Background
The traditional concrete mix proportion design method is only based on the Inconel relation and the volume method and determines the mix proportion and the use amount of each material of the concrete according to experience, however, the Inconel relation only considers the influence of the use amounts of water and cement on the concrete strength, and does not consider the contribution and the influence of the type and the distribution of coarse aggregates on the concrete strength.
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 space two-phase concrete mix proportion design method simplifies a concrete model into coarse aggregate with space distribution and mortar filled in gaps of the coarse aggregate, simplifies the strength of concrete into the concrete consisting of the space distribution strength of the coarse aggregate and the hardening strength of a mortar body, and has the strength formula of concrete materials as follows:
fcu,o=fm×(1-γV)+fgk×γV(1-1) in the formula, fcu,oIs the concrete target strength, unit: MPa; f. ofmIs a measured value of 28-day cubic compressive strength of the mortar material, and the unit is MPa; f. ofgkThe unit is the space distribution strength of the coarse aggregate: MPa; gamma rayVIs the volume occupancy of coarse aggregate in a unit volume of concrete space, gammaV=G/ρG(1-2) in dimensionless units; G. rhoGThe concrete aggregate density is respectively the unit volume of the total coarse aggregate of the concrete, the density of the coarse aggregate, and the unit: kg/m3。
Further, the method comprises the following steps:
step 1: setting the target strength of the concrete: f. ofcu,o=fcu,k+1.645 × σ (1-3), wherein fcu,kThe standard value of the strength of the concrete is unit MPa; sigma is the standard deviation of concrete strength, and the value of sigma refers to the design rule of common concrete mix proportion, unit MPa;
step 2: establishing a perimidine relation of concrete: f. ofcu,o=a0×(W/C)+b0(1-4) wherein W/C is the ratio of water to ash, a0、b0Regression coefficient (regression correlation coefficient R) of measured data fitting2Preferably 0.90 or more);
and step 3: establishing a mortar strength relation: sandThe strength relation is a relation of mortar strength-mortar ratio or a relation of mortar strength-mortar ratio, and the calculation formula is as follows:
or
The formula (1-5a) represents the relation of mortar strength and mortar ratio, the formula (1-5b) represents the relation of mortar strength and mortar ratio, S is the amount of sand used and the unit kg/m3,a1、a2、b1、b2Regression coefficient (regression correlation coefficient R) as fitting equation2Preferably 0.90 or more);
and 4, step 4: establishing a coarse aggregate spatial distribution strength relation: the formula (1-1) can be modified to obtain:
by measuring fcu,oAnd fmF is obtained by inverse calculation of the formula 1-6gkAnd fitting to find fgkAnd fcu,oThe relationship of (1) is:
fgk=a3·fcu,o+b3(1-7) in the formula, fgkIs the spatial distribution strength of coarse aggregate, a3、b3Fitting a regression coefficient (preferably, the regression correlation coefficient is 0.90 or more);
and 5: testing the concrete and mortar cubes and testing the strength of the cubes, and determining a regression coefficient: a0, a1, a2, a3, b0, b1, b2, b 3;
step 6: according to the set slump, determining the net water consumption W in kg/m by referring to the design rule of the mix proportion of common concrete and the actually measured aggregate particle diameter3;
And 7: the volume method is used for calculating the mixing ratio of the material usage:
in the formula, ρ
C、ρ
S、ρ
G、ρ
WThe density of cement, fine aggregate, coarse aggregate and water is respectively unit kg/m
3;W
ZUnit kg/m for total water consumption
3,W
Z=W+W
f,W
fWhen using common natural bone material, W is added as additional water
fWhen a coarse aggregate having a water absorption of more than 4% per hour is used, it is preferable to consider water, W, of 0
f=γ
1hX h, unit kg/m
3;γ
1hWater absorption for one hour for coarse aggregate; alpha is the air content percentage of the concrete, and the value can be 1 when no air entraining agent or air entraining type additive is used;
and 8: according to the relation established in the steps, the following linear equation system is established to solve:
further, the step of determining the regression coefficient is:
step 1: at least 3 groups of different water-cement ratios are set according to gradient, concrete cube test blocks with the size of 100mm multiplied by 100mm are prepared, concrete uniaxial compression test is carried out, the concrete cube compression strength of 28 days is measured, the water-cement ratios in each group of data and the measured compression strength value are subjected to fitting regression by adopting a formula (1-4), and a can be obtained0、b0And the correlation coefficient R2;
Step 2: setting at least 3 groups of different mortar ratios and mortar ratios according to gradient, preparing a mortar cube test block with the size of 100mm multiplied by 100mm, carrying out uniaxial compression test, measuring the compression 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 a horizontal coordinate and the numerical value of the mortar ratio or the mortar ratio as a vertical coordinate, and fitting regression by adopting a formula (1-5a) or (1-5b) to obtain a1、b1Or a2、b2And the correlation coefficient R2;
If R in the relationship of mortar strength-mortar ratio2Higher than in relation of mortar strength-sand-cement ratioR2Then, the formulas (1-5a) and a are adopted1、b1;
If R in the relation of mortar strength-sand-cement ratio2Higher than R in the relation of mortar strength-mortar ratio2Then, the formulas (1-5b) and a are adopted2、b2;
And step 3: the dosage G of the coarse aggregate used in the step 1 and the measured compressive strength f of the concrete cubecu,oAnd the cubic compressive strength f of the mortar measured in the step 2mSubstituting in formula (1-6) to obtain the coarse aggregate spatial distribution strength f of concretegkA1 is to fcu,oAnd fgkFitting regression by formula (1-6) to obtain a3、b3。
Further, in step 3, a mineral admixture is added during preparation, and a calculation formula of the mortar strength relationship is as follows: mortar strength-mortar ratio relationship:
or the relation of mortar strength-sand-cement ratio:
wherein J is the dosage of mineral admixture in kg/m3The value can be obtained by referring to the newly revised design rule of common concrete mix proportion in China, or by experience according to the existing research data.
