A secondary design method for mix proportion of hybrid steel fiber self-compacting concrete based on solid phase surface filling layer customization

Abstract

This invention discloses a secondary design method for the mix proportion of hybrid steel fiber self-compacting concrete based on a customized solid-phase surface filling layer. Starting with a basic mix proportion of fiberless self-compacting concrete, steel fibers are introduced, and a secondary mix proportion design is performed using a secondary design envelope curve to obtain the final mix proportion of the steel fiber self-compacting concrete. This design method can encompass material variations such as different fiber diameters and aggregate systems, and can achieve the mixed incorporation of fibers. This reduces fluctuations in the workability of the mixture caused by material and fiber content, significantly improves stability, optimizes the workability control of fresh self-compacting concrete, greatly reduces the number of mix proportion adjustments, and enables rapid mixing of self-compacting fiber concrete. It provides guidance for the application of fiber concrete and the targeted customization of mix proportions in practical engineering.

Description

Technical Field

[0001] This invention relates to the field of building materials technology, and in particular to a secondary design method for the mix proportion of hybrid steel fiber self-compacting concrete based on a customized solid-phase surface filling layer. Background Technology

[0002] The concept of self-compacting concrete was first proposed by Professor H. Okamura in 1986. By fixing the aggregate volume, adjusting the water-cement ratio and admixture content, and combining rheological experiments, self-compacting concrete that meets rheological properties can be prepared without the need for further mixing. Currently, the mix design of self-compacting concrete has formed five classic mix proportioning theories: 1) empirical mix proportioning methods through mix proportioning parameter adjustments and workability tests; 2) mix proportioning design methods based on compressive strength and recommended mix proportioning ranges; 3) mix proportioning design methods based on aggregate particle filling rate theory and filling density; 4) statistical analysis models based on experimental data; and 5) slurry rheological models based on excess slurry properties and thickness. At the level of specifications and guidelines, these theories mostly provide empirical mix proportioning reference ranges for self-compacting concrete mix proportions.

[0003] Concrete reinforced solely with sand and gravel aggregates / self-compacting concrete lacks sufficient toughness and is prone to brittle fracture and cracking under tensile loads, especially in prefabricated underground structures. At stress concentration points such as joints and corners, it is highly susceptible to breakage and cracking, leading to a significant decline in structural durability. To address this issue, fibers can be added to the concrete to enhance the matrix toughness and improve the crack resistance of the concrete structure. While adding fibers allows for slight adjustments to the coarse aggregate content in traditional vibrated concrete to meet workability requirements, achieving self-compacting properties demands extremely high levels of filling capacity, stability, and gap-passing ability. Fiber incorporation degrades the particle size distribution of the skeleton, significantly reducing the workability of the fresh concrete mixture. Therefore, when preparing fiber-reinforced self-compacting concrete, the original mix proportions must be significantly adjusted to meet workability requirements. However, there are currently no standardized mix design guidelines or recommendations for fiber-reinforced concrete, lacking a reliable reference. In early research, the mix proportions of self-compacting steel fiber concrete were mostly determined through empirical trial mixing. For example, Grünewald introduced concepts and findings from previous research, such as "fiber disturbance volume," "equivalent fiber particle diameter," and "maximum fiber content," to adjust the aggregate particle size distribution of self-compacting fiber concrete and control the maximum fiber content. He then compared and screened about ten different mix proportions using testing methods to obtain a self-compacting fiber concrete mix proportion that met workability requirements. Jen proposed a three-step empirical design method for fiber-reinforced self-compacting concrete: the basic mix proportion uses high-flow self-compacting concrete with a slump flow spread of approximately 700 mm; the sand ratio and mortar volume are increased to mitigate the decrease in filling performance caused by fiber incorporation; and the admixture configuration is optimized to further enhance filling performance. However, these methods typically involve analysis of specific materials and require extensive prior experimental research to determine relevant parameters and mix proportions. They cannot be directly applied when adjusting fiber content and fiber type, making their widespread application in practical engineering challenging.

[0004] Thanks to a deeper understanding of the rheological properties of self-compacting concrete mixtures and the development of mix design methods based on slurry rheology, researchers have gradually incorporated self-compacting fiber-reinforced concrete into this mix design system. Ferrara, through the specific surface area equivalence method, treated steel fibers as spherical aggregates of equal area and proposed a method for calculating the equivalent particle size of fibers, incorporating it into aggregate particle size distribution, thus expanding the method for calculating the minimum slurry thickness in self-compacting concrete based on slurry rheology models. However, this method is only applicable to the preparation of self-compacting concrete with coarse steel fibers, and its effectiveness is poor for fiber proportions such as fine steel fibers, which greatly affect the rheological properties of mortar. Professor Khayat proposed a method for adjusting the mix proportion of self-compacting concrete after fiber incorporation, namely reducing the volume of coarse aggregate and increasing the volume of mortar, while filling the voids between fibers and aggregates and maintaining the same mortar film thickness between fibers and aggregates to maintain the rheological properties of the mixture after fiber incorporation. However, this method can lead to an excessive increase in the sand ratio when using fibers with a large specific surface area, affecting the final strength and shrinkage properties of concrete. He Xiaobing et al. proposed a secondary mix design method for microfiber self-compacting concrete. By analyzing the surface area of ​​the microfibers and the corresponding paste thickness requirements, they calculated the required increase in paste volume and adjusted the self-compacting mix proportion of the foundation. This method has some feasibility, but it is essentially a preparation method that increases paste volume and reduces the overall aggregate volume. Although it can provide better rheological properties, when the paste thickness is large, the consistency of the mortar mixture becomes very low. The fresh concrete will be very sensitive to the dosage of water and water-reducing agent, and segregation is very likely to occur. The reduction in the overall aggregate volume will also exacerbate drying shrinkage.

[0005] Therefore, due to the demand for self-compacting / steel fiber reinforced concrete, scholars both domestically and internationally have conducted extensive research on its mix design. Early empirical mix design methods and more recent slurry rheological model design systems have demonstrated practical feasibility and specific applicability. However, for hybrid steel fiber self-compacting concrete containing both fine and coarse steel fibers, the effects of these two types on the rheological properties of the concrete mixture differ significantly. Currently, there is no mix design method that can simultaneously apply to both. Furthermore, using empirical mix design methods to adjust the fiber content ratio for different performance requirements necessitates a massive amount of experimentation and is difficult to apply simply. Summary of the Invention

[0006] To address the problems existing in the prior art, the purpose of this invention is to provide a secondary design method for the mix proportion of hybrid steel fiber self-compacting concrete based on a customized solid-phase surface filling layer. Building upon the basic mix proportion, a secondary mix proportion design is performed using a secondary design envelope curve. This overcomes the performance fluctuations of fiber self-compacting concrete with different material ratios and fiber content, optimizes the workability of fresh self-compacting concrete, and achieves a scientific and quantitative design of the material mix proportion. This provides guidance for the customized mix design of self-compacting fiber concrete.

[0007] To address the aforementioned technical problems, this invention provides a secondary design method for the mix proportion of hybrid steel fiber self-compacting concrete based on a customized solid-phase surface filling layer. The method includes the following steps: 1) Obtaining the performance parameters of the raw materials and determining the mix proportion parameters of the fiberless self-compacting concrete foundation; 2) Calculating the fiberless self-compacting concrete surface filling layer using experimental testing and / or a compressible filling model; 3) Introducing the voids in the steel fiber and aggregate mixture to plot the secondary design envelope curve of the steel fiber self-compacting concrete solid-phase surface filling layer; 4) Performing secondary mix proportion calculations and adjustments based on the secondary design envelope curve process.

[0008] This invention enables precise calculation of the proportions of fiber-reinforced concrete mixtures by progressively calculating and customizing the excess layer thickness on the surface of the solid phase material in fiberless self-compacting concrete and steel fiber self-compacting concrete. Simultaneously, the configuration range that meets the performance requirements can be determined by the quadratic design curve, thereby achieving accurate customization of the performance of steel fiber self-compacting concrete.

[0009] As a preferred embodiment, the raw materials include: steel fibers, aggregates, cement, fly ash, slag, silica fume, admixtures, and water; the performance parameters of the raw materials include: apparent density ρ of coarse aggregates. ca Bulk density of coarse aggregate ρ′ ca Coarse aggregate system filling rate PD ca PD of fine aggregate system fa Porosity P of coarse aggregate system void-ca Porosity P of fine aggregate system void-fa Apparent density ρ of fine aggregate fa Bulk density of fine aggregate ρ′ fa Coarse aggregate gradation parameters, fine aggregate gradation parameters, coarse aggregate morphology parameters, fine aggregate morphology parameters, and steel fiber density ρ. f morphological parameters of steel fibers, apparent density of cement ρ ce Apparent density ρ of fly ash fla Apparent density ρ of slag slag Apparent density ρ of silica fume si The density of water ρ w Density ρ after preparation with admixtures spThe raw materials used in this invention can be divided into two parts: one part is a solid material composed of steel fibers and aggregates, and the other part is a liquid slurry composed of fly ash, slag, silica fume and other powders and water. Dividing the raw materials into two parts is to minimize the variable parameters of the raw materials and facilitate calculation.

[0010] For coarse aggregates with continuous gradation, after sieving to obtain the target particle size range, the proportion of each single particle size range can be directly tested. For filling rate calculation, a filling rate testing cylinder with an inner diameter of 200 mm and a height of 320 mm is used to test various performance parameters of the coarse aggregate in a loosely packed state. For coarse aggregate skeleton systems with multiple particle size ranges, after setting the volume proportions of the gradation ranges, the filling rate and porosity parameters of the aggregate combination can be determined using the same experimental method as described above, and the volume proportion with the lowest porosity is selected as the actual coarse aggregate mixing ratio. If there are many aggregate particle size ranges, to reduce the amount of experimentation, the loose filling rate α of the coarse aggregate in each single particle size range can be tested first. i Furthermore, a compressible filling model is used to approximate the filling rate under different coarse aggregate size ranges, and the ratio that simultaneously satisfies economy and filling rate can be optimized based on site conditions.

[0011] As a preferred embodiment, the coarse aggregate system has a filling rate PD ca And the porosity P of the coarse aggregate system void-ca The calculation process is as follows:

[0012] Formula 1:

[0013] Formula 2:

[0014] Formula 3: P void-ca =1-PD ca .

