A two-dimensional concrete meso-model generation method based on fan-ring growth space

Abstract

The application discloses a kind of two-dimensional concrete mesoscopic model generation methods based on fan ring growth space, by introducing fan ring aggregate growth space, aggregate placement problem is simplified to set growth space position in given placement space, to ensure that aggregate is closely arranged and position is not conflict;By controlling the size of growth space, the aggregate particle size control is realized;Fan ring growth space under polar coordinates ensures that aggregate exists certain angle and improves the utilization rate of growth space.The method of the application includes three parts of inner ring placement, annular completion and edge filling, first, arrange fan ring growth spaces with different heights at the same radius, complete the remaining available positions to the same height to form a complete annulus, repeat the above steps to reach the preset boundary, then fill the aggregate in the edge and corner parts that cannot form a complete annulus, finally, quickly establish a two-dimensional concrete mesoscopic model with high aggregate proportion and meet the target grading requirements, which is more consistent with the actual situation of concrete section.

Description

Technical Field

[0001] This invention relates to the field of concrete microstructure numerical simulation technology, and in particular to a method for generating a two-dimensional concrete microstructure model based on a fan-shaped growth space. Background Technology

[0002] Concrete is widely used in the construction industry, and its mechanical properties and durability have always been a major research focus for researchers, requiring experimental verification through the construction of various macroscopic models of concrete materials. However, macroscopic model experiments on concrete materials are greatly affected by environmental, human, and material factors, resulting in drawbacks such as long experimental cycles and high costs. Therefore, using numerical simulation to study the mechanics and durability of concrete at the microscopic scale is a very economical research method.

[0003] Studies have shown that the properties of concrete are affected by the shape and distribution of aggregates. Therefore, when using numerical simulation methods to study the influence of aggregate shape and distribution on the mechanical properties and durability of concrete at the mesoscale, it is crucial to efficiently establish an accurate mesoscopic geometric model of concrete.

[0004] Currently, the main problems in the modeling process of two-dimensional concrete microstructure models are that the success rate of modeling decreases as the aggregate volume ratio of concrete increases, and the modeling time also increases significantly. Therefore, it is necessary to further study the modeling method of two-dimensional concrete microstructure models so that the model can quickly generate two-dimensional concrete microstructure models with a high aggregate volume ratio. Summary of the Invention

[0005] The problem to be solved by this invention is to provide a method for generating a two-dimensional concrete microstructure model based on a fan-shaped growth space, which can be used to quickly establish a two-dimensional concrete microstructure model with a high aggregate ratio and meeting the gradation requirements.

[0006] This invention adopts the following technical solution: a method for generating a two-dimensional concrete microstructure model based on a fan-shaped growth space, comprising the following steps:

[0007] S1. Determine the area of ​​various aggregates in the two-dimensional concrete microstructure model: By inputting spatial area information and preset aggregate gradation, based on the Fuller gradation curve, calculate the area of ​​each aggregate size using the Varavian formula, and estimate the number of each type of aggregate.

[0008] S2. Using a fan-shaped ring as the aggregate growth space, the feeding space is decomposed into rings of different heights: the size and position of the aggregate growth space are determined in each ring, and aggregate is generated in the growth space.

[0009] S3. For the remaining portion that cannot form a complete circle, divide the growth space and add aggregate.

[0010] Preferably, in step S1, based on the placement space area information and the Fuller grading curve, the area of aggregates with various particle sizes is calculated through the Walraven formula, and the number of aggregates of each type is estimated, including the following sub-steps:

[0011] S101, Determine the area proportion of concrete aggregates under different grading ranges:

[0012] The coarse aggregate grading curve and the coarse aggregate volume fraction are two main modeling parameters. Through the maximum dense grading curve proposed by Fuller, under this grading curve, the aggregate volume proportion is the largest and the porosity is the smallest. The Fuller expression is as follows:

[0013]

[0014] In the formula, P represents the mass percentage of aggregates passing through a sieve with pore size D0 relative to all aggregates; D0 represents the sieve pore size; D max represents the maximum particle size of the aggregate, and this formula describes the percentage content of aggregates with particle size below D0 in three-dimensional space.

[0015] In order to obtain the area of aggregates with various particle sizes on a two-dimensional section, based on the Fuller grading theory, the formula for converting three-dimensional aggregate grading into two-dimensional planar aggregate grading is derived through the Walraven formula, which is used to determine the area proportion of concrete aggregates under different grading ranges. The Walraven expression is as follows:

[0016]

[0017] In the formula, P c (D<D0) represents the probability that the aggregate particle size in the two-dimensional section is smaller than the sieve pore size D0; P k represents the percentage of concrete sand and gravel in the total volume; D0 and Dmax represent the sieve pore size and the maximum aggregate particle size respectively.

