A method for designing high crack-resistant concrete mix ratio based on multi-scale relationships

Abstract

The present invention provides a method for designing a high-crack-resistant concrete mix ratio based on a multi-scale relationship. The method achieves the coordinated unification of concrete strength growth and deformation development by calculating parameters such as the water-cement ratio, fiber content, sand ratio, water consumption, cement type influence coefficient, and admixture influence coefficient based on changes in the type and quality of raw materials, concrete technical index requirements, fiber type and dosage, thereby achieving the purpose of improving the crack resistance of concrete. Compared with existing technologies and methods, the present application can significantly reduce the experimental workload, improve the efficiency of mix design, improve the crack resistance of concrete, and provide algorithm support for the development of intelligent technologies such as concrete expert support systems and early warning systems.

Description

Technical Field

[0001] The present invention belongs to the field of water conservancy engineering, and aims to propose a high crack-resistant concrete mix ratio design method based on the multi-scale relationship of cement-based materials. Background Art

[0002] Cracks are one of the primary defects in concrete structures, and concrete's crack resistance is a widespread concern in the engineering community. The risk of cracks persists throughout the concrete lifecycle, from setting and hardening to later service. Cracks can create pathways for external moisture penetration and ion attack, threatening the integrity and safe operation of the structure. Therefore, the preparation of highly crack-resistant concrete has significant engineering significance and application value.

[0003] The crack resistance of concrete is related to many factors, including the impact of the service environment, its own deformation capacity, structural layout, load level, and degree of restriction and constraint. Among them, the inherent deformation characteristics of concrete materials have a decisive influence. The inherent deformation characteristics of concrete materials are related to the performance and quality of raw materials on the one hand, and the mutual proportions of various raw materials on the other hand. The performance and quality of raw materials are mainly achieved by optimizing the material type, optimizing the component system, and using functional additives to improve the toughness characteristics and deformation capacity of concrete from the source. The mutual proportions of various raw materials are mainly based on the inherent characteristics of the materials, and comprehensively utilize the compatibility effect of volcanic ash materials, the dense stacking effect of cementitious materials, and the dense filling technology of coarse aggregate and fine aggregate to achieve the coordination and unification of the mechanical properties, deformation properties, and shrinkage properties of various raw materials.

[0004] Concrete raw materials vary widely in their physical properties, chemical composition, mechanical properties, thermal characteristics, size range, and micromorphology. Hardened concrete is also a complex structure containing gas, liquid, and solid phases. Therefore, improving concrete's crack resistance requires a comprehensive systems approach. Common measures to improve concrete's crack resistance include optimizing a reasonable water-binder ratio, replacing part of the cement with admixtures, and adding functional additives to improve matrix properties. For example, using light-burned MgO as an expansion agent can improve the shrinkage and deformation characteristics of concrete during setting and hardening, reducing the risk of shrinkage cracks. Replacing part of the cement with phosphorus slag powder can reduce the adiabatic temperature rise of concrete and minimize the risk of temperature cracks. However, numerous engineering applications have demonstrated that improving the concrete's inherent properties has only a limited effect on improving the overall crack resistance of the structure.

[0005] In recent years, composite material technology has been promoted and applied in the field of concrete, especially the theory of fiber concrete has received widespread attention. Fibers can play a role in strengthening and toughening concrete, and can further play a role in limiting and preventing cracks after cracks appear, thereby improving the energy dissipation process of concrete. The effect of fiber concrete is related to the type and characteristics of the fibers on the one hand, and the bonding characteristics and mechanical properties of the concrete itself on the other hand. Commonly used fibers in concrete include polymer fibers, cellulose fibers, mineral fibers, metal fibers, etc. Among them, polymer fibers are the most economical, technologically mature, and less difficult to construct. However, existing methods for preparing polymer fiber concrete rely on a large number of physical experiments to find a more optimized parameter range through systematic experiments. On the one hand, this increases the experimental workload, increases investment costs, and prolongs the test cycle; on the other hand, it is difficult to ensure the adaptability of the preparation parameters to different types of raw materials, and the rationality and economy of the parameter range are also difficult to guarantee. Summary of the Invention

[0006] In response to the above problems, the present invention integrates the technical characteristics of cement-based materials and provides a high-crack-resistant concrete mix ratio design method based on multi-scale relationships. The method can significantly improve the efficiency of determining the composition ratio of each raw material, save experimental workload, shorten the test cycle, reduce economic costs, and improve the rationality and optimization level of parameter determination; at the same time, the calculation steps involved in the present invention can provide a reference for the compilation of intelligent algorithms such as concrete expert analysis and support systems and mix ratio design software.

