Construction method of discrete element model for asphalt mixture based on intersection discrimination and convex optimization

Abstract

The present invention provides a method for constructing a discrete element model of asphalt mixture based on intersection discrimination and convex optimization, specifically as follows: Step 1: Set a specified area in Matlab and place aggregates inside the specified area; Step 2: Import the aggregate contour information into PFC2D and establish a polygonal wall corresponding to the aggregate contour; Step 3: Construct the same specified area as in Step 1 in PFC2D as the specified area wall; Set the polygonal wall in Step 2 inside the specified area wall; Then generate circular particles inside the specified area wall and fill the entire specified area wall; Step 4: Simulate the aggregates composed of polygonal walls and identify the circular small particles located outside all the polygonal walls as asphalt mortar particles; Step 5: Establish a two-dimensional discrete element model of asphalt mixture with a void ratio of vv. The present invention can effectively avoid generating deformed aggregates and improve the discrete element modeling efficiency of asphalt mixture.

Description

Technical Field

[0001] The present invention relates to the technical field of road engineering. Background Art

[0002] The discrete element method is a commonly used numerical simulation technology for analyzing the mechanical properties of asphalt mixtures in the field of road engineering. The reasonable modeling of the discrete element model of asphalt mixtures is an important basis for the successful simulation of the mechanical properties of asphalt mixtures. Compared with the three-dimensional asphalt mixture model, the two-dimensional model has great advantages in terms of computational efficiency. The existing modeling methods for two-dimensional asphalt mixture discrete element models can generally be divided into two categories. One category is based on the cross-sectional image of the asphalt mixture, which is imported into the PFC2D software after digital image processing to achieve the purpose of modeling. The other category is to establish a discrete element model of asphalt mixture with gradation characteristics by using the material composition characteristics of the asphalt mixture and the random reconstruction technology. The first category of methods cannot reflect the material composition of the entire asphalt mixture specimen only through a certain cross-section of the asphalt mixture. Although the model reconstructed by the second category of methods can reflect the aggregate gradation characteristics, the existing aggregate intersection discrimination methods are relatively conservative, resulting in a long time consumption or even modeling failure when establishing a discrete element model of asphalt mixture with a high aggregate proportion, and it is easy to generate concave polygons that do not conform to the actual aggregate shape. Summary of the Invention

[0003] Object of the Invention: To solve the problems existing in the above-mentioned prior art, the present invention provides a method for constructing a discrete element model of asphalt mixture based on intersection discrimination and convex optimization.

[0004] Technical Solution: The present invention provides a method for constructing a discrete element model of asphalt mixture based on intersection discrimination and convex optimization:

[0005] 1. A method for constructing a discrete element model of asphalt mixture based on intersection discrimination and convex optimization, characterized in that it specifically includes the following steps:

[0006] Step 1: Set a specified area in Matlab according to the composition of the asphalt mixture, and put aggregates in the specified area; set N gears according to the sizes of all the put aggregates, and each gear corresponds to a particle size range; arrange the particle size ranges corresponding to all the gears in descending order and number them in sequence;

[0007] Step 2: Import the aggregate contour information generated in Step 1 into PFC2D, and establish a polygonal wall corresponding to the aggregate based on each aggregate contour information;

[0008] Step 3: Construct the same specified area as in Step 1 in PFC2D as the wall of the specified area; according to the positions of the aggregates in the specified area in Step 1, set the corresponding polygonal walls in Step 2 within the wall of the specified area; then generate circular particles with the same radius within the wall of the specified area and fill the entire wall of the specified area;

[0009] Step 4: Based on the circular particles within the polygonal walls, create Clumps to simulate the aggregates composed of the polygonal walls, and identify the small circular particles located outside all the polygonal walls as asphalt mortar particles;

[0010] Step 5: According to the construction method of the void phase, delete a certain number of asphalt mortar particles to form void units of asphalt mixture, and establish a two-dimensional discrete element model of asphalt mixture with a void ratio of vv.

