Prediction model of void ratio of three-grade coarse aggregate of concrete and its application

Abstract

The application belongs to the technical field of concrete, and discloses a coarse aggregate three-level grading close-packed void ratio prediction model for concrete and application of the model. The model is constructed according to the following steps: a database of shape feature parameters and close-packed void ratios of coarse aggregate single grading and three-level grading is established, a prediction model of the close-packed void ratio of coarse aggregate three-level grading about the coarse aggregate mixing ratio is established under the influence of shape features, edge wall effect and grading, and then a prediction model of the close-packed void ratio about the coarse aggregate mixing ratio is obtained based on the principle that the mixed stacking of multi-level grading coarse aggregate leads to the decrease of the close-packed void ratio. In application, the close-packed void ratio of coarse aggregate three-level grading can be predicted according to the mixing ratio of the coarse aggregate for concrete. The prediction model and the application can be used to quickly determine the optimal solution of the coarse aggregate ratio in different concrete parts in engineering practice, have high precision, and are convenient to use.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of concrete, and mainly relates to a coarse aggregate three-grade matching close-packed void ratio prediction model for concrete and application. BACKGROUND

[0002] Concrete is the most widely used building material in engineering construction. Coarse aggregate is an important component of concrete, which plays a role of framework in concrete and has a significant impact on the performance of concrete. The size of the packing void ratio is an important characteristic attribute to describe the quality of the coarse aggregate. Using coarse aggregate with smaller packing void ratio can improve the fluidity, mechanical properties and durability of concrete. Due to the smaller void ratio, less cement mortar is used to fill the aggregate void, which can save the amount of cement mortar, indirectly increase the amount of coarse aggregate, and improve the volume stability of concrete. At the same time, the packing void ratio also has an impact on the mix design of concrete.

[0003] At present, most of the coarse aggregate for concrete adopts three-grade matching. In theory, there are infinite combinations of three-grade matching coarse aggregate. Therefore, how to efficiently and accurately obtain the size of the packing void ratio of coarse aggregate plays an important role in concrete design. In actual engineering, the main method for measuring the packing void ratio is the volume bucket measurement experiment described in the specification GB / T 14685-2022. This method uses a large capacity cylinder, which is time-consuming and laborious in the measurement process. Moreover, it can only measure the size of the packing void ratio under one aggregate gradation at a time, and can only roughly determine the aggregate gradation with lower packing void ratio by relying on continuous experiments and experience. Therefore, it is of great significance to explore the influencing factors of the packing void ratio of coarse aggregate and establish a reasonable model to predict the packing void ratio of three-grade matching coarse aggregate in actual engineering. SUMMARY

[0004] To solve the problems in the prior art, the application provides a coarse aggregate three-grade matching close-packed void ratio prediction model for concrete and application. The model and application (prediction method) combine three important factors affecting the packing void ratio, i.e. aggregate shape characteristics, gradation, and edge effect, which can quickly and accurately predict the close-packed void ratio of three-grade matching coarse aggregate.

[0005] To achieve the above-mentioned purpose, the application adopts the following technical solutions:

[0006] In a first aspect, the application provides a coarse aggregate three-grade matching close-packed void ratio prediction model for concrete, which is constructed according to the following steps:

[0007] Step one, establish a database of coarse aggregate shape characteristic parameters and close-packed void ratio

[0008] Select three kinds of coarse aggregates, select no less than 200 particles from each kind of coarse aggregate, measure the morphological characteristics of the selected particles, obtain the morphological characteristic parameters and their mean values, and obtain the coarse aggregate single-graded shape characteristic parameter database; the morphological characteristic parameters include the center axis length, sphericity, angularity, elongation rate and flatness rate; measure the close-packed void ratios of the three kinds of coarse aggregate single-graded, and obtain the coarse aggregate single-graded close-packed void ratio database;

[0009] The three kinds of coarse aggregates are mixed in any mixing ratio x t , y t , z t to form no less than 50 groups of coarse aggregate ternary mixtures, and the weighted average values of the morphological characteristic parameters are calculated according to the mixing ratio x t , y t , z t of each group of coarse aggregate ternary mixture, and the coarse aggregate ternary mixture shape characteristic parameter database is obtained; t=1, 2, 3,...; measure the close-packed void ratios of each group of coarse aggregate ternary mixture, and obtain the coarse aggregate ternary mixture close-packed void ratio database;

[0010] Step two, establish a close-packed void ratio prediction model of coarse aggregate ternary mixture affected by morphological characteristics

[0011] Using principal component analysis method, using the data in the coarse aggregate ternary mixture shape characteristic parameter database and the close-packed void ratio database, a close-packed void ratio P sj of coarse aggregate affected by morphological characteristics is established; the expressions about sphericity, angularity, elongation rate and flatness rate; j=1, 2, 3;

[0012] Substitute the data of each kind of coarse aggregate in the coarse aggregate single-graded shape characteristic parameter database into the expression of P sj , and obtain the close-packed void ratios P s1 , P s2 , P s3 of the three kinds of coarse aggregate single-graded affected by morphological characteristics;

[0013] Let the mixing ratio of the j=1, 2, 3 kinds of coarse aggregate be x, y, z, multiply P s1 , P s2 , P s3 by x, y, z and sum them up, and obtain the close-packed void ratio P s of coarse aggregate ternary mixture affected by morphological characteristics, which is a prediction model about the mixing ratio x, y, z of coarse aggregate;

[0014] Step three, establish a close-packed void ratio prediction model of coarse aggregate ternary mixture affected by edge wall effect

[0015] The ratio of the characteristic particle size of coarse aggregate to the diameter of the close packing test container is defined as the coarse aggregate particle size ratio, and the average center axis length in the single-size coarse aggregate shape characteristic parameter database is taken as the characteristic particle size of the single-size coarse aggregate; the characteristic particle sizes of the three single-size coarse aggregates are divided by the diameter of the close packing test container to obtain the particle size ratios of the three single-size coarse aggregates; based on the principle that the close packing porosity of the single-size coarse aggregate is jointly affected by the shape characteristics and the edge wall effect, the data in the close packing porosity database of the single-size coarse aggregate are subtracted from P s1 , P s2 , P s3 to obtain the close packing porosity of the single-size coarse aggregate affected by the edge wall effect P b1 , P b2 , P b3 , P b1 , P b2 , P b3 The function relationship between the close packing porosity of the single-size coarse aggregate affected by the edge wall effect and the particle size ratio is obtained by regression analysis in the form of a power function.

