Construction method of recycled concrete meso-aggregate model based on Fourier transform

Abstract

The present invention discloses a method for constructing a recycled concrete micro-aggregate model based on Fourier transform, comprising: 1. obtaining a digital image of a real concrete cross-section, processing the image and extracting pixel coordinates of the boundary contour of the aggregate; 2. calculating and saving the Fourier coefficients that characterize the shape contour of each aggregate, and establishing a two-dimensional aggregate information database based on real aggregates; 3. randomly selecting aggregates from the database, converting the Fourier coefficients into aggregate contour coordinates, and constructing a common aggregate model; 4. constructing a recycled aggregate model using an aggregate superposition method; and 5. randomly placing common aggregates and recycled aggregates. The construction method of the present invention is simple and efficient. The aggregate model is derived from the real aggregate shape. The aggregate superposition method is proposed to randomly generate a recycled aggregate model. The constructed recycled concrete model is closer to the real recycled concrete cross-sectional structure. The model can flexibly change the recycled aggregate replacement rate and the content of attached old mortar, thereby achieving simulation of the mechanical properties and durability of recycled concrete.

Description

Technical Field

[0001] The present invention relates to the technical field of recycled concrete mesoscopic model construction, and in particular to a two-dimensional five-phase mesoscopic modeling method for recycled concrete based on Fourier transform. Background Art

[0002] Waste concrete can be processed into recycled coarse aggregate, which can be used to prepare recycled concrete instead of natural aggregate. It not only solves the consumption of natural resources such as natural sand and gravel, but also realizes the recycling of waste concrete. It has significant social, economic and environmental benefits and is in line with the concept of green and sustainable development.

[0003] In recent years, many scholars have conducted extensive research on the various properties of recycled concrete, but these studies are mostly based on macroscopic experimental research, ignoring the differences in elastic modulus and strength properties of each phase component, and the results obtained can only meet general engineering requirements. Recycled concrete has a more complex internal structure than ordinary concrete. Starting from the microstructure, it is necessary to study the influence of each phase composition on its performance, which can provide a basis for further improving the performance of recycled concrete. With the development of computer information technology, it has provided a lot of convenience for studying the microstructure of recycled concrete aggregates. Zhu Lihua et al. established a microscopic random aggregate model of recycled concrete based on polygonal aggregates and studied the thermal conductivity and heat transfer mechanism of recycled concrete; Tian Panpan et al. established a two-dimensional recycled concrete microstructure of circles and random polygons and studied the mechanical properties of recycled concrete; CN112464523A proposed a method for constructing a microscopic model of recycled concrete based on concentric elliptical recycled aggregates; CN113591195A proposed a method for constructing a microscopic model of recycled concrete based on random polygonal aggregates. However, the two-dimensional recycled aggregate models used in existing recycled concrete mesoscopic models, such as simplified particle shapes such as circles and ellipses, have certain limitations. Both the shape and attachment position of the mortar in the model are significantly different from the actual attached old mortar, resulting in a large difference between the recycled concrete model and the actual mesoscopic structure. With the rapid development of computer technology, simple models can no longer meet people's simulation needs. Summary of the Invention

[0004] In order to address the shortcomings of the above-mentioned prior art, the present invention proposes a method for constructing a recycled concrete meso-aggregate model based on Fourier transform, in order to construct a recycled concrete model that is closer to the internal structure of real recycled concrete, and to flexibly change the recycled aggregate replacement rate and the content of attached old mortar, thereby realizing simulation of the mechanical properties and durability of recycled concrete, which is conducive to accelerating the research, promotion and efficient application of recycled concrete.

[0005] In order to achieve the above-mentioned object, the present invention adopts the following technical solutions:

[0006] The method for constructing a recycled concrete meso-aggregate model based on Fourier transform of the present invention is characterized in that it comprises the following steps:

[0007] Step 1: With the lower left corner of the rectangular cross section of the concrete specimen as the coordinate origin, the horizontal direction of the rectangular cross section as the x-axis, and the vertical direction of the rectangular cross section as the y-axis, a plane rectangular coordinate system is established, and a plane rectangular domain T with a width of W and a height of H is generated, with the lower left corner of the plane rectangular domain T as the coordinate origin;

[0008] Step 2: Acquire several real cross-sectional digital images of concrete and CT scan cross-sectional images of aggregates, and extract the boundary contour pixel coordinate sequence of each aggregate in each image in the plane rectangular coordinate system. Calculate the Fourier descriptor and phase angle of the boundary contour pixel coordinate sequence of each aggregate, and save them in a numbered manner, thereby establishing a two-dimensional aggregate information database, where the total number of aggregates in the database is N;

[0009] Step 3: Determine the basic parameters, including: cross-sectional width W and height H of the recycled concrete specimen, aggregate volume ratio P k , hole size [D1, D2…D i-1 ,D i ,D i+1 …D max ], recycled aggregate replacement rate R; where D max Indicates the maximum particle size of aggregate; D i Indicates the size of the i-th hole sieve; calculates the theoretical calculation area of ​​aggregate in each particle size range {S i |i=2,3,…,max}, where S i Indicates that the particle size range is (D i-1 ,D i ) Theoretical calculation placement area of ​​aggregate;

[0010] Step 4: Initialize i=max;

[0011] Step 5: Randomly generate the i-th number r i ∈(0,1), if r i >R, the generated particle size range is (D i-1 ,D i ) of the ordinary aggregate model, if r i ≤R, then the aggregate superposition method is used to generate a particle size range of (D i-1 ,D i ) of recycled aggregate model;

[0012] Step 6: Determine the particle size range (D i-1 ,D i) aggregate model satisfies both the boundary conditions and the aggregate interference conditions. If both conditions are met, the particle size range is set to (D i-1 ,D i ) is put into the plane rectangular domain T, and the particle size range is calculated in (D i-1 ,D i ) the area a of the sth aggregate placement is , s=1,2,…,L; L represents the total amount of aggregate put in. When the aggregate model is a recycled aggregate convex polygon model, the area F of the attached mortar polygon model in the kth recycled aggregate convex polygon model is calculated. k , k=1,2,…,L1; where L1 represents the total number of recycled aggregates put in, otherwise, return to step 5; until the particle size range is (D i-1 ,D i ) of the L aggregate placement areas Until formula (1) is satisfied;

[0013] A i ∈((1-σ)S i ,(1+σ)S i ) (1)

[0014] In formula (1), σ represents the parameter between (0,1);

[0015] Step 7: After assigning i-1 to i, return to step 5 and execute sequentially until i<2, thereby obtaining the cumulative placement area of ​​aggregates in each particle size range {A i |i=2,3,4…,max};

[0016] Step 8: Calculate the aggregate placement area ratio S A and the proportion of attached old mortar area S M , used to construct a meso-aggregate model of recycled concrete.

