A method for efficiently constructing a mesoscopic model of three-dimensional random aggregate concrete

Abstract

The present invention provides a method for efficiently constructing a mesoscopic model of three-dimensional random aggregate concrete, including: setting parameters such as the size of concrete, the volume fraction of aggregate, the aggregate particle size range, the thickness of the interfacial transition zone, etc.; determining the aggregate gradation by using the Fuller grading formula; randomly determining the average particle size and the number of vertices of an aggregate by using the aggregate random generation function; randomly determining the vertex coordinates of each aggregate within a predetermined range of the average particle size of the aggregate; calculating the total volume of the aggregates that have been generated currently, and when the total volume of the aggregates that have been generated currently meets the volume fraction of the aggregate, constructing irregular polyhedron aggregates by using the Delaunay triangulation method and the graphic envelope method; constructing the interfacial transition region by using the Delaunay triangulation method and the graphic envelope method; sorting the aggregates according to their volumes and randomly placing them in the concrete region. The construction method of the present invention is simple and efficient, the model placement efficiency is high, the spatial randomness of the aggregates is high, and the universality is strong, and it can be applied to various working conditions in the aspect of concrete durability.

Description

Technical Field

[0001] The present invention relates to the technical field of concrete mesoscopic model construction, and specifically, to a method for efficiently constructing a three-dimensional random aggregate concrete mesoscopic model. Background Art

[0002] Some experimental studies on concrete are often restricted by factors such as site, equipment, and environment, making it impossible to analyze the structural components at the mesoscopic level. Therefore, numerical research on mesoscopic models has become a powerful research method. The construction of a concrete mesoscopic model is the basis for numerical research on concrete. At the mesoscopic scale, concrete can be regarded as a three-phase composite material composed of coarse aggregates, mortar, and the interfacial transition zone (ITZ) between mortar and aggregates. Its mechanical properties, durability, and other characteristics are related to mesoscopic scale characteristics such as aggregate shape, aggregate gradation, aggregate volume fraction, and ITZ thickness. Establishing a concrete mesoscopic model that is closer to the actual concrete aggregate shape and meets the aggregate gradation requirements of experimental research is an important hot topic today.

[0003] Currently, there are mainly two types of methods for constructing concrete mesoscopic models:

[0004] 1) Image recognition and processing are carried out through scanning imaging to distinguish the cement matrix and aggregates and establish a model. For example, the Chinese patent with the application number 201810833630.5 discloses a mesoscopic structure reconstruction method based on the pixel characteristics of concrete CT images. By automatically recognizing and extracting CT images of concrete, the coordinate data of spatial target bodies are determined by judging the gray values of each component, and based on the INP file data of ABAQUS, the unit nodes and sets of spatial target bodies are matched to reconstruct the concrete mesoscopic model. However, this patent has the following problems: the modeling efficiency of this method is low, and it is restricted by experimental equipment. For some equipment with low resolution, it is impossible to distinguish each component well. Another example is the Chinese patent with the application number 202110242982.5, which discloses an efficient method for generating and placing three-dimensional aggregates in concrete - the three-dimensional remaining space method. Three-dimensional aggregates are reconstructed by scanning real concrete slices, the aggregates are separated, fitted into ideal shapes, and their parameters are extracted. Based on the extracted three-dimensional parameters, three-dimensional concrete mesoscopic models with different sizes and different replacement rates are established. However, this patent has the following problems: although the algorithm efficiency of this method has been improved, it still requires the use of real concrete, and the overall efficiency is low. In addition, the constructed model is only applicable to the concrete of specific experiments and does not have universality.

