Method for random generation of two-dimensional geometric structure of concrete aggregate based on coordinate grid

Abstract

A kind of concrete aggregate two-dimensional geometric structure random generation method based on coordinate grid, including the following steps etc.: step 1, determine the physical parameters of concrete mix proportion and each component, specify the width of mortar interface in algorithm, the size of the generated concrete rectangular region;Step 2, according to the specified grading of concrete, its grading is divided into four sections, the area ratio of different section corresponding aggregate is calculated, and the cumulative aggregate area of section grading is calculated;Step 3, randomly select aggregate diameter in the largest section grading, generate the first polygon initial aggregate in the concrete generation area.This method generates random aggregate model, which can realize the three-phase base (aggregate, interface, mortar) material geometric structure simulation of concrete, and the method avoids excessive aggregate coincidence judgment, improves the calculation speed, and helps to realize the mesoscale numerical simulation of concrete structure.

Description

Technical Field

[0001] This invention relates to the technical field of microscopic numerical simulation geometry construction and building materials, specifically to a method for randomly generating two-dimensional geometric structures of concrete aggregates based on coordinate grids. Background Technology

[0002] With the rapid development of civil engineering infrastructure, the demand for research on the performance of engineering structures has gradually increased. Therefore, concrete, as one of the most commonly used and widely applied building materials, has attracted widespread attention from scholars worldwide regarding its mechanical properties. It is well known that the mechanical behavior of concrete is mainly controlled by the individual properties of its components and the bond strength in the transition zone. Therefore, from a materials science perspective, multi-scale (i.e., nano / micro, meso, and macroscale) studies can be conducted to investigate the internal structure, mechanical properties, and failure mechanisms of different types of composite materials.

[0003] Currently, in the study of the mechanical properties of concrete, it is considered a homogeneous material on a macroscopic scale, which is contrary to the non-homogeneous nature of concrete and will lead to limitations in accurately understanding mechanical behavior using macroscopic modeling methods. Summary of the Invention

[0004] Based on this, and in view of the above-mentioned defects in the existing technology, the present invention provides a method for random generation of two-dimensional geometric structures of concrete aggregates based on coordinate grids. This method can realize the establishment of geometric structures in the numerical simulation of concrete structures at the microscale, realize the calculation of geometric coordinates of aggregates and interfaces inside the concrete structure, and provide good preprocessing information for numerical simulation.

[0005] The present invention provides a method for randomly generating two-dimensional geometric structures of concrete aggregates based on coordinate grids, comprising the following steps:

[0006] Step 1: Determine the concrete mix proportion and the physical parameters of each component, and specify the width of the mortar interface and the size of the rectangular area of ​​the generated concrete in the algorithm.

[0007] Step 2: Divide the concrete into four segments according to the specified gradation, calculate the aggregate area ratio corresponding to different segments, and calculate the cumulative aggregate area of ​​the segmented gradation.

[0008] Step 3: Randomly select the aggregate diameter in the maximum segmented gradation and generate the corresponding first polygonal initial aggregate in the concrete generation area;

[0009] Step 4: Divide the concrete generation area into a grid and remove the initial aggregate and the area around the concrete from the grid.

[0010] Step 5: Randomly and uniformly generate other polygonal aggregates with the maximum segmented gradation within the area where concrete has not been removed;

[0011] Step 6: In the second segmented gradation, the same method as in step 5 is used to achieve random distribution of aggregates sequentially, and the algorithm is finally terminated by accumulating the area of ​​aggregates.

[0012] Step 7: In the third segmented gradation, the same method as in step 5 is used to achieve random distribution of aggregates in sequence, and the algorithm is finally terminated by the cumulative area of ​​aggregates.

[0013] Step 8: In the fourth segmented gradation, the same method as in step 5 is used to achieve random distribution of aggregates in sequence, and the algorithm is finally terminated by the cumulative area of ​​aggregates.

[0014] Step 9: After calculating the geometric information of all aggregates and interfaces, draw them.

[0015] Furthermore, in step 3, after selecting the aggregate diameter, the center coordinates of the aggregate are randomly generated in the generation area, the number of sides of the polygonal aggregate is specified, the distance between the angle corresponding to the corner point and the center coordinate is specified, and the area of ​​the polygonal aggregate is recorded.

[0016] Furthermore, in step 5, the method for generating other polygonal aggregates with the maximum segmented gradation is to mark the minimum rectangular search area corresponding to the newly generated aggregate and the interface, determine the minimum marked area through the minimum rectangular search area, and determine the aggregate overlap by using the center coordinates, radius, interface width and polygon corner points of the newly generated aggregate and the existing aggregate.

