A design method for coarse aggregate ultra-high performance concrete based on close packing theory and concrete products

Abstract

The present invention relates to a design method and concrete product of coarse aggregate ultra-high performance concrete based on the close packing theory. The method comprises: optimizing the proportion of the cementitious core material combination system based on the Dinger-Funk model, simulating the gradation data of different proportions by computer software, and comparing the closeness of each gradation distribution to the theoretical most close packing distribution to determine the optimized cementitious material ratio; completing the gradation optimization for two mixed aggregates based on the Aim-Goff model, comparing the actual packing density under the simulated binary system of different mixed aggregates, and finding the optimal ratio; optimizing the distribution ratio of each group based on two theoretical models, and designing concrete with excellent mechanical properties such as density and compression resistance. The present invention not only provides a feasible method for finding the ratio of different raw material combinations to achieve the closest to the most close packing density, but also reduces the production cost of cementitious materials and ensures the performance of concrete products at the same time.

Description

Technical Field

[0001] The invention belongs to the field of building technology, and in particular relates to a coarse aggregate ultra-high performance concrete design method based on close packing theory and a concrete product. Background Art

[0002] Industrial waste residues such as fly ash and slag have been reported to be used as admixtures for cement-based cementitious materials to ensure the strength of concrete, improve its impermeability, and chemical corrosion resistance. This engineering technology of combining cement with industrial waste residues can not only recycle the waste residues, thereby solving the environmental pollution problems caused by their disorderly stacking, but also greatly reduce the amount of cement clinker, further reducing its preparation cost and energy consumption. The problem of powder accumulation involves various fields of various construction industries. In the cement industry, the particle packing density of the cementitious material combination system will affect the physical and chemical properties of the obtained concrete products; in addition, the different mixing ratios of fine aggregate and coarse aggregate bring about differences in the density and porosity of concrete, which in turn affects its mechanical strength and mechanical properties. Therefore, how to predict the packing density of concrete powder raw materials and obtain the maximum density through reasonable theoretical methods, so that the pores after optimizing the material ratio can be filled to the maximum extent is the key to obtaining high-quality concrete. Summary of the invention

[0003] To solve the above problems, the present invention provides a design method for ultra-high performance concrete with coarse aggregate based on the close packing theory. The mix ratio design of the core cementitious material ternary system and the mixed aggregate binary system are based on the relevant calculations of the Dinger-Funk model and the Aim-Goff model, respectively, to complete the design of the ultra-high performance concrete with coarse aggregate and obtain a concrete product with excellent performance.

[0004] The technical solution of the present invention is as follows: A design method of coarse aggregate ultra-high performance concrete based on close packing theory comprises the following steps:

[0005] Step 1: Simulation and proportion optimization of the dense packing state of the gel core material combination system based on the Dinger-Funk model;

[0006] Step 2: Based on the Aim-Goff model, complete the calculation of the compactness of the mixed aggregate and the grading optimization.

[0007] Step 1 includes the following process:

[0008] (1) Determine the particle size distribution and particle size range of each component of the gelling core material system;

[0009] (2) Determine the particle size distribution data of the raw materials obtained in process (1), including the maximum and minimum values; determine the distribution modulus q of the Dinger-Funk model according to the mix design target, and take a value between 0.2 and 0.5;

[0010] The q value reflects the fluidity of the cementitious material: the higher the q value, the lower the fluidity of the cementitious material; the higher the content of large-size particles, the larger the q, and the higher the content of small-size particles, the lower the q;

[0011] (3) Calculate the cumulative passing percentage under each set sieve hole according to the Dinger-Funk model:

[0012]

[0013] Where, P(D) is the particle content corresponding to a specific particle size, %; D is the particle size, μm; D max ——Maximum particle size, μm; D min ——minimum particle size, μm; q——distribution modulus, the ratio of large and small particles;

[0014] (4) based on the cumulative passing percentages at each sieve size under the dense packing state obtained in process (3), the standard particle size distribution of the gelled core material system under the dense packing state is plotted;