[0011] Furthermore, the method of placing aggregates inside the specified area in Step 1 is specifically as follows:

[0012] Step 1.1: Preset n adjacent areas in Matlab. These n adjacent areas are all adjacent to the specified area and can surround the specified area; denote the union of these n adjacent areas as poly3;

[0013] Step 1.2: Randomly generate the centroid coordinates (center.x, center.y) of an aggregate within the specified area, and randomly determine the number of vertices M of the aggregate, where M1 ≤ M ≤ M2, M1 is the lower limit value of the number of vertices, and M2 is the upper limit value of the number of vertices;

[0014] Step 1.3: Generate the angle θ between the polar radius and the polar axis of the i-th vertex according to the following formula i :

[0015] θ i = b + a

[0016] where i = 1, 2, …, M; a = θ i-1 , the initial value of a is 0; b represents the angle between the polar radii of the i-th vertex and the (i - 1)-th vertex, and the expression of b is as follows:

[0017]

[0018] where λ is a random number between 0 and 1; δ is the fluctuation value of the angle, and δ is less than or equal to 1;

[0019] Step 1.4: According to the area areacum of the area that has been generated so far, determine that the aggregate to be generated in Step 1.2 is the j-th grade aggregate, and the corresponding particle size of the j-th grade aggregate is [d j , d j+1, d j represents the lower limit value of the particle size corresponding to the j-th grade aggregate, d j+1 represents the upper limit value of the particle size corresponding to the j-th grade aggregate; and generate a random number η between 0 and 1, and calculate the polar radius of each vertex of the aggregate to be generated according to the following formula:

[0020] If η is greater than or equal to 0.5, the polar radius r of the i-th vertex i is:

[0021]

[0022] If η is less than 0.5, the polar radius r of the i-th vertex i is:

[0023]

[0024] Step 1.5: Calculate the abscissa xi and ordinate y of each vertex of the aggregate to be generated in Step 1.2 according to the following formula i :

[0025]

[0026] Step 1.6: Perform convex optimization on the generated aggregate vertex coordinate vector, and denote the area occupied by the aggregate after convex optimization as poly2;

[0027] Step 1.7: Determine whether there is an intersection between poly2 and poly3. If so, go to Step 1.2 to regenerate the area poly2; otherwise, record the area of the newly generated aggregate as area, and go to Step 1.8:

[0028] Step 1.8: Update poly3: Take the union of poly2 and poly3 as the new poly3; update areacum: Take the sum of the area areacum of the currently generated area and the area area in Step 1.7 as the updated area areacum;

[0029] Step 1.9: Determine whether the updated areacum reaches S sum ; S sum is the total area composed of all aggregates to be generated. If so, stop the loop; otherwise, go to Step 1.2.

[0030] Further, in Step 1.4, determining that the aggregate to be generated is the j-th grade aggregate according to the area areacum of the currently generated area is specifically:

[0031] If areacum ≤ SS1, the generated aggregate is the first grade aggregate; where SS1 is the area composed of all the first grade aggregates in the placed aggregates;

[0032] If SS1 ≤ areacum ≤ SS1 + SS2, the generated aggregate is the second-grade aggregate; SS2 is the area composed of all the second-grade aggregates in the placed aggregates.

[0033] If SS1 + SS2 + … SS p ≤ areacum ≤ SS1 + SS2 + … SS p + SS p+1 , the generated aggregate is the (p + 1)-th grade aggregate; 3 ≤ p ≤ N - 1; SS p is the area composed of all the p-th grade aggregates in the placed aggregates.

[0034] Calculate the area SS of all the aggregates in each grade of aggregates according to the following formula t :

[0035] SS t = S · m · n t

[0036] where t = 1, 2, …, N; S is the area of the specified area, m is the volume ratio of all aggregates in the asphalt mixture specimen; n t represents the mass ratio between the t-th grade aggregate and all aggregates; the expressions of m and n are as follows:

[0037]

[0038]

[0039] where V ag represents the volume of aggregates in the unit mass asphalt mixture specimen; V z represents the volume of the unit mass asphalt mixture specimen; n N+1N+1 represents the passing rate of the aggregate through the sieve hole when the aggregate particle size is the upper limit value of the particle size range corresponding to the N-th grade aggregate; n tt represents the passing rate of the aggregate through the sieve hole when the aggregate particle size is the lower limit value of the particle size range corresponding to the t-th grade aggregate; n t+1t+1 represents the passing rate of the aggregate through the sieve hole when the aggregate particle size is the upper limit value of the particle size range corresponding to the t-th grade aggregate; n 11 represents the passing rate of the aggregate through the sieve hole when the aggregate particle size is the upper limit value of the particle size range corresponding to the first grade aggregate; V ag and V z are expressed as follows:

[0040]

[0041]

[0042]

[0043] Among them, ratio is the asphalt content; ρ 集料 is the apparent density of the aggregate; V as is the volume occupied by asphalt in the asphalt mixture specimen per unit mass, and vv is the preset void ratio of the asphalt mixture.

