CN116451305A - Coarse aggregate geometric modeling method based on real concrete bridge - Google Patents
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Abstract
A coarse aggregate geometric modeling method based on a real concrete bridge relates to an aggregate modeling method. Sampling a real concrete bridge drill core, establishing a test piece frame based on the obtained real distribution characteristics of concrete core sample aggregates, firstly randomly generating a radius and a center position inside to complete generation and throwing of round aggregates, judging interference conditions, then generating random polygonal aggregates based on the round aggregates, judging interference conditions, judging whether to stop generation according to the volume content, and finally judging whether to match with the real coarse aggregates. The shape parameters of the real concrete coarse aggregate are considered, the random polygonal aggregate generated by using a random algorithm has high fitness, and the distribution characteristics of the coarse aggregate in the concrete can be more accurately simulated.
Description
Technical Field
The invention relates to an aggregate modeling method, in particular to a coarse aggregate geometric modeling method based on a real concrete bridge, and belongs to the technical field of bridge engineering material performance analysis.
Background
The bridge is an important component in modern traffic infrastructure networks, and the service performance plays an important role in economic development and social progress of countries and regions. The concrete structure is widely applied to middle and small bridge construction in China by virtue of excellent spanning performance and relatively low construction cost. With the extension of the service time, particularly in severe environments such as cold areas, a large number of concrete bridges have durability problems, if the service performance of the concrete bridges is not evaluated accurately in time, once accidents such as bridge damage and collapse occur, huge life and property loss and severe social influence can be caused.
At present, researchers generally consider concrete as a composite heterogeneous material consisting of coarse aggregate, cement mortar and an interface transition zone. The coarse aggregate is taken as an important component, and the characteristics of volume fraction, shape, particle size distribution and the like of the coarse aggregate have great influence on the strength of the concrete and ion erosion. When the external erosion substances are transported in the concrete, the coarse aggregate can generate a tortuosity effect and an interface area effect on the coarse aggregate to prevent the substances from diffusing. Therefore, the accurate modeling of the coarse aggregate is an important precondition for researching the mechanical property and the durability of the concrete.
The modeling method for concrete coarse aggregate is mainly divided into two types at present: (1) The image processing method is that a concrete internal real structure image is obtained through means such as industrial CT scanning and the like, and a concrete aggregate model is built based on a 2D or 3D imaging technology; (2) The parameterized modeling method is that aggregates which are randomly distributed are generated in a specified space range according to the shape, grading, volume rate and other parameters of coarse aggregates in the concrete, and a concrete microstructure model is built. The parameterized modeling method mainly takes the idea of generation-throwing as a main principle, firstly, aggregates with random shapes and particle sizes are generated, and then the aggregates are randomly thrown into a designated area. The existing models mainly build coarse aggregate into circles, ellipses, polygons and other irregular shapes, have good effects when simulating pebbles, but simplify the shapes when simulating gravels, so that the simulated coarse aggregate has great errors on the blocking effect and the real effect of substance transmission. Therefore, a random model which is matched with the parameters of the real concrete coarse aggregate in shape, grading, volume rate and the like is established, and the method has important significance for researching the mechanical property and the durability of the real concrete bridge.
Disclosure of Invention
In order to solve the defects in the background art, the invention provides a coarse aggregate geometric modeling method based on a real concrete bridge, which considers the shape parameters of the real concrete coarse aggregate, and has the advantages that the random polygonal aggregate generated by using a random algorithm has high anastomosis degree, and the distribution characteristics of the coarse aggregate in the concrete can be more accurately simulated.