[0018] S102, Calculate the aggregate area in different particle size ranges, based on formula (2), calculate the aggregate area in the [D n , D n+1 particle size range:

[0019]

[0020] In the formula, A i represents the total area of aggregates within the [D n , D n+1 particle size range; D i represents the particle size of the i-th type of aggregate; D min represents the minimum particle size of the aggregate; D max represents the maximum particle size of the aggregate; P c (D i) indicates that the particle size within any cross-section is less than D. i The probability of aggregate distribution; P k Indicates the percentage of aggregate and sand in the total volume of concrete; A con This indicates the cross-sectional area of ​​the concrete.

[0021] S103. Using a square as the characteristic shape of the aggregate, the number of aggregates is obtained according to the upper limit of the particle size range.

[0022] Preferably, in step S2, the feeding space is decomposed into rings, and the size and position of the aggregate growth space are determined within each ring, and aggregate is generated within the growth space, including the following sub-steps:

[0023] S201. Determine the common center of the annulus and the initial inner radius r0:

[0024] For circular concrete sections, the center of the circle is used as the center of the concentric rings; for square and rectangular sections, the centroid of the section is used as the center of the concentric rings; for other irregular sections, the center of the largest inscribed circle is selected as the center of the concentric rings.

[0025] The initial value r0 of the inner ring radius is manually input. The radius is not less than half of the minimum aggregate particle size, and the circle formed serves as the aggregate growth space.

[0026] S202. Determine the location of the inner ring growth space:

[0027] To complete the inner ring growth space, it is necessary to determine the ring height (maximum feeding height), the combination of the lower arc length of the growth space, the height of the growth space, and the arrangement order of the growth spaces. Aggregate is generated within the growth space, which includes the following sub-steps:

[0028] S2021. Determine the height H of the annulus. max The maximum height of the ring should be set to be slightly higher than the maximum aggregate size. During the feeding process, the height of the aggregate should not exceed this value.

[0029] S2022. Determine the total usable lower arc length c: based on the inner ring radius r. i Calculate the total usable lower arc length c.

[0030] S023. Determine the arc length combination L under the fan-shaped growth space, L={l 11 , l 12 , ..., l ij}, where l ij It represents the arc length of the j-th growth space in the i-th type of aggregate.

[0031] After obtaining the total available lower arc length c, according to the aggregate particle size range D and the remaining aggregate area S left Allocation: Based on the remaining aggregate area Sleft Estimate the upper limit n of aggregate formation for each particle size. imax The method of random simulation is used to randomly generate the number n of aggregates for each particle size. i and the corresponding arc length l under the growth space ij The sum of the current arc lengths ∑l ij Less than or equal to the sum of the lower arc lengths and ∑l ij When -c<0.1, the generation of lower arc length combinations will stop. When the remaining aggregate area is insufficient to generate a complete inner ring, the upper limit of the number of aggregates will be used to generate the lower arc length combination.

[0032] S024. Determine the height H of the fan-shaped growth space. ij After determining the lower arc length combination L, it is necessary to further confirm the fan ring height H. ij .

[0033] To simplify calculations, the height of each type of aggregate is fixed during the inner ring feeding process. The maximum height of the fan ring does not exceed the maximum available aggregate particle size, and the minimum height is set to the minimum aggregate particle size. The heights of the remaining aggregates are adjusted according to the aggregate particle size to meet the maximum height of the circular ring as much as possible.

[0034] S2025, Growth space arrangement order: In the lower arc length l of the growth space ij and height H ij Once determined, the order will be randomly rearranged to increase the randomness of aggregate placement.

[0035] S203, Aggregate Generation: After the growth space is determined, concrete aggregate is generated within it using the convex hull method, including the following sub-steps:

[0036] S2031. Randomly generate n points within the growth space.

[0037] S2032. Using the convex hull algorithm, calculate the set of convex hull points and use the convex hull points as shape control points for aggregates.

[0038] S2033, Randomly generate the initial angle θ0 of the aggregate.

[0039] S2034. Calculate the minimum bounding rectangle of the aggregate, take the smaller of the length and width as the aggregate particle size, and determine whether it meets the target particle size requirement. If it does not meet the requirement, repeat S2031 and S2032 until aggregate that meets the target particle size requirement is generated.

[0040] S2035. Record aggregate information and update the remaining aggregate area S. left .

[0041] The aggregate information includes: aggregate type, aggregate area, aggregate particle size, lower arc length of growth space, upper arc length of growth space, starting angle of growth space, ending angle of growth space, height of growth space, and set of convex points of each aggregate.

[0042] S204. Determine the location of the growth space to complete the ring, and further divide it into growth spaces: After the inner ring is placed, it is necessary to determine the location of the growth space within the unused space inside the ring, including the following sub-steps:

[0043] S2041. Determine the available padding space S: S = {S1, S2, ..., S...} n}, where S i It refers to the i-th closed space that is not occupied by aggregate during the circular feeding process.

[0044] For a single aggregate that is not connected, its growth space arc and corresponding spatial composition can be represented by the filling space S. i For adjacent aggregates, their outer contour growth space height is the same; therefore, the connected space composed of multiple aggregates can be used as the available filling space S. i .