[0016] The characteristic particle sizes of the three single-size coarse aggregates are multiplied by the mixing proportions x, y and z of the corresponding coarse aggregates and then summed to obtain the average characteristic particle size of the three-size coarse aggregate, and the average characteristic particle size of the three-size coarse aggregate is substituted into the function relationship between the close packing porosity of the single-size coarse aggregate affected by the edge wall effect and the particle size ratio to obtain the close packing porosity of the three-size coarse aggregate affected by the edge wall effect P b The prediction model of the mixing proportions x, y and z of the coarse aggregate;

[0017] Step four, establishing a prediction model for the close packing porosity of the three-size coarse aggregate affected by the grading

[0018] The reduction in packing porosity of two coarse aggregates due to the difference in particle size is defined as the particle contact coefficient k, the particle contact situations in the three-size coarse aggregate are divided into three situations of contact between particles of the same coarse aggregate and three situations of contact between particles of two different coarse aggregates according to the probability theory method, the probability values of the occurrence of the above six situations are obtained according to the mixing proportions x, y and z of the coarse aggregate, and the particle contact coefficients k of the above six situations are weighted and summed according to the obtained probability values to obtain the close packing porosity of the three-size coarse aggregate affected by the grading P G The prediction model is to be determined;

[0019] x t , y t and z t in step one are substituted into the prediction model P s and the prediction model P b , respectively, to obtain the prediction model of the mixing proportions xt 、y t 、z t Corresponding to the corresponding P s Value and P b value; s With P b The sum of the values ​​minus the corresponding data in the database of the void ratio of the three-graded dense packing of coarse aggregate is obtained to obtain the value of x t 、y t 、z t The corresponding P G value, x t 、y t 、z t And the corresponding P G Substitute the value into P G The particle contact coefficient k value is obtained by fitting the undetermined prediction model, and the k value is substituted into P G P is obtained in the undetermined prediction model G Prediction model for coarse aggregate mix proportions x, y, z;

[0020] Step 5: Based on the principle that the void ratio of the three-graded dense packing of coarse aggregate is jointly affected by the morphological characteristics, side wall effect, and gradation, the P obtained from steps 2 to 4 is used to calculate the void ratio of the coarse aggregate. s 、P b 、P G Prediction model, establish the prediction model of coarse aggregate three-graded dense packing void ratio P on coarse aggregate mixing ratio x, y, z: P = P b +P s -P G .

[0021] It should be noted that, in step 1, the angularity, sphericity, flattening rate and elongation in the morphological characteristic parameters are calculated as follows:

[0022]

[0023] FR=d S / d I ;ER=d I / d L

[0024] Where AN represents the angularity, SP represents the sphericity, FR represents the flattening rate, and ER represents the elongation; n is the number of edge points of the coarse aggregate particle, i is the i-th point on the edge of the coarse aggregate particle; θ i is the direction angle of the i-th edge point; d L d I d S They are the lengths of the major axis, median axis, and minor axis of the coarse aggregate particles, respectively, in mm.

[0025] It is to be noted that in step two, the close-packed void ratio P of the coarse aggregate single grading affected by the morphological characteristics sj The expressions for sphericity, angularity, elongation and flatness are:

[0026] P sj = 0.14 + 4.19 x 10 -5 AN-0.1337SP-0.0466FR-0.0691ER

[0027] In the formula, P sj is the close-packed void ratio of the coarse aggregate single grading affected by the morphological characteristics, k = 1, 2, 3; AN represents angularity, SP represents sphericity, FR represents flatness, and ER represents elongation.

[0028] It is to be noted that in step two, the close-packed void ratio P of the coarse aggregate single grading affected by the morphological characteristics s The prediction model for the coarse aggregate mixing proportions x, y, z is:

[0029] P s = x·P s1 +y·P s2 +z·P s3

[0030] In the formula, P s is the close-packed void ratio of the coarse aggregate single grading affected by the morphological characteristics; P s1 , P s2 , and P s3 are the close-packed void ratios of the three kinds of coarse aggregate single grading affected by the morphological characteristics, which can be obtained by substituting the morphological characteristic parameters of the coarse aggregate single grading into the fitting expression of P sk .

[0031] It is to be noted that in step three, the function relationship between the close-packed void ratio of the coarse aggregate single grading affected by the side wall effect and the particle size ratio is:

[0032]

[0033] In the formula, P b is the close-packed void ratio of the coarse aggregate single grading affected by the side wall effect; d is the characteristic particle size of the coarse aggregate, represented by the length of the central axis of the aggregate; B is the diameter of the close-packed test container, which refers to the test container used for measuring the close-packed void ratio in the specification; and b is a fitting parameter.

[0034] It is to be noted that in step three, the close-packed void ratio P of the coarse aggregate three grading affected by the side wall effect b The prediction model for the coarse aggregate mixing proportions x, y, z is:

[0035]

[0036] Where d1, d2, and d3 are the characteristic particle sizes of the three coarse aggregates; d1·x+d2·y+d3z is the average characteristic particle size of the three-graded coarse aggregate.

[0037] It should be noted that in step 4, the three-graded coarse aggregate is affected by the gradation and the close-packed void ratio P G The prediction model to be determined is:

[0038] P G =k sx ·x 2 +k sy ·y 2 +k sz ·z 2 +k oxy 2xy+k oyz ·2yz+k oxz ·2xz

[0039] Where, P G k is the close-packed void ratio of the three-graded coarse aggregate affected by the gradation; sx 、k sy 、k sz k is the particle contact coefficient of three similar coarse aggregate particles in contact with each other; oxy 、k oyz 、k oxz is the particle contact coefficient of three different types of coarse aggregate particles in contact with each other.

[0040] It should be noted that in step 5, the prediction model of the close-packed void ratio P of the three-graded coarse aggregate with respect to the coarse aggregate mixing ratio x, y, and z is:

[0041]

[0042] Where d1, d2, and d3 are the characteristic particle sizes of the three coarse aggregates; B is the diameter of the close-packed test container; b is the fitting parameter; P s1 、P s2 、P s3 k is the close-packed void ratio of three coarse aggregate single gradations affected by morphological characteristics; sx 、k sy 、k sz k is the particle contact coefficient of three similar coarse aggregate particles in contact with each other; oxy 、k oyz 、k oxz is the particle contact coefficient of three different types of coarse aggregate particles in contact with each other.

[0043] It should be noted that when the particle size ranges of the three kinds of coarse aggregates are 5-10mm, 10-20mm and 16.5-31.5mm respectively, the prediction model of the close-packed void ratio P of the coarse aggregate three grading with respect to the mixing ratio x, y, z of the coarse aggregate is:

[0044]

[0045] In the formula, P is the close-packed void ratio of the coarse aggregate three grading; B is the diameter of the close-packed test container.

[0046] In the second aspect, the application of the prediction model of the close-packed void ratio of the coarse aggregate three grading for concrete is: the values of the mixing ratio x, y, z of the coarse aggregate for concrete are substituted into the P prediction model to obtain the predicted close-packed void ratio of the coarse aggregate three grading.

[0047] The present application takes the commonly used building material coarse aggregate as the research material, measures the morphological characteristic parameters and the close-packed void through the test method to obtain the corresponding database, comprehensively considers the influence of the aggregate morphological characteristics, the grading and the side effect on the close-packed void ratio, respectively constructs the reasonable regression model to explain the influence law of the three on the close-packed void ratio, and further constructs the prediction model of the close-packed void ratio of the coarse aggregate three grading. The mathematical model explaining the side effect is constructed through edem modeling, and the accurate side effect parameters are regressed by using the database. When the grading influence is explored, the close-packed problem is converted into the proportion problem of the straight line passing through the particles through the dimension reduction processing, and finally simplified into the contact problem of two particles and the contact coefficient is defined. The coefficient can better explain the complex effect presented by the particle packing. The existing method for predicting the close-packed void ratio can predict the close-packed void ratio size through the morphological characteristics and the grading, and most of them only study the influence of a single factor on the close-packed void ratio, lack the complete explanation of the close-packed void ratio, and the prediction range is also small. The method can comprehensively predict the close-packed void ratio size, is conducive to the efficient utilization of the coarse aggregate, and has an important reference role for the optimization design of the concrete mix proportion.