[0015] (5) The particle distribution at each level and the particle distribution in the tightly packed state are calculated using the programming software Matlab; the volume fractions of component X, component Y, and component Z are marked as x, y, and z, respectively, and the corresponding particle size distribution is recorded as M x , M y and M z ; Set the volume content range of silica fume and fly ash respectively, and the particle size distribution of the final cementitious core material is M D =x×M x +y×M y +z×M z ;

[0016] (6) Optimizing the material grading: Calculate the least squares error E value, evaluate the closeness or range between the distribution of the cementitious core material and the reference particle size distribution at each grading, and obtain a set of simulated volumetric dosages with the smallest error value, which is the optimized proportion closest to the most densely packed curve;

[0017]

[0018] In the formula, E is the least squares error; M1(i) is the element content corresponding to the actual particle size combination; M0(i) is the element content corresponding to the reference particle size combination; length(M0) is the length of the row vector M0. The smaller the E value, the closer the particle size of the cementitious core material system is to the reference filling state, and the tighter the particle size distribution.

[0019] Preferably, in step 1, component X is cement; component Y and component Z are two combinations of mineral powder, fly ash, silica fume, granulated blast furnace slag, limestone powder, steel slag powder, phosphorus slag powder, and zeolite powder; component Y and component Z used in the embodiment of the present invention are fly ash and silica fume.

[0020] Step 2 specifically includes the following processes:

[0021] (1) Determine the characteristic particle size parameters of fine aggregate and coarse aggregate in the mixed aggregate binary system, the characteristic particle size parameters include particle size, single material packing density and true density. Among them, the particle size distribution is determined by screening method; the packing density adopts the minimum water method, and the true density is determined by the historical density bottle;

[0022] (2) Based on the Aim-Goff model and the characteristic parameters described in process (1), the volume fraction at the maximum packing density of the mixed aggregate binary system is calculated:

[0023]

[0024] in, ——Volume fraction of the mixed aggregate binary system at the maximum packing density; d r ——average particle size of fine aggregate; d s ——average particle size of coarse aggregate; ε0——void ratio of single material;

[0025] (3) Based on Matlab programming software, according to the actual volume fraction of fine aggregate mixed r Volume fraction at maximum packing density The relative size of the actual packing density Φ in the binary gradation system of different mixed aggregates under the Aim-Goff model is calculated:

[0026] when When , the calculation formula is

[0027]

[0028] when When , the calculation formula is

[0029]

[0030] (4) Compare the actual packing density of each simulated mixed aggregate binary system to find the optimal grading ratio.

[0031] Preferably, the coarse aggregate in the mixed aggregate in step 2 is a construction type I crushed stone that has been washed, dried and continuously graded; and the fine aggregate is river sand with a fineness modulus in the medium sand range.

[0032] The present invention also provides a concrete product prepared by a coarse aggregate ultra-high performance concrete design method based on the close packing theory, which comprises, by weight, 500-2000 parts of core cementitious material, 500-2000 parts of mixed aggregate, 0-40 parts of concrete admixture, 100-250 parts of water, and 50-200 parts of steel fiber material. The concrete admixture is a polycarboxylate water reducer with a solid content of not less than 40%.

[0033] Preferably, the steel fiber material is a straight or special-shaped one with a diameter of 0.2-0.6 mm and an aspect ratio of 50-100.

[0034] Preferably, a mixing process of first dry and then wet is adopted to ensure uniform distribution of steel fibers and prevent steel fibers from agglomerating during mixing. The adding order is: the mixed aggregate is first added to the mixing machine and dry stirred for 1 to 2 minutes, and then the three components of the cementitious material are added and stirred for 1 to 2 minutes; then water and concrete admixtures are added and wet stirred for 2 to 3 minutes; finally, the steel fibers are added in 3 times while stirring, and the total stirring time is controlled within 10 minutes to form a uniform concrete product.