[0045] S2042, Determine the combination of growth space height H i ':H i '={H 11 ', H 12 ', H 21 '...,H in '} represents the S-th... i Within a space, it is divided into n layers of height H. ij The fan-shaped ring is 'j', where j represents the layer number.

[0046] Due to the height H of the ring max Fixed, in S i The height of the inner ring growth space corresponding to the space is consistent, both being H. ij Then the height is denoted as H. use H use =H max -H ij The corresponding H' i It should satisfy ∑H ij '≤H use And H ij All are within the aggregate particle size range D.

[0047] S2043, Determine to fill in the space S i The lower arc length combination C i ':

[0048] Lower arc length combination C i '={C11 ', C 12 ', C 21 '...,C in '} represents the S-th... i Within each space, the growth space is highly combined with H i 'S i The space is divided into n layers, and the lower arc length of each layer is denoted as C. ij 'j' represents the growth space number.

[0049] In step S2042, the space S will be filled. i Divided into n layers, it is not difficult to deduce that the lower arc length C of each layer is... ij 'All can be made by C i(j-1) 'It is derived.' For a space where multiple aggregates are connected together, C i1 'Equals the sum of the arc lengths over the growth space of the covered aggregates; for a single aggregate that is not connected, the corresponding C...' i1 'This refers to the arc length in the corresponding aggregate growth space.

[0050] S2044, Set the lower arc length combination L i ':L i '={L i1 ', L i2 '..., L in '}, where L ij ' indicates the Sth i Within a given space, the set of all lower arc length combinations in the j-th layer, where the sum of the lower arc lengths in each layer is C in step S2043. ij Once confirmed, determine the lower arc length combination for each layer according to step S2023.

[0051] S2045. After determining the lower arc length combination C' and the growth space height combination H' in steps S2042 and S2044, proceed with step S203 to adjust S... i Aggregate is generated in space.

[0052] S2046. Traverse all available padding spaces S, padding the torus, and repeat steps S2041 to S2045 until all available padding spaces S have been traversed.

[0053] S2047. Correct the delivery results:

[0054] During the deployment process, there may be situations where the remaining area of ​​a certain type of aggregate is used up but the same type of aggregate is still generated. In such cases, the excess aggregate needs to be deleted after the deployment is completed.

[0055] S205. Update the deployment radius r. After the circular deployment ends, the deployment radius of the next circular deployment is r. i =r i-1 +H max.

[0056] S206. Repeat steps S202 to S204 until r exceeds the edge of the delivery space.

[0057] Preferably, in step S3, setting up growth spaces and adding aggregates to other corner areas includes the following sub-steps:

[0058] S301, Aggregate generation at the center:

[0059] There is a circular blank area inside the circular feeding process, where aggregate needs to be fed separately. This circle is used as the growth space, and aggregate is generated in step S203 to obtain the aggregate at the center of the circle.

[0060] S302. Perform growth space generation and aggregate addition for areas where complete circular rings cannot be generated:

[0061] For the part that cannot form a complete circular ring, a fan-shaped ring can be used as the total growth space. In order to determine the location of the total growth space, it is necessary to determine four parameters: the inner diameter r1, the outer diameter r2, the starting angle θ1, and the ending angle θ2 of the fan-shaped ring.

[0062] After determining the total growth space, aggregate generation is carried out in steps S202-S203, which involves inner ring placement and circular ring completion. This includes the following three aspects:

[0063] S3021. Determine the inner diameter r of the fan ring. i-1 outer diameter of the fan ring r i and the upper limit of the outer diameter r max :

[0064] After the circular ring is placed, the radius value in step S205 is used as the initial value r1 of the inner diameter of the fan ring, and the radius of the circumcircle of the placement area is selected as the outer diameter r of the fan ring. max In a multi-ring process, the outer diameter r of each ring... i For r i =r i-1 +H max , where H max This represents the maximum particle size among the remaining aggregates.

[0065] S3022. Determine the starting and ending angles of the fan ring:

[0066] Due to the symmetry of the placement space, only 1 / 4 of the angle needs to be calculated during the process of completing the ring. Let the angle of the 1 / 4 placement area be θ, and the calculation is as follows:

[0067]

[0068] For rectangular cross-sections, there are two cases. The first case is that the projection space on both sides is greater than 90°, and the angle of the projection space of the fan ring on both sides is (-θ, θ) and (180°-θ, 180°+θ). The second case is that the projection space on both sides is less than 90°, and the projection space of the fan ring is (90°-θ, θ), (90°+θ, 180°-θ), (180°+θ, 270°-2θ), and (270°+θ, 360°-2θ).

[0069] S3023. Set up the growth space and generate aggregate. Refer to steps S202 to S204 and steps S3011 and S3012 to complete the aggregate feeding.

