CN107766623A - Random generation method for numerical model of asphalt mixture - Google Patents
Random generation method for numerical model of asphalt mixture Download PDFInfo
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- 239000010426 asphalt Substances 0.000 title claims abstract description 60
- 239000000203 mixture Substances 0.000 title claims abstract description 53
- 238000000034 method Methods 0.000 title claims abstract description 38
- 230000001788 irregular Effects 0.000 claims abstract description 38
- 239000004570 mortar (masonry) Substances 0.000 claims abstract description 11
- 239000002245 particle Substances 0.000 claims description 89
- 238000004364 calculation method Methods 0.000 claims description 4
- 238000007689 inspection Methods 0.000 claims description 3
- 239000004575 stone Substances 0.000 claims description 3
- 230000001172 regenerating effect Effects 0.000 claims description 2
- 229910052500 inorganic mineral Inorganic materials 0.000 abstract description 3
- 239000011707 mineral Substances 0.000 abstract description 3
- 238000010586 diagram Methods 0.000 description 4
- 238000005516 engineering process Methods 0.000 description 4
- 238000004422 calculation algorithm Methods 0.000 description 2
- 230000007547 defect Effects 0.000 description 2
- 238000004088 simulation Methods 0.000 description 2
- NAWXUBYGYWOOIX-SFHVURJKSA-N (2s)-2-[[4-[2-(2,4-diaminoquinazolin-6-yl)ethyl]benzoyl]amino]-4-methylidenepentanedioic acid Chemical compound C1=CC2=NC(N)=NC(N)=C2C=C1CCC1=CC=C(C(=O)N[C@@H](CC(=C)C(O)=O)C(O)=O)C=C1 NAWXUBYGYWOOIX-SFHVURJKSA-N 0.000 description 1
- 230000009286 beneficial effect Effects 0.000 description 1
- 239000002131 composite material Substances 0.000 description 1
- 238000005094 computer simulation Methods 0.000 description 1
- 239000004567 concrete Substances 0.000 description 1
- 238000012217 deletion Methods 0.000 description 1
- 230000037430 deletion Effects 0.000 description 1
- 238000003708 edge detection Methods 0.000 description 1
- 238000003709 image segmentation Methods 0.000 description 1
- 239000012798 spherical particle Substances 0.000 description 1
- 238000006467 substitution reaction Methods 0.000 description 1
- 238000003325 tomography Methods 0.000 description 1
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Abstract
The invention discloses a random generation method of a numerical model of an asphalt mixture, which randomly generates irregular polyhedral aggregates; and generating a numerical model of the asphalt mixture by using the irregular polyhedron aggregate. The invention reflects the random generation of the asphalt mixture three-dimensional discrete element numerical model with irregular shape coarse aggregate, mineral aggregate gradation, asphalt mortar and gap distribution, fully embodies the edge and corner characteristics of the aggregate and avoids the problem of parallel or overlapped cutting surfaces.
Description
Technical Field
The invention relates to the field of numerical simulation modeling of asphalt mixtures, in particular to a random generation method of an asphalt mixture numerical model.
Background
The internal structure of the asphalt mixture is very complex, and the asphalt mixture is a multi-phase composite material consisting of aggregates, asphalt and gaps. For numerical simulation, the first problem to be solved is how to establish a numerical model capable of reflecting the internal characteristics of the asphalt mixture. The existing methods for modeling the asphalt mixture mainly comprise the following steps:
firstly, a traditional method for acquiring a numerical model of an asphalt mixture generally includes the steps of photographing the surface of the mixture or a section of a cut test piece through a digital camera, or carrying out tomography scanning on the asphalt mixture test piece through industrial CT, then acquiring a binary image of the mixture test piece through related digital image processing technologies, such as an image enhancement technology, an image segmentation technology, an image edge detection technology and the like, and carrying out digital reconstruction to obtain the numerical model of the mixture test piece. Although the method can obtain the digital model with high matching degree with the real test piece, the method has the following defects: high test requirements, high cost, incapability of realizing simulation requirements under certain conditions and the like.
Two, direct modeling method
The disadvantage of this method is that the mixture is regarded as a homogeneous mass, which is not the case.
Thirdly, a random reconstruction generation method is adopted,
although the method has achieved great results at present, the current algorithm has the following defects that the cutting surfaces are parallel or overlapped on the aggregate generation algorithm.
