CN113860810B - Concrete mix proportion optimization method based on working performance and construction cost - Google Patents
Concrete mix proportion optimization method based on working performance and construction cost Download PDFInfo
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- CN113860810B CN113860810B CN202111133930.0A CN202111133930A CN113860810B CN 113860810 B CN113860810 B CN 113860810B CN 202111133930 A CN202111133930 A CN 202111133930A CN 113860810 B CN113860810 B CN 113860810B
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- C—CHEMISTRY; METALLURGY
- C04—CEMENTS; CONCRETE; ARTIFICIAL STONE; CERAMICS; REFRACTORIES
- C04B—LIME, MAGNESIA; SLAG; CEMENTS; COMPOSITIONS THEREOF, e.g. MORTARS, CONCRETE OR LIKE BUILDING MATERIALS; ARTIFICIAL STONE; CERAMICS; REFRACTORIES; TREATMENT OF NATURAL STONE
- C04B28/00—Compositions of mortars, concrete or artificial stone, containing inorganic binders or the reaction product of an inorganic and an organic binder, e.g. polycarboxylate cements
- C04B28/02—Compositions of mortars, concrete or artificial stone, containing inorganic binders or the reaction product of an inorganic and an organic binder, e.g. polycarboxylate cements containing hydraulic cements other than calcium sulfates
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- C—CHEMISTRY; METALLURGY
- C04—CEMENTS; CONCRETE; ARTIFICIAL STONE; CERAMICS; REFRACTORIES
- C04B—LIME, MAGNESIA; SLAG; CEMENTS; COMPOSITIONS THEREOF, e.g. MORTARS, CONCRETE OR LIKE BUILDING MATERIALS; ARTIFICIAL STONE; CERAMICS; REFRACTORIES; TREATMENT OF NATURAL STONE
- C04B2111/00—Mortars, concrete or artificial stone or mixtures to prepare them, characterised by specific function, property or use
- C04B2111/00034—Physico-chemical characteristics of the mixtures
- C04B2111/00198—Characterisation or quantities of the compositions or their ingredients expressed as mathematical formulae or equations
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Abstract
The invention discloses a concrete mixing proportion optimization method based on working performance and construction cost, which comprises the following steps: the method comprises the steps of taking the mass of each component of the concrete as a design variable, determining an objective function related to the strength and the cost of the concrete under the constraint condition that the working performance of the concrete meets the use requirement, and obtaining the optimal solution of the design variable through the objective function. The invention has the advantages that: compared with the existing method, the method can simultaneously consider the influence of a plurality of parameter variables in the design, ensure the performance of the concrete and reduce the unit strength cost; the method is not only suitable for self-compacting concrete, but also suitable for optimizing the mixing proportion of common concrete and other special concrete.
Description
Technical Field
The invention relates to the technical field of concrete, in particular to a concrete mixing proportion optimization method based on working performance and manufacturing cost.
Background
Self-compacting concrete is a type of concrete that flows by its own weight without the need for vibrocompaction. The amount of cement used in the design of the self-compacting concrete mix increases the fluidity of the mix, but it results in an increase in the cost of the concrete per unit volume, which is detrimental to the control of construction costs.
In the concrete mixing proportion, the cost of each component material has obvious difference, so the dosage of each material needs to be optimized according to the concrete performance requirement, for example, the dosage of cement can be reduced by adding certain additives, and the dosage of cement can also be reduced by selecting proper aggregate gradation. Achieving mix proportion design at minimum cost is critical to the development and popularization of special concrete such as self-compacting concrete.
Disclosure of Invention
The invention aims to provide a concrete mixing proportion optimization method based on working performance and manufacturing cost according to the defects of the prior art, and the optimal solution of the quality of each component of concrete is obtained by establishing a concrete mixing proportion optimization model.
The purpose of the invention is realized by the following technical scheme:
a concrete mix proportion optimization method based on working performance and manufacturing cost is characterized by comprising the following steps: the method comprises the following steps:
the method comprises the steps of taking the mass of each component of the concrete as a design variable, determining an objective function related to the strength and the cost of the concrete under the constraint condition that the working performance of the concrete meets the use requirement, and obtaining the optimal solution of the design variable through the objective function.
The design variable comprises the mass x of the water 1 Mass x of water reducing agent 2 Mass x of stone powder 3 Mass x of crushed stone 4 Mass x of sand and stone 5 Mass x of cement 6 ；
The objective function includes a cost F per unit volume of the concrete 1 (X) and cost per unit volume F of the concrete 1 (X) and the compressive strength f of the concrete cp Ratio F 2 (X) the two formulas are respectively:
F 1 (X)＝c 1 x 1 +c 2 x 2 +c 3 x 3 +c 4 x 4 +c 5 x 5 +c 6 x 6 ，
wherein, c 1 、c 2 、c 3 、c 4 、c 5 、c 6 The unit mass cost of water, water reducing agent, stone powder, broken stone, sand and stone and cement.
