Prediction model for three-graded close packing void ratio of coarse aggregate for concrete and application of prediction model

Abstract

The invention belongs to the technical field of concrete, and discloses a coarse aggregate three-gradation close packing void ratio prediction model for concrete and application, and the model is constructed according to the following steps: establishing a database containing single-gradation and three-gradation shape characteristic parameters of coarse aggregate and close packing void ratios, the method comprises the following steps: respectively establishing prediction models of the close packing void ratio of coarse aggregate three-grading influenced by morphological characteristics, side wall effects and grading on the coarse aggregate mixing ratio, and then combining to obtain the prediction model of the close packing void ratio on the coarse aggregate mixing ratio on the basis of the principle that the accumulation void ratio is reduced due to multi-grading coarse aggregate mixing and stacking. During application, the three-graded close packing void ratio of the coarse aggregate can be predicted according to the mixing ratio of the coarse aggregate for concrete. The prediction model and the application can be used for rapidly determining the optimal solution of the proportion of the coarse aggregate in different concrete components in engineering practice, and are high in precision and convenient to use.

Description

Technical Field

[0001] The invention belongs to the technical field of concrete, and mainly relates to a prediction model for the void ratio of three-graded and tightly packed coarse aggregate for concrete and its application. Background Art

[0002] Concrete is the largest building material used in engineering construction. Coarse aggregate is an important component of concrete. It plays a skeleton role in concrete and has a significant impact on the performance of concrete. The size of the stacking void ratio is an important characteristic attribute that describes the excellent quality of coarse aggregate. The use of coarse aggregate with a smaller stacking void ratio can improve the fluidity, mechanical properties and durability of concrete. In addition, due to the smaller void ratio, less cement mortar is used to fill the aggregate voids, which can save the amount of cement mortar, indirectly increase the amount of coarse aggregate, and thus improve the volume stability of concrete. At the same time, the stacking void ratio also affects the concrete mix design.

[0003] At present, most of the coarse aggregates used in concrete are three-graded. Theoretically, there are infinite combinations of three-graded coarse aggregates. Therefore, how to efficiently and accurately obtain the size of the coarse aggregate stacking void ratio plays an important role in concrete design. The measurement method of stacking void ratio in actual engineering is mainly the capacity barrel measurement experiment described in the specification GB / T 14685-2022. The capacity barrel used in this method is large, the measurement process is time-consuming and laborious, and the size of the stacking void ratio can only be measured under one aggregate gradation at a time. The aggregate gradation with a lower stacking void ratio can only be roughly determined by continuous experiments and experience. Therefore, it is of great significance in actual engineering to explore the influencing factors of the stacking void ratio of coarse aggregate and establish a reasonable model to predict the stacking void ratio of three-graded coarse aggregate. Summary of the invention

[0004] In order to solve the problems in the prior art, the present invention proposes a prediction model and application of the void ratio of three-graded dense packing of coarse aggregate for concrete. The model and application (prediction method) combine three important factors affecting the packing void ratio, namely, aggregate morphological characteristics, grading, and edge-wall effect, and can quickly and accurately predict the dense packing void ratio of three-graded coarse aggregate.

[0005] To achieve the above object, the present invention adopts the following technical solution:

[0006] In a first aspect, the present invention provides a prediction model for the void ratio of three-graded dense packing of coarse aggregate for concrete, which is constructed according to the following steps:

[0007] Step 1: Establish a database of coarse aggregate shape characteristic parameters and dense packing void ratio

[0008] Select three types of coarse aggregates, select no less than 200 particles from each type of coarse aggregate, measure the morphological characteristics of the selected particles, obtain morphological characteristic parameters and their mean values, and obtain a database of coarse aggregate single-grade shape characteristic parameters; the morphological characteristic parameters include median length, sphericity, angularity, elongation and flattening; measure the close-packed void ratios of the three single-graded coarse aggregates, and obtain a database of coarse aggregate single-graded close-packed void ratios;

[0009] Mix the three coarse aggregates in any proportion x t ,y t 、z t Composed of no less than 50 groups of three-graded coarse aggregates, according to the mixing ratio of each group of three-graded coarse aggregates x t ,y t 、z t Calculate the weighted average of its morphological characteristic parameters to obtain a database of shape characteristic parameters of three-graded coarse aggregate; t=1, 2, 3, ...; measure the close-packed void ratio of each group of three-graded coarse aggregate to obtain a database of close-packed void ratio of three-graded coarse aggregate;

[0010] Step 2: Establish a prediction model for the void ratio of coarse aggregate three-grade distribution affected by morphological characteristics

[0011] The principal component analysis method was used to establish the coarse aggregate close-packed void ratio P affected by the 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;