[0015] For the filling rate of fine aggregate, fine PD fa and fine aggregate skeleton porosity P void-fa The same filling rate test cylinder with an inner diameter of 200 mm and a height of 320 mm was used, and the testing and calculation methods were the same as those for coarse aggregate filling rate testing.

[0016] As a preferred embodiment, the fine aggregate filling rate PD fa Porosity P of fine aggregate skeleton system void-fa The calculation process is as follows:

[0017] Formula 4:

[0018] Formula 5:

[0019] Formula 6: P void-fa=1-PD fa

[0020] In equations 1 to 6: ρ′ ca The bulk density of coarse aggregate is expressed in kg / m³. 3 W ca This refers to the weight of coarse aggregate, in kg; PD ca Vol represents the coarse aggregate filling rate, dimensionless. C The volume of the container used for the test is measured in meters (m). 3 ; Vol ca To measure the absolute volume of coarse aggregate after the container is filled, the dimension is m. 3 ;P void-ca W represents the porosity of the coarse aggregate skeleton system, dimensionless. fa This refers to the weight of coarse aggregate, in kg; PD fa Vol represents the coarse aggregate filling rate, dimensionless. C The volume of the container used for the test is measured in meters (m). 3 ;Vol ca Let m be the absolute volume of the aggregate in the container, with dimensions in meters. 3 ;P void-fa The porosity of the framework system is dimensionless.

[0021] The calculation process for the coarse aggregate gradation parameters is as follows: the coarse aggregate with a particle size greater than 5 mm is divided into 2 to 3 intervals, and the volume percentage h of each particle size interval is determined. i , is used to represent the gradation distribution of coarse aggregate.

[0022] As a preferred embodiment, the calculation process for the fine aggregate gradation parameters is as follows: Aggregates with a diameter of 0.08–5 mm are divided into 6 intervals, and the cumulative sieve residue rate of each interval is calculated, i.e., the particle size is D. i The percentage of particles passing through is denoted as p. i And the average value is taken repeatedly, where p i Fitting was performed using the Funk-Dinger formula:

[0023] Formula 7:

[0024] In Equation 7: p i D represents the cumulative sieve residue rate for each interval, expressed as a percentage (%). min D represents the smallest particle size in fine aggregate, with dimensions in meters. max is the largest particle size in the fine aggregate, with dimensions in meters; q is the gradation index to be fitted, dimensionless; D i Let D be the sieve aperture size within particle size range i. In this invention, for fine aggregates, D... min Take the minimum sieve particle size as 0.075 mm, D maxThe maximum screening particle size is 5.0 mm; for coarse aggregate, D min and D max These represent the upper and lower limits of the particle size, respectively; different gradations of aggregates, after fitting the gradation range, will yield different gradation indices.

[0025] As a preferred embodiment, the calculation process for the coarse aggregate morphology parameters and the fine aggregate morphology parameters is as follows:

[0026] ① The size ratio is calculated using the Heywood particle theory. The calculation process is as follows:

[0027] Formula 8:

[0028] Formula 9:

[0029] Formula 10:

[0030] ② The specific surface area of ​​coarse aggregate is calculated using the discrete method. The calculation process is as follows:

[0031] Formula 11:

[0032] ③ The specific surface area of ​​fine aggregate is calculated using the continuous method. The calculation process is as follows:

[0033] Formula 12:

[0034] In Equations 8-12: L is the aggregate length, in meters (m); B is the aggregate width, in meters (m); T is the aggregate thickness, in meters (m); m and n are projection dimension scaling factors, dimensionless; d p s is the magnification factor of the projected diameter relative to the sieve diameter, dimensionless; ca ρ is the specific surface area of ​​coarse aggregate, with dimensions in m. -1 f is the shape area coefficient, dimensionless; k is the shape volume coefficient, dimensionless; h i The percentage of each particle size range is dimensionless; D i p represents the sieve aperture size within the particle size range i, with dimensions in meters. i s represents the cumulative sieve residue rate for each interval, expressed as a percentage (%). fa The specific surface area of ​​the fine aggregate is given by the unit m. -1 .

[0035] As a preferred embodiment, the morphological parameters of the steel fiber include: fiber length, fiber diameter, and fiber specific surface area. The fiber length and fiber diameter are obtained through measurement, and the fiber specific surface area is calculated as follows:

[0036] Formula 13:

[0037] In Equation 13: s f The specific surface area of ​​steel fibers is expressed in m. -1 ;d f The diameter of the fiber is in meters. -1 .

[0038] As a preferred embodiment, the mix proportion parameters of the fiberless self-compacting concrete foundation include: the absolute volume V of the coarse aggregate. ca and mass m ca The absolute volume V of fine aggregate fa and mass m fa The volume V of the slurry lp The weight of the cementitious material, m b The weight of cement, m ce The weight of fly ash, m fla The weight m of granulated blast furnace slag slag The weight of silica fume m si The weight of water, m w .

[0039] As a preferred embodiment, the calculation of the fiberless self-compacting fiber-reinforced concrete aggregate surface filling layer includes: calculating the porosity P of the aggregate mixture. void-a , aggregate mixture pore volume U void-a Thickness t of excess sand layer filling layer on coarse aggregate surface s The thickness t of the excess slurry filler layer on the surface of the coarse and fine aggregate mixture p .

[0040] As a preferred option,

[0041] The aggregate mixture has voids P void-a The CPM model with interaction correction is used for calculation;

[0042] The thickness t of the excess sand filling layer on the surface of the coarse aggregate s The calculation process is as follows:

[0043] Equation 14: U ca =V ca / PD ca ;

[0044] Equation 15: U fa =V fa / PD fa ;

[0045] Equation 16: U void-ca =P void-ca ·U ca ;

[0046] Equation 17: U EF-fa =Ufa -U void-ca ;

[0047] Equation 18: t s =U EF-fa / (V ca ·s ca );

[0048] In equations 14-18: U ca The volume of the loosely packed coarse aggregate is expressed in meters (m). 3 V ca Let m be the absolute volume of the coarse aggregate, with dimensions in m. 3 V fa Let m be the absolute volume of the fine aggregate, with dimensions in m. 3 U fa The volume of the loose aggregate is given by the unit m. 3 ;P void-ca U represents the porosity of the coarse aggregate skeleton system, dimensionless. EF-fa The volume of the excess sand filling layer is expressed in meters. 3 ;t s The thickness of the excess sand layer filling layer on the surface of the coarse aggregate is given in meters (m).

[0049] As a preferred embodiment, the void volume U of the aggregate mixture is... void-a The calculation method and the thickness t of the excess slurry filling layer on the surface of the coarse and fine aggregate mixture. p The calculation process is as follows:

[0050] Equation 19: U a =U EF-fa +U ca

[0051] Formula 20: U void-a =U a ·P void-a

[0052] Equation 21:

[0053] In equations 19-20: V ca The absolute volume of coarse aggregate is in meters (m). 3 V fa The absolute volume of fine aggregate is given by the unit m. 3 ;P void-a The porosity of coarse and fine aggregate particles is dimensionless; s ca ρ is the specific surface area of ​​coarse aggregate, with dimensions in m. -1 ;s fa The specific surface area of ​​fine aggregate is given by the unit m. -1 V lp Let m be the volume of the slurry. 3;t p P represents the thickness of the excess slurry filler layer on the surface of the coarse and fine aggregate mixture, measured in meters (m). void-a The value can be determined by approximating it using a compressible filling model, or by calculating it using the filling rate test cylinder method.

[0054] As a preferred embodiment, the calculation process of the interaction-corrected CPM model is as follows:

[0055] ① Determine the absolute volume percentage d of fine aggregate in the aggregate system. fa-vol :

[0056] Equation 22:

[0057] ② Calculate the volume percentage y of particle size range i. i :

[0058] Equation 23: For coarse aggregate, y i =h i ·(1-d fa-vol );

[0059] Equation 24: For fine aggregate, y i =(p i -p i-1 )·d fa-vol

[0060] In equations 23-24: i represents the particle size range of fine aggregate; h i This refers to the coarse aggregate particle size range.

[0061] ③ Calculate the virtual filling rate β for each particle size range. i :

[0062] Formula 25:

[0063] ④ Calculate the virtual fill rate γ of the virtual skeleton system:

[0064] Equation 26: a = 1 - (1 - s) 5.0 -1.9·s·(1-s) 3.1 ;

[0065] Equation 27: b = 1 - (1 - s) 1.9 -2.1·s·(1-s) 10.5 -0.2·(1-s) 7.6 ;

[0066] Equation 28:

[0067] ⑤ Calculate the actual filling rate Φ of the aggregate particle skeleton:

[0068] Equation 29:

[0069] Formula 30: P void-a =1-Φ;

[0070] In equations 25-30: β i α is the virtual filling rate for particle size range i, dimensionless; i S is the loose filling rate of aggregates in each particle size range, dimensionless; K is the skeleton compaction coefficient, dimensionless, s = D j / D i Let D be the ratio of the average particle size in particle size intervals j and i. Furthermore, the average particle size D in particle size interval i can be considered as... i The average particle size D greater than particle size range j j a ij and b ij These are the loosening effect coefficient and the wall effect coefficient between particle size intervals i and j, respectively. n is the total number of particle size intervals.

[0071] As a preferred embodiment, the secondary design envelope curve of the steel fiber self-compacting concrete solid phase surface filling layer includes the following parameters: the relative thickness T of the excess sand layer filling layer on the steel fiber surface. sf Scaling factor T of excess slurry filling layer on solid surface after fiber addition pf Two secondary mixing ratio parameters.

[0072] To make the model more closely resemble reality, this invention models from two scale levels and two compositional modes:

[0073] At the solid phase level, ignoring the liquid phase slurry, the solid phase material of steel fiber reinforced concrete is divided into coarse aggregate, steel fiber, and fine aggregate (fine sand) that provides filling and loosening effects. This is called the excess sand layer suspension model on the surface of the solid phase material. Among them, the fine aggregate is further divided into a filling layer that fills the gaps between the coarse aggregate and the fiber, and an excess filling sand layer on the solid phase surface that provides a "rolling effect" on the surface of the coarse aggregate and the steel fiber.

