CN113158454B - Grading random generation method of two-dimensional concrete aggregate - Google Patents
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Abstract
The invention relates to a random generation method of a multistage distribution two-dimensional concrete aggregate model. The method comprises the following steps of 1, determining a two-dimensional target area for feeding aggregate and the area of the target area; step 2, determining three-dimensional grading of aggregates, calculating the probability of aggregates with different grading on a two-dimensional distribution target area according to a Laval's formula, taking the aggregates with different grading as two-dimensional grading, and calculating the theoretical value of the area of each grade of distributed aggregates by combining the total area of the distribution target area determined in the step 1; and 3, in the target area, generating a geometric model which takes a random polygon meeting the two-dimensional grading requirement as an aggregate in a grading order from large to small. The method for generating the random polygonal concrete aggregate can ensure that the particle size of the aggregate is in a design grading range, and meanwhile, a geometric model of the concrete aggregate can be generated by grading according to theoretical calculation values of the contents of all grades of the graded aggregate, so that the difference between the contents of all grades of the graded aggregate and the theoretical calculation values is not more than 4%, and the graded accurate generation of the polygonal random aggregate can be realized.
Description
Technical Field
The invention relates to a two-dimensional random generation method of polygonal concrete aggregate, belonging to the technical field of mesoscopic numerical simulation pretreatment technology and building materials.
Technical Field
The concrete has the advantages of wide raw material source, low price, good durability and the like, and becomes a building material which is widely applied to engineering structures. The hardened concrete can be regarded as a three-phase composite material consisting of aggregate, cement mortar and an Interface (ITZ) between the aggregate and the cement mortar on a microscopic level. With the intensive research on the mechanical properties of concrete, the current research on the mechanical properties of concrete mainly focuses on two aspects, namely the relationship between the macroscopic mechanical properties of concrete and the properties of each microscopic phase medium, and the crack propagation form in the concrete destruction process. In order to study the influence of the mesoscopic components on the macroscopic mechanical properties of the concrete and accurately explore the crack propagation mode in the concrete damage process, it is necessary to begin with the study on the mechanical properties of the concrete from the mesoscopic mechanical model.
The concrete microscopic geometric model close to reality is a necessary premise for obtaining an accurate numerical simulation result, and the numerical result shows a certain difference due to different aggregate shapes, distribution modes and aggregate contents in the model. At present, the simulation of concrete aggregate mostly adopts a circle, an ellipse or a polygon, and the circle and the ellipse cannot reflect the complex characteristics of the concrete aggregate, so that the generation of a polygonal random aggregate model is very important for realizing the simulation of concrete mesoscopic numerical values. In addition, in most of the current concrete aggregate generation methods, only the total content of coarse aggregates is set, and the aggregate content of each gradation is not accurately controlled, so that the method cannot truly reflect the real characteristics of a concrete material with good gradation, the concrete aggregate gradation in a concrete microscopic numerical model is different from the actual concrete gradation, the accuracy of a numerical simulation result is further influenced, and the evaluation of the concrete structure strength and the judgment of instability conditions are influenced.
In summary, there is a need for a random aggregate generation method capable of grading and efficiently generating a concrete aggregate geometric model, so as to provide a more effective geometric model for mesoscopic numerical simulation of the failure process and mechanical mechanism of concrete with different grading requirements.
Disclosure of Invention
The invention aims to solve the problem that the existing numerical simulation technology cannot carry out step-by-step distribution generation on concrete aggregate, and provides a step-by-step distribution generation method of a two-dimensional concrete random aggregate geometric model. By using the method, the random polygonal aggregate can be ensured to meet the requirement of grading particle size. Meanwhile, a geometric model of the concrete aggregate can be prepared step by step according to the theoretical calculated value of the content of the aggregates in each level, so that the difference between the content of the aggregates in each level and the theoretical calculated value is not more than 4%, and the model can truly reflect the real characteristics of the well-graded concrete.
The purpose of the invention is realized by the following technical scheme.