Disclosure of Invention
The invention aims to solve the technical problem that the prior art is not enough, and provides a random generation method of a numerical model of an asphalt mixture, which reflects the random generation of coarse aggregates with irregular shapes, mineral aggregate gradation, asphalt mortar and a numerical model of three-dimensional discrete elements of the asphalt mixture with gap distribution, fully embodies the corner angle characteristics of the aggregates and avoids the problem of parallel or overlapped cutting surfaces.
In order to solve the technical problems, the technical scheme adopted by the invention is as follows: a random generation method of a numerical model of an asphalt mixture comprises the following steps:
1) randomly generating irregular polyhedral aggregate;
2) and generating a numerical model of the asphalt mixture by using the irregular polyhedron aggregate.
The specific implementation process of the step 1) comprises the following steps:
A) filling regularly arranged small-particle-size discrete units in the polyhedron;
B) generating a plurality of random planes to randomly cut a cube to obtain an irregular polyhedral area;
C) judging the centroid position of the small-particle-size discrete unit and the relative position of the polyhedral region obtained in the step B), and taking the small-particle-size discrete unit belonging to the interior of the polyhedral region as an irregular polyhedral aggregate part.
In the step A), the side length of the cube is equal to the grain size of the polyhedral aggregate; the mathematical equation for the cube is as follows:
wherein (x)0，y0，z0) Coordinates of a cube centroid O; 2R is the side length of a square; (x, y, z) is the coordinates of any point within the cube.
In the step B), the number of the random planes is 8; the specific implementation process of the step B) comprises the following steps:
a) randomly generating a normal vector (n) of each quadrant cutting planej1，nj2，nj3) J takes a value of 1-8; n isj1，nj2，nj3The calculation formula is as follows:
t1＝cos(α)
t2＝sin(α)
t3＝cos(β)；
nj1＝t1/tt
nj2＝t2/tt
nj3＝t3/tt
wherein, the urand is a random function, the value range is (0, 1), the int is an integer function, α is the included angle between a line of the space in the horizontal plane and the x axis, β is the included angle between a line of the space in the horizontal plane and the z axis, t1，t2，t3Is the cosine of the included angle between one line of the space and the coordinate axes of x, y and z;
b) solving the distance d from the centroid of the cube to the cutting plane: d ═ R × q; wherein q is a cutting control coefficient;
c) according to the distance d and the normal vector (n)j1，nj2，nj3) Obtaining the intersection point M of the vertical connecting line of the cubic centroid O and the cutting surfacec(xc，yc，zc) The coordinates of (a) are as follows:
xc＝x0+d×nj1
yc＝y0+d×nj2；
zc＝z0+d×nj3
d) determining a random plane P using the following equationj：
Pj＝x×nj1+y×nj2+z×nj3-(xc×nj1+yc×nj2+zc×nj3)＝0；
e) Cutting the square body by using a random plane to obtain an irregular polyhedron region, wherein the mathematical equation of the irregular polyhedron region is as follows:
x-(x0-R)≥0
x-(x0+R)≤0
y-(y0-R)≥0
y-(y0+R)≤0。
z-(z0-R)≥0
z-(z0+R)≤0
Pj≤0
the specific implementation process of the step 2) comprises the following steps:
I) determining the number of aggregate units of each grade of the mixture;
II) feeding graded parent particles according to the number of aggregate units in each grade;
III) reading and storing grading parent particle set information;
IV) deleting the graded parent particles to generate regularly arranged small particles;
v) generating an irregular aggregate model and carrying out grading inspection;
VI) generating gaps in the irregular aggregate model to obtain a numerical model of the asphalt mixture. In the step I), the percentage of the I-th grade aggregate in the total volume of the asphalt mixture test piece is calculated according to the following formula:
wherein,JDithe percentage of the i-th aggregate in the total volume of the asphalt mixture test piece is shown; pDi-1、PDiThe passing rates of the aggregate of the i-1 th grade and the i-th grade are respectively; VV is the porosity; a is the oil-stone ratio; rhocThe density of coarse and fine aggregates; rholIs the pitch density.
The percentage of each grade of aggregate in the total volume of the test piece is calculated through the formula, then the total volume of each grade of aggregate can be known by knowing the volume of the test piece, and then the number of the aggregate particles of each grade can be obtained by dividing the total volume of each grade of aggregate by the volume of single aggregate particles.