[0048] Compared with the prior art, the present application has the following advantages and positive effects:

[0049] 1) The present application combines the three factors affecting the close-packed void ratio of the coarse aggregate, comprehensively analyzes and establishes the overall close-packed void ratio regression model, and fits the various parameters of the regression model more reasonably, which can be directly used for the aggregate with non-extreme morphological characteristics.

[0050] 2) The present application proposes a multi-graded aggregate mixing model, and the defined contact coefficient can more accurately describe the increase and decrease of the close-packed void ratio under the mixing condition of different graded aggregates.

[0051] 3) The close-packed void ratio formula proposed in the present application involves the selection of the mixing ratio of three-grade coarse aggregate and the selection of the size of the test container. In actual engineering, the sizes of concrete in different parts are different. The formula can be used for comprehensive judgment, and different aggregate ratios can be selected in different sizes of concrete parts to achieve the optimal solution. BRIEF DESCRIPTION OF DRAWINGS

[0052] Figure 1 Fig. (a) is the morphological characteristics, and Fig. (b) is the edge wall effect.

[0053] Figure 2 Fig. is an edem software simulation schematic diagram.

[0054] Figure 3 Fig. is a close-packed void ratio model regression schematic diagram affected by the edge wall effect.

[0055] Figure 4 Fig. is a schematic diagram of coarse aggregate particle void area; wherein Fig. (a) is a particle of the same size, and Fig. (b) is a particle of different sizes.

[0056] Figure 5 Fig. is a comparison diagram of the measured close-packed void ratio and the predicted close-packed void ratio; wherein Fig. (a) is the measured value, and Fig. (b) is the predicted value.

[0057] Figure 6 Fig. is a three-dimensional analytical schematic diagram of the close-packed void ratio prediction model in Example 2. DETAILED DESCRIPTION

[0058] The technical solutions in the embodiments of the present application will be described clearly and completely below with reference to the drawings in the embodiments of the present application.

[0059] The present application aims to construct a reasonable calculation method which can efficiently and accurately predict and estimate the close-packed void ratio of three-grade coarse aggregate. First, a three-grade coarse aggregate mixing database is established by indoor test, and then the influence factors of close-packed void ratio of coarse aggregate are quantitatively analyzed, i.e. the influence of aggregate edge wall effect, morphological characteristics and gradation on the packing void ratio is studied, and a regression model is obtained. The regression model of the three factors is combined to obtain a prediction model which can predict and estimate the close-packed void ratio.

[0060] The three factors affecting the size of the close-packed void of coarse aggregate are as follows: coarse aggregate shape characteristics, gradation, and edge wall effect. The shape characteristics refer to the shape characteristics of the aggregate, including two-dimensional and three-dimensional shape characteristics, such as sphericity, roundness, and angularity. The gradation of the aggregate refers to the distribution of the proportion of particles of different sizes. The three-grade gradation refers to the distribution of the particles of three different sizes in the aggregate. Compared with the two-grade and one-grade aggregate conditions, the three-grade aggregate has a more accurate description of the distribution of the particles. The edge wall effect refers to the hollow area caused by the contact between the container wall and the large aggregate particles, which affects the size of the close-packed void. The shape characteristics directly affect the size of the close-packed void of the coarse aggregate. The better the particle shape, the lower the close-packed void. The gradation composition also has a significant effect on the close-packed void. The close-packed void of the aggregate with different gradation compositions has a significant difference. The edge wall effect has a significant effect when the size of the aggregate is much larger than the size of the container.

[0061] Through the study of the above three factors, the influence of the three factors on the close-packed void of the coarse aggregate can be determined, and a mathematical model can be established to accurately predict the close-packed void of the coarse aggregate. This has a positive reference for the design of the concrete mix ratio and the preparation of high-performance concrete.

[0062] Referring to Figures 1-5 , the present application provides a three-grade close-packed void prediction model for coarse aggregate used in concrete, which is constructed according to the following steps:

[0063] Step one, establish the database of coarse aggregate shape characteristic parameters and close-packed void

[0064] Step one, establish the database of coarse aggregate shape characteristic parameters and close-packed void

[0065] Select three kinds of coarse aggregate, select not less than 200 particles from each kind of coarse aggregate, measure the shape characteristics of the selected particles, obtain the shape characteristic parameters and their mean values, and obtain the shape characteristic parameter database of the single-grade coarse aggregate; the shape characteristic parameters include the center axis length, sphericity, angularity, elongation rate, and flatness rate; measure the close-packed void of the single-grade coarse aggregate, and obtain the close-packed void database of the single-grade coarse aggregate;

[0066] The three kinds of coarse aggregate are mixed in any proportion x t , y t , and z t to form not less than 50 groups of three-grade coarse aggregate, and the mixing proportion of each group of three-grade coarse aggregate is x t , y t , and z tThe weighted average of the morphological characteristic parameters is calculated to obtain a coarse aggregate three-grade distribution shape characteristic parameter database; t = 1, 2, 3, …; the close-packed void ratio of each group of coarse aggregate three-grade distribution is measured to obtain a coarse aggregate three-grade distribution close-packed void ratio database.

[0067] Among them, the sphericity, angularity, elongation and flatness in the morphological characteristic parameters are calculated according to the following formula respectively:

[0068]

[0069] FR = d S / d I ; ER = d I / d L ;

[0070] In the formula, AN represents angularity, SP represents sphericity, FR represents flatness, and ER represents elongation; n is the number of edge points of the coarse aggregate particle, i is the i th point on the edge of the coarse aggregate particle, θ i is the direction angle of the i th edge point; d L , d I , d S are the lengths of the long axis, the middle axis and the short axis of the coarse aggregate respectively, with the unit of mm.

[0071] An example of establishing the coarse aggregate shape characteristic parameter database is as follows:

[0072] (1) The particle size ranges of the three kinds of coarse aggregates are 5-10 mm, 10-20 mm and 16.5-31.5 mm respectively. 200 of each are taken for morphological characteristic parameter measurement. The AIMS instrument is used to measure the morphological characteristics, and the long axis, the middle axis, the short axis, the sphericity, the angularity, the needle-like degree (elongation) and the flaky degree (flatness) are recorded. The mean values of the sphericity, the angularity, the elongation and the flatness are calculated (coarse aggregate single-grade distribution shape characteristic parameter database). The close-packed void ratios of the three kinds of coarse aggregate single-grade distribution are also measured.

[0073] (2) The three kinds of coarse aggregates are mixed under different proportions, and the mixing conditions meet the average change. The close-packed void ratios of the three-grade distribution coarse aggregates are measured under different proportions according to the requirements of GB / T 14685-2022 standard. 50 groups of measurement results are obtained.

