Compressible stacking model correction method for gravel concrete binary aggregate

Abstract

The invention relates to concrete, and provides a compressible accumulation model correction method for gravel concrete binary aggregate, which comprises the following steps: acquiring accumulation test data; dividing the binary aggregate into a first class and a second class according to the compactness ratio, and obtaining corrected compaction indexes of the first class and the second class of the binary aggregate through error analysis; adopting a nonlinear regression method to obtain a fitting expression of a correction loosening effect coefficient and a correction wall effect coefficient; and then substituting into the original compressible stacking model to obtain a corrected compressible stacking model. According to the method, the compactness ratio is taken as a discrimination condition, the corrected compressible stacking model suitable for the first type and the second type of gravel concrete binary aggregate is provided, and the limitation that an original compressible stacking model is not high in applicability to the gravel concrete binary aggregate, not high in prediction precision and the like is overcome.

Description

Technical Field

[0001] The present invention relates to the technical field of crushed stone concrete, and in particular, to a method for correcting a compressible packing model for binary aggregates of crushed stone concrete. Background Art

[0002] Concrete, as a composite material, mainly consists of two parts: aggregates and paste. Among them, the aggregates account for 50%-70% of the total volume of concrete. As the main component and load-bearing structure of concrete, a reasonable aggregate gradation can not only significantly improve the mechanical properties and durability of concrete, but also improve the fluidity of concrete by reducing the number of voids between aggregates. The density of the aggregate system refers to the actual volume occupied by the mixed aggregate system per unit volume measured after mixing multiple aggregates into a certain container and applying certain compaction conditions, filling the container and leveling the surface. The sum of it and the void ratio is 1. The maximization of the density of the aggregate system means the minimization of the amount of paste used to fill the voids of the aggregates, so that more paste can be used to lubricate and wrap the aggregates under a fixed aggregate-paste ratio. Therefore, the calculation and prediction of density are of great significance in the design of concrete mix ratios.

[0003] The most primitive compressible packing model (CPM) was first proposed by F.D. Larrard et al. On the basis of the traditional two-parameter model that only considers the looseness effect coefficient and the wall effect coefficient, a key parameter, the compaction index, was introduced, thus overcoming the problem of a large error in the density-fine particle volume fraction curve of the original two-parameter model at the highest point. However, the formulas for the looseness effect coefficient and the wall effect coefficient in the original CPM model were proposed based on a very limited number of crushed stone concrete binary aggregate packing test groups (7 groups), and the accuracy of the fitted formulas for the looseness effect coefficient and the wall effect coefficient themselves is not high. Therefore, the model itself has certain limitations. Due to the advantages of crushed stone aggregates such as wider sources, higher hardness, and better combination with cement-based materials, most of the common concretes on the market currently use crushed stone as the large-size aggregate. For this reason, the inventor verified the crushed stone concrete binary aggregate packing test data obtained by other scholars and found that the original CPM model has a large calculation error and low applicability for the crushed stone concrete binary aggregate particle system. Moreover, the above errors cannot be improved by the method of only correcting the looseness effect coefficient and the wall effect coefficient in the past experience, and additional correction parameters are needed to make the corrected CPM model meet the prediction requirements of the density of the crushed stone concrete binary aggregate system. Based on the above defects, the present invention proposes a method for correcting a compressible packing model for binary aggregates of crushed stone concrete. Summary of the Invention

[0004] The present invention provides a method for correcting the compressible packing model for binary aggregates of crushed stone concrete. By correcting the interaction coefficient and compaction index, it solves the problem of large errors in predicting the density of the binary aggregate particle system of crushed stone concrete using the original CPM model.

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

[0006] A method for correcting the compressible packing model for binary aggregates of crushed stone concrete includes the following steps:

[0007] S1. Obtain packing test data:

[0008] Obtain the data of p groups of packing tests of binary aggregates of crushed stone concrete. Each group of packing tests includes l p packing tests at different fine particle volume fractions. The data includes the average particle size d1 of the crushed stone aggregate and the measured density α1, the average particle size d2 of the fine aggregate and the measured density α2, and the measured density Φ0 of the binary aggregate.

[0009] S2. Correct the compaction index K:

[0010] S21. Respectively determine the value ranges of the loosening effect coefficient a 12 , wall effect coefficient b 12 , and compaction index K in the original compressible packing model. Corresponding m a 12 values, n b 12 values, and t K values are selected from the obtained value ranges;

[0011] S22. For each group of packing tests and for each K value, obtain the minimum average error between Φ0 and the predicted density Φ Substitute the data of l p different packing tests into the original compressible packing model respectively, and perform traversal calculations according to m a 12 values and n b 12 values to obtain l p ×m×n Φ values. Calculate the absolute error of the Φ value relative to the Φ0 value to obtain l p ×m×n absolute errors Δ, and obtain l 12 error contour maps of Δ varying with a 12 and b p . Then average Δ according to l p packing tests to obtain the average error contour maps of the average error varying with a 12 and b 12 . Extract the minimum value from the average error contour maps as the minimum average error

[0012] S23, for each set of stacking tests, obtain the initial correction range of K: plot the minimum average error The curve changes with K value, from the minimum average error The minimum average error is extracted from by As the upper limit of error, select from the obtained curve no more than The K value range is used as the preliminary correction range of K; 1.05≤η≤1.25;

[0013] S24, obtaining a final correction range of K: classifying binary aggregates satisfying the condition α2 / α1≥1.05 into the first category, classifying binary aggregates not satisfying the condition into the second category, taking the intersection of the obtained preliminary correction range of K according to the first category or the second category, respectively, to obtain a final correction range of K of the first category or the second category binary aggregate;