[0017] If the newly generated aggregate overlaps with the already generated aggregate, then the geometric information of the new aggregate will be regenerated;

[0018] If the new aggregate does not overlap with the already generated aggregate, the minimum marked area corresponding to the new aggregate is removed, and the next aggregate is generated in the grid area after removal. This process is repeated until all aggregates in the maximum segmented gradation have been generated.

[0019] Compared with the prior art, the beneficial effects of this invention are as follows:

[0020] Mesoscale models based on the nonhomogeneity of concrete have been widely used to understand its mechanical response. At the mesoscale level, assuming that concrete is composed of coarse aggregate, mortar, and ITZ, its plastic behavior (i.e., crack initiation and propagation, fracture, etc.) can be well simulated and predicted using mesoscale modeling methods. That is, the cracking process and failure mode of concrete and its internal components can be captured by mesoscale modeling. Therefore, it is the most effective method to study the failure behavior and failure mechanism of concrete and other composite materials.

[0021] In summary, the coordinate grid-based random generation method for two-dimensional geometric structure of concrete aggregates of the present invention can achieve accurate simulation and random distribution of concrete aggregate shape, and realize the calculation of geometric information of the three-phase matrix (aggregate, interface, mortar) materials inside the concrete.

[0022] The present invention provides a method for randomly generating two-dimensional geometric structures of concrete aggregates based on coordinate grids. This method is programmed using MATLAB software, which is convenient to operate and has a fast calculation speed. Attached Figure Description

[0023] Figure 1 This is a flowchart of the method for randomly generating two-dimensional geometric structures of concrete aggregates based on coordinate grids according to the present invention;

[0024] Figure 2 This is a schematic diagram illustrating the generation of the aggregate geometry according to the present invention;

[0025] Figure 3 This is a schematic diagram of the aggregate distribution method of the present invention;

[0026] Figure 4 This is a schematic diagram illustrating the aggregate overlap discrimination relationship of the present invention;

[0027] Figure 5 This is a schematic diagram of the aggregate feeding results of the present invention. Detailed Implementation

[0028] The technical solutions of the present invention will be clearly and completely described below with reference to the accompanying drawings. The described examples are merely some embodiments of the present invention, and not all embodiments. All other embodiments obtained by those skilled in the art based on the embodiments of the present invention without creative effort are within the scope of protection of the present invention.

[0029] It should be noted that, Figures 1-5 Chinese R i Let X be the radius of the approximate circle of the aggregate. 0,i ,Y 0,i (X) represents the coordinates of the approximate center of the aggregate circle. j ,Y j ) represents the coordinates of the aggregate corner point, α j The angle between the aggregate corner point and the positive X-axis is given. A, B, and C are the corner points of the inscribed triangles within the approximate circle of the aggregate. D1, D2, D3, and D4 are the aggregate diameters corresponding to the gradation segments.

[0030] Please see Figures 1-5 This invention provides a method for randomly generating two-dimensional geometric structures of concrete aggregates based on coordinate grids, comprising the following steps:

[0031] Step 1: Determine the concrete mix proportions and the physical parameters of each component, and specify the width of the mortar interface and the size of the rectangular area to be generated in the algorithm;

[0032] Step 2: Divide the concrete into four segments according to the specified gradation, calculate the aggregate area ratio corresponding to different segments using the formula, and calculate the cumulative aggregate area of ​​the segmented gradation.

[0033] Step 3: Randomly select the aggregate diameter in the maximum segmented gradation and generate the corresponding first polygonal initial aggregate within the concrete generation area. After selecting the aggregate diameter, randomly generate the center coordinates of the aggregate at the center position of the generation area, specify the number of sides of the polygonal aggregate, specify the distance between the angle corresponding to the corner point and the center coordinates, and record the area of ​​the polygonal aggregate;

[0034] Step 4: Divide the concrete generation area into a grid and remove the initial aggregate and the area around the concrete from the grid.

[0035] Step 5: Randomly and uniformly generate other polygonal aggregates with the maximum segmented gradation within the area where concrete has not been removed.

[0036] Specifically, the minimum rectangular search area corresponding to the newly generated aggregate and the interface is marked, and the minimum marked area is determined by the minimum rectangular search area. Aggregate overlap is determined by the center coordinates, radius, interface width, and corner points of the aggregate polygons of the newly generated aggregate and existing aggregates. When the newly generated aggregate overlaps with the already generated aggregate, the geometric information of the new aggregate is regenerated; if the new aggregate does not overlap with the already generated aggregate, the minimum marked area corresponding to the new aggregate is removed, and the next aggregate is generated in the removed grid area. This process is repeated until all aggregates in the maximum segmented gradation have been generated.

