Self-compacting concrete mix proportion design method based on coarse aggregate close packing

Abstract

The invention relates to self-compacting concrete, and discloses a design method of a self-compacting concrete mix proportion based on coarse aggregate close packing, which simulates a coarse aggregate single-layer close packing phenomenon in a self-leveling state of the self-compacting concrete according to a spherical particle plane triangular packing mode. A prediction model of the volume fraction of the coarse aggregate about the average particle size and the slump expansion degree of the coarse aggregate is established, the volume fraction of the coarse aggregate is predicted according to the prediction model, and then the mix proportion design of the self-compacting concrete is guided. Compared with the prior art, the coarse aggregate volume fraction prediction model and the mix proportion design method are provided on the basis of coarse aggregate close packing, the mixing amount of the coarse aggregate is increased, the performance of the self-compacting concrete is good, the use amount of each component can be given more accurately and scientifically, the economical efficiency is improved, and the method has engineering application value.

Description

Technical Field

[0001] The present invention belongs to the technical field of self-compacting concrete, and mainly relates to a design method for the mix proportion of self-compacting concrete based on the dense packing of coarse aggregates. Background Art

[0002] The main difference between self-compacting concrete (SCC) and ordinary Portland concrete (OPC) is its excellent workability, that is, it has high fluidity, passing ability and segregation resistance. When pouring, it can be evenly and densely formed only by its own weight without vibration, and after hardening, it has good mechanical properties, volume stability and durability. Since its appearance, SCC has received much attention and has become an important development direction of modern concrete technology. [1] .

[0003] In order to enable SCC to move from theory to practical engineering applications, the mix proportion design method of SCC has received the attention of scholars, and many scholars have carried out research on this. Jin Nanguo [2] According to the simple calculation method of the specific surface area of aggregates, a new mix proportion design method of SCC based on aggregate information was proposed. NEPOMUCENO [3] Divided SCC into two phases of mortar and coarse aggregates, and proposed a mix proportion design method of SCC that meets strength and workability. Li, PF [4] Based on the rheological threshold theory of the paste, an improved mix proportion design method of ternary powder self-compacting concrete was proposed based on the packing characteristics of materials. Gao, SP [5] Adopted the orthogonal test design and range analysis method to propose the best mix proportion design method of self-compacting concrete with recycled aggregates.

[0004] However, the above-mentioned SCC mix proportion design methods are partially applicable to SCC under specific conditions, and the amount of cementitious materials in the concrete is large, the amount of mortar is large, and the amount of coarse aggregates is small, resulting in a high cost of SCC, which limits its application range, and does not consider the distribution and packing of aggregate gradation in the self-leveling state of self-compacting concrete, nor the best arrangement of coarse aggregates in SCC. When SCC reaches the self-leveling state under its own weight, if the coarse aggregates are closely arranged and packed, the amount of coarse aggregates is the largest and the amount of mortar is the smallest, which can improve the stability and economy of SCC.

[0005] The "Technical Specification for Application of Self-Compacting Concrete (JGJ / T 283-2012)" in China gives the mix design method for SCC. However, this method is mainly based on experience, providing the workability range of SCC and the corresponding range of raw material dosages, but without specific corresponding formulas. Generally, the larger the slump flow of self-compacting concrete, the smaller the aggregate particle size. The corresponding relationship between the two is not mentioned in the standard method, and the situation where the designed work performance value cannot be achieved may occur in actual operation.

[0006] Based on the dense packing of aggregates, this invention establishes the corresponding relationship between the slump flow of SCC and the average particle size of aggregates under the condition of dense packing of coarse aggregates, making the mix design more accurate on the premise of ensuring the full use of coarse aggregates, and playing a positive role in the development and application of SCC technology.

[0007] References: [1] Long Guangcheng, Xie Youjun. Self-Compacting Concrete [M]. Beijing: Science Press, 2013: p 1-10. [2] Gong Lingli, Jin Nanguo, He Xiaoyong, etc. A New Mix Design Method for Self-Compacting Concrete Based on Aggregate Information [J]. Journal of Zhejiang University (Engineering Science), 2010, 44(4): 826-830. [3] Nepomuceno M C S, Pereira-de-Oliveira L A, Lopes S M R. Methodology for the mix design of self-compacting concrete using different mineral additions in binary blends of powders [J]. Construction and Building Materials, 2014, 64(14): 82-94. [4] Li, PF, Ran, J, Nie, D, Zhang, W. Improvement of mix design method based on paste rheological threshold theory for self-compacting concrete using different mineral additions in ternary blends of powders [J]. Construction and Building Materials, 2021, 276: 122194. [5]Gao, SP, Liu, Q, Han, FX, Fu, Y. Mix Design of Recycled Coarse Aggregate Self-Compacting Concrete Based on Orthogonal Test and Analysis of Mercury Intrusion Porosimetry. Advances In Materials Science And Engineering, 2021, 2021:4829673。 Summary of the Invention

[0008] To address the deficiencies in the prior art, the present invention explores the relationship between the slump flow of SCC and the average particle size of coarse aggregate, and proposes a mix proportion design method for SCC based on the dense packing of coarse aggregate. Using this method, the mix proportion design can be made more accurate while ensuring the workability of SCC, increasing the dosage of coarse aggregate, and improving economy.

[0009] To achieve the above object, the present invention adopts the following technical solutions.