[0017] The method for constructing a recycled concrete meso-aggregate model based on Fourier transform according to the present invention is also characterized in that step 2 comprises:

[0018] Step 2.1: Convert all images into grayscale images and perform binarization to obtain binary images. Perform edge detection on the binary images to obtain the pixel coordinate sequence E of the boundary contour of each aggregate. n ={(x mn ,y mn )|m=1,2,3…M n}, n=1,2,3,…N, where E n Represents the pixel coordinate sequence of the boundary contour of the nth aggregate, (x mn ,y mn) represents the mth coordinate of the nth aggregate boundary contour pixel coordinate sequence, M n The number of coordinates in the pixel coordinate sequence representing the boundary contour of the nth aggregate;

[0019] After the center of the aggregate is moved to the origin of the coordinate system, the boundary contour coordinate sequence of the aggregate when the center of the aggregate is located at the origin of the coordinate system {E' n |n=1,2,3,…N}, where E' n represents the boundary contour coordinate sequence of the nth aggregate when the center is located at the coordinate origin, and E' n ={(x 0 mn ,y 0 mn )|m=1,2,3…M n},(x 0 mn ,y 0 mn ) represents the mth coordinate of the nth aggregate boundary contour pixel coordinate sequence when the center is located at the coordinate origin; the boundary contour coordinate sequence of each aggregate {E' n |n=1,2,3,…N} is converted into polar coordinate sequence {F n |n=1,2,3…N}, where F n represents the polar coordinate sequence of the boundary contour pixels of the nth aggregate, and F n ={(θ mn ,r mn )|m=1,2,3,…M};(θ mn ,r mn ) represents the mth polar coordinate of the polar coordinate sequence of the nth aggregate boundary contour pixel;

[0020] Step 2.2: Select the resampling angle θ = {θ j =j / 2πN1|j=1,2,3,…,N1}, use interpolation method to calculate F n Processing is performed to obtain the extreme radius value R of the nth aggregate contour at the resampling angle θ n ={R jn |j=1,2,3…N1}; thus, the polar radius value {R n |n=1,2,3,…N}; among them, θ j represents the jth resampling angle, R jn Represents the nth aggregate contour at the resampling angle θ j The polar value under, N1 represents the number of sampling points;

[0021] Step 2.3: Calculate the real Fourier descriptor D of the nth aggregate profile n ={Dtn |t=1,2,3…N1} and phase angle δ n ={δ tn |t=1,2,3…N1}, and save them in sequence, establish a two-dimensional aggregate information database for each aggregate file number, and record the number of aggregates N in the database; where D tn The t-th real Fourier descriptor representing the n-th aggregate profile, δ tn represents the tth phase angle of the nth aggregate profile.

[0022] The steps of generating a common aggregate model in step 5 include:

[0023] Step 5.1a: Randomly generate aggregate numbers s∈(1,N) and aggregate profile rotation angles The equivalent particle size control parameter r of the sth aggregate s ∈0.5(D i-1 ,D i );

[0024] Step 5.2a: Use formula (2) to calculate the reconstructed radius value {G js |j=1,2,3…N1}, where G js Indicates the resampling angle θ j The polar value of the reconstructed s-th aggregate contour is obtained; the polar coordinate sequence J of the reconstructed s-th aggregate contour is converted to s ={(θ j ,G js )|j=1,2,3…N1} is converted into a rectangular coordinate sequence and multiplied by the angle After the rotation matrix, the coordinate sequence Z of the sth aggregate contour is obtained s ={(x js ,y js )|j=1,2,3…N1};where, (x js ,y js ) represents the jth coordinate of the sth aggregate contour coordinate sequence;

[0025]

[0026] In formula (6), D ts and δ ts denote the t-th real Fourier descriptor and phase angle of the s-th aggregate profile, respectively, and N2 is the Fourier expansion order;

[0027] Step 5.3a: Calculate the equivalent particle size d of the sth aggregate after reconstruction s , if d s ∈(D i-1 ,D i), then the aggregate pre-delivery center coordinates (x s ,y s ), and Z s The center coordinates are moved to the aggregate pre-delivery center (x s ,y s ) and then obtain the coordinate sequence Z' s , by Z' s The enclosed figure is the sth common aggregate model; otherwise, return to step 5.1a.

[0028] The process of generating the recycled aggregate model by using the aggregate superposition method in step 5 includes:

[0029] Step 5.1b: Repeat steps 5.1a and 5.2a twice to obtain the coordinate sequences Z1 and Z2 of two different common aggregate models. Combine Z1 and Z2 into a set of points, and calculate the boundary coordinate sequence X3 of this set of points. The shape enclosed by X3 is recorded as the composite aggregate.

[0030] Step 5.2b: Calculate the equivalent particle size d of the synthetic aggregate, if d∈(D i-1 ,D i ), the coordinates (x, y) of the pre-placement center of the aggregate are randomly generated, and the center coordinates of X3 and X1 are moved to the pre-placement center (x, y) of the aggregate to obtain the coordinate sequences X'3 and X'1. The figure enclosed by X'1 is the aggregate phase of the recycled aggregate model, and the difference set of the figures enclosed by X'3 and X'1 is the attached mortar phase. The aggregate phase and the attached mortar phase together constitute the recycled aggregate model; otherwise, return to step 5.1b.

[0031] The method for judging whether the aggregate model meets the boundary conditions in step 6 is as follows:

[0032] Determine the minimum circumscribed rectangle T of the aggregate model s The position relationship with the plane rectangular domain T, if T s If it is inside T, it means that the aggregate meets the boundary conditions of the placement area; otherwise, it means that the aggregate model does not meet the boundary conditions.

[0033] In step 6, whether the aggregate model AG satisfies the aggregate interference condition is determined by using the minimum circumscribed rectangle intersection method:

[0034] Step 6.1: Search for the rectangle C that intersects with the minimum bounding rectangle T0 of AG among the minimum bounding rectangles of all the aggregate models that have been placed. f |f=1,2…e}, and the corresponding aggregate set is named AGG, AGG={A f |f=1,2…e}, where c f A represents the minimum bounding rectangle of the fth aggregate model intersecting with T0.f represents the aggregate model whose fth minimum bounding rectangle intersects with T0, and e represents the number of minimum bounding rectangles of the aggregate model intersecting with T0. If C is an empty set, it means that the aggregate interference condition is met. Otherwise, execute step 6.2.

[0035] Step 6.2: Determine whether the maximum inscribed circle of AG intersects with the maximum inscribed circle of any aggregate in AGG. If so, it means that the aggregate interference condition is not met. Otherwise, go to step 6.3.

[0036] Step 6.3: Set f = 1 and proceed to step 6.4.

[0037] Step 6.4: Calculate c f The rectangle E of the overlapping area with T0 f The polar angles of the four vertices of the aggregate model AG in the polar coordinate system with the center of the coordinate origin as ψ={ψ1,ψ2,ψ3,ψ4}, where ψ1,ψ2,ψ3,ψ4 represent E f The polar angle values ​​of the four vertices in the polar coordinate system with the center of the aggregate AG as the coordinate origin; and calculate the rectangular E in the rectangular coordinate system with the center of the aggregate model AG as the coordinate origin f The lower left corner coordinate vertex (X lf ,Y lf ) and E f The center abscissa X cf and E f The height L1, if X cf >0 and Y lf ×(Y lf +L1)<0, then let α={α p =2p·ψ m / N5|p=0,1,2…N5 / 2}∪{α p =ψ n +(4π-2ψ n )·p / N5|p=N5 / 2,N5 / 2+1,…N5}, otherwise, let α={α p =ψ a +p·(ψ b -ψ a ) / N5|p=0,1,2…N5}, where ψ m is the maximum polar angle value in ψ that is less than π, ψ n is the minimum polar angle value greater than π in ψ, a is the minimum polar angle value in the set ψ, b is the maximum polar angle value in ψ, α represents the polar angle value set to be verified, α p represents the pth polar angle value to be verified, and N5 is the number of division points;