Further, in step 7, the mineral admixture is blended during the preparation, and the calculation formula taking the volume method as the calculation mixing ratio is as follows:
(1-11) in the formula, p
JIs the density of mineral admixture and has unit kg/m
3。
Further, in step 8, the system of linear equations (1-9) can be rewritten in the form of a matrix, and two expressions shown below can be obtained:
or
The invention has the beneficial effects that: the concrete model is simplified into the composition of the coarse aggregates distributed in space and the mortar filled in the gaps of the coarse aggregates distributed in space, the concrete strength is simplified into the superposition of the spatial distribution strength of the coarse aggregates and the hardening strength of mortar body, the contribution and the influence of the types and the distribution of the coarse aggregates on the concrete strength are considered through the spatial distribution strength of the coarse aggregates, and the method has definite physical and mechanical significance.
Detailed Description
The present invention will be described in detail with reference to specific examples. The following examples will aid those skilled in the art in further understanding the present invention, but are not intended to limit the invention in any manner.
In the following examples, coral and/or coral reef crushed stones were selected as aggregates to prepare concrete test blocks.
The first embodiment is as follows: fitting to determine regression coefficients
Step 1, establishing a wrapped rice relation: concrete cube test blocks with the size of 100mm multiplied by 100mm are prepared according to different water cement ratios, concrete uniaxial compression tests are carried out, the concrete cube compression strength in 28 days is measured, and the record is as follows:
table 1-1 concrete mix ratio at the trial stage and results
The W/C (water-cement ratio) in Table 1-1 is plotted on the abscissa as the compressive strength fcu,oPlotting scatter plot for ordinate, as shown in FIG. 2, fitting regression line can solve to obtain correlation coefficient R2Is 0.99, and a is taken from the regression line0=-93.33,b087.67, available by substitution in formula (1-4): f. ofcu,o=-93.33×(W/C)+87.67(2-1);
Step 2, establishing a mortar strength relation: preparing cubic mortar test blocks with the sizes of 100mm multiplied by 100mm according to different mortar ratios, carrying out uniaxial mortar compression test, measuring the cubic compression strength of the mortar material for 28 days, and recording as follows:
table 1-2 mortar mix proportion in trial-mix stage
The S/(W + C) (mortar ratio) and S/C (mortar ratio) in Table 1-2 are plotted on the abscissa and the compressive strength f
mAs the ordinate, a scatter plot was plotted, and as shown in FIG. 3(a) and FIG. 3(b), regression lines were fitted and the correlation coefficients were determined from the regression lines shown in FIG. 3(a) and R
2Is 0.98; from FIG. 3(b), R
2Is 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
1When 91 is substituted into formula (1-5a), the following compounds can be obtained:
step 3, establishing a coarse aggregate spatial distribution strength relation:
will step withThe amount G of the coarse aggregate used in the step 1 and the measured cubic compressive strength f of the concretecu,oAnd the cubic compressive strength f of the mortar measured in the step 2mSubstituting in formula (1-6) to obtain the coarse aggregate space distribution strength f of concretegkWith fcu,oAs the abscissa, in fgkPlotting scatter diagram for ordinate, as shown in FIG. 4, fitting regression lines and obtaining correlation coefficient, respectively, and taking a from regression line3=0.84,b3(ii) substitution of-15 with f in formula (1-7) can givegk=0.84·fcu,o-15(2-3)。
Example two:
selecting C25 concrete, i.e. fcu,k=25MPa。
1. Determining target intensity
The test uses a cube test block of 100mm × 100mm × 100mm, and the strength of the cube converted into 150mm × 150mm × 150mm should be divided by a factor of 0.95, i.e., the strength is calculated by considering the size effect
fcu,o=(25+1.645×σ)/0.95=(25+1.645×5)/0.95=34.97MPa;
2. Referring to the existing research and early trial-matching experience, according to the requirements of slump and aggregate particle size, under the condition of ensuring normal construction, the value of the net water consumption is W (200 kg/m)3;
3. Determining the cement consumption C, and changing the water consumption W to 200kg/m3C can be obtained by substituting the formula (1-4) to 343kg/m3;
4. Substituting the established 'mortar strength relation' expression (2-2) and the 'coarse aggregate spatial distribution strength relation' expression (2-3) into the equation system of (1-9) to obtain the following connected equation:
rewriting in the form of a matrix yields:
the regression coefficient obtained in example 1 was substituted into the formula (2-5), and the above equation set was solved to obtain the cement amount C, the sand amount S, the coarse aggregate amount G, and the additional water amount Wf。
And preparing a concrete cubic test block with the size of 100mm multiplied by 100mm according to the dosage of the materials, carrying out a concrete uniaxial compression test, and measuring the cubic compression strength of the concrete material for 28 days.