[0035] Beneficial Effects

[0036] The present invention adopts two different particle packing models to respectively optimize the gradation of each component of the ternary system of cementitious core material and the binary system of mixed aggregate, optimize the packing density of cementitious material and the blending ratio of mixed aggregate, thereby further reducing the void ratio of concrete system and ensuring the performance of concrete products.

[0037] The design method of the mix ratio of the ultra-high performance concrete mixed with coarse aggregates described in the present invention can clarify the mix ratio of different raw material compositions at the optimal stacking density.

[0038] The present invention does not limit the types of mineral admixtures used in the cementitious material components; mineral admixtures can replace part of the cement to recycle industrial waste and greatly reduce the amount of cement and economic costs; the mixing of coarse and fine aggregates also reduces the cost of concrete configuration. The coarse aggregate introduced in the present invention can fully exert its skeleton effect and reduce the additional cost caused by steam curing. BRIEF DESCRIPTION OF THE DRAWINGS

[0039] Figure 1The particle size distribution of each component of the cementitious material and the reference particle size distribution in the most densely packed state. DETAILED DESCRIPTION

[0040] The present invention is further described in detail below in conjunction with specific embodiments and drawings, but the embodiments do not limit the present invention in any form. Anything not described in detail in the present invention is based on conventional techniques in the art.

[0041] The cement used in the embodiment is P.45.5 ordinary Portland cement of Tower Brand, the residue of which is less than 5% at 80μm; the main components are CaO and SiO2; the fly ash is produced in Guizhou, the main component is CaO; the silica ash is produced in Gansu, the SiO2 content exceeds 90%. The specific parameter characteristics are shown in Table 1 and Table 2:

[0042] Table 1 Chemical composition of gelled core materials (wt%)

[0043] Material <![CDATA[SiO2]]> CaO <![CDATA[Fe2O3]]> MgO <![CDATA[SO3]]> <![CDATA[Al2O3]]> <![CDATA[K2O]]> <![CDATA[Na2O]]> <![CDATA[P2O3]]> Impurities cement 19.21 63.33 3.94 1.54 4.02 4.81 0.98 0.03 0.02 2.12 Fly ash 3.1 52.17 0.22 0.85 0.05 1.62 0.63 0.09 0.31 40.96 Silica Fume 91.13 1.47 1.05 2.35 0.68 0.93 0.8 0.14 0.16 1.29

[0044] Table 2 Parameters of cementitious core materials

[0045] Material Volume average diameter / μm <![CDATA[Density / g / cm 3 > cement 31.84 3.45 Silica Fume 1.56 2.20 Fly ash 22.03 2.89

[0046] The particle size distribution of each powder material was tested using a Mastersizer-3000 laser particle size analyzer produced by Malvern Company, UK. Anhydrous ethanol was selected as the dispersion medium during the test.

[0047] The river sand used in the embodiment is a continuously graded river sand that is washed and dried, and is a second-zone medium sand that meets the requirements of GB / 14684-2011 standard, purchased from Qingyuan River Sand Company; the crushed stone is 5-16 mm diabase, produced in Jiangxi. Its quality indicators are shown in Table 3 below, and its gradation distribution is tested by screening method, as shown in Table 4.

[0048] Table 3 Technical indicators of aggregate used in the examples

[0049]

[0050] Table 4 Aggregate gradation used in the examples

[0051]

[0052] The steel fiber used in the embodiment is a short straight steel fiber of copper-plated steel wire cut type, with a diameter of 0.2 mm, an aspect ratio of 70, and a strength of more than 2000 MPa;

[0053] The admixture used in the embodiment is polycarboxylate water reducer 530P, Chongqing Haiyu Chemical Products Co., Ltd.

[0054] Example 1

[0055] A design method for coarse aggregate ultra-high performance concrete based on close packing theory includes optimizing the proportion of a cementitious core material combination system based on a Dinger-Funk model. The cementitious core material used is 1000 parts by weight, including 110-910 parts of cement (10% to 90% by volume), 45-845 parts of silica fume (5% to 85% by volume), and 30-180 parts of fly ash (5% to 20% by volume).