[0010] The present invention provides a mix proportion design method for self-compacting concrete based on the dense packing of coarse aggregate, comprising the following steps: (1) Establish a prediction model for the volume fraction of coarse aggregate with respect to the average particle size of coarse aggregate and the slump flow ; Measure the thickness of the mortar layer on the surface of coarse aggregate particles in self-compacting concrete through the self-compacting concrete slump flow test to obtain a series of data on the thickness of the mortar layer and use regression analysis to fit an empirical formula for the thickness of the mortar layer with respect to the average particle size of coarse aggregate as shown in Equation (1): (1) In the formula, is the average thickness of the mortar layer between coarse aggregates, in mm; is the average particle size of coarse aggregate particles, in mm; is the thickness coefficient of the mortar layer relative to coarse aggregate particles, k and it is recommended to take 0.125; Use the equivalent particle size method to equivalent coarse aggregate particles into spherical particles, and equivalent the mortar layer adhered to the surface of coarse aggregate particles into a spherical shell outside the spherical particles to obtain the volume of each coarse aggregate particle , the cross-sectional area and the cross-sectional area of the mortar layer attached to its surface; the single-layer close packing phenomenon of coarse aggregates in the self-leveling state of self-compacting concrete is simulated by using the plane triangular packing mode of spherical particles, and the area of each void between coarse aggregate particles is obtained ; according to the principle that the self-leveling slump flow area of self-compacting concrete is equal to the total area of coarse aggregates, mortar and voids, the number of circles of coarse aggregates within the slump flow area is obtained and the number of voids , according to the cross-sectional area of each coarse aggregate particle, the cross-sectional area of the mortar layer attached to its surface, and , , the number of coarse aggregate particles is obtained ; according to the volume and the number of coarse aggregate particles, the total volume of coarse aggregates is obtained. The total volume of coarse aggregates is divided by the total volume of self-compacting concrete to obtain the volume fraction of coarse aggregates as shown in Equation (2): (2) In the formula, is the volume fraction of coarse aggregates, L / m 3 ; is the number of coarse aggregate particles, pieces; is the average volume of coarse aggregate particles, m 3 , ; is the total volume of self-compacting concrete, m 3 , and for the slump flow test bucket, it is taken as 0.055 m 3 ; Among them, is obtained according to Equation (3): (3) In the formula, is the slump flow, mm; is the number of voids between coarse aggregates during close packing, pieces; is the area of each void, mm 2 ; is the sum of the cross-sectional areas of coarse aggregate particles and the mortar layer; Substituting Equations (1) and (3) into Equation (2), the volume fraction of coarse aggregates with respect to the average particle size of coarse aggregates and the slump flow The prediction model is as shown in Equation (4): (4) In the formula: is the volume fraction of coarse aggregates, L / m 3 ; is the slump flow, in mm; is the average particle size, in mm; is a constant, and it is recommended to take 69.43; (2) Obtain the average particle size of coarse aggregate by sieving method , and select the slump flow design value according to the performance requirements of self-compacting concrete and the average particle size of coarse aggregate . Substitute the , design values into the prediction model in Equation (4) to obtain the volume fraction of coarse aggregate ; (3) According to the performance requirements of self-compacting concrete and , obtain the volume fraction of fine aggregate , water-binder ratio, and the dosage of admixture relative to the binder. Obtain the dosage of binder and the water consumption according to the water-binder ratio; obtain the initial mix proportion; (4) Proportion and test the performance of self-compacting concrete according to the initial mix proportion. Adjust the sand ratio and the dosage of admixture while keeping the water-binder ratio unchanged according to the test results until the designed mix proportion of self-compacting concrete that meets the performance requirements is obtained.

[0011] It should be noted that the area of each void and the number of voids between coarse aggregates are obtained according to Equations (5) and (6): (5) (6) In the formula, is the number of circles of coarse aggregates within the slump flow area of self-compacting concrete, .

[0012] It should be noted that according to the performance requirements of self-compacting concrete and the average particle size of coarse aggregate , the slump flow design value is selected as follows: For continuously graded coarse aggregate particles, the selection range of the slump flow design value is 570 - 720 mm; When the average particle size of coarse aggregate is small, select a slightly larger slump flow design value. When the average particle size of coarse aggregate is large, select a slightly smaller slump flow design value.

[0013] It should be noted that the volume fraction of fine aggregate Obtained according to formula (7): (7) Wherein, is the volume fraction of fine aggregate, L / m 3 ; is the density of coarse aggregate, kg / m 3 ; is the density of fine aggregate, kg / m 3 ; is the sand ratio, %.

[0014] It should be noted that the dosage of cementitious materials , water consumption are obtained according to formulas (8) to (10) respectively: (8) (9) (10) Wherein, ρ c , ρ m , ρ w are the apparent densities of cement, mineral admixture, and mixing water respectively; , are the dosages of cement and mineral admixture respectively; is the air content of self-compacting concrete, that is, the volume of gas in the concrete, generally taken as 2%; β is the mass fraction of mineral admixture in the cementitious materials of self-compacting concrete; is the water-binder ratio; Water-binder ratio is obtained according to formula (11): (11) Wherein, is the measured compressive strength of cement at 28 days, MPa; is the dosage of cementitious materials per cubic meter of self-compacting concrete, kg; is the water consumption per cubic meter of self-compacting concrete, kg ；f cu,0 is the compressive strength of concrete at 28 days, MPa; γ is the equivalent cementitious coefficient of mineral admixture. For limestone powder, fly ash, slag powder, and silica fume, it can be taken as 0.2, 0.4, 0.9, and 2.5 respectively; Among them, is obtained according to the following formula: (12) Wherein, is the standard value of cube compressive strength, MPa; is the standard deviation of strength.