[0038] Step 6.5: Calculate the polar coordinate value sequence of the contour points of the aggregate model AG under the extreme angle value set α and convert it into the rectangular coordinate sequence Z1={(x' p ,y' p )|p=1,2,3…N5}, where (x' p ,y' p ) represents the pth coordinate to be verified on the contour of the aggregate model AG; if all coordinate points in Z1 are not in E f Internally, the fth aggregate A f Does not interfere with the aggregate model AG, otherwise, calculate all coordinate points in Z1 to the fth aggregate A f The distance between the centers d={d p |p=1,2,3…N5} and all coordinate points in Z1 are based on the fth aggregate A f The polar angle set τ in the polar coordinate system with the center as the origin is τ={τ p |p=1,2,3…N5}, calculate the fth aggregate A f The polar radius value set {I p |p=1,2,3…N5}, where d p Indicates the distance from the pth coordinate point to be verified to the fth aggregate A f The distance between the centers, τ p Indicates that the p-th coordinate point in Z1 is the f-th aggregate A f The polar angle of the polar coordinate system with the center as the origin, I p represents the fth aggregate A f At the pth polar angle τ p The polar value of the lower contour point; if there is I p >d p , then it means the fth aggregate A f Interference with the aggregate model AG, otherwise, it means the fth aggregate A f No interference with the aggregate model AG;

[0039] Step 6.6: Assign f+1 to f, return to step 6.4 and execute sequentially until f>e. If the aggregate model AG does not interfere with all aggregates in AGG, it means that the aggregate interference condition is met; otherwise, it means that the aggregate interference condition is not met.

[0040] The electronic device of the present invention includes a memory and a processor, and is characterized in that the memory is used to store a program that supports the processor to execute the construction method, and the processor is configured to execute the program stored in the memory.

[0041] The present invention provides a computer-readable storage medium, wherein a computer program is stored on the computer-readable storage medium, and the computer program executes the steps of the construction method when the computer program is executed by a processor.

[0042] Compared with the prior art, the present invention has the following beneficial effects:

[0043] 1. Compared with the existing recycled concrete mesoscopic model, the present invention uses Fourier transform to reconstruct the complex shape contours of real aggregates and uses it as a common aggregate model. The aggregate model is realistic and derived from real aggregates. A new method, the aggregate superposition method, is proposed to generate a recycled aggregate model. The attached mortar model has various shapes and random positions. The constructed recycled concrete model is more consistent with the real two-dimensional recycled concrete mesoscopic structure, making the simulation results more accurate.

[0044] 2. Compared with the existing recycled concrete microscopic model, the present invention proposes a minimum circumscribed rectangle method to determine whether there is interference between irregularly shaped aggregates. This method is rigorous, accurate, and efficient, and improves the filling rate of aggregates.

[0045] 3. Compared with the existing recycled concrete microscopic model, the present invention can control the replacement rate of recycled aggregate and the attachment content of old mortar by changing the input parameters. It can be used to simulate and study the effects of the mortar attachment amount and replacement rate of recycled aggregate on various properties of recycled concrete, thereby accelerating the promotion and application of recycled concrete. BRIEF DESCRIPTION OF THE DRAWINGS

[0046] Figure 1 is a flow chart of the method of the present invention;

[0047] Figure 2 Schematic diagram of the extracted aggregate profile of the method of the present invention;

[0048] Figure 3 Schematic diagram of a recycled aggregate model generated by the aggregate superposition method of the present invention;

[0049] Figure 4 This is the boundary condition determination diagram of the present invention;

[0050] Figure 5 This is a schematic diagram of the intersection of irregular-shaped aggregates of the present invention;

[0051] Figure 6a This is a schematic diagram of the minimum circumscribed rectangle intersection method of the present invention;

[0052] Figure 6b This is a schematic diagram of the minimum circumscribed rectangle intersection method used in the present invention;

[0053] Figure 7a This is a micro-aggregate model diagram of recycled concrete with a replacement rate of 30% according to the present invention;

[0054] Figure 7b This is a micro-aggregate model diagram of recycled concrete with a replacement rate of 70% according to the present invention;

[0055] Figure 7c This is a micro-aggregate model diagram of recycled concrete with a replacement rate of 100% according to the present invention. DETAILED DESCRIPTION

[0056] In this embodiment, Figure 1 As shown in the figure, a method for constructing a recycled concrete meso-aggregate model based on Fourier transform extracts the two-dimensional shape contour information of the real aggregate using Fourier transform. Based on this, two types of recycled aggregate models are randomly generated using different methods. The constructed ordinary aggregate model and recycled aggregate model are highly random and more consistent with the shape of the aggregate under the real concrete cross-section. The constructed meso-structural model can simultaneously adjust parameters such as the recycled aggregate replacement rate and mortar adhesion rate. Specifically, the following steps are included:

[0057] Step 1: With the lower left corner of the rectangular cross section of the concrete specimen as the coordinate origin, the horizontal direction of the rectangular cross section as the x-axis, and the vertical direction of the rectangular cross section as the y-axis, a plane rectangular coordinate system is established, and a plane rectangular domain T with a width of W and a height of H is generated, with the lower left corner of the plane rectangular domain T as the coordinate origin;

[0058] Step 2: Cut the concrete specimen, polish the cross section, and take photos to obtain several digital images of the concrete cross section. Scan several aggregates using X-ray CT scanning technology to obtain several CT scan cross-sectional images of the aggregates. Extract the pixel coordinate sequence of the boundary contour of each aggregate in each image in the plane rectangular coordinate system. Calculate the Fourier descriptor and phase angle of the pixel coordinate sequence of the boundary contour of each aggregate, number them, and save them, thereby establishing a two-dimensional aggregate information database. Let the total number of aggregates in the database be N. The steps are as follows:

[0059] Step 2.1: Convert the image into a grayscale image and binarize it. Obtain the pixel coordinate sequence E of the boundary contour of each aggregate by edge detection of digital images. n ={(x mn ,y mn )|m=1,2,3…M n}, n=1,2,3,…N, where E n Represents the pixel coordinate sequence of the boundary contour of the nth aggregate, (x mn ,y mn ) represents the mth coordinate of the nth aggregate boundary contour pixel coordinate sequence, M n The number of coordinates of the pixel coordinate sequence of the boundary contour of the nth aggregate is represented by Eq. (1) to obtain the pixel coordinate sequence of the boundary contour of the aggregate when the center of the aggregate is located at the origin of the coordinates {E'n |n=1,2,3,…N}, where E' n represents the boundary contour coordinate sequence of the nth aggregate when the center is located at the coordinate origin, and E' n ={(x 0 mn ,y 0 mn )|m=1,2,3…M n},(x 0 mn ,y 0 mn ) represents the mth coordinate of the nth aggregate boundary contour pixel coordinate sequence when the center is located at the coordinate origin;

[0060]

[0061] In formula (1), x mn ,y mn Represents the horizontal and vertical coordinates of the mth contour point of the nth aggregate, x 0mn ,y 0mn They represent the horizontal and vertical coordinates of the mth contour point of the nth aggregate when its center is located at the coordinate origin.