[0014] S3, get the corrected loose effect coefficient a1′2 and the corrected wall effect coefficient b1′2:

[0015] For each set of stacking tests, the minimum average error obtained by S23 Reverse deduction The error contour map where the The value corresponding to a 12 Value, b 12 value, and the resulting a 12 Value, b 12 Values are classified as either first or second type binary aggregates;

[0016] According to d1 and d2 obtained in S1, the particle size ratio d2 / d1 of each group of stacking tests is calculated. 12 Value, b 12 The values of d2 / d1 and d2 / d1 are obtained by fitting the nonlinear regression method according to the first or second type of binary aggregates, respectively, to obtain the expression of a1′2 about d2 / d1 and the expression of b1′2 about d2 / d1;

[0017] S4, the modified compressible stacking model is obtained:

[0018] For the first type of binary aggregate, select a modified compaction index from the final correction range of K obtained by S2, and substitute it and the expressions of a1′2 and b1′2 obtained by S3 about d2 / d1 into the original compressible stacking model to obtain the modified compressible stacking model of the first type of binary aggregate; in the same way, obtain the modified compressible stacking model of the second type of binary aggregate; combine the two to obtain the modified compressible stacking model of binary aggregate of crushed stone concrete.

[0019] It should be noted that in S1, the original compressible packing model is expressed by Equations (1.1) to (1.3) as follows:

[0020]

[0021] In the equations: K is the compaction index of the binary aggregate; Ф is the predicted densification of the binary aggregate; K i is the compaction index of the i-th aggregate particle; β i is the virtual residual densification of the i-th aggregate particle; y i is the volume fraction of the i-th aggregate particle; γ i is the virtual densification of the i-th aggregate particle; i = 1, 2, where 1 represents crushed stone aggregate and 2 represents fine aggregate (usually sand); a 12 is the loosening effect coefficient; b 12 is the wall effect coefficient; n is the total number of aggregate types. For binary aggregates, n = 2;

[0022] Among them, a 12 and b 12 are obtained according to Equations (1.4) and (1.5) respectively:

[0023] a 12 = [1 - (1 - d2 / d1) 1.02 0.5 (1.4)

[0024] b 12 = 1 - (1 - d2 / d1) 1.50 (1.5)

[0025] In the equations: d2 is the average particle size (or characteristic diameter) of the fine aggregate particles; d1 is the average particle size (or characteristic diameter) of the crushed stone aggregate particles; the average particle size is taken as the arithmetic mean of the upper and lower endpoints of the particle size range of each type of particle;

[0026] Among them, β i is obtained according to Equation (1.6):

[0027]

[0028] In the equations: α i is the measured densification of the i-th aggregate particle; K i is the compaction index of the i-th aggregate particle; when the compaction condition is dumping, K i = 4.1; when the compaction condition is vibration, K i = 4.75; when the compaction condition is vibration + compaction, K i = 9.

[0029] It should be noted that in S1, p ≥ 15, preferably p ≥ 30; l p ​≥8, preferably l p ≥10.

[0030] It should be noted that in S2, m≥20, preferably m≥40; n≥20, preferably n≥40; t≥6, preferably t≥10.

[0031] It should be noted that in S2, from the range of values of the loosening effect coefficient a 12 , the wall effect coefficient b 12 , and the compaction index K, m values of a 12 , n values of b 12 , and t values of K are uniformly selected.

[0032] It should be noted that in S2, the absolute error Δ and the average error are calculated according to equations (2.1) and (2.2):

[0033] Δ = |Φ - Φ0| (2.1)

[0034]

[0035] It should be noted that in S3, using the non - linear regression method, the expressions of a1′2 with respect to d2 / d1 and b1′2 with respect to d2 / d1 are established using the Logistics function according to equations (3.1) and (3.2):

[0036]

[0037] Where: a1′2 and b1′2 are the modified loosening effect coefficient and the modified wall effect coefficient respectively; A a , B a , C a , A b , B b , C b are the undetermined parameters of the Logistics function.

[0038] It should be noted that in S4, the modified compressible packing model of the gravel - concrete binary aggregate is expressed by equations (4.1) to (4.8) as:

[0039]

[0040] Where: K′ is the modified compaction index of the binary aggregate; Ф is the predicted density of the binary aggregate; K i ′ is the modified compaction index of the i - th aggregate particle; β i ′ is the modified virtual residual density of the i - th aggregate particle; y iis the volume fraction of the i-th type of aggregate particle; i = 1, 2, where 1 represents coarse aggregate particles and 2 represents fine aggregate particles; y1 and y2 are the volume fractions of coarse and fine aggregate particles respectively; a1′2 is the modified loosening effect coefficient; b1′2 is the modified wall effect coefficient; n is the total number of aggregate types, and for binary aggregates, n = 2;

[0041] For the first type of binary aggregate, a1′2 and b1′2 are obtained according to equations (4.4) and (4.5) respectively:

[0042]

[0043] In the formula: d2 is the average particle size of fine aggregate particles, and d1 is the average particle size of crushed stone aggregate particles; A a3 , B a3 , C a3 and A b3 , B b3 , C b3 are the fitting parameters of the modified loosening effect coefficient a1′2 and the modified wall effect coefficient b1′2 for the first type of binary aggregate respectively;

[0044] For the second type of binary aggregate, a 12 , b 12 are obtained according to equations (4.6) and (4.7) respectively:

[0045]

[0046] In the formula: d2 is the average particle size of fine aggregate particles, and d1 is the average particle size of crushed stone aggregate particles; A a4 , B a4 , C a4 and A b4 , B b4 , C b4 are the fitting parameters of the modified loosening effect coefficient a1′2 and the modified wall effect coefficient b1′2 for the second type of binary aggregate respectively;

[0047] Among them, β i ′ is obtained according to equation (4.8):

[0048]

[0049] In the formula: α i is the measured compactness of the i-th type of aggregate; K i ′ is the modified compaction index of the i-th type of aggregate particle; when it is the first type of binary aggregate, K i ′ takes any value within the final modified range [k3, l3]; when it is the second type of binary aggregate, K i′ is taken as any value within the final correction range [k4, l4]; k3, l3 and k4, l4 are the upper and lower endpoint values of the interval of the final correction range of the compaction index K of the first type and the second type of binary aggregate respectively.