[0015] It should be noted that for the self-compacting concrete admixture, a high-range water reducer is selected. The water reduction rate of the high-range water reducer is not less than 20%; the dosage of the high-range water reducer is not less than 0.6% and not more than 2%.

[0016] Based on the main component of self-compacting concrete, coarse aggregate, through the research on the contact model of coarse aggregates in the densely packed state, according to the plane triangular packing mode of spherical particles, the relationship between the volume dosage of coarse aggregates, the average particle size of coarse aggregates, and the slump flow in concrete under the condition of dense packing is established to guide the mix design of self-compacting concrete. Under the constructed dense packing model, the smaller the average particle size of the coarse aggregate, the higher the slump flow. Therefore, in the mix design, for coarse aggregates with different particle sizes, an appropriate slump flow should be selected within the required range of slump flow to ensure that the volume of coarse aggregates is within a reasonable range. This invention presents the corresponding relationship between the two, which has a positive effect on the mix design of concrete. The existing mix design methods for self-compacting concrete focus on different aspects such as the specific surface area of coarse aggregates, the rheological theory of self-compacting concrete, and the relative position of coarse aggregates. Starting from the average particle size of coarse aggregates, this invention explores the relationship between the average particle size of coarse aggregates, the slump flow, and the volume dosage of coarse aggregates under the condition of dense packing, and proposes a denser packing state in the mix design of self-compacting concrete, aiming to increase the proportion of coarse aggregates in the concrete while ensuring the workability of self-compacting concrete, and achieving this by changing the average particle size of coarse aggregates.

[0017] Compared with the prior art, the advantages and positive effects of this invention are as follows: 1) This invention conducts research on coarse aggregates under the condition of dense packing, establishes a dense packing model according to the plane triangular packing mode of spherical particles, and the self-leveling state of SCC in the mix design of self-compacting concrete conforms to this dense packing model; 2) This invention conducts research based on the dense packing model, introduces the average particle size of coarse aggregates in the mix design of SCC, explores the relationship between the particle size and the slump flow and the volume of coarse aggregates in the mix design of concrete. The prediction accuracy of the volume fraction of coarse aggregates is relatively high. Under the obtained mix ratio, the coarse aggregates are densely packed and the performance of self-compacting concrete is good; 3) The present invention introduces the relational formula of the average particle size of coarse aggregate, slump flow and the volume of coarse aggregate. In the mix proportion design, when the actual average particle size of aggregate is determined, the appropriate slump flow can be selected, and then the volume of coarse aggregate can be easily determined. This gets rid of the mix proportion size stipulated by the standard experience and more scientifically gives the dosage size of each component of SCC, which is beneficial to improving the performance of SCC and reducing the blindness in the mix proportion design process and shortening the time-consuming of SCC trial mixing process. BRIEF DESCRIPTION OF THE DRAWINGS

[0018] Figure 1 It is a schematic diagram of five self-leveling states of self-compacting concrete.

[0019] Figure 2 It is a schematic diagram of the plane packing model of coarse aggregate.

[0020] Figure 3 It is a schematic diagram of the mortar layer thickness; where d av represents the aggregate particle diameter, and δ represents the mortar layer thickness.

[0021] Figure 4 It is a schematic diagram of the voids between coarse aggregates when the coarse aggregates are closely packed in a single layer; where the data in the first row represents the number of circles of coarse aggregates n , and the data in the second row represents the number of voids 6 + 12( n -1).

[0022] Figure 5 It is a schematic diagram of the calculation model of the number of coarse aggregate particles within the slump flow area.

[0023] Figure 6 It is a schematic diagram of the test results and fitting of the mortar layer thickness test.

[0024] Figure 7 It is an analytical schematic diagram of the prediction model of the volume fraction of coarse aggregate with respect to the slump flow and the average particle size of coarse aggregate.

[0025] Figure 8 It is a schematic diagram of the slump flow test of fly ash SCC designed with SF = 680mm and d av = 9.9mm in Example 1. DETAILED DESCRIPTION OF THE INVENTION

[0026] 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.

[0027] Based on the condition of dense packing of aggregates, the present invention aims to construct a reasonable mix design method for self-compacting concrete. This method is based on the flowing single-layer model of self-compacting concrete, and through studying the relationship between the average particle size of aggregates and the slump flow in the dense packing model, the mix proportion of concrete is designed. Finally, the mix proportion of self-compacting concrete in the dense packing state is obtained, which has greater advantages in saving mortar and improving the stability of concrete.