[0007] To achieve the above technical objectives, the present invention provides a method for designing a mix ratio of highly crack-resistant concrete based on a multi-scale relationship. The concrete is prepared from water, cement, admixtures, fine aggregate, coarse aggregate, a water reducer, an air entraining agent, and polymer fibers. The amount of each raw material added to the concrete is calculated according to the following steps:

[0008] (1) Based on the design strength grade of concrete, admixture type, reactivity characteristics and cement type, the recommended water-cement ratio of concrete is calculated as follows:

[0009]

[0010]

[0011]

[0012] In the above formula: f c,k is the characteristic value of compressive strength corresponding to the concrete strength grade, MPa;

[0013] f c is the calculated compressive strength of concrete, MPa; e is a natural number, e = 2.718;

[0014] p is the compressive strength guarantee rate of concrete, %; C m is the admixture dosage, %;

[0015] H m is the activity index of the admixture’s 28d compressive strength, %, and the pure cement system is 1.0;

[0016] γ1 is the influence coefficient of admixture dosage; γ2 is the influence coefficient of cement type; w / b is the recommended water-binder ratio of concrete;

[0017] int() is a rounding function, which only retains the integer digits of the calculation result and discards the decimal part of the calculation result;

[0018] Concrete mix design is based on reliability theory, using a guarantee rate as an indicator to characterize the probability of failure. The guarantee rate refers to the probability that material properties will meet the specified specifications under current theoretical and technical conditions. For example, a 70% guarantee rate means there's a 70% chance that the concrete's compressive strength will meet the design requirements, but a 30% chance that it will not. A 95% guarantee rate, on the other hand, means there's a 95% chance that the concrete's compressive strength will meet the design requirements, but the corresponding pass rate is only 5%. Generally speaking, a higher guarantee rate indicates greater material safety, a lower probability of failure, and correspondingly higher technical requirements.

[0019] Rounding functions are used in logical calculations and are commonly used in computing software and algorithm design. They discard decimal places, retaining only the integer portion. For example, int(5 / 3) rounds 5 / 3 to an integer, resulting in a value of 1.

[0020] (2) Calculate the compressive strength f of the concrete based on the fiber elastic modulus, fiber deformation capacity, fiber length, fiber diameter of the polymer fiber and the calculated value in step (1) c The polymer fiber content was calculated according to the following formula:

[0021]

[0022]

[0023] In the above formula: f t is the tensile strength of concrete, MPa; C F is the polymer fiber content, kg / m 3 ;

[0024] l is the length of the fiber, mm; d is the diameter of the fiber, μm; ρ F is the density of the fiber, kg / m 3 ;

[0025] EF is the elastic modulus of the fiber, GPa; ε F is the deformation capacity of the fiber, %;

[0026] (3) Calculate the water consumption m according to the following formula based on the slump of concrete, the water reduction rate of the water reducer, and the fineness modulus of the fine aggregate: W And sand rate s:

[0027]

[0028]

[0029] In the above formula: T is the slump of concrete, mm; m w is the water consumption, kg / m 3 .

[0030] q is the water reducing rate of the water reducing agent, %; s is the concrete sand ratio, %; FM is the fineness modulus of the fine aggregate;

[0031] (4) Based on the density of cement, admixtures, fine aggregate, and coarse aggregate in concrete and the water consumption m calculated in step (3) w , calculate the amount of each raw material in unit volume of concrete:

[0032]

[0033]

[0034]

[0035]

[0036] In the above formula: m c is the amount of cement, kg / m 3 ;m m is the amount of admixture, kg / m 3 ;

[0037] m s is the amount of fine aggregate, kg / m 3 ;m g is the amount of coarse aggregate, kg / m 3 ; s is the sand ratio of concrete, %;

[0038] ρ c is the density of cement in raw materials, kg / m 3 ρ m is the density of the admixture in the raw materials, kg / m 3 ;

[0039] ρ sis the density of fine aggregate in raw materials, kg / m 3 ρ g is the density of coarse aggregate in raw materials, kg / m 3 ;

[0040] (5) According to the dosage of water reducer in concrete j , the amount of air entraining agent C y The amount of water reducer and air entraining agent can be calculated based on the concrete water-binder ratio w / b according to the following formula:

[0041]

[0042]

[0043] In the above formula: m j is the dosage of concrete water reducing agent, kg / m 3 ;m y is the dosage of concrete air entraining agent, kg / m 3 ;

[0044] C j is the dosage of concrete water reducing agent, %; C y is the dosage of concrete air-entraining agent, %.

[0045] A further technical solution of the present invention is that the fine aggregate is artificial sand with a fineness modulus FM of 2.3 to 2.8; the coarse aggregate is artificial crushed stone, which is made by mixing two kinds of stones with particle sizes of (5-20) mm and (20-40) mm in a mass ratio, and the mixing ratio range is m 5-20 :m 20-40 =1.00~1.22.

[0046] A further technical solution of the present invention is: the design strength grades of the concrete are C15, C20, C25, C30, C35, C40, C45, C50 and C55, and the corresponding nominal compressive strength values ​​are 15 MPa, 20 MPa, 25 MPa, 30 MPa, 35 MPa, 40 MPa, 45 MPa, 50 MPa and 55 MPa, respectively.

[0047] A preferred technical solution of the present invention is that the compressive strength guarantee rate of the concrete ranges from 70% to 97.7%.

[0048] A preferred technical solution of the present invention is as follows: the cement is silicate cement, including ordinary silicate (codenamed PO) cement, medium-heat silicate (codenamed PMH) cement and low-heat silicate (codenamed PLH) cement, and the corresponding cement type correction coefficients γ2 are PO cement γ2=1.0, PMH cement γ2=0.98, and PLH cement γ2=0.95.

[0049] A preferred technical solution of the present invention is as follows: the water reducer is a polycarboxylate water reducer (codenamed PCA) or a naphthalene water reducer (codenamed SNF), and the dosage of the water reducer is 0.6% to 1.0%.