In order to achieve the above purpose, the invention adopts the following technical scheme: a coarse aggregate geometric modeling method based on a real concrete bridge comprises the following steps:
step one: sampling a real concrete bridge Liang Zuanxin to obtain a concrete core sample, acquiring a tomographic image of the concrete core sample, introducing the tomographic image into CAD, drawing the edge of coarse aggregate by using a Line command, calculating the area S and the perimeter C, and calculating the circularity e real ：
e real ＝4πS/C 2
Finally, the volume fraction alpha of coarse aggregate with various grain sizes in the same fault in the whole concrete is further calculated real And the average E of the circularity of all coarse aggregates real And standard deviation std real ；
Step two: establishing a test piece frame according to the fault size of the concrete core sample, randomly generating a radius R and a center coordinate (x, y) of the round aggregate in the test piece frame, judging whether interference occurs between the round aggregates, regenerating if interference occurs, storing and outputting the current round aggregate if interference does not occur, and finishing generation and throwing of the round aggregate;
step three: determining the edge number of random polygonal aggregate according to the actually drawn coarse aggregate shape, generating a random rotation angle and a random radius, generating random polygonal aggregate on the basis of round aggregate, and judging whether interference occurs among the random polygonal aggregate
S3.1, respectively generating the edge number n and the kth random radius r of the random polygonal aggregate by using Python language k The Python language function used is as follows:
n＝random.randrange(n min ,n max ,1)
r k ＝R×np.random.uniform(μ 1 ,μ 2 )
wherein n is min Representing the minimum value of the edge number of the random polygonal aggregate, n max Represents the maximum value, mu, of the edge number of the random polygonal aggregate 1 Represents the smallest multiple of variation, mu, of the random radius 2 Representing the maximum multiple of the change in the random radius,
before generating the random rotation angle, the random rotation angle range [ theta ] is required to be formulated min ,θ max ]The kth random rotation angle theta of the random polygonal aggregate k Calculated by the following formula:
θ k ＝θ min +np.random.uniform(β min ,β max )
β min ＝360-θ min ×n-(n-k+1)×(θ max -θ min )-(θ 1 +…+θ k-1 )
β max ＝360-θ min ×n-(θ 1 +…+θ k-1 )
wherein beta is min Generating a lower value of the random rotation angle for the np.random.uniform function, β max Generating an upper limit value of a random rotation angle for the np.
S3.2, calculating the coordinates of each vertex of the random polygonal aggregate, sequentially connecting the vertices to form a closed polygon, and according to the generated random rotation angle and the random radius, calculating the kth vertex coordinate (x k ，y k ) The calculation formula of (2) is as follows:
wherein x and y are the horizontal and vertical coordinates of the circle center of the round aggregate respectively;
s3.3, judging whether interference occurs between random polygonal aggregate, judging whether line segments of the random polygonal aggregate are intersected through a calculation method of a straddling experiment, deleting newly generated random polygonal aggregate for regeneration if the line segments are intersected, and storing vertex coordinates of the current random polygonal aggregate if the line segments are not intersected;
step four: the random polygonal aggregate is formed by splicing a plurality of triangles, and the area formula of the kth triangle is calculated as follows:
the area calculation formula of the random polygonal aggregate is:
setting an allowable error value error of aggregate content 1 Calculating the volume fraction alpha of the random polygonal aggregate occupying the test piece frame while newly generating the random polygonal aggregate theo If the volume fraction alpha of the coarse aggregate is equal to the volume fraction alpha of the real coarse aggregate real The deviation is within the allowable range, namely:
(α theo -α real )/α real ≤error 1
the generation of random polygonal aggregate is stopped,
setting the average E of circularity of the generated random polygonal aggregate theo And standard deviation std theo Error allowable value error of (2) 2 At the same time calculate the average E of circularity of random polygonal aggregate theo And standard deviation std theo If the average value E of the circularity of the true coarse aggregate real And standard deviation std real The deviation is within the allowable range, namely:
(E theo -E real )/E real ≤error 2
(std theo -std real )/std real ≤error 2
the generated random polygonal aggregate meets the requirement, otherwise, the random rotation angle and the random radius range are adjusted to regenerate the random polygonal aggregate,
and finally, outputting the vertex coordinates of all the random polygonal aggregates to obtain the random geometric model based on the true coarse aggregates.
Compared with the prior art, the invention has the beneficial effects that: at present, a concrete coarse aggregate random model established based on a parameter method generally uses regular patterns such as circles, ellipses, polygons and the like, which have larger differences from the actual shape of coarse aggregates, even when the model is established by adopting irregular polygons, a comparison relation with the actual shape parameters of the coarse aggregates is not established, and whether the established model is consistent with a real structure cannot be verified.