[0005] 2) By means of computer modeling, each component is placed and constructed. For example, the Chinese patent with the application number 202111136735.3 discloses a method for modeling a three-dimensional mesoscopic model of fully graded concrete with random defects. Through a random shrinkage process centered on the corresponding nucleation points for each convex polyhedron cell in the three-dimensional Voronoi diagram to meet the aggregate gradation requirements, a random aggregate model with a four-grade distribution is generated; and random spherical pore defects with the required volume content are quickly introduced outside the aggregate distribution area, and finally a mesoscopic model of fully graded concrete with random defects is established. However, this patent has the following problems: the algorithm has a relatively high complexity, and after the division of each aggregate polyhedron, the shrinkage ratio is the same, which will reduce the spatial randomness of the aggregate distribution. Another example is the Chinese patent with the application number 202011230867.8, which discloses a method for constructing a concrete model with multi-gradation and high volume fraction. Through the processes of randomly jittering a uniformly distributed seed lattice, repulsive force rearrangement, weighted Voronoi division, and particle reconstruction, a concrete model with multi-gradation and high volume fraction is constructed. However, this patent only establishes a two-dimensional concrete mesoscopic model and does not construct a three-dimensional concrete mesoscopic model. Summary of the Invention

[0006] Aiming at the defects in the prior art, the purpose of the present invention is to provide a method for efficiently constructing a three-dimensional random aggregate concrete mesoscopic model.

[0007] According to one aspect of the present invention, there is provided a method for efficiently constructing a three-dimensional random aggregate concrete mesoscopic model, including:

[0008] Setting a concrete area with a preset length, preset width, and preset height, the maximum particle size of the concrete aggregate is Dmax, the minimum particle size is Dmin, the aggregate volume fraction is Va, and the thickness of the interfacial transition zone is t; according to the set aggregate particle size range, the Fuller grading formula is used to determine the aggregate gradation;

[0009] According to the Fuller grading curve and the aggregate volume fraction, an aggregate random generation function is used to randomly determine the average particle size and the number of vertices of an aggregate;

[0010] Randomly determining the vertex coordinates of each aggregate within a predetermined range of the average particle size of the aggregate;

[0011] Calculating the total volume of the aggregates that have been generated currently according to the vertex coordinates of the aggregates, and when the total volume of the aggregates that have been generated currently meets the aggregate volume fraction, the Delaunay triangulation method and the graphic envelope method are used to construct irregular polyhedron aggregates;

[0012] According to the thickness of the interfacial transition zone, a layer of interfacial transition region is constructed around the aggregates by using the Delaunay triangulation method and the graphic envelope method;

[0013] Sort the aggregates with the interface transition region according to their volume sizes and randomly place them in the concrete region to obtain a three-dimensional random aggregate concrete mesoscopic model.

[0014] Furthermore, the aggregate gradation is determined by using the Fuller gradation formula, where the Fuller gradation formula is:

[0015]

[0016] where P is the aggregate volume cumulative distribution function, Di is the current average aggregate particle size, D is the average aggregate particle size, Va is the aggregate volume fraction; n is a coefficient ranging from 0.3 to 0.5.

[0017] Furthermore, a random aggregate generation function is used to randomly determine the average particle size and the number of vertices of an aggregate, where the random aggregate generation function is:

[0018]

[0019] where α is a random number ranging from 0 to 1.

[0020] Furthermore, randomly determining the vertex coordinates of each aggregate within a predetermined range of the average particle size of the aggregate includes:

[0021] Determine the number of vertices b according to the average particle size of each aggregate;

[0022] Randomly select a point within the aggregate as the center point of the aggregate, denoted as point O;

[0023] Randomly determine the distance r i , 0.55D i between each vertex of the aggregate and the center point within the range of i as:

[0024] r i = 0.5D0 + 0.05D0(2α - 1), where α is a random number ranging from 0 to 1;

[0025] Iterate through each vertex, denote the current vertex as A and the next vertex as B, and determine the horizontal and vertical components of the AOB angle within the range of [0, 2π / b]:

[0026] θ' i = 2π(1 + (2α - 1)*β / b,

[0027]

[0028]

[0029]

[0030] where θ' i and are intermediate variables, θ i is the horizontal component of the angle AOB, is the vertical component of the angle AOB, and α, β, γ, and η are random numbers between 0 and 1 respectively;

[0031] Convert the spherical coordinates of the aggregate vertex to rectangular coordinates, and the coordinate transformation is:

[0032]

[0033] Obtain the coordinates (xi, yi, zi) of the aggregate vertex relative to the aggregate center.