[0050] A preferred technical solution of the present invention is that the dosage of the air entraining agent is 0.008% to 0.012%.

[0051] A preferred technical solution of the present invention is that the fibers are organic high molecular polymer fibers, including polypropylene fibers (codenamed PP), polyacrylonitrile fibers (codenamed PAN), polyvinyl alcohol fibers (codenamed PVA) and polyoxymethylene fibers (codenamed POM).

[0052] The preferred technical solution of the present invention is: the admixture is Class F fly ash, including Class I fly ash and Class II fly ash, the fly ash dosage is mass dosage, and the addition method is to replace part of the cement with equal mass, and the dosage range is 0-50%.

[0053] Concrete is a material made by mixing, molding, vibrating, and curing raw materials such as cement, fly ash, manufactured sand, and gravel. Its performance is influenced by numerous factors, including the type and quality of raw materials, mix proportions, construction techniques, curing measures, and the service environment. Consequently, different requirements for concrete performance exist at each stage. The design phase primarily considers concrete strength grades, such as C15, C25, and C35, and calculates the structural load and stability performance based on these grades. During the construction phase, concrete is primarily formulated based on these strength grades, while also accounting for fluctuations in raw material quality and construction techniques. The concept of a guaranteed rate is introduced to increase strength reserves. For example, C45 grade concrete has a design compressive strength of 45 MPa. However, to prevent substandard performance during construction, the mix proportions are typically designed for 52.2 MPa, assuming a 90% guaranteed rate. Therefore, concrete parameters include design strength grade, characteristic compressive strength value, and calculated compressive strength.

[0054] Water reduction rate refers to the reduction in water consumption when the water-reducing agent is added to the recommended dosage and the concrete without water-reducing agent has the same flow characteristics as the concrete without water-reducing agent. For example, if the recommended dosage of water-reducing agent is 0.8%, the water consumption of concrete with water-reducing agent is 128kg / m 3 The water consumption of concrete without water reducing agent is 157kg / m 3, the corresponding water-reducing agent has a water-reducing rate of 18.5%. In actual application, the water-reducing agent dosage is generally based on the recommended dosage and adjusted based on the concrete's flow properties. It may be higher or lower than the recommended dosage, but it always fluctuates around the recommended dosage. Water consumption is a key factor affecting concrete slump. Fineness modulus is a key indicator of sand particle grading and fineness, and sand fineness directly affects the concrete sand ratio and water consumption.

[0055] Fibers enhance the strength and toughness of concrete. Commonly used fiber types in concrete include organic and inorganic fibers. Inorganic fibers include steel fibers and mineral fibers, while organic fibers include polymer fibers and plant fibers. In practical applications, steel fibers offer the best results, but they are expensive and carry the risk of corrosion. While plant fibers offer water retention and internal curing properties, their mechanical properties are inferior to those of polymer fibers. Therefore, polymer fibers are primarily used in engineering applications to improve concrete's crack resistance, reduce the risk of premature cracking, and improve the uniformity of crack distribution.

[0056] The present invention combines the multi-scale relationship of cement-based materials and the working principle of fiber reinforcement and toughening theory, and based on the summary of a large number of experimental results and extensive application experience, proposes a mix design method for highly crack-resistant fiber concrete. According to the changes in the type and quality of raw materials, concrete technical indicators, fiber type and dosage, etc., by adjusting and optimizing parameters such as water-binder ratio, fiber dosage, sand ratio, water consumption, cement type influence coefficient, and admixture influence coefficient, the coordinated unification of concrete strength growth and deformation development is achieved, thereby achieving the purpose of improving the crack resistance of concrete. The present invention takes into account the influence of concrete strength grade, raw material properties and quality, fiber type and dosage, etc. on crack resistance.

[0057] Compared with existing technologies and methods, it has the following advantages:

[0058] (1) The existing method requires a large number of experiments, and it is difficult to guarantee that the parameter range is the optimal solution; the present application saves the experimental workload, shortens the experimental cycle, improves the efficiency and accuracy of parameter range determination, and has simple steps and is easy to promote.

[0059] (2) The existing methods for the initial selection of reasonable parameter ranges for concrete are highly subjective and rely heavily on engineering experience. This application summarizes and condenses a large amount of experimental results and application data to construct a multi-scale concrete crack resistance relationship model, taking into account the type, quality and system of raw materials. The parameter determination method proposed is characterized by high objectivity and programmable calculation.

[0060] (3) The crack resistance of the concrete obtained by this application is better than that of the concrete with the same strength index obtained by the existing method, and the rationality, economy, objectivity and reliability of the parameter selection are relatively obvious. BRIEF DESCRIPTION OF THE DRAWINGS

[0061] Figure 1 is a diagram showing the results of a flat plate cracking test in Example 1 of the present invention;

[0062] Figure 2 is a diagram showing the results of a flat plate cracking test in Example 2 of the present invention;

[0063] Figure 3 is a diagram showing the results of a flat plate cracking test in Example 3 of the present invention;

[0064] Figure 4 1 is a graph showing the results of a flat plate cracking test in Example 4 of the present invention. DETAILED DESCRIPTION

[0065] The present invention is further described below with reference to the accompanying drawings and examples. The technical solutions presented in the following examples are specific solutions of the embodiments of the present invention and are not intended to limit the scope of the invention claimed for protection. All other embodiments obtained by ordinary technicians in this field based on the embodiments of the present invention without making any creative efforts are within the scope of protection of the present invention.