Drawings
Part a of fig. 1 is a schematic diagram of the invention for creating a test piece frame and randomly generating round aggregate;
part b of fig. 1 is a schematic diagram of interference between randomly generated round aggregates in the invention;
part c of fig. 1 is a schematic diagram of the random generation of round aggregates without interference in the invention;
FIG. 2 is a schematic diagram of the process of converting round aggregate into random polygonal aggregate in the present invention;
FIG. 3 is a schematic view of the partial interference between polygonal aggregates in the present invention;
part b of fig. 3 is a schematic diagram of the complete interference between polygonal aggregates in the present invention;
FIG. 4 a is a schematic diagram showing the intersection of line segment AB and line segment CD in the random polygonal aggregate interference judgment of the present invention;
fig. 4 b is a schematic diagram of a line segment CD crossing line segment AB in the random polygonal aggregate interference determination according to the present invention;
fig. 4 c is a schematic diagram of a line segment AB crossing a line segment CD in the random polygonal aggregate interference judgment according to the present invention;
FIG. 5 is a schematic diagram of the area calculation principle of the random polygonal aggregate in the invention;
FIG. 6 is a schematic cross-sectional view of a subject in an example;
FIG. 7 is a tomographic image of coarse aggregate in a CAD-drawn concrete core sample in an example;
fig. 8 is a random geometric model based on true coarse aggregate generated by the example.
Detailed Description
The technical solutions of the present invention will be clearly and completely described below with reference to the accompanying drawings in the embodiments of the present invention, and it is apparent that the described embodiments are only some embodiments of the invention, but not all embodiments, and all other embodiments obtained by those skilled in the art without making creative efforts based on the embodiments of the present invention are all within the protection scope of the present invention.
As shown in fig. 1 to 5, the coarse aggregate geometric modeling method based on the real concrete bridge comprises the following steps:
step one: sampling a real concrete bridge Liang Zuanxin, obtaining the real distribution condition of concrete core-like aggregates, drawing the edges of coarse aggregates and calculating the shape parameters of the coarse aggregates
According to the technical standard of concrete structure field detection (GB/T50784-2013), carrying out field core drilling on a real concrete bridge to obtain a concrete core sample, and then obtaining a tomographic image of the concrete core sample, wherein a clear limit between coarse aggregate and cement mortar is ensured when the tomographic image is obtained. The tomographic image can be obtained by scanning a concrete core sample by adopting X-ray CT, and more than three images can be obtained by the same concrete core sample; in addition, the tomographic image can also be obtained by shooting the cut surface under the condition that coarse aggregate in the cut surface is ensured to be clearly visible by adopting a cutting machine to transversely cut the concrete core sample for a plurality of times. Then, the tomographic image of the concrete core sample is introduced into CAD, and the edge of the coarse aggregate is drawn by Line command and the area S and the circumference C are calculated to calculate the circularity e real ：
e real ＝4πS/C 2
Finally, the volume fraction alpha of coarse aggregate with various grain sizes in the same fault in the whole concrete is further calculated real And the average E of the circularity of all coarse aggregates real And standard deviation std real 。
Step two: establishing a test piece frame according to the fault size of the concrete core sample, randomly generating the radius and the center position of the round aggregate in the test piece frame, judging whether interference occurs among the round aggregates, and completing the generation and the throwing of the round aggregate
The round aggregate is used as the basis of the subsequent random polygonal aggregate, and the generation and the throwing of the round aggregate are specifically as follows:
s2.1, defining the length and width of the test piece frame as H and W respectively, referring to FIG. 1 (a), according to the volume fraction alpha obtained in the step one real Calculating the area of coarse aggregate with various grain sizes in the frame of the test piece as an original input parameter of the model;
s2.2, randomly generating circular aggregates with radius R and center coordinates (x, y) according to frame parameters of a test piece and coarse aggregate distribution of particle sizes of all levels, wherein an np.random.uniform function in a Python language is adopted in the process to generate random numbers which accord with uniform distribution in a numerical interval set by a user, and the radius R and the center coordinates (x, y) are generated according to the following commands in order to ensure that the generated circular aggregates can be successfully put into the frame of the test piece:
R＝np.random.uniform(D imin ,D imax )
x＝np.random.uniform(R,H-R)
y＝np.random.uniform(R,W-R)
wherein D is imin Is the minimum particle diameter of the ith grading aggregate, D imax The maximum grain diameter of the i-th graded aggregate;
s2.3, judging whether the newly generated round aggregate interferes with the generated round aggregate, if so, returning the newly generated round aggregate to the previous step, and randomly generating radius R and center coordinates (x, y) of the round aggregate again, if not, storing and outputting the radius R and center coordinates (x, y) of the current round aggregate, and if so, judging the calculation formula of the interference is as follows:
wherein x is n 、y n Respectively the abscissa and the ordinate of the circle center and x of the newly generated round aggregate j 、y j Respectively the abscissa and the ordinate of the circle center of the generated round aggregate, r n 、r j Radius of the newly-formed round aggregate and radius of the generated round aggregate are respectively, and eta is an influence coefficient of the aggregate interference range.