A random generation method of two-dimensional concrete aggregate comprises the following steps:
step one, determining a two-dimensional target area for feeding aggregate and the area of the target area;
determining three-dimensional grading of aggregates, calculating the probability of the aggregates with different grading on a two-dimensional throwing target area according to a Laval formula, taking the aggregates as the two-dimensional grading of the aggregates, and calculating the theoretical value of the area of each grade of the aggregates by combining the total area of the throwing target area determined in the step 1;
step three, in the target area, according to the sequence of gradation from big to small, generating a random polygon meeting the two-dimensional gradation requirement as a geometric model of the aggregate in a stepwise manner;
step 3.1: generating a series of random circles with the particle size in the first-order matching range, and recording geometric information of all the random circles, including the coordinates and the radius of the circle center. The coordinates and the radius of the circle center are randomly generated by using a Martensine spiral algorithm (Mersenne Twister), and each circle is ensured not to be intersected with the boundary of the throwing area.
Step 3.2: the positional relationship of each random circle generated in step 3.1 is determined. The judging method comprises the following steps: when the distance between the centers of the two circles is smaller than the sum of the radii, judging that the positions of the two circles are overlapped, deleting the circle generated later in time sequence, and keeping the circle generated first;
step 3.3: randomly selecting points on the circumference of each random circle obtained in the step 3.2, sequentially connecting the points to form line segments with random lengths, and cutting each random circle into random polygons;
step 3.4: verification of aggregate content
Introducing the information of the random line segments obtained in the step 3.3 into AutoCAD, calculating the area of the graded aggregate, comparing the area with the theoretical value of the area obtained in the step two, and if the difference of the area fractions is not more than 4%, generating the next grade of the graded aggregate;
step 3.5: and generating the next grade of aggregate.
And 3.1 and 3.2 are repeated to generate next-level aggregate, the position relation between the random circle generated at this time and the random circle generated in the previous-level aggregate is calculated according to the method in 3.2, and the circle with the position overlapped with the random circle generated in the previous-level aggregate in the random circles generated in the current-level aggregate is deleted. And (5) repeating the step 3.3 and the step 3.4 to generate a random polygon meeting the grading requirement.
Step 3.6: and repeating the steps until all graded aggregate geometric models are generated.
Advantageous effects
1) Compared with the prior art, the invention can realize the continuous feeding of the multi-level aggregate, ensure that the aggregate content of each level is basically consistent with the theoretical calculated value, and realize the accurate generation of the grading of the aggregate content.
2) The invention controls the shape of the polygon without influencing the grain diameter by changing the random point number generated on the circumference, and has strong use value.
3) According to the two-dimensional concrete aggregate grading random generation method, the generation method of the aggregate geometric model is based on the EXCEL platform, the measurement of the aggregate content is based on AUTOCAD, and the related software is simple and has the advantage of convenience and rapidness in operation.
Drawings
FIG. 1 is a flow chart of a method for generating the geometric shape of an aggregate according to the present invention;
FIG. 2 is a diagram of the process of generating random polygonal aggregate and corresponding discrete meta-model according to the present invention,
FIG. 3 shows a random polygonal aggregate geometric model (random polygon) and an aggregate placement area (random polygonal peripheral circle) in example 1 of the present invention;
FIG. 4 shows a random polygonal aggregate geometric model (random polygon) and an aggregate placing region (random polygon peripheral square) in example 2;
wherein, a is a random circle and a grain diameter calibration point, b is the limit positions of four calibration points of an upper semicircle, c is the end point of a random line segment generated randomly, d is the geometric shape of a random polygon generated, e is all aggregate geometric models (three random polygons) of a first-level aggregate (16mm-20mm) and an aggregate putting region (a random polygon outer dimension circle)
Detailed Description
For better illustrating the objects and advantages of the present invention, the following description is provided in conjunction with the accompanying drawings and examples.
Example 1
Example 1 random aggregate geometry model for concrete Brazilian discs
Step one, determining a two-dimensional target area for feeding aggregate and the area of the target area
In this embodiment, the target placement area is a circle, the radius R is 75mm, and the area of the target area is 17671.46mm2。
And step two, determining three-dimensional grading of aggregates, calculating the probability of the aggregates with different grades appearing on a two-dimensional throwing target area according to a Laval formula, taking the aggregates as the two-dimensional grading of the aggregates, and calculating the theoretical value of the area of each grade of the aggregates by combining the total area of the throwing target area determined in the step one.
In this embodiment, a polygon is constructed only for aggregates graded into three grades of 5mm to 10mm, 10mm to 16mm, and 16mm to 20mm in particle size, and aggregates having a particle size of 5mm or less are regarded as a cement mortar matrix, and polygon generation is not performed.