[0066] An embodiment of the present invention provides a method for designing a mix ratio of highly crack-resistant concrete based on a multi-scale relationship, wherein the concrete is prepared from water, cement, admixtures, fine aggregate, coarse aggregate, a water reducer, an air entraining agent, and polymer fibers; and the amount of each raw material added to the concrete is calculated according to the following steps:

[0067] (1) Based on the design strength grade of concrete, admixture type, reactivity characteristics and cement type, the recommended water-cement ratio of concrete is calculated as follows:

[0068]

[0069]

[0070]

[0071] In the above formula: f c,k is the characteristic value of compressive strength corresponding to the concrete strength grade, MPa;

[0072] f c is the calculated compressive strength of concrete, MPa; e is a natural number, e = 2.718;

[0073] p is the compressive strength guarantee rate of concrete, %; C mis the admixture dosage, %;

[0074] H m is the activity index of the admixture’s 28d compressive strength, %, and the pure cement system is 1.0;

[0075] γ1 is the influence coefficient of admixture dosage; γ2 is the influence coefficient of cement type; w / b is the recommended water-binder ratio of concrete;

[0076] int() is a rounding function, which only retains the integer digits of the calculation result and discards the decimal part of the calculation result;

[0077] Formula ① above constructs a formula for calculating concrete compressive strength that includes standard deviation, based on the requirements of concrete mix design specifications and the relationship between the guarantee rate and probability coefficient. Formula ② was derived through statistical analysis and regression fitting, based on a summary of experimental results and the influence of admixtures on concrete properties. Formula ③ considers the correlation between concrete compressive strength and water-binder ratio, the influence of admixtures on concrete properties, and, after summarizing numerous experimental results, takes into account the guarantee rate and data fluctuations, resulting in a statistical fit.

[0078] (2) Calculate the compressive strength f of the concrete based on the fiber elastic modulus, fiber deformation capacity, fiber length, fiber diameter of the polymer fiber and the calculated value in step (1) c The polymer fiber content was calculated according to the following formula:

[0079]

[0080]

[0081] In the above formula: f t is the tensile strength of concrete, MPa; C F is the polymer fiber content, kg / m 3 ;

[0082] l is the length of the fiber, mm; d is the diameter of the fiber, μm; ρ F is the density of the fiber, kg / m 3 ;

[0083] E F is the elastic modulus of the fiber, GPa; ε F is the deformation capacity of the fiber, %;

[0084] Concrete is a typical heterogeneous, multi-scale, multi-phase composite material. Its performance indicators lack accurate physical models and mathematical derivations. Therefore, analysis often draws on methods from disciplines such as material mechanics, engineering mechanics, and elastoplasticity, combined with statistical laws. Formula ④ above is derived through numerical analysis and regression modeling, based on experimental data on concrete's splitting tensile and compressive strengths, combined with formulas derived from elastic mechanics, and taking into account the requirements for engineering application convenience and allowable deviations. Formula ⑤ assumes uniform fiber distribution within the concrete and good contact between the fibers and the hardened cement paste. It was derived through theoretical derivation and statistical analysis based on the principles of material mechanics, as well as the force characteristics and pullout patterns of fibers during concrete cracking.

[0085] (3) Calculate the water consumption m according to the following formula based on the slump of concrete, the water reduction rate of the water reducer, and the fineness modulus of the fine aggregate: W And sand rate s:

[0086]

[0087]

[0088] In the above formula: T is the slump of concrete, mm; m w is the water consumption, kg / m 3 ;

[0089] q is the water reducing rate of the water reducing agent, %; s is the concrete sand ratio, %; FM is the fineness modulus of the fine aggregate;

[0090] Slump is a key indicator of concrete flow properties, and water content and sand ratio have a significant impact on concrete slump. Using the discrete element method and rheological theory, concrete slump can be effectively predicted. Formula ⑥ was derived through statistical analysis and regression fitting based on a slump prediction model, combining laboratory and field measurement data with ease of use. Formula ⑦ was derived through statistical analysis and data fitting, taking into account factors such as the thickness of the water film on the sand surface, the dispersion properties of the mortar, and the relationship between the sand fineness modulus and water content.

[0091] (4) Based on the density of cement, admixtures, fine aggregate, and coarse aggregate in concrete and the water consumption m calculated in step (3) w , calculate the amount of each raw material in unit volume of concrete:

[0092]

[0093]

[0094]

[0095]

[0096] In the above formula: m c is the amount of cement, kg / m 3 ;m m is the amount of admixture, kg / m 3 ;

[0097] m s is the amount of fine aggregate, kg / m 3 ;m g is the amount of coarse aggregate, kg / m 3 ; s is the sand ratio of concrete, %;

[0098] ρ c is the density of cement in raw materials, kg / m 3 ρ m is the density of the admixture in the raw materials, kg / m 3 ;

[0099] ρ s is the density of fine aggregate in raw materials, kg / m 3 ρ g is the density of coarse aggregate in raw materials, kg / m 3 ;

[0100] Formula⑧~ The absolute volume method is used to calculate the amount of raw materials for concrete, which is obtained through mathematical deduction based on the calculation results of the above-mentioned water consumption, sand ratio, water-cement ratio, and admixture dosage. The concrete material ratio calculation method mainly includes the assumed mass method and the absolute volume method. The assumed mass method mainly assumes the density of fresh concrete and then calculates the amount of each raw material, but it has shortcomings such as large error in the results and the need for later correction. The absolute volume method calculates the response volume based on the density of each raw material and keeps the total volume of concrete constant. In practical applications, the assumed mass method is simple, but has large errors; while the absolute volume method is complex, but the results are accurate. Therefore, this application uses the absolute volume method to calculate the concrete ratio.