[0044] Furthermore, the convex optimization of the generated aggregate vertex coordinate vector in step 1.6 is specifically as follows:

[0045] Step A: Place the generated aggregate vertex coordinates in a plane rectangular coordinate system. Among them, take the vertex with the minimum y-axis value as the starting point, denoted as P0, and consider this point to belong to the aggregate vertices after convex optimization;

[0046] Step B: Take the remaining M - 1 vertices as the ends, and connect P0 to the M - 1 ends; count the counterclockwise angles between the M - 1 connections and the positive x-axis; arrange these angles in ascending order; arrange the M - 1 vertices in the corresponding angle order to obtain the vertices P1 to P M ;

[0047] Step C: Connect P0 and P1 to form a line segment P0 - P1;

[0048] Step D: Connect the previous vertex and the current vertex P c to form a line segment; c = 2, 3, 4…, M;

[0049] Step E: Determine whether each vertex in the contour formed by the current all line segments is a convex vertex. If so, retain the vertex P c and go to step F; otherwise, go to step E;

[0050] Step E: Delete the previous vertex and the line segments related to the previous vertex, take the vertex before the previous one as the previous vertex, and go to step D;

[0051] Step F: Determine whether all vertices have been traversed. If so, stop the loop; otherwise, go to step D.

[0052] Furthermore, step 5 is specifically as follows: Calculate the number of circular particles to be deleted according to the required void area to be generated and the area occupied by a single circular particle. Then, randomly delete the corresponding number of circular particles in the asphalt mortar phase to complete the construction of the void phase in the asphalt mixture; The expression SSV of the required void area to be generated is as follows:

[0053] SSV = S·vv

[0054] Among them, S is the area of the specified region, and vv is the preset porosity.

[0055] Furthermore, eight gears are set. The particle size range corresponding to the first gear is [26.5, 31.5]; the particle size range corresponding to the second gear is [19, 26.5], the particle size range corresponding to the third gear is [16, 19]; the particle size range corresponding to the fourth gear is 13.2, 16; the particle size range corresponding to the fifth gear is [9.5, 13.2]; the particle size range corresponding to the sixth gear is [4.75, 9.5]; the particle size range corresponding to the seventh gear is [2.36, 4.75]; the particle size range corresponding to the eighth gear is [1.18, 2.36]; the unit is mm for all.

[0056] Beneficial effects: Based on the method proposed in the present invention, it is possible to quickly and accurately model the discrete element model of asphalt mixture with a relatively high aggregate proportion. At the same time, by performing convex optimization on the aggregates, it is possible to effectively avoid generating deformed aggregates, improve the accuracy of discrete element simulation of the mechanical properties of asphalt mixture, and overcome the deficiencies of existing methods. Brief Description of the Drawings

[0057] Figure 1 is the flow chart of the present invention;

[0058] Figure 2 is the grading curve of AC-13 asphalt mixture;

[0059] Figure 3 is the schematic diagram of the generation of AC13 asphalt mixture aggregates based on the Matlab algorithm;

[0060] Figure 4 is the schematic diagram of the aggregate convex optimization method;

[0061] Figure 5 is the schematic diagram of the polygonal aggregate wall generated based on the aggregate contour information;

[0062] Figure 6 is the schematic diagram of uniformly distributed circular small ball particles in PFC2D;

[0063] Figure 7 is the schematic diagram of the generation of AC13 aggregates in the PFC2D model;

[0064] Figure 8 is the schematic diagram of the generation of an AC13 asphalt mixture specimen with voids in the PFC2D model. Detailed Embodiment

[0065] The drawings constituting a part of the present invention are used to provide a further understanding of the present invention. The schematic embodiments of the present invention and their descriptions are used to explain the present invention and do not constitute an improper limitation of the present invention.

[0066] Such as Figure 1As shown in the figure, this embodiment provides a method for constructing a discrete element model of asphalt mixture based on intersection discrimination and convex optimization, which mainly includes the following steps:

[0067] (1) According to the composition of the asphalt mixture, set a specified area in Matlab and place aggregates inside the specified area; set N grades according to the sizes of all the placed aggregates, and each grade corresponds to a particle size range; arrange the particle size ranges corresponding to all grades in descending order and number them in sequence; in this embodiment, the specified area is set as a circular area with a radius of 50 mm, and the mineral aggregate gradation curve of AC-13 adopted in this embodiment is as Figure 2 shown.