[0012] Substitute the data of each coarse aggregate in the coarse aggregate single gradation shape characteristic parameter database into P sj The close-packed void ratio P of three single-graded coarse aggregates affected by morphological characteristics is obtained from the expression of s1 , P s2 , P s3 ;

[0013] Assume that the mixing ratio of the jth type of coarse aggregate is x, y, z, and P s1 , P s2 , P s3 Multiply by x, y, and z and sum to get the close-packed void ratio P of the three-grade coarse aggregate affected by the morphological characteristics. s Prediction model for coarse aggregate mix proportions x, y, z;

[0014] Step 3: Establish a prediction model for the void ratio of three-graded coarse aggregate in close packing affected by the side wall effect

[0015] 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-graded shape characteristic parameter database is used as the characteristic particle size of the coarse aggregate single-graded. The characteristic particle sizes of the three coarse aggregate single-graded configurations are divided by the diameter of the close-packed test container to obtain the particle size ratios of the three coarse aggregate single-graded configurations. Based on the principle that the close-packed void ratio of the coarse aggregate single-graded configuration is jointly affected by the morphological characteristics and the sidewall effect, the data in the coarse aggregate single-graded 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 in the form of a power function using regression analysis, and the functional relationship between the close-packed void ratio and the particle size ratio of single-graded coarse aggregates affected by the side wall effect was obtained.

[0016] The characteristic particle sizes of the three single-graded coarse aggregates are multiplied by the mixing ratios 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 single-graded coarse aggregate characteristic particle size in the functional relationship between the tight packing void ratio affected by the side wall effect and the particle size ratio of the single-graded coarse aggregates to obtain the tight packing 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;

[0017] Step 4: Establish a prediction model for the void ratio of coarse aggregate with three-grade distribution affected by the gradation

[0018] The reduction in the stacking void ratio caused by the difference in particle size when two coarse aggregates are tightly packed is defined as the particle contact coefficient k. 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 the above six situations are obtained according to the coarse aggregate mixing ratio 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;

[0019] Replace x in step 1 t ,y t 、z t Substitute into P s Prediction model, P b In the prediction model, we gett ,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 in the undetermined prediction model, and the k value is substituted into P G P is obtained in the prediction model to be determined 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, the side wall effect, and the 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-grade compact packing void ratio P about 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 edge angle, SP represents the sphericity, FR represents the flatness, 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 should be noted that in step 2, the close-packed void ratio P of the coarse aggregate single gradation affected by the morphological characteristics is sj The expressions for sphericity, angularity, elongation and flattening are:

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

[0027] Where P sj is the close-packed void ratio of single-graded coarse aggregate affected by morphological characteristics, k = 1, 2, 3; AN represents the angular angle, SP represents the sphericity, FR represents the flattening rate, and ER represents the elongation.

[0028] It should be noted that 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 mixing ratio x, y, z is:

[0029] P s = x·P s1 +y·P s2 +z·P s3

[0030] 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 is the close packing void ratio of three single-graded coarse aggregates affected by morphological characteristics. Substitute the morphological characteristic parameters of single-graded coarse aggregates into P sk It can be obtained from the fitting expression of .

[0031] It should be noted that 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:

[0032]

[0033] 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, expressed as the length of the aggregate center axis; B is the diameter of the close-packed test container, and the test container refers to the test container specified in the specification for measuring the close-packed void ratio; b is the fitting parameter.

[0034] It should be noted that 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 mixing ratio 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 close-packed void ratio P of the coarse aggregate three-grade distribution is affected by the grading. 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 packing void ratio of the three-graded coarse aggregate affected by the grading; 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, 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 single-graded coarse aggregates affected by their 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 coarse aggregates are 5-10 mm, 10-20 mm, and 16.5-31.5 mm, respectively, 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:

[0044]

[0045] Where P is the close-packed void ratio of the three-graded coarse aggregate; B is the diameter of the close-packed test container.

[0046] In the second aspect, the application of the three-graded densely packed void ratio prediction model of coarse aggregate for concrete of the present invention is: substituting the values ​​of the mixing proportions x, y, and z of the coarse aggregate for concrete into the P prediction model to obtain the predicted densely packed void ratio of the three-graded coarse aggregate for concrete.