[0074] (3) The shape characteristic parameters are weighted and averaged according to the mixing proportions of the coarse aggregates in (2) to obtain 50 groups of shape characteristic parameter data of the three-grade distribution mixed coarse aggregates (coarse aggregate three-grade distribution shape characteristic parameter database). The group of coarse aggregate database is established.

[0075] The morphological characteristics of coarse aggregate mainly include shape, edges and corners, and surface texture, each of which contains multiple parameters. The present invention selects four key parameters for modeling and analysis.

[0076] Step 2: Establish a prediction model for the void ratio of tightly packed coarse aggregates under the influence of morphological characteristics

[0077] The principal component analysis method was used to establish the coarse aggregate close-packed void ratio P affected by morphological characteristics using the data from the three-graded shape characteristic parameter database and the close-packed void ratio database. sj Expressions for sphericity, angularity, elongation, and flattening; j = 1, 2, 3;

[0078] Substitute the data of each coarse aggregate in the coarse aggregate single gradation shape characteristic parameter database into P sj The expression of the close-packed void ratio P of the three coarse aggregate single gradations affected by morphological characteristics is obtained. s1 、P s2 、P s3 ;

[0079] Assume that the mixing ratio of the jth type = 1, 2, and 3 coarse aggregates is x, y, and z, and P s1 、P s2 、P s3 Multiplying by x, y, and z and summing them, we can get the close-packed void ratio P of the coarse aggregate three-grade distribution affected by the morphological characteristics. s Prediction model for coarse aggregate mix proportions x, y, z;

[0080] Li Changzhi [1] Through experiments and data analysis (including principal component analysis), the expression of the tightly packed void ratio of coarse aggregate with particle size distribution of 4.75-9.5mm, 9.5-16mm, 16-19mm and 19-26.5mm was established. [1] The principal component analysis method in the paper establishes the expression of the void ratio of coarse aggregate in close packing with respect to sphericity, angularity, elongation and flatness. [1] The obtained expression of the void ratio of coarse aggregate tightly packed with respect to sphericity, roundness, angularity, elongation and flattening is:

[0081] P c =0.377+2.796×10 -5 ·AN+0.0893×Rd-0.1219SP-0.0309FR-0.0456ER

[0082] Where, P c The void ratio of tightly packed coarse aggregate.

[0083] Li Changzhi[1] The test results of the person and the research results of the subject group in which part of the inventors of the present application are located are the research results of the present application, the same or similar coarse aggregates are used, the size quantification formula of the packing void ratio of the single-graded coarse aggregate is studied, the formula is well verified in other various aggregates under the condition of single-graded, and the influence effect size of the morphological characteristics on the packing void ratio can be explained. Therefore, the present application directly uses the results in the literature, and the specific process is not described again.

[0084] In the formula, the composition element 0.377 of the close packing void ratio is a fixed factor (i.e. the influence of the side effect and the grading mixing), and the latter part is the influence of the morphological characteristics on the close packing void ratio, so the latter part is extracted for research and analysis. Since the roundness Rd and the angularity AN are both two-dimensional influence factors, and they have great correlation with the angularity AN and the sphericity SP, in order to facilitate and simplify data processing, the roundness Rd is equivalently replaced as the influence of the remaining four factors, and a linear function is used for equivalent replacement, that is:

[0085] P sj =a+b*(2.796×10 -5 ·AN-0.1219SP-0.0309FR-0.0456ER)

[0086] In the formula, P sj is the close packing void ratio of the single-graded coarse aggregate affected by the morphological characteristics; a and b are to-be-determined parameters; j=1, 2, 3.

[0087] The 50 groups of close packing void ratio data of the coarse aggregate of the three-graded are subtracted by the fixed element 0.377, to obtain the corresponding 50 groups of P sj data, the morphological characteristics data of the 50 groups of coarse aggregate of the three-graded and the corresponding 50 groups of P sj data are substituted into the above formula, and regression analysis is performed by using SPSS software, the regression analysis result is a=0.14, b=1.50, R 2 is 0.998, the fitting effect is very good, and finally the expression of P sj is obtained as follows:

[0088] P sj =0.14+4.19×10 -5 ·AN-0.1337SP-0.0466FR-0.0691ER

[0089] In the formula, P sj represents the close packing void ratio of the single-graded coarse aggregate caused by the morphological characteristics, AN represents the angularity, SP represents the sphericity, FR represents the flatness, ER represents the elongation, and j=1, 2, 3.

[0090] It should be noted that only adding the pending parameter b cannot meet the fitting accuracy requirement, and cannot well explain the influence of morphological characteristics on the close-packed porosity, while using the linear function form, that is, adding two pending parameters a and b, can keep the fitting result accurate and well explain the influence of morphological characteristics on the close-packed porosity. Although the present application uses the data of coarse aggregate three-level distribution to fit, the obtained P sk expression actually reflects the common characteristics of coarse aggregate (5-31.5 mm) for concrete. Under the condition of single-level distribution (5-31.5 mm), the influence of P sk value on the close-packed porosity is consistent with the result obtained by Li Changzhi [1] , which can better explain the influence of morphological characteristics on the close-packed porosity.

[0091] Therefore, under the condition of three-level distribution mixing, the close-packed porosity P s of coarse aggregate caused by morphological characteristics is determined by the following formula:

[0092] P s = x·P s1 + y·P s2 + z·P s3

[0093] In the formula, P s is the close-packed porosity of coarse aggregate three-level distribution affected by morphological characteristics; P s1 , P s2 , and P s3 are the close-packed porosities of three kinds of coarse aggregate single-level distribution affected by morphological characteristics, which can be obtained by substituting the morphological characteristic parameters of coarse aggregate single-level distribution into the fitting expression of P sk ; x, y, and z represent the mixing proportions of the three kinds of coarse aggregate.

[0094] When the particle size ranges of the three kinds of coarse aggregate are 5-10 mm, 10-20 mm, and 16.5-31.5 mm, respectively, the following formula can be fitted: P s = 0.0377x + 0.0495y + 0.042z.

[0095] Reference: Li Changzhi, Zhou Xinbin, Wei Shigong, et al. Research on the difference of coarse aggregate morphological characteristics and its relationship with packing porosity [J / OL]. Materials Review, 1-15 [2024-07-15].

[0096] Step three, establish a prediction model for the close-packed porosity of coarse aggregate three-level distribution affected by the edge wall effect

[0097] The ratio of the characteristic particle size of coarse aggregate to the diameter of the tight packing test container is defined as the coarse aggregate particle size ratio, and the average center axis length in the shape characteristic parameter database of the coarse aggregate single-graded shape is taken as the characteristic particle size of the coarse aggregate single-graded shape. The characteristic particle sizes of the three kinds of coarse aggregate single-graded shapes are respectively divided by the diameter of the tight packing test container to obtain the particle size ratios of the three kinds of coarse aggregate single-graded shapes. Based on the principle that the tight packing void ratio of the coarse aggregate single-graded shape is jointly affected by the shape characteristics and the edge wall effect, the data in the tight packing void ratio database of the coarse aggregate single-graded shape are subtracted from P s1 , P s2 , P s3 to obtain the tight packing void ratio P b1 of the coarse aggregate single-graded shape affected by the edge wall effect. b2 , P b3 , P b1 , P b2 , P b3 The regression analysis method is used to fit the function relationship between the tight packing void ratio of the coarse aggregate single-graded shape affected by the edge wall effect and the particle size ratio in the form of a power function.

