A method of calculating the connectivity of the interfacial transition zone around an ovoid aggregate particle

Abstract

The application provides a method for calculating the connectivity of the interface transition zone around the spheroid aggregate particles, relates to the concrete defect characterization and simulation calculation field, and can more truly characterize the connectivity degree of the interface transition zone in the concrete by constructing the aggregate accumulation system, defining the equivalent diameter of the aggregate particles and the characteristic equivalent diameter of the aggregate particles, and simultaneously considering the shape distribution and size distribution characteristics of the aggregate particles; by adopting the combination method of the rough judgment and the accurate judgment of the interface transition zone, the required calculation time is greatly reduced, so that the rapid calculation of the percolation probability of the interface transition zone under the preset condition is realized, the situation of the generation of the connected cluster of the interface transition zone is evaluated, and then the performance of the concrete is improved by adjusting the aggregate volume fraction, the aggregate grading size and the like in the field, and the connectivity of the interface transition zone in the concrete is designed and evaluated in advance.

Description

Technical Field

[0001] This invention relates to the field of concrete defect characterization and simulation calculation, and in particular to a method for calculating the connectivity of the interface transition zone around ovoid aggregate particles. Background Technology

[0002] At a microscale, both mortar and concrete can be viewed as three-phase composite materials consisting of cement paste, aggregate particles, and the interfacial transition zone (ITZ) surrounding the aggregate particles. Due to the effects of sidewall effects, micro-area bleeding effects, and unilateral growth effects, cement particles and their hydration products are sparsely distributed around the aggregate particles, resulting in a higher porosity in the interfacial transition zone compared to the solid matrix further away from the aggregate particles. Therefore, the interfacial transition zone has a significant impact on the macroscopic mechanical properties and transport properties of concrete.

[0003] When studying the impact of the interfacial transition zone on concrete using a three-phase composite material model, scholars typically consider the interfacial transition zone as a soft, intersecting shell of equal thickness surrounding aggregate particles, and assume that the thickness of the interfacial transition zone is related to the maximum particle size of cement. As the aggregate volume fraction increases, the connectivity of the interfacial transition zone within the concrete gradually increases. When a cluster of interconnected interfacial transition zones spanning the aggregate packing system appears, percolation is considered to have occurred in the interfacial transition zone of the concrete. Once percolation occurs, the interconnected clusters of interfacial transition zones, characterized by high connectivity and high porosity, provide pathways for external corrosive media to transport into the concrete interior, thereby negatively altering the macroscopic properties of the concrete.

[0004] Previous studies have simplified the shape of aggregate particles to regular particles such as circles and spheres, and ignored the influence of the coupling effect of the shape distribution and size distribution of aggregate particles on the permeability of the interfacial transition zone. This has limited the application scope of the calculation results and resulted in low guidance significance for the actual preparation of concrete.

[0005] In actual concrete preparation, the aggregate particles used include natural sand and gravel. Due to water erosion and other effects, the surface of natural sand and gravel is smooth, and their shapes are mostly close to oval. Therefore, it is necessary to propose a method for calculating the connectivity of the interfacial transition zone around oval aggregate particles. By obtaining the connectivity of the interfacial transition zone, the mechanical properties and durability of concrete can be evaluated, providing guidance for concrete mix design optimization. Summary of the Invention

[0006] In view of the above problems, the present invention aims to propose a calculation method applicable to characterizing the connectivity of the interface transition zone around multi-shaped and multi-sized ovoid aggregate particles. This method overcomes the problems of low accuracy and narrow applicability of existing interface transition zone connectivity calculation methods. Compared with existing calculation methods, it can more accurately evaluate and characterize the percolation behavior of the interface transition zone in concrete under known concrete gradation dimensions and aggregate volume fraction.

[0007] A method for calculating the connectivity of the interface transition region around ovoid aggregate particles includes the following steps:

[0008] S01: Construct an aggregate packing system, wherein the aggregate packing system is a three-dimensional cube, wherein aggregate particles of various shapes are distributed in the three-dimensional cube, and an interface transition zone is provided on the surface of the aggregate particles;

[0009] S02: Calculate whether percolation occurs in the interfacial transition zone of the aggregate packing system. If percolation occurs, S p =1 is recorded in the first tag set. p If the result is ≥1 and a natural number, proceed to step S03; otherwise, ... S p =0 is recorded in the first tag set, and step S03 is continued; the... S p =1 indicates that, under preset conditions, the simulation calculation result for the aggregate packing system is that permeation occurs in the interface transition zone; S p =0 indicates that, under preset conditions, the simulation calculation result of the aggregate packing system is that no permeation occurs in the interface transition zone; the first set of markers is used to record the results of the simulation calculation of whether permeation occurs in the interface transition zone of the aggregate packing system.

[0010] S03: Repeat steps S01~S02 until the preset number of simulation calculations is performed. G This yields the first set of tags;

[0011] S04: Count the "" in the first tag set S p The number of "=1" is used to obtain the quantity. N ;

[0012] S05: Calculation N / G The probability of percolation occurring in the interfacial transition zone of the aggregate packing system is obtained. P ITZ .

[0013] According to the technical solution provided by the present invention, constructing the aggregate packing system includes the following steps:

[0014] S011: Preset side length of the 3D cube L Aggregate particle size distribution and aggregate volume fraction V f The gradation size refers to the size distribution range of the aggregate particles. D agg,min , D agg,max ],in, D agg,max The maximum equivalent diameter of aggregate particles, D agg,min The minimum equivalent diameter of the aggregate particle; the equivalent diameter is the diameter of a spherical aggregate particle with the same volume as the non-spherical aggregate particle.

[0015] S012: Preset the aggregate particle shape distribution rules using sphericity, aspect ratio, and taper parameters;

[0016] S013: Use numerical values D agg,m The distribution range of gradation size [ D agg,min , D agg,max Divided into 10 secondary distribution intervals[ D agg,m , D agg,(m+1) ], m ≥1 and is a natural number;

[0017] Wherein, the numerical value D agg,m Based on the rules of arithmetic progression, the calculation formula is:

[0018] Formula (2)

[0019] In the formula, D agg,m To divide the distribution range of gradation size [ D agg,min , D agg,max The first m A number, m ≥1 and is a natural number; D agg,max The maximum equivalent diameter of the aggregate particles; D agg,min The minimum equivalent diameter of the aggregate particles;

[0020] S014: Calculate all secondary distribution intervals [ D agg,m , D agg,(m+1)The corresponding equivalent diameter of aggregate particles, i.e., the secondary distribution interval [ D agg,m , D agg,(m+1) The equivalent diameter of all aggregate particles within the range is represented by the characteristic equivalent diameter of the aggregate particles; the formula for calculating the characteristic equivalent diameter of the aggregate particles is:

[0021] D aggs,n =[ D aggs,m + D aggs,(m+1) ] / 2 formula (3)

[0022] In the formula, D agg,n Indicates the second-order distribution interval [ D agg,m , D agg,(m+1) The corresponding equivalent diameter of aggregate particles, 1≤ n ≤10 and is a natural number, and n = m ;

[0023] S015: Using the characteristic equivalent diameter of the aggregate particles D aggs,n Calculate the corresponding second-order distribution interval [ D agg,m , D agg,(m+1) The number of aggregate particles to be generated within the specified range N pn The calculation formula is:

[0024] Formula (4)

[0025] In the formula, L Let be the side length of the three-dimensional cube; V f This refers to the aggregate volume fraction. D agg,m , D agg,(m+1) To divide the distribution range of gradation size [ D agg,min , D agg,max The value of ]; D agg,n Indicates the second-order distribution interval [ D agg,m , D agg,(m+1) The corresponding equivalent diameter of aggregate particles; f NIt is the basis probability density function; m ≥1 and is a natural number; 1≤ n ≤10 and is a natural number, and n = m ;

[0026] D agg The equivalent diameter of the aggregate particles is expressed by the formula:

[0027] Formula (1)

[0028] In the formula, D agg The equivalent diameter of the aggregate particles; V pa π represents the volume of the aggregate particles; π is the mathematical constant pi.

[0029] S016: According to the Monte Carlo principle and the equivalent diameter of aggregate particles D aggs,n Generate sequentially in the three-dimensional cube in descending order of size. N pn Each size is D aggs,n The process of obtaining an existing aggregate particle set includes the following steps:

[0030] S0161: Generate aggregate particles P1 to be added in the three-dimensional cube according to the Monte Carlo principle. The size of the aggregate particles P1 is the characteristic equivalent diameter of the aggregate particles. D aggs,10 And mark it as an existing aggregate particle O1, and include it in the existing aggregate particle set;

[0031] S0162: Generate aggregate particles P to be added in the three-dimensional cube according to the Monte Carlo principle. i+1 , i The number is ≥1 and is a natural number, and is compared one by one with the existing aggregate particles in the existing aggregate particle set to determine whether they intersect. For example, the aggregate particle P to be added... i+1 If the aggregate particle P to be added does not intersect with any existing aggregate particles in the existing aggregate particle set, then the aggregate particle P to be added will be... i+1 Marked as existing aggregate particles O i+1 If the aggregate particles are included in the existing aggregate particle set, proceed to step S0163; otherwise, return to step S0162.