[0070] The present invention also provides: an electronic device, comprising:

[0071] One or more processors;

[0072] A storage device on which one or more programs are stored;

[0073] When the one or more programs are executed by the one or more processors, the one or more processors implement any of the above-described methods for generating two-dimensional concrete microstructure models based on fan-shaped growth spaces.

[0074] The present invention also provides a computer-readable storage medium storing a computer program thereon, which, when executed by a processor, implements the steps in any of the above-mentioned methods for generating a two-dimensional concrete microstructure model based on a fan-shaped growth space.

[0075] Compared with the prior art, the present invention, employing the above technical solution, has the following technical effects:

[0076] 1. Fast modeling speed: The two-dimensional concrete microstructure model generation method of this invention ensures that there is no positional conflict between aggregates during the aggregate placement process by using a preset growth space and generating aggregates within the growth space, thus avoiding positional conflict detection and improving modeling efficiency.

[0077] 2. Ensuring the randomness of aggregate position: The two-dimensional concrete micro-model generation method of this invention adopts a fan-shaped growth space, which allows for a certain tilt angle during the aggregate generation process, thereby improving the randomness of aggregate position and better reflecting the actual situation of concrete cross-section.

[0078] 3. High aggregate volume ratio: The two-dimensional concrete microstructure model generation method of this invention has a tight bond between aggregates, which reduces cross-sectional area loss and increases the aggregate volume ratio. Attached Figure Description

[0079] Figure 1This is a flowchart of the method for generating a two-dimensional concrete microstructure model according to the present invention;

[0080] Figure 2 This invention uses the convex hull method to generate aggregates of different particle sizes;

[0081] Figure 3 This is a schematic diagram illustrating the process of establishing a two-dimensional concrete microstructure model according to the present invention.

[0082] Figure 4 This is a schematic diagram illustrating the aggregate generation in different growth spaces according to the present invention;

[0083] Figure 5 This is a schematic diagram illustrating the method for defining aggregate particle size according to the present invention;

[0084] Figure 6 This is a schematic diagram illustrating the definition of filling space in this invention;

[0085] Figure 7 This is a schematic diagram showing the result of dividing the growth space within the supplementary space according to the present invention. Detailed Implementation

[0086] To make the objectives, technical solutions, and advantages of this invention clearer, the technical solutions of the application will be further described in detail below with reference to the accompanying drawings. The described embodiments are only a part of the embodiments involved in this invention. All non-innovative embodiments based on these embodiments by other researchers in the art are within the protection scope of this invention. Furthermore, the step numbers in the embodiments of this invention are only set for ease of explanation and do not limit the order of the steps. The execution order of each step in the embodiments can be adaptively adjusted according to the understanding of those skilled in the art.

[0087] In one embodiment of the present invention, for a concrete section with a height of 150mm and a width of 150mm, the aggregate particle sizes are 5-10mm, 10-15mm, and 15-20mm, respectively, and the aggregate volume fraction P... k =0.75, generate a two-dimensional concrete microstructure model, such as Figure 1 As shown, the specific method is as follows:

[0088] S1. Calculate the area of ​​aggregates of each size by combining the spatial area information, Fuller gradation curve and Walraven formula, and estimate the number of aggregates of each type.

[0089] S101. Determine the area ratio of concrete aggregate under different gradation ranges.

[0090] In this embodiment, Pc(D) is calculated based on the length and width of the projection space according to the Fuller expression (1). iThe values ​​are 0.3992, 0.5622, 0.6773, and 0.7485, respectively.

[0091] S102. Calculate the aggregate area and estimate the aggregate quantity within different particle size ranges. Based on the Varavan expression (2), calculate the aggregate area within different particle size ranges.

[0092] S103. Using squares as the characteristic shape of aggregates, the number of aggregates was obtained according to the upper limit of the particle size range. The results are shown in Table 1.

[0093] Table 1 Area of ​​various aggregates

[0094]

[0095] S2. Decompose the feeding space into rings, determine the size and position of the aggregate growth space in each ring, and generate aggregate in the growth space.

[0096] It is important to note that the growth space refers to the space within which the aggregate boundary will not exceed during the construction of the concrete microstructure model. This space controls the position, shape, and area of ​​the aggregate. The size of the growth space directly affects the upper limit of the aggregate area; by changing the size of the growth space during aggregate generation, the upper limit of the aggregate particle size can be determined. The shape of the growth space affects the shape of the generated aggregate. When using a rectangular growth space, especially in the process of generating slender aggregates with a certain angle of inclination, the utilization rate of the growth space is not high.

[0097] like Figure 4 As shown, when generating the same tilt angle and the same slender aggregate, the fan-shaped ring will have a higher growth space utilization rate. Correspondingly, polar coordinates will be used instead of traditional rectangular coordinates during the placement process. This allows the growth space to have a certain angle, which more closely reflects the actual aggregate distribution of concrete cross-sections.