The Laval formula is shown in formula (1):
in the formula: dmaxAt the maximum aggregate particle diameter, PKThe percentage of the aggregate (including coarse aggregate and fine aggregate) in the total volume of the concrete, D0The upper limit value, P, of the aggregate diameter for each gradecAnd (3) the probability of the aggregate distributed for each grade on a two-dimensional plane is the area fraction of the aggregate distributed for each grade in the total area of the distribution area. According to the formula (1), the theoretical values of the area fraction of each graded aggregate are respectively as follows: 3.83%, 12.72%, 16.21%, the theoretical area values are: 676.82mm2，2261.95mm2，2597.7mm2。
And step three, in the target area, generating a geometric model which takes a random polygon meeting two-dimensional grading requirements as aggregate in a grading order from large to small.
Firstly, generating a geometric model of the first-stage aggregate.
Step 3.1: generating random circles with the particle size within the first-level matching range, and recording geometric information of all the random circles, including the coordinates and the radius of the circle center. The coordinates and the radius of the circle center are randomly generated by using a Martensine spiral algorithm (Mersenne Twister), and each circle is ensured not to be intersected with the boundary of the throwing area.
In the examples, the aggregate radius is indicated by r and is between 8 and 10 mm. Using a Matt spiral algorithm, a set of random numbers x is generatediAnd the distance between the abscissa of the circle center and the boundary is larger than the radius of the circle in order to prevent the aggregate from intersecting the boundary of the throwing area. Center of circle ordinate yiAnd determining according to the shape of the target throwing area.
In the examples, xiIs a random number with an absolute value between [0, R-R) ], xiThe value is assigned randomly. Circular ordinate yiIs between
Random number between, yiThe positive and negative values are also randomly assigned.
Step 3.2: the positional relationship of each random circle generated in step 3.1 is determined. The judging method comprises the following steps: when the distance between the centers of the two circles is smaller than the sum of the radii, the positions of the two circles are judged to be overlapped, the circles generated later in the time sequence are deleted, and the circles generated earlier are reserved.
Let the radius of the circle be r1The center coordinate is (x)1,y1) (ii) a Radius of the circle being r2The center coordinate is (x)2,y2). And (3) when the two circles satisfy the formula (2), judging that the two circles do not coincide with each other, and if not, deleting the circle generated after deleting.
Step 3.3: and (3) randomly selecting points on the circumference of each random circle obtained in the step (3.2), sequentially connecting the points to form line segments with random lengths, and cutting each random circle into random polygons.
And (3) taking two end points of the diameter parallel to the horizontal axis of the macroscopic coordinate system on the circle reserved in the step (3.2) as particle size calibration points for calibrating the size of the aggregate, and simultaneously recording the coordinates of the two points. The aggregate is divided into an upper part and a lower part by taking the diameter as a dividing line. Respectively randomly generating n1And n21-100 random numbers are respectively calculated, the proportion of each random number in the group of random numbers is respectively calculated, and the upper and lower semi-circles are respectively divided into n according to the proportion1And n2And calculating the central angle corresponding to each sector. Repeatedly generating n again within the numerical range of each central angle of the upper and lower semicircles without repetition1And n2Calculating points corresponding to the central angle on the circumference according to the random number (i.e. a random central angle value) generated at the moment, sequentially connecting the points with the particle size calibration points, and respectively obtaining (n) at the upper and lower semi-circles1+1) and (n)2+1) line segments, by means of which the circle can be divided into random polygons.