The working properties of the concrete include compressive strength f cp And slump s p ；
The constraint condition also comprises that the design variables are respectively in the upper limit value range and the lower limit value range;
the constraint condition formula is as follows:
f cp ≥f c ，
s p ≥s，
x il ≤x i ≤x iu ,i＝1,2,...,6，
wherein f is c The minimum compressive strength required to be satisfied by the concrete, s is the minimum slump required to be satisfied by the concrete, V m Is the volume of the concrete, which is 1, gamma 1 、γ 2 、γ 3 、γ 4 、γ 5 、γ 6 Respectively the specific gravity of water, water reducing agent, stone powder, broken stone, sand stone and cement, V a Is the volume of air in the concrete, x i For the design variable, x iu And x il Are respectively the design variable x i Upper and lower limit values of (2).
Fitting the compressive strength f of the concrete by a nonlinear regression analysis method based on the test data of the existing literature cp Slump s of the concrete p And fitting a model according to the relation of the design variables, wherein the fitting model comprises the following steps:
wherein, a 1 、a 2 、a 3 、a 4 、a 5 、a 6 、a 7 Is the compressive strength f of the concrete cp The fitting parameters of (a) are obtained by the least square method, b 1 、b 2 、b 3 、b 4 、b 5 、b 6 、b 7 Is slump s of the concrete p The fitting parameters of (2) are obtained by a least square method.
Solving the optimal solution of the design variable by adopting a sequence quadratic programming method;
in the objective function F 1 (X) and F 2 (X) the minimum values are:
min F 1 (X)＝c 1 x 1 +c 2 x 2 +c 3 x 3 +c 4 x 4 +c 5 x 5 +c 6 x 6 ，
the constraint conditions are as follows:
x il ≤x i ≤x iu ,i＝1,2,...,6。
the invention has the advantages that: compared with the existing method, the method can simultaneously consider the influence of a plurality of parameter variables in the design, ensure the performance of the concrete and reduce the unit strength cost; the method is not only suitable for self-compacting concrete, but also suitable for optimizing the mixing proportion of common concrete and other special concrete.
Drawings
FIG. 1 is a table of the mix proportions of the self-compacting concrete of the present invention;
FIG. 2 is a table of fitting parameters of compressive strength and slump of the self-compacting concrete of the present invention.
Detailed Description
The features of the present invention and other related features are described in further detail below by way of example in conjunction with the following drawings to facilitate understanding by those skilled in the art:
example (b): the embodiment relates to a concrete mixing proportion optimization method based on working performance and construction cost, which comprises the following steps:
1. the quality of each component of the concrete is taken as a design variable, and the design variables are independent as much as possible. In this embodiment, the concrete is self-compacting concrete, and the components thereof are water, water reducing agent, stone powder, coarse aggregate, sand, and cement, that is, the design variables are the mass x of water 1 Mass x of water reducing agent 2 Mass x of stone powder 3 Mass x of coarse aggregate 4 Mass x of sand 5 Mass x of cement 6 . Of course, other components of the concrete may be selected as design variables depending on the concrete composition.
2. An objective function is determined with respect to the strength and cost of the concrete. The target function mainly considers two factors of the compressive strength and the cost of the concrete, and the cost F of the concrete with the unit volume is designed as the target function 1 (X) and cost per unit volume of concrete F 1 (X) compressive Strength f with concrete cp Ratio F 2 (X) the two formulas are respectively:
F 1 (X)＝c 1 x 1 +c 2 x 2 +c 3 x 3 +c 4 x 4 +c 5 x 5 +c 6 x 6 ，
wherein, c 1 、c 2 、c 3 、c 4 、c 5 、c 6 The unit mass cost of water, water reducing agent, stone powder, coarse aggregate, sand and cement.
3. The objective function is constrained by a constraint. The main constraint of the constraint condition is that the working performance of the concrete should meet the use requirement, in this embodiment, the working performance of the concrete includes the compressive strength f cp And slump s p And compressive strength f cp And slump s p Should be within the specification tolerance range, the secondary constraint of the constraint condition is that the design variables are within the upper and lower limit values respectively, and the formula of the constraint condition is:
f cp ≥f c ，
s p ≥s，
x il ≤x i ≤x iu ,i＝1,2,...,6，
wherein, f c Minimum compressive strength to be met by the concrete, s minimum slump to be met by the concrete, V m Is the volume of concrete, which is 1m 3 ，γ 1 、γ 2 、γ 3 、γ 4 、γ 5 、γ 6 Respectively the specific gravity of water, water reducing agent, stone powder, coarse aggregate, sand and cement, V a Is the volume of air in the concrete, x i To design variables, x iu And x il Are respectively a design variable x i The upper and lower limit values of (2).
4. Compressive strength f cp And slump s p Is an estimate of the corresponding mix ratio. Fitting the compressive strength f by a nonlinear regression analysis method based on the test data of the existing literature cp Slump s p And (3) relating to design variables, and expressing the fitting model as follows:
wherein, a 1 、a 2 、a 3 、a 4 、a 5 、a 6 、a 7 Compressive strength f of concrete cp Is obtained by the least square method, b 1 、b 2 、b 3 、b 4 、b 5 、b 6 、b 7 Is slump of concrete s p The fitting parameters of (2) are obtained by a least square method. Compressive strength f when the number of design variables is i cp And slump s p I +1 fitting parameters are required.