[0032] S0163: Repeat step S0162 until all secondary distribution intervals are generated in the three-dimensional cube. D agg,m , D agg,(m+1) Corresponding quantityN pn Aggregate particles, 1≤ n If the number is ≤10 and is a natural number, an existing aggregate particle set is obtained; the existing aggregate particle set includes all existing aggregate particles generated in the three-dimensional cube.

[0033] S017: According to the Minkowski summation theory, for each existing aggregate particle in the existing aggregate particle concentration, an interface transition region of equal thickness is constructed on its surface to obtain the aggregate packing system, including the following steps:

[0034] S0171: In the existing aggregate particle set, obtain the existing aggregate particle O1, and perform point discretization on the surface of the existing aggregate particle O1 to obtain the second set of discrete points.

[0035] S0172: Obtain discrete points from the second set of discrete points. W 1. And calculate the discrete points. W Normal vector of 1 ;

[0036] discrete points W i The formula for calculating the normal vector is:

[0037] Formula (9)

[0038] In the formula, a Wi , b Wi and c Wi These are existing aggregate particles O i exist x , y and z The length of the half-axis of the shaft; T i For existing aggregate particles O i Tapering parameters; x Wi , y Wi , z Wi ) is a discrete point W i The coordinates of the point; For discrete points W i The normal vector; Normal vector of x coordinate; Normal vector of y coordinate; Normal vector of z coordinate;

[0039] S0173: Along the normal vector on the surface of the existing aggregate particle O1 outward extension distance t To obtain discrete points The discrete points It is a point on the outer side of the interface transition zone surrounding the existing aggregate particle O1;

[0040] S0174: Repeat S0172~S0173 to obtain the discrete points in the second set of discrete points one by one. W i until the distance is extended outward along the normal vector of all discrete points. t A third set of discrete points is obtained. All discrete points in the third set of discrete points form the outer surface of the interface transition zone around the existing aggregate particle O1, which together with the surface of the existing aggregate particle O1 forms a thickness of [missing information]. t The interface transition area ITZ1;

[0041] S0175: Repeat S0171~S0174 until all existing aggregate particles in the existing aggregate particle set have completed the construction of a thickness of [missing information]. t The interface transition zone is obtained, and the aggregate packing system and the first interface transition zone set are obtained. The first interface transition zone set includes the interface transition zones constructed on the surfaces of all existing aggregate particles in the three-dimensional cube.

[0042] According to the technical solution provided by the present invention, in step S0162, it is determined that the aggregate particle P to be added is... i+1 Determining whether it intersects with any existing aggregate particle in the existing aggregate particle set includes the following steps:

[0043] S01621: Obtain existing aggregate particles O1 in the existing aggregate particle set, and obtain the aggregate particles P to be added. i+1 Perform a rough judgment with the existing aggregate particles O1. If they do not intersect, continue to step S01625; otherwise, continue to step S01622.

[0044] Among them, the aggregate particles P to be added i+1 A rough assessment of existing aggregate particles O1 is performed, including the following steps:

[0045] Calculate the particle size P of the aggregate to be added i+1 center point x coordinate x i+1 Center point of existing aggregate particles O1 x coordinate x01 The distance between them, to obtain the distance ;

[0046] Calculate the particle size P of the aggregate to be added i+1 center point y coordinate y i+1 Center point of existing aggregate particles O1 y coordinate y 01 The distance between them, to obtain the distance ;

[0047] Calculate the particle size P of the aggregate to be added i+1 center point z coordinate z i+1 Center point of existing aggregate particles O1 z coordinate z 01 The distance between them, to obtain the distance ;

[0048] Calculate and obtain the particle size P of the aggregate to be added. i+1 From the center point to the aggregate particle P to be added i+1 Maximum distance of the surface ;

[0049] Calculate and obtain the maximum distance from the center point of existing aggregate particle O1 to the surface of existing aggregate particle O1. ;

[0050] Calculate the maximum distance and maximum distance The sum of these gives the distance. ;

[0051] Compare separately , and With distance ,like > or > or > Then the aggregate particles P to be added i+1 If the aggregate particle O1 does not intersect with the existing aggregate particle, proceed to step S01625; otherwise, proceed to step S01622.

[0052] S01622: For the addition of aggregate particles P i+1 Perform a rough judgment with the existing aggregate particles O1. If they do not intersect, continue to step S01625; otherwise, continue to step S01623.

[0053] Among them, the aggregate particles P to be added i+1 A rough assessment of the existing aggregate particles O1 is performed, including the following steps:

[0054] Calculate the particle size P of the aggregate to be added i+1 Distance between the center point and the center point of the existing aggregate particle O1 ;

[0055] Calculate and obtain the particle size P of the aggregate to be added. i+1 From the center point to the aggregate particle P to be added i+1 Maximum distance of the surface ;

[0056] Calculate and obtain the maximum distance from the center point of existing aggregate particle O1 to the surface of existing aggregate particle O1. ;

[0057] Calculate the maximum distance and maximum distance The sum of these gives the distance. ;

[0058] Compare distances With distance ,like > Then the aggregate particles P to be added i+1 If the aggregate particle O1 does not intersect with the existing aggregate particle, proceed to step S01625; otherwise, proceed to step S01623.

[0059] S01623: Treatment of aggregate particles P i+1 Perform a rough judgment with the existing aggregate particle O1. If they intersect, return to step S0162; otherwise, continue to step S01624.

[0060] Among them, the aggregate particles P to be added i+1 A rough assessment of the existing aggregate particles O1 is performed, including the following steps:

[0061] Calculate the particle size P of the aggregate to be added i+1 Distance between the center point and the center point of the existing aggregate particle O1 ;

[0062] Calculate and obtain the particle size P of the aggregate to be added. i+1 From the center point to the aggregate particle P to be added i+1 Minimum distance of the surface ;

[0063] Calculate and obtain the minimum distance from the center point of existing aggregate particle O1 to the surface of existing aggregate particle O1. ;

[0064] Calculate the minimum distance minimum distance The sum of these gives the distance. ;

[0065] Compare distances With distance ,like < Then the aggregate particles P to be added i+1 If it intersects with an existing aggregate particle O1, return to step S0162; otherwise, continue to step S01624.

[0066] S01624: Treatment of aggregate particles P i+1 Perform a precise judgment with the existing aggregate particle O1. If they intersect, return to step S0162; otherwise, continue to step S01625.

[0067] Among them, the aggregate particles P to be added i+1 The fourth step involves accurately determining the composition of existing aggregate particles O1, including the following steps:

[0068] Treating the addition of aggregate particles P i+1 The surface is discretized to obtain a first set of discrete points, which includes the aggregate particles P to be added. i+1 All discrete points on the surface;

[0069] In the first set of discrete points, obtain discrete points M one by one. i+1 Calculate discrete point M i+1 To the geometric potential of existing aggregate particles O1 G psovoid and judge G psovoid Is it less than or equal to 0, when G psovoid When ≤0, then the discrete point M i+1 Located on or inside the surface of existing aggregate particle O1, indicating that the aggregate particle P to be added... i+1 Intersecting with existing aggregate particle O1, return to step S0162. If the geometric potential of all discrete points in the first discrete point set is greater than 0, it indicates that the aggregate particle P to be added is... i+1 Since it does not intersect with existing aggregate particles O1, continue with step S01625;

[0070] S01625: Repeat step S01621 until the aggregate particles to be added P are complete. i+1 The determination of whether it intersects with all existing aggregate particles in the existing aggregate particle set, such as the aggregate particle P to be added. i+1 If the aggregate particle to be added does not intersect with any existing aggregate particle in the existing aggregate particle set, then the aggregate particle P to be added will be... i+1Marked as existing aggregate particles O i+1 If the aggregate particles are included in the existing aggregate particle set, proceed to step S0163; otherwise, return to step S0162.

[0071] According to the technical solution provided by the present invention, in step S02, calculating whether percolation occurs in the interfacial transition zone of the aggregate packing system includes the following steps:

[0072] S021: The six faces of the three-dimensional cube are respectively designated as the front surface, back surface, left surface, right surface, top surface, and bottom surface;

[0073] Among them, the left and right surfaces form the first investigation group, the front and rear surfaces form the second investigation group, and the upper and lower surfaces form the third investigation group.