Step three: determining the edge number of random polygonal aggregate according to the actually drawn coarse aggregate shape, generating a random rotation angle and a random radius, generating random polygonal aggregate on the basis of round aggregate, and judging whether interference occurs among the random polygonal aggregate
S3.1, respectively generating the edge number n and the kth random radius r of the random polygonal aggregate by using Python language k The Python language function used is as follows:
n＝random.randrange(n min ,n max ,1)
r k ＝R×np.random.uniform(μ 1 ,μ 2 )
wherein n is min Representing the minimum value of the edge number of the random polygonal aggregate, n max Represents the maximum value, mu, of the edge number of the random polygonal aggregate 1 Represents the smallest multiple of variation, mu, of the random radius 2 Representing the maximum fold change in random radius.
Before generating the random rotation angle, the random rotation angle range [ theta ] is required to be formulated min ,θ max ]The kth random rotation angle theta of the random polygonal aggregate k Calculated by the following formula:
θ k ＝θ min +np.random.uniform(β min ,β max )
β min ＝360-θ min ×n-(n-k+1)×(θ max -θ min )-(θ 1 +…+θ k-1 )
β max ＝360-θ min ×n-(θ 1 +…+θ k-1 )
wherein beta is min Generating a lower value of the random rotation angle for the np.random.uniform function, β max Generating an upper limit value of a random rotation angle for the np.
S3.2, calculating the coordinates of each vertex of the random polygon aggregate, and sequentially connecting the vertices to form a closed polygon, wherein the kth vertex coordinate (x k ，y k ) The calculation formula of (2) is as follows:
wherein x and y are the horizontal and vertical coordinates of the circle center of the round aggregate respectively;
s3.3, judging whether interference occurs between random polygonal aggregates, wherein the mode of mutual interference between the polygonal aggregates is divided into two modes: since the case of the complete interference (see fig. 3 (a)) and the case of the complete interference (see fig. 3 (b)) are eliminated when it is determined in S2.3 that the round aggregate is interfered, only the partial interference is determined in this step, and when the polygonal aggregate is partially interfered, the polygonal line segments are necessarily intersected with each other, as shown in fig. 4 (a).
Judging whether the segments of the random polygonal aggregate are intersected or not through a calculation method of the cross-over experiment, deleting newly generated random polygonal aggregate for regeneration if the segments are intersected, and storing the vertex coordinates of the current random polygonal aggregate if the segments are not intersected.
The principle of the straddling experiment is that one line segment is used as a standard, and if two end points of the second line segment are positioned at two ends of the first line segment, the second line segment is considered to straddle the first line segment. When two line segments cross each other, the two line segments intersect. At this time, the physical concept of vector multiplication is adopted, that is, for line segment AB and line segment CD, if:
(AB×AC)·(AB×AD)≤0
the directions of rotation of the vector AC and the vector AD with respect to the vector AB are different, that is, the line CD spans the line AB, as shown in fig. 4 (b), and the same applies if:
that is, it is considered that the line segment AB intersects with the line segment CD, as shown in FIGS. 4 (b) and 4 (c),
wherein AB, AC, AD, CD, CA, CB denotes a vector, ab= (x) B -x A ,y B -y A ) Other vector calculation methods and so on.
