphalt mixture gradation is AC-20, and the gradation pass rate is shown in Table 1. The coarse aggregate volume fraction is set at 60%, and aggregates smaller than 1.18mm are considered fine aggregate. The target volume of each coarse aggregate grade is calculated using the following formula, and the calculation results are shown in Table 2.

[0066]

[0067] Among them, V agg P represents the target volume of coarse aggregate. u P represents the pass rate of the coarse aggregate through the upper limit of the sieve opening. d V represents the passing rate of the coarse aggregate through the lower limit of the sieve opening, and C represents the volume of the specimen. agg This indicates the volume fraction of the aggregate.

[0068] Table 1. Passing Rate of AC-20 Asphalt Mixture Gradation

[0069] Sieve aperture size (mm) Pass rate (%) 26.6 100 19 95 16 85 13.2 71 9.5 61 4.75 41 2.36 28 1.18 24

[0070] Table 2 Target Volume of Coarse Aggregate Particles

[0071]

[0072]

[0073] S3. Randomly generate coarse aggregate particles within the boundary of the asphalt mixture specimen. Once the total volume of each generated coarse aggregate particle equals its target volume, no new coarse aggregate particles are generated. Store the global coordinates of the centroid of each generated coarse aggregate particle and the local coordinates of its vertices; the origin of the local coordinates of the vertices of the generated coarse aggregate particles is the centroid of the coarse aggregate particle. Figure 3 The diagram shown illustrates the formation process of a single aggregate particle. Figure 4 The image shown is a schematic diagram of randomly generated coarse aggregate particles.

[0074] The random generation of coarse aggregate particles includes the following steps:

[0075] S3.1 Generate a regular icosahedron. The distance from the vertex of the regular icosahedron to its centroid satisfies the following equation:

[0076]

[0077] In the formula, d 下 d represents the lower limit of the actual coarse aggregate particle sieve opening. 上 This indicates the upper limit of the actual coarse aggregate particle sieve opening, and d represents the distance from the vertex of the icosahedron to its centroid.

[0078] S3.2. Divide each side of the regular icosahedron into two equal parts. Connect the points on one face of the regular icosahedron with straight lines. Set the distance from the points generated by the bisection to the centroid of the regular icosahedron as d. Transform the regular icosahedron into a sphere with edges.

[0079] S3.3. Using each vertex of the prism as the center, randomly fluctuate the coordinates of each vertex to generate new vertices. The distance between the newly generated vertex and the original vertex does not exceed d / 2, forming a concave-convex surface.

[0080] S3.4 Delete all the original vertices, leaving the newly generated vertices, and calculate the convex body of the smallest convex hull formed by the newly generated vertices;

[0081] S3.5. Randomly stretch a convex body in any direction in space. The stretching ratio depends on the slenderness ratio of the coarse aggregate particles to form coarse aggregate particles.

[0082] S4. Set the total modeling time for the asphalt mixture to 200s, and divide the total time into 2000 sub-time steps of equal length, each sub-time step having a step size of 0.1s; set the pressure plate to move periodically up and down in the vertical direction, with a period of 1s, and set the minimum descent height of the pressure plate to be equal to the height of the asphalt mixture specimen. Figure 5 The figure shows a schematic diagram of the change in distance from the pressure plate to the top surface of the asphalt mixture specimen within one cycle.

[0083] All coarse aggregate particles, the boundaries of the asphalt mixture specimens, and the pressure plate are treated as rigid bodies. Based on rigid body dynamics collision response, the global coordinates of the centroids and the local coordinates of the vertices of the coarse aggregate particles are calculated sequentially at the end of each sub-time step. The coarse aggregate particles at the end of the last sub-time step are used as the coarse aggregate model of the asphalt mixture specimen. Figure 6 The diagram shown illustrates the coarse aggregate particle distribution of the asphalt mixture at time 0s; Figure 7 The figure shown is a schematic diagram of the coarse aggregate particles of the asphalt mixture at 200s, which is also the coarse aggregate model of the final asphalt mixture specimen.