[0074] S022: Set the left surface of the first investigation group as the initial surface and the right surface as the termination surface;

[0075] S023: Obtain the interface transition areas ITZ in the first set of interface transition areas one by one. i ITZ determines the interface transition area. i Whether it intersects with the initial surface; if it intersects, then the interface transition zone ITZ will be determined. i Include it in the second interface transition area set; otherwise, remove the interface transition area ITZ. i Included in the third interface transition area set;

[0076] S024: Obtain any interface transition region ITZ from the set of third interface transition regions. k , k ≥1 and is a natural number, is compared one by one with all interface transition regions in the second interface transition region set to determine whether they intersect, such as interface transition region ITZ. k If it intersects with any interface transition region in the second set of interface transition regions, then the interface transition region ITZ will be... k Remove it from the third interface transition area set and add it to the second interface transition area set to obtain a new third interface transition area set and a new second interface transition area set; otherwise, the interface transition area ITZ is removed. k It remains in the set of transition areas of the third interface;

[0077] S025: Based on the new set of third interface transition areas and the new set of second interface transition areas, repeat step S024 until there are no interface transition areas in the new set of third interface transition areas that intersect with the interface transition areas in the new set of second interface transition areas.

[0078] S026: In the new set of second interface transition zones, each interface transition zone is acquired one by one. It is determined whether the interface transition zone intersects with the termination surface. If they intersect, the aggregate packing system generates a cluster of interconnected interface transition zones, and percolation occurs in the interface transition zones. S p =1 is recorded in the first tag set, and step S03 is executed; otherwise, step S027 is executed.

[0079] S027: Repeat steps S022-S026 to determine whether the second and third investigation groups have generated interconnected clusters in the interface transition zone, and whether percolation has occurred in the interface transition zone. If the first, second, and third investigation groups do not intersect with the interface transition zone, it indicates that percolation has not occurred in the interface transition zone of the aggregate packing system. S p =0 is recorded in the first tag set, and step S03 continues; otherwise, it indicates that the aggregate packing system has generated interconnected clusters in the interface transition zone, and percolation has occurred in the interface transition zone. S p =1 is recorded in the first tag set, and step S03 is continued.

[0080] According to the technical solution provided by the present invention, in step S023, the interface transition zone ITZ is determined. i Whether it intersects with the initial surface includes the following steps:

[0081] Obtain the discrete points in the third discrete point set one by one. And calculate discrete points Directed distance to the initial surface d i This yields the set of directed distances;

[0082] Among them, directed distance d i The formula for calculation is,

[0083] Formula (10)

[0084] In the formula, d i Point The directed distance to the initial or final surface; , , Points of x Coordinate values y Coordinate values z Coordinate values; A , B , C , D For coefficients;

[0085] Obtain the maximum value in the directed distance set. d max and minimum value d min ;

[0086] Calculate the maximum value d max and minimum value d min The product of , to obtain the product ,like If ≤0, it indicates that the interface transition zone ITZ i Intersecting with the initial surface, the interface transition zone ITZ is formed. i Include it in the second interface transition area set; otherwise, the interface transition area ITZ i Included in the third interface transition area set.

[0087] According to the technical solution provided by the present invention, in step S024, the interface transition region ITZ in the third interface transition region set is determined. k Determining whether the interface transition area intersects with the interface transition area in the second set of interface transition areas includes the following steps:

[0088] S0241: Obtain all discrete points on the outer surfaces of all interface transition zones that make up the second interface transition zone set, and form a first point set;

[0089] S0242: In the existing aggregate particle set, obtain the interface transition zone ITZ with the third interface transition zone set. k Corresponding existing aggregate particles O k ;

[0090] S0243: Obtain the composition of existing aggregate particles O k All discrete points on the surface form a second set of points;

[0091] S0244: Calculate the distance between all discrete points in the first set of points and all discrete points in the second set of points to obtain the first distance set;

[0092] S0245: Obtain the minimum distance in the first distance set. ;

[0093] S0246: Compare the minimum distance With distance t ,like ≤ t This indicates the ITZ interface transition area. k Interface transition zone ITZ in the second interface transition zone set j intersect, jIf the value is ≥1 and is a natural number, then the interface transition area ITZ will be... k Remove it from the third interface transition area set and add it to the second interface transition area set to obtain a new third interface transition area set and a new second interface transition area set; otherwise, the interface transition area ITZ is removed. k It remains in the set of transition areas of the third interface.

[0094] In summary, this invention discloses a method for calculating the connectivity of the interface transition zone around multi-shape and multi-size ovoid aggregate particles, which has the following advantages compared with the prior art:

[0095] First, it can simultaneously consider the shape and size distribution characteristics of aggregate particles; compared with other existing methods for calculating the connectivity of interface transition zones, it can more realistically characterize the connectivity of the interface transition zones inside concrete.

[0096] Second, it can effectively improve the efficiency of connectivity calculation in the interface transition zone; compared with the prior art, the present invention adopts a method combining coarse judgment and precise judgment in the process of aggregate accumulation system generation, which greatly reduces the calculation time required.

[0097] Third, it can design the connectivity of the interface transition zone in concrete in advance; compared with the prior art, the present invention can quickly calculate the probability of percolation in the interface transition zone under preset conditions, assess the situation of the formation of interconnected clusters in the interface transition zone, and guide the field to improve the performance of concrete by adjusting the aggregate volume fraction, aggregate gradation size, etc. Attached Figure Description

[0098] Other features, objects, and advantages of the invention will become more apparent from the following detailed description of non-limiting embodiments with reference to the accompanying drawings.

[0099] Figure 1 This is a schematic diagram of the shape and distribution of aggregate particles in a three-dimensional cube according to Embodiment 1 of the present invention.

[0100] Figure 2 This is a schematic diagram of the uniform thickness interface transition zone around the aggregate particles of the present invention;

[0101] Figure 3 This is a schematic diagram showing the intersection of the interface transition zone and the initial surface in Embodiment 1 of the present invention;

[0102] Figure 4 This is a schematic diagram of the interconnected clusters in the interface transition region of Embodiment 1 of the present invention;

[0103] Figure 5 Let P be the probability ITZ With aggregate volume fraction V f The change graph. Detailed Implementation

[0104] The present invention will now be described in further detail with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are for illustrative purposes only and are not intended to limit the invention. Furthermore, it should be noted that, for ease of description, only the parts relevant to the invention are shown in the accompanying drawings. The present invention will now be described in detail with reference to the accompanying drawings and embodiments.

[0105] Example 1

[0106] A method for calculating the connectivity of the interface transition region around ovoid aggregate particles includes the following steps:

[0107] S01: Construct an aggregate packing system, wherein the aggregate packing system is a three-dimensional cube, and aggregate particles of various shapes are distributed within the three-dimensional cube, such as... Figure 1 As shown, the surface of the aggregate particles is provided with an interface transition zone.

[0108] The aggregate particles are further filled with cement paste, and the interface transition zone is located between the surface of the aggregate particles and the cement paste.

[0109] Constructing an aggregate stockpiling system includes the following steps:

[0110] S011: Preset side length of the 3D cube L Aggregate particle size distribution and aggregate volume fraction V f The gradation size includes the size distribution range of aggregate particles. D agg,min , D agg,max ], where the maximum equivalent diameter of aggregate particles D agg,max 、 Minimum equivalent diameter of aggregate particles D agg,min ;

[0111] Specifically, the side length of the three-dimensional cube L The maximum equivalent diameter of the aggregate particles is 20 mm. D agg,max The minimum equivalent diameter of the aggregate particles is 1.18 mm. D agg,min The aggregate volume fraction is 0.3 mm. V f The ratio of the volume of all aggregate particles to the volume of the three-dimensional cube is 0.121.

[0112] When quantitatively characterizing a specific spherical particle, diameter can completely describe the size information of the sphere, and a similar metric parameter is needed for non-spherical particles. To address this, the present invention employs the concept of equivalent diameter. Based on equivalent diameter, regardless of the shape of the non-spherical particle, the distribution of equivalent diameter can be used to characterize its size distribution features.

[0113] The equivalent diameter of an aggregate particle is the diameter of a spherical aggregate particle with the same volume as a non-spherical aggregate particle. Therefore, the formula for calculating the equivalent diameter of an aggregate particle is:

[0114] Formula (1)

[0115] In the formula, D agg The equivalent diameter of the aggregate particles; V pa π represents the volume of the aggregate particles; π is the mathematical constant pi.

[0116] S012: Preset the aggregate particle shape distribution rules using sphericity, aspect ratio, and taper parameters.