[0028] The present invention provides a mix design method for self-compacting concrete based on the dense packing of coarse aggregates, comprising the following steps: (1) Establish a prediction model for the volume fraction of coarse aggregates with respect to the average particle size of coarse aggregates and the slump flow :

[0029] In the formula: is the volume fraction of coarse aggregates, L / m 3 ; is the slump flow, mm; is the average particle size, mm; is a constant, and it is recommended to take 69.43; The specific construction process of this prediction model is as follows: The most important property of self-compacting concrete SCC is its good workability, which can self-level and be uniform under its own weight. Using the equivalent particle size method, the coarse aggregate particles and the mortar adhering to the particle surface are equivalent to spherical particles (the coarse aggregate particles are equivalent to small spheres, and the mortar layer is equivalent to a spherical shell attached to the surface of the small spheres, and the two form the above spherical particles). The mixing model of mortar (including other materials except coarse aggregates) and coarse aggregates in the self-leveling state is as Figure 1 .

[0030] In states Ⅰ and Ⅱ, the self-leveling state is not reached, and the fluidity of the concrete is poor and does not meet the design requirements. In state Ⅲ, although the self-leveling state is reached, the uniformity is poor, the viscosity of the mortar is low, and segregation and bleeding occur. In state Ⅳ, the gap between the mortar and the coarse aggregates is large. Under this condition, the amount of mortar is large, the viscosity of the concrete is small, the yield stress is small, and although the self-leveling state can be reached, slight segregation is likely to occur and the amount of coarse aggregates used is small, and the volume stability after hardening is poor. In state Ⅴ, there are more coarse aggregates, the thickness of the mortar layer between the aggregates is small, the viscosity of the concrete is moderate, the yield stress is small, and it also meets the use requirements of SCC. Moreover, the stability after hardening is good, and the usage amount of coarse aggregates is increased. State Ⅴ is the dense packing state. The important factors affecting state Ⅴ are the packing method of coarse aggregates and the particle size of coarse aggregates.

[0031] Considering the stacking mode of coarse aggregates in the Ⅴ state, there are various types, including triangular stacking, quadrilateral stacking, pentagonal stacking, etc. As Figure 2 . It can be relatively easily obtained that the ratio of the area of the voids between coarse aggregates to the area of the polygon (i.e., the area of the equivalent spherical particles of coarse aggregates), which is the void ratio, is:

[0032] In the formula, x is the number of sides when the coarse aggregates are stacked in a polygon.

[0033] When x increases, the denominator increases monotonically, the numerator decreases monotonically, and this formula increases monotonically. So when x = 3, it is the position with the smallest voids, and the triangle has stability. When the polygon stacking model is closely packed, the positions of the aggregates will continuously move to reach the stable triangular state, and at this time, it reaches the close packing. When, the void area is:

[0034] Substitute into Equation (2) to get value, and then substitute value into Equation (3) to get Equation (4):

[0035] Among them, is the average particle size of coarse aggregates, is the average thickness of the mortar layer between coarse aggregates.

[0036] The stacking model of coarse aggregates in the self-leveling state when closely packed in a plane triangular state is as Figure 3 . As the number of circles of coarse aggregates increases, such as Figure 4 , the increase in the number of voids of coarse aggregates has the following law: The number of voids increased in each circle is:

[0037] The overall number of voids increased is: 6 + 18 + 30 +...... +

[0038] That is, the sum of an arithmetic progression is used to obtain the total number of voids of coarse aggregates : (5) Among them, n is the number of circles of aggregates.

[0039] Under the self-leveling state of self-compacting concrete, the coarse aggregate is paved in one layer. The plane triangular packing mode of spherical particles is used to simulate the single-layer close packing phenomenon of coarse aggregate under the self-leveling state of self-compacting concrete. Considering the relationship that the slump flow area of self-compacting concrete under the self-leveling state is equal (approximately equal) to the total area of coarse aggregate, mortar and voids, the paved self-compacting concrete is approximately regarded as a circle, and its paving situation is as follows Figure 5 , it can be seen that there is the following relationship between the slump flow and the number of circles of coarse aggregate packing:

[0040] Under the self-leveling state of self-compacting concrete, an equation can be constructed according to the principle of equal area for the slump flow SF and the total number of coarse aggregate particles, that is, Equation (7):

[0041] Among them, m is the maximum number of coarse aggregate particles required when the average diameter is and the slump flow of the coarse aggregate is SF.

[0042] Substitute Formulas (4), (5), and (6) into Formula (7), and then the solution gives Formula (8):

[0043] Accordingly, by multiplying the volume of a single coarse aggregate particle by the number of coarse aggregate particles, the volume fraction of the coarse aggregate during the slump flow test (the volume of the test bucket is 0.055 cubic meters) can be obtained. There is the following formula:

[0044]

[0045] Overall volume fraction of coarse aggregate:

[0046]

[0047] Among them, represents the volume of a single coarse aggregate particle, represents the total volume of the aggregate in the slump flow test bucket, represents the volume fraction of the aggregate; m is the total number of coarse aggregate particles (the number in the slump flow test).

[0048] It should be noted that the void area, the cross-sectional area of the coarse aggregate particles, and the cross-sectional area of the mortar layer mentioned in the present invention all rely on the plane triangular packing mode of spherical particles shown in the appendix Figure 2-5 . For example, the cross-sectional area of the coarse aggregate particles represents the maximum cross-sectional area after the coarse aggregate particles are equivalent to spherical particles.