[0101] (5) According to the dosage of water reducer in concrete j , the amount of air entraining agent C y The amount of water reducer and air entraining agent can be calculated based on the concrete water-binder ratio w / b according to the following formula:

[0102]

[0103]

[0104] In the above formula: m j is the dosage of concrete water reducing agent, kg / m 3 ;m y is the dosage of concrete air entraining agent, kg / m3 ;

[0105] C j is the dosage of concrete water reducing agent, %; C y is the dosage of concrete air-entraining agent, %.

[0106] The above formula and This model formula is mathematically derived based on the definitions of water-reducing agent and air-entraining agent dosages. Both the water-reducing agent and air-entraining agent dosages are preferred values ​​within a typical range, based on engineering experience and the state of the concrete mix. This application imposes restrictions on the water-reducing agent and air-entraining agent dosage ranges, taking into account factors such as the method's calculation performance and general engineering conditions.

[0107] The fine aggregate in the above embodiment is artificial sand with a fineness modulus FM of 2.3 to 2.8; the coarse aggregate is artificial crushed stone, which is made by mixing two types of stones with particle sizes of (5-20) mm and (20-40) mm in a mass ratio, and the mixing ratio range is m 5-20 :m 20-40 =1.00~1.22; the design strength grades of the concrete are C15, C20, C25, C30, C35, C40, C45, C50 and C55, and the corresponding nominal compressive strength values ​​are 15MPa, 20MPa, 25MPa, 30MPa, 35MPa, 40MPa, 45MPa, 50MPa and 55MPa, respectively; the compressive strength guarantee rate of the concrete is in the range of 70%~97.7%; the cement is Portland cement, including ordinary Portland (codenamed PO) cement, medium heat Portland (codenamed PMH) cement and low heat Portland (codenamed PLH) cement, and the corresponding cement type correction coefficients γ2 are PO cement γ2 and γ2 respectively. =1.0, PMH cement γ2=0.98, PLH cement γ2=0.95; the water reducer is polycarboxylate water reducer (codename PCA) or naphthalene water reducer (codename SNF), and the water reducer dosage is 0.6% to 1.0%; the air entraining agent dosage is 0.008% to 0.012%; the fiber is an organic high molecular polymer fiber, including polypropylene fiber (codename PP), polyacrylonitrile fiber (codename PAN), polyvinyl alcohol fiber (codename PVA) and polyoxymethylene fiber (codename POM); the admixture is Class F fly ash, including Class I fly ash and Class II fly ash, the fly ash dosage is by mass, and the incorporation method is to replace part of the cement by equal mass, and the dosage range is 0 to 50%.

[0108] The effects of the present invention will be further described below with reference to specific embodiments.

[0109] Example 1: For crack-resistant concrete in a project in Shannan City, Tibet Autonomous Region, the design strength grade fc,k is C25, the nominal compressive strength is 25 MPa, the compressive strength guarantee rate is 70%, and the slump is 140 ± 10 mm. Experts recommend a technical solution without adding fly ash. The properties and technical indicators of the raw materials are as follows:

[0110] ① Concrete is made of ordinary silicate (PO), and the cement density is 3.06×10 3 kg / m 3 ;

[0111] ②Use artificial sand as fine aggregate, with fineness modulus FM of 2.3 and density ρ s 2.68×10 3 kg / m 3 ;

[0112] ③Use artificial crushed stone as coarse aggregate, the coarse aggregate is composed of two sizes of stones (5-20) mm and (20-40) mm, and the composition ratio is m 5-20 :m 20-40 =1.00, density ρ g 2.71×10 3 kg / m 3 ;

[0113] ④Use polycarboxylate water reducer (PCA), dosage C j is 0.6%, and the water reduction rate q is 28.5%;

[0114] ⑤ The dosage of air entraining agent C y 0.008%;

[0115] ⑥ The fiber used is polypropylene fiber (PP), with a length l of 6 mm, a diameter d of 40 μm, and an elastic modulus E F is 3.8GPa, and the deformation capacity ε F The density is 930kg / m 3 ;

[0116] According to the technical requirements of concrete and the test results of raw material properties, the compressive strength f is calculated according to the above formula. c is 27.3MPa, the admixture influence coefficient γ1 is 1.20, the cement type influence coefficient γ2 is 1.00, the calculated water-binder ratio w / b is 0.66, and the corresponding tensile strength f t is 2.38MPa, fiber content C F 24.7kg / m 3 , water consumption m w 118kg / m 3 , cement consumption m c 179kg / m3 , admixture dosage m m 0g / m 3 , sand rate s is 38%, artificial sand dosage m s 806kg / m 3 , the amount of crushed stone m g 1323kg / m 3 , of which (5-20) mm stone dosage m 5-20 661kg / m 3 , (20-40) mm stone dosage m 20-40 661kg / m 3 , water reducing agent dosage m j 1.073kg / m 3 , air entraining agent dosage m g 0.014kg / m 3 .