[0047] The present invention uses coarse aggregate, a commonly used building material, as a research material, measures its morphological characteristic parameters and closely packed voids through an experimental method to obtain a corresponding database, comprehensively considers the influence of aggregate morphological characteristics, gradation and side wall effect on closely packed void ratio, and respectively constructs a reasonable regression model to explain the influence of the three on closely packed void ratio, and then constructs a three-graded closely packed void ratio prediction model of coarse aggregate. A mathematical model to explain the side wall effect is constructed through EDM modeling, and accurate side wall effect parameters are regressed using the database. When exploring the influence of gradation, the complex stacking problem is converted into a proportional problem of a straight line passing through the particles through dimensionality reduction processing, and is finally simplified to a contact problem of two particles and a contact coefficient is defined, which can better explain the complex effects presented by particle stacking. The existing methods for predicting stacking void ratio include predicting the size of the stacking void ratio through morphological characteristics, and predicting the stacking void ratio through gradation. Most of them only study the influence of a single factor on the stacking void ratio, lack a complete explanation of the stacking void ratio, and the range of their prediction is also relatively small. This method can more comprehensively predict the size of the tight-packed void ratio, which is conducive to the efficient utilization of coarse aggregate and plays an important reference role in the optimization design of concrete mix ratio.

[0048] Compared with the prior art, the advantages and positive effects of the present invention are as follows:

[0049] 1) The present invention combines three factors that affect the tight packing void ratio of coarse aggregate, comprehensively analyzes and establishes a regression model for the overall packing void ratio, and fits various relatively reasonable parameters of the regression model, so that aggregates with non-extreme morphological characteristics can be directly used.

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

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

[0052] Figure 1 Schematic diagram of the morphological characteristics and side wall effect of coarse aggregate; Figure (a) shows the morphological characteristics, and Figure (b) shows the side wall effect.

[0053] Figure 2 This is a simulation diagram of the EDM software.

[0054] Figure 3 Schematic diagram of the regression of the close-packed void fraction model affected by the edge-wall effect.

[0055] Figure 4 Schematic diagram of the void area of ​​coarse aggregate particles; Figure (a) shows particles with the same particle size, and Figure (b) shows particles with different particle sizes.

[0056] Figure 5 It is a comparison chart of the measured close-packed porosity and the predicted close-packed porosity; among them, Figure (a) is the measured one, and Figure (b) is the predicted one.

[0057] Figure 6 Schematic diagram of the three-dimensional analysis of the close-packed void fraction prediction model in Example 2. DETAILED DESCRIPTION

[0058] The technical solutions in the embodiments of the present invention will be described clearly and completely below in conjunction with the accompanying drawings in the embodiments of the present invention.

[0059] The present invention aims to construct a reasonable calculation method, which can efficiently and accurately predict and estimate the size of the dense packing void ratio of three-graded coarse aggregate. Firstly, a three-graded coarse aggregate mixed database is established by indoor test, and then the influencing factors of the dense packing void ratio of coarse aggregate are quantitatively analyzed, that is, the influence of aggregate side wall effect, morphological characteristics, and gradation on the stacking void ratio is studied, and a regression model is obtained. The regression models of the three major factors are combined to obtain a prediction model, which can predict and estimate the dense packing void ratio.

[0060] The following three factors affect the size of the voids in the dense packing of coarse aggregates, namely, the morphological characteristics, gradation and side wall effect of coarse aggregates. Morphological characteristics refer to the appearance characteristics of aggregates, including two-dimensional and three-dimensional morphological characteristics, such as sphericity, roundness, angularity, etc. Aggregate gradation refers to the distribution of the proportion of particles of different sizes. The three-grade distribution refers to the distribution of aggregate particle sizes when three different particle sizes are mixed. Compared with the conditions of secondary and primary aggregates, the three-grade aggregate has more gradation distributions and higher description accuracy. The side wall effect refers to the hollow area produced by the contact between the container wall and the large aggregate particles, which affects the size of the stacking void ratio. The quality of the morphological characteristics directly affects the size of the stacking void ratio of coarse aggregates. The better the particle shape of the aggregate, the lower the stacking void ratio. The gradation composition also has a significant effect on the stacking void ratio. The stacking void ratio of aggregates with different gradation compositions is significantly different. The side wall effect has a significant effect when the ratio of aggregate particle size to container size is large.

[0061] Through the study of the above three factors, we can explore the influence of the above three factors on the porosity of coarse aggregate packing, and construct a mathematical model to accurately predict the porosity of coarse aggregate packing, which has a positive reference role in the actual engineering concrete mix design and the preparation of high-performance concrete.

[0062] See also Figure 1-5 The present invention provides a prediction model for the void ratio of three-graded densely packed coarse aggregate for concrete, which is constructed according to the following steps:

[0063] Step 1: Establish a database of coarse aggregate shape characteristic parameters and dense packing void ratio

[0064] Step 1: Establish a database of coarse aggregate shape characteristic parameters and dense packing void ratio

[0065] Select three types of coarse aggregates, select no less than 200 particles from each type of coarse aggregate, measure the morphological characteristics of the selected particles, obtain morphological characteristic parameters and their mean values, and obtain a database of coarse aggregate single-grade shape characteristic parameters; the morphological characteristic parameters include median length, sphericity, angularity, elongation and flattening; measure the close-packed void ratios of the three single-graded coarse aggregates, and obtain a database of coarse aggregate single-graded close-packed void ratios;

[0066] Mix the three coarse aggregates in any proportion x t ,y t 、z t Composed of no less than 50 groups of three-graded coarse aggregates, according to the mixing ratio of each group of three-graded coarse aggregates x t ,y t 、z tThe weighted average of the morphological characteristic parameters is calculated to obtain a database of the shape characteristic parameters of the three-graded coarse aggregate; t=1, 2, 3, ...; the close-packed void ratio of each group of three-graded coarse aggregate is measured to obtain a database of the close-packed void ratio of the three-graded coarse aggregate.