[0084] Based on the rigid body dynamics collision response, the global coordinates of the centroid of the coarse aggregate particles and the local coordinates of the vertices are calculated sequentially after each sub-time step, where the initial time of the k-th sub-time step is t. k-1 The end time is t. k The calculation of the global coordinates of the centroid of coarse aggregate particles and the local coordinates of their vertices at the k-th sub-time step includes the following steps:

[0085] S4.1 Calculate the change in translational velocity of coarse aggregate particles in the gravitational field;

[0086] △v a =g△t

[0087] Where g represents gravitational acceleration; Δv a This represents the change in the centroidal translational velocity of coarse aggregate particles in a gravitational field.

[0088] S4.2 Determine whether all coarse aggregate particles intersect or collide with the boundary or pressure plate of the asphalt mixture specimen. If they do not intersect, the changes in the translational velocity and angular velocity of the centroid of the coarse aggregate particles caused by the collision with the boundary or pressure plate of the asphalt mixture specimen are 0. If they intersect, the changes in the translational velocity and angular velocity of the centroid of the coarse aggregate particles are as follows:

[0089]

[0090] Where, △v b and △ω b These represent the changes in the translational velocity and angular velocity of the centroid of the coarse aggregate particles caused by their collision with the boundary or pressure plate of the asphalt mixture specimen; j ndenoted by , m represents the normal impulse of the collision surface between the coarse aggregate particles and the boundary or pressure plate of the asphalt mixture specimen; denoted by , m represents the mass of the coarse aggregate particles; denoted by , I represents the moment of inertia of the coarse aggregate particles; denoted by , μ represents the coefficient of sliding friction between the coarse aggregate particles and the boundary or pressure plate of the asphalt mixture specimen; denoted by , r represents the offset of the centroid of the coarse aggregate particles from the point of collision; denoted by , n represents the normal of the boundary or pressure plate of the asphalt mixture specimen, which always points towards the coarse aggregate particles; denoted by , t represents the projection of the velocity of the coarse aggregate particles at the point of collision onto the collision surface, with the direction consistent with the direction of the velocity of the coarse aggregate particles at the point of collision.

[0091] S4.3 Determine whether all coarse aggregate particles collide with each other. If they do not collide, the changes in the translational velocity and angular velocity of the centroid of the coarse aggregate particles caused by the collisions are 0. If they collide, the changes in the translational velocity and angular velocity of the centroid of the coarse aggregate particles caused by the collisions are as follows:

[0092]

[0093] in, and This represents the change in translational velocity and angular velocity of the centroid of the i-th coarse aggregate particle in the two colliding coarse aggregate particles; j n This represents the normal impulse of the collision surface between two coarse aggregate particles; m i I represents the mass of the i-th coarse aggregate particle among the two colliding coarse aggregate particles; i The moment of inertia of the i-th coarse aggregate particle in the two colliding coarse aggregate particles is represented by r. i denoted by μ, which represents the offset of the centroid of the i-th coarse aggregate particle from the point of collision between the two colliding coarse aggregate particles; μ represents the sliding friction coefficient between the coarse aggregate particles; n represents the normal of the collision surface, which always points from the second coarse aggregate particle to the first coarse aggregate particle; t represents the projection of the velocity of the first coarse aggregate particle at the point of collision onto the collision surface, and its direction is consistent with the direction of the velocity of the first coarse aggregate particle at the point of collision.

[0094] S4.4 Calculate the velocity of coarse aggregate particles after the current sub-time step ends, as shown in the following formula.

[0095]

[0096] Where, v(t) k-1 ) and v(t) k ) represent the translation velocities at the initial and final moments of the current sub-time step, respectively; ω(t) k ) and ω(t k-1 ) represent the angular velocities at the initial and final moments of the current sub-time step, respectively;

[0097] S4.5. Calculate the coordinates of the centroid of the coarse aggregate particles after the current time step using Euler's formula, as shown in the following formula.