5. And (4) solving the optimal solution of the design variable in the objective function by adopting a sequence quadratic programming method.
In the objective function F 1 (X) and F 2 (X) minimum values are:
min F 1 (X)＝c 1 x 1 +c 2 x 2 +c 3 x 3 +c 4 x 4 +c 5 x 5 +c 6 x 6 ，
the constraint conditions are as follows:
x il ≤x i ≤x iu ,i＝1,2,...,6。
in this embodiment, 27 sets of self-compacting concrete mix proportions and the compressive strength and slump measured by the test (as shown in fig. 1) are given according to the existing literature test, and under the constraint conditions that the minimum compressive strength required by the design of the self-compacting concrete mix proportions is 20MPa and the minimum slump is 500mm, the fitting parameters of the compressive strength and the slump of the self-compacting concrete (as shown in fig. 2) are calculated. According to the general market price, the water price is 10 yuan/t, the price of the water reducing agent is 10000 yuan/t, the price of the stone powder is 80 yuan/t, the price of the coarse aggregate is 145 yuan/t, the price of the sand is 80 yuan/t, and the price of the cement is 110 yuan/t, the optimal mixing ratio which accords with the design conditions is calculated as follows: 188kg of water is used for each cubic concrete, 7.5kg of water reducing agent, 151kg of stone powder, 878kg of coarse aggregate, 758.4kg of sand and 464kg of cement, and the price of each cubic concrete with the lowest unit strength and manufacturing cost is 328 yuan.
In summary, compared with the existing method, the method of the embodiment can simultaneously consider the influence of multiple parameter variables in the design, and reduce the unit strength cost while ensuring the concrete performance. The method is not only suitable for self-compacting concrete, but also suitable for optimizing the mixing proportion of common concrete and other special concrete.
Although the conception and the embodiments of the present invention have been described in detail with reference to the drawings, those skilled in the art will recognize that various changes and modifications can be made therein without departing from the scope of the appended claims, and therefore, the description is not necessary here.
Claims (1)
1. A concrete mix proportion optimization method based on working performance and construction cost is characterized by comprising the following steps:
determining an objective function related to the strength and the cost of the concrete by taking the mass of each component of the concrete as a design variable under the constraint condition that the working performance of the concrete meets the use requirement, and solving the optimal solution of the design variable through the objective function;
the design variable includes a mass of water x 1 Mass x of water reducing agent 2 Mass x of stone powder 3 Mass of crushed stone x 4 Mass x of sand and stone 5 Mass of cement x 6 ；
The objective function includes a cost F per unit volume of the concrete 1 (X) and cost per unit volume F of the concrete 1 (X) resistance to compression with said concreteStrength f cp Ratio F 2 (X) is:
F 1 (X)＝c 1 x 1 +c 2 x 2 +c 3 x 3 +c 4 x 4 +c 5 x 5 +c 6 x 6 ，
wherein, c 1 、c 2 、c 3 、c 4 、c 5 、c 6 The unit mass cost of water, water reducing agent, stone powder, broken stone, sand and stone and cement respectively;
the working properties of the concrete include compressive strength f cp And slump s p ；
The constraint condition also comprises that the design variables are respectively in the upper limit value range and the lower limit value range;
the constraint condition formula is as follows:
f cp ≥f c ，
s p ≥s，
x il ≤x i ≤x iu ,i＝1,2,...,6，
wherein f is c The minimum compressive strength required to be satisfied by the concrete, s is the minimum slump required to be satisfied by the concrete, V m Is the volume of the concrete, which is 1, gamma 1 、γ 2 、γ 3 、γ 4 、γ 5 、γ 6 Respectively the specific gravity of water, water reducing agent, stone powder, broken stone, sand stone and cement, V a Is the volume of air in the concrete, x i For the design variable, x iu And x il Are respectively the design variable x i Upper and lower limit values of (d); based on experimental data of the existing literature, by nonlinear regressionAnalysis method of regression fitting the compressive strength f of said concrete cp Slump s of the concrete p And fitting a model according to the relation of the design variables, wherein the fitting model comprises the following steps:
wherein, a 1 、a 2 、a 3 、a 4 、a 5 、a 6 、a 7 Is the compressive strength f of the concrete cp Is obtained by the least square method, b 1 、b 2 、b 3 、b 4 、b 5 、b 6 、b 7 Is slump s of the concrete p The fitting parameters are obtained by a least square method;
solving the optimal solution of the design variable by adopting a sequence quadratic programming method;
in the objective function F 1 (X) and F 2 (X) the minimum values are:
min F 1 (X)＝c 1 x 1 +c 2 x 2 +c 3 x 3 +c 4 x 4 +c 5 x 5 +c 6 x 6 ，
the constraint conditions are as follows:
x il ≤x i ≤x iu ,i＝1,2,...,6。
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