阅读说明：本技术 一种基于工作性能和造价的混凝土配合比优化方法 (Concrete mix proportion optimization method based on working performance and construction cost ) 是由 张绳忠 刘亚帅 盛灿军 杜显平 黄瑞堂 刘锋 付炳科 于 2021-09-27 设计创作，主要内容包括：本发明公开了一种基于工作性能和造价的混凝土配合比优化方法,所述方法包括以下步骤：以混凝土的各组分质量为设计变量,在包括所述混凝土的工作性能满足使用要求的约束条件下,确定关于所述混凝土的强度和成本的目标函数,通过所述目标函数求得所述设计变量的最优解。本发明的优点是：相比较现有方法,可同时考虑设计中的多个参数变量的影响,在保证混凝土性能的同时,降低单位强度成本；不仅适用于自密实混凝土,对普通混凝土和其他特种混凝土的配合比优化同样适用。(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.)

1. A concrete mix proportion optimization method based on working performance and construction cost is characterized by comprising 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.

2. The concrete mix proportion optimizing method based on workability and construction cost according to claim 1,

the design variable comprises the mass x of the water₁Mass x of water reducing agent₂Mass x of stone powder₃Mass x of crushed stone₄Mass x of sand and stone₅Mass x of cement₆；

The objective function includes a cost F per unit volume of the concrete₁(X) and cost per unit volume F of the concrete₁(X) and the compressive strength f of the concrete_cpRatio F₂(X), respectively:

F₁(X)＝c₁x₁+c₂x₂+c₃x₃+c₄x₄+c₅x₅+c₆x₆，

wherein, c₁、c₂、c₃、c₄、c₅、c₆The unit mass cost of water, water reducing agent, stone powder, broken stone, sand and stone and cement.

3. The concrete mix proportion optimizing method based on workability and construction cost according to claim 2,

the concreteIncluding the compressive strength f_cpAnd 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_cThe minimum compressive strength required to be satisfied by the concrete, s is the minimum slump required to be satisfied by the concrete, V_mIs the volume of the concrete, which is 1, gamma₁、γ₂、γ₃、γ₄、γ₅、γ₆Respectively the specific gravity of water, water reducing agent, stone powder, broken stone, sand stone and cement, V_aIs the volume of air in the concrete, x_iFor the design variable, x_iuAnd x_ilAre respectively the design variable x_iUpper and lower limit values of (2).

4. A concrete mix proportion optimizing method based on workability and construction cost according to claim 3,

fitting the compressive strength f of the concrete by a non-linear regression analysis method based on the test data of the existing literature_cpSlump s of the concrete_pAnd fitting a model according to the relation of the design variables, wherein the fitting model comprises the following steps:

wherein, a₁、a₂、a₃、a₄、a₅、a₆、a₇Is the compressive strength f of the concrete_cpIs obtained by the least square method, b₁、b₂、b₃、b₄、b₅、b₆、b₇Is slump s of the concrete_pThe fitting parameters of (2) are obtained by a least square method.

5. The concrete mix proportion optimizing method based on workability and construction cost according to claim 4,

solving the optimal solution of the design variable by adopting a sequence quadratic programming method;

in the objective function F₁(X) and F₂(X) the minimum values are:

minF₁(X)＝c₁x₁+c₂x₂+c₃x₃+c₄x₄+c₅x₅+c₆x₆，

the constraint conditions are as follows:

x_il≤x_i≤x_iu,i＝1,2,...,6。

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. In the design process of the self-compacting concrete mixing ratio, the cement dosage can improve the fluidity of the mixture, but the concrete cost per unit volume can be increased, which is not favorable for controlling the construction cost.