Assuming a cylindrical test piece volume of
V＝πd2h/4；
Wherein d is the diameter of the bottom circle of the cylinder; h is the height of the cylinder; then the number of aggregates per grade is:
wherein r isiIs the average radius of the i-th grade aggregate particles, where r is takeni＝(Di-1+Di) /4 wherein Di-1、DiThe screen sizes of the i-1 th gear and the i-th gear are respectively.
The specific implementation process of the step II) comprises the following steps: and (3) throwing the aggregate particles into the cylindrical model according to the number of the aggregate units of each grade, scanning the aggregate particles of each grade, calculating the volume fraction of the aggregate particles of each grade, and if the volume fraction is consistent with the actual volume fraction, correctly throwing.
In step IV), after the grading mother particles are deleted, arranging the aggregate particles with the particle size smaller than the minimum particle size of the coarse aggregate particles according to the following rules: all aggregate particles are ensured to be regularly arranged in the horizontal direction and the vertical direction, and each particle in the middle position is arranged adjacent to one particle in the upper, lower, left, right, front and back six directions.
In the step V), when the percentage of each grade of aggregate particles to the total particles of the whole cylinder model is within a percentage threshold value, the grading test is successful; otherwise, regenerating the grade of aggregate until the percentage of aggregate particles in the grade of aggregate to the total particles of the whole cylinder model is within the percentage threshold, and then generating the next grade of aggregate; finally obtaining the irregular aggregate model.
The concrete implementation process of the step VI) is as follows: and generating a random number in the maximum particle range of the irregular aggregate model, judging whether the particle address with the random number as the serial number is empty, if not, judging whether the particle with the random number as the serial number is asphalt mortar, if so, deleting the particles until n _ del particles are deleted, and obtaining the asphalt mixture numerical model.
Compared with the prior art, the invention has the beneficial effects that: the invention reflects the random generation of the asphalt mixture three-dimensional discrete element numerical model with irregular shape coarse aggregate, mineral aggregate gradation, asphalt mortar and gap distribution, fully embodies the edge and corner characteristics of the aggregate and avoids the problem of parallel or overlapped cutting surfaces.
Drawings
FIG. 1 is a diagram of aggregate placement according to the present invention;
FIG. 2 is a diagram of regularly arranged particles according to the present invention;
FIG. 3 is a drawing of an irregular aggregate test piece (no voids) of the present invention;
FIG. 4 is a gap profile of the present invention;
FIG. 5(A) a diagram of an irregular aggregate model; FIG. 5(B) vertical section view of irregular aggregate module; FIG. 5(C) transverse section view of irregular aggregate model.
Detailed Description
The specific implementation process of the invention is as follows:
1) randomly generating irregular polyhedral aggregate;
1.1) filling regularly arranged small-particle-size discrete units;
1.2) generating eight random planes to randomly cut a cube;
1.3) judging the relative position (the centroid position of the small-particle-size discrete unit (actually, the spherical center coordinate (x, y, z)) and the relative position of the irregular polyhedral area);
2) generating a numerical model of the asphalt mixture;
the asphalt mixture is generally considered to be composed of three phases of aggregate, asphalt mortar and voids, step 1) provides a method for generating single aggregate, and step 2) generates the asphalt mixture on the basis of step 1).
2.1) determining the number of grading units;
2.2) putting the graded parent particles;
2.3) reading and storing geometric information of the graded parent particles;
2.4) deleting parent particles to generate regularly arranged small particles;
2.5) loading an irregular aggregate generation program; generating irregular aggregates and carrying out grading inspection;
2.6) creation of voids.
Step 1.1): and programming a program to regularly fill the particles with smaller particle sizes in a specified cube region according to a certain sequence, and setting the side length of the region to be equal to the particle size of the aggregate. The mathematical equation for the cube is as follows (1):
in the formula, x0，y0，z0-a cube centroid O coordinate; 2R-cube side length, namely the particle size of the aggregate; (x, y, z) is the coordinates of any point in space.
Step 1.2): the random plane is generated as follows:
a) generating a normal vector (n) for each quadrant cutting planej1，nj2，nj3) The normal vector is generated randomly, wherein j is equal to 1-8, nj1，nj2，nj3Calculated from equation (2).
t1＝cos(α)
t2＝sin(α)
t3＝cos(β) (2)
nj1＝t1/tt
nj2＝t2/tt
nj3＝t3/tt
In the formula, urand is a random function inside the computer, the range is (0, 1), and int is a rounding function inside the computer.