Step four: judging whether generation is stopped or not by the volume content of the random polygonal aggregate, and judging whether the random polygonal aggregate is matched with the real coarse aggregate or not by calculating the shape parameters of the random polygonal aggregate
S4.1, the random polygonal aggregate generated by the random rotation angle and the random radius can be regarded as being formed by splicing a plurality of triangles, and referring to FIG. 5, the area formula of the kth triangle is calculated as follows:
the area calculation formula of the random polygonal aggregate is:
s4.2, setting an allowable error value error of aggregate content 1 Calculating the volume fraction alpha of the random polygonal aggregate occupying the test piece frame while newly generating the random polygonal aggregate theo If the volume fraction alpha of the coarse aggregate is equal to the volume fraction alpha of the real coarse aggregate real The deviation is within the allowable range, namely:
(α theo -α real )/α real ≤error 1
stopping generating the random polygonal aggregate;
s4.3, setting the average value E of circularity of the generated random polygonal aggregate theo And standard deviation std theo Error allowable value error of (2) 2 At the same time calculate the average E of circularity of random polygonal aggregate theo And standard deviation std theo If the average value E of the circularity of the true coarse aggregate real And standard deviation std real The deviation is within the allowable range, namely:
(E theo -E real )/E real ≤error 2
(std theo -std real )/std real ≤error 2
and if the generated random polygonal aggregate meets the requirement, otherwise, adjusting the random rotation angle and the random radius range to regenerate the random polygonal aggregate.
And S4.4, outputting the vertex coordinates of all the random polygonal aggregates to obtain the random geometric model based on the true coarse aggregates.
Examples
In the embodiment, a half-retired prestressed concrete simple support beam is taken as a test object, specifically a half-bridge, the actual service life of the bridge is 27 years, the total length is 15.96m, the calculated span is 15.40m, the single beam width is 1.24m, the web thickness is 0.23m, the midspan section is shown by referring to FIG. 6, the concrete material grade is C40, the aggregate particle size is 5-20mm, the cement is ordinary silicate 42.5 cement, and the cement ratio is 0.45.
Step one: drilling cores at different positions within the full length range of the prestressed concrete simple support plate beam to obtain concrete core samples, scanning by adopting X-ray CT to obtain three tomographic images of the same concrete core sample, introducing the three tomographic images into the coarse aggregate drawn after CAD (computer aided design) and referring to FIG. 7, calculating the area S, the perimeter C and the circularity e of all the coarse aggregates real And the aggregate content of the three faults, and taking the average value of the geometric parameters of the coarse aggregate in the three faults to obtain the following results: volume fraction alpha real Mean value E of circularity of coarse aggregate of 29.3% real And standard deviation std real 0.647 and 0.130, respectively.
Step two: establishing a test piece frame parameter as H=W=90 mm, and generating circular aggregate and circle center coordinates in Python according to actual coarse aggregate particle size grading by the following commands:
R＝np.random.uniform(5,20)
x＝np.random.uniform(R,90-R)
y＝np.random.uniform(R,90-R)
the influence coefficient eta of the aggregate interference range is 1.05, and the generation and the throwing of the round aggregate are completed.
Step three: according to the drawing result of the actual coarse aggregate edge, taking the range of the edge number n of the random polygonal aggregate as [4,8], the variation multiple range of the random radius as [0.75,1.10], and the range of the random rotation angle as [10, 150], namely, the command of inputting parameters in the Python language is:
n＝random.randrange(4,8,1)
r k ＝R×np.random.uniform(0.75,1.10)
θ k ＝10+np.random.uniform(β min ,β max )
β min ＝360-10×n-(n-k+1)×140-(θ 1 +…+θ k-1 )
β max ＝360-10×n-(θ 1 +…+θ k-1 )
and calculating the coordinates of each vertex of the polygon, and judging whether the random polygon aggregate line segments are intersected or not through a straddling test.