[0068] The specific process of placing aggregates in the circular area is as follows:

[0069] Step ①: Determine the mineral aggregate gradation of the AC-13 asphalt mixture to be generated. Among them, the passing rates of some sieve holes in the mineral aggregate gradation are shown in the following table;

[0070] Particle size / mm 31.5 26.5 19 16 13.2 9.5 4.75 2.36 1.18 Passing rate / % 100 100 100 100 95 79.7 49.8 37.6 26.4

[0071] According to the above table, 8 grades are set in this embodiment. The particle size range corresponding to the first grade is [26.5, 31.5]; the particle size range corresponding to the second grade is [19, 26.5]; the particle size range corresponding to the third grade is [16, 19]; the particle size range corresponding to the fourth grade is [13.2, 16]; the particle size range corresponding to the fifth grade is [9.5, 13.2]; the particle size range corresponding to the sixth grade is [4.75, 9.5]; the particle size range corresponding to the seventh grade is [2.36, 4.75]; the particle size range corresponding to the eighth grade is [1.18, 2.36]; the unit is mm.

[0072] Step ②: Calculate the volumes of aggregates, asphalt, and the asphalt mixture specimen per unit mass of the asphalt mixture specimen respectively by using the following formulas:

[0073]

[0074]

[0075]

[0076] In the formula: ratio—the asphalt content; ρ 集料 —the apparent density of aggregates; V ag —the volume of aggregates per unit mass of the asphalt mixture specimen; ρ 沥青 —the density of asphalt; V as —the volume of asphalt per unit mass of the asphalt mixture specimen; vv—the void ratio; V z— The volume occupied by the asphalt mixture specimen per unit mass.

[0077] In this embodiment, ratio = 4.85%; ρ 集料 = 2640 kg / m 3 ; ρ 沥青 = 1100 kg / m 3 ; vv = 4%.

[0078] Step ③: Calculate the volume ratio of the aggregate with a particle size greater than or equal to 1.18 mm and the mass ratio of each size fraction of aggregate to the total aggregate according to the following formula:

[0079]

[0080]

[0081] Where: m — the volume ratio of the aggregate with a particle size greater than or equal to 1.18 mm in the asphalt mixture specimen; n t — the mass ratio between the t-th size fraction of aggregate and all aggregates, n N+1N+1 represents the passing rate of the aggregate through the sieve hole when the particle size of the aggregate is the upper limit value of the particle size range corresponding to the N-th size fraction of aggregate; n tt represents the passing rate of the aggregate through the sieve hole when the particle size of the aggregate is the lower limit value of the particle size range corresponding to the t-th size fraction of aggregate; n t+1t+1 represents the passing rate of the aggregate through the sieve hole when the particle size of the aggregate is the upper limit value of the particle size range corresponding to the t-th size fraction of aggregate; n 11 represents the passing rate of the aggregate through the sieve hole when the particle size of the aggregate is the upper limit value of the particle size range corresponding to the 1st size fraction of aggregate; V ag and V z are expressed as follows; in this embodiment, there are a total of N = 8 size fractions of aggregate, and the value of t in n t ranges from 1 to 8, representing the percentage of the aggregate with particle sizes in the ranges of 26.5 - 31.5 mm, 19 - 26.5 mm, 16 - 19 mm, 13.2 - 16 mm, 9.5 - 13.2 mm, 4.75 - 9.5 mm, 2.36 - 4.75 mm, and 1.18 - 2.36 mm in the mass of the aggregate with a particle size greater than 1.18 mm (i.e., all aggregates).

[0082] Step ④: Calculate the area occupied by each size fraction of aggregate and the area occupied by the voids respectively according to the following formula;

[0083] SS t = S·m·n t (6)

[0084]

[0085] SSV = S·vv (8)

[0086] Where: S—the area of the specified region; SS i —the area occupied by the aggregate in the i-th grade; S sum —the total area of the aggregate to be generated; SSV—the area occupied by the voids.

[0087] Step ⑤: Preset n adjacent regions in Matlab. The n adjacent regions are all adjacent to the specified region, and the n adjacent regions can enclose the specified region; denote the union of the n adjacent regions as poly3.

[0088] Step ⑥: Determine whether the cumulative area areacum of the generated aggregate has exceeded S sum . If not, proceed to Step ⑦. Otherwise, all the aggregates have been generated and the loop ends.

[0089] Step ⑦: Randomly generate the centroid coordinates (center.x, center.y) of an aggregate within the specified region, and randomly determine the number of vertices M of the aggregate, where M1 ≤ M ≤ M2. In this embodiment, M1 = 6 and M2 = 10; M1 is the lower limit value of the number of vertices, and M2 is the upper limit value of the number of vertices.

[0090] Step ⑧: Traverse all the vertices of the aggregate, and generate the angle b between the polar radius of the i-th vertex and the previous vertex (i.e., the (i - 1)-th vertex) and the angle θ between the polar radius of the i-th vertex and the polar axis according to the following formula i .