Reply headnote 5: α -angle in the xoy plane (which can be considered to be in the horizontal plane) from the x-axis, starting counterclockwise from the x-axis, similar to the azimuth;
β -angle with the z-axis, similar to tilt.
t1，t2，t3The cosine of the angle between a line in the space and the x, y, z coordinate axes.
In practice, the spatial straight line is determined by determining the random angle α in the xoy plane and then determining the random angle β in the vertical direction.
b) The distance d from the centroid of the cube to the cutting plane is shown by equation (3).
d＝R×q (3)
In the formula: q is a cutting control coefficient and is between 0 and 1.0.
c) From the distance d and normal vector (n) in frontj1，nj2，nj3) So as to obtain the intersection point M of the vertical connecting line of the cubic centroid O and the cutting surfacec(xc，yc，zc) The coordinates of (a) are as follows:
xc＝x0+d×nj1
yc＝y0+d×nj2(4)
zc＝z0+d×nj3
the random plane equation is then:
Pj＝x×nj1+y×nj2+z×nj3-(xc×nj1+yc×nj2+zc×nj3)＝0 (5)
d) cutting the square body according to the randomly generated cutting surface to obtain an irregular polyhedral area, wherein the mathematical equation of the irregular polyhedral area is as shown in formula (6):
x-(x0-R)≥0
x-(x0+R)≤0
y-(y0-R)≥0
y-(y0+R)≤0 (6)
z-(z0-R)≥0
z-(z0+R)≤0
Pj≤0
step 2.1): when the quantity of each grade of particles needed by the model is calculated, the passing rate of the grading in the specification is calculated by the mass representation, so that in order to represent the grading characteristics of the mixture in the model, the density of the aggregate is assumed to be equal, the grading is converted into the quantity represented by the mass, the quantity represented by the mass is converted into the quantity represented by the volume, the number of grading ball units is calculated according to the volume fraction, namely the volume of a test piece occupied by a certain grade of aggregate is calculated according to the volume fraction, then the quantity of the grade of aggregate particles can be obtained by dividing the volume fraction by the average volume of the balls to obtain the number of the grade of aggregate particles, and the radius of the balls is half of the average value of the upper limit and the lower. The key to reflecting the grading is therefore to calculate the volume fraction of aggregate per grade, which is now deduced as follows:
assuming that the densities of the coarse and fine aggregates are all rhocDensity of asphalt is rholThe oilstone ratio is a, the designed porosity is VV, and the volume of the cylindrical test piece is V ═ pi d2h/4, wherein d is the diameter and h is the height. And the volume of the asphalt is set as VlVolume of coarse aggregate is VcVolume of fine aggregate is VxAnd the passing rate of the aggregate is shown in the table 1, and the volume percentage of the aggregate and the asphalt mortar in each grade in the asphalt mixture test piece is calculated.
TABLE 1 passage of each grade of aggregate
According to the oil-stone ratio calculation formula, namely:
ml、mc、mxthe method comprises the following steps: asphalt mass, coarse aggregate mass, fine aggregate mass. The oilstone ratio is the ratio of the mass of bitumen to the mass of aggregate.
The contents of asphalt in the obtained numerical test pieces were as follows:
according to the volume composition of the whole test piece, the following components are provided:
V(1-VV)＝Vl+Vc+Vx(9)
by bringing formula (8) into formula (9), it is possible to obtain:
according to the gradation passage table, it can be obtained:
and because the densities are equal, then:
the substitution of formula (12) for formula (10) includes:
the volume fraction formula of the test piece with each grade of aggregate occupation value can be obtained by combining the gradation passing rate table as follows:
thus, the following equations (10) and (14) yield:
further, the density parameter ρ of the asphalt mortar can be derived from the formulas (7) and (9)s：
And bringing formula (8) into formula (16) to:
the AC-13 mixture gradation is calculated by taking the AC-13 standard gradation median as shown in Table 2, and the asphalt density is 1.03, the aggregate density is 2.7, the oilstone ratio is 5 percent, and the porosity is 4 percent. The cylindrical test piece had a diameter of 100mm and a height of 100 mm. According to the formula, the number of particles in each grade is calculated and is shown in table 3.