[0067] Among them, the sphericity, angularity, elongation and flatness of the above morphological characteristic parameters are calculated as follows:

[0068]

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

[0070] Where AN is the angular angle, SP is the sphericity, FR is the flattening rate, and ER is 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, and θ is 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, in mm.

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

[0072] (1) The particle size ranges of the three coarse aggregates are 5-10mm, 10-20mm, and 16.5-31.5mm, respectively. 200 particles of each were taken for morphological characteristic parameter measurement. The morphological characteristics were measured using an AIMS instrument, and their long, medium, and short axes, sphericity, angularity, needle-like degree (elongation), and flake-like degree (flattening) were recorded. The mean values ​​of sphericity, angularity, elongation, and flattening were calculated (coarse aggregate single-grade shape characteristic parameter database); at the same time, the close-packed void ratios of the three single-graded coarse aggregates were measured.

[0073] (2) Three different coarse aggregates with different particle sizes are mixed under different proportions. The mixing conditions are consistent with the average variation, and all mixing conditions of the three coarse aggregates can be roughly described. Under different proportions, the close-packed void ratio of the three-graded coarse aggregate is measured according to the requirements of GB / T 14685-2022. 50 groups of measurement results are obtained.

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

[0075] The morphological characteristics of coarse aggregate mainly include shape, edges and corners, and surface texture, etc., 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 coarse aggregate three-grade distribution affected by morphological characteristics

[0077] The principal component analysis method was used to establish the coarse aggregate close-packed void ratio P affected by the 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 close-packed void ratio P of three single-graded coarse aggregates affected by morphological characteristics is obtained from the expression of s1 , P s2 , P s3 ;

[0079] Assume that the mixing ratio of the jth type of coarse aggregate is x, y, z, and P s1 , P s2 , P s3 Multiply by x, y, and z and sum to get the close-packed void ratio P of the three-grade coarse aggregate 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 close packing 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 closely packed with respect to sphericity, roundness, angularity, elongation and flatness 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 experimental results of et al. are the research results of the research group of some inventors in the present invention. The coarse aggregates used are the same or similar. They studied the quantitative formula for the stacking void ratio of single-graded coarse aggregates. The formula has been well verified in other aggregates under single-graded conditions, which can explain the effect of morphological characteristics on the stacking void ratio. Therefore, the present invention directly borrows the results in this document and does not repeat the specific process.

[0084] In this formula, the component element 0.377 of the close-packed porosity is a fixed factor (i.e., the influence of the edge wall effect and the graded mixing), and the latter part is the influence of the morphological characteristics on the close-packed porosity, so the present invention extracts the latter part for research and analysis. Since the roundness Rd and the angular angle AN are both two-dimensional influencing factors, and they have a large correlation with the angular angle AN and the sphericity SP, in order to facilitate and simplify data processing, the roundness Rd is equivalently replaced by the influence of the other four factors, and the equivalent replacement is performed in the form of a linear function, that is:

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

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

[0087] Subtract the fixed element 0.377 from the 50 groups of coarse aggregate three-graded close-packed void ratio data to obtain the corresponding 50 groups of P sj Data, 50 groups of coarse aggregate three-graded morphological characteristic data and the corresponding 50 groups of P sj Substituting the data into the above formula, using SPSS software for regression analysis, the regression analysis results are a = 0.14, b = 1.50, R 2 The final result is P sj The expression is:

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

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

[0090] It should be noted that only adding the undetermined parameter b cannot meet the fitting accuracy requirements, nor can it well explain the influence of morphological characteristics on the close-packed void ratio. However, using the form of a linear function, that is, adding two undetermined parameters a and b, can keep the fitting results accurate and well explain the influence of morphological characteristics on the packing void ratio. Although the present invention uses the data of the three-graded coarse aggregate for fitting, the obtained P sk The expression actually reflects the common characteristics of coarse aggregate (5-31.5mm) used in concrete. Under the condition of single gradation (5-31.5mm), P sk The influence of the value on the porosity of close packing and Li Changzhi [1] The obtained results are consistent, which can well illustrate the influence of morphological characteristics on the porosity of close-packed materials.