[0074] At the liquid phase level, fiber-reinforced concrete is divided into coarse and fine aggregates, steel fibers, and a slurry that fills and lubricates the solid phase surface, termed a suspended model of excess slurry layer on the solid phase surface. The slurry is further divided into a filling layer that fills the voids in the solid phase mass and an excess filling slurry layer on the solid phase surface that provides a "lubricating effect." For ease of calculation, this suspension model can also be equivalent to an excess slurry layer on the solid phase surface.

[0075] As a preferred embodiment, the relative thickness T of the excess sand filling layer on the steel fiber surface sf Scaling factor T of excess slurry filling layer on solid surface after fiber addition pf The definition of is:

[0076] T sf The thickness t of the excess sand filling layer on the surface of the steel fiber is... sf Compared to the thickness t of the excess sand layer on the surface of coarse aggregate in fiberless self-compacting concrete s The ratio;

[0077] T pf The thickness t of the excess slurry filling layer on the surface of the solid phase component after incorporation of steel fibers. pf The excess slurry filler layer thickness t relative to the surface of the coarse and fine aggregate mixture p The ratio of .

[0078] This invention achieves its goals by setting a secondary proportioning parameter T. sf and T pf The corresponding mix proportion parameters were calculated sequentially. A self-compacting concrete slump spread flow meter was used to test the slump spread of specific materials and paste components. A slump spread greater than or equal to 600 mm was considered a passing standard for filling performance. Plots were drawn at different T... sf The value of T that just satisfies the filling performance requirement. pf The lower limit envelope curve of the value serves as the liquid phase design envelope curve of the secondary mix ratio of the solid phase surface filling layer to meet the filling performance requirements in the mix ratio of fiberless self-compacting concrete foundation.

[0079] As a preferred embodiment, the design process for the secondary design envelope curve of the steel fiber self-compacting concrete solid phase surface filling layer is as follows:

[0080] ① The filling rate PD′ of the coarse aggregate system under steel fiber disturbance was calculated using a modified CPM model with added hard fibers. ca and porosity P′ void-ca Filling rate PD′ of fine aggregate system under steel fiber disturbance fa and porosity P′ void-fa And calculate the proportion of densely packed coarse aggregate volume λ′ in the solid-phase mixed packing system. ca The calculation process is as follows:

[0081] Equation 31:

[0082] The volume percentage of fine aggregate in the steel fiber-aggregate mixture system d′ fa-vol The calculation process is as follows:

[0083] Formula 32: U′ ca =U′ a ·λ′ ca ;

[0084] Equation 33: V′ ca-solid =U′ ca ·PD′ ca=U′ a ·λ′ ca ·PD′ ca ;

[0085] Formula 34: U′ EF-fa =U′ a -U′ ca =(1-λ′) ca )·U′ a ;

[0086] Formula 35: U′ fa =U′ ca ·P′ ca +U′ EF-fa ;

[0087] Equation 36: V′ fa-solid =PD′ fa ·U′ fa ;

[0088] Equation 37:

[0089] ② The aggregate filling rate PD′ under steel fiber disturbance was calculated using the CPM model. tol and aggregate porosity P′ void-a And calculate the thickness t of the excess slurry filling layer on the surface. pf The calculation process is as follows:

[0090] Equation 38:

[0091] The proportion of densely packed aggregate volume in the fiber-reinforced concrete mixture system is λ′. tol The calculation process is as follows:

[0092] Formula 39:

[0093] The volume of the slurry in the fiber-reinforced concrete mixture system is V′ lp The excess slurry volume at the solid surface is V′. EF-lp The calculation process is as follows:

[0094] Formula 40:

[0095] Equation 41:

[0096] The aggregate-fiber solid phase packing volume in the fiber-reinforced concrete mixture system is U′. a The absolute volume of coarse aggregate is V′ ca The absolute volume of fine aggregate is V′ fa The calculation process is as follows:

[0097] Formula 42: U′a =λ′ tol ·V t ;

[0098] Equation 43: V′ fa =U′ a ·PD′ tol ·d′ fa-vol ;

[0099] Equation 44: V′ ca =U′ a ·PD′ tol ·(1-d′ fa-vol );

[0100] ③ Calculate the number of powder systems ρ respectively lp The calculation process for the mass of each component in a unit volume of fiber-reinforced concrete mix is ​​as follows:

[0101] Formula 45:

[0102] Equation 46: m′ b =(V′) lp -V air )·ρ lp ;

[0103] Equation 47: m′ ce =m′ b ·β ce ;

[0104] Equation 48: m′ fla =m′ b ·β fla ;

[0105] Equation 49: m′ slag =m′ b ·β slag ;

[0106] Equation 50: m′ si =m′ b ·β si ;

[0107] Equation 51: m′ w =m′ b • (W / B);

[0108] Equation 52: m′ fa =V′ fa ·ρ fa ;

[0109] Equation 53: m′ ca =V′ ca ·ρ ca ;

[0110] Formula 54: m f (k)=V f (k)·ρ f ;

[0111] In equations 31 to 54: λ′ ca V represents the proportion of densely packed coarse aggregate in the solid-phase mixed packing system, dimensionless; k represents the kth type of steel fiber, dimensionless; r represents the total amount of steel fiber of all types, dimensionless; f (k) represents the unit volume content of the k-th type of fiber, with dimensions in m. 3 ;s f (k) represents the specific surface area of ​​the k-th type of fiber, with dimensions in m. -1 ;T sf (k) represents the relative thickness of the excess sand filling layer on the surface of the steel fiber of the k-th type of fiber, dimensionless; f (k) represents the length of a single fiber of the kth type of fiber; n f (k) represents the number of fibers of the kth type per unit volume, dimensionless; t s The thickness of the excess sand layer filling layer on the surface of coarse aggregate in fiberless concrete, in meters (m); t p PD′ is the thickness of the excess grout filler layer in fiberless self-compacting concrete, in meters (m). ca P′ represents the fill ratio of the coarse aggregate system under steel fiber disturbance, dimensionless. void-ca PD′ represents the porosity of the coarse aggregate system under steel fiber perturbation, dimensionless. fa P′ represents the filler ratio of the fine aggregate system under steel fiber disturbance, dimensionless. void-fa U′ represents the porosity of the fine aggregate system under steel fiber perturbation, dimensionless. ca Let m be the bulk volume of coarse aggregate in the solid-phase mixture system, with dimensions m. 3 ;V′ ca-solid The absolute volume of coarse aggregate in the solid-phase mixture system is given by the dimension m. 3 ;U′ EF-fa The volume of excess sand filling layer on the surface of steel fiber-coarse aggregate in a solid-phase mixed system is given by the dimension m. 3 ; U′ fa The volume of fine aggregate in a solid-phase mixture is given by the dimension m. 3 ;V′ fa-solid Let m be the absolute volume of fine aggregate in the solid-phase mixture system, with dimensions m. 3 ;d′ fa-vol PD′ represents the volume percentage of fine aggregate in a steel fiber-aggregate mixture within a solid-state hybrid system; it is dimensionless. tol P′ represents the aggregate filling ratio under steel fiber disturbance, dimensionless. void-at represents the porosity of the aggregate mass under steel fiber disturbance, dimensionless; pf T represents the thickness of the excess slurry filling layer on the surface of the solid component, in meters (m). pf (k) is the scaling factor of the excess slurry filling layer on the solid surface under the k-th type of fiber, which is dimensionless; λ′ tol The percentage of densely packed aggregate volume in the fiber-reinforced concrete mixture system is dimensionless; s ca The specific surface area of ​​coarse aggregate, in units of m. -1 ;s fa The specific surface area of ​​the fine aggregate is given by the unit m. -1 ;V′ lp The volume of the slurry in the fiber-reinforced concrete mixture system is expressed in meters (m). 3 ;V′ EF-lp The excess slurry volume at the solid surface is expressed in m. 3 ;U′ a The aggregate-fiber solid phase packing volume in the fiber-reinforced concrete mixture system is expressed in m. 3 ;V′ ca The absolute volume of coarse aggregate in the fiber-reinforced concrete mixture system, with dimensions in m. 3 ;V′ fa The absolute volume of fine aggregate in the concrete mixture system, with dimensions in m. 3 ;ρ lp V is the number of the powder system, dimensionless; air The volume of air contained in concrete is expressed in meters. 3 W / B is the water-cement ratio, dimensionless; SP / B is the proportion of admixtures in the cementitious material, dimensionless; β ce β represents the mass percentage of cement in the powder, dimensionless; fla β represents the mass percentage of fly ash in the powder, dimensionless; slag β represents the mass percentage of slag in the powder, dimensionless; si m′ represents the mass percentage of silica fume in the powder, dimensionless. b The mass of cementitious material in a hybrid steel fiber self-compacting concrete mixture is expressed in kg; m′ ce The mass of cement in the mixed steel fiber self-compacting concrete mixture is expressed in kg; m′ fla The mass of fly ash in the mixed steel fiber self-compacting concrete mixture is expressed in kg; m′ slag The mass of slag in the mixed steel fiber self-compacting concrete mixture is expressed in kg; m′ si The mass of silica fume in the mixed steel fiber self-compacting concrete mixture is expressed in kg; m′ w The mass of water in the mixed steel fiber self-compacting concrete mixture is expressed in kg; m′ faThe mass of fine aggregate in a mixed steel fiber self-compacting concrete mixture is expressed in kg; m′ ca The mass of coarse aggregate in a mixed steel fiber self-compacting concrete mixture is expressed in kg; m f (k) represents the mass of the kth type of steel fiber in the hybrid steel fiber self-compacting concrete, with the dimension in kg.

[0112] As a preferred embodiment, the parameter correction process for the rigid fiber externally modified CPM model is as follows:

[0113] ① Calculate the micro-disturbance volume v of a single fiber on the surrounding aggregate. p :

[0114] Equation 55: d f-eq (k)={1.5·[d f (k)] 2 ·l f (k)} 1 / 3 ;

[0115] Equation 56: s eq (i,k)=d f-eq (k) / D i ;

[0116] Equation 57:

[0117] Equation 58:

[0118] ② Calculate the virtual filling rate of each aggregate particle size range i under fiber disturbance.