[0034] Further, determining the number of vertices b of each aggregate according to the average particle size of each aggregate includes:

[0035] When the average particle size of the aggregate is less than 5 mm, the number of aggregate vertices is 18 to 23;

[0036] When the average particle size of the aggregate is greater than 5 mm and less than 9.5 mm, the number of aggregate vertices is 20 to 26;

[0037] When the average particle size of the aggregate is greater than 9.5 mm and less than 18 mm, the number of aggregate vertices is 21 - 28;

[0038] When the average particle size of the aggregate is greater than 18 mm, the number of aggregate vertices is 24 to 32.

[0039] Further, the construction of irregular polyhedron aggregates using the Delaunay triangulation method and the graphic envelope method includes:

[0040] Using the Delaunay triangulation method, traverse each vertex of the aggregate, construct a triangular pyramid grid for every four vertices, and using the graphic envelope method, only retain the outermost surface of the graphic and delete the remaining triangular pyramids to obtain irregular polyhedron aggregates.

[0041] Further, after calculating the total volume of the aggregates that have been generated currently according to the vertex coordinates of the aggregates, it further includes:

[0042] Judge whether the total volume of the aggregates that have been generated currently meets the requirement of the aggregate volume fraction; if the total volume of the aggregates that have been generated currently does not meet the requirement of the aggregate volume fraction, then return to the step of randomly determining the average particle size and the number of vertices of an aggregate using the aggregate random generation function according to the Fuller grading curve and the aggregate volume fraction.

[0043] Further, constructing an interfacial transition zone around the aggregate by using the Delaunay triangulation method and the graphic envelope method includes:

[0044] Expanding the vertex coordinates of the aggregate outward:

[0045]

[0046] After obtaining the vertex coordinates of the interfacial transition zone, using the Delaunay triangulation method to traverse each vertex of the interfacial transition zone, constructing a triangular pyramid grid for every four vertices, and using the graphic envelope method to only retain the outermost surface of the graphic and delete the remaining triangular pyramids to obtain an irregular polyhedron aggregate.

[0047] Further, sorting the aggregates with the interfacial transition zone according to the volume size and randomly placing them in the concrete area includes:

[0048] Traversing all the aggregates and sorting them in descending order of volume;

[0049] Placing the aggregates in descending order of volume in turn. The coordinates of the center point of the aggregate are:

[0050]

[0051] where r max is the maximum distance between the vertex and the center of the aggregate; e is the minimum distance between the aggregates; α, β, and γ are random numbers between 0 and 1 respectively;

[0052] Calculating the distance between the centers of the aggregates. When the distance between the centers of the aggregates is greater than the sum of the circumradii of the two aggregates, the placement of this aggregate is completed.

[0053] Further, after calculating the distance between the centers of the aggregates, it also includes: judging whether the aggregates overlap according to the distance between the centers of the aggregates. If the distance between the centers of the aggregates is less than the sum of the circumradii of the two aggregates, it is judged that the aggregates overlap, and then this aggregate is re-placed until the placement of this aggregate is completed.

[0054] Compared with the prior art, the present invention has at least one of the following beneficial effects:

[0055] 1. The method for efficiently constructing a three-dimensional random aggregate concrete mesoscopic model of the present invention has a simple and efficient method process. The generated concrete model has a high spatial randomness of aggregates and is closer to the morphology and distribution of real concrete aggregates; moreover, the model adopts an adjustable Fuller grading, which can meet various grading and aggregate volume fraction requirements.

[0056] 2. The method for efficiently constructing a mesoscopic model of three-dimensional random aggregate concrete in the present invention uses the Delaunay triangulation and graphic envelope method. The generated polyhedral aggregates do not need to judge concavity and convexity, making the model construction process more concise and efficient.

[0057] 3. The method for efficiently constructing a mesoscopic model of three-dimensional random aggregate concrete in the present invention can generate concrete models with different shapes and types of aggregates by changing initial parameters (such as the maximum aggregate size, minimum aggregate size, number of aggregate vertices, etc.). Moreover, the model includes the mortar-aggregate interfacial transition zone, with strong generality and a wide range of applications. It can meet the needs of the vast majority of experimental and numerical studies and can be applied to various working conditions in concrete durability. BRIEF DESCRIPTION OF THE DRAWINGS

[0058] By reading the detailed description of the non-limiting embodiments with reference to the following drawings, other features, objectives, and advantages of the present invention will become more apparent:

[0059] Figure 1 It is a schematic flow chart of the method for efficiently constructing a mesoscopic model of three-dimensional random aggregate concrete in an embodiment of the present invention;

[0060] Figure 2 It is the aggregate size density distribution function adopted in an embodiment of the present invention and the generated aggregate size density distribution diagram;

[0061] Figure 3 It is a schematic diagram of the Delaunay triangulation method adopted in an embodiment of the present invention;

[0062] Figure 4 It is a schematic diagram of constructing aggregates by the graphic envelope method adopted in an embodiment of the present invention;

[0063] Figure 5 It is a schematic diagram of the interfacial transition zone (ITZ) constructed in an embodiment of the present invention;

[0064] Figure 6 It is a schematic diagram after the aggregates are placed in an embodiment of the present invention;

[0065] Figure 7 It is a schematic diagram of the final three-dimensional random aggregate concrete mesoscopic model in an embodiment of the present invention. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0066] The present invention will be described in detail below with reference to specific embodiments. The following embodiments will help those skilled in the art to further understand the present invention, but do not limit the present invention in any form. It should be noted that for those of ordinary skill in the art, without departing from the concept of the present invention, several modifications and improvements can be made. These all belong to the protection scope of the present invention.

[0067] An embodiment of the present invention provides a method for efficiently constructing a mesoscopic model of three-dimensional random aggregate concrete. Refer to Figure 1 , the method includes:

[0068] S1. According to specific experimental requirements, set a concrete area with a length of L, a width of W, and a height of H. The maximum particle size of the concrete aggregate is Dmax, the minimum particle size is Dmin, Va is the aggregate volume fraction, and the thickness of the interfacial transition zone is t; according to the set aggregate particle size range, use the Fuller grading formula to determine the aggregate grading;

[0069] S2. According to the Fuller grading curve and the aggregate volume fraction Va set in S1, use the aggregate random generation function to randomly determine the average particle size and the number of vertices of an aggregate;

[0070] S3. Randomly determine the vertex coordinates of each aggregate within a predetermined range of the average particle size of the aggregate generated in S2;

[0071] S4. Calculate the total volume of the aggregates that have been generated currently according to the aggregate vertex coordinates determined in S3. When the total volume of the aggregates that have been generated currently meets the aggregate volume fraction Va set in S1, use the Delaunay triangulation method and the graphic envelope method to construct irregular polyhedron aggregates; otherwise, repeat steps S2 - S4;

[0072] S5. According to the thickness t of the interfacial transition zone set in S1, use the Delaunay triangulation method and the graphic envelope method to construct an interfacial transition region around the aggregates;

[0073] S6. Sort the aggregates constructed in S4 with the interfacial transition region generated in S5 according to the volume size, and randomly place them in the concrete area set in S1 to obtain a mesoscopic model of three-dimensional random aggregate concrete.

[0074] In the method for constructing a mesoscopic model of three-dimensional random aggregate concrete in the embodiment of the present invention, the process is simple and efficient. The generated concrete model has a high spatial randomness of aggregates, which is closer to the morphology and distribution of real concrete aggregates; moreover, the model adopts an adjustable Fuller grading, which can meet various grading and aggregate volume fraction requirements.

[0075] In some preferred embodiments, in step S1, using the Fuller grading formula to determine the aggregate grading includes: The Fuller grading formula is:

[0076]

[0077] where P is the aggregate volume accumulation distribution function, Di is the current average particle size of the aggregate, D is the average particle size of the aggregate, Va is the aggregate volume fraction; n is a coefficient from 0.3 to 0.5, which can be adjusted according to specific experimental requirements.

[0078] In some preferred embodiments, in step S2, a random aggregate generation function is used to randomly determine the average particle size and the number of vertices of an aggregate, including: The random aggregate generation function is:

[0079]

[0080] where α is a random number between 0 and 1.