[0091] Therefore, the close packing void ratio P of coarse aggregate caused by its morphological characteristics under the three-graded mixing condition is s The prediction model for the coarse aggregate mixing ratio x, y, z is determined by the following formula:

[0092] P s = x·P s1 +y·P s2 +z·P s3

[0093] 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 is the close packing void ratio of three single-graded coarse aggregates affected by morphological characteristics. Substitute the morphological characteristic parameters of single-graded coarse aggregates into P sk It can be obtained from the fitting expression of ; x, y, z represent the mixing ratio of the three coarse aggregates.

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

[0095] References: Li Changzhi, Zhou Xinbin, Wei Shigong, et al. Study on the differences in morphological characteristics of coarse aggregate and its relationship with stacking void ratio [J / OL]. Materials Guide, 1-15[2024-07-15].

[0096] Step 3: Establish a prediction model for the void ratio of three-graded coarse aggregate in close packing affected by the side wall effect

[0097] 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-graded shape characteristic parameter database is used as the characteristic particle size of the coarse aggregate single-graded. The characteristic particle sizes of the three coarse aggregate single-graded configurations are divided by the diameter of the close-packed test container to obtain the particle size ratios of the three coarse aggregate single-graded configurations. Based on the principle that the close-packed void ratio of the coarse aggregate single-graded configuration is jointly affected by the morphological characteristics and the sidewall effect, the data in the coarse aggregate single-graded 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 in the form of a power function using regression analysis, and the functional relationship between the close-packed void ratio and the particle size ratio of single-graded coarse aggregates affected by the side wall effect was obtained.

[0098] The characteristic particle sizes of the three single-graded coarse aggregates are multiplied by the mixing ratios 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 single-graded coarse aggregate characteristic particle size in the functional relationship between the tight packing void ratio affected by the side wall effect and the particle size ratio of the single-graded coarse aggregates to obtain the tight packing 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.

[0099] The formula for predicting the porosity of densely packed structures affected by the side wall effect was constructed mainly by using the EDM discrete element software. Using the sphere packing model and fitting different formulas, it was found that the power function had a better fitting effect. b The expression of the theoretical model is:

[0100]

[0101] Where P b represents the close-packed void fraction caused by the edge-wall effect; d represents the characteristic particle size of coarse aggregate, expressed as the length of the aggregate center axis; B represents the size of the close-packed test container, and the test container refers to the test container specified in the specification for measuring the close-packed void fraction; a and b represent the unknown parameters of the model.

[0102] For the three-graded coarse aggregate, we have:

[0103]

[0104] Where d1, d2, and d3 are the characteristic particle sizes of the three coarse aggregates.

[0105] Specifically, five different forms of aggregate shapes (strip, disc, triangular pyramid, triangular prism, pentagonal prism) with the same size as the actual aggregate characteristic size were constructed in the EDM software to simulate the actual edge wall effect, and the power function model was used for fitting regression. The regression results of the measurement results are:

[0106]

[0107] In this formula, the first term is the stacking porosity affected by the edge wall effect, and the latter term 0.056 is the stacking porosity caused by the morphological characteristics of the simulated particles. Substituting the morphological characteristics of ordinary spheres into P s , the result is -0.078, the packing void ratio of the sphere in the infinite size model is The A value of the sphere is 0.476-(-0.078), that is, a=0.55, and the a value is determined to be 0.55.

[0108] The combined effect of edge wall effect and morphological characteristics is the main factor affecting the aggregate under single gradation conditions. The morphological characteristic parameter data of three single gradation coarse aggregates are found in the database, and the corresponding coarse aggregate particle size ratio is obtained. The close-packed void ratio and particle size ratio are input to P b In the theoretical model, regression analysis is performed, and the actual regression result of the edge effect can be obtained as follows:

[0109]

[0110] It can be found from the above formula that the actual measured regression result 0.114 is basically consistent with the edem result 0.116. In the present invention, a is taken as 0.55 and b is taken as 0.114.

[0111] Since the operation of EDM software is very cumbersome, it is very inconvenient to calculate the close-packed void ratio by simulating the edge wall effect of particles. The a value can be basically determined to be 0.55, so the b value can be inversely calculated based on the close-packed void ratio of single-graded coarse aggregate. In the case of single-graded coarse aggregate, the close-packed void ratio is affected by the edge wall effect and morphological characteristics, so:

[0112]

[0113] So we can get the calculation formula of b value:

[0114]

[0115] Where P represents the close-packed void ratio of single-graded coarse aggregate (obtained from the database), P sRepresents the size of the densely packed void fraction caused by the morphological characteristics (corresponding to P in step 2 s1 , P s2 , P s3 ); Represents the particle size ratio, where d is the characteristic particle size, represented by the median axis length of the particle.