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 construction cost is characterized in that: 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 water₁Mass x of water reducing agent₂Mass x of stone powder₃Mass x of crushed stone₄Mass x of sand and stone₅Mass x of cement₆；

The objective function includes a cost F per unit volume of the concrete₁(X) and cost per unit volume F of the concrete₁(X) resistance to compression with said concreteStrength f_cpRatio F₂(X) which are respectively represented by the following formulas:

F₁(X)＝c₁x₁+c₂x₂+c₃x₃+c₄x₄+c₅x₅+c₆x₆，

wherein, c₁、c₂、c₃、c₄、c₅、c₆The 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_cpAnd 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_cThe minimum compressive strength required to be satisfied by the concrete, s is the minimum slump required to be satisfied by the concrete, V_mIs the volume of the concrete, which is 1, gamma₁、γ₂、γ₃、γ₄、γ₅、γ₆Respectively the specific gravity of water, water reducing agent, stone powder, broken stone, sand stone and cement, V_aIs the volume of air in the concrete, x_iFor the design variable, x_iuAnd x_ilAre respectively the design variable x_iUpper and lower limit values of (2).

Scoring by non-linear regression based on experimental data in the literatureMethod of fitting the compressive strength f of said concrete_cpSlump s of the concrete_pAnd fitting a model according to the relation of the design variables, wherein the fitting model comprises the following steps:

wherein, a₁、a₂、a₃、a₄、a₅、a₆、a₇Is the compressive strength f of the concrete_cpIs obtained by the least square method, b₁、b₂、b₃、b₄、b₅、b₆、b₇Is slump s of the concrete_pThe 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 F₁(X) and F₂(X) the minimum values are:

min F₁(X)＝c₁x₁+c₂x₂+c₃x₃+c₄x₄+c₅x₅+c₆x₆，

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 showing the mixing ratio of the self-compacting concrete according to 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 water₁Mass x of water reducing agent₂Mass x of stone powder₃Mass x of coarse aggregate₄Mass x of sand₅Mass x of cement₆. 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 function₁(X) and cost per unit volume of concrete F₁(X) compressive Strength f with concrete_cpRatio F₂(X) which are respectively represented by the following formulas:

F₁(X)＝c₁x₁+c₂x₂+c₃x₃+c₄x₄+c₅x₅+c₆x₆，

wherein, c₁、c₂、c₃、c₄、c₅、c₆The 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, and in this embodiment, the working performance of the concrete includes the compressive strength f_cpAnd slump s_pAnd compressive strength f_cpAnd slump s_pShould 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 is_cMinimum compressive strength to be met by the concrete, s minimum slump to be met by the concrete, V_mIs the volume of concrete, which is 1m³，γ₁、γ₂、γ₃、γ₄、γ₅、γ₆Respectively the specific gravity of water, water reducing agent, stone powder, coarse aggregate, sand and cement, V_aIs the volume of air in the concrete, x_iTo design variables, x_iuAnd x_ilAre respectively a design variable x_iUpper and lower limit values of (2).

4. Compressive strength f_cpAnd slump s_pIs 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_cpSlump s_pAnd (3) relating to design variables, and expressing the fitting model as follows:

wherein, a₁、a₂、a₃、a₄、a₅、a₆、a₇Compressive strength f of concrete_cpIs obtained by the least square method, b₁、b₂、b₃、b₄、b₅、b₆、b₇Is slump of concrete s_pThe fitting parameters of (2) are obtained by a least square method. Compressive strength f when the number of design variables is i_cpAnd slump s_pI +1 fitting parameters are required.

5. And solving the optimal solution of the design variable in the objective function by adopting a sequential quadratic programming method.

In the objective function F₁(X) and F₂(X) the minimum values are:

min F₁(X)＝c₁x₁+c₂x₂+c₃x₃+c₄x₄+c₅x₅+c₆x₆，

the constraint conditions are as follows:

x_il≤x_i≤x_iu,i＝1,2,...,6。

in the embodiment, 27 sets of self-compacting concrete mix proportions and compressive strength and slump measured by tests are given according to the existing literature tests (as shown in fig. 1), 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, fitting parameters of the compressive strength and the slump of the self-compacting concrete are calculated (as shown in fig. 2). According to the general market price, the water price is 10 yuan/t, the water reducing agent price is 10000 yuan/t, the stone powder price is 80 yuan/t, the coarse aggregate price is 145 yuan/t, the sand price is 80 yuan/t, and the cement price is 110 yuan/t, the optimal mixing proportion which meets the design conditions is calculated as follows: 188kg of water 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 a plurality of 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, they are not to be considered repeated herein.