In the asphalt mixture, aggregates with different grain diameters are divided into different gears, the proportion of the total mass of each gear is different, thereby forming gradation, the number of the aggregate particles of each gear is determined, which is equivalent to determining the proportion of the aggregate particles, thereby obtaining the number of gradation units.
TABLE 2 AC-13 mixture gradation
TABLE 3 calculation of the number of AC-13 bituminous mixes
Step 2.2): and (3) putting the aggregates into a model according to the calculated number of the aggregates, as shown in figure 1, scanning each grade of particles and calculating a corresponding volume fraction, and finding that the volume fraction is consistent with an actual value, which indicates that the putting is correct. Step 2.3): the program is written, the grading sphere unit is scanned (namely all the particle units generated above are scanned), and then the information of each aggregate particle, namely the coordinate (x, y, z), the radius r and the like are extracted as the geometric parameters for generating the polygonal aggregate.
Step 2.4): the original particles are deleted, and the particles with smaller particle size are regularly filled in the region according to a certain sequence (the regular arrangement is horizontal and vertical, and one particle is arranged adjacent to 6 particles in the vertical, left, right, front and back directions), as shown in fig. 2.
Step 2.5): loading an irregular aggregate generation program, and carrying out grading check, wherein the grading check principle is that the percentage of all small spherical particles in each grade of aggregate accounts for the total particles of the whole model, and when the percentage of the particles is within a target percentage range (such as +/-5 percent and +/-10 percent), the required precision is met, otherwise, the grade of aggregate is regenerated by adjusting a cutting control coefficient until the requirement is met, and then the next grade of aggregate is regenerated. The resulting irregular aggregate model is shown in fig. 3.
Step 2.6): in order to generate a certain gap for the model, a random deletion method is adopted to randomly delete partial particles of the asphalt mortar so as to represent the gap of the mixture. If the porosity is VV, the number n _ del of the asphalt mortar particles to be removed is calculated by the formula (18).
n_del＝int(VV*n_total) (18)
In the formula: n _ total is the total number of small particles of the model.
By programming, a random number is generated in the maximum particle range of the model each time, whether the particle address with the number as the serial number is not an empty address and whether the particle is asphalt mortar is judged, if yes, the particle is deleted until n _ del particles are deleted, the distribution diagram of the gap is shown in fig. 4, and the cylindrical numerical model of the asphalt mixture is shown in fig. 5(A), fig. 5(B) and fig. 5 (C).
For example, if the total number of particles in the model is 48040 and the porosity is 4%, the number of particles n _ del to be deleted is 1921.
Claims (10)
1. A random generation method of a numerical model of an asphalt mixture is characterized by comprising the following steps:
1) randomly generating irregular polyhedral aggregate;
2) and generating a numerical model of the asphalt mixture by using the irregular polyhedron aggregate.
2. The method for randomly generating the numerical model of the asphalt mixture according to claim 1, wherein the specific implementation process of the step 1) comprises the following steps:
A) filling regularly arranged small-particle-size discrete units in the polyhedron;
B) generating a plurality of random planes to randomly cut a cube to obtain an irregular polyhedral area;
C) judging the centroid position of the small-particle-size discrete unit and the relative position of the polyhedral region obtained in the step B), and taking the small-particle-size discrete unit belonging to the interior of the polyhedral region as an irregular polyhedral aggregate part.