[0049] In formula (11), the thickness of the mortar layer is an unknown parameter, but generally has a certain relationship with the particle size of coarse aggregate. Through the slump flow test of self-compacting concrete indoors, the thickness of the mortar layer on the surface of coarse aggregate particles in self-compacting concrete is measured to obtain a series of thicknesses of the mortar layer data. Using the regression analysis method, the thickness of the mortar layer and the average particle size of coarse aggregate data are fitted according to a linear function:

[0050] In the formula, is the average thickness of the mortar layer between coarse aggregates, in mm; is the average particle size of coarse aggregate particles, in mm; is the thickness coefficient of the mortar layer relative to coarse aggregate particles, and its value is related to the mortar material.

[0051] In the present invention, multiple groups of mortar layer thickness data are measured, and the measurement results are as shown in Figure 6 . It can be seen from Figure 6 that there is generally a linear relationship between the thickness of the mortar layer and the average particle size of coarse aggregate particles, and multiple fitting equations are obtained. For example, y = -0.627 + 0.138x, where x represents the horizontal axis , and y represents the vertical axis ; Theoretically, when is equal to 0, is also equal to 0. Therefore, the constant term is removed, and the average value of the first-order term coefficient is obtained. Finally, it is obtained that:

[0052] Substituting this formula (13) into formula (11), formula (14) is finally obtained:

[0053] In the formula: is the volume fraction of coarse aggregate, in L / m 3 ; is the slump flow, in mm; is the average particle size, in mm; Take 69.43.

[0054] This formula establishes the relationship between the volume fraction of coarse aggregate and the slump flow , the average particle size of coarse aggregate , that is, a prediction model of the volume fraction of coarse aggregate is obtained.

[0055] (2) The average particle size of coarse aggregate is obtained by the sieving method , according to the performance requirements of self-compacting concrete and the average particle size of coarse aggregate Select the slump flow design value, and substitute , the design value into the prediction model of formula (1) to obtain the volume fraction of coarse aggregate ; The calculation of the average particle size of coarse aggregate can be carried out by weighted average, that is, there is a formula:

[0056] Among them, represents the average particle size when the grading interval is i, that is, the average value of the sizes of two adjacent sieve holes, represents the overall proportion occupied by this grading. That is, the cumulative sieve residue percentage.

[0057] For the 5-20mm continuous grading interval, it can also be calculated according to the following formula:

[0058] This formula is the calculation formula of the average particle size, d represents the average particle size in a certain particle size range, d the subscript of represents the particle size range, represents the overall proportion of coarse aggregate occupied by this grading, i = 1~5.

[0059] Based on the above prediction model, the present invention further explores the relationship between the average particle size of coarse aggregate and the slump flow, so that the slump flow can be selected according to the average particle size of coarse aggregate. The particle size intervals of the 5-20mm continuous grading coarse aggregate are shown in Table 1 below.

[0060]

[0061]

[0062]

[0063] Under the 5-20mm continuous grading, the average particle size of the coarse aggregate is between 9.02mm and 12.63mm.

[0064] According to formula (14), draw a schematic diagram of the relationship between the volume of coarse aggregate and SF and the average particle size of coarse aggregate Figure 7 as shown. According to the requirements for the mix proportion of self-compacting concrete in the "Technical Specification for Application of Self-Compacting Concrete (JGJ / T283-2012)", the volume range of coarse aggregate is 280-350 ​。The shaded part in the figure is the particle size and spread distribution under this condition. From this figure, it can be directly seen that the spread range of 570mm - 720mm is more appropriate in the mix design.

[0065] According to formula (14), Table 2a - 2f can also be listed. This table is the corresponding chart of the slump flow SF, average coarse aggregate particle size and the final volume fraction of coarse aggregate V g . In the mix design, this table can play a role in assisting the selection of the volume of coarse aggregate and spread.

[0066]

[0067]

[0068]

[0069]

[0070]

[0071]

[0072] To sum up, according to the average diameter of the coarse aggregate , select the appropriate design value of slump flow SF with reference to Table 2a - 2f: for the continuously graded coarse aggregate particles with a particle size range of 5 - 20mm, the selection range of the design value of slump flow SF is 570mm - 720mm; If the average coarse aggregate particle size is smaller, select a slightly larger SF design value. If the average diameter of the coarse aggregate is larger, select a slightly smaller SF design value.

[0073] Substitute the , design values into the prediction model of formula (14) to obtain the volume fraction of coarse aggregate .

[0074] (3) According to the performance requirements of self - compacting concrete and , obtain the volume fraction of fine aggregate , water - binder ratio, admixture dosage relative to the binder. According to the water - binder ratio, obtain the binder dosage , water dosage ; obtain the initial mix proportion; Step (3) further includes the following steps: 1) Select an appropriate sand ratio SP , according to the volume fraction of coarse aggregate , the volume fraction of fine aggregate is calculated according to Equation (16). , the sand ratio of 49% can be first selected as the initial sand ratio of the mix proportion.

[0075] (16) In the formula: V s is the volume fraction of fine aggregate, L / m 3 ; ρ g is the density of coarse aggregate, kg / m 3 ; ρ s is the density of fine aggregate, kg / m 3 ; SP is the sand ratio, that is, the mass of sand / (the mass of sand + the mass of gravel), %.

