CN112185485B - Design method for mixing proportion of space two-phase concrete - Google Patents
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Abstract
The invention discloses a design method of a space two-phase concrete mix proportion, which relates to the technical field of concrete mix proportion calculation, and the method simplifies a concrete model into space-distributed coarse aggregate and mortar filled among gaps of the coarse aggregate, wherein the strength of the concrete is simplified to be composed of the space-distributed strength of the coarse aggregate and the hardening strength of a mortar body, and in the space two-phase concrete model, the concrete strength, the mortar strength and the materials have the following three relations: a coated rice relationship, a mortar strength relationship and a coarse aggregate spatial distribution strength relationship. The influence of the type of the coarse aggregate and the distribution thereof on the strength of the concrete is considered through the spatial distribution strength of the coarse aggregate, and the method is suitable for the strength design method of the concrete adopting different types of coarse aggregates.
Description
Technical Field
The invention relates to a concrete mix proportion calculating method, in particular to a space two-phase concrete mix proportion designing method.
Background
The traditional concrete mixing proportion design method is only based on a coated rice relation and a volume method, and the mixing proportion amount of each material of the concrete is determined according to experience, however, the coated rice relation only considers the influence of the amount of water and cement on the strength of the concrete, and does not consider the contribution and influence of the coarse aggregate type and the distribution thereof on the strength of the concrete.
Disclosure of Invention
In order to solve the defects in the prior art, the invention provides a concrete mix proportion design method suitable for adopting different types of coarse aggregates, which specifically adopts the following technical scheme:
a design method of a space two-phase concrete mix proportion simplifies a concrete model into coarse aggregates which are spatially distributed and mortar filled among gaps of the coarse aggregates, the strength of the concrete is simplified to be composed of the spatial distribution strength of the coarse aggregates and the hardening strength of mortar, and the strength formula of the concrete material is as follows:
f cu,o =f m ×(1-γ V )+f gk ×γ V (1-1) wherein f cu,o The unit is the target strength of the concrete: MPa; f (f) m Is a measured value of 28-day cubic compressive strength of mortar material, and is singleBit MPa; f (f) gk The spatial distribution strength of the coarse aggregate is as follows: MPa; gamma ray V Gamma, the volume occupancy of coarse aggregate in concrete space per unit volume V =G/ρ G (1-2) being dimensionless units; G. ρ G The concrete total coarse aggregate consumption and coarse aggregate density in unit volume are respectively as follows: kg/m 3 。
Further, the method comprises the following steps:
step 1: setting target strength of concrete: f (f) cu,o =f cu,k +1.645×σ (1-3), where f cu,k Is the standard strength value of concrete, and is expressed in MPa; sigma is the standard deviation of the concrete strength, and the value of sigma refers to the common concrete mix proportion design rule, unit MPa;
step 2: establishing a concrete covered rice relation: f (f) cu,o =a 0 ×(W/C)+b 0 (1-4) wherein W/C is the water-ash dosage ratio, a 0 、b 0 Regression coefficient of actual measurement data fitting (regression correlation coefficient R 2 Preferably 0.90 or more);
step 3: establishing a mortar strength relation: the sand strength relation is a mortar strength-mortar ratio relation or a mortar strength-mortar ratio relation, and the calculation formula is as follows:or->
The formula (1-5 a) represents the relation between the mortar strength and the mortar ratio, the formula (1-5 b) represents the relation between the mortar strength and the mortar ratio, S represents the amount of sand, and the unit is kg/m 3 ,a 1 、a 2 、b 1 、b 2 For fitting regression coefficients (regression correlation coefficient R 2 Preferably 0.90 or more);
step 4: establishing a coarse aggregate spatial distribution strength relation: the modification of the formula (1-1) can be carried out:
by measuring f cu,o And fm, obtaining f by inverse calculation of the formula 1-6 gk And fitting to find f gk And f cu,o The relation of (2) is:
f gk =a 3 ·f cu,o +b 3 (1-7) wherein f gk Is the space distribution strength of coarse aggregate, a 3 、b 3 Fitting regression coefficients (regression correlation coefficients are preferably 0.90 or more);
step 5: fitting concrete and mortar cubes and testing the strength of the concrete and mortar cubes to determine regression coefficients: a, a 0 、a 1 、a 2 、a 3 、b 0 、b 1 、b 2 、b 3 ;
Step 6: according to the set slump, the net water consumption W is determined according to the common concrete mix proportion design rule and the actual measured aggregate particle diameter, and the unit is kg/m 3 ;