[0117] The amounts of various raw materials used in the concrete in Example 1 were calculated and shown in Table 1:

[0118] Table 1 Amount of raw materials used in concrete for a certain project in Tibet (kg / m 3 )

[0119] water cement fly ash fiber Artificial sand Pebbles water reducer air-entraining agent 118 179 / 24.7 805 1323 1.073 0.014

[0120] Concrete specimen A was prepared according to the formula in Table 1. The compressive strength of concrete specimen A at 28 days was tested. The compressive strength of concrete specimen A at 28 days was 28.4 MPa. The crack resistance of concrete specimen A was tested by flat plate method. The test results are as follows: Figure 1 As shown, the test results show that the crack resistance grade of concrete is Grade I.

[0121] Example 2 is for a certain project in Fukang City, Xinjiang, with a design strength grade of anti-cracking concrete. c,k The material is C35, with a nominal compressive strength of 35 MPa, a compressive strength guarantee rate of 85%, and a slump of 130 ± 10 mm. Experts recommend the use of Class F, Grade I fly ash. The performance and technical indicators of the raw materials are as follows:

[0122] ① Concrete was prepared using moderately hot silicate (PMH) with a cement density of 3.12×10 3 kg / m 3 , the influence coefficient of cement type is 0.98;

[0123] ②Use artificial sand as fine aggregate, with fineness modulus FM of 2.6 and density ρ s 2.66×10 3 kg / m 3 ;

[0124] ③Use artificial crushed stone as coarse aggregate, the coarse aggregate is composed of two sizes of stones (5-20) mm and (20-40) mm, and the composition ratio is m 5-20 :m 20-40 =1.10, density ρ g 2.69×10 3 kg / m 3 ;

[0125] ④Use polycarboxylate water reducer (PCA), dosage C j is 0.8%, and the water reduction rate q is 27%;

[0126] ⑤ The dosage of air entraining agent C y 0.01%;

[0127] ⑥ Use Class F Grade I fly ash with an activity index of 85% and a fly ash content of 20%;

[0128] ⑦ The fiber used is polyvinyl alcohol (PVA) fiber with a length of 8 mm, a diameter of 35 μm, and an elastic modulus of E F is 5.4GPa, and the deformation capacity ε F The carbon content is 31% and the density is 980kg / m 3 ;

[0129] According to the technical requirements of concrete and the test results of raw material properties, the compressive strength f is calculated according to the above method. c The admixture influence coefficient γ1 is 0.89, the cement type influence coefficient γ2 is 0.98, the calculated water-binder ratio w / b is 0.40, and the corresponding tensile strength f t is 2.90MPa, fiber content C F 16.8kg / m 3 , water consumption m w 116kg / m 3 , cement consumption m c 230kg / m 3 , admixture dosage m m 57kg / m 3 , sand rate s is 33%, artificial sand dosage m s 656kg / m 3 , the amount of crushed stone m g 1353kg / m 3 , of which (5-20) mm stone dosage m 5-20 644kg / m 3 , (20-40) mm stone dosage m 20-40 708kg / m 3 , water reducing agent dosage m j2.297kg / m 3 , air entraining agent dosage m g 0.023kg / m 3 .

[0130] The amounts of various raw materials used in the concrete in Example 2 were calculated and shown in Table 2:

[0131] Table 2 Amount of raw materials used in concrete for a certain project in Xinjiang (kg / m 3 )

[0132] water cement fly ash fiber Artificial sand Pebbles water reducer air-entraining agent 116 230 57 16.8 656 1353 2.297 0.023

[0133] Concrete specimen B was prepared according to the formula in Table 2. The compressive strength of concrete specimen B at 28 days was tested. The compressive strength of concrete specimen B at 28 days was 41.9 MPa. The crack resistance of concrete specimen B was tested by flat plate method. The test results are as follows: Figure 2 As shown, the test results show that the crack resistance grade of concrete is Grade I.

[0134] Example 3: For a crack-resistant concrete project in Yueyang City, Hunan Province, the design strength grade fc,k is C45, the nominal compressive strength value is 45 MPa, the compressive strength guarantee rate is 90%, and the slump is 160±10 mm. The performance and technical indicators of the raw materials are as follows:

[0135] ① Concrete is made of ordinary silicate (PO), and the cement density is 3.09×10 3 kg / m 3 , the cement type influence coefficient is 1.0;

[0136] ②Use artificial sand as fine aggregate, with fineness modulus FM of 2.7 and density ρ s 2.65×10 3 kg / m 3 ;

[0137] ③Use artificial crushed stone as coarse aggregate, the coarse aggregate is composed of two sizes of stones (5-20) mm and (20-40) mm, and the composition ratio is m 5-20 :m 20-40 =1.22, density ρ g 2.73×10 3 kg / m 3 ;

[0138] ④Use polycarboxylate water reducer (PCA), dosage C j is 1.0%, and the water reduction rate q is 26.5%;

[0139] ⑤ The dosage of air entraining agent C y 0.009%;

[0140] ⑥ Use F-class II fly ash, activity index is 75%, fly ash content is 10%, density ρ m 2.19×10 3 kg / m 3 ;