[0056] (1) The particle size distribution and particle size range of the components of the cementitious core material system were tested by a laser particle size distribution analyzer for each raw material including cement, silica fume and fly ash, see Table 5.

[0057] (2) Determine the maximum and minimum particle size based on the raw material particle size distribution data obtained in process (1); and determine the distribution modulus q of the Dinger-Funk model based on the mix design target.

[0058] The higher the content of large-size particles, the greater q is; the higher the content of small-size particles, the lower q is. From Table 5, the particle size of the three raw material particles used in the present invention is below 60 μm, accounting for 80%, which contributes greatly to the strength of the cementitious material. max =120μm, D min =0.05μm, q=1 / 3.

[0059] Table 5 Particle size distribution of each cementitious material component

[0060]

[0061] (3) According to the Dinger-Funk model, the cumulative passing percentage of each set sieve hole under the maximum theoretical simulation density is calculated. The results are shown in Table 6:

[0062]

[0063] Where, P(D) is the particle content corresponding to a specific particle size, %; D is the particle size, μm; D max ——Maximum particle size, μm; D min ——minimum particle size, μm; q——distribution modulus, the ratio of large and small particles;

[0064] Table 6 Benchmark particle size distribution under the most densely packed condition

[0065]

[0066] (4) Based on the simulation results of the ideal state of uniform particle distribution obtained in process (3), the stacking distribution of each gelling raw material and the standard particle size distribution of the system under the most densely packed state are plotted, see Figure 1 .

[0067] (5) Matlab was used to calculate the particle distribution of each level and the particle distribution in the tightly packed state. Specifically, the volume fractions of cement, silica fume and fly ash are marked as x, y and z respectively, and the corresponding particle size distribution is recorded as M. x , M y and M z The volume content of silica fume is set to 0.05-0.30, the floating range of fly ash is 0.05-0.20, and the particle size distribution under the combined system is M D =x×M x +y×M y +z×M z , the calculation results are shown in Table 7.

[0068] (6) Optimize material grading: Calculate the least squares error E value. The results are shown in Table 7.

[0069]

[0070] Where, E is the least squares error; M1(i) is the element content corresponding to the actual particle size combination; M0(i) is the element content corresponding to the reference particle size combination; length(M0) is the length of the row vector M0.

[0071] Table 7 Particle distribution (particle size: μm) and E value of each raw material under different gradations

[0072]

[0073]

[0074] It can be seen from the model that the most compact packing state can only be achieved when the actual particle size distribution of the powder is infinitely close to the reference particle size distribution. In the actual packing process, due to mutual friction, different morphology and size, and different stirring degrees, the particles cannot fully play their filling role and achieve the ideal filling state. The E value is an evaluation index to measure the degree of closeness. The smaller the value, the higher the degree of closeness, and the greater the corresponding packing density.

[0075] From Table 7, the powder particle size is mainly concentrated in the micron range, the van der Waals force and friction force have a significant impact on the particles, the distribution between particles is uneven, and the filling is insufficient. Under the same silica fume content, the greater the volume content of fly ash, the greater the E value of the composite cementitious system; and under the same fly ash output, the greater the proportion of silica fume, the smaller the E value. Figure 1 As shown in Table 5, the particle size of silica fume is the smallest, followed by fly ash, and cement is the largest. When the particle size distribution of each component is quite different, the distribution is better after combination, that is, the fine silica fume particles can more easily fill the gaps between the coarse cement particles, making it easier to achieve a denser gradation.

[0076] Furthermore, the volume content of fly ash is fixed at 0.05, the range of silica fume is 0.20-0.75, and the floating range of cement particles is 0.75-0.20. The particle size distribution M under the combined system is calculated. D =x×M x +y×M y +z×M z , the calculation results are shown in Table 8.

