Dispersion-reinforced fine-grained modified concrete

. Fine-grained modified concrete, reinforced with polyvinyl chloride fiber, is an innovative material, the production of which is at the development stage in Russian construction. Polyvinyl chloride fiber has high technical characteristics, is not prone to corrosion and is absolutely neutral to the environments that are created during the hardening of concrete and the operation of products, and also does not affect the nature of the hardening of the binder. The article presents the results of scientific research aimed at developing the basics of methods for predicting the properties of products, as well as choosing and optimizing the costs of the main raw materials. The conducted active experiment and the processing of its results made it possible to obtain regression equations for the compressive strength of fiber-reinforced concrete, as well as its average density, depending on variable factors. So, to obtain fiber-reinforced concrete with a compressive strength of 46.5 – 47.5 MPa; with an average density of 1668 – 1674 kg / m3, Portland cement with an activity of at least 45 MPa should be used; at a PVC fiber consumption of 5.9 – 6.0 kg/m3, a plasticizer consumption of 7.6 – 7.8%, as well as a consumption of finely ground construction waste 673 – 676 kg/m3. Based on the results of an active experiment, their statistical and analytical processing, the basics of the method for selecting the composition of fiber-reinforced concrete, depending on the specified values of variable factors, have been developed.


Introduction
In the technology of products based on concrete or reinforced concrete, the following trends have been observed in the last decades.First, there is an emphasis on achieving results that have a minimal negative impact on the environment.Secondly, we can state the desire to use waste from construction or other industries.thirdly, new types of products and structures are introduced into construction practice based on the use of textile concrete or dispersed reinforced concrete [1][2][3].
Reinforcement of products provides their increased resistance to mechanical stress (mainly bending loads), increases crack resistance.In order to provide the developing construction industry with the necessary quantity of this type of product, it is necessary to increase their production.The expediency of the production of reinforced slabs is due to the growing demand for this type of product, associated with the growing volume of construction and the versatility of their application.
The scope of modified fine-grained concrete and its characteristics depend on the properties of the fibrous material [4,5].Currently, three main types of dispersed reinforcement are used abroad: fibers in the form of short pieces of thin steel wire, glass and polypropylene fibers (Table 1).
The best characteristics of bending strength are observed in samples with a content of 3% amorphous fiber.This confirms that the amorphous fiber cooperates effectively with the concrete matrix during bending.Samples with basalt fiber show comparable results with samples reinforced with amorphous fiber [6,7].At the same time, the composite fiber shows an increase in flexural strength with increasing concentration, while the values of the basalt fiber remain almost constant.All other samples show lower results, but there is still an increase in flexural strength.The only exceptions are samples with polypropylene fiber, which show lower values compared to control samples.
The use of technological waste and waste from other industries, as well as recycled concrete, allows, on the one hand, to reduce the negative burden on the environment (which consists in the alienation of land intended for the storage of such waste), and on the other hand, it involves expanding the possibilities of creating new construction materials using such waste.Taking into account the specific properties of waste, the best results were obtained when creating cement polymer concrete [8][9][10].At the same time, it is important to develop updated methods for selecting the composition and predicting the properties of such materials.
The purpose of the research presented in the article was to develop the fundamentals of methods for predicting the properties of products, as well as the selection and optimization of the costs of the main raw materials components of modified fiber-reinforced concrete.