[0062] Use formula (2) to transform the rectangular coordinate sequence E' of each aggregate into n Convert to polar coordinate sequence {F n |n=1,2,3…N}, where F n represents the polar coordinate sequence of the boundary contour pixels of the nth aggregate, and F n ={(θ mn ,r mn )|m=1,2,3,…M};(θ mn ,r mn ) represents the mth polar coordinate of the polar coordinate sequence of the nth aggregate boundary contour pixel;

[0063]

[0064] In formula (2), x 0mn ,y 0mn Respectively represent the horizontal and vertical coordinates of the mth contour point when the center of the nth aggregate is located at the coordinate origin, θ mn ,r mn They represent the polar angle and polar diameter of the mth contour point when the center of the nth aggregate is located at the origin of polar coordinates. atan2 is the inverse tangent function that takes the quadrant into consideration.

[0065] Step 2.2: Select the resampling angle θ = {θ j =j / 2πN1|j=1,2,3…N1}(θ j∈(0,2π)), use interpolation method to calculate F n Processing is performed to obtain the extreme radius value R of the nth aggregate contour at the resampling angle θ n ={R jn |j=1,2,3…N1}; thus, the polar radius value {R n |n=1,2,3,…N}; among them, θ j represents the jth resampling angle, R jn Represents the nth aggregate contour at the resampling angle θ j The polar value under the , N1 represents the number of sampling points. The number of sampling points N1 should satisfy the L power of 2 to ensure that the FFT fast algorithm can be used, and N1 should be no less than 128 to ensure that the detailed information of the particle contour can be retained;

[0066] Step 2.3: Calculate the discrete Fourier coefficients {(A tn ,B tn )|t=1,2,3…N1} and the average polar radius r n , (n=1,2,3,…N), then use formula (4) to calculate the real Fourier descriptor D of the nth aggregate contour n ={D tn |t=1,2,3…N1} and phase angle δ n ={δ tn |t=1,2,3…N1}, and save them in txt files or excel files in sequence, so that the files can be extracted later for scaling, reconstruction, and re-deployment of aggregate contours (such as Figure 2 As shown), a two-dimensional aggregate information database is established for each aggregate file number, and the number of aggregates N in the database is recorded, and N should not be less than 100;

[0067]

[0068] In formula (3), R jn Represents the nth aggregate profile at the jth resampling angle θ j The extreme value under A tn ,B tn Represents the nth aggregate contour R n (θ j )’s Fourier coefficient, r n It represents the average polar diameter value of the nth aggregate contour under all resampling angles θ.

[0069]

[0070] In formula (4), D tn and δ tn Represents the nth aggregate contour Rn (θ j ) real Fourier descriptors and phase angles.

[0071] Step 3: Obtain the basic parameters, including: the cross-sectional width W and height H of the recycled concrete specimen, the percentage P of the aggregate volume in the total volume of the recycled concrete k , the sieve sizes [D1, D2…D i-1 , D i , D i+1 …D max , the recycled aggregate replacement rate R ∈ (0, 1); where D max represents the maximum aggregate size; D i represents the size of the i-th sieve; determine the area proportion of each particle size aggregate according to the Walraven formula (Equation (5)), and calculate the theoretical calculated placement area {S i |i = 2, 3, …, max} of the aggregate in each particle size range according to Equation (6), where S i represents the theoretical calculated placement area of the aggregate with a particle size range in (D i-1 , D i );

[0072]

[0073] S i = [P i (D < D i ) - P i-1 (D < D i-1 )] × W × H (6)

[0074] In Equations (5) and (6), P(D < D0) is the probability that the aggregate particle size D in the cross-section is less than the sieve hole D0, P k is the percentage of the aggregate volume in the total volume of the recycled concrete, D max is the maximum aggregate size, S i represents the theoretical calculated aggregate placement area with a particle size range in (D i-1 , D i ), P i (D < D i ) is the probability that the aggregate particle size D in the cross-section is less than the sieve hole D i , W is the cross-sectional width of the specimen, and H is the cross-sectional height of the specimen.

[0075] Step 4: Initialize i = max and place the aggregates in order from the largest particle size to the smallest;

[0076] Step 5: Randomly generate a number r ∈ (0, 1). If r > R, then generate a particle size range in (D i-1 , D i) is divided into the following steps:

[0077] Step 5.1a: Randomly generate the aggregate number integer s∈(1,N) and the aggregate profile rotation angle Equivalent particle size control parameter r of aggregate s ∈0.5(D i-1 ,D i+1 );

[0078] Step 5.2a: The aggregate profile R s (θ j ) Formula (7) can be expressed by Fourier series. The real Fourier descriptor and phase angle of the sth aggregate stored in the database can be used to reconstruct the aggregate contour. The reconstructed polar radius value {G js |j=1,2,3…N1}, where G js Indicates the resampling angle θ j The reconstructed polar radius value of the sth aggregate contour is obtained, and the polar coordinate sequence J of the reconstructed sth aggregate contour is converted to s ={(θ j ,G js )|j=1,2,3…N1} is converted into a rectangular coordinate sequence and multiplied by the angle The rotation matrix (6) ensures the randomness of the aggregate and obtains Z s ={(x js ,y js )|j=1,2,3…N1}, where (x js ,y js ) represents the jth coordinate of the sth aggregate contour coordinate sequence;

[0079]

[0080] In formula (7), D ts and δ ts Respectively represent the sth aggregate contour G s (θ j )’s t-th real Fourier descriptor and phase angle, θ j represents the jth resampling angle, r s is the equivalent particle size control parameter of aggregate, G js Indicates the jth resampling angle θ j The reconstructed polar radius value of the sth aggregate contour, N2 is the Fourier expansion order, according to the Nyquist sampling theorem, N2 ≤ (N1 / 2).

[0081]

[0082] In formula (8) is the rotation angle of the sth aggregate, RT s is the rotation matrix of the sth aggregate.

[0083] Step 5.3a: Calculate the equivalent particle size d of the sth aggregate after reconstruction according to formula (8): s (equivalent Feret short diameter of ellipse);

[0084]

[0085] In formula (9), S s is the area of ​​the sth aggregate after reconstruction, a s is the maximum Feret diameter after reconstruction of the sth aggregate, d s is the equivalent particle size of the sth aggregate after reconstruction.

[0086] If d s ∈(D i-1 ,D i ), the particle size range of the aggregate model generated on the surface meets the requirements, and the pre-placement center coordinates of the aggregate are randomly generated (x s ,y s ), Z s The center coordinates are moved to the aggregate pre-delivery center (x s ,y s ), get the coordinate sequence Z' s ={(x' js ,y' jsz )|j=1,2,3…N1},Z' s The enclosed figure is used as the common aggregate model. Otherwise, return to step 5.1a;

[0087] If r≤R, the aggregate superposition method is used to generate a particle size range of (D i-1 ,D i ) of recycled aggregate models, such as Figure 3 The specific steps are as follows:

[0088] Step 5.1b: Repeat steps 5.1a and 5.1b twice to obtain the rectangular coordinate sequences X1 and X2 of two different common aggregate models. Combine X1 and X2 into a set of points, and calculate the boundary coordinate sequence X3 of this set of points. The shape enclosed by X3 is recorded as the composite aggregate.