[0098] Choosing a fan-shaped growth space allows for the formation of a complete ring through appropriate combinations. This ring contains aggregates of varying sizes, further simplifying the problem to satisfying gradation requirements within a given space while dividing the feeding space into rings of varying heights, thus minimizing the utilization efficiency of the feeding space. Therefore, this invention employs a fan-shaped ring as the aggregate growth space, decomposing the growth space arrangement process into two main steps: inner ring feeding and ring completion.

[0099] Furthermore, after determining the location and size of the aggregate growth space, aggregate needs to be generated within the growth space. This invention employs the convex hull method to generate concrete aggregate. A convex hull is the smallest convex set containing all objects in a set R. By randomly generating n points within a specified growth space, the convex hull point set is calculated using the convex hull algorithm and considered as the point model of the coarse aggregate. The shape of the aggregate becomes closer to the shape of the growth space as the number of randomly generated points increases, and the shape of the aggregate can be controlled by the size of the conditional growth space.

[0100] In a two-dimensional microstructure model of concrete, the aggregate size is generally defined as the minimum length and width of the minimum external tangent matrix of the aggregate after eliminating all concave vertices. Using a fan-shaped ring as the aggregate growth space, the generation results of aggregates with different sizes are shown below. Figure 2 As shown.

[0101] Before adding aggregates, an inspection should be conducted to ensure that the generated aggregates simultaneously meet the particle size requirements. If the requirements are not met, aggregates should be generated again until an aggregate that meets the requirements is generated.

[0102] S201. Establish a polar coordinate system and determine the common center O of the annulus and the initial inner radius r0.

[0103] Since the cross-sectional shape is square, the centroid of the square is selected as the common center O of the ring. In this embodiment, the initial radius r0 of the inner ring is set to 10mm. With point O as the origin of polar coordinates, the starting angle is 0° to the right horizontally and positive counterclockwise, thus establishing a polar coordinate system.

[0104] S202. Determine the location of the inner ring growth space.

[0105] To complete the inner ring growth space, it is necessary to determine the ring height (maximum placement height), the arc length combination of the growth space, the height of the growth space, and the arrangement order of the growth spaces. Aggregate is generated within the growth space, which includes the following 5 sub-steps.

[0106] S2021. Determine the ring height H based on the particle size range. max Set the height H of the ring. max ={22, 22, 21}.

[0107] S2022. Determine the total usable lower arc length c: Based on the inner ring radius r0, the total usable lower arc length c = 62.8 mm is calculated.

[0108] S2023. Determine the arc length combination L under the fan-shaped growth space:

[0109] For the initial application, this embodiment randomly generates the quantity and corresponding length of aggregate according to Table 1. After the total length of the lower arc is less than or equal to and close to the total available lower arc length c, the solution process ends and the combination of lower arc lengths in the growth space is output.

[0110] S2024. Determine the height H of the fan-shaped growth space: Set the growth space height for each type of aggregate to 7.33mm, 14.67mm, and 22mm.

[0111] S2025, Growth Spatial Arrangement Order:

[0112] The lower arc length l of the growth space ij and height H ij Once determined, the order will be randomly rearranged to increase the randomness of aggregate placement.

[0113] S203. Aggregate generation: After the growth space is determined, concrete aggregate is generated within it using the convex hull method, including the following sub-steps:

[0114] S2031. Randomly generate n points within the growth space.

[0115] Under the polar coordinate boundary conditions corresponding to the growth space, this embodiment randomly generates 30 points at different locations. The process of establishing the two-dimensional concrete microstructure model is as follows: Figure 3 As shown.

[0116] S2032. Using the convex hull algorithm, calculate the set of convex hull points and use the convex hull points as shape control points for aggregates.

[0117] S2033, Randomly generate the initial angle of the aggregate;

[0118] S2034. Calculate the minimum bounding rectangle of the aggregate, taking the smaller of the length and width as the aggregate size, such as... Figure 5 As shown; if the generated particle size is not within the aggregate particle size range D, it is regenerated until aggregate that meets the target particle size requirement is generated.

[0119] S2035. Record aggregate information and update the remaining aggregate area S. left The delivery results are as follows Figure 3 As shown in (a) below, the aggregate information for the inner ring is shown in Table 2.

[0120] Table 2 Information on Aggregate Placement in the Inner Ring Road

[0121]

[0122] S204, Determining the location of the growth space for ring completion.

[0123] After the inner ring is deployed, the growth space within the unused space inside the ring needs to be determined. The specific process includes the following sub-steps:

[0124] S2041. Determine the available padding space S.

[0125] Available padding space S = {S1, S2, ..., S...} n}, where S i This refers to the i-th unoccupied closed space during the circular feeding process, such as... Figure 6 As shown.

[0126] During this round of deployment, two No. 1 aggregates form a connected and complete space, while the rest are independent connected spaces.

[0127] S2042, Determine the combination of growth space height H i '.