[0076] 2) Calculate the water-binder ratio of SCC; According to the concrete strength grade required by the engineering structure and combined with the properties of the binder, the water-binder ratio of SCC is calculated. The calculation of the water-binder ratio is shown in Formulas (17) to (18). When the water-binder ratio is greater than 0.42, take 0.42; When the designed concrete strength grade is less than C60, the concrete strength shall be calculated according to (17): (17) In the formula, is the standard cubic compressive strength of concrete; is the strength standard deviation; f cu,0 is the 28-day compressive strength of concrete; The water-binder ratio is calculated according to Formula (18): (18) In the formula: f ce is the measured 28-day compressive strength of cement, MPa; m b is the dosage of binder (cement, mineral admixture) for 1 m 3 of SCC, kg; β is the mass fraction of mineral admixture in SCC in the binder, γ is the equivalent binder coefficient of the mineral admixture. For limestone powder, fly ash, slag powder and silica fume, 0.2, 0.4, 0.9 and 2.5 can be taken respectively; m w is the water consumption for 1 m 3 of SCC, kg.

[0077] 3) Calculate the paste volume, binder dosage and unit water consumption; According to the volumes of sand and stone aggregates per unit volume of concrete, the paste volume can be calculated according to Formulas (19) and (20) V p (considering = 2% air content, calculate the volume of the actual paste under compacted conditions), and combined with the water-binder ratio and the apparent density of the binder material, calculate the mass dosage of the binder material according to the following formula and the unit water consumption .

[0078] (19) (20) Binder material dosage: (21) (22) Water consumption (23) In the formula: V c , V m , V w are the volumes of cement, mineral admixture, and mixing water, respectively; ρ c , ρ m , ρ w are the apparent densities of cement, mineral admixture, and mixing water, respectively; 、 、 are the dosages of binder material, cement, and mineral admixture, respectively.

[0079] 4) Selection of admixtures: The chemical admixtures used in SCC generally include high-range water reducers and thickeners. High-range water reducers are essential components of SCC. To make the fresh concrete mixture have appropriate viscosity coefficient and yield shear stress, it is necessary to reasonably select the variety and dosage of high-range water reducers. When the viscosity of the paste is too small, thickener components can also be added to improve the stability of the mixture. The variety and dosage of high-range water reducers selected for SCC generally should meet: 1) The water reduction rate is not less than 20%; 2) The dosage is not less than 0.6% (calculated based on the total mass of the binder material in the concrete), and it is not more than its saturation dosage value, that is, not more than 2%.

[0080] 3) The water reducer has good compatibility with the binder material and small slump loss.

[0081] According to the above principles, verify and determine the optimal dosage of the admixture through tests. The selection of other admixtures is prior art and will not be elaborated here.

[0082] Thus, the initial mix proportion is obtained: 、 , , The dosage of admixture relative to the cementitious material.

[0083] (4) Conduct trial mixing and performance testing on the self-compacting concrete according to the initial mix proportion. Based on the test results, adjust the sand ratio and the dosage of admixture while keeping the water-binder ratio unchanged until the designed mix proportion of self-compacting concrete that meets the performance requirements is obtained.

[0084] When conducting trial mixing according to the calculated initial mix proportion, first perform trial mixing to check the properties of the mixture. When the workability of the tested mixture does not meet the requirements, it can be achieved by adjusting the admixture or the sand ratio under the condition of keeping the water-binder ratio unchanged. Specifically: without changing the volume content of coarse aggregate, the sand ratio can be increased or decreased by 1 percentage point for adjustment, or the admixture can be increased or decreased by 0.5 percentage point for adjustment until it meets the requirements, and the designed mix proportion of self-compacting concrete that meets the performance requirements is obtained.

[0085] The main innovation points of the present invention are as follows: 1) Introduce the average particle size of coarse aggregate into the SCC mix proportion design, explore the relationship among the slump flow, the average particle size of coarse aggregate, and the dosage of coarse aggregate in concrete under the condition of dense packing, and construct a prediction model for the volume fraction of coarse aggregate. 2) Use the average particle size of coarse aggregate to construct a prediction model for the volume fraction of coarse aggregate. The average particle size of coarse aggregate can better measure the influence of the contact and filling of coarse aggregate on the workability of SCC, providing more accurate guidance for the SCC mix proportion design.

[0086] Based on the dense packing of coarse aggregate, the present invention establishes a prediction model for the volume fraction of coarse aggregate with respect to the average particle size of coarse aggregate and the slump flow through theoretical derivation, which more accurately describes the increasing and decreasing relationship between the average particle size of coarse aggregate and the slump flow . In formula (11), the constant C consists of two parts, where 87.87 is a simplified expression of the theoretical derivation process, is a ratio, reflecting the average ability of the mortar adhered to the surface of coarse aggregate particles. This ratio can be obtained by taking the average value after measuring the thickness of the mortar layer adhered to the surface of coarse aggregate multiple times, and its calculation error is small. Therefore, the prediction accuracy of this prediction model is relatively high. By using this prediction model, the volume fraction of coarse aggregate The determination becomes extremely simple, which is beneficial for those skilled in the art to accurately determine the dosage of each material during mix proportion design. Moreover, it can even increase the dosage of coarse aggregate, save the dosage of mortar, and achieve the purpose of improving the workability and economy of SCC. In addition, in the present invention, the measurement process of the mortar layer thickness is very simple and time-consuming is short. On the premise of accurate proportioning, SCC is more likely to meet the designed work performance, and the time-consuming of the SCC trial mixing process can be reduced.