[0098] The characteristic particle sizes of the three kinds of coarse aggregate single-graded shapes are multiplied by the mixing proportions x, y and z of the corresponding coarse aggregates and then summed to obtain the average characteristic particle size of the coarse aggregate three-graded shape. The average characteristic particle size of the coarse aggregate three-graded shape is substituted into the function relationship between the tight packing void ratio of the coarse aggregate single-graded shape affected by the edge wall effect and the particle size ratio to obtain the tight packing void ratio P b of the coarse aggregate three-graded shape affected by the edge wall effect.

[0099] The construction of the formula of the tight packing void ratio prediction model affected by the edge wall effect is mainly completed by the edem discrete element software. When different formulas are used for fitting, it is found that the fitting effect of the power function is better, and P b The expression of the theoretical model is as follows:

[0100]

[0101] In the formula, P b represents the tight packing void ratio caused by the edge wall effect; d represents the characteristic particle size of the coarse aggregate, represented by the center axis length of the aggregate; B represents the size of the tight packing test container, and the test container refers to the test container specified in the specification for measuring the tight packing void ratio; and a and b represent the undetermined parameters of the model.

[0102] For the coarse aggregate three-graded shape, there is:

[0103]

[0104] In the formula, d1, d2, d3 are characteristic particle sizes of three kinds of coarse aggregates.

[0105] Specifically, five different forms of particle shapes (strip, disc, three-pyramid, three-prism, five-prism) similar to the aggregate morphology with the same size as the actual aggregate characteristic size are constructed in the edem software to simulate the actual aggregate effect, a power function model is used for fitting regression, and the regression result of the measurement result is:

[0106]

[0107] In the formula, the first term is the packing void ratio affected by the aggregate effect, and the second term 0.056 is the packing void ratio caused by the morphological characteristics of the simulated particles. The ordinary spherical morphological characteristics are substituted into P s , and the result is -0.078. The packing void ratio of the spherical infinite size model is The value of the sphere A is 0.476-(-0.078), that is, a=0.55, and the value of a is determined as 0.55.

[0108] The combined effect of the aggregate effect and the morphological characteristics is the main factor affecting the aggregate under the condition of single grading. The morphological characteristic parameter data of three kinds of coarse aggregates under the condition of single grading are found in the database, the corresponding coarse aggregate particle size ratio is obtained, and the tight packing void ratio and the particle size ratio are input into P b In the theoretical model, regression analysis is performed, and the actual regression result of the aggregate effect is:

[0109]

[0110] From the above formula, it can be found that the actual measurement regression result 0.114 is basically consistent with the edem result 0.116. In the present application, the value of a is 0.55, and the value of b is 0.114.

[0111] Since the edem software is extremely cumbersome to operate, it is extremely inconvenient to calculate the tight packing void ratio by simulating the aggregate effect of the particles. The value of a can be basically determined as 0.55, so the value of b can be calculated according to the tight packing void ratio of the coarse aggregate under the condition of single grading. Under the condition of single grading, the tight packing void ratio of the coarse aggregate is affected by the combined effect of the aggregate effect and the morphological characteristics, so:

[0112]

[0113] Therefore, the calculation formula of the value of b can be obtained:

[0114]

[0115] In the formula, P represents the tight packing void ratio of the coarse aggregate under the condition of single grading (obtained from the database), and P sPd represents the close-packed porosity size caused by morphological characteristics (corresponding to Pd in step two) s1 , Pd s2 , Pd s3 ); Pd represents the particle size ratio, where d is the characteristic particle size represented by the central axis length of the particle.

[0116] The close-packed porosity of three single-grade coarse aggregates was measured, and the Pd s1 , Pd s2 , Pd s3 values obtained in step two were used to calculate the b values of the three coarse aggregates using the formula. The average of the parameter b values obtained for the three coarse aggregates is the accurate b value.

[0117] The above is the study of the edge effect by edem software. The purpose of the research process is to obtain the calculation formula of the edge effect. In actual application, Pd b is not directly obtained by edem (it is more troublesome to operate edem each time), and the result is that can more accurately reflect the influence of the edge effect on the close-packed porosity. In actual application, b can be calculated by the above formula, and then the calculation formula of Pd b is obtained. This method is more convenient and suitable for engineering practical application.

[0118] Step four, establish a prediction model for the close-packed porosity of coarse aggregate three-grade affected by grading

[0119] The reduction of the close-packed porosity caused by the difference in particle size of two coarse aggregates is defined as the particle contact coefficient k. According to the probability theory, the particle contact conditions in coarse aggregate three-grade are divided into three cases of similar coarse aggregate particles contacting each other and three cases of two different coarse aggregate particles contacting each other. The probability values of the six cases are obtained according to the coarse aggregate mixing proportions x, y, and z. The particle contact coefficients k of the six cases are weighted and summed according to the obtained probability values to obtain the close-packed porosity Pd G of coarse aggregate three-grade affected by grading, which is the to-be-determined prediction model.

[0120] Substitute x t , y t , z t in step one into Pd s prediction model and Pd b prediction model to obtain the corresponding Pd s values and Pd b values corresponding to x t , y t , z t ; compare Pd s with Pdb The sum of the values ​​minus the corresponding data in the database of the void ratio of the coarse aggregate three-graded close packing is obtained to get the value of x t 、y t 、z t The corresponding P G value, x t 、y t 、z t And the corresponding P G Substitute the value into P G The particle contact coefficient k value is obtained by fitting the undetermined prediction model, and the k value is substituted into P G P is obtained in the undetermined prediction model G Prediction model for coarse aggregate mix proportions x, y, and z.

[0121] The influence of gradation on the morphological characteristics of coarse aggregate is more complex. When aggregates are in a natural stacking state, they will contact with the adjacent aggregates in pairs. The two-dimensional model of contact is as follows: Figure 4 As shown in the figure, the particles in the model are established using the equivalent sphere method, where the ratio of the black area (void area) to the gray area (average area of ​​the two particles) can reflect, to a certain extent, the ability of the two aggregate particles to produce voids when they come into contact, and can be used as a qualitative factor for analysis.

[0122] The construction process of the two-dimensional contact model is as follows: the equivalent particle size method is used to equate particles of arbitrary shapes to spherical particles, and the edges of the two spheres are allowed to contact. Due to the mixed stacking between the three-graded particles of coarse aggregate, it is difficult to accurately characterize the contact between the particles in a three-dimensional stacking manner. The present invention converts the complex three-dimensional stacking problem into a two-dimensional contact problem through dimensionality reduction processing. At this time, the centers of the two spheres are coplanar. The plane is taken as the research object, that is, the two-dimensional contact plane of the coarse aggregate particles. It is assumed that the two particles are arranged horizontally (for two particles that are not arranged horizontally, they can also be converted into a horizontal arrangement). A horizontal straight line is set and the straight line is swept vertically, and the straight line always intersects with the particles during the sweep. Then the area between the two spheres swept by the straight line is taken as the gap area, that is Figure 4 The black area in the figure. When a third particle is in contact with the two particles mentioned above, the area of ​​the gap between the two particles will decrease. When a fourth particle is present, the area of ​​the newly generated gap will also decrease. However, for the same batch of equivalent spherical particles, their tightly packed void ratio is fixed. Figure 4As can be seen from (a) and (b) in the figure, the greater the difference between the particle sizes of the two particles in contact, the smaller the void area. In actual projects, even for coarse aggregates of a certain particle size range, the particle sizes of the particles are different, and the difference in particle size will cause the change of the close-packed void ratio. Therefore, the present application takes the reduction of the close-packed void ratio caused by the difference in particle size of the two coarse aggregates in close packing as the particle contact coefficient k.