[0098] p(t k )=p(t k-1 )+v(t k )△t

[0099] Where p(t) k-1 ) and p(t k ) represent the global coordinates of the centroid of the coarse aggregate particles at the initial and final times of the current sub-time step, respectively;

[0100] The coordinates of the coarse aggregate particles at the end of the current time step are calculated using the quaternion method, as shown in the following formula. p l (t k )= ω (t k ) p l (t k-1 ) ω (t k ) -1

[0101] in, p l (t k-1 )and p l (t k ) represent the quaternions of the local coordinates of the vertices of coarse aggregate particles at the initial and final times of the current sub-time step, respectively; ω (t k ) represents the angular velocity ω(t) of the coarse aggregate particles. k Quaternions;

[0102] S4.6 Start the calculation for the next time step, using the position and velocity information of the coarse aggregate particles at the end of the previous time step as the initial values ​​for the position and velocity of the coarse aggregate particles in the next time step.

[0103] S5. Set the void ratio of the asphalt mixture to 4%. Using the coarse aggregate model of the asphalt mixture specimen as a reference, expand along the centroid of each coarse aggregate particle with equal thickness. Calculate the remaining volume fraction of the asphalt mixture specimen. Stop expansion when the remaining volume fraction of the asphalt mixture specimen is the same as the void ratio of the asphalt mixture specimen. The expanded area is the asphalt mortar, and the area with the final remaining space of the asphalt mixture specimen is the void.

[0104] like Figure 8The figure shows a cross-section of the coarse aggregate particle thickness expansion process. When the expansion thickness is 0.9 mm, the remaining volume fraction of the asphalt mixture is 4%, which is equal to the porosity. The expanded area is considered asphalt mortar, and the remaining space is voids. At this point, the three-dimensional microstructure of the asphalt mixture is modeled, as shown in the figure. Figure 9 As shown, this is the final established void model for the Marshall specimen of asphalt mixture. Figure 10 As shown, the void distribution along the specimen height is the same for the final asphalt mixture model and the actual CT scan of the asphalt mixture. It can be seen that the void distribution of the two is basically the same, indicating that the asphalt mixture modeled by this method is very reliable.

[0105] This method simulates the rearrangement of coarse aggregate particles during the actual compaction of asphalt mixtures. The resulting coarse aggregate particle packing structure exhibits stable skeletal support characteristics, closely matching the actual packing structure of coarse aggregate particles in asphalt mixtures, thus overcoming problems neglected by traditional random coarse aggregate generation methods. Based on the assumption of equal thickness of the asphalt mortar film, this method models the asphalt mortar component in the asphalt mixture, and simultaneously models the void component, ultimately achieving a three-dimensional model of the three components of the asphalt mixture. The three-dimensional model of the asphalt mixture established using this modeling method can be applied to numerical simulation calculations at the microscale of asphalt mixtures, providing a possibility for studying and predicting the mechanical and thermal properties of asphalt mixtures. Furthermore, this modeling method provides an important technical means for optimizing pavement material design methods by utilizing the spatial distribution of asphalt mixture components.

[0106] In addition to the embodiments described above, the present invention may have other implementations. All technical solutions formed by equivalent substitution or equivalent transformation fall within the protection scope claimed by the present invention.

Claims

1. A method for modeling the three-dimensional microstructure of asphalt mixtures, characterized in that: Includes the following steps S1. Determine the shape and size of the asphalt mixture specimen to be modeled, establish the boundary of the asphalt mixture specimen, remove the top surface of the boundary of the asphalt mixture specimen, establish the pressure plate of the asphalt mixture specimen, and set the pressure plate directly above the asphalt mixture specimen. S2. Determine the gradation curve, volume fraction of aggregates, and size of fine aggregates for asphalt mixture specimens, and calculate the target volume of each grade of coarse aggregate. S3. Randomly generate coarse aggregate particles within the boundary of the asphalt mixture specimen. Once the total volume of each generated coarse aggregate particle equals its own target volume, no new coarse aggregate particles are generated. Store the global coordinates of the centroid of each generated coarse aggregate particle and the local coordinates of its vertices. S4. Set the total time for modeling the asphalt mixture, and divide the total time into sub-time steps with equal step sizes, each step size being Δt. Set the pressure plate to move up and down periodically in the vertical direction, and set the minimum height of the pressure plate descent to be equal to the height of the asphalt mixture specimen. Treat all coarse aggregate particles, the boundaries of the asphalt mixture specimen, and the pressure plate as rigid bodies, and calculate the global coordinates of the centroid of the coarse aggregate particles and the local coordinates of the vertices of the coarse aggregate particles after each sub-time step based on the rigid body dynamics collision response in time sequence. Use the coarse aggregate particles after the last sub-time step as the coarse aggregate model of the asphalt mixture specimen. S5. Set the void ratio. Using the coarse aggregate model of the asphalt mixture specimen as a reference, expand along the centroid of each coarse aggregate particle with equal thickness. Calculate the remaining volume fraction of the asphalt mixture specimen. Stop expansion when the remaining volume fraction of the asphalt mixture specimen is the same as the void ratio of the asphalt mixture specimen. The expanded area is the asphalt mortar, and the area with the final remaining space of the asphalt mixture specimen is the void.