[0050] It should be noted that for the first type of binary aggregate, a1′2 and b1′2 are obtained according to formulas (4.9) and (4.10) respectively:

[0051]

[0052] For the second type of binary aggregate, a1′2 and b1′2 are obtained according to formulas (4.11) and (4.12) respectively:

[0053]

[0054] When it is the first type of binary aggregate, K i ′ is taken as 4.66; when it is the second type of binary aggregate, K i ′ is taken as 2.33.

[0055] It should be noted that the error contour map is replaced by an error surface map.

[0056] Compared with the prior art, the present invention has the following beneficial technical effects:

[0057] By introducing the discrimination condition of the density ratio α2 / α1≥1.05, the present invention proposes a modified CPM model suitable for the first type and the second type of gravel concrete binary aggregate, including the determination rule of the modified compaction index K and the modified loosening effect coefficient a 12 and the wall effect coefficient b 12 general calculation formula, which overcomes the limitations of the existing CPM model such as poor applicability to gravel concrete binary aggregate, low accuracy of the interaction coefficient formula, and independence of the compaction index from the compaction conditions. As an experimental prediction formula, the modified CPM model can greatly reduce the experimental workload, has a wide application range, high prediction accuracy, avoids the blindness in the operation of the existing model, and has good operability and practicability for predicting the density and porosity of the gravel concrete binary aggregate system. Brief Description of the Drawings

[0058] Figure 1 It is a scatter plot of the prediction error of the original CPM model.

[0059] Figure 2 It is an error contour cloud map of the absolute error and the average error varying with the values of a 12 , b 12 value.

[0060] Figure 3 It is a curve graph of the minimum average error varying with the compaction index K value.

[0061] Figure 4 The error contour cloud diagram of the average error varying with the values of a 12 , b 12 under different K values; where Fig. (a) shows K = 3 and Fig. (b) shows K = 6.

[0062] Figure 5 is the fitting curve of the correction loosening effect coefficient a 12 of the first type of binary aggregate.

[0063] Figure 6 is the fitting curve of the correction loosening effect coefficient a 12 of the second type of binary aggregate.

[0064] Figure 7 is the fitting curve of the binary aggregate wall effect coefficient b 12 of crushed stone concrete, and the first type and the second type of binary aggregates are fitted into the same curve.

[0065] Figure 8 is the scatter diagram of the prediction error of the corrected CPM model.

[0066] Figure 9 is the scatter diagram of the prediction error of the corrected CPM model for the Kechkar packing test data. Specific implementation manners

[0067] Next, the technical solutions in the embodiments of the present invention will be clearly and completely described in conjunction with the accompanying drawings in the embodiments of the present invention; obviously, the described embodiments are only a part of the embodiments of the present invention, rather than all the embodiments; based on the embodiments of the present invention, all other embodiments obtained by those of ordinary skill in the art without creative efforts shall fall within the protection scope of the present invention.

[0068] Embodiment 1;

[0069] First, the original CPM model of binary aggregate is given in this embodiment, which is expressed by formulas (1.1) - (1.3) as:

[0070]

[0071]

[0072] In the formulas: K is the compaction index of binary aggregate; Ф is the predicted density of binary aggregate; K i is the compaction index of the i-th type of aggregate particle; β i is the virtual residual density of the i-th type of aggregate particle; y i is the volume fraction of the i-th type of aggregate particle; γ iis the virtual compactness of the i-th type of aggregate particle; i = 1, 2, where 1 represents crushed stone aggregate and 2 represents fine aggregate (usually sand); a 12 is the loosening effect coefficient; b 12 is the wall effect coefficient; n is the total number of aggregate types. For binary aggregates, n = 2;

[0073] Among them, a 12 and b 12 are obtained according to formulas (1.4) and (1.5) respectively:

[0074] a 12 = [1 - (1 - d2 / d1) 1.02 0.5 (1.4)

[0075] b 12 = 1 - (1 - d2 / d1) 1.50 (1.5)

[0076] In the formula: d2 is the average particle size (or characteristic diameter) of the fine aggregate particles; d1 is the average particle size (or characteristic diameter) of the crushed stone aggregate particles; the average particle size is taken as the arithmetic mean of the upper and lower endpoints of each type of particle size interval;

[0077] Among them, β i is obtained according to formula (1.6):

[0078]

[0079] In the formula: α i is the measured compactness of the i-th type of aggregate particle; K i is the compaction index of the i-th type of aggregate particle; when the compaction condition is dumping, K i = 4.1; when the compaction condition is vibration, K i = 4.75; when the compaction condition is vibration + compaction, K i = 9.

[0080] It should be noted that, without special instructions, such as the "2" in n = 2 is a numerical value. Except for specific numerical values, the present invention assigns symbolic meanings to "1" and "2". i = 1 or 2, where 1 represents crushed stone aggregate and 2 represents fine aggregate. a 12 and b 12 respectively represent the interaction coefficients of the binary aggregate obtained by mixing crushed stone aggregate (i = 1) and fine aggregate (i = 2), that is, the loosening effect coefficient and the wall effect coefficient.

