Additive manufacturing technology of concrete products

. The article analyzes the use of 3D-printing technologies in the construction industry. The main trends in the development of this area related to the development of modern software for 3D printers, printer designs and forming extrusion heads of printers, and also to the development of formulations of building mixes used for 3D printing are noted. The relevance of the use of 3D printing technologies using concrete is conditioned by the creation of unique structural elements, objects of landscape gardening architecture or buildings. From the point of view of building materials science, this task includes considering technological factors, and, in particular, the requirements for the concrete mixture. The special attractiveness of these technologies is associated with the possibility of carrying out work on a construction site, with a high degree of mechanization of processes and with an increasing of labor productivity when performing construction and installation work. The purpose of the research described in the article is to develop a methodology for the selection of modifying additives and reinforcing fibers from the condition of obtaining products with the maximum coefficient of structural quality. The article outlines the features of the selection of the composition of concrete for the construction 3D printing. This mixture must have sufficient mobility for pumping it through pipes, set quickly and have good strength characteristics.


Introduction
3D printed concrete technologies began to develop in the late 90s of the last century in North America and the Pacific region. Significant funds were invested in the development and production of 3D printers, software development and concrete formulations [1][2][3]. The leading countries in the development of 3D technology are the United States, China, Japan, and Germany [4][5][6]. In Russia, these technologies began to develop in the last decade, so foreign commercial products, equipment and formulations are mainly used [7][8][9].
3D technology is also of interest in the construction industry for some reasons. Firstly, it is possible to automate and computerize both the production of building materials and the work on the construction site [6][7][8][9]. Secondly, it is possible to increase labor productivity and use qualified personnel as operators. Thirdly, it is the possibility of organizing control in the production of building materials and in the process of performing construction and installation works [10][11][12][13].
The opportunity to realize an automated building construction system (3D printing) at the construction site in short time will reduce the technological backlog of the construction industry and will increase its efficiency (Fig. 1.). However, a small number of specialized organizations, insufficient information about the using of the technology, as well as the lack of trust of major construction companies that caused by the uncertainty in passing the state examination do not allow the using of this technology everywhere [14,15]. The purpose of the research, that can be formulated as the creation of the scientific prerequisites for the promotion of 3D construction based on concrete, includes some technological and organizational tasks. Firstly, it is necessary to develop a method for selecting the composition of fine-grained concrete. In this case, the concrete mixture must meet the following requirements: maintains mobility for the entire time of the delivery from the mixer to the forming head of the printer; at laying in the structure, keeps the shape well, sets quickly and ensures the standard strength of the concrete at hardening. Secondly, it is necessary to develop printer designs.
Such printers are of two types: to work in the work division (production of individual parts or gardening objects) or to work on the construction site (construction of monolithic structures). Thirdly, appropriate designs of the buildings or the parts are needed, as well as software that supports the operation of the construction printer. Now both the equipment and the software for the domestic facilities are supplied from abroad. For the widespread introduction of 3D construction technologies, qualified personnel and the interest of construction companies are needed.

Materials and methods
The research presented in this article consisted in the implementation of the first of these tasks, concerning the selection of the composition of fine-grained modified concrete for 3D printing. The experiment used the method of the mathematical planning and the analytical optimization of the results [4,5]. The composition of fine-grained modified concrete included: Portland cement, polyvinyl acetate dispersion, sand, liquid glass, alkali-resistant glass fiber, plasticizer.
The conditions of the experiment are presented in table 1. The content of Portland cement and sand was assumed to be constant (30% and 60%, respectively). The water consumption was assumed to be 0.24...0.28 and was set based on the required mobility of the concrete mixture with the introduced additives.
The intervals of variation of the factors were established based on the analysis of a priori information presented in the sources (see Introdaction), as well as on the basis of the goals of the planned experiment. The consumption of liquid glass, plasticizer, and glass fiber varied in the intervals shown in table 1. The compressive strength of the samples of fine-grained modified concrete (Y1) and its average density (Y2) are taken as the response function. The structural quality coefficient KKK=Y1/Y2 is accepted as the optimization parameter.
The experiments were carried out according to standard methods for determining the density and compressive strength established by regulatory documents.

Results
The implementation of the experiment and statistical processing of its results allowed us to establish regression equations that, taking into account the significance of the coefficients (confidence intervals Δb1 =0. 8 The analysis of the coefficients of the obtained mathematical polynomials allows us to estimate the magnitude and direction of the influence of factors (in the intervals of variation established by the experimental conditions, in Table 1 on results: response functions (1).
An increase in the consumption of liquid glass, plasticizer, and chopped glass fiber contributes to an increase in strength (coefficients at X1, X2, and X3). The greatest influence is exerted by the consumption of the plasticizer (the coefficient at X2 is equal to 5.1). It is established that there is a joint effect (the coefficient at X2X3 is equal to 2.8), which is presumably due to better wettability and, accordingly, better adhesion of glass fibers to the concrete matrix in the presence of a plasticizer. The positive value of the coefficient suggests the possibility of a synergistic effect, the establishment of which is one of the tasks of the subsequent study of the technology.
The influence of varying factors on the average density of concrete is unambiguous: it is insignificant, but the increase in the cost of each of the varying factors causes an increase in the density of fine-grained concrete. There are also prerequisites for a synergistic effect in the pair interaction (X2X3), but the coefficient is commensurate with the experimental error (confidence interval 18 kg/m 3 ) and affects the overall result slightly.
The effect of liquid glass consumption on the strength is extreme, which is due to the coefficient at X1 equal to 4.2 and the coefficient at X1 2 equal to minus 3.2. This suggests that with an increase in the flow rate of liquid glass from the minimum to the average values, the strength increases, and a further increase in the flow rate of liquid glass leads to a decrease in strength. This type of polynomial makes it possible to apply the analytical optimization method to the system of equations.