[0123] In fact, based on the above two-dimensional contact model, it is difficult to obtain the accurate value of the particle contact coefficient. The actual aggregate contact is not a circular contact, and other factors also affect it. The physical model only qualitatively explains why the greater the difference between the particle sizes of the aggregates, the smaller the void. The present application obtains the particle contact coefficient by establishing a mathematical model and through regression analysis.

[0124] The defined particle contact coefficient k can reflect the ability of the aggregate particles to produce voids when in contact (the regression results show that the greater the difference between the particle sizes of the two aggregates, the greater the contact coefficient, which is consistent with the results of the model), and the main influencing factor of the coefficient is the ratio of the characteristic particle sizes of different gradations. The particle contact coefficient k of the same coarse aggregate particles in contact s The particle contact coefficient k of different coarse aggregate particles in contact o s o All contain three situations.

[0125] There are six situations of two-by-two contact of three particle size coarse aggregates, and the total probability is:

[0126] 1=x 2 +y 2 +z 2 +2xy+2yz+2xz

[0127] Where x, y, z represent the proportions of small, medium and large aggregates respectively, and z=1-x-y.

[0128] Each term in the above formula represents the probability of a situation occurring, for example, 2xy represents the probability of contact between small and medium aggregate particles in three particle size coarse aggregates, and the proportion of six two-by-two contact aggregate situations is six different probabilities. They can be calculated according to the mixing proportions of different particle size coarse aggregates x, y, z. Multiply the probabilities of the above six situations by the corresponding particle contact coefficients and sum them up, and the close-packed void ratio of the coarse aggregate ternary gradation affected by the gradation can be obtained, i.e. P G The to-be-determined prediction model is:

[0129] P G =k sx ·x 2 +k sy ·y 2 ​​+k sz ·z 2 +k oxy ·2xy+k oyz ·2yz+k oxz ·2xz

[0130] where P G is the close-packed void ratio of coarse aggregate with three-level grading; x, y, z are the mixing ratio of three kinds of coarse aggregate; k sx , k sy , k sz are the particle contact coefficient of three kinds of coarse aggregate with the same kind of particle; k oxy , k oyz , k oxz are the particle contact coefficient of three kinds of coarse aggregate with different kinds of particle.

[0131] The stacking of coarse aggregate with multi-level grading is a filling mixing effect, which will reduce the size of the close-packed void ratio, P s + P b is the formula of the close-packed void ratio of coarse aggregate with single-level grading, and the stacking of coarse aggregate with multi-level grading is considered, that is,

[0132] P = (P s + P b ) - P G

[0133] where P is the close-packed void ratio of coarse aggregate with three-level grading; P G is the decrease of the close-packed void ratio caused by grading.

[0134] The mixing ratio x t , y t , z t of 50 groups of coarse aggregate with three-level grading in step one is substituted into the P s prediction model and the P b prediction model, and the value of P s and the value of P b are calculated, and the close-packed void ratio of 50 groups of coarse aggregate with three-level grading has been determined, that is, the close-packed void ratio P G of 50 groups of coarse aggregate with three-level grading caused by the mixing of grading is obtained by P s = (P b + P G ) - P.

[0135] According to the 50 groups of data in the database of the close-packed void ratio of coarse aggregate with three-level grading constructed in step one, the close-packed void ratio P G corresponding to each mixing ratio is obtained, and the SPSS software is used to analyze the value of P G and the mixing ratio x t, y t , z t The regression analysis was carried out, and the size of the contact coefficient of each particle was shown in Table 1. The total distribution of the three kinds of aggregate was wide, which could well explain the coarse aggregate gradation in different situations. The six coefficients were representative, which could be well used in engineering practice. Some regression data were shown in Table 2.

[0136] Table 1 contact coefficient of particles in six situations

[0137]

[0138] Table 2 P G Calculation process and prediction of P

[0139]

[0140] According to Table 1, the close-packed void ratio P affected by gradation was obtained G :

[0141] P G =-0.017x 2 +0.014y 2 +0.013z 2 +0.119xy+0.108yz+0.171xz.

[0142] The mathematical meaning of the contact coefficient of particles is the decrease of the close-packed void ratio of coarse aggregate due to the difference in particle size. For example, in the above formula, k sx =-0.017 means that when the coarse aggregate particles with a particle size range of 5-10 mm contact with the coarse aggregate particles with a particle size range of 5-10 mm, the close-packed void ratio will increase by 1.7%, and k sxy =0.0595 indicates that when the coarse aggregate particles with a particle size range of 5-10 mm contact with the coarse aggregate particles with a particle size range of 10-20 mm, the close-packed void ratio will decrease by 5.95%. The value of k is obtained by regression analysis, which reflects the decrease of the close-packed void ratio when a certain type of coarse aggregate contacts with another type of coarse aggregate. The value is universal, that is, it is applicable to the contact of the two types of coarse aggregate, and the contact coefficient of particles can be used to predict the close-packed void ratio of the same three-grade coarse aggregate mixed in different proportions.

[0143] Step five, based on the principle that the close-packed void ratio of coarse aggregate three-grade is affected by the shape characteristics, edge wall effect and gradation, the prediction model of the close-packed void ratio P of coarse aggregate three-grade about the mixing ratio x, y, z of coarse aggregate was established according to the prediction models P s , P b , P G obtained in steps two to four: P=Pb +P s -P G The established P prediction model is used to predict the close-packed void ratio of coarse aggregate three-grade distribution;

[0144] According to the foregoing discussion, the final value of the coarse aggregate packing void ratio is defined as:

[0145] P=P b +P s -P G

[0146] In the formula, P is the close-packed void ratio of coarse aggregate three-grade distribution; P G is the packing void ratio reduction caused by the distribution.

[0147] The P s prediction model in steps two to four, the P b prediction model, and the P G prediction model are substituted into the above formula, and the following can be obtained:

[0148]

[0149] In the formula, b represents the side effect coefficient (P b undetermined parameter of the regression model), which can generally be taken as 0.114, d1, d2, and d3 respectively represent three kinds of distribution aggregate characteristic particle sizes, P s represents the close-packed void ratio of the corresponding three-grade distribution coarse aggregate caused by the morphological characteristics, k represents the contact coefficient, and B represents the diameter of the measuring container, which is generally 294 mm.