[0081] To modify the original CPM model to be suitable for the binary aggregate of crushed stone concrete, the inventor statistically analyzed Gong [1] , Bala [2] , Kwan [3] ​, Larrard [4] , Moini [5] , Fennis [6] , Fung [7] , Moutasson [8] The binary coarse and fine particle packing test data in the research of eight scholars such as the above. The common point of the above data is that the coarse particles are all crushed stone aggregates, and the fine particles are coarse sand or river sand aggregates. There are a total of 36 groups of binary aggregate packing test data. Each group of binary aggregate packing tests contains several test points under different fine particle volume fractions y i and a total of 413 packing test data points. Subsequently, the original CPM model was used to calculate the predicted density Φ of the binary aggregate system. It was found that the error of the original CPM model exceeded 1.5% for 180 points (accounting for 43.6% of the total data points), exceeded 2.5% for 91 points (accounting for 22.0% of the total data points), and exceeded 100% for 31 points (accounting for 7.5% of the total data points). This is an unacceptable error for the prediction of the density Φ of the binary aggregate system (such as Figure 1 ). Of course, the packing test data can also be obtained by conducting the packing test of the binary aggregate of crushed stone concrete by oneself.

[0082] [1] Gong et al. Parameter modification and extension of the compressible packing model (CPM) for steel fiber-aggregate mixtures. Powder Technology, 2023, 422: 118479.

[0083] [2] Bala et al. Parameter determination of the Compressible Packing Model (CPM) for concrete application. Powder Technology, 2020, 367: 56 - 66.

[0084] [3] Kwan et al. A 3-parameter packing density model for angular rock aggregate particles. Powder Technology, 2015, 274: 154 - 162.

[0085] [4] Larrard et al. Concrete mixture proportioning: a scientific approach. CRC press, 1999.

[0086] [5] Moini et al. Modeling and experimental evaluation of aggregate packing for effective application in concrete. Journal of Materials in Civil Engineering, 2019, 31(3): 04019001.

[0087] [6] Fennis. Design of ecological concrete by particle packing optimization. 2011. Delft, Netherlands: Technische Universiteit.

[0088] [7] Fung et al. Effect of particle interlock on flow of aggregate through opening. Powder Technology, 2014, 253: 198 - 206.

[0089] [8] Moutasson. Assessment of Packing Density Models and Optimizing Concrete Mixtures. International Journal of Civil, Mechanical and Energy Science, 2016, 2(4): 29 - 36.

[0090] Based on this, the inventor intends to correct the loosening effect coefficient a 12 and the wall effect coefficient b 12 in the original CPM model. However, during the correction process, it is found that the prediction error of the original CPM model cannot be improved by the method of only correcting the loosening effect coefficient and the wall effect coefficient in the past experience, and additional correction parameters are needed to reduce the prediction error. Therefore, the inventor proposes to correct the loosening effect coefficient a 12 and the wall effect coefficient b 12Systematically correct the compaction index K. The main method of correction is to perform traversal calculations of the above coefficients in the numerical calculation software MATLAB to select the optimal coefficient values.

[0091] Therefore, this embodiment provides a method for correcting the compressible packing model of binary aggregate of crushed stone concrete, which includes the following steps:

[0092] S1. Obtain packing test data.

[0093] Obtain the data of p groups of packing tests of binary aggregate of crushed stone concrete. Each group of packing tests includes l p packing tests under different fine particle volume fractions. The data includes the average particle size d1 of the crushed stone aggregate and the measured compactness α1, the average particle size d2 of the fine aggregate and the measured compactness α2, and the measured compactness Φ0 of the binary aggregate.

[0094] All the required packing test data can be obtained from the research of the above eight scholars. There are a total of 36 groups of binary aggregate packing test data and a total of 413 packing test data.

[0095] S2. Correct the compaction index K.

[0096] S21. Respectively determine the value ranges of the loosening effect coefficient a 12 , the wall effect coefficient b 12 , and the compaction index K in the original compressible packing model. Corresponding to select m a 12 values, n b 12 values, and t K values from the obtained value ranges.

[0097] For the loosening effect coefficient a 12 and the wall effect coefficient b 12 , their values can only vary within the range of [0, 1]. Therefore, in order to obtain higher accuracy in this embodiment, these two coefficients are set to start from 0 and increase by a gradient of 0.02 to 1, with a total of 51×51 calculations; that is, m = 51 and n = 51;

[0098] For the compaction index K, its value can vary within the range of (0, +∞), but according to the research of Larrard [4] and Bala [2] and others, it is found that the K value basically varies within the range of (0, 10]. Therefore, the compaction index is set to start from 1 and increase by a gradient of 1 to 10, with a total of 10 calculations, that is, t = 10;

[0099] S22. For each group of packing tests and for each K value, obtain the minimum average error between Φ0 and the predicted compactness Φ For l pData from different compaction tests are respectively substituted into the original compressible compaction model, and traversal calculations are performed according to m a 12 values and n b 12 values to obtain l p ×m×n Φ values. Calculate the absolute error of the Φ value relative to the Φ0 value to obtain l p ×m×n absolute errors Δ, and obtain l 12 error contour maps showing the variation of Δ with a 12 and b p . Then, average Δ over l p compaction tests to obtain the average error error contour maps showing the variation of the average error 12 with a 12 and b . Extract the minimum value from the average error