[0141] ⑦ The fiber used is polyacrylonitrile (PAN) fiber with a length of 10 mm, a diameter of 42 μm, and an elastic modulus of E F is 4.8GPa, and the deformation capacity ε F The density is 26% and the density is 1340kg / m 3 ;

[0142] According to the technical requirements of concrete and the test results of raw material properties, the compressive strength f is calculated according to the above method. c is 52.2MPa, the admixture influence coefficient γ1 is 0.87, the cement type influence coefficient γ2 is 1.00, the calculated water-binder ratio w / b is 0.33, and the corresponding tensile strength f t is 3.24MPa, fiber content C F 32.6kg / m 3 , water consumption m w 130kg / m 3 , cement consumption m c 356kg / m 3 , admixture dosage m m 40kg / m 3 , sand rate s is 31%, artificial sand dosage m s 572kg / m 3 , the amount of crushed stone m g 1327kg / m 3 , of which (5-20) mm stone dosage m 5-20 598kg / m 3 , (20-40) mm stone dosage m 20-40 729kg / m 3 , water reducing agent dosage m j 3.959kg / m 3 , air entraining agent dosage m g 0.032kg / m 3 The amounts of the raw materials used in the concrete in Example 3 were calculated and shown in Table 3:

[0143] Table 3 Amount of raw materials used in concrete for a project in Yueyang, Hunan (kg / m 3 )

[0144] water cement fly ash fiber Artificial sand Pebbles water reducer air-entraining agent 130 356 40 32.6 572 1327 3.959 0.032

[0145] Concrete specimen C was prepared according to the formula in Table 3. The compressive strength of the concrete specimen C at 28 days was tested. The compressive strength of the concrete specimen C at 28 days was 54.6 MPa. The flat plate method was used to test the crack resistance of the concrete specimen C. The test results are as follows: Figure 3 As shown, the test results show that the crack resistance grade of concrete is Grade I.

[0146] Example 4 is for a certain project in Chengde, Hebei Province, with a design strength grade of anti-cracking concrete. c,k C55, with a nominal compressive strength of 55 MPa, a compressive strength guarantee rate of 97.7%, and a slump of 160 ± 10 mm. Experts recommend not using fly ash. The performance and technical indicators of the raw materials used are as follows:

[0147] ① Concrete is prepared using low heat silicate (PLH) with a cement density of 3.15×10 3 kg / m 3 , the influence coefficient of cement type is 0.95;

[0148] ②Use artificial sand as fine aggregate, with fineness modulus FM of 2.8 and density ρ s 2.69×10 3 kg / m 3 ;

[0149] ③Use artificial crushed stone as coarse aggregate, the coarse aggregate is composed of two sizes of stones (5-20) mm and (20-40) mm, and the composition ratio is m 5-20 :m 20-40 =1.22, density ρ g 2.72×10 3 kg / m 3 ;

[0150] ④Use polycarboxylate water reducer (PCA), dosage C j is 0.9%, and the water reduction rate q is 27.5%;

[0151] ⑤ The dosage of air entraining agent C y 0.008%;

[0152] ⑥ The fiber used is polyoxymethylene (POM) fiber with a length l of 12 mm, a diameter d of 43 μm, and an elastic modulus E F is 5.6GPa, and the deformation capacity ε F The density is 24% and 1510kg / m 3 ;

[0153] According to the technical requirements of concrete and the test results of raw material properties, the compressive strength f is calculated. cis 66.4MPa, the admixture influence coefficient γ1 is 1.20, the cement type influence coefficient γ2 is 0.95, the calculated water-binder ratio w / b is 0.33, and the corresponding tensile strength f t is 3.49MPa, fiber content C F 33.2kg / m 3 , water consumption m w 128kg / m 3 , cement consumption m c 383kg / m 3 , admixture dosage m m 0kg / m 3 , sand rate s is 31%, artificial sand dosage m s 605kg / m 3 , the amount of crushed stone m g 1334kg / m 3 , of which (5-20) mm stone dosage m 5-20 601kg / m 3 , (20-40) mm stone dosage m 20-40 733kg / m 3 , water reducing agent dosage m j 3.450kg / m 3 , air entraining agent dosage m g 0.031kg / m 3 .

[0154] The amounts of various raw materials used in the concrete in Example 4 were calculated and are shown in Table 4.

[0155] Table 4 Amount of raw materials used in concrete for a project in Chengde, Hebei Province (kg / m 3 )

[0156] water cement fly ash fiber Artificial sand Pebbles water reducer air-entraining agent 128 383 / 33.2 605 1334 3.450 0.031

[0157] Concrete specimen D was prepared according to the formula in Table 4. The compressive strength of the concrete specimen D at 28 days was tested. The compressive strength of the concrete specimen D at 28 days was 56.2 MPa. The crack resistance of the concrete specimen D was tested by the flat plate method. The test results are as follows: Figure 4 As shown, the test results show that the crack resistance grade of concrete is Grade I.