[0116] The close-packed void ratios of the three single-graded coarse aggregates were measured respectively. According to the P obtained in step 2, s1 , P s2 , P s3 The b values ​​corresponding to the three coarse aggregates can be calculated using this formula, and the accurate b values ​​can be obtained by averaging the b values ​​of the three coarse aggregates.

[0117] The above is a study of the edge wall effect using the EDM software. It is just a research process, the purpose is to obtain the calculation formula of the edge wall effect. In actual application, P is not directly obtained through EDM. b (It is troublesome to operate edem every time), the result is It can more accurately reflect the influence of the edge-wall effect on the porosity of dense packing. In practical application, b can be calculated by the above formula first, and then P can be obtained. b This method is more convenient and easy to apply in practical engineering.

[0118] Step 4: Establish a prediction model for the void ratio of coarse aggregate with three-grade distribution affected by the gradation

[0119] The reduction in the stacking void ratio caused by the difference in particle size when two coarse aggregates are tightly packed is defined as the particle contact coefficient k. 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 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;

[0120] Replace x in step 1 t ,y t 、z t Substitute into P 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 Pb 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 in the undetermined prediction model, and the k value is substituted into P G P is obtained in the prediction model to be determined G Prediction model for coarse aggregate mix proportions x, y, z.

[0121] The influence of gradation on the morphological characteristics of coarse aggregate is more complex. When aggregates are in a natural accumulation state, they will contact with the adjacent aggregates one by one. 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, in which 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 any shape 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 the 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, the void area between the two particles will decrease. When a fourth particle is present, the newly generated void area will also decrease. However, for the same batch of equivalent spherical particles, their tightly packed void ratio is determined. Figure 4It is not difficult to find from (a) and (b) that the larger the difference in particle size between two particles in contact with each other, the smaller the void area. In actual engineering, even for coarse aggregates within a certain particle size range, the particle sizes of the particles are different, and the difference in particle size will bring about a change in the close-packed void ratio. Therefore, the present invention defines the reduction in the stacking void ratio caused by the difference in particle size when two coarse aggregates are closely packed as the particle contact coefficient k.

[0123] In fact, based on the above two-dimensional contact model, it is difficult to obtain an accurate value of the particle contact coefficient. The actual aggregate contact is not a circular contact, and there are other factors that affect it. The physical model only qualitatively explains why the larger the difference in aggregate particle size, the smaller the gap. The present invention establishes a mathematical model and obtains the particle contact coefficient through regression analysis.

[0124] The particle contact coefficient k defined can reflect the ability of aggregate particles to produce voids when in contact (the regression results in the following text show that the larger the difference in particle size between the two aggregate particles, the larger the contact coefficient, which is consistent with the results of this model). The main influencing factor of this coefficient is the ratio of the characteristic particle sizes of aggregates of different graded aggregates. s , the particle contact coefficient k when different types of coarse aggregate particles come into contact o , k s , k o All three situations are included.

[0125] There are 6 situations in total where the three sizes of coarse aggregates come into contact with each other, and the overall probability is:

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

[0127] Among them, x, y, z represent the proportion of small, medium and large aggregates respectively and z = 1-xy.

[0128] Each term in the above formula represents the probability of a situation occurring. For example, 2xy represents the probability of small aggregate and medium aggregate particles in three sizes of coarse aggregate contacting each other. The proportions of the six situations of contacting each other are six different probabilities. They can be calculated based on the mixing ratios x, y, and z of coarse aggregates of different particle sizes. By multiplying the probability of the occurrence of the above six situations by the corresponding particle contact coefficient and then summing them, we can get the close packing void ratio of the three-graded coarse aggregate affected by the grading, that is, P G The prediction model to be determined 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 packing void ratio of the three-graded coarse aggregate affected by the grading; x, y, z are the mixing proportions of the three coarse aggregates; k 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.

[0131] The stacking of multi-graded coarse aggregate is a filling and mixing effect, which will reduce the size of the stacking void ratio, P s +P b This is the formula for the void ratio of coarse aggregate calculated and fitted under single-gradation conditions. Under multi-gradation conditions, considering the mixed stacking of aggregates, we have:

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

[0133] Where, P is the close-packed void ratio of the three-graded coarse aggregate; P G It is the reduction of stacking void ratio caused by grading.

[0134] For the mixing ratio x of the three-graded coarse aggregate of 50 groups in step 1 t ,y t 、z t Substitute P s Prediction model, P b In the prediction model, P s Value and P b The value is calculated, and the close-packed void ratio of 50 groups of coarse aggregate three-grade distribution has been determined, that is, through P G =(P s +P b )-P to obtain the close packing void ratio P of 50 groups of coarse aggregate three-graded mixtures caused by mixing with the graded mixture G value.