[0087] Example 1: Concrete mix proportion design is carried out for SCC with slump flow SF requirements of 680 mm and 640 mm. The material information is as follows: Cement: P.O 32.5 cement produced by Hunan Jinlei Southern Cement Co., Ltd., with a density of 3.09 g / cm 3 , specific surface area of 330 m 2 / kg, standard consistency water demand of 28.5%, 7-day and 28-day compressive strengths of 19.5 MPa and 38.5 MPa respectively; Fly ash: F-class fly ash produced by Xiangtan Power Plant, with a density of 2.34 g / cm 3 ; Fine aggregate: River sand from the Xiangjiang River, fineness modulus of 2.8, bulk density of 1.46 g / cm 3 , apparent density of 2.66 g / cm 3 ; Coarse aggregate: Limestone with a particle size of 5 - 20 mm, apparent density of 2.65 g / mm 3 ; Through screening, the average particle sizes of the two kinds of coarse aggregates are 9.90 mm and 11.27 mm respectively; Water reducing agent: Polycarboxylate superplasticizer, water reducing rate of 17.8%, solid content of 21.5%; Mixing water is tap water.

[0088] The prepared concrete is self-compacting concrete for lining tunnels with a strength grade of C25.

[0089] 1) Determine the dosage of coarse aggregate and fine aggregate: The average particle sizes of the two kinds of coarse aggregates are 9.9 mm and 11.27 mm respectively. According to Table 2, the design slump flows are selected as 680 mm and 640 mm respectively. Taking the aggregate with a particle size of 9.9 mm as an example, a sand ratio of 49% is selected as the initial sand ratio for mix proportion design and mix proportion design calculation is carried out.

[0090] Volume fraction of coarse aggregate:

[0091] Mass of coarse aggregate per cubic meter: kg Volume fraction of fine aggregate:

[0092] Mass of fine aggregate per cubic meter: kg 2) Calculation of water-binder ratio: Calculation is carried out under the condition that the strength of tunnel lining concrete is C25, and the mineral admixture is fly ash. Take for calculation and , and the calculation example is as follows:

[0093]

[0094] 3) Calculate the dosage of cementitious materials and the unit water consumption; Dosage of cementitious materials:

[0095] Mass of cementitious materials:

[0096] Unit water consumption:

[0097] Cement dosage:

[0098] Fly ash dosage:

[0099] 4) Selection of admixtures: Select an admixture content of 0.8%, and the dosage of water reducer is: .

[0100] Figure 8 For Example 1, the design is for the slump flow of fly ash SCC with SF = 680 mm and d av = 9.9 mm.

[0101] Similarly, for SCC with a particle size of 11.27 mm, the mix proportion design is carried out to obtain Table 3.

[0102]

[0103] The mix proportion design of SCC is carried out by the method of the specification JGJ / T283 - 2012 "Technical Specification for Application of Self-Compacting Concrete", and the results are as follows:

[0104]

[0105] The slump flow test and the subsequent concrete performance test are carried out on the self-compacting concrete prepared according to the mix proportion shown in Table 3, and the results are shown in Table 6 below. The test results of the performance of self-compacting concrete with the standard mix proportion are shown in Table 7.

[0106]

[0107] In Table 6, T 500 is the spreading time from when the slump cone is lifted until the diameter of the spread surface reaches 500 mm; PA is the difference between the slump spread and the J-ring spread; SR is the segregation rate.

[0108]

[0109] The SCC mix design method in the specification is mainly empirical. Although it gives the aggregate gradation range and the alternative range of the slump spread SF, it does not give the corresponding relationship between SF and the aggregate particle size. The specification method is a relatively rough mix design method, which has certain reference significance and value. However, in fact, the aggregate gradation and particle size are different in different projects. Generally, the larger the slump spread of the self-compacting concrete, the relatively smaller its aggregate particle size. According to the specification method, it may be impossible to reach the designed SCC work performance value during actual proportioning (please refer to Figure 7 ), and adjusting the designed SCC work performance value will increase the burden and cycle of the mix design and increase the material loss in the mix design.

[0110] By comparing Table 3 and Table 4, it can be concluded that the mix design method of the present invention is more refined than the specification, and the control of the dosage of various materials is more accurate; by comparing Table 3 and Table 5, it can be concluded that compared with other mix design methods, according to the mix design method of the present invention, the dosage of coarse aggregate has been significantly increased. By controlling the aggregate particle size, the dosage of coarse aggregate has been increased, while the dosage of mortar has been reduced, improving the stability and economy of the self-compacting concrete.

[0111] As can be seen from Table 6 and Table 7, the SCC concrete proportioned according to the present invention meets the requirements of the specification in all aspects. The strength of the SCC can basically reach the 28-day standard compressive strength specified in the specification, and the spreading time T 500 is extended, the aggregates are closely packed, the dosage of mortar is saved, the compressive strength difference is small, and the dosage of coarse aggregate is increased under the same conditions, increasing the stability of the concrete.

[0112] The above is only used to illustrate the technical solution of the present invention and is not intended to limit it. Modifications or substitutions made by other technical personnel in the same professional field to the technical solution, as long as they do not depart from the connotation of the technical solution of the present invention, shall be covered by the scope of the claims of the present invention.