2. The method for modeling the three-dimensional microstructure of asphalt mixtures according to claim 1, characterized in that: In step S2, the target volume of each grade of coarse aggregate is calculated using the following formula: wherein V agg represents the target volume of coarse aggregate, P u represents the passing rate of the upper limit of the sieve opening of coarse aggregate, P d represents the passing rate of the lower limit of the sieve opening of coarse aggregate, V represents the volume of the test piece, C agg represents the volume fraction of aggregate.

3. The method for modeling the three-dimensional microstructure of asphalt mixtures according to claim 1, characterized in that: In step S3, the random generation of coarse aggregate particles includes the following steps: S3.1 Generate a regular icosahedron. The distance from the vertex of the regular icosahedron to its centroid satisfies the following equation: In the formula, d 下 d represents the lower limit of the actual coarse aggregate particle sieve opening. 上 This indicates the upper limit of the actual coarse aggregate particle sieve opening, and d represents the distance from the vertex of the icosahedron to its centroid. S3.

2. Divide each side of the regular icosahedron into two equal parts. Connect the points on one face of the regular icosahedron with straight lines. Set the distance from the points generated by the bisection to the centroid of the regular icosahedron as d. Transform the regular icosahedron into a sphere with edges. S3.

3. Using each vertex of the prism as the center, randomly fluctuate the coordinates of each vertex to generate new vertices. The distance between the newly generated vertex and the original vertex does not exceed d / 2, forming a concave-convex surface. S3.4 Delete all the original vertices, leaving the newly generated vertices, and calculate the convex body of the smallest convex hull formed by the newly generated vertices; S3.

5. Randomly stretch a convex body in any direction in space. The stretching ratio depends on the slenderness ratio of the coarse aggregate particles to form coarse aggregate particles.

4. The method for modeling the three-dimensional microstructure of asphalt mixtures according to claim 3, characterized in that: In step S3, the origin of the local coordinates of the generated coarse aggregate particle vertices is the centroid of the coarse aggregate particle.