[0100] error contour maps as the minimum average error i Specifically, considering that each group of binary coarse and fine aggregate compaction tests contains l p test points at different fine particle volume fractions y 12 and wall effect coefficient b 12 after traversal calculations of the loosening effect coefficient a p ×51×51 calculated densification degrees will be obtained; the calculated densification degree is also the predicted densification degree Φ value;

[0101] By subtracting the 51×51 calculated densification degrees of each test from the measured binary aggregate densification degree Φ0 of the corresponding test and taking the absolute value, 51×51 densification absolute errors Δ can be obtained. According to the obtained data, an error contour map showing the variation of the absolute error Δ with a 12 and b 12 can be drawn; then for the l p test points in each group of compaction tests, a total of l p ×51×51 densification absolute errors Δ will be obtained, and thus an error contour map showing the variation of the absolute error Δ with a 12 and b 12 can be drawn; p In addition to drawing error contour maps, a three-dimensional surface map showing the variation of the absolute error Δ with a

[0102] and b 12 can also be drawn, or other error analysis diagrams that can obtain the minimum error value; the following steps are the same, so they will not be elaborated. 12 Meanwhile, since each group of binary coarse and fine aggregate systems has l

[0103] p ​The same loosening effect coefficient a should be shared for the tests 12 and the wall effect coefficient b 12 , so the l p groups of 51×51 absolute errors Δ can be superposed correspondingly according to the same a 12 and b 12 , and averaged according to l p compaction tests, so as to finally obtain a group of 51×51 average errors with a 12 and b 12 as variables in the binary fine and coarse aggregate system. For each compaction test, an error contour map of the average error changing with a , b 12 , b 12 can be drawn at each K value. As shown in Figure 2 , Figure 2 , the right figure in [1] is the error contour map of the average error of the first compaction test group by Gong Figure 2 et al. at K = 4.1, and the left figures are the error contour maps when the volume fraction of fine aggregate y2 = 0.1, 0.3, 0.5, 0.7 and 0.9 respectively. According to Figure 2 , the minimum value can be extracted from using the min function in the numerical calculation software MATLAB as the minimum average error , and at the same time, the corresponding optimal a 12 and b 12 values can also be obtained.

[0104] Through the calculation in step S22, the minimum average error for each compaction test at each K value and the corresponding a , b 12 , b 12 values can be obtained. Next, the variation law of with the K value will be explored.

[0105] S23. For each compaction test, obtain the preliminary correction range of K: draw the curve of the minimum average error changing with the K value, extract the minimum value from the minimum average error as the minimum average error . Using as the error upper limit, select the K value range not exceeding from the obtained curve as the preliminary correction range of K; 1.05 ≤ η ≤ 1.25.

[0106] For each compaction test, traverse and calculate according to t = 10 K values, and a total of 10 groups of average errors of compactness changing with a12 and b 12 A changing error contour map. The minimum average error is extracted by the min function in the numerical calculation software and the minimum average error is thus established The relationship curve between the minimum average error and the compaction index K. As Figure 3 , Figure 3 is for Moini [5] and others' first group of stacking tests of the minimum average error The relationship curve between the minimum average error and the compaction index K. Obviously, there is a lowest point of the minimum average error i.e., the minimum average error According to the optimal K value point can be preliminarily determined, but if only this K value point is used as the correction value, it will lead to a lower adaptability of the obtained corrected CPM model to the prediction of the binary aggregate density in other groups of stacking tests.

[0107] That is, the method of selecting such a single point will cause other K values with a similarly small minimum average error to be ignored, thus severely restricting the K value correction process. Therefore, in the above correction process, the K value range with a minimum average error less than a certain limit is finally adopted. This limit represents the acceptable error deviation. In this embodiment, the minimum average error times the minimum average error is used as the limit regulation, i.e., η = 1.20. Then, the K value range not exceeding can be selected from the obtained curve as the preliminary correction range of K. Considering that Figure 3 a range of K values is obtained, and when selecting a K value within this range, it is necessary to determine whether the K value will affect a 12 and b 12 's distribution, that is, whether different K values will result in different a 12 , b 12 . If so, there is a coupling relationship between the K value and a 12 , b 12 , and the K value cannot be simply selected using the K value range but must be selected using a single point method. Therefore, the inventor extracted the average error cloud maps at different K values. As Figure 4 , Figure 4 is the average error cloud map at different K values of Moini and others [5] 's second group of stacking tests, where Figure 4 (a) is for K = 3, Figure 4 (b) is for K = 6. Although Figure 4 only the average error cloud maps at two K values are provided, in fact, the cloud maps when K = 4 or 5 are basically the same. Thus, the inventor found that when the minimum average error When it is less than a certain limit, such as a very small average error times the minimum average error When this is the case, the value of K does not affect a 12 , b 12 's distribution, that is, it can be considered that a 12 , b 12 and K are independent of each other and do not affect each other. Therefore, the next step of the final correction process of the value of K can be carried out according to step S24.

[0108] S24, obtain the final correction range of K: Classify the binary aggregates that satisfy the condition α2 / α1≥1.05 into the first category, classify the binary aggregates that do not satisfy the said condition into the second category, and take the intersection of the obtained preliminary correction range of K for the first category or the second category respectively to obtain the final correction range of K for the binary aggregates of the first category or the second category.

[0109] According to the above correction and selection of the compaction index K, the preliminary correction range of K for each group of binary aggregate systems of each scholar can be obtained. For the convenience of display in this embodiment, the central K value corresponding to this preliminary correction range is directly selected and statistically shown in Tables 1a - 1b.