[0117] Specifically, based on the distribution rules of aggregate particle shape, aggregate packing systems can be divided into single-shape aggregate packing systems and multi-shape aggregate packing systems. For single-shape aggregate packing systems, the shape of the aggregate particles can be determined by the aspect ratio and taper parameter. T It is determined that the aspect ratio of the ovoid aggregate particle is... z The length of the half shaft and x The ratio of the length of the half-axis to the length of the axial axis. For multi-shaped aggregate packing systems, sphericity needs to be added to further describe the morphological characteristics of the aggregate particles. This invention simulates and calculates non-spherical aggregate particles. After collecting, screening, and statistically summarizing a large amount of data characterizing non-spherical aggregate particles, 11 common and representative sphericity values ​​were determined, as shown in Table 1. To make the aggregate packing system more realistic, this invention adopts a multi-aggregate packing system, and the rules for the distribution of aggregate particle shapes are shown in Table 1.

[0118] Table 1. Rules for the distribution of aggregate particle shape

[0119]

[0120] S013: Use numerical values D agg,m The distribution range of gradation size [ D agg,min , D agg,max Divided into 10 secondary distribution intervals[ D agg,m , D agg,(m+1) ], mIt is greater than or equal to 1 and is a natural number.

[0121] Specifically, in order to ensure the rationality of aggregate particle size distribution and improve computational efficiency, this invention defines the aggregate particle size distribution range as follows: D agg,min , D agg,max The distribution is divided into 10 secondary distribution intervals for classification. D agg,min , D agg,max The value of ] is D agg,m , m ≥1 and is a natural number. This invention determines the numerical value based on the rules of arithmetic progression. D agg,m , D agg,m The formula for calculation is,

[0122] Formula (2)

[0123] In the formula, D agg,m To divide the distribution range of gradation size [ D agg,min , D agg,max The first m A number, m ≥1 and is a natural number; D agg,max The maximum equivalent diameter of the aggregate particles; D agg,min The minimum equivalent diameter of the aggregate particles.

[0124] S014: Calculate all secondary distribution intervals [ D agg,m , D agg,(m+1) The corresponding equivalent diameter of aggregate particles, i.e., the secondary distribution interval [ D agg,m , D agg,(m+1) The equivalent diameter of all aggregate particles within the range is represented by the characteristic equivalent diameter of the aggregate particles.

[0125] Specifically, in order to further simplify the aggregate packing system and improve computational efficiency, this invention sets the secondary distribution interval [ D agg,m , D agg,(m+1) The equivalent diameter of all aggregate particles within the range is determined by the characteristic equivalent diameter of the aggregate particles. D aggs,n The representative, its calculation formula is,

[0126] D aggs,n =[ D aggs,m + D aggs,(m+1) ] / 2 formula (3)

[0127] In the formula, D aggs,n Indicates the second-order distribution interval [ D agg,m , D agg,(m+1) The corresponding equivalent diameter of aggregate particles, 1≤ n ≤10 and is a natural number, and n = m .

[0128] S015: Using the characteristic equivalent diameter of aggregate particles D aggs,n Calculate the corresponding second-order distribution interval [ D agg,m , D agg,(m+1) The number of aggregate particles that need to be generated within the specified range.

[0129] Specifically, the characteristic equivalent diameter of aggregate particles is D aggs,n The number of aggregate particles can be calculated using the following formula:

[0130] Formula (4)

[0131] In the formula, L Let be the side length of the three-dimensional cube; V f This refers to the aggregate volume fraction. D agg,m , D agg,(m+1) To divide the distribution range of gradation size [ D agg,min , D agg,max The value of ]; D agg,n Indicates the second-order distribution interval [ D agg,m , D agg,(m+1) The corresponding equivalent diameter of aggregate particles; f N It is the basis probability density function; m ≥1 and is a natural number; 1≤ n ≤10 and is a natural number, and n = m.

[0132] The aggregate particles of this invention are distributed in a Fuller distribution form, therefore the characteristic equivalent diameter of the aggregate particles is... D aggs,n The formula for calculating the number basis probability density function of aggregate particles is:

[0133] Formula (5)

[0134] S016: According to the Monte Carlo principle and the equivalent diameter of aggregate particles D aggs,n Generate sequentially in the three-dimensional cube in descending order of size. N pn Each size is D aggs,n The process of obtaining an existing aggregate particle set includes the following steps:

[0135] S0161: Generate aggregate particles P1 to be added in the three-dimensional cube according to the Monte Carlo principle. The size of the aggregate particles P1 is the characteristic equivalent diameter of the aggregate particles. D aggs,10 It is then marked as an existing aggregate particle O1 and included in the existing aggregate particle set.

[0136] Specifically, at this point, the aggregate particle P1 to be added is the first aggregate particle generated in the three-dimensional cube. Therefore, there is no need to determine whether the aggregate particle P1 intersects with existing aggregate particles, and it is directly marked as an existing aggregate particle O1. The coordinates of the center point of the existing aggregate particle O1 are ( x 01 , y 01 , z 01 ).

[0137] S0162: Generate aggregate particles P to be added in the three-dimensional cube according to the Monte Carlo principle. i+1 , i The number is ≥1 and is a natural number. It is compared one by one with the existing aggregate particles in the existing aggregate particle set to determine whether they intersect. For example, the aggregate particle P to be added... i+1 If the aggregate particle P to be added does not intersect with any existing aggregate particles in the existing aggregate particle set, then the aggregate particle P to be added will be... i+1 Marked as existing aggregate particles O i+1 If the aggregate particles are included in the existing aggregate particle set, proceed to step S0163; otherwise, return to step S0162.

[0138] Specifically, the aggregate particles P to be added i+1 The dimensions should be based on the equivalent diameter of the aggregate particles. Daggs,n The rules are generated from largest to smallest, and the equivalent diameter of the aggregate particles is... D aggs,10 corresponding N p10 After each aggregate particle is generated sequentially, the next aggregate particle with the characteristic equivalent diameter is then added sequentially. D aggs,9 corresponding N p9 One aggregate particle at a time, and so on, until all aggregate particles corresponding to all secondary distribution intervals have been generated.

[0139] To improve the ability to judge the particle P of aggregate to be added i+1 The calculation efficiency for determining whether an aggregate particle intersects with all aggregate particles in an existing aggregate particle set. This invention establishes four judgment methods: coarse judgment one, coarse judgment two, coarse judgment three, and precise judgment four.

[0140] Therefore, it is determined that the aggregate particles P to be added are... i+1 Determining whether it intersects with any existing aggregate particle in an existing aggregate particle set includes the following steps:

[0141] S01621: Obtain aggregate particles O1 from the existing aggregate particle set, and aggregate particles P to be added. i+1 Perform a rough judgment with the existing aggregate particles O1. If no intersection occurs, continue to step S01625; otherwise, continue to step S01622.

[0142] Specifically, regarding the application of aggregate particles P i+1 A rough assessment of existing aggregate particles O1 is performed, including the following steps:

[0143] Calculate the particle size P of the aggregate to be added i+1 center point x coordinate x i+1 Center point of existing aggregate particles O1 x coordinate x 01 The distance between them, to obtain the distance ;

[0144] Calculate the particle size P of the aggregate to be added i+1 center point y coordinate y i+1 Center point of existing aggregate particles O1 y coordinate y 01 The distance between them, to obtain the distance ;

[0145] Calculate the particle size P of the aggregate to be added i+1 center pointz coordinate z i+1 Center point of existing aggregate particles O1 z coordinate z 01 The distance between them, to obtain the distance ;

[0146] Calculate and obtain the particle size P of the aggregate to be added. i+1 From the center point to the aggregate particle P to be added i+1 Maximum distance of the surface Specifically, calculating the maximum or minimum distance from the center point of a sphere or non-sphere to its surface is common knowledge to those skilled in the art and will not be elaborated upon here.

[0147] Calculate and obtain the maximum distance from the center point of existing aggregate particle O1 to the surface of existing aggregate particle O1. ;

[0148] Calculate the maximum distance and maximum distance The sum of these gives the distance. ;

[0149] Compare separately , and With distance ,like > or > or > Then the aggregate particles P to be added i+1 If the aggregate particle O1 does not intersect with the existing aggregate particle, proceed to step S01625; otherwise, proceed to step S01622.

[0150] S01622: For the addition of aggregate particles P i+1 Perform a rough judgment with the existing aggregate particles O1. If they do not intersect, continue to step S01625; otherwise, continue to step S01623.

[0151] Specifically, regarding the application of aggregate particles P i+1 A rough assessment of the existing aggregate particles O1 is performed, including the following steps:

[0152] Calculate the particle size P of the aggregate to be added i+1 Center point coordinates ( x i+1 , y i+1 , z i+1) and the coordinates of the center point of existing aggregate particle O1 ( x 01 , y 01 , z 01 Distance between ) Specifically, the distance between two points in computational space is common knowledge to those skilled in the art and will not be elaborated upon here.