[0081] In some preferred embodiments, in step S3, within a predetermined range of the average particle size of the aggregate generated in S2, the vertex coordinates of each aggregate are randomly determined, including:

[0082] S31. Determine the number of vertices b of each aggregate according to its average particle size;

[0083] S32. Randomly select a point within the aggregate range as the center point of the aggregate, denoted as point O;

[0084] S33. To avoid sharp corners that affect the mechanical properties of the aggregate, within the range of [0.45D i , 0.55D i , randomly determine the distance r between each vertex of the aggregate and the center point: i is:

[0085] r i = 0.5D0 + 0.05D0(2α - 1); where α is a random number between 0 and 1;

[0086] It should be noted that the aggregate range can be adjusted according to experimental requirements. The larger the interval, the greater the probability of sharp corners in the aggregate, and the smaller the interval, the more regular the shape of the aggregate tends to be.

[0087] S34. Iterate through each vertex, denote the current vertex as A and the next vertex as B, and determine the horizontal and vertical components of the AOB angle within the range of [0, 2π / b]:

[0088] θ' i = 2π(1 + (2α - 1)*β / b,

[0089]

[0090]

[0091]

[0092] where θ' i , is an intermediate variable, θ i is the horizontal component of the AOB angle, is the vertical component of the AOB angle, and α, β, γ, and η are random numbers between 0 and 1 respectively;

[0093] S35. Convert the spherical coordinates of the aggregate vertex to rectangular coordinates, and the coordinate transformation is:

[0094]

[0095] Obtain the coordinates (xi, yi, zi) of the aggregate vertex relative to the aggregate center.

[0096] In some preferred embodiments, in step S31, determining the number of vertices b of each aggregate according to the average particle size of each aggregate includes:

[0097] When the average particle size of the aggregate is less than 5 mm, the number of aggregate vertices is 18 - 23;

[0098] When the average particle size of the aggregate is greater than 5 mm and less than 9.5 mm, the number of aggregate vertices is 20 - 26;

[0099] When the average particle size of the aggregate is greater than 9.5 mm and less than 18 mm, the number of aggregate vertices is 21 - 28;

[0100] When the average particle size of the aggregate is greater than 18 mm, the number of aggregate vertices is 24 - 32.

[0101] In some preferred embodiments, in step S4, constructing an irregular polyhedron aggregate by using the Delaunay triangulation method and the graphic envelope method includes: using the Delaunay triangulation method, traversing each vertex of the aggregate, constructing a triangular pyramid grid for every four vertices, and using the graphic envelope method to only retain the outermost surface of the graphic and delete the remaining triangular pyramids to obtain an irregular polyhedron aggregate. By using the Delaunay triangulation and the graphic envelope method, the generated polyhedron aggregate does not need to judge the concavity and convexity, making the model construction process more concise and efficient.

[0102] In some preferred embodiments, in step S4, after calculating the total volume of the currently generated aggregate according to the aggregate vertex coordinates determined in S3, it further includes:

[0103] Judging whether the total volume of the currently generated aggregate meets the aggregate volume fraction requirement; if the total volume of the currently generated aggregate does not meet the aggregate volume fraction requirement, return to step S2.

[0104] In some preferred embodiments, in step S5, constructing an interface transition region around the aggregate by using the Delaunay triangulation method and the graphic envelope method includes:

[0105] Expand the aggregate vertex coordinates outwards:

[0106] After obtaining the vertex coordinates of the interfacial transition zone, the Delaunay triangulation method is used to traverse each vertex of the interfacial transition zone. A triangular pyramid mesh is constructed for every four vertices. Using the graphic envelope method, only the outermost surface of the graphic is retained, and the remaining triangular pyramids are deleted to obtain irregular polyhedron aggregates. By using the Delaunay triangulation and graphic envelope methods, the generated interfacial transition zone has a uniform thickness, that is, the distance from the aggregate is equal everywhere, and the algorithm is simple and efficient.

[0107] In some preferred embodiments, in step S6, the aggregates constructed in S4 with the interfacial transition region generated in S5 are sorted according to volume size and randomly placed in the concrete region set in S1, including:

[0108] S61. Traverse all aggregates and sort the aggregates from largest to smallest in volume;

[0109] S62. Place the aggregates in order from largest to smallest in volume. The coordinates of the center point of the aggregate are:

[0110]

[0111] where r max is the maximum distance between the vertex and the center of the aggregate; e is the minimum distance between the aggregates; α, β, and γ are random numbers between 0 and 1 respectively;

[0112] S63. Calculate the distance between the centers of the aggregates. When the distance between the centers of the aggregates is greater than the sum of the circumradius of the two aggregates, the placement of this aggregate is completed.