Step 7: the volume method is used for calculating the mixing ratio of the consumption of each material:
wherein ρ is C 、ρ S 、ρ G 、ρ W The density of cement, fine aggregate, coarse aggregate and water is respectively expressed in kg/m 3 ;W Z Is the total water consumption, the unit is kg/m 3 ,W Z =W+W f ,W f For adding water, when using common natural aggregate, W f =0, additional water is preferably considered when using coarse aggregates with a water absorption of more than 4% for one hour, W f =γ 1h Xh, unit kg/m 3 ;γ 1h The water absorption rate of the coarse aggregate is one hour; alpha is the gas content percentage of the concrete, and the value of alpha can be 1 when an air entraining agent or an air entraining additive is not used;
step 8: according to the relation established in the steps, establishing the following linear equation system to solve:
further, the step of determining the regression coefficients is:
step 1: setting at least 3 groups of different water-cement ratios according to gradients, preparing concrete cube test blocks with the size of 100mm multiplied by 100mm, performing a concrete uniaxial compression test, measuring the compressive strength of the concrete cube for 28 days, fitting and regressing the water-cement ratio in each group of data and the measured compressive strength value by adopting the formula (1-4), and obtaining a 0 、b 0 Correlation coefficient R 2 ;
Step 2: setting at least 3 groups of different mortar ratios and mortar ratios according to gradients, preparing a mortar cube test block with the size of 100mm multiplied by 100mm, performing a uniaxial compression test, measuring the compressive strength of the mortar cube for 28 days, drawing a scatter diagram by taking the numerical value of the mortar ratio or the mortar ratio as an abscissa and taking the measured compressive strength value as an ordinate, fitting and regressing by adopting a formula (1-5 a) or a formula (1-5 b) to obtain a 1 、b 1 Or a 2 、b 2 Correlation coefficient R 2 ;
If R in the relation of mortar strength and mortar ratio 2 Higher than R in relation of mortar strength and sand-lime ratio 2 Then adopting the formula (1-5 a) and a 1 、b 1 ;
If R in relation of mortar strength and sand-lime ratio 2 Higher than R in the relation of mortar strength and mortar ratio 2 Then adopting the formula (1-5 b) and a 2 、b 2 ;
Step 3: the coarse aggregate amount G used in the step 1 and the measured compressive strength f of the concrete cube cu,o And the compressive strength f of the mortar cube measured in the step 2 m Substituting into (1-6) to obtain the coarse aggregate spatial distribution strength f of the concrete gk Will f cu,o And f gk Fitting regression is performed by adopting the formula (1-6) to obtain a 3 、b 3 。
Further, in the step 3, mineral admixture is doped during preparation, and the calculated formula of the mortar strength relation is as follows: mortar strength-mortar ratio relationship:or sandSlurry strength-sand-lime ratio relationship:
wherein J is the amount of mineral admixture, and the unit is kg/m 3 The value can be obtained by referring to the rule of design of common concrete proportion revised recently in China, or obtained empirically according to the existing research data.
In step 7, the mineral admixture is blended during the preparation, and the calculated formula of the calculated mixing ratio by using a volumetric method is as follows:wherein ρ is J The density of the mineral admixture is expressed in kg/m 3 。
Further, in step 8, the linear equation set (1-9) may be rewritten in the form of a matrix, resulting in two expressions as follows:
or (b)
The beneficial effects of the invention are as follows: the method simplifies the concrete model into the space distribution coarse aggregate and mortar filled among the space distribution coarse aggregate, simplifies the concrete strength into the superposition of the space distribution strength of the coarse aggregate and the hardening strength of the mortar body, considers the contribution and influence of the coarse aggregate type and the distribution thereof to the concrete strength through the space distribution strength of the coarse aggregate, has clear physical and mechanical significance, and is suitable for the strength design method of the concrete adopting different types of coarse aggregates, including but not limited to common aggregate concrete, lightweight aggregate concrete and the like.
Drawings
FIG. 1 is a schematic diagram of a theoretical model of a spatial two-phase concrete;
the concrete of fig. 2 has a covered meter relationship;
mortar strength relationship of the mortar of fig. 3, wherein: FIG. 3 (a) shows the mortar specific strength relationship, and FIG. 3 (b) shows the mortar specific strength relationship;
FIG. 4 is a graph showing the spatial distribution strength relationship of coarse aggregate of concrete.
Detailed Description
The invention will now be described in detail with reference to specific examples which will assist those skilled in the art in further understanding the invention, but which are not intended to limit the invention in any way.