[0110] Table 1a Statistical table of the preliminary correction range of K and other parameters

[0111]

[0112]

[0113] Table 1b Statistical table of the preliminary correction range of K and other parameters

[0114]

[0115] According to the method for determining the value of K in the original CPM framework, the tests of Bala [2] and Larrard [4] adopted the compaction conditions of vibration + stirring, and the corresponding value of K should be taken as 9. However, after adopting the above correction means, it is found that there are several groups of optimized K values after correction that are much lower than 9; the compaction conditions of the remaining scholars are all dumping. According to the original method for specifying the compaction conditions, the value of K should be taken as 4.1. However, after correction, it is found that the new value of K has basically no correlation with the compaction conditions, but is mainly related to α2 / α1. α2 / α1 represents the inherent characteristic difference between the particles in the binary aggregate system. The inventor believes that although the energy corresponding to different compaction conditions acts on the aggregate system, it is not like that of scholar Larrard [4]The greater the imagined compaction energy, the higher the degree of compaction. The main effect of compaction energy is to make the particles (especially fine particles) move closer together, including overcoming the friction between particles and causing particle displacement. However, this particle movement is affected by the ratio α2 / α1 of the measured compaction degree (or initial compaction degree). The increase in compaction degree largely depends on the filling of voids by fine particles. Theoretically, only when the compaction degree of fine particles is greater than that of coarse particles to a certain extent (i.e., α2 / α1 > 1.05), can the increase in compaction energy really play a positive role. On the contrary, the filling of fine particles will not only not increase the overall compaction degree, but may even reduce the overall compaction degree. In this case, the K value should be taken as a smaller value.

[0116] In view of this, this embodiment also gives the calculated values of α2 / α1 in the binary aggregate stacking tests of each group in Table 1a - 1b. It can be found from Table 1a - 1b that the central K values can be roughly divided into two categories: high and low. The high K values fluctuate around approximately 4.66, and the low K values fluctuate around approximately 2.33. At the same time, through the statistics and classification of α2 / α1, it is found that when α2 / α1 ≥ 1.05, it corresponds to a high K value, and for the remaining conditions where α2 / α1 < 1.05, it corresponds to a low K value. Therefore, the present invention classifies the binary aggregates that satisfy the condition α2 / α1 ≥ 1.05 into the first category, and classifies the binary aggregates that do not satisfy the said condition, i.e., α2 / α1 < 1.05, into the second category. Then, according to the first - type or second - type binary aggregates, the preliminary correction ranges of the obtained K are classified. The first category is the high K value, and the second category is the low K value, and the intersections are taken respectively. Finally, the final correction range [k3, l3] of K corresponding to the first - type binary aggregates is [2.33, 2.33], and the final correction range [k4, l4] of K corresponding to the second - type binary aggregates is [4, 4.66]. Further, if according to the highest occurrence frequency of the central K value, when α2 / α1 < 1.05, the K value can all be selected as 2.33, and for the remaining conditions (α2 / α1 ≥ 1.05), the K value is selected as 4.66. Thus, the compaction index K value has been corrected.

[0117] S3. Obtain the corrected loosening effect coefficient a1′2 and the corrected wall effect coefficient b1′2:

[0118] For each group of stacking tests, according to the minimum average error obtained in S23 Back - calculate to obtain The error contour map where it is located, and extract from the obtained error contour map the value corresponding to a 12 value and the b 12 value, and classify the obtained a 12 value and b 12 value according to the first - type or second - type binary aggregates;

[0119] According to d1 and d2 obtained from S1, calculate the particle size ratio d2 / d1 for each group of compaction tests. According to the a 12 value and b 12 value and d2 / d1, respectively for the first type or the second type of binary aggregates, use the non-linear regression method to fit and obtain the expressions of a1′2 with respect to d2 / d1 and b1′2 with respect to d2 / d1.

[0120] Furthermore, carry out the correction work on the loosening effect coefficient a 12 and the wall effect coefficient b 12 . Based on the aforementioned method for correcting the K value, the corrected K value (which can also be expressed by the final correction range) and the corresponding optimal a 12 , b 12 values are given in Tables 2a - 2b. Table 2a is for the optimal a 12 , b 12 values of the first type of binary aggregates (α2 / α1≥1.05), and Table 2b is for the optimal a 12 , b 12 values of the second type of binary aggregates (α2 / α1<1.05). Among them, for each group of compaction tests, the selection of the optimal a 12 , b 12 values mainly uses the min function selection function of the numerical calculation software to determine the average error varying with a 12 , b 12 in the t error contour cloud diagrams, and the a , b 12 coordinates corresponding to the minimum average error 12 .

[0121] Table 2a Revised a 12 , b 12 , K and other parameter statistical tables

[0122]

[0123] Table 2b Revised a 12 , b 12 , K and other parameter statistical tables

[0124]

[0125] In this embodiment, using the non-linear regression method, the expressions of a1′2 with respect to d2 / d1 and b1′2 with respect to d2 / d1 are established by the Logistics function according to Equations (3.1) and (3.2):

[0126]

[0127] where: a1′2 and b1′2 are the modified loosening effect coefficient and the modified wall effect coefficient respectively; A a , B a , C a , A b , B b , C b are the undetermined parameters of the Logistics function.