3. The method for randomly generating the numerical model of the asphalt mixture according to claim 2, wherein in the step A), the side length of the cube is equal to the grain size of the polyhedral aggregate; the mathematical equation for the cube is as follows:
<mrow> <mtable> <mtr> <mtd> <mrow> <mi>x</mi> <mo>-</mo> <mrow> <mo>(</mo> <msub> <mi>x</mi> <mn>0</mn> </msub> <mo>-</mo> <mi>R</mi> <mo>)</mo> </mrow> <mo>&GreaterEqual;</mo> <mn>0</mn> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mi>x</mi> <mo>-</mo> <mrow> <mo>(</mo> <msub> <mi>x</mi> <mn>0</mn> </msub> <mo>+</mo> <mi>R</mi> <mo>)</mo> </mrow> <mo>&le;</mo> <mn>0</mn> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mi>y</mi> <mo>-</mo> <mrow> <mo>(</mo> <msub> <mi>y</mi> <mn>0</mn> </msub> <mo>-</mo> <mi>R</mi> <mo>)</mo> </mrow> <mo>&GreaterEqual;</mo> <mn>0</mn> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mi>y</mi> <mo>-</mo> <mrow> <mo>(</mo> <msub> <mi>y</mi> <mn>0</mn> </msub> <mo>+</mo> <mi>R</mi> <mo>)</mo> </mrow> <mo>&le;</mo> <mn>0</mn> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mi>z</mi> <mo>-</mo> <mrow> <mo>(</mo> <msub> <mi>z</mi> <mn>0</mn> </msub> <mo>-</mo> <mi>R</mi> <mo>)</mo> </mrow> <mo>&GreaterEqual;</mo> <mn>0</mn> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mi>z</mi> <mo>-</mo> <mrow> <mo>(</mo> <msub> <mi>z</mi> <mn>0</mn> </msub> <mo>+</mo> <mi>R</mi> <mo>)</mo> </mrow> <mo>&le;</mo> <mn>0</mn> </mrow> </mtd> </mtr> </mtable> <mo>;</mo> </mrow>
wherein (x)0，y0，z0) Coordinates of a cube centroid O; 2R is the side length of a square; (x, y, z) is the coordinates of any point within the cube.
4. The method for randomly generating the numerical model of the asphalt mixture according to claim 3, wherein in the step B), the number of the random planes is 8; the specific implementation process of the step B) comprises the following steps:
a) randomly generating a normal vector (n) of each quadrant cutting planej1，nj2，nj3) J takes a value of 1-8; n isj1，nj2，nj3The calculation formula is as follows:
<mrow> <mtable> <mtr> <mtd> <mrow> <mi>&alpha;</mi> <mo>=</mo> <mi>u</mi> <mi>r</mi> <mi>a</mi> <mi>n</mi> <mi>d</mi> <mo>&times;</mo> <mfrac> <mi>&pi;</mi> <mn>2.0</mn> </mfrac> <mo>+</mo> <mrow> <mo>(</mo> <mi>j</mi> <mo>-</mo> <mn>1.0</mn> <mo>)</mo> </mrow> <mo>&times;</mo> <mfrac> <mi>&pi;</mi> <mn>2.0</mn> </mfrac> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mi>&beta;</mi> <mo>=</mo> <mi>u</mi> <mi>r</mi> <mi>a</mi> <mi>n</mi> <mi>d</mi> <mo>&times;</mo> <mfrac> <mi>&pi;</mi> <mn>2.0</mn> </mfrac> <mo>+</mo> <mrow> <mo>(</mo> <mi>int</mi> <mo>(</mo> <mrow> <mrow> <mo>(</mo> <mrow> <mi>j</mi> <mo>-</mo> <mn>1.0</mn> </mrow> <mo>)</mo> </mrow> <mo>/</mo> <mn>4.0</mn> </mrow> <mo>)</mo> <mo>)</mo> </mrow> <mo>&times;</mo> <mfrac> <mi>&pi;</mi> <mn>2.0</mn> </mfrac> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <msub> <mi>t</mi> <mn>1</mn> </msub> <mo>=</mo> <mi>cos</mi> <mrow> <mo>(</mo> <mi>&alpha;</mi> <mo>)</mo> </mrow> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <msub> <mi>t</mi> <mn>2</mn> </msub> <mo>=</mo> <mi>sin</mi> <mrow> <mo>(</mo> <mi>&alpha;</mi> <mo>)</mo> </mrow> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <msub> <mi>t</mi> <mn>3</mn> </msub> <mo>=</mo> <mi>cos</mi> <mrow> <mo>(</mo> <mi>&beta;</mi> <mo>)</mo> </mrow> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mi>t</mi> <mi>t</mi> <mo>=</mo> <msqrt> <mrow> <msubsup> <mi>t</mi> <mn>1</mn> <mn>2</mn> </msubsup> <mo>+</mo> <msubsup> <mi>t</mi> <mn>2</mn> <mn>2</mn> </msubsup> <mo>+</mo> <msubsup> <mi>t</mi> <mn>3</mn> <mn>2</mn> </msubsup> </mrow> </msqrt> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <msub> <mi>n</mi> <mrow> <mi>j</mi> <mn>1</mn> </mrow> </msub> <mo>=</mo> <msub> <mi>t</mi> <mn>1</mn> </msub> <mo>/</mo> <mi>t</mi> <mi>t</mi> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <msub> <mi>n</mi> <mrow> <mi>j</mi> <mn>2</mn> </mrow> </msub> <mo>=</mo> <msub> <mi>t</mi> <mn>2</mn> </msub> <mo>/</mo> <mi>t</mi> <mi>t</mi> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <msub> <mi>n</mi> <mrow> <mi>j</mi> <mn>3</mn> </mrow> </msub> <mo>=</mo> <msub> <mi>t</mi> <mn>3</mn> </msub> <mo>/</mo> <mi>t</mi> <mi>t</mi> </mrow> </mtd> </mtr> </mtable> <mo>;</mo> </mrow>