[0091]

[0092] θ i = b + a (10)

[0093] where i = 1, 2, …, M; a = θ i-1 , and the initial value of a is 0.

[0094] Step ⑨: Determine that the aggregate to be generated in Step 1.2 is the aggregate of the j-th grade according to the area areacum of the region that has been generated so far (i.e., the area of the region generated in the previous step). The particle size range corresponding to the aggregate of the j-th grade is [d j , d j+1 , where d j represents the lower limit value of the particle size corresponding to the aggregate of the j-th grade, and d j+1 represents the upper limit value of the particle size corresponding to the aggregate of the j-th grade; generate a random number η between 0 and 1, and calculate the polar radius of each vertex of the aggregate to be generated according to the following formula:

[0095] If η is greater than or equal to 0.5, the polar radius of the i-th vertex is:

[0096]

[0097] If η is less than 0.5, the polar radius of the i-th vertex is:

[0098]

[0099] In the formula: j represents the j-th aggregate, and j takes values from 1 to 8; d j — represents the lower limit of the j-th aggregate; d j+1 — represents the upper limit of the j-th aggregate.

[0100] Step ⑩: Determine whether the traversal of the aggregate vertices is completed. If not, go to Step ⑧; otherwise, go to Step

[0101] Step Calculate the coordinates of each vertex of the aggregate according to the following formula:

[0102]

[0103] Among them, x i is the abscissa of the i-th vertex of the generated aggregate, and y i is the ordinate of the i-th vertex of the generated aggregate; form an array with all the generated vertex coordinates for convenient processing by Matlab software.

[0104] Step Perform convex optimization on the generated aggregate vertex coordinate vector. The area occupied by the aggregate after convex optimization is poly2.

[0105] Step Perform a logical judgment on the areas poly2 and poly3 occupied by the aggregate to analyze whether there is a common area between the two regions. If there is a common area, it is considered that the aggregate is an intersecting aggregate, and go back to Step ⑥ to regenerate the area poly2; if there is no common area, it is considered that the aggregate is not an intersecting aggregate, meets the aggregate generation requirements, and go to Step

[0106] Step Take the union of poly2 and poly3, denoted as the new poly3, and complete the area accumulation of the newly generated aggregate according to the following formula; then go to Step ⑥.

[0107] areacum = areacum + area(15)

[0108] In the formula: areacum—the cumulative area of the generated aggregates; area—the area of the newly generated aggregates. The meaning of Formula 15 is to update the total generated area areacum: the total area generated in the previous step is accumulated with the area of the aggregates generated currently as the current generated area areacum.

[0109] In this embodiment, the schematic diagram of generating AC13 asphalt mixture aggregates within a specified area based on the Matlab algorithm is as Figure 3 shown.

[0110] In step ⑨ of placing aggregates in the specified area, the specific method for determining the particle size range of the generated aggregates by areacum is as follows:

[0111] If areacum ≤ SS1, the generated aggregates are the first-grade aggregates; where SS1 is the area composed of all the first-grade aggregates in the placed aggregates.

[0112] If SS1 ≤ areacum ≤ SS1 + SS2, the generated aggregates are the second-grade aggregates; SS2 is the area composed of all the second-grade aggregates in the placed aggregates.

[0113] If SS1 + SS2 + … SS p ≤ areacum ≤ SS1 + SS2 + … SS p + SS p+1 , the generated aggregates are the (p + 1)-th grade aggregates; 3 ≤ p ≤ N - 1; SS p is the area composed of all the p-th grade aggregates in the placed aggregates.

[0114] Specifically corresponding in this embodiment:

[0115] If areacum ≤ SS1, the particle size range of the generated aggregates should be in the interval [26.5 mm, 31.5 mm];

[0116] If SS1 ≤ areacum ≤ SS1 + SS2, the particle size range of the generated aggregates should be in the interval [19 mm, 26.5 mm];

[0117] If SS1 + SS2 ≤ areacum ≤ SS1 + SS2 + SS3, the particle size range of the generated aggregates should be in the interval [16 mm, 19 mm];

[0118] If SS1 + SS2 + SS3 ≤ areacum ≤ SS1 + SS2 + SS3 + SS4, the particle size range of the generated aggregates should be in the interval [13.2 mm, 16 mm];

[0119] If SS1 + SS2 + SS3 + SS4 ≤ areacum ≤ SS1 + SS2 + SS3 + SS4 + SS5, the generated aggregate particle size range should be in the interval [9.5 mm, 13.2 mm];