[0119] Equation 59: N f (k)=V f (k) / V f_single (k);

[0120] Formula 60:

[0121] Equation 61:

[0122] In equations 55-61: d f-eq (k) represents the equivalent spherical particle size of the k-th type of steel fiber, with dimensions in m; d f (k) represents the diameter of the kth type of steel fiber, in meters (m); f (k) — The length of the kth type of steel fiber, in meters; s eq The k-th type of steel fiber is the equivalent particle size ratio to aggregates in each particle size range, dimensionless; k F v is the volume factor for the micro-perturbation of the surrounding aggregate by a single fiber, dimensionless; pThe volume of the micro-disturbance exerted by a single fiber on the surrounding aggregate is given by the dimension m. 3 V f Microfiber content per unit volume, in units of m 3 N f Let be the number of fibers of the k-th type of fiber in the concrete, dimensionless; Δ(i) is the disturbance coefficient of fiber influence in each aggregate particle size range i, dimensionless; α i denoted as , which is the loose filling rate of aggregates in each particle size range, dimensionless; K is the skeleton compaction coefficient, dimensionless.

[0123] As a preferred embodiment, the secondary mix proportion calculation and adjustment process includes: setting T sf T pf After calculating the initial secondary mix proportions, the expected work performance is determined. If the work performance does not meet the standard, the secondary design envelope curve is adjusted until the work performance meets the standard. When the work performance meets the standard, a strength test is performed. If the strength test passes, the initial secondary mix proportion is output as the final mix proportion. If the strength test fails, the mix proportion of the fiberless self-compacting concrete foundation is adjusted until the strength test passes, and the initial secondary mix proportion is output as the final mix proportion.

[0124] In this invention, the secondary mix design envelope curve is an important tool for correcting the final mix proportion. The initial secondary mix proportion is obtained by referring to the secondary mix design envelope curve, based on fiber type and dosage, specifying a small amount of slurry, meeting the filling performance and gap passage performance, and then calculating the initial mix proportion parameters in sequence according to the above calculation process.

[0125] After obtaining the initial secondary mix proportions, macroscopic testing is required. Freshly mixed concrete is prepared according to the initial secondary mix proportions, and the slump spread flowability and gap-passing capacity of the self-compacting concrete are tested. The distribution of aggregates and fibers in the slump spread discs is observed to determine the stability of the mixture. If the filling performance or gap-passing capacity is insufficient, the T is slightly increased. sf T pf Value; if stability is insufficient, T can be appropriately increased. sf And reduce T pf If the adjusted filling performance, gap-passing capacity, and stability still fail to meet the requirements, the mix proportions of the fiberless self-compacting concrete (powder, aggregate, etc.) can be readjusted. After adjusting the self-compacting concrete components, the slurry viscosity can be controlled between 0.4 and 0.6 Pa·s by using admixtures, or by visually inspecting the mortar and concrete mixture after mixing with sand and gravel aggregates to ensure there are no obvious bubbles, black slurry, or slurry stratification phenomena. In this case, the original solid phase filling layer design envelope curve can still be used for mix design, and the curve can be fine-tuned based on the workability test results.

[0126] After the workability meets the standards, cast cubic compressive strength test blocks and test their 28-day compressive strength. If the strength is insufficient, the T value in the secondary mix design can be reduced, provided that the workability is still met. sf T pf The values ​​can be adjusted, or the mix proportion parameters in fiberless self-compacting concrete can be modified, such as reducing the water-cement ratio or increasing the proportion of cement and silica fume in the powder. If the strength is too high (exceeding 15% of the target strength), the T value in the secondary mix design can be increased, provided that the workability is met. sf T pf The values ​​can be adjusted, or the mix proportion parameters in fiberless self-compacting concrete can be modified, such as increasing the water-cement ratio or increasing the proportion of mineral admixtures such as fly ash and slag.

[0127] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0128] (1) The secondary mix proportion curve used in the technical solution of the present invention is used for mix proportion design. It can quantify the "rolling effect" of fine aggregate and the "filling and lubrication effect" of paste on the basis of basic mix proportion. It overcomes the performance fluctuation of fiber self-compacting concrete with different material ratios and fiber content. It can quantitatively calculate the excess layer thickness to customize the work performance of fresh concrete and optimize the work performance control of fresh self-compacting concrete.

[0129] (2) The technical solution of the present invention has good simulation effect for different types of steel fibers. In the proportioning design method, the surface filling layer can be customized for solid materials such as steel fibers of different sizes and aggregates of different sizes, which greatly reduces the number of trial mixes.

[0130] (3) By using the mix design envelope to customize the filling layer thickness parameters, the density of the fiber and aggregate packing is reasonably controlled, the slurry thickness is appropriate, and under the appropriate slurry viscosity control, better stability can be achieved, and the phenomenon of fiber segregation in self-compacting concrete can be reduced. Attached Figure Description

[0131] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the example figures. Obviously, the figures described below are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0132] Figure 1 This is a flowchart of the mix proportion design of the present invention;

[0133] Figure 2 This is a schematic diagram of the three-dimensional projection dimensions of the aggregate surface contour according to the present invention;

[0134] Figure 3 This is a schematic diagram of the calculation model for the excess sand layer filling layer on the surface of coarse aggregate in fiberless self-compacting concrete according to the present invention.

[0135] Figure 4 This is a schematic diagram of the calculation model for the excess slurry filling layer on the surface of the fiberless self-compacting concrete aggregate of the present invention;

[0136] Figure 5 This is a schematic diagram of the calculation model for the suspension of the excess sand layer filling layer on the steel fiber surface of the steel fiber self-compacting concrete according to the present invention;

[0137] Figure 6 This is a schematic diagram of the calculation model for compacting the excess sand layer filling layer on the steel fiber surface of the steel fiber self-compacting concrete of the present invention;

[0138] Figure 7 This is a schematic diagram of the calculation model for the suspension of the excess slurry filling layer on the solid phase surface of steel fiber self-compacting concrete according to the present invention;

[0139] Figure 8 This is a schematic diagram of the calculation model for compacting the excess slurry filling layer on the solid phase surface of steel fiber self-compacting concrete according to the present invention;

[0140] 1-Front view projection of coarse aggregate, 2-Top view projection of coarse aggregate, 3-Side view projection of coarse aggregate, 4-Coarse aggregate, 5-Fine aggregate, 6-Excess sand layer on the surface of coarse aggregate, 7-Sand filling the voids between coarse aggregate skeletons, 8-Mortar, 9-Excess slurry on the surface of aggregate, 10-Slurry filling the voids of aggregate, 11-Micro-fine steel fiber, 12-Macro-coarse steel fiber, 13-Excess sand layer on the surface of steel fiber, 14-Excess sand layer on the surface of solid phase after fiber disturbance, 15-Excess slurry layer on the surface of solid phase after fiber disturbance;

[0141] Figure 9 This is a schematic diagram of typical extended flow of self-compacting concrete obtained in Example 1;

[0142] Figure 10 This is a schematic diagram of the flow of concrete obtained from mix proportion 3 in Comparative Example 1.

[0143] Figures 11-13 This is the envelope curve of the mix design for the filling performance of self-compacting concrete according to the present invention. Detailed Implementation

[0144] The following specific embodiments are intended to further illustrate the content of this invention, rather than to limit the scope of protection of the claims. All embodiments obtained by those skilled in the art based on the embodiments of this invention without inventive effort are within the scope of protection of this invention.

[0145] Example 1:

[0146] A precast tunnel segment yard plans to introduce a production line to produce self-compacting steel fiber precast shield tunnel segments. In order to adapt to different load and service environments, it is necessary to adaptively adjust the amount and type of steel fiber and customize the corresponding mix ratio.

[0147] This embodiment provides a mix design method for hybrid steel fiber self-compacting concrete, applicable to the above-mentioned situation.

[0148] See Figure 1 The method for designing the mix proportions of self-compacting hybrid steel fiber reinforced concrete includes the following steps:

[0149] Step S1, Determination / Calculation of Performance Parameters of Raw Materials

[0150] The raw materials include solid-phase materials and liquid-phase materials. The solid-phase materials include coarse and fine aggregates and steel fibers. The liquid-phase materials include powders, admixtures, and water. The powders include cement, fly ash, slag, and silica fume. The admixtures include water-reducing agents and viscosity modifiers. The performance parameters include the apparent density ρ of the coarse aggregate. ca Bulk density of coarse aggregate ρ′ ca Coarse aggregate system filling rate PD ca PD of fine aggregate system fa Porosity P of coarse aggregate system void-ca Porosity P of fine aggregate system void-fa Apparent density ρ of fine aggregate fa Bulk density of fine aggregate ρ′ fa Coarse aggregate gradation parameters, fine aggregate gradation parameters, coarse aggregate morphology parameters, fine aggregate morphology parameters, and steel fiber density ρ. f Steel fiber morphological parameters (length l) f Diameter d f ), apparent density of cement ρ ce Apparent density ρ of fly ash fla Apparent density ρ of slag slag Apparent density ρ of silica fume si The density of water ρ w Density ρ after preparation with admixtures sp .

[0151] Step S2, Customizing the Mix Proportion of Fiber-Free Self-Compacting Concrete Foundation

[0152] Using calculation and trial mixing methods, the mix proportion parameters of fiberless self-compacting concrete foundations that meet the requirements for filling and stability were determined, including the absolute volume V of coarse aggregate. ca and mass m ca The absolute volume V of fine aggregate fa and mass m fa The volume V of the slurry lpThe weight of the cementitious material, m b The weight of cement, m ce The weight of fly ash, m fla The weight m of granulated blast furnace slag slag The weight of silica fume m si The weight of water, m w .

[0153] Step S3, Calculation of the surface filling layer of fiberless self-compacting concrete aggregate

[0154] Based on the raw material parameters and referring to the basic mix proportion of fiberless self-compacting concrete, the thickness t of the excess sand layer on the surface of the coarse aggregate is calculated sequentially. s Porosity P of coarse and fine aggregate mixture void-a Excess filler slurry layer thickness t on aggregate surface p ,like Figure 3 , Figure 4 .

[0155] Step S4: Customization of secondary mix proportion parameters for the steel fiber self-compacting concrete solid phase surface filling layer.