Discussions
The method of the mathematical optimization was developed at NRU MGSU [16][17][18] and is based on the fact that the obtained polynomials are considered as purely mathematical (analytical) functions of several variables (in this case, three variables), to which the methods of the mathematical analysis are applicable. The method includes two stages at the first, the optimal value of the factor (in this case, Х1), is determined, and at the second, polynomials 1 and 2 are solved with Х1=opt and mathematical functions are obtained in the form optimized for Х1.
To find the extremum of a function Y1 = f (X1, X2, X3) we must differentiate this function by Х1 and equate the partial derivative 0: In true terms (2), the optimal consumption of liquid glass will be: 2.0+0.2×0.65 = 2.13 and taking into account the experimental error, the discharge will be 2.1…2.2%.
Using the obtained optimization solution, we obtain the final form of the optimized function (Y1, Y2) = f (X1, X2, X3) with Х1 equal 0.65: 1. For compressive strength: 2. For medium density: Taking into account that the coefficient of structural quality of fine-grained heavy concrete is equal to the ratio of compressive strength to average density, we find a function that is an optimition function for the coefficient of structural quality (5) The graphic interpretation of the obtained optimized function for the structural quality factor (Fig. 2.) can be used to determine the optimal consumption of plasticizer and glass chopped alkali-resistant fiber depending on the established strength and density of finegrained modified concrete for 3D printing.
The resulting nomogram can be used to select the consumption of glass fiber and plasticizer based on the strength and density of fine-grained modified concrete when the water glass consumption obtained as a result of analytical optimization is equal to 2.1-2.2%. In order to assess the compressive strength and average density of fine-grained fiberreinforced concrete specimens at an optimal flow rate of liquid glass equal to 2.1 ... 2.2%. depending on the consumption of plasticizer and glass fiber, graphical interpretation of dependencies (3) and (4) was carried out and a nomogram was obtained (Fig. 3). Nomograms ( Fig. 2 and Fig. 3) can be used to predict the properties of the material, as well as to select the consumption of glass fiber and plasticizer at a given value of the coefficient of structural quality of the material. With a given coefficient of constructive quality (for example, equal to 2.5), the optimal consumption of plasticizer and glass fiber is determined, which are equal, respectively (Fig. 2: 0.055% and 1.14%). Based on these values (according to the nomogram, Fig. 3), the strength and density of the projected material are determined, respectively 51 MPa with an average density of 1950 kg/m 3 .
Variation intervals with a structural quality factor equal to 2.5 and optimal consumption of fiber and plasticizer, the strength of fine-grained modified concrete specimens is 49.0-50 MPa with an average density of 1940-1950 kg / m 3 of the experiment. The technological characteristics of the concrete mixture, namely plasticity (rheological mobility) and setting time, were determined according to the standard method using the Rebinder device. It was found that in the intervals of fiber consumption 1.0-1.2% and plasticizer consumption 0.06-0.07% The mobility of the mixture is quite consistent with the conditions for pumping it through the pipeline system, which ensures the delivery of the concrete mixture from the concrete mixing bridle to the printing head of the 3D printer. The setting of the mixture begins 30-35 minutes after mixing it with water, which is technologically acceptable, but does not form a reserve stock in time. The calculated selection of the concrete composition is adjusted according to the results of the production of control samples.
The results obtained using the nomogram are corrected by conducting a control series of experiments. Other properties of fine-grained modified concrete for 3D printing were not studied in these studies; these experiments are supposed to be implemented in further studies.

Conclusion
The conducted studies have shown that the development and implementation of construction 3D printing methods in the domestic construction is possible and, in the near future, may become a completely self-sufficient technology for the production of construction parts and the organization of construction production. Particular attention will be paid to the methods of automation of printers for concrete, the creation of universal software and technological aspects of «preparation of ink» for the printer, that is, the development of formulations and study of the rheological characteristics of fine-grained modified concrete, which is the basis of 3D printing.
In the composition of fine-grained modified cement concrete, Portland cement, slag Portland cement (or its analogues), magnesia and aluminate cements can be used as the base binder. In the composition of fine-grained modified cement concrete, Portland cement, slag Portland cement or its analogs can be used as the base binder.
The reinforcing fiber must be crack-resistant (since it works in a concrete environment), soft, with diameters up to 5 microns and a length of no more than 0.5 mm (otherwise the printer head may clog). These requirements are met by thin glass fibers and cellulose fibers, both natural and synthetic.
It was found that in the intervals of glass fiber consumption of 1.0-1.2% and plasticizer consumption of 0.06-0.07%, the mobility of the mixture is quite consistent with the conditions for pumping it along piping system. The setting of the mixture begins 30-35 minutes after mixing it with water, which is technologically permissible, but does not form a reserve stock in time.
The nomogram obtained from the results of optimization of analytical dependencies can be used to develop a method for selecting the composition of modified fine-grained fiberreinforced concrete.