[0120] If SS1 + SS2 + SS3 + SS4 + SS5 ≤ areacum ≤ SS1 + SS2 + SS3 + SS4 + SS5 + SS6, the generated aggregate particle size range should be in the interval [4.75 mm, 9.5 mm];

[0121] If SS1 + SS2 + SS3 + SS4 + SS5 + SS6 ≤ areacum ≤ SS1 + SS2 + SS3 + SS4 + SS5 + SS6 + SS7, the generated aggregate particle size range should be in the interval [2.36 mm, 4.75 mm];

[0122] If SS1 + SS2 + SS3 + SS4 + SS5 + SS6 + SS7 ≤ areacum ≤ SS1 + SS2 + SS3 + SS4 + SS5 + SS6 + SS7 + SS8, the generated aggregate particle size range should be in the interval [1.18 mm, 2.36 mm].

[0123] The step of placing the aggregate in the specified area In, the aggregate convex optimization is as Figure 4 shown, and the specific process is:

[0124] Step A: Place the vertex coordinates of the generated aggregate in a plane rectangular coordinate system. Among them, take the vertex with the minimum y-axis value as the starting point, denoted as P0, and consider that this point belongs to the aggregate vertex after convex optimization.

[0125] Step B: Take the remaining M - 1 vertices as the ends, and connect P0 to the M - 1 ends; count the counterclockwise angles between the M - 1 connections and the positive x-axis; arrange these angles in ascending order; arrange the M - 1 vertices in the corresponding angle order to obtain the vertices P1 to P M .

[0126] Step C: Connect P0 and P1 to form a line segment P0 - P1.

[0127] Step D: Connect the previous vertex to the current vertex P c to form a line segment; c = 2, 3, 4…, M;

[0128] Step E: Determine whether each vertex in the contour formed by the current all line segments is a convex vertex. If so, retain the vertex P c and go to Step F; otherwise, go to Step E.

[0129] Step E: Delete the previous vertex and the line segments associated with the previous vertex. Set the vertex before the previous vertex as the previous vertex, and go to Step D.

[0130] For example: After connecting P4 and P3, each vertex (P0, P1, P2, P3, P4) in the contour formed by all line segments (P0 - P1, P1 - P2, P2 - P3, P4 - P3) bulges outwards. At this time, keep P4.

[0131] After connecting P5 and P4, it is found that vertex P4 in the contour formed by all line segments concaves inwards. Then, at this time, delete vertex P4 and the line segments associated with P4 (line segment P5 - P4 and line segment P4 - P3); connect vertex P5 and P3 again, and it is found that vertex P3 in the contour formed by all line segments concaves inwards. Then, at this time, delete vertex P3, line segment P5 - P3 and line segment P3 - P2; connect vertex P5 and P2 again, and each vertex in the contour formed by all line segments bulges outwards. At this time, keep P5.

[0132] Step F: Determine whether all vertices have been traversed. If so, stop the loop; otherwise, go to Step D.

[0133] In this embodiment, connect P0 to the points P1, P2, P5, P7, P9 in the stack and P 11 This is the aggregate after convex optimization of the aggregate.

[0134] (2) Import the aggregate contour information generated in Step 1 into PFC2D, and build a polygonal wall based on each aggregate contour information, as Figure 5 shown. And start from 1 to continuously number the polygonal walls.

[0135] (3) In PFC2D, construct the same specified area as in Step 1 as the specified area wall; according to the position of the aggregate in the specified area in Step 1, set the corresponding polygonal wall in Step 2 in the specified area wall; then generate circular particles with a radius of 0.3 mm in the specified area wall (in this embodiment, generate circular particles according to the arrangement rule of "hexagon") and fill the entire specified area wall as Figure 6 shown.

[0136] (4) Group the circular particles located in the wall according to the wall number. The circular particles that are not grouped are identified as the asphalt mortar phase. Then, use the Clump command to assemble the circular particles in each group to generate several individual polygonal aggregates, and identify the small circular particles located outside all polygonal walls as the asphalt mortar part, as Figure 7 shown.

[0137] (5) Calculate the number of circular particles to be deleted based on the required void area calculated above and the area occupied by a single circular particle. Then, randomly delete the corresponding number of circular particles in the asphalt mortar phase to complete the construction of the void phase in the asphalt mixture, as Figure 8 shown.

[0138] As can be seen from Figure 8 , the two-dimensional discrete element model of asphalt mixture with a large aggregate content and more in line with the true morphological characteristics of aggregates generated by the method proposed in the present invention demonstrates the rationality and scientificity of the two-dimensional discrete element model modeling method of asphalt mixture based on intersection discrimination and convex optimization.