[0156] Referencing the secondary design envelope curve of the solid phase surface filling layer of steel fiber self-compacting concrete ( Figures 11-13 In addition to performance requirements, the secondary mix proportion parameters (T) of the solid phase surface of the concrete after incorporating steel fibers are customized. sf T pf ), and refer to Figures 5-8 The calculation model for steel fiber self-compacting concrete can calculate the initial mix proportion parameters (m′) after the secondary mix proportion parameters are customized. ce m′ fla m′ slag m′ si m′ w m′ fa m′ ca m f (k)).

[0157] Step S5: Performance testing and secondary proportioning curve adjustment

[0158] After calculating the initial secondary mix proportion parameters, fresh steel fiber reinforced concrete was mixed according to this proportion. Referring to the "Technical Specification for Application of Self-Compacting Concrete" (JGJ / T 283-2012), the slump spread flowability and gap passage capacity of the fresh concrete were tested by slump spread test. The distribution of aggregates and fibers in the slump spread disc was observed to determine the stability of the mixture.

[0159] If the filling performance or gap-passing capacity is insufficient, slightly increase T. sf T pfValue; if stability is insufficient, T can be appropriately increased. sf And reduce T pf If the adjusted filling performance, gap-passing capacity, and stability still fail to meet the requirements, the mix proportions of the fiberless self-compacting concrete (powder, aggregate, etc.) can be readjusted. After adjusting the self-compacting concrete components, the slurry viscosity can be controlled between 0.4 and 0.6 Pa·s by using admixtures, or by visually inspecting the mortar and concrete mixture after mixing with sand and gravel aggregates to ensure there are no obvious bubbles, black slurry, or slurry stratification phenomena. In this case, the original solid phase filling layer design envelope curve can still be used for mix design, and the curve can be fine-tuned based on the workability test results.

[0160] After the workability meets the standards, cast cubic compressive strength test blocks and test their 28-day compressive strength. If the strength is insufficient, the T value in the secondary mix design can be reduced, provided that the workability is still met. sf T pf The values ​​can be adjusted, or the mix proportion parameters in fiberless self-compacting concrete can be modified, such as reducing the water-cement ratio or increasing the proportion of cement and silica fume in the powder. If the strength is too high (exceeding 15% of the target strength), the T value in the secondary mix design can be increased, provided that the workability is met. sf T pf The values ​​can be adjusted, or the mix proportion parameters in fiberless self-compacting concrete can be modified, such as increasing the water-cement ratio or increasing the proportion of mineral admixtures such as fly ash and slag.

[0161] Step S1 specifically includes the following processes:

[0162] Step S1.1: The apparent density of the raw materials is tested using the liquid displacement method and the specific gravity bottle method.

[0163] The grades and apparent densities of the raw materials are as follows (the mineral admixtures in the powder are only fly ash and silica fume):

[0164] The apparent density ρ of coarse aggregate (basalt crushed stone) ca =2680kg / m 3 The apparent density ρ of fine aggregate (river sand) fa =2600kg / m 3 The apparent density ρ of cement (grade 52.5R) ce =3100kg / m 3 The apparent density ρ of fly ash (specifically, Class I fly ash) fla =2400kg / m 3 The apparent density ρ of silica fume (specifically S95 silica fume) si =2330kg / m 3 The density of the admixture (98% water-reducing agent + 2% thickener) is ρ. sp = 1080kg / m3 The density ρ of steel fiber f =7850kg / m 3 .

[0165] Step S1.2: Test the bulk density ρ′ of the coarse aggregate system. ca PD (Fill Rate) ca Porosity P void-ca

[0166] The coarse aggregate used in concrete preparation has a particle size range of 5–16 mm. A cylindrical bulk density test jar is used to measure the weight of the loosely packed coarse aggregate after filling the jar. The volume of the bulk density test jar used for the test is Vol. C The capacity is 10L. After testing, the weight W of the coarse aggregate after filling was obtained. ca Since the weight is 15.973 kg, the bulk density of the coarse aggregate system can be calculated separately:

[0167]

[0168] The calculation results for the filling rate of the corresponding coarse aggregate system are as follows:

[0169]

[0170] The porosity of the coarse aggregate system is:

[0171] P void-ca =1-PD ca =0.404

[0172] Step S1.3: Test the bulk density ρ′ of the fine aggregate system. fa PD (Fill Rate) fa Porosity P void-fa .

[0173] The fine aggregate used in concrete preparation has a gradation size range of 0.075mm to 5mm, and uses the same filling density test hopper (vol). C The weight W of the loose fine aggregate pile after it was filled was obtained by testing (10L). fa Given a weight of 15.470 kg, the bulk density of the fine aggregate system can be calculated as follows:

[0174]

[0175] Filling rate PD of fine aggregate system fa

[0176]

[0177] Porosity P of fine aggregate system void-fa :

[0178] P void-fa =1-PD fa =0.405

[0179] Step S1.4: Testing of coarse aggregate gradation and morphological parameters.

[0180] For ease of analysis, coarse aggregate with a particle size of 5–16 mm was sieved through a circular sieve into two intervals: the first interval and the second interval. The particle size range of the first interval is 10–16 mm, and that of the second interval is 5–10 mm. The ratios of the volume of particles in the first and second intervals to the total volume of coarse aggregate are h1 = 0.6 and h2 = 0.4, respectively.

[0181] The morphology of coarse aggregate is primarily characterized by its specific surface area. Since coarse aggregate is crushed stone with an uneven surface, its specific surface area s is calculated based on Heywood's particle theory. ca First, select 100 stones with characteristic shapes. Then, trace the outlines of the coarse aggregate on white paper using frontal, top, and side projections. Use a ruler to measure the projected length L, width B, and thickness T of each outline. Figure 2 A total of 100 sets of experimental data were tested. The average value of the corresponding projection size scale factor was calculated using the following formula:

[0182]

[0183]

[0184] In the formula, m p n is the average proportionality coefficient between the projected width B and the projected thickness T; p It is the average proportionality coefficient between the projection length L and the projection width B.

[0185] Furthermore, through m p and n p The projection magnification factor d of the coarse aggregate was calculated. p :

[0186]

[0187] Therefore, the specific surface area of ​​the coarse aggregate can be further obtained by using the discrete method:

[0188]

[0189] In the formula: the ratio of f / k is 7.5.

[0190] Step S1.5: Testing of gradation and morphological parameters of fine aggregate.

[0191] The fine aggregate gradation parameters were mainly obtained by referring to the standard "Sand for Construction" (GB / T 14684-2011). Fine aggregate with a nominal diameter of 0.075–5 mm was sieved into six intervals using a circular sieve. The particle sizes of each interval were 0.075–0.16 mm, 0.16–0.315 mm, 0.315–0.63 mm, 0.63–1.25 mm, 1.25–2.5 mm, and 2.5–5 mm, respectively. After sieving, the aggregate was weighed, and the cumulative sieve residue rate p of each interval was calculated. i The percentages were 7.33%, 16.84%, 29.76%, 46.74%, 69.58%, and 100%, respectively, corresponding to the sieve aperture size D within the particle size range. i The thicknesses are 0.16mm, 0.315mm, 0.63mm, 1.25mm, 2.5mm, and 5mm respectively, D min This represents the lower limit of the particle size range for fine aggregates, which is 0.075 mm in this case; D max is the upper limit of the particle size range of fine aggregate, which is 5mm here; q is the gradation index fitted by the fine aggregate, which is 0.41341 here after fitting using the least squares method.

[0192] For the fine aggregate used, the Funk-Dinger formula used to characterize it is:

[0193]

[0194] The morphological parameters of fine aggregates are also expressed in terms of specific surface area s. fa Characterization. For fine aggregate, the local river sand has good roundness and can be regarded as approximately spherical. The projection size ratio coefficient is set to 1, and no projection magnification is required. At the same time, the ratio of the shape area coefficient to the shape volume coefficient of fine aggregate, f / k, is 6.0. The specific surface area of ​​fine aggregate can be calculated using the continuous method.

[0195]

[0196] In the above formula, dp i The cumulative sieve residue rate function p of fine aggregate i The differential.

[0197] In step S2, the base mix proportion of the fiberless self-compacting concrete is customized.

[0198] The mix design of the fiberless self-compacting concrete foundation was customized in accordance with the "Technical Specification for Application of Self-Compacting Concrete" (JGJ / T 283-2012). The mix design parameters were adjusted to meet performance requirements through slump expansion flowability testing, gap-passing capacity testing, and visual stability assessment. A water-cement ratio of 0.35 was selected. The mix design parameters for each component of the concrete per cubic meter volume prepared from this material to meet self-compacting performance are as follows: coarse aggregate mass m...ca The weight is 823 kg, and the absolute volume of coarse aggregate is V. ca It is 0.307 m 3 Fine aggregate quality m fa The absolute volume V of the fine aggregate is 774 kg. fa It is 0.298m 3 The volume V of the slurry lp It is 0.395m 3 The weight of the cementitious material, m b The weight of cement is 525 kg, m ce The weight of fly ash is 325 kg, m flag It weighs 157 kg, and the weight of the silica ash is m. si The weight is 42 kg, and the weight of water is 183.7 kg.

[0199] Step S3 specifically includes the following steps:

[0200] Step S3.1, Reference Figure 3 The thickness t of the excess sand layer on the surface of the coarse aggregate is calculated according to the following formula. s ,

[0201] U ca =V ca / PD ca =0.307 / 0.596 = 0.515m 3 ;

[0202] U fa =V fa / PD fa =0.298 / 0.595=0.501m 3 ;

[0203] U void-ca =P void-ca ·U ca =0.404 × 0.515 = 0.208m 3 ;

[0204] U EF-fa =U fa -U void-ca =0.501-0.208=0.293m 3 ;

[0205] t s =U EF-fa / (V ca ·s ca )=0.293 / (0.307×624)=0.0015m=1.5mm;

[0206] Step S3.2: Calculate the porosity of the aggregate mixture system using the CPM model with interaction correction.