[0089] Step 5.2b: Calculate the equivalent particle size d of the synthetic aggregate according to formula (9). If d∈(D i-1 ,D i), randomly generate the pre-deployment center coordinates (x, y) of the recycled aggregate model, move the center coordinates of X3 and X1 to the aggregate pre-deployment center (x, y) to obtain the coordinate sequence X'3 and X'1, the figure surrounded by X'1 is used as the aggregate phase of the recycled aggregate model, and the difference set of the figures surrounded by X'3 and X'1 is used as the attached mortar phase, and the two together constitute the recycled aggregate model. When the recycled aggregate model has one piece of residual mortar, it is recorded as type 1 recycled aggregate, and when it has two pieces of attached mortar, it is recorded as type 2 recycled aggregate model (such as Figure 3 Otherwise, return to step 5.1a;

[0090] Step 6: Determine the particle size range (D i-1 ,D i ) Whether the aggregate model generated by the generated aggregate model satisfies both the boundary conditions and the aggregate interference conditions. If both conditions are satisfied, the particle size range is set within (D i-1 ,D i ) is put into the plane rectangular domain, and the particle size range is calculated in (D i-1 ,D i ) the area a of the sth aggregate placement is , s=1,2,…,L (When the aggregate model is a recycled aggregate convex polygon model, calculate the area F of the attached mortar polygon model in the kth recycled aggregate convex polygon model k , k=1,2,…,L1); otherwise, return to step 5; when the particle size (D i-1 ,D i ) Cumulative aggregate placement area A i Smaller than the theoretical calculation area S of this particle size i When the aggregate is 100%, return to step 5 and continue to add the aggregate of the particle size segment; A i Greater than S i When the last aggregate is abandoned, a smaller aggregate is generated in the same particle size range and the particles are continuously added until the particle size range is (D i-1 ,D i ) of the L aggregate placement areas Until formula (1) is satisfied;

[0091] A i ∈((1-σ)S i ,(1+σ)S i )(10)

[0092] In formula (10), σ represents the parameter between (0,1), S i Indicates that the particle size range is (D i-1 ,D i ) is the theoretical calculation area of ​​aggregate, A i Indicates that the particle size range is (D i-1 ,D i) of the aggregate; in order to make the cumulative placement area A of each particle size i As close as possible to the theoretical calculation area S of the particle size i , σ can be taken as 0.2.

[0093] The aggregate model first determines the boundary conditions: Figure 4 As shown in , if the minimum bounding rectangle of the aggregate model is inside the placement rectangle, the aggregate must meet the boundary conditions, otherwise, it is judged as not meeting the boundary conditions. s (The minimum circumscribed rectangle side is parallel to the coordinate axis of the coordinate system generated in step 4) and the position relationship with the plane rectangle T, if T s If it is inside T, it means that the aggregate meets the boundary conditions of the placement area. Otherwise, it means that the aggregate model does not meet the boundary conditions. The aggregate model that meets the boundary conditions further determines the aggregate interference conditions and follows the following steps to determine the particle size range (D i-1 ,D i ) whether the aggregate model AG satisfies the aggregate interference condition:

[0094] Step 6.1: In order to improve the efficiency of aggregate interference judgment, the position relationship of the aggregates is roughly judged by whether the minimum bounding rectangles of the irregular aggregates intersect. If the minimum bounding rectangle of AG does not intersect with the minimum bounding rectangles of all the aggregates that have been placed, then AG must not interfere with other aggregates and is directly placed in the plane rectangular domain generated in step 4. Otherwise, further judgment is required. Search the bounding rectangles of all the aggregate models that have been placed for the rectangle C that intersects with the bounding rectangle T0 of AG. f |f=1,2…e}, and the corresponding aggregate set is named AGG, AGG={A f |f=1,2…e}, where c f A represents the bounding rectangle of the fth aggregate model that intersects with T0. f represents the fth aggregate model whose circumscribed rectangle intersects with T0, and e represents the number of circumscribed rectangles of aggregate models intersecting with T0; if C is an empty set, it means that the aggregate interference condition is met, otherwise, execute step 6.2;

[0095] Step 6.2: Use the maximum inscribed circle of the aggregate to further determine whether the maximum inscribed circle of AG intersects with the maximum inscribed circle of any aggregate in AGG. If so, it means that the aggregate interference condition is not met. Otherwise, execute step 6.3;

[0096] Step 6.3: Set f = 1 and proceed to step 6.4.

[0097] Step 6.4: Further judgment requires the use of the minimum bounding rectangle intersection method, such as Figure 5 As shown in the figure, if the minimum circumscribed rectangles of two irregular aggregates 1 and 2 intersect, any interference between the aggregates must occur in the rectangle of the overlapping area. Calculate c f The rectangle E of the overlapping area with T0 f The polar angles ψ of the four vertices in the polar coordinate system with the center of aggregate AG as the coordinate origin are ψ={ψ1,ψ2,ψ3,ψ4}, where ψ1,ψ2,ψ3,ψ4 represent the rectangle E f The polar angle values ​​of the four vertices of the aggregate AG in the polar coordinate system with the center of the aggregate AG as the coordinate origin; and calculate the rectangular E in the rectangular coordinate system with the center of the aggregate AG as the coordinate origin f The lower left corner coordinate vertex (X lf ,Y lf ) and E f The center abscissa X cf and E f The height L1 (the length of the side parallel to the y-axis), if X cf >0 and Y lf ×(Y lf +L1)<0, then let α={α p =2p·ψ m / N5|p=0,1,2…N5 / 2}∪{α p =ψ n +(4π-2ψ n )·p / N5|p=N5 / 2,N5 / 2+1,…N5}, otherwise, α={α p =ψ a +p·(ψ b -ψ a ) / N5|p=0,1,2…N5}, where ψ m is the maximum polar angle value in ψ that is less than π, ψ n is the minimum polar angle value greater than π in ψ, a is the minimum polar angle value in the set ψ, b is the maximum polar angle value in ψ, α represents the polar angle value set to be verified, α p It represents the pth extreme angle value to be verified, and N5 is the number of division points. It is only necessary to reconstruct the contour coordinates of the aggregate AG under the extreme angle α to determine whether these points are within the aggregate AG. f AG and AG can be obtained from the inside f Whether interference occurs.

[0098] Step 6.5: When the minimum bounding rectangles of two irregular aggregates intersect, the interference condition must satisfy Figure 6aThere are four cases in the equation. When cases (1) and (2) occur, although the minimum circumscribed rectangles of aggregates 1 and 2 intersect, all the contour points of at least one aggregate are not inside the rectangle EOB. In these two cases, the aggregates will not interfere. When cases (3) and (4) occur, that is, some of the contour points of aggregates 1 and 2 are inside the EOB, the aggregates may or may not interfere, and further judgment is needed. Calculate the polar coordinate value sequence of the contour points of the aggregate model AG under the extreme angle value set α and convert it into a rectangular coordinate sequence