In the following examples, coral and/or coral reef crushed stones were selected as aggregate to prepare concrete test blocks.
Embodiment one: trial and error to determine regression coefficients
Step 1, establishing a covered rice relation: concrete cubes with the dimensions of 100mm multiplied by 100mm are prepared according to different water cement ratios respectively, and are subjected to a concrete uniaxial compression test, and the compressive strength of the concrete cubes within 28 days is measured and recorded as follows:
TABLE 1-1 concrete mix ratio at trial stage and results
The compressive strength f is shown on the abscissa of W/C (water cement ratio) in Table 1-1 cu,o As the ordinate, a scatter diagram is drawn, and as shown in figure 2, a regression line is fitted to obtain a correlation coefficient R 2 0.99, a is taken from the regression line 0 =-93.33,b 0 =87.67, and substitution into formula (1-4) can be obtained: f (f) cu,o =-93.33×(W/C)+87.67(2-1);
Step 2, establishing a mortar strength relation: mortar cube test blocks with the dimensions of 100mm multiplied by 100mm are prepared according to different mortar ratios respectively, a single-shaft mortar compression test is carried out, the compressive strength of a mortar material cube for 28 days is measured, and the following steps are recorded:
TABLE 1-2 mortar mix at trial formulation stage
S/(W+C) (mortar ratio), S/C (sand-lime ratio) in tables 1-2 are taken as abscissa, and compressive strength f is taken as m On the ordinate, a scatter diagram is drawn, regression lines are fitted and correlation coefficients are solved as shown in FIG. 3 (a) and FIG. 3 (b), R 2 0.98; from FIG. 3 (b), R 2 0.97. Since the goodness of fit in FIG. 3 (a) is high, a is taken from the regression line in FIG. 3 (a) 1 =-30.0,b 1 =91, and substitution into formula (1-5 a) can be obtained:
step 3, establishing a coarse aggregate spatial distribution strength relation:
the coarse aggregate dosage G used in the step 1 and the measured compressive strength f of the concrete cube cu,o And the compressive strength f of the mortar cube measured in the step 2 m Substituting into (1-6) to obtain the coarse aggregate spatial distribution strength f of the concrete gk At f cu, o is the abscissa, f gk Drawing a scatter diagram with ordinate, respectively fitting regression lines and obtaining correlation coefficients as shown in FIG. 4, and taking a from the regression lines 3 =0.84,b 3 = -15, substituting f into formula (1-7) to obtain f gk =0.84·f cu,o -15(2-3)。
Embodiment two:
selecting C25 concrete, i.e. f cu,k =25MPa。
1. Determining target intensity
The test uses a 100mm x 100mm cube test block, and when considering the size effect, calculating, the intensity of a cube converted into 150mm by 150mm should be divided by a factor of 0.95, i.e
f cu,o =(25+1.645×σ)/0.95=(25+1.645×5)/0.95=34.97MPa;
2. Referring to the existing research and early trial-and-preparation experience, according to slump and aggregate particle size requirements, under the condition that normal construction can be met, the value of the net water consumption is W=200 kg/m 3 ;
3. The cement amount C is determined, and the water consumption W=200 kg/m 3 Substituting (1-4) to obtain C=343 kg/m 3 ;
4. The following simultaneous equations are obtained by substituting the established mortar strength relation formula (2-2) and coarse aggregate space distribution strength relation formula (2-3) into the equation set of (1-9):
the overwriting in the form of a matrix can be achieved:
substituting regression coefficient obtained in example 1 into equation (2-5), solving the above equation to obtain cement amount C, sand amount S, coarse aggregate amount G, and additional water amount W f 。
And according to the dosage of the materials, preparing concrete cube test blocks with the dimensions of 100mm multiplied by 100mm, performing a concrete uniaxial compression test, and measuring the compressive strength of the concrete cube for 28 days.