[0153] Calculate and obtain the particle size P of the aggregate to be added. i+1 From the center point to the aggregate particle P to be added i+1 Maximum distance of the surface ;

[0154] Calculate and obtain the maximum distance from the center point of existing aggregate particle O1 to the surface of existing aggregate particle O1. ;

[0155] Calculate the maximum distance and maximum distance The sum of these gives the distance. ;

[0156] Compare distances With distance ,like > Then the aggregate particles P to be added i+1 If the aggregate particle O1 does not intersect with the existing aggregate particle, proceed to step S01625; otherwise, proceed to step S01623.

[0157] S01623: Treatment of aggregate particles P i+1 Perform a rough judgment with the existing aggregate particles O1. If they intersect, return to step S0162; otherwise, continue to step S01624.

[0158] Specifically, regarding the application of aggregate particles P i+1 A rough assessment of the existing aggregate particles O1 is performed, including the following steps:

[0159] Calculate the particle size P of the aggregate to be added i+1 Distance between the center point and the center point of the existing aggregate particle O1 ;

[0160] Calculate and obtain the particle size P of the aggregate to be added. i+1 From the center point to the aggregate particle P to be added i+1 Minimum distance of the surface ;

[0161] Calculate and obtain the minimum distance from the center point of existing aggregate particle O1 to the surface of existing aggregate particle O1. ;

[0162] Calculate the minimum distance minimum distance The sum of these gives the distance. ;

[0163] Compare distances With distance ,like < Then the aggregate particles P to be added i+1 If it intersects with an existing aggregate particle O1, return to step S0162; otherwise, continue to step S01624.

[0164] S01624: Treatment of aggregate particles P i+1 Perform a precise judgment with the existing aggregate particle O1. If they intersect, return to step S0162; otherwise, continue to step S01625.

[0165] Specifically, regarding the application of aggregate particles P i+1 The fourth step involves accurately determining the composition of existing aggregate particles O1, including the following steps:

[0166] Treating the addition of aggregate particles P i+1 The surface is discretized to obtain a first set of discrete points, which includes the aggregate particles P to be added. i+1 All discrete points on the surface;

[0167] In the first set of discrete points, obtain discrete points M one by one. i+1 Calculate discrete point M i+1 To the geometric potential of existing aggregate particles O1 G psovoid and judge G psovoid Is it less than or equal to 0, when G psovoid When ≤0, then the discrete point M i+1 Located on or inside the surface of existing aggregate particle O1, indicating that the aggregate particle P to be added... i+1 Intersecting with existing aggregate particle O1, return to step S0162. If the geometric potential of all discrete points in the first discrete point set is greater than 0, it indicates that the aggregate particle P to be added is... i+1 Since it does not intersect with existing aggregate particles O1, continue with step S01625.

[0168] The geometric potential G psovoid The formula for calculation is,

[0169] Formula (6)

[0170] In the formula,x i+1 For discrete point M i+1 of x Coordinate values; y i+1 For discrete point M i+1 of y Coordinate values; z i For discrete point M i of z Coordinate values; a i , b i and c i These are existing aggregate particles O i of x Coordinate direction y Coordinate direction z The length of the semi-axis in the coordinate direction; T i For existing aggregate particles O i Tapering parameters; i It is greater than or equal to 1 and is a natural number.

[0171] S01625: Repeat step S01621 until the aggregate particles to be added P are complete. i+1 The determination of whether it intersects with all existing aggregate particles in the existing aggregate particle set, such as the aggregate particle P to be added. i+1 If the aggregate particle to be added does not intersect with any existing aggregate particle in the existing aggregate particle set, then the aggregate particle P to be added will be... i+1 Marked as existing aggregate particles O i+1 If the aggregate particles are included in the existing aggregate particle set, proceed to step S0163; otherwise, return to step S0162.

[0172] S0163: Repeat step S0162 until all secondary distribution intervals are generated in the three-dimensional cube. D agg,m , D agg,(m+1) Corresponding quantity N pn Aggregate particles, 1≤ n ≤10 and are natural numbers, resulting in the existing aggregate particle set (O1, O2, ..., O i The existing aggregate particle set includes all existing aggregate particles generated in the three-dimensional cube.

[0173] S017: According to the Minkowski summation theory, for each existing aggregate particle in the existing aggregate particle concentration, an interface transition region of equal thickness is constructed on its surface to obtain the aggregate packing system, including the following steps:

[0174] S0171: In the existing aggregate particle set, obtain aggregate particle O1, and perform point discretization on the surface of the existing aggregate particle O1 to obtain a second set of discrete points.

[0175] S0172: Obtain discrete points from the second set of discrete points. W 1. And calculate the discrete points. W Normal vector of 1 ;

[0176] Specifically, discrete points W i ( x Wi , y Wi , z Wi The following formula can be used to express this:

[0177] Formula (7)

[0178] Formula (8)

[0179] In the formula, x Wi For discrete points W i of x Coordinate values; y Wi For discrete points W i of y Coordinate values; z Wi For discrete points W i of z Coordinate values; a Wi 、b Wi and c Wi These are existing aggregate particles O i exist x , y and z The length of the half-axis of the shaft; T i For existing aggregate particles O i Tapering parameters; i ≥1 and is a natural number; θ and φ For existing aggregate particles O i The three-dimensional polar angle.

[0180] normal vector The formula for calculation is,

[0181] Formula (9)

[0182] In the formula: a Wi , b Wi and c Wi These are existing aggregate particles O i exist x , y and z The length of the half-axis of the shaft; T i For existing aggregate particles O i Tapering parameters; x Wi , y Wi , z Wi ) is a discrete point W i The coordinates of the point; For discrete points W i Normal vector: Normal vector The x-coordinate; Normal vector y-coordinate; Normal vector The z-coordinate.

[0183] S0173: Along the normal vector on the surface of the existing aggregate particle O1 outward extension distance t To obtain discrete points The discrete points It is a point on the outer side of the interface transition zone surrounding the existing aggregate particle O1;

[0184] S0174: Repeat S0172~S0173 to obtain the discrete points in the second set of discrete points one by one. W i until the distance is extended outward along the normal vector of all discrete points. t A third set of discrete points is obtained. All discrete points in the third set of discrete points form the outer surface of the interface transition zone around the existing aggregate particle O1, which together with the surface of the existing aggregate particle O1 forms a thickness of [missing information]. t The interface transition area ITZ1, such as Figure 2 As shown, t =0.1mm.

[0185] S0175: Repeat S0171~S0174 until all existing aggregate particles in the existing aggregate particle set have completed the construction of a thickness of [missing information]. t The interface transition zone is obtained to form the aggregate packing system and the first interface transition zone set, which includes the interface transition zones constructed on the surfaces of all existing aggregate particles in the three-dimensional cube.

[0186] S02: Calculate whether percolation occurs in the interfacial transition zone of the aggregate packing system. If percolation occurs, S p =1 is recorded in the first tag set, and step S03 is continued; otherwise, S p =0 is recorded in the first tag set, and step S03 is continued; the... S p =1 indicates that, under preset conditions, the simulation calculation result for the aggregate packing system is that permeation occurs in the interface transition zone; S p =0 indicates that, under preset conditions, the simulation calculation result of the aggregate packing system is that no permeation occurs in the interface transition zone; the first set of markers is used to record the results of the simulation calculation of whether permeation occurs in the interface transition zone of the aggregate packing system.

[0187] The calculation of whether percolation occurs in the interfacial transition zone of the aggregate packing system includes the following steps:

[0188] S021: As follows Figure 1 The six faces of the three-dimensional cube shown are designated as the front surface, back surface, left surface, right surface, top surface, and bottom surface.

[0189] Among them, the left and right surfaces form the first investigation group, the front and rear surfaces form the second investigation group, and the upper and lower surfaces form the third investigation group.

[0190] S022: Preset the left surface in the first investigation group as the initial surface and the right surface as the termination surface; specifically, if any one surface in a certain investigation group is selected as the initial surface, then the other surface is the termination surface;

[0191] S023: Retrieve the interface transition areas (ITZ) from the first interface transition area set one by one. i ITZ determines the interface transition area. i Whether it intersects with the initial surface; if it intersects, then the interface transition zone ITZ will be determined. i Include it in the second interface transition area set; otherwise, remove the interface transition area ITZ. i Include in the third interface transition area set; such as Figure 3 The diagram shows the intersection of the interface transition zone and the initial surface.

[0192] ITZ for determining the interface transition zone i Whether it intersects with the initial surface includes the following steps:

[0193] Obtain points in the third discrete point set one by one and calculate the points Directed distance to the initial surface d i This yields the set of directed distances;

[0194] Specifically, points located within a three-dimensional cube A point located outside the three-dimensional cube with a positive directed distance to the initial face. The directed distance to the initial surface is negative when point When it is exactly on the initial surface, the directed distance is 0.