[0207] (1) For ease of analysis, the aggregate gradation range is divided into three intervals. The coarse aggregate includes the first particle size interval of 10-16 mm and the second particle size interval of 5-10 mm. The fine aggregate is divided into a single gradation interval of 0.075-5 mm. According to steps S1.2 and S1.3, the filling rates α1, α2 and α3 of the corresponding three particle size intervals are tested and calculated to be 0.581, 0.578 and 0.595, respectively.

[0208] (2) Calculate the absolute volume percentage d of fine aggregate in the aggregate system. fa-vol

[0209]

[0210] (3) Calculate the volume percentage y of particle size range i. i :

[0211] Coarse aggregate: y i =h i ·(1-d fa-vol )

[0212] y1=h1·(1-d fa-vol = 0.6 × (1 - 0.4926) = 0.3044

[0213] y2=h2·(1-d fa-vol = 0.4 × (1 - 0.4926) = 0.2030

[0214] Fine aggregate: y i =(p i -p i-1 )·d fa-vol

[0215] y3=(p3-0·)d fa-vol =1.0 × 0.4926 = 0.4926

[0216] (4) Calculate the virtual filling rate for each particle size range.

[0217]

[0218]

[0219]

[0220] (5) Calculate the virtual fill rate γ of the skeleton system:

[0221] Calculate the loosening effect coefficient α between the first and second particle size ranges.12 The loosening effect coefficient α between the first and third particle size ranges. 13 The loosening effect coefficient α between the second and third particle size ranges. 23 :

[0222] a 12 = 1 - (1 - s) 5.0 -1.9·s·(1-s) 3.1 =0.9103

[0223] a 13 = 1 - (1 - s) 5.0 -1.9·s·(1-s) 3.1 =0.3596

[0224] a 23 = 1 - (1 - s) 5.0 -1.9·s·(1-s) 3.1 =0.5517

[0225] Calculate the wall effect coefficient b between the first and second particle size ranges. 21 The wall effect coefficient b between the first and third particle size ranges 31 The wall effect coefficient b between the second and third particle size ranges 32 :

[0226] b 21 = 1 - (1 - s) 1.9 -2.1·s·(1-s) 10.5 -0.2·(1-s) 7.6 =0.8045

[0227] b 31 = 1 - (1 - s) 1.9 -2.1·s·(1-s) 10.5 -0.2·(1-s) 7.6 =0.1214

[0228] b 32 = 1 - (1 - s) 1.9 -2.1·s·(1-s) 10.5 -0.2·(1-s) 7.6 =0.3532

[0229] In the formula: s is the ratio of the average particle size between particle size intervals. For the first and second particle size intervals, the values ​​are 1.7333, 7.222, and 4.1667, respectively.

[0230] The virtual filling density dominated by different particle size ranges is as follows:

[0231]

[0232]

[0233]

[0234] (6) Calculate the filling ratio Φ of the aggregate system:

[0235]

[0236] The fill ratio Φ after aggregate mixing can be calculated to be 0.683, therefore:

[0237] P void-a =1 - 0.683 = 0.317

[0238] Step S3.3, Reference Figure 4 The thickness t of the excess slurry layer on the surface of the aggregate is calculated sequentially according to the following formula. p .

[0239] U a =U EF-fa +U ca =0.293 + 0.515 = 0.808m 3

[0240] U void-a =U a ·P void-a =0.808 × 0.320 = 0.259m 3

[0241]

[0242] In the formula: V air The air content in the concrete mix design is set to 0.02 m³ / m³ in this example. 3 .

[0243] In step S4, the secondary mix proportion parameters (T) of the solid phase surface of the concrete after incorporating steel fibers are determined. sf T pf The specific customization method is as follows:

[0244] (1) Customization of target ratio

[0245] Based on the load environment and hardening performance requirements, the target fiber content is determined. In this example, four types of steel fibers and their contents are customized according to the requirements. The types of steel fibers and their contents are as follows.

[0246] Ratio 1:

[0247] Steel fiber type 0535, fiber length lf =35mm, fiber diameter d f =0.5mm, fiber volume fraction V f =0.5%.

[0248] Formula 2:

[0249] Steel fiber type 0690, fiber length l f =60mm, fiber diameter d f =0.9mm, fiber volume fraction V f =0.5%.

[0250] Ratio 3:

[0251] Steel fiber type 0213, fiber length l f =13mm, fiber diameter d f =0.2mm, fiber volume fraction V f =0.5%.

[0252] Mixing ratio 4: Mixed working condition

[0253] Steel fiber type 0535+0213, 0535 fiber volume fraction V f =0.75%, 0213 fiber volume fraction V f =0.25%.

[0254] (2) Selection of secondary mix proportion parameters for the solid phase surface of concrete

[0255] Reference Figures 11-13 The corresponding secondary mix design envelope curve is obtained by selecting the secondary mix parameters on the design envelope to obtain the steel fiber self-compacting concrete mix proportion that satisfies self-compacting properties.

[0256] Formula 1: Reference Figure 12 (a) Selecting the secondary proportioning parameter (T) sf =0.35, T pf =1.2), and the mix proportion is customized.

[0257] Formula 2: Refer to Figure 13 (a) Selecting the secondary proportioning parameter (T) sf =0.5, T pf =1.0), and the mixing ratio is customized.

[0258] Formula 3: Refer to Figure 11 (a) Selecting the secondary proportioning parameter (T) sf =0.33, T pf =1.25), and the mix proportion is customized.

[0259] Formula 4: (Refer to) Figure 11 (a), Figure 12 (a) Selecting the secondary blending parameters, there are two types of fibers, with the number of fiber types r = 2. Let k = 1 represent 0535 fiber and k = 2 represent 0213 fiber. Then, select the secondary blending parameters (T) respectively. sf (1) = 0.35, T pf (1) = 1.30, T sf (2) = 0.33, T pf (1) = 1.125

[0260] In step S4, the calculation process for the mix proportion is as follows:

[0261] (1) Calculate the filling rate PD′ of the coarse aggregate system after steel fiber incorporation. ca and porosity P′ void-ca PD′ of fine aggregate system fa and porosity P′ void-fa The calculation process and results are as follows:

[0262] ① Calculate the disturbance volume of a single fiber on the surrounding aggregate using the following procedure:

[0263] d f-eq (k)={1.5·[d f (k)] 2 ·l f (k)} 1 / 3

[0264] s eq (i,k)=d f-eq (k) / D i

[0265]

[0266]

[0267] The equivalent particle size d was calculated. f-eq Size ratio s eq Disturbance volume coefficient k F Disturbance volume v p The matrices are respectively

[0268] Equivalent particle size d f-eq Result matrix

[0269]

[0270] Size ratio s eq Result matrix

[0271]

[0272] Disturbance volume factor k FResult matrix

[0273]

[0274]

[0275] Disturbance volume v p Result matrix

[0276]

[0277] ②: Calculate the virtual filling rate of each aggregate particle size range i under fiber disturbance.

[0278] N f (k)=V f (k) / V f_single (k);

[0279]

[0280]

[0281] Calculate N for each ratio f Δ i , The resulting matrix is ​​as follows

[0282] Equivalent particle size d f-eq Result matrix

[0283]

[0284] Correction coefficient Δ i Result matrix

[0285]

[0286] ③: The porosity of the aggregate system under fiber disturbance at each proportion was calculated using the parameter-corrected CPM model. The calculation results are as follows.

[0287] Porosity of aggregate system under fiber disturbance

[0288]

[0289] (2) Calculate the initial proportion parameters after the secondary proportion parameters are customized.

[0290] ① Calculate the volume percentage λ′ of the dense coarse aggregate packing in the solid-phase mixed packing system. ca

[0291]

[0292] Porosity of aggregate system under fiber disturbance

[0293]

[0294]

[0295] ② Calculate the volume percentage d′ of fine aggregate in the steel fiber-aggregate mixture system. fa-vol :

[0296] U′ ca =U′ a ·λ′ ca ;

[0297] V′ ca-solid =U′ ca ·PD′ ca =U′ a ·λ′ ca ·PD′ ca ;

[0298] U′ EF-fa =U′ a -U′ ca =(1-λ′) ca )·U′ a ;

[0299] U′ fa =U′ ca ·P′ ca +U′ EF-fa ;

[0300] V′ fa-solid =PD′ fa ·U′ fa ;

[0301]

[0302] The resulting matrix is ​​as follows:

[0303] Volume percentage calculation matrix under fiber perturbation

[0304]

[0305] ③ Calculate the thickness t of the excess slurry filling layer on the solid surface. pf :

[0306]

[0307] Thickness of excess filler layer on solid surface under fiber disturbance (mm)

[0308]

[0309] ④ The proportion of densely packed aggregate volume in the fiber-reinforced concrete mixture system is λ′ tol

[0310]

[0311] Volume ratio of dense aggregate under fiber disturbance

[0312]

[0313] ④ Calculate the volume of the paste in the concrete mixture system as V′ lp The excess slurry volume at the solid surface is V′. EF-lp ,

[0314]

[0315]

[0316] Slurry volume and excess slurry volume under fiber disturbance (m³) 3 )

[0317]

[0318] ⑤ The aggregate-fiber solid phase packing volume in the fiber-reinforced concrete mixture system is U′ a The absolute volume of coarse aggregate is V′ ca The absolute volume of fine aggregate is V′ fa .

[0319] U′ a =λ′ tol ·V t ;

[0320] V′ fa =U′ a ·PD′ tol ·d′ fa-vol ;

[0321] V′ ca =U′ a ·PD′ tol ·(1-d′ fa-vol );

[0322] V′ a =V′ ca +V′ fa .

[0323] Calculation results of aggregate volume under fiber disturbance (m) 3 )

[0324]

[0325] ⑥ Final mix proportions (per cubic meter of concrete).

[0326] Calculated mix proportions of fresh steel fiber self-compacting concrete (kg)

[0327]

[0328] In step S5, the specific performance testing process is as follows:

[0329] (1) Performance testing

[0330] The concrete mixture was prepared according to the above mix proportions, and the viscosity of the paste was controlled by the amount of water-reducing agent. The appropriate amount of water-reducing agent was determined by visual inspection to be when the paste exhibited sufficient fluidity without significant component separation or bubbling. After preparing the fresh steel fiber reinforced concrete, the fluidity and stability were tested using a slump cone and slump spread plate, referring to the "Technical Specification for Application of Self-Compacting Concrete" (JGJ / T 283-2012). The slump spread diameter (SF) was used to reflect the filling performance of the fresh concrete. When SF is greater than 600 mm, it can be considered to have achieved stable filling capacity. The uniformity of component distribution and bleeding in the mixture were used as the Visual Stability Index (VSI). The corresponding values ​​and evaluation of the Visual Stability Index (VSI) are shown in the table below.