[0128] For aggregate #1, its usable height during the replenishment process is 14.76mm, so it can be used to create one or two layers. For aggregate #2, its usable height during the replenishment process is 7.33mm, which can be used to create one layer of aggregate. For aggregate #3, its usable height is insufficient to generate aggregates within any particle size range, therefore no aggregate replenishment is performed. During this replenishment process, if... Figure 7 As shown, the filling space corresponding to the two No. 1 aggregates is divided into two layers for placement. The height of the first layer is 6.43mm and the height of the second layer is 8.23mm.

[0129] S2043, Determine to fill in the space S i The lower arc length combination C i '.

[0130] The lower arc length of each layer can be derived from the upper arc length of the growth space of the previous layer. For spaces where multiple aggregates are connected together, the lower arc length of the filling space is equal to the sum of the upper arc lengths of the growth spaces of the covering aggregates; for single aggregates without connectivity, it corresponds to the upper arc length of the aggregate growth space during the initial ring placement process. In this embodiment, the specific information on the ring filling growth space is shown in Table 3 below.

[0131] Table 3. Information on the growth space of the circular rings.

[0132]

[0133]

[0134] S2044, Set the lower arc length combination L i '.

[0135] The combination of lower arc lengths is denoted as L. i '={Li1 ', L i2 '..., L in '}, L ij ' indicates the Sth i Within a space, the set of all lower arc length combinations of the j-th layer.

[0136] In step S2043, the total arc length of each layer is C ij Once confirmed, determine the lower arc length combination for each layer according to step S2023.

[0137] S2045. After determining the lower arc length combination C' and the growth space height combination H' in steps S2042 and S2044, proceed with step S203 to adjust S... i Aggregate is generated in space.

[0138] S2046. Traverse all available padding spaces S, padding the torus, and repeat steps S2041 to S2045 until all available padding spaces S have been traversed.

[0139] S2047, Correct the delivery results.

[0140] During this process, there is no situation where the remaining area of ​​aggregate is 0, so no correction is needed.

[0141] S205. Update the deployment radius r. After the circular deployment is completed, the deployment radius of the next circular deployment is r2 = 32mm.

[0142] S206. Repeat steps S202 to S204 until r exceeds the edge of the delivery space. In this embodiment, the specific delivery result is as follows: Figure 3 As shown in (b) and (c) in the table, the results of each round of deployment and the remaining area are shown in Table 4.

[0143] Table 4. Statistics on Aggregate Feeding Information in Circular Circular Feeding

[0144]

[0145] S3. Create growth space in other corner areas and add aggregate.

[0146] S301, Aggregate formation at the center.

[0147] Within the circular feeding process, there is a circular blank area that requires separate aggregate feeding. This circle is used as the growth space, and aggregate generation is performed in step S203 to obtain the aggregate at the center of the circle. The aggregate area is 220.7 mm². 2 With a particle size of 14.78 mm, the remaining area of ​​the second type of aggregate is 37 mm². 2 This is insufficient to generate a new type 2 aggregate.

[0148] S302. For areas where a complete circular ring cannot be generated, perform growth space generation and aggregate delivery.

[0149] For the part that cannot form a complete circular ring, a fan-shaped ring can be used as the total growth space. In order to determine the location of the growth space, it is necessary to determine four parameters: the inner diameter, outer diameter, starting angle, and ending angle of the fan-shaped ring. After the location of the total growth space is determined, aggregate generation is carried out by referring to the two steps of inner ring placement and circular ring completion in steps S202 to S203.

[0150] This step includes the following aspects.

[0151] S3021. Determine the inner diameter r of the fan ring. i-1 outer diameter of the fan ring r i and the placement height H max Upper limit of outer diameter r max .

[0152] After the circular ring is placed, the radius value in step S205 is used as the initial value of the inner diameter of the fan ring, r1 = 75. The radius of the circumcircle of the placement area is selected as the outer diameter r of the fan ring. max =106.06.

[0153] In a multi-ring process, the outer diameter r of each ring i For r i =r i-1 +H max H max Let H be the maximum available remaining aggregate size during each aggregate feeding process. Since the first type of aggregate was not completely fed, the remaining area of ​​the second type of aggregate cannot generate a new No. 2 aggregate. Therefore, let H be... max =8mm.

[0154] S3022. Determine the starting angle and ending angle of the fan ring.

[0155] Due to the symmetry of the placement space, only 1 / 4 angle needs to be calculated during the process of completing the ring. Let the angle of the 1 / 4 placement area be θ, the final radius r1 = 75, and the aggregate particle size height is calculated by formula (1) to obtain θ = 45.498°.

[0156] S3023. Set up the growth space and generate aggregate. Referring to steps S202-S204 and steps S3021 and S3022, complete the aggregate feeding. In this embodiment, the final feeding result is as follows: Figure 3 (d) In this context, the overall aggregate input information is shown in Table 5.