[0113] In some preferred embodiments, after calculating the distance between the centers of the aggregates, it further includes: judging whether the aggregates overlap according to the distance between the centers of the aggregates. If the distance between the centers of the aggregates is less than the sum of the circumradius of the two aggregates, it is judged that the aggregates overlap, and then this aggregate is re-placed until the placement of this aggregate is completed.

[0114] The present invention uses the Delaunay triangulation method and the graphic envelope method. First, an aggregate library is established, and then the aggregates are placed. The spatial randomness of the aggregates is high, approaching the real morphology and distribution of concrete aggregates. The construction process is simple and efficient. For the method for efficiently constructing a three-dimensional random aggregate concrete mesoscopic model in the embodiments of the present invention, a specific embodiment is described in more detail.

[0115] Step 1. Set a cube-shaped concrete with a length of 50 mm, a width of 50 mm, and a height of 50 mm. The aggregate particle size range is set to 2.5 mm to 10 mm, the aggregate volume fraction is set to 50%, and the interfacial transition zone thickness is set to 60 μm.

[0116] Step 2. According to the set aggregate particle size range, use the Fuller grading formula to determine the optimal aggregate grading. The aggregate grading curve is as shown in curve Figure 2 , and the adopted Fuller grading formula is:

[0117]

[0118] where P is the aggregate volume accumulation distribution function, D i is the current average aggregate particle size, D is the particle size smaller than the current aggregate particle size, V a is the aggregate volume fraction, taking 50%, D max is the maximum aggregate particle size, taking 10 mm, and n takes 0.5.

[0119] Step 3. Randomly determine the average particle size D of each aggregate according to the Fuller grading curve and the aggregate volume fraction. The generated aggregate particle size density is as shown in i , and the adopted aggregate random generation function is: Figure 2 where

[0120]

[0121] α is a random number from 0 to 1.

[0122] Step 4. Randomly determine the vertex coordinates of the aggregate within the range of 0.45 to 0.55 times the average particle size of each aggregate. The specific operation steps are as follows:

[0123] 4.1) Determine the number of vertices b of each aggregate according to its average particle size:

[0124] When the average particle size of the aggregate is less than 5 mm, the number of aggregate vertices is 18 - 23;

[0125] When the average particle size of the aggregate is greater than 5 mm and less than 9.5 mm, the number of aggregate vertices is 20 - 26;

[0126] When the average particle size of the aggregate is greater than 9.5 mm and less than 18 mm, the number of aggregate vertices is 21 - 28;

[0127] When the average particle size of the aggregate is greater than 18 mm, the number of aggregate vertices is 24 - 32.

[0128] It should be noted that those skilled in the art can make any appropriate adjustment to the number of vertices b according to specific experimental requirements.

[0129] 4.2) Randomly select a point within the aggregate as the center point of the aggregate, denoted as point O.

[0130] 4.3) Within [0.45D i , 0.55D i] Randomly determine the distance r between each vertex and the center of the aggregate i for:

[0131] r i =0.5D0+0.05D0(2α-1),

[0132] Here, α is a random number between 0 and 1.

[0133] 4.4) Traverse each vertex, record the current vertex as A, record the next vertex as B, and determine the horizontal and vertical components of the angle AOB in the range [0, 2π / b]:

[0134] θ' i =2π(1+(2α-1)*β / b,

[0135]

[0136]

[0137]

[0138] Among them, θ' i , is the intermediate variable, θ i is the horizontal component of the AOB angle, is the vertical component of the AOB angle, and α, β, γ and η are random numbers ranging from 0 to 1 respectively.

[0139] 4.5) Convert the spherical coordinates of the aggregate vertices into rectangular coordinates. The coordinate transformation is:

[0140]

[0141] Get the coordinates of the aggregate vertex relative to the center of the aggregate (x i ,y i , z i ).

[0142] Step 5: Calculate the total volume of the aggregates currently generated. If the aggregate volume fraction requirement is not met, repeat steps 3 and 4. If the aggregate volume fraction requirement is met, proceed to the next step. When the volume fraction requirement of 50% is reached, a total of 957 aggregates are generated.