In the embodiment, a geometric model generation process of one aggregate is selected for detailed description. As shown in FIG. 2-a, the index point is P1And P2Nominal diameter of l1In 1 with1For boundary, the circle is divided into an upper semicircle S and a lower semicircle S1And S2The number of sides of the polygon is determined by the number of random points selected in the upper and lower semi-circles. Taking the generation process of the semicircular random points on the aggregate as an example:
as shown in fig. 2-b, n is scaled using the mott-screw algorithm1The value is set to 4, four random numbers [2,75,1,43 ] between 1-100 are generated]Each random number is in a proportion of [0.0165,0.6198,0.0083,0.3554 ] to the sum of the random numbers in the group]. According to the proportion, the upper semicircle is divided, and the following can be obtained:
wherein P isU4' position and index point P2And (4) overlapping. The positions of the four points at this time are the extreme positions of the desired random points. At (0,0.0165 pi)]，(0.0165π,0.6363π]，(0.6363π,0.6446π]，(0.6446π,π]Random numbers are generated to obtain a group of random circle center angle values. As shown in FIG. 2-c, the corresponding point on the circumference of each central angle is PU1，PU2，PU3，PU4Each is between P1And PU1′，PU1' and PU2′，PU2' and PU3′，PU3' and PU4' in the meantime. Then P isU1，PU2，PU3，PU4The coordinate values of (c) can be obtained by the following formula:
wherein (x)0,y0) α represents a central angle as a position coordinate of the aggregate. By calculation, PU1，PU2，PU3，PU4Are (28.529,27.748), (27.389,31.711), (16.011,35.280), (11.840, 31.066); index point P1And P2The coordinates of (2) are (28.537,27.378), (11.026,27.378), respectively. The points, which are the end points of the random line segment for cutting the upper semicircle, are sequentially connected with P1，PU1，PU2，PU3，PU4，PU5，P2And obtaining each random line segment for cutting the upper semicircle.
The same calculation method is adopted for the lower semicircle, and the coordinates of the random point can be obtained. After obtaining the coordinates of all the random points and the calibration points, a geometric model of the polygon can be drawn in AUTOCAD, as shown in FIG. 2-c, where the random points determined on the lower semi-circle are PL1,PL2,PL3,PL4,PL5. Connect P in order2，PL1，PL2,PL3,PL4,PL5，P1Thus, random line segments cutting the lower semicircle can be obtained, and through the above steps, the actual shape of the obtained aggregate is shown in fig. 2-d.
Step 3.4: and verifying the content of the aggregate. And (3) introducing the information of all the random line segments obtained in the step (3.3) into AutoCAD, calculating the area of the graded aggregate, comparing the area with the theoretical value of the area obtained in the step (2), and if the difference of the area fractions is not more than 4%, generating the next grade of the graded aggregate.
The aggregate of the first gradation (particle size of 16-20mm) has a total area of 684.5472mm2The proportion of the area of the circular feeding area is 3.87%, the theoretical proportion of the area of the circular feeding area is 3.83%, and the difference is 0.04%, which indicates that the random aggregates generated in the particle size range of 16-20mm meet the requirements, and the geometric shapes of the three aggregates and the feeding area are shown in figure 2-e.
Step 3.5: and generating the next grade of aggregate. And 3.1 and 3.2 are repeated to generate next-level aggregate, the position relation between the random circle generated at this time and the random circle generated in the previous-level aggregate is calculated according to the method in 3.2, and the circle with the position overlapped with the random circle generated in the previous-level aggregate in the random circle generated in the current-level aggregate is deleted. And (5) repeating the step 3.3 and the step 3.4 to generate a random polygon meeting the grading requirement.
Step 3.6: and repeating the steps until the generation of the geometric models of all graded aggregates is finished.
The two-dimensional random aggregate geometric model for concrete Brazilian splitting mesoscopic numerical simulation obtained by the concrete aggregate step-by-step distribution generation method is shown in figure 3. The area fractions of the aggregates of the actually produced three grades (16-20mm,10-16mm,5-10mm) were 3.86%, 12.76%, and 12.44%, respectively, and the theoretical results were 3.83%, 12.72%, and 16.21%, respectively, with errors of 0.03%, 0.04%, and 3.77%, respectively, as compared with the theoretical results.
Example 2:
example 2 is a two-dimensional random aggregate geometry model for concrete uniaxial compression mesoscopic simulation. The aggregate feeding area is a square with the size of 100mm multiplied by 100mm, the aggregates are fed in a single-stage distribution mode, and the particle sizes of the coarse aggregates are respectively 5-10 mm. The final two-dimensional random aggregate geometric model obtained by the invention is shown in figure 4. The area fractions of the aggregates were 16.9% respectively, and the theoretical calculation results were 16.6% respectively. The errors are respectively 0.3%.
The method can set any gradation according to requirements, and generate the required concrete aggregate geometric model according to the theoretical content of aggregates of all levels.