[0157] Table 5. Statistics on Aggregate Input Information

[0158]

[0159] In summary, the method of the present invention can generate a two-dimensional concrete microstructure model. The aggregate gradation of the model meets the expected requirements, and the aggregates all have a certain tilt angle, which is more consistent with the actual concrete cross-section. Due to the characteristics of the growth space during the placement process, there is no need to detect the position between the aggregates.

[0160] In this embodiment of the invention, an electronic device is also provided, comprising: one or more processors; a storage device storing one or more programs thereon; when the one or more programs are executed by the one or more processors, the one or more processors implement any of the two-dimensional concrete microstructure model generation methods based on fan-shaped growth space in the above embodiments.

[0161] In this embodiment of the invention, a computer-readable storage medium is also provided, on which a computer program is stored. When the program is executed by a processor, it implements the steps in any of the above embodiments of the method for generating a two-dimensional concrete microstructure model based on a fan-shaped growth space.

[0162] The above description is only a preferred embodiment of the present invention. It should be noted that for those skilled in the art, several improvements and modifications can be made without departing from the principle of the present invention, and these improvements and modifications should also be considered within the scope of protection of the present invention.

Claims

1. A method for generating a two-dimensional concrete mesoscopic model based on a fan-shaped growth space, characterized in that, Includes the following steps: S1. Determine the area of ​​various aggregates in the two-dimensional concrete microstructure model: By inputting spatial area information and preset aggregate gradation, based on the Fuller gradation curve, calculate the area of ​​each aggregate size using the Varavian formula, and estimate the number of each type of aggregate. S2. Using a fan-shaped ring as the aggregate growth space, the feeding space is decomposed into rings of varying heights: within each ring, the size and location of the aggregate growth space are determined, and aggregate is generated within the growth space, including the following sub-steps: S201. Determine the common center of the circular rings and the initial inner ring radius: The initial value of the inner ring radius is manually input. The radius is not less than half of the minimum aggregate particle size. The circle formed serves as the aggregate growth space. S202. Determine the location of the inner ring growth space, including: determining the ring height, the total arc length of the lower arc of the growth space, the height of the growth space, and the arrangement order of the growth spaces; S203. Determine the location of the growth space to fill the ring. After the inner ring is placed, determine the location of the growth space in the unused space inside the ring and generate aggregate in the growth space. S204, Update the delivery radius; S205. Repeat steps S202 to S204 until the delivery radius exceeds the edge of the delivery space. S3. For the remaining portion that cannot form a complete circle, divide the growth space and add aggregate.

2. The method for generating a two-dimensional concrete microstructure model based on a fan-shaped growth space according to claim 1, characterized in that, In step S1, by using the spatial area information of the placement area and based on the Fuller gradation curve, the area of ​​aggregates of each particle size is calculated using the Varavan formula, and the number of each type of aggregate is estimated. This includes the following sub-steps: S101. Determine the area ratio of concrete aggregates within different particle size ranges; calculate the aggregate particle size distribution in three-dimensional space using the Fuller gradation curve. The percentage content below; Using the Varavan formula, a formula for transforming three-dimensional spatial aggregate gradation into two-dimensional planar aggregate gradation is derived, obtaining the area of ​​various aggregate particle sizes on the two-dimensional cross-section, and determining the area ratio of concrete aggregates under different gradation ranges. : S102. Calculate the aggregate area and estimate the aggregate quantity within different particle size ranges: ； In the formula, Indicates in The total area of ​​aggregates within the particle size range; Indicates the particle size of the i-th type of aggregate; Indicates the minimum particle size of the aggregate; Indicates the maximum particle size of the aggregate; This indicates that the particle size within any cross-section is less than D. i The probability of aggregate distribution; This indicates the percentage of aggregate and sand in the total volume of concrete. Indicates the cross-sectional area of ​​the concrete; S103. Using a square as the characteristic shape of the aggregate, the number of aggregates in each particle size range is obtained according to the upper limit of the particle size range.

3. The method for generating a two-dimensional concrete microstructure model based on a fan-shaped growth space according to claim 2, characterized in that, The Fuller gradation curve is represented as follows: ； In the formula, Indicates that the sieve aperture size is The percentage of aggregate by mass of all aggregates; Indicates the sieve aperture size; The Varavan formula is expressed as follows: ； In the formula, This indicates that the aggregate particle size in the two-dimensional cross-section is smaller than the sieve aperture size. The probability of; This indicates the volume percentage of coarse aggregate in concrete.

4. The method for generating a two-dimensional concrete microstructure model based on a fan-shaped growth space according to claim 2, characterized in that, In step S202, the location of the inner ring growth space is determined as follows: S2021. Determine the height of the ring. This serves as the maximum height for aggregate placement. S2022, based on the inner ring radius r i Determine the total usable lower arc length c; S2023. Based on the total available lower arc length c, according to the aggregate particle size range D and the remaining aggregate area... The allocation is performed to determine the arc length combination L under the fan-shaped growth space. ,in, This represents the arc length of the j-th growth space in the i-th aggregate type; S2024. Determine the height of the fan-shaped growth space. During the inner ring feeding process, the aggregate height is adjusted according to the aggregate particle size to meet the maximum height of the ring; S2025, Lower arc length based on growth space and height This allows for adjustments to the growth space sequence, increasing the randomness of aggregate placement.