[0150] When the particle size ranges of the three kinds of coarse aggregates are 5-10 mm, 10-20 mm, and 16.5-31.5 mm respectively, the packing void ratio calculation formula of the batch of aggregates, i.e. the close-packed void ratio prediction model of coarse aggregate three-grade distribution, is as follows:

[0151]

[0152] The key of the present application is to establish the database of step one, and the close-packed void ratio prediction model formula of the coarse aggregate three-grade distribution can be constructed by measuring the aggregate morphological characteristics, so that the size of the coarse aggregate packing void ratio under different conditions can be directly estimated.

[0153] When the above prediction model is applied in engineering projects, the values ​​of the mixing ratios x, y, and z of the coarse aggregate for concrete are substituted into the P prediction model to obtain the predicted densely packed void ratio of the three-graded coarse aggregate for concrete. Specifically, for three identical coarse aggregates, the densely packed void ratio of the three-graded coarse aggregate can be predicted by substituting the mixing ratios x, y, and z. For three coarse aggregates with the same particle size gradation but different other conditions, the morphological characteristic parameters and single-graded densely packed void ratio of the corresponding coarse aggregate can be measured through indoor experiments to obtain a morphological characteristic parameter database, a single-graded densely packed void ratio database, and an average characteristic particle size. These can be substituted into the corresponding steps above, and finally the corresponding P prediction model can be updated for prediction with high accuracy. Since the morphological characteristic parameters, single-graded densely packed void ratio, and average characteristic particle size of the coarse aggregate are relatively easy to obtain, there is no need for measured data of the three-graded coarse aggregate mixture, so the prediction efficiency is relatively high.

[0154] Example 1:

[0155] The batch of three-graded coarse aggregate was randomly mixed according to a certain mixing ratio, and its dense packing void ratio was measured. The measured results and predicted results are as follows:

[0156] Table 3 Comparison of some measured results and predicted results

[0157]

[0158] The above table shows that the prediction model can well predict the void ratio of tightly packed three-graded coarse aggregate, with an error of less than 1.5%.

[0159] Example 2:

[0160] During the concrete construction process of a certain project, coarse aggregate was mixed according to empirical ratios to produce a three-grade coarse aggregate mix: 20% coarse aggregate with a particle size of 5-10 mm, 50% coarse aggregate with a particle size of 10-20 mm, and 30% coarse aggregate with a particle size of 16.5-31.5 mm (i.e., Comparative Example 1). Table 4 shows the measured close-packed void ratios for different mix ratios. Table 5 shows partial data from the test report for Comparative Example 1.

[0161] Table 4 Comparative Examples and Examples

[0162]

[0163] Table 5 Test report of three-graded coarse aggregate (partial)

[0164]

[0165]

[0166] The comparative examples 1-4 in Table 4 above are from actual engineering, the comparative example 1 is the experience data of the proportioning of the three-grade coarse aggregate of the project described in the present example 2, and the example 1 is the point with the minimum close-packed void ratio in the triangle under the condition of continuous grading, and it is obvious that the ratio is superior to the actual experience selection.

[0167] The above x=0.2, y=0.5, z=0.3 is input into the close-packed void ratio prediction P prediction model formula, the close-packed void ratio is measured according to the specification requirement, B=294mm, and the P prediction value is obtained as:

[0168]

[0169] The actual measurement result of the close-packed void ratio of the coarse aggregate is 39.48%, and the error The error is within the allowable range of 5%. However, the mixing ratio is not the best scheme. In order to obtain the best mixing ratio of the three coarse aggregates with the particle size ranges of 5-10mm, 10-20mm and 16.5-31.5mm respectively, the partial derivative of the formula is calculated, and the partial derivative is equal to zero to obtain the minimum value.

[0170]

[0171] z=1-x-y

[0172] The formula is calculated by the origin software, and it is known that the lowest void ratio point ratio is x=0.4, y=0.2, z=0.4, i.e. small aggregate: medium aggregate: large aggregate = 40:20:40, at this time, the close-packed void ratio of the coarse aggregate is the lowest, and the value is 38.6%, which is less than 39.48%. However, the grading belongs to the discontinuous grading interval, and the discontinuous grading concrete can be beneficial to reduce the cement consumption, but is easy to cause segregation and delamination. If continuous grading is used, according to the formula, when the small aggregate: medium aggregate: large aggregate = 30:30:40, the coarse aggregate is in the continuous grading and the close-packed void ratio is 38.8%, which is relatively small and also less than 39.48%, and the ratio can be used for the coarse aggregate proportioning in the actual construction process.

[0173] The above description is only used to illustrate the technical scheme of the present application and not to limit it, and the modifications or replacements of the technical scheme by other technical personnel in the same field should be covered in the scope of the claims of the present application as long as they do not deviate from the connotation of the technical scheme of the present application.