[0128] Finally, the optimal a 12 , b 12 data of the stacking tests of each group of scholars are obtained as Figures 5 - 7 . For the first or second type of binary aggregate, the b 12 data has a similar variation law. Therefore, a 12 is respectively fitted using the Logistics function according to the first or second type of binary aggregate, while for b 12 , regardless of whether it is the first or second type, it is fitted using the same Logistics function. The final fitting results are as follows:

[0129] For the first type of binary aggregate, a1′2 and b1′2 are obtained according to equations (4.9) and (4.10) respectively:

[0130]

[0131] For the second type of binary aggregate, a1′2 and b1′2 are obtained according to equations (4.11) and (4.12) respectively:

[0132]

[0133] Therefore, the specific modified compressible packing model of the binary aggregate of crushed stone concrete can be expressed by equations (4.1) to (4.3) as:

[0134]

[0135]

[0136] where: K′ is the modified compaction index of the binary aggregate; Ф is the predicted density of the binary aggregate; K i ′ is the modified compaction index of the i-th aggregate particle; β i ′ is the virtual residual density of the i-th aggregate particle; y i is the volume fraction of the i-th aggregate particle; γ i ′ is the virtual density of the i-th aggregate particle; i = 1, 2, 1 represents the coarse aggregate particle, 2 represents the fine aggregate particle; a1′2 is the modified loosening effect coefficient; b1′2 is the modified wall effect coefficient; n is the total number of aggregate types. For binary aggregates, n = 2;

[0137] Among them, a1′2 and b1′2 are obtained according to formulas (4.9) to (4.12) respectively;

[0138] Among them, β i ′ is obtained according to formula (4.8):

[0139]

[0140] In the formula: when it is the first type of binary aggregate, K i ′ is taken as 4.66; when it is the second type of binary aggregate, K i ′ is taken as 2.33.

[0141] It should be noted that for the number of stacking test groups, it is recommended to take p≥15, preferably p≥30. The more the number of stacking test groups, the more reliable the fitting results of a1′2 and b1′2; in each group of stacking tests, the number of stacking tests is recommended to take l p ≥8, preferably l p ≥10; for the traversal values of a 12 and b 12 , it is recommended to take m≥20, n≥20, preferably m, n≥40. The more the cutting, the more accurate it is in determining the optimal a corresponding to the minimum average error 12 and b 12 data, but the calculation amount is larger; for the traversal values of the K value, it is recommended to take t≥6, preferably t≥10. The larger t is, the more accurate the preliminary correction range of K is, and its final correction range is also more accurate; from the value ranges of a 12 and b 12 and K, when selecting m a 12 values, n b 12 values and t K values, it is necessary to make the selected values cover the corresponding value ranges. For example, t K values need to be relatively evenly distributed in the value range of K. The most convenient way is to select them in the way of an arithmetic progression. The specific selection of the above parameters is a conventional technical means in the field, so it will not be elaborated here.

[0142] To verify the above-mentioned modified CPM model, the inventor calculated the prediction errors of the density of 413 stacking test data points again. The results are as Figure 8 shown. According to the calculation results and Figure 8 it can be known that only 57 stacking test data points have prediction errors exceeding 1.5% (accounting for 13.8% of the total data points), and only 20 stacking test data points have prediction errors exceeding 2% (accounting for 4.8% of the total data points). There are no stacking test data points with prediction errors exceeding 100%. Compared with the original CPM model, the prediction errors of the modified CPM model are significantly reduced, indicating that the modified CPM model has a good fitting effect.

[0143] In addition, the inventor also selected Kechkar [9] to conduct a generalization verification of the modified CPM model using the experimental data of the binary aggregate packing of crushed stone concrete (as shown in Figure 9 ). This batch of data includes 9 groups of binary aggregate packing tests, with each group corresponding to 11 different fine aggregate volume fractions, for a total of 99 packing test data points. The measured values, predicted values, and prediction errors of the compactness are shown in Tables 3 - 5.

[0144] [9] Kechkar. Contribution a l’étude des empilements granulaires. 2008, laboratoire de génie civil et d’hydraulique (LGCH), Université 08mai 45, Guelma, Algérie.

[0145] Table 3 Measured Compactness

[0146]

[0147] Table 4 Predicted Compactness

[0148]

[0149] Table 5 Compactness Prediction Error

[0150]

[0151] According to Figure 9 and Tables 3 - 5, there are a total of 50 packing test data points with a prediction exceeding 1.5%, accounting for 50.5% of the total data points. However, the prediction errors are all within 2%, indicating that the modified CPM model has good generalization ability and good versatility, and its prediction accuracy has been effectively improved.