Materials and Methods
This type of fiber-reinforced concrete products is made from rigid concrete mixtures containing a smaller amount of water and, accordingly, a reduced amount of cement in comparison with mobile mixtures for concretes of equal strength.Portland cement and its varieties must be used as a binder for the preparation of a concrete mixture for this type of product.As a filler, recycled and prepared waste concrete scrap, and quartz sand are used.Polyvinyl chloride fiber (PVC fiber) has the following characteristics: equivalent diameter (diameter of a circle whose area corresponds to the average cross-sectional area of the fiber) 3.4 mm; fiber shape (specific appearance of the fiber, which concerns both the shape in length and the shape of the cross section, as well as possible surface treatments and / or grouping of fibers): a periodic profile that provides good adhesion to the mineral matrix (hardened concrete); tensile strength: 170-180 MPa; modulus of elasticity: up to 30 GPa; fiber length: up to 40 mm.
The preparation of fiber-reinforced concrete mixtures was carried out in accordance with GOST 26633-2015 «Concrete is heavy and fine-grained.Specifications", GOST 7473-2010 "Concrete mixes.Specifications".Compressive strength tests of samples were carried out in accordance with GOST 10180-2012 "Concrete.Methods for determining strength from control samples».
As variable factors, the costs of Portland cement, finely ground waste, plasticizer and reinforcing component are taken.The water flow rate is set in accordance with the W/C depending on the required mix workability and is not an independent factor.The plasticizer consumption in % of the water consumption was 6%.The response functions are the compressive strength of concrete (U1) and its average density (U2).The experimental conditions are presented in Table .2. As an optimization parameter, we take the coefficient of structural quality of fine-grained modified concrete (CCC), equal to the ratio of compressive strength to the average density of this concrete (U1 / U2).Processing the results of the experiment and obtaining algebraic models was carried out in the program Statistika.

Experimental Results and Discussion
Mathematical and statistical processing of the results of an active full factorial experiment made it possible to obtain regression equations for the average density (U2) and compressive strength (U1).Significant coefficients were determined by comparing the modulus of each coefficient of the regression equation with the confidence interval Δb calculated from Student's t-tests (t-test) for strength and density in parallel experiments.Accordingly, Δb1 = 0.6 MPa, and Δb2 = 0.6 kg/m3, Δb3 = 0.4 MPa.
The following mathematical models (polynomials) have been obtained: -for compressive strength: -for medium density: The resulting models were tested for adequacy using the Fisher criterion.The calculated values of the Fisher criteria are also equal for the compressive strength model F1 = 17.2; for the medium density model F2=16.1;for the bending strength model F2=16.7.The tabular values of the criteria, respectively, are 19.2, 19.3 and 19.3.The calculated values of the F-criterion do not exceed the tabular one, and with the corresponding confidence level (98%), the model can be considered adequate.This fact will be taken into account in the analytical optimization of mathematical models.The analysis of polynomials (1, 2) allows us to draw a number of particular conclusions and assumptions.The activity of Portland cement has the greatest influence on the compressive strength (the coefficient at X1 is 3.6).The influence of the consumption of finely ground waste and PVC fiber is also positive (the coefficients at X2, X3 are equal to 1.5; 1.9, respectively), while at high consumption of PVC fiber, the compressive strength begins to decrease (the coefficients at X32 are respectively minus 0.9 and 4.0).This is due to the possibility of sticking together of individual particles of PVC fiber at high costs.The optimal value of these factors will be determined in the process of analytical optimization.
Paired interactions of the combined effect of the activity of Portland cement and the consumption of finely ground waste are also significant (coefficient at Х1Х2 equal to 1.2).The influence of pair interactions is not necessarily associated with a synergistic effect and suggests additional research in this direction.Considering that the treated waste concrete scrap can contain up to 10% of non-reacted components of Portland cement clinker, these components can act as centers of crystallization of neoplasms in the process of hydration of the modified binder with an increase in the strength characteristics of the material.
The increase in the average density of modified concrete is most affected by the activity of Portland cement (coefficient at X1 equal to 41); an increase in the costs all other factors also leads to a slight increase in the average density of the modified concrete (the coefficients at X2, X3, X4 are equal to the corresponding 20; 12; 6).
The greatest influence on the increase in bending strength is exerted by the consumption of PVC fiber (the coefficient at X1 is 41), which is due to its reinforcing effect.The effect of plasticizer consumption is insignificant.The influence of other factors is also positive, but less significant (the coefficients at X1, X3 are equal to 2.6; 1.5).
An analysis of polynomial (1), which describes the relationship between compressive strength and variable factors, shows that this function (in a function of several variables) for two of these variables, namely, polymer consumption (X2) and reinforcing fiber consumption (X4), has local extrema.Therefore, we can use the mathematical apparatus of analytical local optimization.