Embodiment III:
selecting C30 concrete, i.e. f cu,k =30MPa。
1. Determining target intensity
The test uses a 100mm x 100mm cube test block, and when considering the size effect, calculating, the intensity of a cube converted into 150mm by 150mm should be divided by a factor of 0.95, i.e
f cu,o =(30+1.645×σ)/0.95=(30+1.645×5)/0.95=40.24MPa;
2. Ginseng radixBased on the existing research and early trial experience, according to slump and aggregate particle size requirements, the value of the net water consumption is W=200 kg/m under the condition of ensuring that normal construction can be met 3 ;
3. The cement amount C is determined, and the water consumption W=200 kg/m 3 Substituting (1-4) to obtain C=343 kg/m 3 ;
4. The following simultaneous equations are obtained by substituting the established mortar strength relation formula (2-2) and coarse aggregate space distribution strength relation formula (2-3) into the equation set of (1-9):
the overwriting in the form of a matrix can be achieved:
substituting regression coefficient obtained in example 1 into equation (2-7), solving the above equation to obtain cement amount C, sand amount S, coarse aggregate amount G, and additional water amount W f 。
And according to the dosage of the materials, preparing concrete cube test blocks with the dimensions of 100mm multiplied by 100mm, performing a concrete uniaxial compression test, and measuring the compressive strength of the concrete cube for 28 days.
Embodiment four:
selecting C35 concrete, i.e. f cu,k =35MPa。
1. Determining target intensity
The test uses a 100mm x 100mm cube test block, and when considering the size effect, calculating, the intensity of a cube converted into 150mm by 150mm should be divided by a factor of 0.95, i.e
f cu,o =(35+1.645×σ)/0.95=(35+1.645×5)/0.95=45.5MPa;
2. By referring to the existing research and early trial experience, the slump and aggregate particle size requirements can be metIn the case of construction, the net water consumption has a value of w=200 kg/m 3 ;
3. The cement amount C is determined, and the water consumption W=200 kg/m 3 Substituting (1-4) to obtain C=343 kg/m 3 ;
4. The following simultaneous equations are obtained by substituting the established mortar strength relation formula (2-2) and coarse aggregate space distribution strength relation formula (2-3) into the equation set of (1-9):
the overwriting in the form of a matrix can be achieved:
substituting regression coefficient obtained in example 1 into formula (2-9), solving the above equation to obtain cement amount C, sand amount S, coarse aggregate amount G, and additional water amount W f 。
And according to the dosage of the materials, preparing concrete cube test blocks with the dimensions of 100mm multiplied by 100mm, performing a concrete uniaxial compression test, and measuring the compressive strength of the concrete cube for 28 days.
Fifth embodiment:
this example is the verification example of examples 2-4.
The amounts of materials used and the compressive strength values measured in examples two, three and four were counted and recorded as in tables 1 to 3:
as can be seen from tables 1 to 3:
1. for C25 concrete, the compressive strength is 35.7MPa and is more than 34.97MPa of target strength;
2. for C30 concrete, the compressive strength is 41.5MPa and is more than the target strength of 40.24MPa;
3. for C35 concrete, the compressive strength is 45.6MPa and is larger than the target strength of 45.5MPa.
The concrete prepared by the mixing proportion design method can meet the requirement of concrete compressive strength design.
Claims (5)
1. A design method of a space two-phase concrete mixing proportion is characterized in that a concrete model is simplified into coarse aggregates which are spatially distributed and mortar filled among gaps of the coarse aggregates, the strength of the concrete is simplified to be composed of the spatially distributed strength of the coarse aggregates and the hardening strength of mortar bodies, and the strength formula of a concrete material is as follows:
f cu,o =f m ×(1-γ V )+f gk ×γ V (1-1) wherein f cu,o The unit is the target strength of the concrete: MPa; f (f) m The measured value of the 28-day cubic compressive strength of the mortar material is expressed in MPa; fgk the spatial distribution strength of coarse aggregate, unit: MPa; gamma ray V Gamma, the volume occupancy of coarse aggregate in concrete space per unit volume V =G/ρ G (1-2) being dimensionless units; G. ρ G The concrete is characterized by respectively comprising the following components in unit volume: kg/m 3 ;
The method comprises the following steps:
step 1: setting target strength of concrete: f (f) cu,o =f cu,k +1.645×σ (1-3), where f cu,k Is the standard strength value of concrete, and is expressed in MPa; sigma is the standard deviation of concrete strength, and the value of sigma refers to the design rule of common concrete mix proportion, and the unit is MPa;
step 2: establishing a concrete covered rice relation: f (f) cu,o =a 0 ×(W/C)+b 0 (1-4) wherein W/C is the water-ash dosage ratio, a 0 、b 0 Fitting regression coefficients to the measured data;
regression correlation coefficient R 2 0.90 or more;