Step four: setting an allowable error value error of aggregate content 1 1% of the volume fraction alpha of the newly formed random polygonal aggregate theo 29.2%, and within the error allowable range, stopping generating random polygonal aggregate at this time, and setting a mean value E of circularity of the generated random polygonal aggregate as shown in FIG. 8 as the finally obtained random geometric model theo And standard deviation std theo Error allowable value error of (2) 2 Calculating the average value E of the circularity of the random polygonal aggregate to be 3 percent theo And standard deviation std theo 0.66 and 0.132, respectively, are within the error allowable range, which shows that the random polygonal aggregate and the true concrete coarse aggregate generated by the embodiment have goodAnastomosis effect.
It will be evident to those skilled in the art that the invention is not limited to the details of the foregoing illustrative embodiments, and that the present invention may be embodied in other specific forms without departing from the spirit or essential characteristics thereof. The present embodiments are, therefore, to be considered in all respects as illustrative and not restrictive, the scope of the invention being indicated by the appended claims rather than by the foregoing description, and all changes which come within the meaning and range of equivalency of the claims are therefore intended to be embraced therein. Any reference sign in a claim should not be construed as limiting the claim concerned.
Furthermore, it should be understood that although the present disclosure describes embodiments, not every embodiment is provided with a separate embodiment, and that this description is provided for clarity only, and that the disclosure is not limited to the embodiments described in detail below, and that the embodiments described in the examples may be combined as appropriate to form other embodiments that will be apparent to those skilled in the art.
Claims (4)
1. A coarse aggregate geometric modeling method based on a real concrete bridge is characterized by comprising the following steps of: the method comprises the following steps:
step one: sampling a real concrete bridge Liang Zuanxin to obtain a concrete core sample, acquiring a tomographic image of the concrete core sample, introducing the tomographic image into CAD, drawing the edge of coarse aggregate by using a Line command, calculating the area S and the perimeter C, and calculating the circularity e real ：
e real ＝4πS/C 2
Finally, the volume fraction alpha of coarse aggregate with various grain sizes in the same fault in the whole concrete is further calculated real And the average E of the circularity of all coarse aggregates real And standard deviation std real ；
Step two: establishing a test piece frame according to the fault size of the concrete core sample, randomly generating a radius R and a center coordinate (x, y) of the round aggregate in the test piece frame, judging whether interference occurs between the round aggregates, regenerating if interference occurs, storing and outputting the current round aggregate if interference does not occur, and finishing generation and throwing of the round aggregate;
step three: determining the edge number of random polygonal aggregate according to the actually drawn coarse aggregate shape, generating a random rotation angle and a random radius, generating random polygonal aggregate on the basis of round aggregate, and judging whether interference occurs among the random polygonal aggregate
S3.1, respectively generating the edge number n and the kth random radius r of the random polygonal aggregate by using Python language k The Python language function used is as follows:
n＝random.randrange(n min ,n max ,1)
r k ＝R×np.random.uniform(μ 1 ,μ 2 )
wherein n is min Representing the minimum value of the edge number of the random polygonal aggregate, n max Represents the maximum value, mu, of the edge number of the random polygonal aggregate 1 Represents the smallest multiple of variation, mu, of the random radius 2 Representing the maximum multiple of the change in the random radius,
before generating the random rotation angle, the random rotation angle range [ theta ] is required to be formulated min ,θ max ]The kth random rotation angle theta of the random polygonal aggregate k Calculated by the following formula:
θ k ＝θ min +np.random.uniform(β min ,β max )
β min ＝360-θ min ×n-(n-k+1)×(θ max -θ min )-(θ 1 +…+θ k-1 )
β max ＝360-θ min ×n-(θ 1 +…+θ k-1 )
wherein beta is min Generating a lower value of the random rotation angle for the np.random.uniform function, β max Generating an upper limit value of a random rotation angle for the np.