[0143] Step 6: Use the Delaunay triangulation method to traverse each vertex of the aggregate and construct a triangular pyramid mesh for every four vertices, such as Figure 3 As shown. Using the graphic envelope method, retain the outermost surface and delete the remaining triangular pyramids to obtain irregular polyhedron aggregates, as shown Figure 4 shown.

[0144] Step 7: Expand the aggregate vertex coordinates outward according to the thickness of the interfacial transition zone:

[0145]

[0146] After obtaining the vertex coordinates of the interfacial transition zone, the interfacial transition zone is generated by the Delaunay triangulation method, as Figure 5 shown.

[0147] Step 8: Randomly place the aggregates into the concrete area, and the specific steps are as follows:

[0148] 8.1) Traverse all aggregates and sort the aggregates from largest to smallest by volume.

[0149] 8.2) Place the aggregates one by one from largest to smallest by volume. The coordinates of the center point of the aggregate are:

[0150]

[0151] where r max is the maximum distance between the vertex and the center of the aggregate; e is the minimum distance between the aggregates, taking 0.5 mm; α, β, and γ are random numbers from 0 to 1 respectively.

[0152] 8.3) Determine whether the aggregates overlap: Calculate the distance between the centers of the aggregates. When the distance between the centers of the aggregates is greater than the sum of the circumradii of the two aggregates, the placement of this aggregate is completed; when the distance between the centers of the aggregates is less than the sum of the circumradii of the two aggregates, re-place this aggregate until the placement of this aggregate is completed. After the placement is completed, as Figure 6 shown.

[0153] The finally obtained three-dimensional irregular aggregate concrete mesoscopic model is as Figure 7 shown. The aggregates in this model have a high degree of spatial randomness and are closer to the morphology and distribution of real concrete aggregates; the model contains the mortar-aggregate interfacial transition zone, has strong versatility, a wide range of applications, can meet the needs of most experimental and numerical studies, and can be applied to various working conditions in concrete durability.

[0154] The specific embodiments of the present invention have been described above. It should be understood that the present invention is not limited to the above specific embodiments, and those skilled in the art can make various deformations or modifications within the scope of the claims, which does not affect the essence of the present invention. The above preferred features can be combined arbitrarily without conflict.

Claims

1. A method for efficiently constructing a mesoscopic model of three-dimensional randomly aggregated concrete, characterized in that Including: Set a concrete area with a preset length, width, and height. The maximum particle size of the concrete aggregate is Dmax, the minimum particle size is Dmin, the aggregate volume fraction is Va, and the thickness of the interfacial transition zone is t. According to the set aggregate particle size range, use the Fuller grading formula to determine the aggregate grading; According to the Fuller grading curve and the aggregate volume fraction, use the aggregate random generation function to randomly determine the average particle size and the number of vertices of an aggregate; Randomly determine the vertex coordinates of each aggregate within a predetermined range of the average particle size of the aggregate; Calculate the total volume of the aggregates that have been generated currently according to the vertex coordinates of the aggregates. When the total volume of the aggregates that have been generated currently meets the aggregate volume fraction, use the Delaunay triangulation method and the graphic envelope method to construct irregular polyhedron aggregates; According to the thickness of the interfacial transition zone, use the Delaunay triangulation method and the graphic envelope method to construct a layer of interfacial transition zone around the aggregates; Sort the aggregates with the interfacial transition zone according to their volume sizes and randomly place them in the concrete area to obtain a three-dimensional random aggregate concrete mesoscopic model; where: The Fuller grading formula is used to determine the aggregate grading, where the Fuller grading formula is: Where P is the aggregate volume cumulative distribution function, Di is the current average particle size of the aggregate, D is the average particle size of the aggregate, Va is the aggregate volume fraction; n is a coefficient between 0.3 and 0.5; The aggregate random generation function is used to randomly determine the average particle size and the number of vertices of an aggregate, where the aggregate random generation function is: Among them, α is a random number between 0 and 1; Randomly determining the vertex coordinates of each aggregate within a predetermined range of the average particle size of the aggregate includes: Determine the number of vertices b of each aggregate according to its average particle size; Randomly select a point within the aggregate as the center point of the aggregate, denoted as point O; within [0.45D i , 0.55D i , randomly determine the distance r between each vertex of the aggregate and the center point i as follows: r i = 0.5D0 + 0.05D0(2α - 1), where α is a random number between 0 and 1; Iterate through each vertex. Denote the current vertex as A and the next vertex as B. Determine the horizontal and vertical components of the AOB angle within the range of [0, 2π / b]; θ′ i = 2π(1 + (2α - 1) * β / b, Among them, θ′ i and are intermediate variables, θ i is the horizontal component of the included angle of AOB, is the vertical component of the included angle of AOB, and α, β, γ, and η are random numbers respectively ranging from 0 to 1; Convert the spherical coordinates of the aggregate vertices to rectangular coordinates, and the coordinate transformation is: Obtain the coordinates (xi, yi, zi) of the aggregate vertices relative to the aggregate center; Using the Delaunay triangulation method and the graphic envelope method to construct irregular polyhedron aggregates includes: Using the Delaunay triangulation method, iterate through each vertex of the aggregate. Construct a triangular pyramid grid for every four vertices. Using the graphic envelope method, only retain the outermost surface of the graph and delete the remaining triangular pyramids to obtain irregular polyhedron aggregates; Using the Delaunay triangulation method and the graphic envelope method to construct a layer of interfacial transition zone around the aggregates includes: Expand the aggregate vertex coordinates outward; After obtaining the vertex coordinates of the interfacial transition zone, use the Delaunay triangulation method, iterate through each vertex of the interfacial transition zone, construct a triangular pyramid grid for every four vertices. Using the graphic envelope method, only retain the outermost surface of the graph and delete the remaining triangular pyramids to obtain irregular polyhedron aggregates.