The above detailed description is intended to illustrate the objects, aspects and advantages of the present invention, and it should be understood that the above detailed description is only exemplary of the present invention and is not intended to limit the scope of the present invention, and any modifications, equivalents, improvements and the like made within the spirit and principle of the present invention should be included in the scope of the present invention.
Claims (3)
1. A random generation method for grading of two-dimensional concrete aggregate is characterized by comprising the following steps: the method comprises the following steps:
step 1, determining a two-dimensional target area for feeding aggregate and the area of the target area
Step 2, determining three-dimensional grading of aggregates, calculating the probability of aggregates with different grading on a two-dimensional distribution target area according to a Laval's formula, taking the aggregates with different grading as two-dimensional grading, and calculating the theoretical value of the area of each grade of distributed aggregates by combining the total area of the distribution target area determined in the step 1;
step 3, in the target area, generating a geometric model which takes a random polygon meeting two-dimensional grading requirements as aggregate in a grading sequence from large to small;
the method comprises the following specific steps:
step 3.1: generating a series of random circles with the particle sizes within a first-level matching range, recording geometric information of all the random circles, wherein the geometric information comprises circle center coordinates and radiuses, the circle center coordinates and the radiuses are randomly generated by using a Marsen spiral algorithm (Mersenne Twister), and each circle is ensured not to intersect with the boundary of a throwing area;
step 3.2: and (3) judging the position relation of each random circle generated in the step (3.1), wherein the judging method comprises the following steps: when the distance between the centers of the two circles is smaller than the sum of the radii, judging that the positions of the two circles are overlapped, deleting the circle generated later in time sequence, and keeping the circle generated first;
step 3.3: randomly selecting points on the circumference of each random circle obtained in the step 3.2, sequentially connecting the points to form line segments with random lengths, and cutting each random circle into random polygons;
step 3.4: verification of aggregate content
Introducing the information of all the random line segments obtained in the step 3.3 into AutoCAD, calculating the area of the graded aggregate, comparing the area with the theoretical value of the area obtained in the step 2, and if the difference of the area fractions is not more than 4%, generating the next grade of the graded aggregate;
step 3.5: generating the next grade of aggregate
Repeating the steps 3.1 and 3.2 to generate next-level aggregate, calculating the position relation between the random circle generated at this time and the random circle generated in the previous-level aggregate according to the method in the step 3.2, and deleting the circle which has position overlapping with the random circle generated in the previous-level aggregate from the random circles generated in the current-level aggregate; repeating the steps 3.3 and 3.4 to generate a random polygon meeting the current-level configuration requirement;
step 3.6: and repeating the steps until all graded aggregate geometric models are generated.
2. The method of claim 1 for randomly generating a gradation of a two-dimensional concrete aggregate, wherein: the random polygon generation method in the step 3.3 is to calibrate the particle size of the aggregate by using the diameter of a random circle, select two points on the circle diameter as particle size calibration points on the circumference for calibrating the particle size of the aggregate, and divide the circle into an upper semicircle and a lower semicircle by using the diameter as a boundary line; using the Matt's spiral algorithm in EXCEL to randomly generate n1 and n2 random numbers between 0-100, and respectively calculating the proportion of each random number in the group of random numbers, and according to the proportion, dividing the upper and lower semi-circles into n1And n2A random sector, each sector being calculatedA corresponding central angle; repeatedly generating n again within the numerical range of each central angle of the upper and lower semicircles without repetition1And n2Calculating points corresponding to the central angle on the circumference according to the random numbers generated at the moment, and sequentially connecting the points with the particle size calibration points to respectively obtain (n)1+1) and (n)2+1) line segments, which can divide the circle into random polygons, and by changing n1 and n2, the shape of the aggregate can be controlled, but the value of the line segments does not affect the particle size of the aggregate; and generating geometric models of all the random polygonal aggregates in each gradation synchronously.
3. A method of randomly generating gradation of a two-dimensional concrete aggregate as claimed in claim 1, wherein: the method for calculating the aggregate area of a certain grading polygon in the step 3.4 is to import the geometric information of the random line segments generated in the EXCEL into the AutoCAD in batches, generate the geometric figure of the random polygon in the AutoCAD software, close all polygons by using a region command, combine all polygons into a whole by using an union command, and finally calculate the total area of the current grading aggregate by using an area command.
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