5. The method for generating a two-dimensional concrete microstructure model based on a fan-shaped growth space according to claim 2, characterized in that, In step S203, concrete aggregate is generated using the convex hull method, as follows: S2031. Randomly generate n points within the growth space; S2032. Calculate the set of convex hull points using the convex hull algorithm, and use the convex hull points as shape control points for aggregates; S2033, Randomly generate the initial angle of the aggregate; S2034. Calculate the minimum bounding rectangle of the aggregate, take the smaller of the length and width as the aggregate particle size, and determine whether it meets the target particle size requirement. If it does not meet the requirement, S2031 and S2032 need to be repeated until aggregate that meets the target particle size requirement is generated. S2035. Record aggregate information and update the remaining aggregate area.

6. The method for generating a two-dimensional concrete microstructure model based on a fan-shaped growth space according to claim 2, characterized in that, In step S204, the location for the ring to complete the growth space is determined and further divided into growth spaces, as follows: S2041. Determine the available padding space S. , among which, S i Let i be the i-th closed space not occupied by aggregate during the circular feeding process; For a single aggregate that is not connected, the arc in the growth space and the corresponding space can be used to fill the space; For connected aggregates, the outer contour growth space has the same height, and the connected space formed by multiple aggregates is used as the available filling space; S2042, Determine the combination of growth space heights , , indicating that at the Sth i Within a space, it is divided into n layers with a height of The sector ring, where j represents the layer number; Due to the height H of the ring max Fixed, S i The inner ring of the space corresponds to the same growth space height, which is H. ij The usable height is , Corresponding satisfy and All are within the aggregate particle size range D; S2043, Determine to fill in the space S i lower arc length combination , , indicating that at the Sth i Within each space, the growth space is highly combined. S i The space is divided into n layers, and the lower arc length of each layer is... ; For spaces where multiple aggregates are connected together This equals the sum of the arc lengths covering the growth space of the aggregate; for a single aggregate that is not connected, the corresponding... To correspond to the arc length of the aggregate growth space; S2044, Set the lower arc length combination , ,in, Indicates the Sth i Within a space, the set of all lower arc length combinations of the j-th layer; S2045. Based on the determined lower arc length combination and growth space height combination, proceed with step S203 to process S... i Aggregate generation takes place in space; S2046. Traverse all available padding spaces S, pad the annulus, and repeat steps S2041~S2045 until all available padding spaces S have been traversed. S2047, Correct the delivery results.

7. The method for generating a two-dimensional concrete mesoscopic model based on a fan-shaped growth space according to claim 2, characterized in that, In step S3, after all the complete circular rings have been placed, the corner areas are divided into growth spaces and aggregates are placed there, as follows: S301, Aggregate generation in the center area: During the circular feeding process, there is a circular blank area at the center of the fan-shaped area. The center area is used as the growth space, and aggregate is generated in step S203 to obtain the aggregate at the center. S302. For areas where complete circular rings cannot be generated, a fan-shaped ring is used as the total growth space for generating the growth space and adding aggregates: S3021. Determine the inner diameter r of the fan ring. i-1 outer diameter of the fan ring r i and the upper limit of the outer diameter r max ; Using the radius value in step S205 as the initial value r1 of the inner diameter of the fan ring, the radius of the circumcircle of the deployment area is selected as the outer diameter r of the fan ring. max When multiple rings exist, the outer diameter r of each ring is... i for , where H max This represents the maximum particle size among the remaining aggregates. S3022. Determine the starting angle and ending angle of the fan ring; Due to the symmetry of the placement space, the angle θ of 1 / 4 of the placement area is calculated during the process of completing the circular ring: ； For a rectangular cross-section, when the projection space on both sides is greater than 90°, the angle of the projection space of the fan rings on both sides is (-θ, θ) (180°-θ, 180°+θ). When the projection space range on both sides is less than 90°, the projection space range of the fan ring is (90°-θ,θ), (90°+θ, 180°-θ), (180°+θ, 270°-2θ), (270°+θ, 360°-2θ). S3023. Set up the growth space and generate aggregates. Complete the aggregate feeding according to steps S202~S204 and steps S3011~S3012.

8. An electronic device, characterized in that, include: One or more processors; A storage device on which one or more programs are stored; When the one or more programs are executed by the one or more processors, the one or more processors implement the method for generating a two-dimensional concrete microstructure model based on a fan-shaped growth space as described in any one of claims 1 to 7.

9. A computer-readable storage medium, characterized in that, It stores a computer program that, when executed by a processor, implements the steps in the method for generating a two-dimensional concrete microstructure model based on a fan-shaped growth space as described in any one of claims 1 to 7.

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