step 3: establishing a mortar strength relation: the sand strength relation is a relation of mortar strength and mortar ratio or a relation of mortar strength and mortar ratioThe formula is:or->
The formula (1-5 a) represents the relation between the mortar strength and the mortar ratio, the formula (1-5 b) represents the relation between the mortar strength and the mortar ratio, S represents the amount of sand, and the unit is kg/m 3 ,a 1 、a 2 、b 1 、b 2 Is a regression coefficient of fitting type; regression correlation coefficient R 2 0.90 or more;
step 4: establishing a coarse aggregate spatial distribution strength relation: the modification of the formula (1-1) can be carried out:
by measuring f cu,o And f m F is obtained by back calculation from 1-6 gk And fitting to find f gk And f cu,o The relation of (2) is:
f gk =a 3 ·f cu,o +b 3 (1-7) wherein f gk Is the space distribution strength of coarse aggregate, a 3 、b 3 Fitting regression coefficients; the regression correlation coefficient is more than or equal to 0.90;
step 5: fitting concrete and mortar cubes and testing the strength of the concrete and mortar cubes to determine regression coefficients: a, a 0 、a 1 、a 2 、a 3 、b 0 、b 1 、b 2 、b 3 ;
Step 6: according to the set slump, the net water consumption W is determined according to the design rules of the common concrete mix proportion and the actual measured aggregate particle diameter, and the unit kg/m 3 ;
Step 7: the volume method is used for calculating the mixing ratio of the consumption of each material:
wherein ρ is C 、ρ S 、ρ G 、ρ W The density of cement, fine aggregate, coarse aggregate and water is respectively expressed in kg/m 3 ;W Z Is the total water consumption, the unit is kg/m 3 ,W Z =W+W f ,W f For adding water, when using common natural aggregate, W f =0, additional water was considered when using coarse aggregates with a water absorption of more than 4% for one hour, W f =γ 1h Xh, unit kg/m 3 ;γ 1h The water absorption rate of the coarse aggregate is one hour; alpha is the gas content percentage of the concrete, and the value of alpha is 1 when an air entraining agent or an air entraining additive is not used;
step 8: according to the relation established in the steps, establishing the following linear equation system to solve:
2. the method for designing a spatial two-phase concrete mix according to claim 1, wherein the step of determining regression coefficients is:
step 1: setting at least 3 groups of different water-cement ratios according to gradients, preparing concrete cube test blocks with the size of 100mm multiplied by 100mm, performing a concrete uniaxial compression test, measuring the compressive strength of the concrete cube for 28 days, performing fitting regression on the water-cement ratio in each group of data and the measured compressive strength value by adopting the formula (1-4), and obtaining a 0 、b 0 Correlation coefficient R 2 ;
Step 2: setting at least 3 groups of different mortar ratios and mortar ratios according to gradients, preparing a mortar cube test block with the size of 100mm multiplied by 100mm, performing a uniaxial compression test, measuring the compressive strength of the mortar cube for 28 days, drawing a scatter diagram by taking the numerical value of the mortar ratio or the mortar ratio as an abscissa and taking the measured compressive strength value as an ordinate, fitting regression by adopting (1-5 a) or (1-5 b) and obtaining a 1 、b 1 Or a 2 、b 2 Correlation coefficient R 2 ;
If R in the relation of mortar strength and mortar ratio 2 Higher than sandR in relation of slurry strength and sand-lime ratio 2 Then adopting the formula (1-5 a) and a 1 、b 1 ;
If R in relation of mortar strength and sand-lime ratio 2 Higher than R in the relation of mortar strength and mortar ratio 2 Then adopting the formula (1-5 b) and a 2 、b 2 ;
Step 3: the coarse aggregate amount G used in the step 1 and the measured compressive strength f of the concrete cube cu,o And the compressive strength f of the mortar cube measured in the step 2 m Substituting into (1-6) to obtain the coarse aggregate spatial distribution strength f of the concrete gk Will f cu,o And f gk Fitting with (1-6) to obtain a 3 、b 3 。
3. The method for designing a spatial two-phase concrete mix ratio according to claim 1, wherein in step 3, mineral admixture is added during the preparation, and the calculation formula of the mortar strength relation is as follows: mortar strength-mortar ratio relationship:or mortar strength-sand-lime ratio relationship: />
Wherein J is the amount of mineral admixture, and the unit is kg/m 3 The values are either referred to the normal concrete mix design protocol or empirically based on existing research data.
4. The method for designing the mixing proportion of the space two-phase concrete according to claim 1, wherein in the step 7, mineral admixture is doped during the preparation, and the volumetric method is used as a calculation formula for calculating the mixing proportion, wherein the calculation formula is as follows:wherein ρ is J The density of the mineral admixture is expressed in kg/m 3 。
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