[0099] Z1={(x' p ,y' p )|p=1,2,3…N5}, where (x' p ,y' p ) represents the pth coordinate to be verified on the contour of the aggregate model AG; if all coordinate points in Z1 are not in E f Internal, then satisfy one of the conditions (1) or (2), then the fth aggregate A f There must be no interference with aggregate AG, otherwise the situation is (3) or (4), further judgment is required to calculate all coordinate points in Z1 to the fth aggregate A f The distance between the centers d={d p |p=1,2,3…N5} and all coordinate points in Z1 are based on the fth aggregate A f The polar angle set τ in the polar coordinate system with the center as the origin is τ={τ p |p=1,2,3…N5}, calculate the fth aggregate A f The polar radius value set {I p |p=1,2,3…N5}, where d p Indicates the distance from the pth coordinate point to be verified to the fth aggregate A f The distance between the centers, τ p Indicates that the p-th coordinate point in Z1 is the f-th aggregate A f The polar angle of the polar coordinate system with the center as the origin, I p represents the fth aggregate A f At the pth polar angle τ p The polar value of the lower contour point; Figure 6b , if there is I p >d p , indicating that the pth point in Z1 is in aggregate A f The interior of the f-th aggregate A f It must interfere with aggregate AG, otherwise, it means that the fth aggregate A f No interference with aggregate AG; this method can accurately, quickly and efficiently determine whether there is interference between two irregularly shaped aggregates;

[0100] Step 6.6: Assign f+1 to f, and return to step 6.4 and execute sequentially until f>e. If aggregate AG does not interfere with all aggregates in AGG, the aggregate interference condition is satisfied; otherwise, the aggregate interference condition is not satisfied.

[0101] Step 7: After assigning i-1 to i, return to step 4 and execute in sequence, placing aggregate models of each size in the order of large to small, until i<2, and calculate the cumulative placement area of ​​aggregates in each size range {A i |i=2,3,…,max};

[0102] Step 8: Calculate the total aggregate placement area ratio S according to formula (11) A and the proportion of attached old mortar area S M , used to construct a meso-aggregate model of recycled concrete.

[0103]

[0104] In formula (11), S A and S M are the total aggregate area ratio and the area ratio of attached old mortar, A i (D i-1 ,D i ) is the actual area of ​​aggregate placed in the particle size segment, max is the number of holes in the sieve, W and H are the width and height of the specimen section, L1 is the number of particles of recycled aggregate placed, F k is the area of ​​the attached mortar polygonal model in the kth recycled aggregate convex polygonal model.

[0105] In this embodiment, an electronic device includes a memory and a processor, wherein the memory is used to store a program that supports the processor to execute the above-mentioned construction method, and the processor is configured to execute the program stored in the memory.

[0106] In this embodiment, a computer-readable storage medium stores a computer program, and when the computer program is executed by a processor, the steps of the above-mentioned construction method are executed.

[0107] Example: The following steps are used to construct a recycled concrete meso-aggregate model based on Fourier transform:

[0108] Step 1: Prepare and cut a 10 cm × 10 cm × 10 cm concrete specimen. After polishing the obtained cross section, take photos to obtain several digital images of the concrete cross section, or scan several coarse aggregates using X-ray CT scanning technology to obtain several CT scan cross-sectional images of the aggregates.

[0109] Step 2: Write a program to batch process the images obtained in step 1, extract the pixel coordinate sequence of the boundary outline of all aggregates in each image, use the built-in function fft in Matlab to obtain the Fourier coefficients of each aggregate coordinate sequence, and then calculate the Fourier descriptor and phase angle of each aggregate coordinate sequence. Save the files as txt files and store all the txt files of the aggregates in the same folder for easy access. By processing 500 images, a two-dimensional aggregate information database with 1997 aggregates was established.

[0110] Step 3: Determine basic parameters:

[0111] The cross-sectional width of the recycled concrete specimen is W = 100 mm, the height is H = 100 mm, and the percentage of aggregate volume to the total volume of recycled concrete is P k =0.75, minimum aggregate particle size D min =4.75mm, maximum aggregate size D max =25mm, the sieve hole sizes are 4.75mm, 9.5mm, 16mm, 19mm, and 25mm, and the replacement rates of recycled aggregate are 30%, 70%, and 100%, respectively, that is, R = 0.3, 0.6, and 1; calculate the area proportion of aggregates of each size within the aggregate placement area: According to the Walraven formula, the area for aggregate placement with a size of 19 to 25mm is 674mm 2 The aggregate with a particle size of 16 to 19 mm is placed on an area of ​​494 mm. 2 The aggregate with a particle size of 9.5 to 16 mm is placed on an area of ​​1401 mm. 2 The aggregate with a particle size of 4.75 to 9.5 mm is placed on an area of ​​1434 mm. 2 , the total aggregate input area accounts for 40%.

[0112] Step 4: With the lower left corner of the rectangular cross section of the specimen as the coordinate origin, the horizontal direction of the rectangular cross section as the x-axis, and the vertical direction of the rectangular cross section as the y-axis, establish a plane rectangular coordinate system and generate a plane rectangular domain with a width of W and a height of H. Initialize i = 5;

[0113] Step 5: Randomly generate a number r=rand(1) in the range of (0,1). When r>R, a common aggregate model with a particle size range of (D4,D5) is generated: use the built-in function randi in Matlab to randomly generate an aggregate number integer s=randi(1997,1), an aggregate profile rotation angle Equivalent particle size control parameter r of aggregate s =0.5×[D i-1 +(D i -D i-1 )×rand(1)] and the coordinates of the aggregate pre-placement center x s=W×rand(1),y s =H×rand(1); retrieve the data information of the sth aggregate from the database and convert it into the coordinate sequence Z' whose particle size meets the requirements s , use Matlab built-in function fill to Z' s Filling to obtain the ordinary aggregate model; if r>R, the generated particle size range is (D i-1 ,D i ) recycled aggregate model: First, two different ordinary aggregate models are generated to obtain the rectangular coordinate sequences X1 and X2 of the two different ordinary aggregate models. X1 and X2 are combined into a group of points. The boundary coordinate sequence X3 of the group of points is calculated using the built-in function boundry in Matlab to obtain the synthetic aggregate that meets the particle size requirements. The pre-delivery center coordinates x = W × rand(1), y = H × rand(1) of the recycled aggregate model are generated. The center coordinates of X3 and X1 are moved to the aggregate pre-delivery center (x, y) to obtain the coordinate sequences X'3 and X'1. The built-in function fill in Matlab is used to fill X'1 to obtain the aggregate phase of the recycled aggregate model. The difference set of the figure enclosed by filling X'3 and X'1 is used as the attached mortar phase. The two together constitute the recycled aggregate model.

[0114] Step 6: First determine the particle size range (D i-1 ,D i ) Whether the aggregate model generated by the method satisfies the boundary conditions:

[0115] A Matlab function was compiled to determine whether two rectangles are contained within each other. The minimum enclosing rectangle of each aggregate to be placed is determined to be within the larger placement area rectangle. If this condition is met, the next step is to determine aggregate interference. Otherwise, the process returns to step 5. Aggregate models that meet boundary conditions are further tested for aggregate interference conditions: a Matlab function was compiled to determine whether two rectangles intersect. The minimum enclosing rectangle of the newly generated aggregate intersects with the minimum enclosing rectangle of any already placed aggregate. If not, the aggregate is placed directly. Otherwise, the process continues. A function was compiled to determine whether two circles intersect. The minimum enclosing circle of the newly generated aggregate intersects with the minimum enclosing circle of the surrounding aggregate (the aggregate whose minimum enclosing rectangle intersects the minimum enclosing rectangle of the newly generated aggregate). If so, the process returns to step 5. Otherwise, the process continues. A function was compiled to determine whether two irregularly shaped aggregates intersect based on the minimum enclosing rectangle intersection method. If the newly generated aggregate meets the aggregate interference condition, the aggregate is placed successfully. Otherwise, the process returns to step 5.