[0195] Calculate discrete points Directed distance to a certain plane d i The formula for calculation is,

[0196] Formula (10)

[0197] In the formula, d i Representing discrete points The directed distance to the initial or final surface; , , Points The x, y, and z coordinate values; A , B , C , D is a coefficient.

[0198] Once a certain face is determined, such as the initial face, it can be determined by the following formula. A , B , C , D The specific value and calculation process are common knowledge to those skilled in the art and will not be elaborated here.

[0199] Formula (11)

[0200] In the formula, A , B , C , D For coefficients, x p , y p , z pRepresenting points on a certain face x Coordinate values y Coordinate values z Coordinate values.

[0201] Obtain the maximum value in the directed distance set. d max and minimum value d min ;

[0202] Calculate the maximum value d max and minimum value d min The product of , to obtain the product ,like If ≤0, it indicates that the interface transition zone ITZ i Intersecting with the initial surface, the interface transition zone ITZ is formed. i Include it in the second interface transition area set; otherwise, the interface transition area ITZ i Included in the third interface transition area set.

[0203] S024: Obtain any interface transition region ITZ from the set of third interface transition regions. k , k ≥1 and is a natural number, is compared one by one with all interface transition regions in the second interface transition region set to determine whether they intersect, such as interface transition region ITZ. k If it intersects with any interface transition region in the second set of interface transition regions, then the interface transition region ITZ will be... k Remove it from the third interface transition area set and add it to the second interface transition area set to obtain a new third interface transition area set and a new second interface transition area set; otherwise, the interface transition area ITZ is removed. k It remains in the set of transition areas of the third interface;

[0204] Determine the interface transition zone ITZ in the third interface transition zone set. k Determining whether the interface transition area intersects with the interface transition area in the second set of interface transition areas includes the following steps:

[0205] S0241: Obtain all discrete points on the outer surfaces of all interface transition zones that make up the second interface transition zone set, and form a first point set;

[0206] S0242: In the existing aggregate particle set, obtain the interface transition zone ITZ with the third interface transition zone set. k Corresponding existing aggregate particles O k ;

[0207] S0243: Obtain the composition of existing aggregate particles O kAll discrete points on the surface form a second set of points;

[0208] S0244: Calculate the distance between all discrete points in the first set of points and all discrete points in the second set of points to obtain the first distance set;

[0209] S0245: Obtain the minimum distance in the first distance set. ;

[0210] S0246: Compare the minimum distance With distance t ,like ≤ t This indicates the ITZ interface transition area. k Interface transition zone ITZ in the second interface transition zone set j intersect, j If the value is ≥1 and is a natural number, then the interface transition area ITZ will be... k Remove it from the third interface transition area set and add it to the second interface transition area set to obtain a new third interface transition area set and a new second interface transition area set; otherwise, the interface transition area ITZ is removed. k It remains in the set of transition areas of the third interface.

[0211] S025: Based on the new set of third interface transition areas and the new set of second interface transition areas, repeat step S024 until there are no interface transition areas in the new set of third interface transition areas that intersect with the interface transition areas in the new set of second interface transition areas.

[0212] S026: In the new set of second interface transition zones, obtain each interface transition zone one by one, and determine whether the interface transition zone intersects with the termination surface. The specific determination method is the same as step S023, and will not be repeated here. If they intersect, the aggregate packing system generates a cluster of interconnected interface transition zones, and percolation occurs in the interface transition zones. Figure 4 As shown, S p =1 is recorded in the first tag set, and step S03 is executed; otherwise, step S027 is executed. S p =1 indicates that, under preset conditions, the simulation calculation result for the aggregate packing system is that permeation occurs in the interface transition zone; S p =0 indicates that, under preset conditions, the simulation calculation result of the aggregate packing system is that no permeation occurs in the interface transition zone; the first set of markers is used to record the results of the simulation calculation of whether permeation occurs in the interface transition zone of the aggregate packing system.

[0213] S027: Repeat steps S022-S026 to determine whether the second and third investigation groups have generated interconnected clusters in the interface transition zone, and whether percolation has occurred in the interface transition zone. If the first, second, and third investigation groups do not intersect with the interface transition zone, it indicates that percolation has not occurred in the interface transition zone of the aggregate packing system. S p =0 is recorded in the first mark set, and step S03 continues; otherwise, it indicates that the aggregate packing system has generated an interface transition zone connected cluster, that is, the initial surface and the terminal surface are connected through the interface transition zone, and percolation occurs in the interface transition zone. S p =1 is recorded in the first tag set, and step S03 is continued.

[0214] S03: Repeat steps S01~S02 until the preset number of simulation calculations is performed. G The first set of markers is obtained; specifically, the number of simulation calculations in this invention is preset to 2000.

[0215] S04: Count the "" in the first tag set S p The number of "=1" is used to obtain the quantity. N =1848;

[0216] S05: Calculation N / G The probability of percolation in the interfacial transition zone of the aggregate packing system is obtained. P ITZ =0.924.

[0217] This indicates that the above gradation dimensions (i.e., the maximum equivalent diameter of aggregate particles) are... D agg,max =1.18mm 、 Minimum equivalent diameter of aggregate particles D agg,min =0.3mm), aggregate volume fraction V f Under preset conditions such as 0.121, calculations using the method provided by this invention show that connected clusters are generated in the interface transition zone, and the probability of permeation is 92.4%. This means that when concrete is prepared according to the above mix proportions, there is a greater than 50% probability of permeation in the interface transition zone, providing a path for external corrosive media to penetrate into the concrete, resulting in poor concrete durability. To improve concrete durability, it is necessary to optimize the concrete mix proportions, such as reducing the aggregate volume fraction. V f .

[0218] Example 2

[0219] Among the many proportioning parameters, aggregate volume fraction V f The aggregate volume fraction is one of the main factors affecting whether percolation occurs in the interfacial transition zone. Therefore, in order to further evaluate the influence of changes in aggregate volume fraction on the probability of percolation in the interfacial transition zone, this invention takes 24 different aggregate volume fractions within the range of [0.07, 0.14]. V f Other preset conditions are the same as in Example 1. Then, using the method provided in Example 1, after simulation calculation, the probability of percolation occurring in the interface transition zone is determined. P ITZ As shown in Table 2.

[0220] Table 2. Probability of percolation in the interfacial transition zone under different aggregate volume fractions

[0221]

[0222] Based on the data in Table 2, the following can be plotted: Figure 5 The probabilities shown P ITZ With aggregate volume fraction V f The change graph, through analysis Figure 5 Medium probability P ITZ With aggregate volume fraction V f The invention uses an error function to fit the variation curve of aggregate volume fraction and considers its practical guiding significance on-site. Figure 5 From the data, the probability is derived. P ITZ The aggregate volume fraction corresponding to =0.5 V f =0.11, and with V f =0.11 is used as the threshold for evaluating percolation in the interfacial transition zone under preset conditions. That is, the preset adjustment is made while other proportioning parameters remain unchanged, and the aggregate volume fraction is adjusted accordingly. V f Less than the threshold This can effectively increase the difficulty of generating interconnected clusters in the interface transition zone, cut off the path of external corrosive media to the interior of concrete, thereby improving the durability of concrete and enabling rapid evaluation and optimization of on-site concrete mix proportions.

[0223] In summary, for multi-shaped aggregate particles, under the preset gradation size and aggregate volume fraction... V fUnder certain conditions, the method for calculating the connectivity of the interfacial transition zone around ovoid aggregate particles provided by this invention can calculate the probability and threshold of percolation in the interfacial transition zone, thereby quickly guiding the optimization of concrete mix proportion parameters such as aggregate volume fraction on site. For example, when the aggregate volume fraction is less than the percolation threshold of the interfacial transition zone... This can effectively increase the difficulty of generating interconnected clusters in the interface transition zone, thereby cutting off the path for external corrosive media to be transported into the concrete, and thus improving the durability of the concrete.

[0224] The above embodiments of the present invention are merely examples for clearly illustrating the present invention, and are not intended to limit the implementation of the present invention. For those skilled in the art, other variations or modifications can be made based on the above description. It is impossible to exhaustively list all the implementation methods here. Any obvious variations or modifications derived from the technical solutions of the present invention are still within the protection scope of the present invention.