Claims

1. A model for predicting the void ratio of three-graded densely packed coarse aggregate for concrete, characterized by: Follow these steps to build: Step 1: Establish a database of coarse aggregate shape characteristic parameters and dense packing void ratio Three coarse aggregates are selected, and no less than 200 particles are selected from each coarse aggregate. The morphological characteristics of the selected particles are measured to obtain morphological characteristic parameters and their mean values, thereby obtaining a database of coarse aggregate single-gradation shape characteristic parameters. The morphological characteristic parameters include median length, sphericity, angularity, elongation, and flattening. The close-packed void ratios of three single-graded coarse aggregates were measured to obtain a database of close-packed void ratios of single-graded coarse aggregates. Mix the three coarse aggregates in any proportion x t 、y t 、z t Make up no less than 50 groups of coarse aggregate three-graded, according to the mixing ratio of each group of coarse aggregate three-graded x t 、y t 、z t Calculating the weighted average of its morphological characteristic parameters to obtain a database of shape characteristic parameters of the three-graded coarse aggregate; t = 1, 2, 3, ...; measuring the close-packed void ratio of each group of the three-graded coarse aggregate to obtain a database of the close-packed void ratio of the three-graded coarse aggregate; Step 2: Establish a prediction model for the void ratio of tightly packed coarse aggregates under the influence of morphological characteristics The principal component analysis method was used to establish the coarse aggregate close-packed void ratio P affected by morphological characteristics using the data from the three-graded shape characteristic parameter database and the close-packed void ratio database. sj Expressions for sphericity, angularity, elongation, and flattening; j = 1, 2, 3; Substitute the data of each coarse aggregate in the coarse aggregate single gradation shape characteristic parameter database into P sj The expression of the close-packed void ratio P of the three coarse aggregate single gradations affected by morphological characteristics is obtained. s1 、P s2 、P s3 ; Assume that the mixing ratio of the jth type = 1, 2, and 3 coarse aggregates is x, y, and z, and P s1 、P s2 、P s3 Multiplying by x, y, and z and summing them, we can get the close-packed void ratio P of the coarse aggregate three-grade distribution affected by the morphological characteristics. s Prediction model for coarse aggregate mix proportions x, y, z; Step 3: Establish a prediction model for the void ratio of tightly packed coarse aggregate with three-grade distribution affected by the side wall effect The ratio of the characteristic particle size of coarse aggregate to the diameter of the close-packed test container is defined as the coarse aggregate particle size ratio. The mean value of the median length in the coarse aggregate single-gradation shape characteristic parameter database is used as the characteristic particle size of the coarse aggregate single-gradation. The characteristic particle sizes of the three coarse aggregate single-gradations are divided by the close-packed test container diameter to obtain the particle size ratios of the three coarse aggregate single-gradations. Based on the principle that the close-packed void ratio of the coarse aggregate single-gradation is affected by the morphological characteristics and the side wall effect, the corresponding data in the coarse aggregate single-gradation close-packed void ratio database are subtracted from P. s1 、P s2 、P s3 The void ratio P of the tightly packed coarse aggregate single gradation affected by the side wall effect is obtained b1 、P b2 、P b3 , for P b1 、P b2 、P b3 The particle size ratio of three single-graded coarse aggregates was fitted with a power function using regression analysis, and the functional relationship between the close-packed void ratio and particle size ratio of single-graded coarse aggregates affected by the side wall effect was obtained. The characteristic particle size of the three single-graded coarse aggregates is multiplied by the mixing ratio x, y, and z of the corresponding coarse aggregates, and then the sum is obtained to obtain the average characteristic particle size of the three-graded coarse aggregates. The average characteristic particle size of the three-graded coarse aggregates is used to replace the characteristic particle size of the single-graded coarse aggregates in the functional relationship between the close-packed void ratio affected by the side wall effect and the particle size ratio of the coarse aggregates to obtain the close-packed void ratio P of the three-graded coarse aggregates affected by the side wall effect. b Prediction model for coarse aggregate mix proportions x, y, z; Step 4: Establish a prediction model for the tight packing void ratio of coarse aggregate three-grade distribution affected by gradation The particle contact coefficient k is defined as the reduction in the stacking void ratio caused by the difference in particle size when two coarse aggregates are tightly packed. According to the probability theory method, the particle contact situations in the three-graded coarse aggregate are divided into three situations in which the same coarse aggregate particles contact each other and three situations in which two different coarse aggregate particles contact each other. The probability values ​​of each of the above six situations are obtained according to the coarse aggregate mixing ratios x, y, and z. The particle contact coefficients k of the above six situations are weighted summed according to the obtained probability values ​​to obtain the tight stacking void ratio P of the three-graded coarse aggregate affected by the gradation. G Prediction model to be determined; Change x in step 1 t 、y t 、z t Substitute into P respectively s Prediction model, P b In the prediction model, we get t 、y t 、z t Corresponding to the corresponding P s Value and P b value; s With P b The sum of the values ​​minus the corresponding data in the database of the void ratio of the three-graded dense packing of coarse aggregate is obtained to obtain the value of x t 、y t 、z t The corresponding P G value, x t 、y t 、z t And the corresponding P G Substitute the value into P G The particle contact coefficient k value is obtained by fitting the undetermined prediction model, and the k value is substituted into P G P is obtained in the undetermined prediction model G Prediction model for coarse aggregate mix proportions x, y, z; Step 5: Based on the principle that the void ratio of the three-graded dense packing of coarse aggregate is jointly affected by the morphological characteristics, side wall effect, and gradation, the P obtained from steps 2 to 4 is used to calculate the void ratio of the coarse aggregate. s 、P b 、P G Prediction model, establish the prediction model of coarse aggregate three-graded dense packing void ratio P on coarse aggregate mixing ratio x, y, z: P = P b +P s -P G .

2. The prediction model according to claim 1, wherein: In step 1, the angularity, sphericity, flattening rate and elongation of the morphological characteristic parameters are calculated as follows: FR=d S / d I ;ER=d I / d L Where AN represents the angularity, SP represents the sphericity, FR represents the flattening rate, and ER represents the elongation; n is the number of edge points of the coarse aggregate particle, i is the i-th point on the edge of the coarse aggregate particle; θ i is the direction angle of the i-th edge point; d L d I d S are the lengths of the major axis, median axis, and minor axis of the coarse aggregate particles, respectively.

3. The prediction model according to claim 1, wherein: In step 2, the close-packed void ratio P of the coarse aggregate single gradation is affected by the morphological characteristics. sj The expressions for sphericity, angularity, elongation, and flattening are: P sj =0.14+4.19×10 -5 ·AN-0.1337SP-0.0466FR-0.0691ER Where, P sj is the close-packed void ratio of coarse aggregate in single gradation affected by morphological characteristics, j = 1, 2, 3; AN represents the angularity, SP represents the sphericity, FR represents the flattening rate, and ER represents the elongation.

4. The prediction model according to claim 1, wherein: In step 2, the close-packed void ratio P of the coarse aggregate three-grade distribution is affected by the morphological characteristics. s The prediction model for the coarse aggregate mix ratio x, y, z is: P s =x·P s1 +y·P s2 +z·P s3 Where, P s P is the close-packed void ratio of the three-graded coarse aggregate affected by its morphological characteristics; s1 、P s2 、P s3 The close-packed void ratio of three single-graded coarse aggregates affected by their morphological characteristics.

5. The prediction model according to claim 1, wherein: In step 3, the functional relationship between the close-packed void ratio and the particle size ratio of the single-graded coarse aggregate affected by the side wall effect is: Where, P b is the close-packed void ratio of single-graded coarse aggregate affected by the side wall effect; d is the characteristic particle size of coarse aggregate; B is the diameter of the close-packed test container; and b is the fitting parameter.

6. The prediction model according to claim 1, wherein: In step 3, the close-packed void ratio P of the coarse aggregate three-grade distribution affected by the side wall effect is b The prediction model for the coarse aggregate mix ratio x, y, z is: Where, P b is the close-packed void ratio of the three-graded coarse aggregate affected by the side wall effect; B is the diameter of the close-packed test container; d1, d2, and d3 are the characteristic particle sizes of the three coarse aggregates; and b is the fitting parameter.

7. The prediction model according to claim 1, wherein: In step 4, the three-graded coarse aggregate is affected by the gradation and the close-packed void ratio P G The pending prediction model is: P G =k sx ·x 2 +k sy ·y 2 +k sz ·z 2 +k oxy ·2xy+k oyz ·2yz+k oxz ·2xz Where, P G k is the close-packed void ratio of the three-graded coarse aggregate affected by the gradation; sx 、k sy 、k sz k is the particle contact coefficient of three similar coarse aggregate particles in contact with each other; oxy 、k oyz 、k oxz is the particle contact coefficient of three different types of coarse aggregate particles in contact with each other.

8. The prediction model according to claim 1, wherein: The prediction model of the close-packed void ratio P of the three-graded coarse aggregate with respect to the coarse aggregate mixing ratio x, y, z is: Where d1, d2, and d3 are the characteristic particle sizes of the three coarse aggregates; B is the diameter of the close-packed test container; b is the fitting parameter; P s1 、P s2 、P s3 k is the close-packed void ratio of three coarse aggregate single gradations affected by morphological characteristics; sx 、k sy 、k sz k is the particle contact coefficient of three similar coarse aggregate particles in contact with each other; oxy 、k oyz 、k oxz is the particle contact coefficient of three different types of coarse aggregate particles in contact with each other.

9. The use of the prediction model according to any one of claims 1 to 8, characterized in that: Substituting the values ​​of the mixing proportions x, y, and z of the coarse aggregate for concrete into the P prediction model, the predicted close-packed void ratio of the three-graded coarse aggregate for concrete was obtained.

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