[0139] In addition, it should be noted that, without contradiction, the various specific technical features described in the above specific embodiments can be combined in any suitable manner. To avoid unnecessary repetition, the present invention will not further elaborate on various possible combination methods.

Claims

1. A method for constructing a discrete element model of asphalt mixture based on intersection discrimination and convex optimization, characterized in that Specifically, it includes the following steps: Step 1: According to the composition of the asphalt mixture, set a specified area in Matlab and place aggregates within the specified area; set N grades based on the sizes of all the placed aggregates, with each grade corresponding to a particle size range; arrange the particle size ranges corresponding to all grades in descending order and number them in sequence; Step 2: Import the aggregate contour information generated in Step 1 into PFC2D and establish a polygonal wall corresponding to the aggregate based on each aggregate contour information; Step 3: Construct the same specified area as in Step 1 in PFC2D as the specified area wall; set the corresponding polygonal walls in Step 2 within the specified area wall according to the positions of the aggregates in the specified area in Step 1; then generate circular particles with the same radius within the specified area wall to fill the entire specified area wall; Step 4: Based on the circular particles within the polygonal wall, create a Clump to simulate the aggregate composed of the polygonal wall and identify the small circular particles outside all the polygonal walls as asphalt mortar particles; Step 5: According to the construction method of the void phase, delete a certain number of asphalt mortar particles to form a void unit of the asphalt mixture and establish a two-dimensional discrete element model of the asphalt mixture with a void ratio of vv.

2. The method for constructing a discrete element model of asphalt mixture based on intersection discrimination and convex optimization according to claim 1, wherein: The method of placing aggregates within the specified area in Step 1 is specifically as follows: Step 1.1: Preset n adjacent areas in Matlab. These n adjacent areas are all adjacent to the specified area and can surround the specified area; denote the union of these n adjacent areas as poly3; Step 1.2: Randomly generate the centroid coordinates (center.x, center.y) of an aggregate within the specified area and randomly determine the number of vertices M of the aggregate, where M1 ≤ M ≤ M2, M1 is the lower limit value of the number of vertices, and M2 is the upper limit value of the number of vertices; Step 1.3: Generate the angle θ between the polar radius and the polar axis of the i-th vertex according to the following formula i : θ i = b + a where \(i = 1,2,\cdots,M\); \(a=\theta\) i-1 , the initial value of \(a\) is \(0\); \(b\) represents the angle between the polar radius of the \(i\)-th vertex and the \((i - 1)\)-th vertex, and the expression of \(b\) is as follows: where λ is a random number between 0 and 1; δ is the fluctuation value of the angle, and δ is less than or equal to 1; Step 1.4: Based on the area areacum of the currently generated area, determine that the aggregate to be generated in Step 1.2 is the j-th grade aggregate, and the particle size corresponding to the j-th grade aggregate is [d j , d j+1 , d j represents the lower limit value of the particle size corresponding to the j-th grade aggregate, and d j+1 represents the upper limit value of the particle size corresponding to the j-th grade aggregate; and generate a random number η between 0 and 1, and calculate the polar radius of each vertex of the aggregate to be generated according to the following formula: If η is greater than or equal to 0.5, then the polar radius r of the i-th vertex i is as follows: If η is less than 0.5, the polar radius r of the i-th vertex i is: Step 1.5: Calculate the abscissa x of each vertex of the aggregate to be generated in Step 1.2 according to the following formula i and the ordinate y i : Step 1.6: Perform convex optimization on the generated aggregate vertex coordinate vector, and denote the area occupied by the aggregate after convex optimization as poly2; Step 1.7: Determine whether there is an intersection between poly2 and poly3. If so, go to Step 1.2 to regenerate the area poly2; otherwise, denote the area of the newly generated aggregate as area and go to Step 1.8: Step 1.8: Update poly3: Take the union of poly2 and poly3 as the new poly3; update areacum: Take the sum of the area areacum of the currently generated area and the area area in Step 1.7 as the updated area areacum; Step 1.9: Determine whether the updated areacum has reached S sum ; S sum is the total area composed of all aggregates to be generated. If so, stop the loop; otherwise, go to Step 1.2 3. The method for constructing a discrete element model of asphalt mixture based on intersection discrimination and convex optimization according to claim 2, characterized in that: The specific method of determining that the aggregate to be generated is the j-th grade aggregate according to the area areacum of the currently generated area in Step 1.4 is as follows: If areacum ≤ SS1, the generated aggregate is the first grade aggregate; where SS1 is the area composed of all the first grade aggregates among the placed aggregates; If SS1 ≤ areacum ≤ SS1 + SS2, the aggregate generated is the second-grade aggregate; SS2 is the area composed of all the second-grade aggregates in the placed aggregates. If SS1 + SS2 + … SS p ≤ areacum ≤ SS1 + SS2 + … SS p + SS p+1 , the aggregate generated is the (p + 1)-th grade aggregate; 3 ≤ p ≤ N - 1; SS p is the area formed by all the p-th grade aggregates in the aggregates put in place. Calculate the area SS of all aggregates in each grade of aggregates according to the following formula t :[[-END]] SS t = S·m·n t where \(t = 1, 2, \cdots, N\); \(S\) is the area of the specified region, \(m\) is the volume ratio of all aggregates in the asphalt mixture specimen; \(n\) t represents the mass ratio between the \(t\)-th grade aggregate and all aggregates; the expressions of \(m\) and \(n\) are as follows: Among them, V ag represents the volume of aggregates in the asphalt mixture specimen per unit mass; V z represents the volume of the asphalt mixture specimen per unit mass; n N+1N+1 represents the passing rate of the aggregate through the sieve hole when the aggregate particle size is the upper limit value of the particle size range corresponding to the Nth grade aggregate; n tt represents the passing rate of the aggregate through the sieve hole when the aggregate particle size is the lower limit value of the particle size range corresponding to the tth grade aggregate; n t+1t+1 represents the passing rate of the aggregate through the sieve hole when the aggregate particle size is the upper limit value of the particle size range corresponding to the tth grade aggregate; n 11 represents the passing rate of the aggregate through the sieve hole when the aggregate particle size is the upper limit value of the particle size range corresponding to the 1st grade aggregate; V ag and V z The expressions of are as follows: Among them, ratio is the asphalt content; ρ 集料 is the apparent density of the aggregate; V as is the volume occupied by asphalt in the asphalt mixture specimen per unit mass, and vv is the preset void ratio of the asphalt mixture.