[0037] Step 6: In the second segmented gradation, the same method as in Step 5 is used to achieve random distribution of aggregates, and the algorithm is finally terminated by accumulating the area of ​​aggregates.

[0038] Step 7: In the third segmented gradation, the same method as in step 5 is used to achieve random distribution of aggregates, and the algorithm is finally terminated by accumulating the area of ​​aggregates.

[0039] Step 8: In the fourth segmented gradation, the same method as in step 5 is used to achieve random distribution of aggregates, and the algorithm is finally terminated by accumulating the area of ​​aggregates.

[0040] Step 9: After calculating the geometric information of all aggregates and interfaces, draw the diagram.

[0041] Specifically, this invention provides a method for randomly generating two-dimensional geometric structures of concrete aggregates based on coordinate grids, with detailed steps as follows:

[0042] Step 1.1: Determine the concrete mix proportions and the densities of coarse aggregate (particle size D>5mm), fine aggregate (particle size D<5mm), cement, water, and admixtures; specify the width R of the mortar interface. itz The dimensions (H, L) of the rectangular concrete region and the maximum aggregate size D4 are generated.

[0043] Step 1.2: Calculate the total volume percentage P of all aggregates (coarse and fine) in the overall concrete. k And the two-dimensional area A of the concrete formation region. con ;

[0044] Step 2.1: According to the concrete gradation distribution curve, the coarse aggregate part is divided into four segments from small to large: [D0,D1], [D1,D2], [D2,D3], and [D3,D4]. Among them, D0 = 5mm, that is, the aggregate smaller than 5mm is fine aggregate, and the mortar formed after it is combined with cement is considered a homogeneous body.

[0045] Step 2.2: Calculate the aggregate area ratio corresponding to different segmented gradations using the Varavan formula (1) and calculate the cumulative aggregate area of ​​the segmented gradations using formula (2);

[0046]

[0047] A agg [D i D i+1 ] = A con ×[P c (D i+1 -P c (D i (2)

[0048] Step 3.1: Calculate the first initial approximate circle radius of aggregate using uniform distribution in the [D3,D4] gradation segment, and specify the center coordinates (H / 2,L / 2);

[0049] Step 3.2: Calculate the number of corner points X of the first initial aggregate in a uniform distribution from 7 to 12, and calculate the angle α between each corner point and the horizontal X-axis using formula (3). j , where j is the corner index and rand is a random number between 0 and 1 that satisfies a uniform distribution;

[0050]

[0051] Step 3.3: As Figure 2 As shown, a predetermined angle α is randomly selected within the aggregate. jLet the corner point be taken as the first vertex A of the approximate inscribed triangle and its coordinates be calculated. Then, select the nearest corner point as the second vertex B of the approximate inscribed triangle and calculate its coordinates. Let the included angle α between vertex A and vertex B be calculated. j Add 180° to obtain the third vertex C of the inscribed triangle on the approximate circle and calculate its coordinates. Find the initial aggregate corner point that is closest to the newly calculated C coordinates and replace it. Finally, the corner point of the first initial aggregate contains the three vertices of the inscribed triangle on the approximate circle.

[0052] Step 3.4: Based on the angle α between each corner point of the initial aggregate j and the coordinates of the approximate circle center (X) 0,i ,Y 0,i The coordinates of the corner points other than points A, B, and C are calculated using formula (4).

[0053]

[0054] Step 3.5: Calculate the area S of the aggregate based on the triangle formed by the approximate center of the first initial aggregate and its adjacent corner points. all ;

[0055] Step 3.6: Using the approximate center of the circle as the base point, perform radius (R) calculations on the corner points of the first initial aggregate. itz The width is equidistantly expanded, and the geometric coordinates of the expanded aggregate corner points, including the width of the interface, are calculated.

[0056] Step 4.1: As Figure 3 As shown, the concrete generation region X∈(0,H),Y∈(0,L) is meshed based on a unit mesh of element size D0 / 8;

[0057] Step 4.2: Based on the center coordinates, approximate circle radius, and corner coordinates of the initial expanded aggregate, mark the minimum rectangular search area corresponding to the aggregate and interface (i.e., the minimum rectangular area containing the aggregate and interface composed of grids within the concrete generation area). Determine the minimum marked area (i.e., the minimum area containing the aggregate and interface composed of grids within the concrete generation area) through the minimum rectangular search area and remove its minimum marked area.