Claims

1. A method for modifying the compressible packing model of binary aggregates for crushed stone concrete, characterized in that: The steps include: S1, obtain stacking test data: Obtain the data of p groups of binary aggregate packing tests of crushed stone concrete. Each group of packing tests includes packing tests at l p different fine particle volume fractions. The data includes the average particle size d1 and the measured compactness α1 of the crushed stone aggregate, the average particle size d2 and the measured compactness α2 of the fine aggregate, and the measured binary aggregate compactness Φ0; S2, modified compaction index K: S21. Determine the loosening effect coefficient a in the original compressible packing model respectively 12 , the wall effect coefficient b 12 , and the value range of the compaction index K. Corresponding m a 12 values, n b 12 values, and t K values are selected from the obtained value ranges; S22. For each set of compaction tests and for each K value, obtain the minimum average error between Φ0 and the predicted compaction degree Φ Substitute the data of l p different compaction tests into the original compressible compaction model respectively, and perform traversal calculations according to m a 12 values and n b 12 values to obtain l p ×m×n Φ values, calculate the absolute error of the Φ value relative to the Φ0 value, and obtain l p ×m×n absolute errors Δ, and obtain l 12 error contour maps showing the variation of Δ with a 12 and b p . Then average Δ according to l p compaction tests to obtain the average error contour maps showing the variation of the average error with a 12 and b 12 . Extract the minimum value from the average error contour map as the minimum average error S23. For each group of stacking tests, obtain the preliminary correction range of K: Plot the curve of the minimum average error changing with the K value, and extract the minimum value from the minimum average error as the minimum average error Taking as the error upper limit, select the range of K values not exceeding from the obtained curve as the preliminary correction range of K; 1.05 ≤ η ≤ 1.25; S24, obtaining a final correction range of K: classifying binary aggregates satisfying the condition α2 / α1≥1.05 into the first category, classifying binary aggregates not satisfying the condition into the second category, taking the intersection of the obtained preliminary correction range of K according to the first category or the second category, respectively, to obtain a final correction range of K of the first category or the second category binary aggregate; S3, get the corrected loose effect coefficient a1′2 and the corrected wall effect coefficient b1′2: For each set of stacking tests, the minimum average error obtained according to S23 is inversely deduced to obtain the error contour map where it is located, and extract from the obtained error contour map the a value corresponding to the 12 value, the b 12 value, and classify the obtained a 12 value and b 12 value according to the first or second type of binary aggregate; Based on d1 and d2 obtained from S1, calculate the particle size ratio d2 / d1 for each packing test. According to the a 12 value and b 12 value and d2 / d1, respectively for the first type or the second type of binary aggregates, use the non-linear regression method to fit and obtain the expressions of a1′2 with respect to d2 / d1 and the expression of b1′2 with respect to d2 / d1; S4, the modified compressible stacking model is obtained: For the first type of binary aggregate, select any modified compaction index from the final modified range of K obtained by S2, and substitute it and the expressions of a1′2 and b1′2 obtained by S3 about d2 / d1 into the original compressible stacking model to obtain the modified compressible stacking model of the first type of binary aggregate; in the same way, obtain the modified compressible stacking model of the second type of binary aggregate; combine the two to obtain the modified compressible stacking model of crushed stone concrete binary aggregate.

2. The method for correcting the compressible packing model for the binary aggregate of crushed stone concrete according to claim 1, characterized in that: In S1, p ≥ 15; l p ≥ 8.

3. The method for correcting the compressible packing model for the binary aggregate of crushed stone concrete according to claim 1, wherein: m≥20; n≥20; t≥6.

4. The method for correcting the compressible packing model for the binary aggregate of crushed stone concrete according to claim 1, wherein: From the loosening effect coefficient a 12 , the wall effect coefficient b 12 , and m a values, n b values, and t K values are uniformly selected from the value ranges of the compaction index K 12 respectively. 12 ​ 5. The method for correcting the compressible packing model for the binary aggregate of crushed stone concrete according to claim 1, characterized in that: In S2, the absolute error Δ and the average error are calculated according to Equations (2.1) and (2.2): Δ=|Φ-Φ0| (2.1) 6. The method for correcting the compressible packing model for binary aggregates of crushed stone concrete according to claim 1, characterized in that: In S3, using the nonlinear regression method, the expression of a1′2 with respect to d2 / d1 and the expression of b1′2 with respect to d2 / d1 are established using the Logistics function according to equations (3.1) and (3.2): Where: a1′2 and b1′2 are the modified loosening effect coefficient and the modified wall effect coefficient respectively; A a 、B a 、C a 、A b 、B b 、C b are the undetermined parameters of the Logistics function.

7. The method for correcting the compressible packing model for the binary aggregate of crushed stone concrete according to claim 1, wherein: In S4, the modified compressible stacking model of binary aggregate of crushed stone concrete is expressed according to equations (4.1) to (4.8): Where: K′ is the modified compaction index of the binary aggregate; Ф is the predicted density of the binary aggregate; K i ′ is the modified compaction index of the i-th aggregate particle; β i ′ is the modified virtual residual density of the i-th aggregate particle; γ i ′ is the modified virtual density of the i-th aggregate particle; i = 1, 2, where 1 represents the crushed stone aggregate particle and 2 represents the fine aggregate particle; y1 and y2 are the volume fractions of the crushed stone aggregate and the fine aggregate respectively; a1′2 is the modified loosening effect coefficient; b1′2 is the modified wall effect coefficient; n is the total number of aggregate types, for the binary aggregate, n = 2; For the first type of binary aggregate, a1′2 and b1′2 are obtained according to formula (4.4) and (4.5) respectively: Where: A a3 , B a3 , C a3 and A b3 , B b3 , C b3 are respectively the fitting parameters of the first type of binary aggregate modified loosening effect coefficient a1′2 and the modified wall effect coefficient b1′2; For the second type of binary aggregate, a 12 and b 12 are obtained according to Equations (4.6) and (4.7) respectively: Where: A a4 , B a4 , C a4 and A b4 , B b4 , C b4 are the fitting parameters of the modified loosening effect coefficient a1′2 and the modified wall effect coefficient b1′2 of the second type of binary aggregate, respectively; where β i ' is obtained according to Equation (4.8): Where: α i is the measured compactness of the i-th type of aggregate; when it is the first type of binary aggregate, K i ' is taken as any value within the final correction range [k3, l3]; when it is the second type of binary aggregate, K i ' is taken as any value within the final correction range [k4, l4].

8. The method for correcting the compressible packing model for binary aggregates of crushed stone concrete according to claim 7, characterized in that: For the first type of binary aggregate, a1′2 and b1′2 are obtained according to formula (4.9) and (4.10) respectively: For the second type of binary aggregate, a1′2 and b1′2 are obtained according to formula (4.11) and (4.12) respectively: When it is the first type of binary aggregate, K i ' takes 4.66; when it is the second type of binary aggregate, K i ' takes 2.

33.

9. The method for correcting the compressible packing model for the binary aggregate of crushed stone concrete according to any one of claims 1-8, characterized in that: The error contour map is replaced by an error surface map.

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