[0077] Table 8 Particle distribution (particle size: μm) and E value of each raw material under different gradations

[0078]

[0079]

[0080] From Table 8, under the same fly ash proportion, with the increase of silica fume proportion, the E value of the core cementitious system shows a pattern of first decreasing and then increasing; especially when the silica fume proportion exceeds 40%, the E value increases significantly and the stacking degree decreases significantly; combined with actual production, silica fume is a granular material with high specific surface area and high water absorption. Excessive dosage will also cause the agglomeration of silica fume particles and reduce the effective water-cement ratio, which is not conducive to the strength and mechanical properties of cement. Therefore, there is an optimal value for the doping amount of silica fume. When the volume fractions of cement, silica fume and fly ash are 0.70, 0.25 and 0.05 respectively, there is a minimum E value of 0.251, which is the ratio closest to the most compact stacking curve under the combination system of the three.

[0081] Example 2-Example 7

[0082] The concrete product obtained by the coarse aggregate ultra-high performance concrete design method based on the Dinger-Funk theory described in Example 1 is prepared as follows:

[0083] A. Weigh 150 parts of steel fiber material, 10 parts of concrete admixture, 150 parts of water, 1400 parts of mixed aggregate and 1000 parts of core cementitious material by weight, accurate to g;

[0084] The volume ratio of crushed stone and river sand used in the mixed aggregate is fixed at 0.8:0.2, while the cement, silica fume and fly ash are in different proportions, and the specific contents are shown in Table 9.

[0085] B. Add the mixed aggregate into the mixer and stir dry for 1 to 2 minutes, then add the three components of cementitious materials and continue stirring for 1 to 2 minutes; then add water and concrete admixtures and continue wet stirring for 2 to 3 minutes; finally, add the steel fiber in 3 times while stirring, and control the total stirring time within 10 minutes to form a uniform concrete product.

[0086] Concrete compressive strength performance test: According to GB / T 50081 "Standard for Test Methods of Physical and Mechanical Properties of Concrete", the test block method was used to make a cubic specimen with a side length of 10 cm, and the curing time was set to 7 days, 24 days and 28 days. The pressure measuring instrument is the YA-2000 electro-hydraulic pressure testing machine.

[0087] The concrete curing room is an intelligent automatic temperature and humidity control device; the curing methods are divided into steam curing (90℃±3℃, relative humidity above 90%) and standard curing (20℃±2℃, relative humidity above 95%). The compressive strength data of the test are shown in Table 10.

[0088] Table 9 Design mix ratio of cementitious core material system (volume ratio)

[0089] Serial number cement / % Silica fume / % Fly ash / % E Example 2 90 5 5 1.232 Example 3 80 10 10 0.857 Example 4 75 5 20 1.276 Example 5 70 25 5 0.251 Example 6 55 40 5 0.822 Example 7 50 45 5 1.207

[0090] Table 10 Compressive strength of concrete with different cementitious core material compositions

[0091]

[0092] From Example 2 and Example 3, the compressive strength of concrete decreases to a certain extent when the proportion of silica ash and fly ash increases by the same amount; from Example 2 and Example 4, when the silica ash content is very small, the increase in the proportion of fly ash has a small impact on the system stacking degree; from Example 4 and Example 5, when the cement content is similar, the increase in the silica ash content causes the compressive strength of the concrete product to increase and the degree of change is higher than that of fly ash; from Example 6 and Example 7, the silica ash ratio continues to increase, but the stacking density decreases accordingly, accompanied by a decrease in compressive strength. The minimum error value E in the model corresponding to Example 5 is the lowest, and the corresponding compressive strength is also the largest, which is consistent with the theoretical simulation results.

[0093] Example 8

[0094] A design method for coarse aggregate ultra-high performance concrete based on close packing theory includes optimizing the gradation of two components of aggregate based on the Aim-Goff model. The mixed aggregate used is 1400 parts by weight, including 105-735 parts of river sand (volume ratio is 10% to 60%) and 665-1295 parts of crushed stone (volume ratio is 40%-90%).