Claims

1. A method for designing high crack-resistant concrete mix ratio based on multi-scale relationships, characterized in that The concrete is prepared from water, cement, admixtures, fine aggregate, coarse aggregate, water reducer, air entraining agent and polymer fiber; the amount of each raw material added to the concrete is calculated according to the following steps: (1) Based on the design strength grade of concrete, admixture type, activity characteristics and cement type, the recommended water-cement ratio of concrete is calculated as follows: In the above formula: f c,k is the characteristic value of compressive strength corresponding to the concrete strength grade, MPa; f c is the calculated compressive strength of concrete, MPa; e is a natural number, e = 2.718; p is the compressive strength guarantee rate of concrete, %; C m is the admixture dosage, %; H m is the activity index of the admixture’s 28d compressive strength, %, and the pure cement system is 1.0; γ1 is the influence coefficient of admixture dosage; γ2 is the influence coefficient of cement type; w / b is the recommended water-binder ratio of concrete; int() is a rounding function, which only retains the integer digits of the calculation result and discards the decimal part of the calculation result; (2) Calculate the compressive strength f of the concrete based on the fiber elastic modulus, fiber deformation capacity, fiber length, fiber diameter of the polymer fiber and the calculated value in step (1) c The polymer fiber content was calculated according to the following formula: In the above formula: f t is the tensile strength of concrete, MPa; C F is the polymer fiber content, kg / m 3 ; l is the length of the fiber, mm; d is the diameter of the fiber, μm; ρ F is the density of the fiber, kg / m 3 ; E F is the elastic modulus of the fiber, GPa; ε F is the deformation capacity of the fiber, %; (3) Calculate the water consumption m according to the following formula based on the slump of concrete, the water reduction rate of the water reducer, and the fineness modulus of the fine aggregate: W And sand rate s: In the above formula: T is the slump of concrete, mm; m w is the water consumption, kg / m 3 ; q is the water reducing rate of the water reducing agent, %; s is the concrete sand ratio, %; FM is the fineness modulus of the fine aggregate; (4) Based on the density of cement, admixtures, fine aggregate, and coarse aggregate in concrete and the water consumption m calculated in step (3) w , calculate the amount of each raw material in unit volume of concrete: In the above formula: m c is the amount of cement, kg / m 3 ; m m is the amount of admixture, kg / m 3 ; m s is the amount of fine aggregate, kg / m 3 ; m g is the amount of coarse aggregate, kg / m 3 ; s is the sand ratio of concrete, %; ρ c is the density of cement in raw materials, kg / m 3 ; ρ m is the density of the admixture in the raw materials, kg / m 3 ; ρ s is the density of fine aggregate in raw materials, kg / m 3 ; ρ g is the density of coarse aggregate in raw materials, kg / m 3 ; (5) According to the dosage of water reducer in concrete C j , the amount of air entraining agent C y The dosage of water reducer and air entraining agent can be calculated according to the following formula based on the water-binder ratio of concrete: In the above formula: m j is the dosage of concrete water reducing agent, kg / m 3 ;m y is the dosage of concrete air entraining agent, kg / m 3 ; C j is the dosage of concrete water reducing agent, %; C y is the dosage of concrete air-entraining agent, %.

2. The method for designing a high crack-resistant concrete mix ratio based on a multi-scale relationship according to claim 1, wherein: The fine aggregate is artificial sand with a fineness modulus FM of 2.3 to 2.8; the coarse aggregate is artificial crushed stone, which is made by mixing two types of stones with a particle size of 5 to 20 mm and a particle size of 20 to 40 mm in a mass ratio. 5-20 :m 20-40 =1.00~1.

22.

3. The method for designing a high crack-resistant concrete mix ratio based on a multi-scale relationship according to claim 1, wherein: The design strength grades of the concrete are C15, C20, C25, C30, C35, C40, C45, C50 and C55, and the corresponding nominal compressive strength values ​​are 15MPa, 20MPa, 25MPa, 30MPa, 35MPa, 40MPa, 45MPa, 50MPa and 55MPa, respectively.

4. The method for designing a high crack-resistant concrete mix ratio based on a multi-scale relationship according to claim 1, wherein: The compressive strength guarantee rate of the concrete is in the range of 70% to 97.7%.

5. The method for designing a high crack-resistant concrete mix ratio based on a multi-scale relationship according to claim 1, wherein: The cement is silicate cement, including ordinary silicate cement, medium-heat silicate cement and low-heat silicate cement. The corresponding cement type correction coefficients γ2 are γ2=1.0 for ordinary silicate cement, γ2=0.98 for medium-heat silicate cement, and γ2=0.95 for low-heat silicate cement.

6. The method for designing a high crack-resistant concrete mix ratio based on a multi-scale relationship according to claim 1, wherein: The water reducer is a polycarboxylic acid water reducer or a naphthalene water reducer, and the dosage of the water reducer is 0.6% to 1.0%.

7. The method for designing a high crack-resistant concrete mix ratio based on a multi-scale relationship according to claim 1, wherein: The dosage of the air entraining agent is 0.008% to 0.012%.

8. The method for designing a high crack-resistant concrete mix ratio based on a multi-scale relationship according to claim 1, wherein: The polymer fibers are organic high molecular polymer fibers, including polypropylene fibers, polyacrylonitrile fibers, polyvinyl alcohol fibers and polyoxymethylene fibers.

9. The method for designing a high crack-resistant concrete mix ratio based on a multi-scale relationship according to claim 1, wherein: The admixture is F-type fly ash, including Class I fly ash and Class II fly ash. The fly ash dosage is mass dosage, and the addition method is to replace part of the cement with equal mass. The dosage range is 0-50%.

Images