4. The method for constructing a discrete element model of asphalt mixture based on intersection discrimination and convex optimization according to claim 2, characterized in that: In step 1.6, the convex optimization of the generated aggregate vertex coordinate vector is specifically as follows: Step A: Place the vertex coordinates of the generated aggregate in a plane rectangular coordinate system. Among them, take the vertex with the minimum y-axis value as the starting point, denoted as P0, and consider that this point belongs to the aggregate vertices after convex optimization. Step B: Take the remaining M - 1 vertices as the ends, and connect P0 to the M - 1 ends; count the counterclockwise angles between the M - 1 connections and the positive x-axis; arrange these angles in ascending order; arrange the M - 1 vertices in the order corresponding to the angles to obtain the vertices P1 to P arranged in order M ; Step C: Connect P0 and P1 to form a line segment P0 - P1. Step D: Connect the previous vertex and the current vertex P c to form a line segment; c = 2, 3, 4, …, M; Step E: Determine whether each vertex in the contour formed by all the current line segments is a protruding vertex. If so, retain vertex P c and proceed to Step F; otherwise, return to Step E; Step E: Delete the previous vertex and the line segment related to the previous vertex, take the vertex before the previous vertex as the previous vertex, and go to step D. Step F: Determine whether all vertices have been traversed. If so, stop the loop; otherwise, go to step D.

5. The method for constructing a discrete element model of asphalt mixture based on intersection discrimination and convex optimization according to claim 2, characterized in that: Step 5 is specifically as follows: According to the required void area to be generated and the area occupied by a single circular particle, calculate the number of circular particles to be deleted, and then randomly delete the corresponding number of circular particles in the asphalt mortar phase to complete the construction of the void phase in the asphalt mixture; the expression SSV of the required void area to be generated is as follows: SSV = S·vv Where S is the area of the specified area, and vv is the preset void ratio of the asphalt mixture.

6. The method for constructing a discrete element model of asphalt mixture based on intersection discrimination and convex optimization according to claim 1, wherein: Set 8 grades. The particle size range corresponding to the first grade is [26.5, 31.5]; the particle size range corresponding to the second grade is [19, 26.5], the particle size range corresponding to the third grade is [16, 19]; the particle size range corresponding to the fourth grade is [13.2, 16]; the particle size range corresponding to the fifth grade is [9.5, 13.2]; the particle size range corresponding to the sixth grade is [4.75, 9.5]; the particle size range corresponding to the seventh grade is [2.36, 4.75]; the particle size range corresponding to the eighth grade is [1.18, 2.36]; the unit is mm.

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