wherein, the urand is a random function, the value range is (0, 1), the int is an integer function, α is the included angle between a line of the space in the horizontal plane and the x axis, β is the included angle between a line of the space in the horizontal plane and the z axis, t1，t2，t3Is the cosine of the included angle between one line of the space and the coordinate axes of x, y and z;
b) solving the distance d from the centroid of the cube to the cutting plane: d ═ R × q; wherein q is a cutting control coefficient;
c) according to the distance d and the normal vector (n)j1，nj2，nj3) Obtaining the intersection point M of the vertical connecting line of the cubic centroid O and the cutting surfacec(xc，yc，zc) The coordinates of (a) are as follows:
<mrow> <mtable> <mtr> <mtd> <mrow> <msub> <mi>x</mi> <mi>c</mi> </msub> <mo>=</mo> <msub> <mi>x</mi> <mn>0</mn> </msub> <mo>+</mo> <mi>d</mi> <mo>&times;</mo> <msub> <mi>n</mi> <mrow> <mi>j</mi> <mn>1</mn> </mrow> </msub> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <msub> <mi>y</mi> <mi>c</mi> </msub> <mo>=</mo> <msub> <mi>y</mi> <mn>0</mn> </msub> <mo>+</mo> <mi>d</mi> <mo>&times;</mo> <msub> <mi>n</mi> <mrow> <mi>j</mi> <mn>2</mn> </mrow> </msub> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <msub> <mi>z</mi> <mi>c</mi> </msub> <mo>=</mo> <msub> <mi>z</mi> <mn>0</mn> </msub> <mo>+</mo> <mi>d</mi> <mo>&times;</mo> <msub> <mi>n</mi> <mrow> <mi>j</mi> <mn>3</mn> </mrow> </msub> </mrow> </mtd> </mtr> </mtable> <mo>;</mo> </mrow>
d) determining a random plane P using the following equationj：
Pj＝x×nj1+y×nj2+z×nj3-(xc×nj1+yc×nj2+zc×nj3)＝0；
e) Cutting the square body by using a random plane to obtain an irregular polyhedron region, wherein the mathematical equation of the irregular polyhedron region is as follows:
<mrow> <mtable> <mtr> <mtd> <mrow> <mi>x</mi> <mo>-</mo> <mrow> <mo>(</mo> <msub> <mi>x</mi> <mn>0</mn> </msub> <mo>-</mo> <mi>R</mi> <mo>)</mo> </mrow> <mo>&GreaterEqual;</mo> <mn>0</mn> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mi>x</mi> <mo>-</mo> <mrow> <mo>(</mo> <msub> <mi>x</mi> <mn>0</mn> </msub> <mo>+</mo> <mi>R</mi> <mo>)</mo> </mrow> <mo>&le;</mo> <mn>0</mn> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mi>y</mi> <mo>-</mo> <mrow> <mo>(</mo> <msub> <mi>y</mi> <mn>0</mn> </msub> <mo>-</mo> <mi>R</mi> <mo>)</mo> </mrow> <mo>&GreaterEqual;</mo> <mn>0</mn> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mi>y</mi> <mo>-</mo> <mrow> <mo>(</mo> <msub> <mi>y</mi> <mn>0</mn> </msub> <mo>+</mo> <mi>R</mi> <mo>)</mo> </mrow> <mo>&le;</mo> <mn>0</mn> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mi>z</mi> <mo>-</mo> <mrow> <mo>(</mo> <msub> <mi>z</mi> <mn>0</mn> </msub> <mo>-</mo> <mi>R</mi> <mo>)</mo> </mrow> <mo>&GreaterEqual;</mo> <mn>0</mn> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mi>z</mi> <mo>-</mo> <mrow> <mo>(</mo> <msub> <mi>z</mi> <mn>0</mn> </msub> <mo>+</mo> <mi>R</mi> <mo>)</mo> </mrow> <mo>&le;</mo> <mn>0</mn> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <msub> <mi>P</mi> <mi>j</mi> </msub> <mo>&le;</mo> <mn>0</mn> </mrow> </mtd> </mtr> </mtable> <mo>.</mo> </mrow>
5. the method for randomly generating the numerical model of the asphalt mixture according to claim 1, wherein the specific implementation process of the step 2) comprises the following steps:
I) determining the number of aggregate units of each grade of the mixture;
II) feeding graded parent particles according to the number of aggregate units in each grade;
III) reading and storing grading parent particle set information;
IV) deleting the graded parent particles to generate regularly arranged small particles;
v) generating an irregular aggregate model and carrying out grading inspection;
VI) generating gaps in the irregular aggregate model to obtain a numerical model of the asphalt mixture.