Claims

1. A self-compacting concrete mix design method based on dense packing of coarse aggregate, characterized by: The steps include: (1) Establishing the volume fraction of coarse aggregate About the average particle size of coarse aggregate Slump spread prediction models; Measuring the thickness of the mortar layer on the surface of coarse aggregate particles in self-compacting concrete by the self-compacting concrete expansion test , and obtain a series of mortar layer thicknesses The thickness of the mortar layer was obtained by fitting the data using regression analysis. About the average particle size of coarse aggregate The empirical formula is as follows: （1）； In the formula, It is the thickness of the mortar layer adhered to the surface of each coarse aggregate particle in self-compacting concrete; is the average particle size of coarse aggregate particles; is the thickness coefficient of the mortar layer relative to the coarse aggregate particles; The equivalent particle size method is used to equate the coarse aggregate particles to spherical particles, and the mortar layer attached to the surface of the coarse aggregate particles is equated to the spherical shell outside the spherical particles, and the volume of each coarse aggregate particle is obtained. , cross-sectional area and the cross-sectional area of ​​the mortar layer attached to its surface; the plane triangle stacking mode of spherical particles is used to simulate the tight stacking phenomenon of coarse aggregate single layer under the self-leveling state of self-compacting concrete, and the area of ​​each gap between coarse aggregate particles is obtained. According to the principle that the expansion area of ​​the self-leveling collapse of self-compacting concrete is equal to the total area of ​​coarse aggregate, mortar and voids, the number of circles of coarse aggregate in the collapse expansion area is obtained. and the number of gaps According to the cross-sectional area of ​​each coarse aggregate particle and the cross-sectional area of ​​the mortar layer attached to its surface and , , Get the number of coarse aggregate particles ; According to the volume of coarse aggregate particles and quantity To obtain the total volume of coarse aggregate, divide the total volume of coarse aggregate by the total volume of self-compacting concrete Get the volume fraction of coarse aggregate As shown in formula (2): （2）； In the formula, is the volume fraction of coarse aggregate; is the number of coarse aggregate particles; is the volume of coarse aggregate particles; is the total volume of self-compacting concrete; in, According to formula (3), we can get: （3）； In the formula, is the slump spread; It is the number of voids between coarse aggregates when densely packed; is the area of ​​each gap; Substituting equations (1) and (3) into equation (2), we can obtain the volume fraction of coarse aggregate: Average particle size of coarse aggregate Slump spread The prediction model is as follows: （4）； Where: is a constant; (2) Use the screening method to obtain the average particle size of coarse aggregate According to the performance requirements of self-compacting concrete and the average particle size of coarse aggregate Select slump spread The design value will , Substituting the design value into the prediction model of formula (4), we get the volume fraction of coarse aggregate: ; (3) According to the performance requirements of self-compacting concrete and , and the volume fraction of fine aggregate is obtained , water-binder ratio, the amount of admixture relative to the cementitious material, and the amount of cementitious material used according to the water-binder ratio , Water consumption ; Get the initial mix ratio; (4) Carry out trial mixing and performance testing of self-compacting concrete according to the initial mix ratio. Based on the test results, adjust the sand ratio and admixture dosage while keeping the water-cement ratio unchanged until the designed mix ratio of self-compacting concrete that meets the performance requirements is obtained.

2. The method according to claim 1, characterized in that: Void Area , the number of voids between coarse aggregate According to formula (5) and (6), we can get: （5）； （6）； In the formula, is the number of circles of coarse aggregate within the collapse expansion area of ​​self-compacting concrete, .

3. The method according to claim 1, characterized in that: According to the performance requirements of self-compacting concrete and the average particle size of coarse aggregate , slump spread The design values ​​are selected as follows: For continuously graded coarse aggregate particles, the slump spread The design value selection range is 570-720mm; When the average particle size of coarse aggregate If the slump is smaller, choose a slightly larger slump expansion Design value, when the average particle size of coarse aggregate If the slump is larger, choose a smaller slump expansion Design value.

4. The method according to claim 1, characterized in that: Volume fraction of fine aggregate According to formula (7), we can get: （7）； In the formula, is the volume fraction of fine aggregate; is the density of coarse aggregate; is the density of fine aggregate; is the sand rate.

5. The method according to claim 1, characterized in that: Amount of cementitious material , Water consumption According to equations (8) to (10), we can obtain: （8）； （9）； （10）； In the formula, ρ c , ρ m , ρ w are the apparent densities of cement, mineral admixtures, and mixing water, respectively; , are the amounts of cement and mineral admixtures, respectively; is the water-to-binder ratio; β is the mass fraction of mineral admixtures in cementitious materials in self-compacting concrete; is the air content of self-compacting concrete; Among them, the water-to-binder ratio According to formula (11), we can get: （11）； In the formula, f ce is the 28d measured compressive strength of cement; m b It is the amount of cementitious material in each cubic meter of self-compacting concrete; m w is the amount of water used per cubic meter of self-compacting concrete; f cu,0 is the 28d compressive strength of concrete; γ is the equivalent gelling coefficient of mineral admixture; in, According to formula (12), we get: （12）； In the formula, is the standard compressive strength of concrete cube; is the intensity standard deviation.

6. The method according to claim 1, characterized in that: The self-compacting concrete admixture shall use high-efficiency water-reducing agent, and the water reduction rate of the high-efficiency water-reducing agent shall not be less than 20%; the dosage of the high-efficiency water-reducing agent shall not be less than 0.6% and not more than 2%.

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