Example three:
selecting C30 concrete, i.e. fcu,k=30MPa。
1. Determining target intensity
The test uses a cube test block of 100mm × 100mm × 100mm, and the strength of the cube converted into 150mm × 150mm × 150mm should be divided by a factor of 0.95, i.e., the strength is calculated by considering the size effect
fcu,o=(30+1.645×σ)/0.95=(30+1.645×5)/0.95=40.24MPa;
2. Referring to the existing research and early trial-matching experience, according to the requirements of slump and aggregate particle size, under the condition of ensuring normal construction, the value of the net water consumption is W (200 kg/m)3;
3. Determining the cement consumption C, and changing the water consumption W to 200kg/m3C can be obtained by substituting the formula (1-4) to 343kg/m3;
4. Substituting the established 'mortar strength relation' expression (2-2) and the 'coarse aggregate spatial distribution strength relation' expression (2-3) into the equation system of (1-9) to obtain the following connected equation:
rewriting in the form of a matrix yields:
the regression coefficient obtained in example 1 was substituted into the formula (2-7) to obtainSolving the equation set to obtain the cement dosage C, the sand dosage S, the coarse aggregate dosage G and the additional water dosage Wf。
And preparing a concrete cubic test block with the size of 100mm multiplied by 100mm according to the dosage of the materials, carrying out a concrete uniaxial compression test, and measuring the cubic compression strength of the concrete material for 28 days.
Example four:
selecting C35 concrete, i.e. fcu,k=35MPa。
1. Determining target intensity
The test uses a cube test block of 100mm × 100mm × 100mm, and the strength of the cube converted into 150mm × 150mm × 150mm should be divided by a factor of 0.95, i.e., the strength is calculated by considering the size effect
fcu,o=(35+1.645×σ)/0.95=(35+1.645×5)/0.95=45.5MPa;
2. Referring to the existing research and early trial-matching experience, according to the requirements of slump and aggregate particle size, under the condition of ensuring normal construction, the value of the net water consumption is W (200 kg/m)3;
3. Determining the cement consumption C, and changing the water consumption W to 200kg/m3C can be obtained by substituting the formula (1-4) to 343kg/m3;
4. Substituting the established 'mortar strength relation' expression (2-2) and the 'coarse aggregate spatial distribution strength relation' expression (2-3) into the equation system of (1-9) to obtain the following connected equation:
rewriting in the form of a matrix yields:
the regression coefficient obtained in example 1 was substituted into the formula (2-9), and the above equation set was solved to obtain the cement amount C, the sand amount S, the coarse aggregate amount G, and the additional water amount Wf。
And preparing a concrete cubic test block with the size of 100mm multiplied by 100mm according to the dosage of the materials, carrying out a concrete uniaxial compression test, and measuring the cubic compression strength of the concrete material for 28 days.
Example five:
this example is a verification example of examples 2-4.
The amount of the materials used and the measured compressive strength values in examples two, three and four were counted and recorded as in tables 1 to 3:
as can be seen from tables 1-3:
1. for C25 concrete, the compressive strength is 35.7MPa which is greater than the target strength of 34.97 MPa;
2. for C30 concrete, the compressive strength is 41.5MPa which is greater than the target strength of 40.24 MPa;
3. for C35 concrete, the compressive strength is 45.6MPa greater than the target strength of 45.5 MPa.
The concrete prepared by the method can meet the design requirement of the compressive strength of the concrete.