[0135] According to the 50 sets of data in the coarse aggregate three-graded dense packing void ratio database constructed in step 1, the dense packing void ratio P corresponding to each mixing ratio is obtained. G SPSS software was used to analyze P G Value, mixing ratio x t,y t 、z t Regression analysis was performed, and the values ​​of the contact coefficients of each particle were obtained as shown in Table 1. The overall distribution of these three particle sizes of aggregate is relatively wide, which can better explain the gradation of coarse aggregate in different situations. These six coefficients are representative and can be better applied in engineering practice. Some regression data are shown in Table 2.

[0136] Table 1 Particle contact coefficients for six cases

[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 grading can be obtained. G for:

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

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

[0143] 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, the side wall effect, and the gradation, the P s , P b , P G Prediction model, establish the prediction model of coarse aggregate three-grade compact packing void ratio P about coarse aggregate mixing ratio x, y, z: P = Pb +P s -P G ; The established P prediction model is used to predict the close-packed void ratio of three-graded coarse aggregate;

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

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

[0146] Where, P is the close-packed void ratio of the three-graded coarse aggregate; P G It is the reduction of stacking void ratio caused by grading.

[0147] Replace P in steps 2 to 4 s Prediction model, P b Prediction model, P G Substituting the prediction model into the above formula, we can get:

[0148]

[0149] Where b represents the edge effect coefficient (P b The undetermined parameter of the regression model is generally 0.114. d1, d2, and d3 represent the characteristic particle sizes of the three graded aggregates, respectively. s It represents the close packing void ratio of the corresponding three-graded coarse aggregate caused by its morphological characteristics, k represents the contact coefficient, and B represents the diameter of the measuring container, which is generally specified as 294mm.

[0150] When the particle size ranges of the three coarse aggregates are 5-10mm, 10-20mm, and 16.5-31.5mm, respectively, the calculation formula for the bulk void ratio of this batch of aggregates, i.e., the prediction model for the compact void ratio of the three-graded coarse aggregates, is:

[0151]

[0152] The key to the present invention is to establish the database of step one. By measuring the aggregate morphological characteristics, the prediction model formula of the tight packing void ratio of the three-graded coarse aggregate can be constructed, and 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, 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 tests to obtain a morphological characteristic parameter database, a single-graded densely packed void ratio database, and an average characteristic particle size, which are substituted into the above corresponding steps, and finally the corresponding P prediction model is 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 convenient to obtain, there is no need for the measured data of the three-graded mixed coarse aggregate, so the prediction efficiency is relatively high.

[0154] Example 1:

[0155] The batch of three-graded coarse aggregates were randomly mixed according to a certain mixing ratio, and their dense packing void ratio was measured. The measurement 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 size of the void ratio of the tightly packed three-graded coarse aggregate, and the error is basically less than 1.5%.

[0159] Example 2:

[0160] In the concrete construction process of a certain project, coarse aggregate was used according to the empirical ratio to obtain a three-grade coarse aggregate, and the mixing ratio was 20% of coarse aggregate with a particle size of 5-10 mm, 50% of coarse aggregate with a particle size of 10-20 mm, and 30% of 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 ratio under different ratios. Table 5 shows part of the test report of Comparative Example 1.

[0161] Table 4 Comparative Examples and Examples

[0162]

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

[0164]

[0165]

[0166] Comparative Examples 1-4 in Table 4 above are from actual projects. Comparative Example 1 is the empirical data of the proportion of the three-graded coarse aggregate of the project described in Example 2. Example 1 is the point that satisfies the minimum void ratio of the tightly packed triangle under continuous grading. It is obvious that this ratio is better than the actual empirical selection.

[0167] Input the above x=0.2, y=0.5, z=0.3 into the prediction model formula of close-packed void fraction prediction P, measure the close-packed void fraction according to the specification requirements, B=294mm, and get the predicted value of P:

[0168]

[0169] The actual measured result of the coarse aggregate compaction void ratio is 39.48%, with an error of The error is within the 5% allowable range. However, this mixing ratio is not the best solution. In order to obtain the best mixing ratio when the particle size ranges of the three coarse aggregates are 5-10mm, 10-20mm, and 16.5-31.5mm, the partial derivative of the formula is taken and the partial derivative is set equal to zero to obtain its minimum value.

[0170]

[0171] z=1-xy

[0172] By calculating the formula with origin software, we can know that the lowest void ratio is x=0.4, y=0.2, z=0.4, that is, small aggregate: medium aggregate: large aggregate=40:20:40. At this time, the coarse aggregate is tightly packed with the lowest void ratio, which is 38.6%, less than 39.48%. However, this gradation belongs to the discontinuous gradation interval. This discontinuous gradation concrete can help reduce the amount of cement, but it is easy to cause segregation and stratification. If continuous gradation is used, according to the formula, when small aggregate: medium aggregate: large aggregate=30:30:40, the coarse aggregate is in continuous gradation and the tightly packed void ratio is 38.8%, which is slightly different from the measured value and is also less than 39.48%. This ratio can be used for the coarse aggregate ratio in the actual construction process.