The methodology of analytical local optimization is based on the use of non-linear dependencies, which were obtained as a result of mathematical processing and statistical analysis of experimental data.These dependencies are mathematical models that accurately describe the phenome non under study, and their adequacy is confirmed by testing statistical hypotheses.
On the other hand, these dependencies are second-order polynomials and mathematical functions of several variables, to which methods of algebraic analysis of such functions in general and, in particular, determination of their local extrema can be applied.Local extrema of such functions are determined by differentiating the function with respect to the parameter of interest to us (in this case, from the beginning along X4, then along X2) and equating the result of differentiation to zero.The subsequent solution of the linear dependence makes it possible to find the value of the factor corresponding to the extremum on the domain of definition of this factor.
Analytical optimization based on the fact that the functions for compressive strength, average density Y1 = f1(X1, X2, X3) and Y2 = f2(X1, X2, X3) are mathematical polynomials, that is, algebraic functions of several variables, and methods can be applied to them mathematical analysis, provided that the condition of adequacy will not be violated.We determine the partial derivative of the function Y1 = f1(X1, X2, X3) with respect to X3 and equate the result to 0: In coded form, the optimal consumption of PVC fiber is X3 = 0.95, and in natural terms (see Table 2 data) is: We calculate mathematical models (polynomials) for the optimized value of the factor X3 = 0.95.The optimized functions have the form: -for compressive strength: The nomogram includes two sectors.In sector I, a relationship is established between the compressive strength of fiber-reinforced concrete and variable factors.In sector II -the relationship between the average density of fiber-reinforced concrete and variable factors.Using the nomogram, you can solve direct and inverse problems of mathematical modeling: predicting the properties of the material and selecting the composition of the material depending on the specified properties.
An example solution is shown in red lines in Fig. 4. Initially specified in the example under consideration are the consumption of finely ground concrete waste (670 kg / m3), which corresponds to the point "a" and the required strength of fiber-reinforced concrete (36 MPa).From the point "a" we draw a straight line perpendicular to the y-axis through sectors I and II.In sector I, at the intersection with the curved line of strength equal to 36 MPa, we get the point "b".From the point "b" we lower the perpendicular to the abscissa axis and get the point "c", which corresponds to the established activity of the binder, equal to 44.2 MPa.In the second sector.From the point "d", which corresponds to the binder activity of 44.2 MPa, a straight line is drawn parallel to the y-axis until it intersects with the straight line (a, b) and we get the point "e", which corresponds to an average density of 1696 kg / m3.The coefficient of constructive quality is equal to 21.2 kPa •m3 / kg.
When solving a direct prognostic problem, when it is necessary to evaluate the values of property indicators depending on the values of variable factors at the optimal consumption of PVC fiber equal to 5.90 ... 6.0 kg / m3, the values of these factors are set and graphically determine the compressive strength and average density.For example, the consumption of finely ground concrete waste is set to 660 kg/m3 and the activity of the binder is 45 MPa.In sector I, from the points with the indicated parameters, we draw perpendiculars to the intersection and obtain a compressive strength value equal to 36 MPa; further, in the second sector, we similarly obtain the value of the average density of fiber-reinforced concrete, equal to 1695 kg/m3.The coefficient of constructive quality is respectively equal to 21.2 kPa •m3/kg.
Verification of the reliability of the results obtained is carried out by conducting control batches and determining the actual values of the density and strength of fiber-reinforced concrete samples.

Conclusion
The problem of increasing the efficiency of building systems and structures is a complex problem and includes a target component that takes into account energy costs for the entire life cycle of the material; a component that takes into account safety conditions and a component that evaluates the durability of the operation of systems or materials.
For fiber-reinforced concrete, performance indicators will be the possibility of reducing material consumption per unit area through the use of thinner products while maintaining all standard characteristics and operational stability.Also important is the possibility of replacing part of the clinker with active mineral components, or activated waste from construction and renovation.
The results of the studies show that as active mineral components in the composition of the binder and concrete, processed and specially prepared construction waste (concrete scrap), as well as cement-containing products of the renovation of raw materials as a fine aggregate, can be used.

E3SFig. 3 .Fig. 4 .
Fig. 3. Dependence of the average density of fiber-reinforced concrete samples on the activity of Portland cement and the consumption of finely ground waste at the optimal consumption of PVC fiber equal to 5.90...6.0 kg/m 3 .

Table 1 .
Specifications of various fibers

Table 2 .
Conditions of the experiment to optimize the composition of the material