[0331] Visual Stability Index (VSI) Values ​​and Evaluation

[0332]

[0333] Since the spacing of the reinforcing bars in this example is always more than three times the length of the steel fibers, the spacing capacity is not tested for the time being. The filling performance test results of the mixtures under each mix proportion are as follows:

[0334] Performance test

[0335]

[0336] It is evident that the mixtures at all proportions can achieve self-compacting properties without the need to adjust the secondary proportion range. However, proportions 3 and 4 exhibit decreased stability due to excessive excess slurry. Therefore, they can be combined with... Figures 11-12 In (b) and (c), the range of values ​​for the secondary mix proportioning parameters should be adjusted appropriately to control the slurry content.

[0337] (2) Strength test

[0338] Freshly mixed concrete was poured into standard cubic specimens (150mm × 150mm × 150mm) and cured for 28 days. Strength tests were then conducted on these standard cubic specimens. The test results are as follows:

[0339] Strength test (MPa)

[0340]

[0341] It can be seen that, except for ratio 2, all other ratios meet the performance requirements of C60. In actual configuration, the water-to-binder ratio of ratio 2 can be adjusted to 0.34 to improve compressive strength.

[0342] Comparative Example 1

[0343] In this comparative example, the increase in excess filler layer on the solid phase surface after the incorporation of steel fibers is not considered. Therefore, the secondary proportioning parameters are not specifically customized. That is, the above-mentioned secondary proportioning parameters are uniformly set to (T). sf =0.0、 T pf =1.0), and with the same self-compacting base mix proportion, fresh self-compacting concrete is prepared according to the fiber content in Example 1, with the following mix proportion parameters:

[0344] The proportion of fresh steel fiber in the comparative example (kg)

[0345]

[0346]

[0347] After being mixed into fresh concrete, the same proportion of water-reducing agent was added. In accordance with the "Technical Specification for Application of Self-Compacting Concrete" (JGJ / T 283-2012), the filling performance and stability tests were carried out, and the test results are as follows.

[0348] Performance test results in the comparative example

[0349]

[0350] As can be seen from the above examples and comparative examples, without considering the secondary mix proportioning parameters, the fresh steel fiber reinforced concrete obtained in the foundation self-compacting concrete cannot meet the self-compacting performance requirements.

Claims

1. A secondary design method for the mix proportion of hybrid steel fiber self-compacting concrete based on a customized solid-phase surface filling layer, characterized in that: Includes the following steps: 1) Obtain the performance parameters of the raw materials and determine the mix proportion parameters of the fiberless self-compacting concrete foundation; 2) Calculate the thickness of the surface filling layer of the fiberless self-compacting concrete using experimental testing and / or a compressible infill model; 3) Plot the secondary design envelope curve of the solid phase surface filling layer of the steel fiber self-compacting concrete by introducing the voids in the mixed accumulation of steel fibers and aggregates; 4) Perform secondary mix proportion calculation and adjustment based on the secondary design envelope curve process. The secondary design envelope curve of the steel fiber self-compacting concrete solid phase surface filling layer includes the following parameters: the relative thickness of the excess sand layer filling layer on the steel fiber surface. Scaling factor of excess slurry filling layer on solid surface after fiber addition Two secondary mix proportion parameters; The relative thickness of the excess sand filling layer on the steel fiber surface Scaling factor of excess slurry filling layer on solid surface after fiber addition The definition of is: The thickness of the excess sand layer filling layer on the surface of the steel fiber is [not specified]. Compared to the thickness of the excess sand layer on the surface of coarse aggregate in fiberless self-compacting concrete The ratio; The thickness of the excess slurry filling layer on the surface of the solid phase component after incorporation of steel fibers. The excess slurry filler layer thickness relative to the surface of the coarse and fine aggregate mixture The ratio; The thickness of the excess slurry filling layer on the surface The calculation process is as follows: ； in, The thickness of the excess slurry filler layer on the surface of the coarse and fine mixed aggregate is measured in meters. For the first The unit volume content of a certain type of fiber, in units of m 3 ; For the first The scaling factor of the excess slurry filling layer on the solid surface under fiber adsorption is dimensionless.

2. The method for secondary design of mix proportion of hybrid steel fiber self-compacting concrete based on a customized solid-phase surface filling layer according to claim 1, characterized in that: The raw materials include: steel fiber, aggregate, cement, fly ash, slag, silica fume, admixtures, and water; the performance parameters of the raw materials include: apparent density of coarse aggregate. bulk density of coarse aggregate Coarse aggregate system filling rate , fine aggregate system filling rate Porosity of coarse aggregate system Porosity of fine aggregate system Apparent density of fine aggregate Bulk density of fine aggregate Coarse aggregate gradation parameters, fine aggregate gradation parameters, coarse aggregate morphology parameters, fine aggregate morphology parameters, and steel fiber density. morphological parameters of steel fibers and apparent density of cement Apparent density of fly ash Apparent density of slag apparent density of silica fume The density of water Density after mixing with admixtures .

3. The method for secondary design of mix proportion of hybrid steel fiber self-compacting concrete based on a customized solid-phase surface filling layer according to claim 2, characterized in that: The coarse aggregate system filling rate Porosity of coarse aggregate system The calculation process is as follows: Formula 1: ; Formula 2: ; Formula 3: ; The fine aggregate filling rate Porosity of fine aggregate skeleton system The calculation process is as follows: Formula 4: ; Formula 5: ; Formula 6: ; In equations 1-6: The bulk density of coarse aggregate is expressed in kg / m³. 3 ; The weight of coarse aggregate is expressed in kg. The coarse aggregate filling rate is dimensionless. The volume of the container used for the test is measured in meters (m). 3 ; To measure the absolute volume of coarse aggregate after the container is filled, the dimension is m. 3 ; The porosity of the coarse aggregate skeleton system is dimensionless. The weight of coarse aggregate is expressed in kg. The coarse aggregate filling rate is dimensionless. The volume of the container used for the test is measured in meters (m). 3 ; Let m be the absolute volume of the aggregate in the container, with dimensions in meters. 3 ; The porosity of the framework system is dimensionless. The calculation process for the coarse aggregate gradation parameters is as follows: divide the coarse aggregate with a particle size greater than 5 mm into 2-3 intervals, and determine the volume percentage of each particle size interval. , used to represent the gradation distribution of coarse aggregate; The calculation process for the fine aggregate gradation parameters is as follows: Aggregates with a diameter of 0.08~5mm are divided into 6 intervals, and the cumulative sieve residue rate of each interval is calculated, i.e., the particle size distribution is... The percentage of particles passing through is denoted as And the average value is taken repeatedly, where, Fitting was performed using the Funk-Dinger formula: Formula 7: ; In Equation 7: The cumulative sieve residue rate for each interval is expressed in %; The smallest particle size in fine aggregate is denoted by m. is the largest particle size in the fine aggregate, with dimensions in meters; The gradation index to be fitted is dimensionless; Let i be the sieve aperture size within the particle size range i; The calculation process for the coarse aggregate morphology parameters and fine aggregate morphology parameters is as follows: ① The size ratio is calculated using the Heywood particle theory. The calculation process is as follows: Formula 8: ; Formula 9: ; Formula 10: ; ② The specific surface area of ​​coarse aggregate is calculated using the discrete method. The calculation process is as follows: Formula 11: ; ③ The specific surface area of ​​fine aggregate is calculated using the continuous method. The calculation process is as follows: Formula 12: ; In equations 8-12: is the length of the aggregate, in meters; The width of the aggregate is measured in meters (m). The aggregate thickness is expressed in meters (m). and This is the projection size scaling factor, which is dimensionless. The magnification factor of the projected diameter relative to the sieve diameter is dimensionless; ρ is the specific surface area of ​​coarse aggregate, with dimensions in m. -1 ; The shape area coefficient is dimensionless. The shape and volume coefficient is dimensionless. This represents the proportion of each particle size range, dimensionless. Let be the sieve aperture size of particle size range i, with dimensions in m; The cumulative sieve residue rate for each interval is expressed in %; The specific surface area of ​​the fine aggregate is given by the unit m. -1 ; The morphological parameters of the steel fiber include: fiber length, fiber diameter, and fiber specific surface area. The fiber length and fiber diameter are obtained through measurement, and the fiber specific surface area is calculated as follows: Formula 13: ; In Equation 13: The specific surface area of ​​steel fibers is expressed in m. -1 ; The diameter of the fiber is in meters. -1 .

4. The method for secondary design of mix proportion of hybrid steel fiber self-compacting concrete based on a customized solid-phase surface filling layer according to claim 1, characterized in that: The mix proportion parameters for the fiber-free self-compacting concrete foundation include: the absolute volume of coarse aggregate. and quality The absolute volume of fine aggregate and quality The volume of the slurry The weight of cementitious materials The weight of cement The weight of fly ash The weight of granulated blast furnace slag The weight of silica fume The weight of water .

5. The method for secondary design of mix proportion of hybrid steel fiber self-compacting concrete based on a customized solid-phase surface filling layer according to claim 1, characterized in that: The calculation of the surface filling layer of the fiberless self-compacting fiber concrete aggregate includes: calculating the porosity of the aggregate mixture. Porous volume of aggregate mixture Thickness of excess sand layer filling layer on coarse aggregate surface Excess slurry filler layer thickness on the surface of coarse and fine aggregates .

