CN112185485A - Space two-phase concrete mix proportion design method - Google Patents

Space two-phase concrete mix proportion design method Download PDF

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CN112185485A
CN112185485A CN202011013563.6A CN202011013563A CN112185485A CN 112185485 A CN112185485 A CN 112185485A CN 202011013563 A CN202011013563 A CN 202011013563A CN 112185485 A CN112185485 A CN 112185485A
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杨海峰
蒋家盛
甘麟雄
杨超
邓志恒
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Guangxi University
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Abstract

本发明公开了一种空间二相混凝土配合比设计方法，涉及一种混凝土配合比计算技术领域，该方法将混凝土模型简化为空间分布的粗骨料和填充于粗骨料空隙间的砂浆，混凝土的强度简化为由粗骨料空间分布强度、砂浆体硬化强度组成，在空间二相混凝土模型中，混凝土强度、砂浆强度及各材料间具有如下的三关系：包罗米关系、砂浆强度关系、粗骨料空间分布强度关系。通过粗骨料空间分布强度来考虑粗骨料类型及其分布对混凝土强度的影响，适用于采用了不同类型粗骨料的混凝土的强度设计方法。

Figure 202011013563

The invention discloses a mixing ratio design method for two-phase concrete in space, and relates to the technical field of concrete mixing ratio calculation. In the spatial two-phase concrete model, the concrete strength, mortar strength and each material have the following three relationships: the Baume relationship, the mortar strength relationship, the coarse Aggregate spatial distribution strength relationship. Considering the influence of coarse aggregate type and its distribution on concrete strength through the spatial distribution of coarse aggregate strength, it is suitable for the strength design method of concrete using different types of coarse aggregate.

Figure 202011013563

Description

Space two-phase concrete mix proportion design method
Technical Field
The invention relates to a concrete mixing proportion calculation method, in particular to a spatial two-phase concrete mixing proportion design method.
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:
Figure BDA0002698337490000021
or
Figure BDA0002698337490000022
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:
Figure BDA0002698337490000023
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:
Figure BDA0002698337490000031
in the formula, ρC、ρS、ρG、ρWThe density of cement, fine aggregate, coarse aggregate and water is respectively unit kg/m3；WZUnit kg/m for total water consumption3，WZ＝W+Wf，WfWhen using common natural bone material, W is added as additional waterfWhen a coarse aggregate having a water absorption of more than 4% per hour is used, it is preferable to consider water, W, of 0f＝γ1hX h, unit kg/m3；γ1hWater 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:
Figure BDA0002698337490000032
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:
Figure BDA0002698337490000041
or the relation of mortar strength-sand-cement ratio:
Figure BDA0002698337490000042
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:
Figure BDA0002698337490000051
(1-11) in the formula, pJIs the density of mineral admixture and has unit kg/m3。
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:
Figure BDA0002698337490000052
or
Figure BDA0002698337490000053
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.
Drawings
FIG. 1 is a schematic diagram of a theoretical model of spatial two-phase concrete;
FIG. 2 is a Permitron relationship for concrete;
FIG. 3 mortar strength relationship for mortar, wherein: FIG. 3(a) is a mortar ratio strength relationship, and FIG. 3(b) is a mortar ratio strength relationship;
FIG. 4 is the strength relationship of the spatial distribution of coarse aggregate in concrete.
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
Figure RE-GDA0002772381320000061
Figure RE-GDA0002772381320000071
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
Figure BDA0002698337490000072
The S/(W + C) (mortar ratio) and S/C (mortar ratio) in Table 1-2 are plotted on the abscissa and the compressive strength fmAs 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 R2Is 0.98; from FIG. 3(b), R2Is 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，b1When 91 is substituted into formula (1-5a), the following compounds can be obtained:
Figure BDA0002698337490000081
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:
Figure BDA0002698337490000091
rewriting in the form of a matrix yields:
Figure BDA0002698337490000092
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:
Figure BDA0002698337490000111
rewriting in the form of a matrix yields:
Figure BDA0002698337490000112
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:
Figure BDA0002698337490000121
rewriting in the form of a matrix yields:
Figure BDA0002698337490000131
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:
Figure BDA0002698337490000132
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.

Claims (6)

1. A space two-phase concrete mix proportion design method is characterized in that a concrete model is simplified into coarse aggregates distributed in space and mortar filled in gaps among the coarse aggregates, the strength of concrete is simplified into the concrete model consisting of the space distribution strength of the coarse aggregates and the hardening strength of a mortar body, and the strength formula of a concrete material is as follows:
fcu,o＝fm×(1-γV)+fgk×γV(1-1) in the formula, fcu,oTarget strength for concrete, unit: MPa; f. ofmIs a measured value of 28-day cubic compressive strength of the mortar material, and the unit is MPa; fgk is the space distribution strength of the coarse aggregate, unit: 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 is characterized by comprising the following components in parts by volume: kg/m3。
2. The spatial two-phase concrete mix proportion design method according to claim 1, characterized by comprising 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 standard difference of concrete strength, and the value of sigma refers to 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) fitted to measured data2Preferably 0.90 or more);
and 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 ratio, and the calculation formula is as follows:
Figure FDA0002698337480000011
or
Figure FDA0002698337480000012
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) for fitting2Preferably 0.90 or more);
and 4, step 4: establishing a coarse aggregate spatial distribution strength relation: modification of formula (1-1) yields:
Figure FDA0002698337480000021
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 spatially distributed strength of the 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: a is0、a1、a2、a3、b0、b1、b2、b3；
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:
Figure FDA0002698337480000022
in the formula, ρC、ρS、ρG、ρWThe density of cement, fine aggregate, coarse aggregate and water is respectively unit kg/m3；WZThe total water consumption is unit kg/m3，WZ＝W+Wf，WfWhen using common natural aggregate for additional water consumption, WfWhen a coarse aggregate having a water absorption of more than 4% per hour is used, it is preferable to consider water, W, of 0f＝γ1hX h, unit kg/m3；γ1hWater absorption for one hour for coarse aggregate; alpha is the percentage of air content of the concrete, and 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:
Figure FDA0002698337480000031
3. the spatial two-phase concrete mix proportion design method according to claim 2, wherein 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 carrying out fitting regression by adopting (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 R in the relation of mortar strength-sand-cement ratio2Then, 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 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 spatial distribution strength f of concretegkA1 is to fcu，oAnd fgkFitting by the formula (1-6) can obtain a3、b3。
4. The method for designing the mixing proportion of the spatial two-phase concrete according to claim 2, wherein in the step 3, the mineral admixture is mixed during the preparation, and the calculation formula of the mortar strength relation is as follows: mortar strength-mortar ratio relationship:
Figure FDA0002698337480000041
or the relation of mortar strength-sand-cement ratio:
Figure FDA0002698337480000042
wherein J is the dosage of mineral admixture in kg/m3The value can be obtained by referring to the latest revised design rule of common concrete mix proportion in China, or by experience according to the existing research data.
5. The method for designing the mixing proportion of the spatial two-phase concrete according to claim 2, wherein in the step 7, the mineral admixture is mixed during the preparation, and the volume method is taken as a calculation formula for calculating the mixing proportion:
Figure FDA0002698337480000043
in the formula, ρJIs the density of mineral admixture and has unit kg/m3。
6. A space two-phase concrete mix proportion design method according to claim 2, characterized in that in step 8, the linear equations (1-9) can be rewritten in the form of matrix, and two expressions are obtained as follows:
Figure FDA0002698337480000051
or
Figure FDA0002698337480000052
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