6. The method for randomly generating the numerical model of the bituminous mixture according to claim 5, wherein in step I), the number of aggregate particles of each grade is calculated by using the following formula, and the number of aggregate units of each grade is obtained according to the number of the aggregate particles of each grade:
<mrow> <msub> <mi>n</mi> <mi>i</mi> </msub> <mo>=</mo> <mrow> <mo>(</mo> <mi>V</mi> <mo>&times;</mo> <msub> <mi>J</mi> <mrow> <mi>D</mi> <mi>i</mi> </mrow> </msub> <mo>)</mo> </mrow> <mo>/</mo> <mrow> <mo>(</mo> <mfrac> <mn>4</mn> <mn>3</mn> </mfrac> <msubsup> <mi>&pi;r</mi> <mi>i</mi> <mn>3</mn> </msubsup> <mo>)</mo> </mrow> <mo>;</mo> </mrow>
wherein, V is pi d2h/4 is the volume of the cylinder model, d is the diameter of the bottom circle of the cylinder model; h is the height of the cylinder model;the percentage of the i-th aggregate in the total volume of the asphalt mixture test piece is shown; pDi-1、PDiThe passing rates of the aggregate of the i-1 th grade and the i-th grade are respectively; VV is the porosity; a is the oil-stone ratio; rhocThe density of coarse and fine aggregates; rholIs the density of the asphalt; r isi＝(Di-1+Di)/4，Di-1、DiThe screen sizes of the i-1 th gear and the i-th gear are respectively.
7. The method for randomly generating the numerical model of the asphalt mixture according to claim 5, wherein the specific implementation process of the step II) comprises the following steps: and (3) throwing the aggregate particles into the cylindrical model according to the number of the aggregate units of each grade, scanning the aggregate particles of each grade, calculating the volume fraction of the aggregate particles of each grade, and if the volume fraction is consistent with the actual volume fraction, correctly throwing.
8. The method for randomly generating a numerical model of an asphalt mixture according to claim 7, wherein in the step IV), after the grading mother particles are deleted, the aggregate particles with the particle size smaller than the minimum particle size of the coarse aggregate particles are arranged according to the following rules: all aggregate particles are ensured to be regularly arranged in the horizontal direction and the vertical direction, and each particle in the middle position is arranged adjacent to one particle in the upper, lower, left, right, front and back six directions.
9. The method for randomly generating the numerical model of the asphalt mixture according to claim 8, wherein in the step V), when the percentage of aggregate particles of each grade to the total particles of the whole cylinder model is within a percentage threshold value, the grading test is successful; otherwise, regenerating the grade of aggregate until the percentage of aggregate particles in the grade of aggregate to the total particles of the whole cylinder model is within the percentage threshold, and then generating the next grade of aggregate; finally obtaining the irregular aggregate model.
10. The method for randomly generating the numerical model of the asphalt mixture according to claim 5, wherein the specific implementation process of the step VI) is as follows: generating a random number in the maximum particle range of the irregular aggregate model, judging whether a particle address with the random number as a serial number is empty, if not, judging whether a particle with the random number as a serial number is asphalt mortar, if so, deleting the particle until n _ del particles are deleted, and obtaining an asphalt mixture numerical model; wherein:
n_del＝int(VV*n_total)；
in the formula: n _ total is the total number of particles of the irregular aggregate model; VV is the porosity.
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