Claims

1. A method of calculating the connectivity of interfacial transition zones around ovoid aggregate particles, characterized by, The method comprises the following steps: S01: constructing an aggregate accumulation system, the aggregate accumulation system being a three-dimensional cube in which polyhedral aggregate particles are distributed, the aggregate particles being provided with an interface transition zone on the surface; The construction of the aggregate accumulation system comprises the following steps: S011: presetting the edge length L of the three-dimensional cube, the gradation size of the aggregate particles, and the aggregate volume fraction Vf; the gradation size is the size distribution interval [Dagg,min, Dagg,max] of the aggregate particles, wherein Dagg,max is the maximum equivalent diameter of the aggregate particles, and Dagg,min is the minimum equivalent diameter of the aggregate particles; the equivalent diameter is the diameter of a spherical aggregate particle having the same volume as the non-spherical aggregate particle; S012: presetting the aggregate particle shape distribution rule by using the sphericity, the aspect ratio, and the tapering parameter; S013: dividing the distribution interval [Dagg,min, Dagg,max] of the gradation size into 10 secondary distribution intervals [Dagg,m, Dagg,(m+1)] by using the numerical value Dagg,m, wherein m is a natural number greater than or equal to 1; wherein the numerical value Dagg,m is determined according to the rule of arithmetic progression, and the calculation formula is, Equation (2) wherein Dagg,m is the mth numerical value of the distribution interval [Dagg,min, Dagg,max] of the gradation size, m is a natural number greater than or equal to 1; Dagg,max is the maximum equivalent diameter of the aggregate particles; and Dagg,min is the minimum equivalent diameter of the aggregate particles; S014: calculating the characteristic equivalent diameters of the aggregate particles corresponding to all the secondary distribution intervals [Dagg,m, Dagg,(m+1)], that is, the equivalent diameters of all the aggregate particles in the range of the secondary distribution interval [Dagg,m, Dagg,(m+1)] are represented by the characteristic equivalent diameters of the aggregate particles; the calculation formula of the characteristic equivalent diameters of the aggregate particles is, Daggs,n=[Daggs,m+Daggs,(m+1)] / 2 formula (3) wherein Daggs,n represents the characteristic equivalent diameter of the aggregate particles corresponding to the secondary distribution interval [Dagg,m, Dagg,(m+1)], 1≤n≤10 and n=m; S015: calculating the number Npn of the aggregate particles needed to be generated in the corresponding secondary distribution interval [Dagg,m, Dagg,(m+1)] by using the characteristic equivalent diameters Daggs,n of the aggregate particles, and the calculation formula is, Equation (4) wherein L is the edge length of the three-dimensional cube; Vf is the aggregate volume fraction; Dagg,m and Dagg,(m+1) are the numerical values of the distribution interval [Dagg,min, Dagg,max] of the gradation size; Daggs,n represents the characteristic equivalent diameter of the aggregate particles corresponding to the secondary distribution interval [Dagg,m, Dagg,(m+1)]; fN is the number-based probability density function; m is a natural number greater than or equal to 1; 1≤n≤10 and n=m; Dagg represents the equivalent diameter of the aggregate particles, and the calculation formula is, Equation (1) In the formula, Dagg is the equivalent diameter of the aggregate particle; Vpa is the volume of the aggregate particle; π is the circular constant; S016: According to the Monte Carlo principle and the order of the characteristic equivalent diameters Daggs,n from large to small, Npn aggregate particles with the size of Daggs,n are sequentially generated in the three-dimensional cube to obtain an existing aggregate particle set; S017: According to the Minkowski sum theory, an interface transition zone with equal thickness is constructed on the surface of each existing aggregate particle in the existing aggregate particle set to obtain the aggregate packing system; S02: Calculate whether the interface transition zone of the aggregate packing system is percolated, when percolation occurs, record Sp=1 in the first mark set, p≥1 and is a natural number, and continue to execute step S03, otherwise, record Sp=0 in the first mark set, and continue to execute step S03; Sp=1 indicates that the simulation calculation result of the aggregate packing system under the preset condition is that the interface transition zone is percolated; Sp=0 indicates that the simulation calculation result of the aggregate packing system under the preset condition is that the interface transition zone is not percolated; the first mark set is used to record the result of whether the interface transition zone of the aggregate packing system is percolated; S03: Repeat steps S01-S02 to a preset number of simulation calculations G to obtain a first mark set; S04: Count the number of "Sp=1" in the first mark set to obtain a number N; S05: Calculate N / G to obtain the probability PITZ that the interface transition zone of the aggregate packing system is percolated.

2. The method for calculating the connectivity of the interface transition zone around the ovoid aggregate particle according to claim 1, characterized in that, S016: According to the Monte Carlo principle and the order of the characteristic equivalent diameters Daggs,n from large to small, Npn aggregate particles with the size of Daggs,n are sequentially generated in the three-dimensional cube to obtain an existing aggregate particle set, including the following steps: S0161: According to the Monte Carlo principle, generate a to-be-placed aggregate particle P1 in the three-dimensional cube, the size of the to-be-placed aggregate particle P1 is the characteristic equivalent diameter Daggs,10, and mark it as an existing aggregate particle O1, and count it into the existing aggregate particle set; S0162: According to the Monte Carlo principle, generate a to-be-placed aggregate particle Pi+1 in the three-dimensional cube, i≥1 and is a natural number, and compare it with each existing aggregate particle in the existing aggregate particle set one by one to determine whether it intersects, if the to-be-placed aggregate particle Pi+1 does not intersect with all existing aggregate particles in the existing aggregate particle set, then mark the to-be-placed aggregate particle Pi+1 as an existing aggregate particle Oi+1, and count it into the existing aggregate particle set, and continue to execute step S0163, otherwise, return to execute step S0162; S0163: Repeat step S0162 until all the secondary distribution intervals [Dagg,m, Dagg,(m+1)] corresponding to the number Npn of aggregate particles, 1≤n≤10 and is a natural number, are generated in the three-dimensional cube, to obtain a set of existing aggregate particles; the set of existing aggregate particles includes all the existing aggregate particles generated in the three-dimensional cube; S017: According to the Minkowski sum theory, for each existing aggregate particle in the set of existing aggregate particles, an interface transition zone with equal thickness is constructed on its surface to obtain the aggregate packing system, including the following steps: S0171: In the set of existing aggregate particles, an existing aggregate particle O1 is obtained, and the surface of the existing aggregate particle O1 is point-discretized to obtain a second set of discrete points; S0172: In the second discrete point set, a discrete point W1 is acquired, and a normal vector of the discrete point W1 is calculated ; The normal vector of the discrete point Wi is calculated as, Equation (9) In the formula, aWi, bWi, and cWi are the semi-axis lengths of the existing aggregate particle Oi in the x, y, and z axes, respectively; Ti is the spheroidization parameter of the existing aggregate particle Oi; (xWi, yWi, zWi) is the point coordinates of the discrete point Wi; is the normal vector of the discrete point Wi; represents the x coordinate of the normal vector ; represents the y coordinate of the normal vector ; represents the z coordinate of the normal vector ; S0173: a surface of the existing aggregate particle O1 along a normal vector extends outward by a distance t to a discrete point , which is a point that makes up an outer side surface of the interface transition zone around the existing aggregate particle O1 ​ S0174: Repeat S0172-S0173 to obtain the discrete points Wi in the second set of discrete points one by one until the distance t is extended along the normal vector of all discrete points to obtain a third set of discrete points, all the discrete points in the third set of discrete points form the outer side of the interface transition zone around the existing aggregate particle O1, and the surface of the existing aggregate particle O1 together forms the interface transition zone ITZ1 with a thickness of t; S0175: Repeat S0171-S0174 until all the existing aggregate particles in the set of existing aggregate particles complete the construction of the interface transition zone with a thickness of t to obtain the aggregate packing system and a first set of interface transition zones, the first set of interface transition zones includes the interface transition zones constructed on the surfaces of all the existing aggregate particles in the three-dimensional cube.