5. The method for modeling the three-dimensional microstructure of asphalt mixtures according to claim 1, characterized in that: In step S4, based on the rigid body dynamics collision response, the global coordinates of the centroid of the coarse aggregate particles and the local coordinates of the vertices are calculated sequentially after each sub-time step, where the initial time of the k-th sub-time step is t. k-1 The end time is t. k The calculation of the global coordinates of the centroid of coarse aggregate particles and the local coordinates of their vertices at the k-th sub-time step includes the following steps: S4.1 Calculate the change in translational velocity of coarse aggregate particles in the gravitational field; △v a =g△t Where g represents gravitational acceleration; Δv a This represents the change in the centroidal translational velocity of coarse aggregate particles in a gravitational field. S4.2 Determine whether all coarse aggregate particles intersect or collide with the boundary or pressure plate of the asphalt mixture specimen. If they do not intersect, the changes in the translational velocity and angular velocity of the centroid of the coarse aggregate particles caused by the collision with the boundary or pressure plate of the asphalt mixture specimen are 0. If they intersect, the changes in the translational velocity and angular velocity of the centroid of the coarse aggregate particles are as follows: Where, △v b and △ω b These represent the changes in the translational velocity and angular velocity of the centroid of the coarse aggregate particles caused by their collision with the boundary or pressure plate of the asphalt mixture specimen; j n denoted by , m represents the normal impulse of the collision surface between the coarse aggregate particles and the boundary or pressure plate of the asphalt mixture specimen; denoted by , m represents the mass of the coarse aggregate particles; denoted by , I represents the moment of inertia of the coarse aggregate particles; denoted by , μ represents the coefficient of sliding friction between the coarse aggregate particles and the boundary or pressure plate of the asphalt mixture specimen; denoted by , r represents the offset of the centroid of the coarse aggregate particles from the point of collision; denoted by , n represents the normal of the boundary or pressure plate of the asphalt mixture specimen, which always points towards the coarse aggregate particles; denoted by , t represents the projection of the velocity of the coarse aggregate particles at the point of collision onto the collision surface, with the direction consistent with the direction of the velocity of the coarse aggregate particles at the point of collision. S4.3 Determine whether all coarse aggregate particles collide with each other. If they do not collide, the changes in the translational velocity and angular velocity of the centroid of the coarse aggregate particles caused by the collisions are 0. If they collide, the changes in the translational velocity and angular velocity of the centroid of the coarse aggregate particles caused by the collisions are as follows: in, and This represents the change in translational velocity and angular velocity of the centroid of the i-th coarse aggregate particle in the two colliding coarse aggregate particles; j n This represents the normal impulse of the collision surface between two coarse aggregate particles; m i I represents the mass of the i-th coarse aggregate particle among the two colliding coarse aggregate particles; i The moment of inertia of the i-th coarse aggregate particle in the two colliding coarse aggregate particles is represented by r. i denoted by μ, which represents the offset of the centroid of the i-th coarse aggregate particle from the point of collision between the two colliding coarse aggregate particles; μ represents the sliding friction coefficient between the coarse aggregate particles; n represents the normal of the collision surface, which always points from the second coarse aggregate particle to the first coarse aggregate particle; t represents the projection of the velocity of the first coarse aggregate particle at the point of collision onto the collision surface, and its direction is consistent with the direction of the velocity of the first coarse aggregate particle at the point of collision. S4.4 Calculate the velocity of coarse aggregate particles after the current sub-time step ends, as shown in the following formula. Where, v(t) k-1 ) and v(t) k ) represent the translation velocities at the initial and final moments of the current sub-time step, respectively; ω(t) k ) and ω(t k-1 ) represent the angular velocities at the initial and final moments of the current sub-time step, respectively; S4.

5. Calculate the coordinates of the centroid of the coarse aggregate particles after the current time step using Euler's formula, as shown in the following formula. p(t k )=p(t k-1 )+v(t k )△t Where p(t) k-1 ) and p(t k ) represent the global coordinates of the centroid of the coarse aggregate particles at the initial and final times of the current sub-time step, respectively; The coordinates of the coarse aggregate particles at the end of the current time step are calculated using the quaternion method, as shown in the following formula. p l (t k )= ω (t k ) p l (t k-1 ) ω (t k ) -1 in, p l (t k-1 )and p l (t k ) represent the quaternions of the local coordinates of the vertices of coarse aggregate particles at the initial and final times of the current sub-time step, respectively; ω (t k ) represents the angular velocity ω(t) of the coarse aggregate particles. k Quaternions; S4.6 Start the calculation for the next time step, using the position and velocity information of the coarse aggregate particles at the end of the previous time step as the initial values ​​for the position and velocity of the coarse aggregate particles in the next time step.

6. The method for modeling the three-dimensional microstructure of asphalt mixtures according to claim 5, characterized in that: In step S4.2, the solution for the normal impulse of the boundary or pressure plate collision surface between the coarse aggregate particles and the asphalt mixture specimen is as follows: In the formula, e represents the coefficient of restitution, which represents the energy loss during the collision process between coarse aggregate particles and the boundary or pressure plate of the asphalt mixture specimen, and v p This indicates the translational velocity of coarse aggregate particles at the point of impact.

7. The method for modeling the three-dimensional microstructure of asphalt mixtures according to claim 5, characterized in that: In step S4.3, the solution for the normal impulse of the collision surface of the two coarse aggregate particles is as follows: Where e represents the coefficient of restitution, which represents the energy loss during the collision process between coarse aggregate particles, and v p1 and v p2 These represent the translational velocities of the first and second coarse aggregate particles at the point of collision, respectively.

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