[0095] (1) Determine the characteristic particle size parameters of river sand and crushed stone mixed aggregates. The specific data are presented in Tables 3 and 4;

[0096] (2) Based on the Aim-Goff model and the characteristic parameters described in process (1), the volume fraction of the river sand and gravel binary system at the maximum packing density is calculated:

[0097]

[0098] in, ——The maximum packing density of river sand fine aggregate; d r ——average particle size of river sand fine aggregate; d s ——average particle size of crushed stone coarse aggregate; ε0——void ratio of single material;

[0099] In the present invention, small-sized river sand is added to large-sized crushed stone particles, the porosity of a single crushed stone particle is 0.40, and the volume fraction under the maximum packing density of the mixture is calculated as

[0100]

[0101] The actual packing density of river sand and crushed stone binary systems with different gradations under the Aim-Goff model was calculated using Matlab programming software. The Aim-Goff model is a compact packing equation for admixtures from the perspective of the particle size distribution and the packing density of the mixture system. The amount of river sand added was set to increase from 0.10 to 0.60, while the volume fraction of crushed stone decreased from 0.90 to 0.40 accordingly. The volume fraction of crushed stone coarse aggregate under different mixing conditions was compared with the volume fraction of 0.17 at the maximum packing density calculated in process (2), and the packing density of the actual coarse aggregate binary system was calculated.

[0102] when When , the calculation formula is

[0103]

[0104] when When , the calculation formula is

[0105]

[0106] The calculation results are shown in Table 11.

[0107] Table 11 Packing density of binary aggregate mixture system

[0108]

[0109]

[0110] The actual packing density of each simulated mixed aggregate binary system was compared to find the optimal grading ratio. As shown in Table 11, when the volume mixing amount of crushed stone and river sand is 0.8 and 0.2 respectively, the maximum packing density is 0.717 when the weight is 1183 parts and 217 parts respectively.

[0111] Example 9-Example 14

[0112] The concrete product prepared by the coarse aggregate ultra-high performance concrete design method based on the Aim-Goff model theory described in Example 8 is prepared in the same manner as in Example 2 to Example 7, except that the volume ratio of cement, silica fume, and fly ash in the core cementitious material is fixed at 0.70:0.25:0.05, and the mixed aggregate is crushed stone and river sand in different proportions. The volume ratio of the mixed aggregate is shown in Table 12; the compressive strength of the corresponding concrete is tested, and the data is shown in Table 13.

[0113] Table 12 Designed mix ratio of mixed aggregate system (volume ratio)

[0114] Serial number gravel / % River sand / % Packing density Example 9 90 10 0.667 Example 10 80 20 0.717 Embodiment 11 70 30 0.700 Example 12 60 40 0.684 Example 13 50 50 0.668 Embodiment 14 40 60 0.653

[0115] Table 13 Compressive strength of concrete under different aggregate compositions

[0116]

[0117]

[0118] From Example 9 to Example 14, the volume mixing amounts of crushed stone and river sand at the maximum density calculated by the Aim-Goff model are 0.8 and 0.2, respectively, and by weight, they are 1183 parts and 217 parts, respectively. The prepared concrete has the best compressive strength performance in terms of early age and 28d strength.

[0119] The above embodiments are preferred implementation modes of the present invention, but the implementation modes of the present invention are not limited to the above embodiments. Any other changes, modifications, substitutions, combinations, and simplifications that do not deviate from the spirit and principles of the present invention should be equivalent replacement methods and are included in the protection scope of the present invention.