3. A method of calculating the connectivity of the interfacial transition zone surrounding an ovoid aggregate particle according to claim 2, wherein, In step S0162, it is judged whether the to-be-placed aggregate particle Pi+1 intersects with any existing aggregate particle in the set of existing aggregate particles, including the following steps: S01621: An existing aggregate particle O1 in the set of existing aggregate particles is obtained, and a rough judgment one is performed on the to-be-placed aggregate particle Pi+1 and the existing aggregate particle O1, if they do not intersect, step S01625 is continued, otherwise, step S01622 is continued; Wherein, the rough judgment one performed on the to-be-placed aggregate particle Pi+1 and the existing aggregate particle O1 includes the following steps: The distance between the center point x coordinate xi+1 of the to-be-discharged aggregate particle Pi+1 and the center point x coordinate x01 of the existing aggregate particle O1 is calculated to obtain the distance ; The distance between the center point y coordinate yi+1 of the to-be-discharged aggregate particle Pi+1 and the center point y coordinate y01 of the existing aggregate particle O1 is calculated to obtain the distance ; The distance between the z coordinate zi+1 of the center point of the to-be-discharged aggregate particle Pi+1 and the z coordinate z01 of the center point of the existing aggregate particle O1 is calculated to obtain the distance ; calculating and obtaining a maximum distance from a center point of the to-be-placed aggregate particle Pi+1 to a surface of the to-be-placed aggregate particle Pi+1 ; calculating and obtaining a maximum distance from a center point of the existing aggregate particle O1 to a surface of the existing aggregate particle O1 ; calculating the maximum distance the sum of the maximum distance , obtaining the distance ; Comparing , and with the distance , such as > or > or > , if the to-be-discharged aggregate particle Pi+1 does not intersect with the existing aggregate particle O1, step S01625 is continuously executed, otherwise, step S01622 is continuously executed; S01622: A rough judgment two is performed on the to-be-placed aggregate particle Pi+1 and the existing aggregate particle O1, if they do not intersect, step S01625 is continued, otherwise, step S01623 is continued; Wherein, the rough judgment two performed on the to-be-placed aggregate particle Pi+1 and the existing aggregate particle O1 includes the following steps: calculating the distance between the center point of the to-be-dropped aggregate particle Pi+1 and the center point of the existing aggregate particle O1 ; calculating and obtaining a maximum distance from a center point of the to-be-placed aggregate particle Pi+1 to a surface of the to-be-placed aggregate particle Pi+1 ; calculating and obtaining a maximum distance from a center point of the existing aggregate particle O1 to a surface of the existing aggregate particle O1 ; calculating the maximum distance the sum of the maximum distance , obtaining the distance ; Comparing distances With distance As > If the to-be-dropped aggregate particle Pi+1 does not intersect with the existing aggregate particle O1, step S01625 is continuously executed, otherwise, step S01623 is continuously executed. S01623: A rough judgment three is performed on the to-be-placed aggregate particle Pi+1 and the existing aggregate particle O1, if they intersect, step S0162 is returned, otherwise, step S01624 is continued; Wherein, the rough judgment three performed on the to-be-placed aggregate particle Pi+1 and the existing aggregate particle O1 includes the following steps: calculating the distance between the center point of the to-be-dropped aggregate particle Pi+1 and the center point of the existing aggregate particle O1 ; calculating and obtaining a minimum distance from a center point of the to-be-placed aggregate particle Pi+1 to a surface of the to-be-placed aggregate particle Pi+1 ; calculating and obtaining a minimum distance from a center point of the existing aggregate particle O1 to a surface of the existing aggregate particle O1 ; Computing the minimum distance with the sum of the minimum distances , obtaining the distance ; Comparing the distance With the distance As < If the to-be-dropped aggregate particle Pi+1 intersects with the existing aggregate particle O1, return to step S0162, otherwise, continue to step S01624; S01624: performing accurate judgment four on the to-be-placed aggregate particle Pi+1 and the existing aggregate particle Oi, if intersecting, returning to perform step S0162, otherwise, continuing to perform step S01625; wherein, the accurate judgment four on the to-be-placed aggregate particle Pi+1 and the existing aggregate particle Oi includes the following steps: performing point discretization on the surface of the to-be-placed aggregate particle Pi+1 to obtain a first discrete point set, the first discrete set including all discrete points constituting the surface of the to-be-placed aggregate particle Pi+1; in the first discrete point set, acquiring discrete points Mi+1 one by one, calculating the geometric potential Gpsovoid of the discrete point Mi+1 to the existing aggregate particle Oi, and judging whether Gpsovoid is less than or equal to 0, when Gpsovoid≤0, the discrete point Mi+1 is located on the surface or inside the existing aggregate particle Oi, indicating that the to-be-placed aggregate particle Pi+1 intersects with the existing aggregate particle Oi, returning to perform step S0162, if the geometric potential of all discrete points in the first discrete point set is greater than 0, it indicates that the to-be-placed aggregate particle Pi+1 does not intersect with the existing aggregate particle Oi, and the step S01625 is continuously performed; S01625: repeatedly performing step S01621 until judging whether the to-be-placed aggregate particle Pi+1 intersects with all existing aggregate particles in the existing aggregate particle set is completed, if the to-be-placed aggregate particle Pi+1 does not intersect with any existing aggregate particle in the existing aggregate particle set, marking the to-be-placed aggregate particle Pi+1 as an existing aggregate particle Oi+1 and counting into the existing aggregate particle set, and then performing step S0163, otherwise, returning to perform step S0162.

4. A method of calculating the connectivity of the interface transition zone around an ovoid aggregate particle according to claim 2, wherein, In step S02, calculating whether the interface transition zone percolation occurs in the aggregate packing system includes the following steps: S021: setting the 6 faces of the three-dimensional cube as front surface, back surface, left surface, right surface, upper surface and lower surface respectively; wherein, the left surface and the right surface constitute a first investigation group, the front surface and the back surface constitute a second investigation group, and the upper surface and the lower surface constitute a third investigation group; S022: setting the left surface in the first investigation group as an initial surface and the right surface as a terminal surface; S023: acquiring interface transition zones ITZi in the first interface transition zone set one by one, judging whether the interface transition zone ITZi intersects with the initial surface, if intersecting, counting the interface transition zone ITZi into the second interface transition zone set, otherwise, counting the interface transition zone ITZi into the third interface transition zone set; S024: Acquire any interface transition zone ITZk in the third interface transition zone set, k≥1 and is a natural number, compare with all interface transition zones in the second interface transition zone set one by one, judge whether to intersect, if the interface transition zone ITZk intersects with any interface transition zone in the second interface transition zone set, delete the interface transition zone ITZk from the third interface transition zone set, and count into the second interface transition zone set, obtain a new third interface transition zone set and a new second interface transition zone set, otherwise, the interface transition zone ITZk remains in the third interface transition zone set; S025: Based on the new third interface transition zone set and the new second interface transition zone set, repeat step S024 until there is no interface transition zone in the new third interface transition zone set intersecting with the interface transition zone in the new second interface transition zone set; S026: In the new second interface transition zone set, acquire the interface transition zone one by one, judge whether the interface transition zone intersects with the termination surface, if so, the aggregate accumulation system produces an interface transition zone connected cluster, the interface transition zone percolates, Sp=1 is recorded in the first mark set, and step S03 is continued to execute, otherwise, step S027 is continued to execute; S027: Repeat steps S022-S026 to respectively complete the judgment of whether the second investigation group and the third investigation group produce an interface transition zone connected cluster and the interface transition zone percolates, if the first investigation group, the second investigation group and the third investigation group do not intersect with the interface transition zone, it is indicated that the interface transition zone of the aggregate accumulation system does not percolate, Sp=0 is recorded in the first mark set, and step S03 is continued to execute, otherwise, it is indicated that the aggregate accumulation system produces an interface transition zone connected cluster and the interface transition zone percolates, Sp=1 is recorded in the first mark set, and step S03 is continued to execute.

5. A method of calculating the connectivity of the interfacial transition zone surrounding an ovoid aggregate particle according to claim 4, wherein, In step S023, judging whether the interface transition zone ITZi intersects with the initial surface includes the following steps: Obtain the discrete points in the third discrete point set one by one. And calculate discrete points The directed distance di to the initial surface is used to obtain the set of directed distances; Wherein, the calculation formula of the directed distance di is, Equation (10) In the formula, di represents a point a directed distance to the initial face or the terminal face; 、 、 are respectively x coordinate value, y coordinate value, z coordinate value of a point ; A, B, C, D are coefficients; Acquire the maximum value dmax and the minimum value dmin in the directed distance set; The product of the maximum value dmax and the minimum value dmin is calculated to obtain a product As If dmin ≤ 0, it indicates that the interface transition zone ITZi intersects with the initial face, and the interface transition zone ITZi is counted into the second interface transition zone set, otherwise, the interface transition zone ITZi is counted into the third interface transition zone set.

6. A method of calculating the connectivity of the interface transition zone around an ovoid aggregate particle according to claim 5, wherein, In step S024, judging whether the interface transition zone ITZk in the third interface transition zone set intersects with the interface transition zone in the second interface transition zone set includes the following steps: S0241: Acquire all discrete points on the outer side surface of all interface transition zones constituting the second interface transition zone set to form a first point set; S0242: In the existing aggregate particle set, acquire the existing aggregate particle Ok corresponding to the interface transition zone ITZk in the third interface transition zone set; S0243: Acquire all discrete points constituting the surface of the existing aggregate particle Ok to form a second point set; S0244: Calculate the distance between all discrete points in the first point set and all discrete points in the second point set to obtain a first distance set; S0245: obtaining a minimum distance in the first distance set ; S0246: comparing the minimum distance with the distance t, as ≤ t, which means that the interface transition zone ITZk intersects with the interface transition zone ITZj in the second interface transition zone set, j ≥ 1 and is a natural number, then the interface transition zone ITZk is deleted from the third interface transition zone set and is counted into the second interface transition zone set, to obtain a new third interface transition zone set and a new second interface transition zone set, otherwise, the interface transition zone ITZk remains in the third interface transition zone set.

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