6. The method for secondary design of mix proportion of hybrid steel fiber self-compacting concrete based on a customized solid-phase surface filling layer according to claim 5, characterized in that: The voids in the aggregate mixture The CPM model with interaction correction is used for calculation; The thickness of the excess sand filling layer on the surface of the coarse aggregate The calculation process is as follows: Formula 14: ; Formula 15: ; Formula 16: ; Formula 17: ; Formula 18: ; In equations 14-18: The volume of the loosely packed coarse aggregate is expressed in meters (m). 3 ; Let m be the absolute volume of the coarse aggregate, with dimensions in m. 3 ; Let m be the absolute volume of the fine aggregate, with dimensions in m. 3 ; The volume of the loose aggregate is given by the unit m. 3 ; The porosity of the coarse aggregate skeleton system is dimensionless. The volume of the excess sand filling layer is expressed in meters. 3 ; The thickness of the excess sand layer filling layer on the surface of the coarse aggregate is expressed in meters. The void volume of the aggregate mixture The calculation method and the thickness of the excess slurry filling layer on the surface of the coarse and fine mixed aggregate. The calculation process is as follows: Formula 19: ; Formula 20: ; Equation 21: ; In equations 19-21: The absolute volume of coarse aggregate is in meters (m). 3 ; The absolute volume of fine aggregate is given by the unit m. 3 ; The packing void ratio of coarse and fine mixed aggregate particles is dimensionless. ρ is the specific surface area of ​​coarse aggregate, with dimensions in m. -1 ; The specific surface area of ​​fine aggregate is given by the unit m. -1 ; Let m be the volume of the slurry, with dimensions in m. 3 ; The thickness of the excess slurry filling layer on the surface of the coarse and fine aggregate mixture is expressed in meters (m).

7. The method for secondary design of mix proportion of hybrid steel fiber self-compacting concrete based on a customized solid-phase surface filling layer according to claim 6, characterized in that: The calculation process of the interaction-corrected CPM model is as follows: Determine the absolute volume percentage of fine aggregate in the aggregate system : Equation 22: ; Calculate the volume percentage of particle size range i : Equation 23: For coarse aggregate, ; Equation 24: For fine aggregate, ; In Equations 23-24: i represents the particle size range of fine aggregate; This refers to the coarse aggregate particle size range. Calculate the virtual filling rate for each particle size range. : Formula 25: ; Calculate the virtual fill rate of the virtual skeleton system : Equation 26: ; Equation 27: ; Equation 28: ; Calculate the actual filling rate of aggregate particle skeleton : Equation 29: ; Formula 30: ; In equations 25-30: Let be the virtual filling rate for particle size range i, which is dimensionless; The loose filling rate of aggregates in each particle size range is dimensionless. The skeleton compaction coefficient is dimensionless. The ratio of the average particle size in particle size ranges j and i is given. and These are the loosening effect coefficient and the wall effect coefficient between particle size ranges i and j, respectively; This represents the total number of particle size intervals.

8. The method for secondary design of mix proportion of hybrid steel fiber self-compacting concrete based on a customized solid-phase surface filling layer according to claim 1, characterized in that: The design process for the secondary design envelope curve of the steel fiber self-compacting concrete solid phase surface filling layer is as follows: ① The filling rate of the coarse aggregate system under steel fiber perturbation was calculated using a modified CPM model with added hard fibers. and porosity Filling rate of fine aggregate system under steel fiber disturbance and porosity And calculate the proportion of densely packed coarse aggregate in the solid-phase mixed packing system. The calculation process is as follows: Equation 31: ; Fine aggregate volume ratio in steel fiber-aggregate mixture system The calculation process is as follows: Equation 32: ; Equation 33: ; Equation 34: ; Formula 35: ; Equation 36: ; Equation 37: ; ② The aggregate filling rate under steel fiber disturbance was calculated using the CPM model. and aggregate porosity The calculation process is as follows: The proportion of dense aggregate volume in the fiber-reinforced concrete mixture system is: The calculation process is as follows: Equation 38: ; The volume of the slurry in the fiber-reinforced concrete mixture system is The excess slurry volume at the solid surface is The calculation process is as follows: Formula 39: ; Formula 40: ; The aggregate-fiber solid phase packing volume in the fiber-reinforced concrete mixture system is The absolute volume of coarse aggregate is The absolute volume of fine aggregate is The calculation process is as follows: Equation 41: ; Equation 42: ; Equation 43: ; ③ Calculate the number of powder systems separately The calculation process for the mass of each component in a unit volume of fiber-reinforced concrete mix is ​​as follows: Equation 44: ; Formula 45: ; Equation 46: ; Equation 47: ; Formula 48: ; Equation 49: ; Formula 50: ; Equation 51: ; Equation 52: ; Equation 53: ; In equations 31-53: The proportion of densely packed coarse aggregate in a solid-phase mixed packing system is dimensionless. For the first One type of steel fiber, dimensionless; The total quantity of steel fibers is dimensionless. For the first The unit volume content of a certain type of fiber, in units of m 3 ; For the first The specific surface area of ​​the fiber type, in units of m² -1 ; For the first The relative thickness of the excess sand filling layer on the surface of the steel fiber of the fiber type, dimensionless; For the first The length of a single fiber of a certain type of fiber; For the first The number of fibers per unit volume of a certain type of fiber, dimensionless; The thickness of the excess sand layer filling layer on the surface of coarse aggregate in fiberless concrete is measured in meters. The thickness of the excess grout filling layer in fiberless self-compacting concrete is measured in meters (m). The filling rate of the coarse aggregate system under steel fiber disturbance is dimensionless. The porosity of the coarse aggregate system under steel fiber perturbation is dimensionless. The fill rate of the fine aggregate system under steel fiber disturbance is dimensionless. The porosity of the fine aggregate system under steel fiber disturbance is dimensionless. Let m be the bulk volume of coarse aggregate in the solid-phase mixture system, with dimensions m. 3 ; The absolute volume of coarse aggregate in the solid-phase mixture system is given by the dimension m. 3 ; The volume of excess sand filling layer on the surface of steel fiber-coarse aggregate in a solid-phase mixed system is given by the dimension m. 3 ; The volume of fine aggregate in a solid-phase mixture is given by the dimension m. 3 ; Let m be the absolute volume of fine aggregate in the solid-phase mixture system, with dimensions m. 3 ; The volume percentage of fine aggregate in the steel fiber-aggregate mixture in the solid-phase mixture system is dimensionless. The aggregate filling rate under steel fiber disturbance is dimensionless. is the porosity of aggregate mass under steel fiber disturbance, dimensionless; The thickness of the excess slurry filling layer on the surface of the solid component is given in meters. For the first The scaling factor of the excess slurry filling layer on the solid surface under fiber adsorption, dimensionless; The proportion of densely packed aggregate volume in the fiber-reinforced concrete mixture system is dimensionless. The specific surface area of ​​coarse aggregate, in units of m. -1 ; The specific surface area of ​​the fine aggregate is given by the unit m. -1 ; The volume of the slurry in the fiber-reinforced concrete mixture system is expressed in meters (m). 3 ; The excess slurry volume at the solid surface is expressed in m. 3 ; The aggregate-fiber solid phase packing volume in the fiber-reinforced concrete mixture system is expressed in m. 3 ; The absolute volume of coarse aggregate in the fiber-reinforced concrete mixture system, with dimensions in m. 3 ; The absolute volume of fine aggregate in the concrete mixture system, with dimensions in m. 3 ; The number of powder systems is dimensionless. The volume of air contained in concrete is expressed in meters. 3 ; The water-to-binder ratio is dimensionless. The percentage of admixtures in cementitious materials is dimensionless. The mass percentage of cement in the powder is dimensionless. The mass percentage of fly ash in the powder material is dimensionless. The mass percentage of slag in the powder is dimensionless. The mass percentage of silica fume in the powder is dimensionless. The mass of cementitious material in the mixed steel fiber self-compacting concrete mixture is expressed in kg. The mass of cement in the mixed steel fiber self-compacting concrete mixture is expressed in kg. The mass of fly ash in the mixed steel fiber self-compacting concrete mixture is expressed in kg. The mass of slag in the mixed steel fiber self-compacting concrete mixture is expressed in kg. The mass of silica fume in the mixed steel fiber self-compacting concrete mixture is expressed in kg. The mass of water in the mixed steel fiber self-compacting concrete mixture is expressed in kg. The mass of fine aggregate in the mixed steel fiber self-compacting concrete mixture is expressed in kg. The mass of coarse aggregate in the mixed steel fiber self-compacting concrete mixture is expressed in kg. Let K be the mass of the kth type of steel fiber in hybrid steel fiber self-compacting concrete, in kg.

9. The method for secondary design of mix proportion of hybrid steel fiber self-compacting concrete based on a customized solid-phase surface filling layer according to claim 8, characterized in that: The parameter correction process for the modified CPM model with external addition of rigid fibers is as follows: ① Calculate the micro-disturbance volume of a single fiber on the surrounding aggregate. : Equation 54: ; Equation 55: ; Equation 56: ; Equation 57: ; ② Calculate the virtual filling rate of each aggregate particle size range i under fiber disturbance. : Equation 58: ; Equation 59: ; Formula 60: ; In equations 54-60: For the first The equivalent spherical particle size of the various types of steel fibers, in meters; For the first The diameter of the type of steel fiber, in meters; ——No. The length of the steel fiber of each type, in meters; For the first The equivalent particle size ratio of various types of steel fibers to aggregates in various particle size ranges is dimensionless. The volume factor representing the micro-perturbation of a single fiber on the surrounding aggregate is dimensionless. The volume of the micro-disturbance exerted by a single fiber on the surrounding aggregate is given by the dimension m. 3 ; Microfiber content per unit volume, in units of m 3 ; For the first in concrete The number of fibers in a type of fiber, dimensionless; , is the perturbation coefficient of fiber influence for each aggregate particle size range i, dimensionless; The loose filling rate of aggregates in each particle size range is dimensionless. is the skeleton compaction coefficient, which is dimensionless.

10. The method for secondary design of mix proportion of hybrid steel fiber self-compacting concrete based on a customized solid-phase surface filling layer according to claim 1, characterized in that: The secondary mix proportion calculation and adjustment process includes: setting , After calculating the initial secondary mix proportions, the expected work performance is determined. If the work performance does not meet the standard, the secondary design envelope curve is adjusted until the work performance meets the standard. When the work performance meets the standard, a strength test is performed. If the strength test passes, the initial secondary mix proportion is output as the final mix proportion. If the strength test fails, the mix proportion of the fiberless self-compacting concrete foundation is adjusted until the strength test passes, and the initial secondary mix proportion is output as the final mix proportion.

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