[0116] Step 7: After assigning i-1 to i, return to step 4 and execute sequentially until i<2, thereby obtaining the cumulative placement area of ​​each particle size range; when the cumulative placement area of ​​aggregate of a certain particle size is less than the theoretically calculated area of ​​the particle size, continue to place aggregate of this particle size segment; when the cumulative placement area is greater than the theoretically calculated area, abandon the placement of the last aggregate and generate a smaller aggregate in the particle size segment and continue to place it until the cumulative placement area of ​​the current particle size aggregate reaches 0.98 to 1.02 times the theoretically calculated area of ​​the particle size aggregate, then place the next particle size aggregate until all particle size segments are placed;

[0117] Step 8: Calculate the total aggregate placement area ratio S A and the proportion of attached old mortar area S M .

[0118] Figure 7a The model diagram of recycled concrete meso-aggregate with a replacement rate of 30% is shown in the figure. A is 43.98%, S M 9.77%; Figure 7b The random aggregate model diagram of recycled concrete with a replacement rate of 70% is shown in the figure. The S A is 43.02%, S M 16.63%; Figure 7c The random aggregate model diagram of recycled concrete with a replacement rate of 100% is shown in the figure. The S A is 42.97%, S M It is 25.70%.

Claims

1. A method for constructing a recycled concrete meso-aggregate model based on Fourier transform, characterized in that: The following steps are involved: Step 1: With the lower left corner of the rectangular cross section of the concrete specimen as the coordinate origin, the horizontal direction of the rectangular cross section as the x-axis, and the vertical direction of the rectangular cross section as the y-axis, a plane rectangular coordinate system is established, and a plane rectangular domain T with a width of W and a height of H is generated, with the lower left corner of the plane rectangular domain T as the coordinate origin; Step 2: Acquire several real cross-sectional digital images of concrete and CT scan cross-sectional images of aggregates, and extract the boundary contour pixel coordinate sequence of each aggregate in each image in the plane rectangular coordinate system. Calculate the Fourier descriptor and phase angle of the boundary contour pixel coordinate sequence of each aggregate, and save them in a numbered manner, thereby establishing a two-dimensional aggregate information database, where the total number of aggregates in the database is N; Step 3: Determine the basic parameters, including: cross-sectional width W and height H of the recycled concrete specimen, aggregate volume ratio P k , hole size [D1, D2…D i-1 ,D i ,D i+1 …D max ], recycled aggregate replacement rate R; where D max Indicates the maximum particle size of aggregate; D i Indicates the size of the i-th hole sieve; calculates the theoretical calculation area of ​​aggregate in each particle size range {S i |i=2,3,…,max}, where S i Indicates that the particle size range is (D i-1 ,D i ) Theoretical calculation placement area of ​​aggregate; Step 4: Initialize i=max; Step 5: Randomly generate the i-th number r i ∈(0,1), if r i >R, the generated particle size range is (D i-1 ,D i ) of the ordinary aggregate model, if r i ≤R, then the aggregate superposition method is used to generate a particle size range of (D i-1 ,D i ) of recycled aggregate model; Step 6: Determine the particle size range (D i-1 ,D i ) aggregate model satisfies both the boundary conditions and the aggregate interference conditions. If both conditions are met, the particle size range is set to (D i-1 ,D i ) is put into the plane rectangular domain T, and the particle size range is calculated in (D i-1 ,D i ) the area a of the sth aggregate placement is , s=1,2,…,L; L represents the total amount of aggregate put in. When the aggregate model is a recycled aggregate convex polygon model, the area F of the attached mortar polygon model in the kth recycled aggregate convex polygon model is calculated. k , k=1,2,…,L1; where L1 represents the total number of recycled aggregates put in, otherwise, return to step 5; until the particle size range is (D i-1 ,D i ) of the cumulative placement area of ​​L aggregates Until formula (1) is satisfied; A i ∈((1-σ)S i ,(1+σ)S i ) (1) In formula (1), σ represents the parameter between (0,1); Step 7: After assigning i-1 to i, return to step 5 and execute sequentially until i<2, thereby obtaining the cumulative placement area of ​​aggregates in each particle size range {A i |i=2,3,4…,max}; Step 8: Calculate the aggregate placement area ratio S A and the proportion of attached old mortar area S M , used to construct a meso-aggregate model of recycled concrete.

2. The method for constructing a recycled concrete meso-aggregate model based on Fourier transform according to claim 1, characterized in that: The step 2 includes: Step 2.1: Convert all images into grayscale images and perform binarization to obtain binary images. Perform edge detection on the binary images to obtain the pixel coordinate sequence E of the boundary contour of each aggregate. n ={(x mn ,y mn )|m=1,2,3…M n }, n=1,2,3,…N, where E n Represents the pixel coordinate sequence of the boundary contour of the nth aggregate, (x mn ,y mn ) represents the mth coordinate of the nth aggregate boundary contour pixel coordinate sequence, M n The number of coordinates in the pixel coordinate sequence representing the boundary contour of the nth aggregate; After the center of the aggregate is moved to the origin of the coordinate system, the boundary contour coordinate sequence of the aggregate when the center of the aggregate is located at the origin of the coordinate system {E' n |n=1,2,3,…N}, where E' n represents the boundary contour coordinate sequence of the nth aggregate when the center is located at the coordinate origin, and E' n ={(x 0 mn ,y 0 mn )|m=1,2,3…M n },(x 0 mn ,y 0 mn ) represents the mth coordinate of the nth aggregate boundary contour pixel coordinate sequence when the center is located at the coordinate origin; the boundary contour coordinate sequence of each aggregate {E' n |n=1,2,3,…N} is converted into polar coordinate sequence {F n |n=1,2,3…N}, where F n represents the polar coordinate sequence of the boundary contour pixels of the nth aggregate, and F n ={(θ mn ,r mn )|m=1,2,3,…M};(θ mn ,r mn ) represents the mth polar coordinate of the polar coordinate sequence of the nth aggregate boundary contour pixel; Step 2.2: Select the resampling angle θ = {θ j =j / 2πN1|j=1,2,3,…,N1}, use interpolation method to calculate F n Processing is performed to obtain the extreme radius value R of the nth aggregate contour at the resampling angle θ n ={R jn |j=1,2,3…N1}; thus, the polar radius value {R n |n=1,2,3,…N}; among them, θ j represents the jth resampling angle, R jn Represents the nth aggregate contour at the resampling angle θ j The polar value under, N1 represents the number of sampling points; Step 2.3: Calculate the real Fourier descriptor D of the nth aggregate profile n ={D tn |t=1,2,3…N1} and phase angle δ n ={δ tn |t=1,2,3…N1}, and save them in sequence, establish a two-dimensional aggregate information database for each aggregate file number, and record the number of aggregates N in the database; where D tn The t-th real Fourier descriptor representing the n-th aggregate profile, δ tn represents the tth phase angle of the nth aggregate profile.