[0058] Step 4.3: As Figure 3 As shown, a ring-shaped area with a width of D4 / 2 around the concrete generation area is marked and removed to ensure that the aggregate generated subsequently does not exceed the concrete generation area.

[0059] Step 5.1: Calculate the approximate circle radius of the newly generated aggregate using a uniform distribution in the [D3,D4] gradation segment, and randomly generate the center coordinates of the aggregate in the unremoved concrete generation area;

[0060] Step 5.2: Repeat the methods in steps 3.2 to 3.6 to calculate the corner coordinates of the aggregate, as well as the enlarged corner coordinates and area including the interface;

[0061] Step 5.3: Based on the center coordinates, approximate circle radius, and corner coordinates of the enlarged aggregate, mark the minimum rectangular search area corresponding to the aggregate and the interface, and determine the minimum marked area through the minimum rectangular search area;

[0062] Step 5.4: Use formula (5) to control the distribution distance between the newly generated enlarged aggregate and the existing enlarged aggregate, and use it as the first criterion for whether they overlap:

[0063] (X o,i -X o,i+1 ) 2 +(Y o,i -Y o,i+1 ) 2 >[(R i +R i+1 )η] 2 (5)

[0064] Where η is the scaling factor, when D i When ∈[D3,D4], it takes 2.5; when D i When ∈[D2,D3], it takes 1.5; when D i When ∈[D1,D2], it takes the value of 0.7; when D... i When ∈[D0,D1], it takes the value 0.7;

[0065] Step 5.5: As Figure 4 As shown, formula (6) is used as the second discriminant to determine whether the newly generated aggregate overlaps with the existing aggregate, based on the sum of the areas of the triangles formed by the corner points of the newly generated aggregate and the adjacent corner points of the existing aggregate:

[0066]

[0067] In the formula S i S' is the area of ​​the triangle formed by the newly generated enlarged aggregate corner point and the adjacent corner points of the existing enlarged aggregate. all This represents the total area of ​​the existing expanded aggregate;

[0068] Step 5.6: If both of the above criteria are met simultaneously, the new and old aggregates at the interface are considered not to overlap. If the aggregates overlap, return to step 5.1 and repeat steps 5.1 to 5.3 until the aggregates do not overlap, then proceed to the next step.

[0069] Step 5.7: Remove the minimum marked area corresponding to the newly generated expanded aggregate, and repeat steps 5.1 to 5.6 in the areas that were not removed, continuously generating aggregates that satisfy the [D3,D4] gradation segment one after another, until the cumulative area of ​​all aggregates generated in that segment satisfies A. agg [D3,D4];

[0070] Step 5.8: Restore the annular area with a width of D4 / 2 around the concrete generation area, and mark and remove it using an annular area with a width of D3 / 2;

[0071] Step 6.1: Calculate the approximate circle radius of the newly generated aggregate using a uniform distribution in the [D2,D3] gradation segment, and randomly generate the center coordinates of the aggregate in the unremoved concrete generation area;

[0072] Step 6.2: Repeat the methods in steps 3.2 to 3.6 to calculate the coordinates of the corner points and the area of ​​the aggregate and the enlarged aggregate including the interface;

[0073] Step 6.3: Repeat the methods in steps 5.3 to 5.6 to determine the location of aggregates and interfaces in the concrete generation zone;

[0074] Step 6.4: Remove the minimum marked area corresponding to the newly generated aggregate and the interface, and repeat steps 5.1 to 5.6 in the unremoved areas, continuously generating aggregates that satisfy the [D2,D3] gradation segment one after another, until the cumulative area of ​​all aggregates generated in that segment satisfies A. agg [D2,D3];

[0075] Step 6.5: Restore the annular area with a width of D3 / 2 around the concrete generation area, and mark and remove it using an annular area with a width of D2 / 2;

[0076] Step 7.1: Calculate the approximate circle radius of the newly generated aggregate using a uniform distribution in the [D1,D2] gradation segment, and randomly generate the center coordinates of the aggregate in the unremoved concrete generation area;

[0077] Step 7.2: Repeat the methods in steps 3.2 to 3.6 to calculate the coordinates of the corner points and the area of ​​the aggregate and the enlarged aggregate including the interface;

[0078] Step 7.3: Repeat the methods in steps 5.3 to 5.6 to determine the location of aggregates and interfaces in the concrete generation zone;

[0079] Step 7.4: Remove the minimum marked area corresponding to the newly generated aggregate, and repeat steps 5.1 to 5.6 in the unremoved areas, continuously generating aggregates that satisfy the [D1,D2] gradation segment one after another, until the cumulative area of ​​all aggregates generated in that segment satisfies A.agg [D1,D2];