[0173] The above description is only used to illustrate the technical solution of the present invention and is not intended to limit it. Any modification or replacement of the technical solution made by other technicians in this professional field should be included in the scope of the claims of the present invention as long as it does not deviate from the connotation of the technical solution of the present invention.

Claims

1. A prediction model for 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 Select three types of coarse aggregates, select no less than 200 particles from each type of coarse aggregate, measure the morphological characteristics of the selected particles, obtain morphological characteristic parameters and their mean values, and obtain a database of coarse aggregate single-grade shape characteristic parameters; The morphological characteristic parameters include median length, sphericity, angularity, elongation and flattening rate; the close-packed void ratios of three single-graded coarse aggregates are 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 Composed of no less than 50 groups of three-graded coarse aggregates, according to the mixing ratio of each group of three-graded coarse aggregates x t ,y t 、z t Calculate the weighted average of its morphological characteristic parameters to obtain a database of shape characteristic parameters of three-graded coarse aggregate; t=1, 2, 3, ...; measure the close-packed void ratio of each group of three-graded coarse aggregate to obtain a database of close-packed void ratio of three-graded coarse aggregate; Step 2: Establish a prediction model for the void ratio of coarse aggregate three-grade distribution affected by morphological characteristics The principal component analysis method was used to establish the coarse aggregate close-packed void ratio P affected by the 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 close-packed void ratio P of three single-graded coarse aggregates affected by morphological characteristics is obtained from the expression of s1 , P s2 , P s3 ; Assume that the mixing ratio of the jth type of coarse aggregate is x, y, z, and P s1 , P s2 , P s3 Multiply by x, y, and z and sum to get the close-packed void ratio P of the three-grade coarse aggregate 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 three-graded coarse aggregate in close packing 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-graded shape characteristic parameter database is used as the characteristic particle size of the coarse aggregate single-graded. The characteristic particle sizes of the three coarse aggregate single-graded configurations are divided by the diameter of the close-packed test container to obtain the particle size ratios of the three coarse aggregate single-graded configurations. Based on the principle that the close-packed void ratio of the coarse aggregate single-graded configuration is jointly affected by the morphological characteristics and the sidewall effect, the data in the coarse aggregate single-graded 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 in the form of a power function using regression analysis, and the functional relationship between the close-packed void ratio and the particle size ratio of single-graded coarse aggregates affected by the side wall effect was obtained. The characteristic particle sizes of the three single-graded coarse aggregates are multiplied by the mixing ratios 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 single-graded coarse aggregate characteristic particle size in the functional relationship between the tight packing void ratio affected by the side wall effect and the particle size ratio of the single-graded coarse aggregates to obtain the tight packing 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 void ratio of coarse aggregate with three-grade distribution affected by the gradation The reduction in the stacking void ratio caused by the difference in particle size when two coarse aggregates are tightly packed is defined as the particle contact coefficient k. 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 the above six situations are obtained according to the coarse aggregate mixing ratio 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; Replace x in step 1 t ,y t 、z t Substitute into P 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 in the undetermined prediction model, and the k value is substituted into P G P is obtained in the prediction model to be determined 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, the side wall effect, and the 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-grade compact packing void ratio P about coarse aggregate mixing ratio x, y, z: P = P b +P s -P G .

2. The prediction model according to claim 1, characterized in that: In step 1, the angularity, sphericity, flattening rate and elongation in the morphological characteristic parameters are calculated as follows: FR S / d I ;ER=d I / d L Where AN represents the edge angle, SP represents the sphericity, FR represents the flatness, 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, characterized in that: 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 single-graded coarse aggregate affected by morphological characteristics, j = 1, 2, 3; AN represents the angular angle, SP represents the sphericity, FR represents the flattening rate, and ER represents the elongation.

4. The prediction model according to claim 1, characterized in that: 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 mixing 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, characterized in that: 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, characterized in that: In step 3, the close-packed void ratio P of the coarse aggregate three-grade distribution affected by the side wall effect b The prediction model for the coarse aggregate mixing 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, d3 are the characteristic particle sizes of the three coarse aggregates; b is the fitting parameter.

7. The prediction model according to claim 1, characterized in that: In step 4, the three-graded coarse aggregate is affected by the grading and the close-packed void ratio P G The prediction model to be determined 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 packing void ratio of the three-graded coarse aggregate affected by the grading; 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, characterized in that: 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 single-graded coarse aggregates affected by their 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.

Images