3. The method for constructing a recycled concrete meso-aggregate model based on Fourier transform according to claim 2, characterized in that: The steps of generating a common aggregate model in step 5 include: Step 5.1a: Randomly generate aggregate numbers s∈(1,N) and aggregate profile rotation angles The equivalent particle size control parameter r of the sth aggregate s ∈0.5(D i-1 ,D i ); Step 5.2a: Use formula (2) to calculate the reconstructed radius value {G js |j=1,2,3…N1}, where G js Indicates the resampling angle θ j The polar value of the reconstructed s-th aggregate contour is obtained; the polar coordinate sequence J of the reconstructed s-th aggregate contour is s ={(θ j ,G js )|j=1,2,3…N1} is converted into a rectangular coordinate sequence and multiplied by the angle After the rotation matrix, the coordinate sequence Z of the sth aggregate contour is obtained s ={(x js ,y js )|j=1,2,3…N1};where, (x js ,y js ) represents the jth coordinate of the sth aggregate contour coordinate sequence; In formula (6), D ts and δ ts denote the t-th real Fourier descriptor and phase angle of the s-th aggregate profile, respectively, and N2 is the Fourier expansion order; Step 5.3a: Calculate the equivalent particle size d of the sth aggregate after reconstruction s , if d s ∈(D i-1 ,D i ), then the aggregate pre-delivery center coordinates (x s ,y s ), and Z s The center coordinates are moved to the aggregate pre-delivery center (x s ,y s ) and then obtain the coordinate sequence Z' s , by Z' s The enclosed figure is the sth common aggregate model; otherwise, return to step 5.1a.

4. The method for constructing a recycled concrete meso-aggregate model based on Fourier transform according to claim 3, characterized in that: The process of generating the recycled aggregate model by using the aggregate superposition method in step 5 includes: Step 5.1b: Repeat steps 5.1a and 5.2a twice to obtain the coordinate sequences Z1 and Z2 of two different common aggregate models. Combine Z1 and Z2 into a set of points, and calculate the boundary coordinate sequence X3 of this set of points. The shape enclosed by X3 is recorded as the composite aggregate. Step 5.2b: Calculate the equivalent particle size d of the synthetic aggregate, if d∈(D i-1 ,D i ), the coordinates (x, y) of the pre-placement center of the aggregate are randomly generated, and the center coordinates of X3 and X1 are moved to the pre-placement center (x, y) of the aggregate to obtain the coordinate sequences X'3 and X'1. The figure enclosed by X'1 is the aggregate phase of the recycled aggregate model, and the difference set of the figures enclosed by X'3 and X'1 is the attached mortar phase. The aggregate phase and the attached mortar phase together constitute the recycled aggregate model; otherwise, return to step 5.1b.

5. The method for constructing a recycled concrete meso-aggregate model based on Fourier transform according to claim 1, characterized in that: The method for judging whether the aggregate model meets the boundary conditions in step 6 is as follows: Determine the minimum circumscribed rectangle T of the aggregate model s The position relationship with the plane rectangular domain T, if T s If it is inside T, it means that the aggregate meets the boundary conditions of the placement area; otherwise, it means that the aggregate model does not meet the boundary conditions.

6. The method for constructing a recycled concrete meso-aggregate model based on Fourier transform according to claim 1, characterized in that: In step 6, whether the aggregate model AG satisfies the aggregate interference condition is determined by using the minimum circumscribed rectangle intersection method: Step 6.1: Search for the rectangle C that intersects with the minimum bounding rectangle T0 of AG among the minimum bounding rectangles of all the aggregate models that have been placed. f |f=1,2…e}, and the corresponding aggregate set is named AGG, AGG={A f |f=1,2…e}, where c f A represents the minimum bounding rectangle of the fth aggregate model intersecting with T0. f represents the aggregate model whose fth minimum bounding rectangle intersects with T0, and e represents the number of minimum bounding rectangles of the aggregate model intersecting with T0. If C is an empty set, it means that the aggregate interference condition is met. Otherwise, execute step 6.

2. Step 6.2: Determine whether the maximum inscribed circle of AG intersects with the maximum inscribed circle of any aggregate in AGG. If so, it means that the aggregate interference condition is not met. Otherwise, go to step 6.

3. Step 6.3: Set f = 1 and proceed to step 6.

4. Step 6.4: Calculate c f The rectangle E of the overlapping area with T0 f The polar angles of the four vertices of the aggregate model AG in the polar coordinate system with the center of the coordinate origin as ψ={ψ1,ψ2,ψ3,ψ4}, where ψ1,ψ2,ψ3,ψ4 represent E f The polar angle values ​​of the four vertices in the polar coordinate system with the center of the aggregate AG as the coordinate origin; and calculate the rectangular E in the rectangular coordinate system with the center of the aggregate model AG as the coordinate origin f The lower left corner coordinate vertex (X lf ,Y lf ) and E f The center abscissa X cf and E f The height L1, if X cf >0 and Y lf ×(Y lf +L1)<0, then let α={α p =2p·ψ m / N5|p=0,1,2…N5 / 2}∪{α p =ψ n +(4π-2ψ n )·p / N5|p=N5 / 2,N5 / 2+1,…N5}, otherwise, let α={α p =ψ a +p·(ψ b -ψ a ) / N5|p=0,1,2…N5}, where ψ m is the maximum polar angle value in ψ that is less than π, ψ n is the minimum polar angle value greater than π in ψ, a is the minimum polar angle value in the set ψ, b is the maximum polar angle value in ψ, α represents the polar angle value set to be verified, α p represents the pth polar angle value to be verified, and N5 is the number of division points; Step 6.5: Calculate the polar coordinate value sequence of the contour points of the aggregate model AG under the extreme angle value set α and convert it into the rectangular coordinate sequence Z1={(x' p ,y' p )|p=1,2,3…N5}, where (x' p ,y' p ) represents the pth coordinate to be verified on the contour of the aggregate model AG; if all coordinate points in Z1 are not in E f Internally, the fth aggregate A f Does not interfere with the aggregate model AG, otherwise, calculate all coordinate points in Z1 to the fth aggregate A f The distance between the centers d={d p |p=1,2,3…N5} and all coordinate points in Z1 are based on the fth aggregate A f The polar angle set τ in the polar coordinate system with the center as the origin is τ={τ p |p=1,2,3…N5}, calculate the fth aggregate A f The polar radius value set {I p |p=1,2,3…N5}, where d p Indicates the distance from the pth coordinate point to be verified to the fth aggregate A f The distance between the centers, τ p Indicates that the p-th coordinate point in Z1 is the f-th aggregate A f The polar angle of the polar coordinate system with the center as the origin, I p represents the fth aggregate A f At the pth polar angle τ p The polar value of the lower contour point; if there is I p >d p , then it means the fth aggregate A f Interference with the aggregate model AG, otherwise, it means the fth aggregate A f No interference with the aggregate model AG; Step 6.6: Assign f+1 to f, return to step 6.4 and execute sequentially until f>e. If the aggregate model AG does not interfere with all aggregates in AGG, it means that the aggregate interference condition is met; otherwise, it means that the aggregate interference condition is not met.

7. An electronic device comprising a memory and a processor, characterized in that: The memory is used to store a program that supports a processor to execute the construction method according to any one of claims 1 to 6, and the processor is configured to execute the program stored in the memory.

8. A computer-readable storage medium having a computer program stored thereon, characterized in that: When the computer program is executed by a processor, the steps of the construction method according to any one of claims 1 to 6 are executed.

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