[0080] Step 7.5: Restore the annular area with a width of D2 / 2 around the concrete generation area, and mark and remove it using an annular area with a width of D1 / 2;

[0081] Step 8.1: Calculate the approximate circle radius of the newly generated aggregate using a uniform distribution in the [D0,D1] gradation segment, and randomly generate the center coordinates of the aggregate in the unremoved concrete generation area;

[0082] Step 8.2: Repeat the methods in steps 3.2 to 3.5 to calculate the coordinates and area of ​​the corner points corresponding to the aggregate and the enlarged aggregate including the interface;

[0083] Step 8.3: Repeat the methods in steps 5.3 to 5.6 to determine the location of aggregates and interfaces in the concrete generation zone;

[0084] Step 8.4: Remove the minimum marked area corresponding to the newly generated aggregate, and repeat steps 5.1 to 5.6 in the unremoved areas, continuously generating aggregates that satisfy the [D0, D1] gradation segment one after another, until the cumulative area of ​​all aggregates generated in that segment satisfies A. agg [D0,D1];

[0085] Step 9: After calculating the geometric information of all aggregates and interfaces, draw the diagram as shown below. Figure 5 As shown;

[0086] The present invention provides a method for random generation of two-dimensional geometric structures of concrete aggregates based on coordinate grids, which can achieve accurate simulation and random distribution of concrete aggregate shapes and realize the calculation of geometric information of the three-phase matrix (aggregate, interface, and mortar) materials inside the concrete.

[0087] The present invention provides a method for randomly generating two-dimensional geometric structures of concrete aggregates based on coordinate grids. This method is programmed using MATLAB software, which is convenient to operate and has a fast calculation speed.

[0088] Finally, it should be noted that the above description is only a preferred embodiment of the present invention and is not limited to the present invention. Although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art can still modify the technical solutions described in the foregoing embodiments or make equivalent substitutions for some of the technical features. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A method for randomly generating two-dimensional geometric structures of concrete aggregates based on coordinate grids, characterized in that, Includes the following steps: Step 1: Determine the concrete mix proportion and the physical parameters of each component, and specify the width of the mortar interface and the size of the rectangular area of ​​the generated concrete in the algorithm. Step 2: Divide the concrete into four segments according to the specified gradation, calculate the aggregate area ratio corresponding to different segments, and calculate the cumulative aggregate area of ​​the segmented gradation. Step 3: Randomly select the aggregate diameter in the maximum segmented gradation and generate the corresponding first polygonal initial aggregate in the concrete generation area; Step 4: Divide the concrete generation area into a grid and remove the initial aggregate and the area around the concrete from the grid. Step 5: Randomly and uniformly generate other polygonal aggregates with the maximum segmented gradation within the area where concrete has not been removed; Step 6: In the second segmented gradation, the same method as in step 5 is used to achieve random distribution of aggregates sequentially, and the algorithm is finally terminated by accumulating the area of ​​aggregates. Step 7: In the third segmented gradation, the same method as in step 5 is used to achieve random distribution of aggregates in sequence, and the algorithm is finally terminated by the cumulative area of ​​aggregates. Step 8: In the fourth segmented gradation, the same method as in step 5 is used to achieve random distribution of aggregates in sequence, and the algorithm is finally terminated by the cumulative area of ​​aggregates. Step 9: After calculating the geometric information of all aggregates and interfaces, draw the diagram. In step 5, the method for generating other polygonal aggregates with the maximum segmented gradation is to mark the smallest rectangular search area corresponding to the newly generated aggregate and the interface, determine the smallest marked area through the smallest rectangular search area, and determine the aggregate overlap by using the center coordinates, radius, interface width and polygon corner points of the newly generated aggregate and the existing aggregate. If the newly generated aggregate overlaps with the already generated aggregate, then the geometric information of the new aggregate will be regenerated; If the new aggregate does not overlap with the already generated aggregate, the minimum marked area corresponding to the new aggregate is removed, and the next aggregate is generated in the grid area after removal. This process is repeated until all aggregates in the maximum segmented gradation have been generated.

2. The method for randomly generating two-dimensional geometric structures of concrete aggregates based on coordinate grids as described in claim 1, characterized in that, In steps 3 to 8, after selecting the aggregate diameter, the center coordinates of the aggregate are randomly generated in the generated area, the number of sides of the polygonal aggregate is specified, the distance between the angle corresponding to the corner point and the center coordinate is specified, and the area of ​​the polygonal aggregate is recorded.

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