S3.2, calculating the coordinates of each vertex of the random polygonal aggregate, sequentially connecting the vertices to form a closed polygon, and generating a random rotation angle according to the generated random rotation angleAnd a random radius, a kth vertex coordinate (x k ，y k ) The calculation formula of (2) is as follows:
wherein x and y are the horizontal and vertical coordinates of the circle center of the round aggregate respectively;
s3.3, judging whether interference occurs between random polygonal aggregate, judging whether line segments of the random polygonal aggregate are intersected through a calculation method of a straddling experiment, deleting newly generated random polygonal aggregate for regeneration if the line segments are intersected, and storing vertex coordinates of the current random polygonal aggregate if the line segments are not intersected;
step four: the random polygonal aggregate is formed by splicing a plurality of triangles, and the area formula of the kth triangle is calculated as follows:
the area calculation formula of the random polygonal aggregate is:
setting an allowable error value error of aggregate content 1 Calculating the volume fraction alpha of the random polygonal aggregate occupying the test piece frame while newly generating the random polygonal aggregate theo If the volume fraction alpha of the coarse aggregate is equal to the volume fraction alpha of the real coarse aggregate real The deviation is within the allowable range, namely:
(α theo -α real )/α real ≤error 1
the generation of random polygonal aggregate is stopped,
setting the average E of circularity of the generated random polygonal aggregate theo And standard deviation std theo Error allowable value error of (2) 2 Simultaneous calculation of the follow-upMean value E of circularity of polygonal aggregate theo And standard deviation std theo If the average value E of the circularity of the true coarse aggregate real And standard deviation std real The deviation is within the allowable range, namely:
(E theo -E real )/E real ≤error 2
(std theo -std real )/std real ≤error 2
the generated random polygonal aggregate meets the requirement, otherwise, the random rotation angle and the random radius range are adjusted to regenerate the random polygonal aggregate,
and finally, outputting the vertex coordinates of all the random polygonal aggregates to obtain the random geometric model based on the true coarse aggregates.
2. The coarse aggregate geometric modeling method based on the real concrete bridge, according to claim 1, is characterized in that: and in the first step, the interruption layer image is obtained by scanning a concrete core sample by adopting X-ray CT, and more than three images are obtained by the same concrete core sample.
3. The coarse aggregate geometric modeling method based on the real concrete bridge, according to claim 1, is characterized in that: the second step specifically comprises the following steps:
s2.1, defining the length and the width of a test piece frame as H and W respectively, and according to the volume fraction alpha obtained in the step one real Calculating the area of coarse aggregate with various grain sizes in the frame of the test piece as an original input parameter of the model;
s2.2, randomly generating circular aggregates with radius R and center coordinates (x, y) according to frame parameters of a test piece and coarse aggregate distribution of particle sizes of all levels, wherein an np.random.uniform function in a Python language is adopted in the process to generate random numbers which accord with uniform distribution in a numerical interval set by a user, and the radius R and the center coordinates (x, y) are generated according to the following commands:
R＝np.random.uniform(D imin ,D imax )
x＝np.random.uniform(R,H-R)
y＝np.random.uniform(R,W-R)
wherein D is imin Is the minimum particle diameter of the ith grading aggregate, D imax The maximum grain diameter of the i-th graded aggregate;
s2.3, judging whether the newly generated round aggregate interferes with the generated round aggregate, if so, deleting the newly generated round aggregate, returning to the previous step, randomly generating radius R and center coordinates (x, y) of the round aggregate again, and if not, storing and outputting the radius R and center coordinates (x, y) of the current round aggregate.
4. A method for modeling coarse aggregate geometry based on a real concrete bridge according to claim 3, characterized in that: the calculation formula of the interference judgment condition in the step S2.3 is as follows:
wherein x is n 、y n Respectively the abscissa and the ordinate of the circle center and x of the newly generated round aggregate j 、y j Respectively the abscissa and the ordinate of the circle center of the generated round aggregate, r n 、r j Radius of the newly-formed round aggregate and radius of the generated round aggregate are respectively, and eta is an influence coefficient of the aggregate interference range.
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