Claims

1. A design method for coarse aggregate ultra-high performance concrete based on close packing theory, characterized in that , including the following steps: Step 1: Simulation and proportion optimization of the dense packing state of the gel core material combination system based on the Dinger-Funk model; Step 2: Calculate the compactness of mixed aggregates and optimize grading based on the Aim-Goff model; The step 1 includes the following process: (1) Determine the particle size distribution and particle size range of each component of the gelling core material system; (2) Determine the particle size distribution data of the raw materials obtained in process (1), including the maximum and minimum values; determine the distribution modulus q of the Dinger-Funk model according to the mix design target, and q is between 0.2 and 0.5; (3) According to the Dinger-Funk model, refer to formula ① to calculate the cumulative passing percentage under each set sieve hole: Where, P(D) is the particle content corresponding to a specific particle size, %; D is the particle size, μm; D max ——Maximum particle size, μm; D min ——minimum particle size, μm; q——distribution modulus, the ratio of large and small particles; (4) based on the cumulative passing percentage of each sieve size under the dense packing state obtained in process (3), the standard particle size distribution of the gel core material system under the dense packing state is plotted; (5) The particle distribution at each level and the particle distribution in the tightly packed state are calculated using the programming software Matlab; the volume fractions of component X, component Y, and component Z are marked as x, y, and z, respectively, and the corresponding particle size distribution is recorded as M x , M y and M z ; Set the volume content range of component Y and component Z respectively, and the particle size distribution of the final gel core material is M D =x×M x +y×M y +z×M z ; (6) Optimize the material grading: Calculate the least squares error E value according to formula ②, evaluate the closeness or range between the particle size distribution of the cementitious core material and the reference particle size distribution at each grade, and obtain a set of simulated volumetric dosages with the smallest error value, which is the optimized proportion closest to the most densely packed curve; In the formula, E is the least squares error; M is D (i)——element content corresponding to the actual particle size combination; M0(i)——element content corresponding to the reference particle size combination; length(M0)——length of row vector M0; Step 2 The process includes: (1) determining characteristic particle size parameters of fine aggregate and coarse aggregate in a mixed aggregate binary system, wherein the characteristic particle size parameters include particle size, packing density of a single material, and true density; (2) Based on the Aim-Goff model and the characteristic parameters described in process (1), the volume fraction at the maximum packing density of the mixed aggregate binary system is calculated according to formula ④: in, ——Volume fraction of the mixed aggregate binary system at the maximum packing density; d r ——average particle size of fine aggregate; d s ——average particle size of coarse aggregate; ε0——void ratio of single material; (3) Based on Matlab programming software, according to the actual volume fraction of fine aggregate R mixed r Volume fraction at maximum packing density The relative size of the aggregates is calculated by using formulas ⑤ and ⑥ respectively to calculate the actual packing density Φ in the binary gradation system of different mixed aggregates under the Aim-Goff model: when When , the calculation formula is when When , the calculation formula is (4) Compare the actual packing density of each simulated mixed aggregate binary system to find the optimal grading ratio.

2. The method for designing coarse aggregate ultra-high performance concrete based on close packing theory according to claim 1, characterized in that: In step 1, component X is cement; component Y and component Z are two combinations of mineral powder, fly ash, silica fume, granulated blast furnace slag, limestone powder, steel slag powder, phosphorus slag powder, and zeolite powder.

3. The method for designing coarse aggregate ultra-high performance concrete based on close packing theory according to claim 1, characterized in that: The coarse aggregate in the mixed aggregate of step 2 is construction type I crushed stone that has been washed, dried and continuously graded; the fine aggregate is river sand with a fineness modulus in the range of medium sand.

4. The concrete product prepared by the design method of coarse aggregate ultra-high performance concrete based on close packing theory according to any one of claims 1 to 3, characterized in that: By weight, it includes 500-2000 parts of core cementitious material, 500-2000 parts of mixed aggregate, 50-200 parts of steel fiber material, and 1-40 parts of concrete admixture; 100-250 parts of water; the concrete admixture is a polycarboxylate water-reducing agent with a solid content of not less than 40%.

5. The concrete product according to claim 4, characterized in that The steel fiber material is a straight or special-shaped one with a diameter of 0.2-0.6 mm and an aspect ratio of 50-100.

6. The concrete product according to claim 4, characterized in that The mixing process of first dry and then wet is adopted to ensure the uniform distribution of steel fibers and prevent the steel fibers from agglomerating during mixing. The order of adding is: the mixed aggregate is first added to the mixing machine and dry stirred for 1 to 2 minutes, and then the three cementitious material components are added and stirred for 1 to 2 minutes; then water and concrete admixtures are added and wet stirred for 2 to 3 minutes; finally, the steel fibers are added in 3 times while stirring, and the total mixing time is controlled within 10 minutes to form a uniform concrete product.

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