2. The method for efficiently constructing a mesoscopic model of three-dimensional random aggregate concrete according to claim 1, characterized in that Determining the number of vertices b of each aggregate according to its average particle size includes: When the average particle size of the aggregate is less than 5 mm, the number of vertices of the aggregate is 18 - 23; When the average particle size of the aggregate is greater than 5 mm and less than 9.5 mm, the number of vertices of the aggregate is 20 - 26; When the average particle size of the aggregate is greater than 9.5 mm and less than 18 mm, the number of vertices of the aggregate is 21 - 28; When the average particle size of the aggregate is greater than 18 mm, the number of vertices of the aggregate is 24 - 32.

3. The method for efficiently constructing a mesoscopic model of three-dimensional random aggregate concrete according to claim 1, characterized in that After calculating the total volume of the aggregates that have been generated currently according to the vertex coordinates of the aggregates, it further includes: Judging whether the total volume of the aggregates that have been generated currently meets the requirement of the aggregate volume fraction; if the total volume of the aggregates that have been generated currently does not meet the requirement of the aggregate volume fraction, return to the step of randomly determining the average particle size and the number of vertices of an aggregate by using the aggregate random generation function according to the Fuller grading curve and the aggregate volume fraction.

4. The method for efficiently constructing a mesoscopic model of three-dimensional random aggregate concrete according to claim 1, characterized in that Sorting the aggregates with the interface transition region according to the volume size and randomly placing them in the concrete region, including: Traversing all the aggregates and sorting the aggregates from large to small according to the volume; Placing the aggregates in order from large to small according to the volume, and the coordinates of the center point of the aggregate are: where r max is the maximum distance from the vertex of the aggregate to the center; e is the minimum distance between aggregates; α, β, and γ are random numbers between 0 and 1, respectively; Calculating the distance between the centers of the aggregates, and when the distance between the centers of the aggregates is greater than the sum of the circumradius of two aggregates, the placement of this aggregate is completed.

5. The method for efficiently constructing a mesoscopic model of three-dimensional random aggregate concrete according to claim 4, wherein After calculating the distance between the centers of the aggregates, it further includes: judging whether the aggregates overlap according to the distance between the centers of the aggregates. If the distance between the centers of the aggregates is less than the sum of the circumradius of two aggregates, it is judged that the aggregates overlap, and then this aggregate is placed again until the placement of this aggregate is completed.

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