OPTIMIZATION OF PLASTICIZER CONCENTRATION IN CONSTRUCTION COMPOSITES THROUGH MATHEMATICAL MODELING

ABSTRACT

It has been studied the influence of different concentrations of plasticizer on the strength of dry building mixtures, as well as their direct dependence on changes in the ratio of water and binder. The article provides information on the production of dry building mixtures for decorative plaster based on local fillers, the use of a plasticizer in their composition and its effect. The chemical, physicochemical and physic mechanical properties of dry building mixtures were studied in accordance with the requirements of GOST. Based on the research results, a universal mathematical equation was developed expressing the ratio of the plasticizer and other components necessary to obtain a mixture of the required composition.

АННОТАЦИЯ

Проанализировано влияние различных концентраций пластификатора на прочность сухих строительных смесей, а также их прямая зависимость от изменения соотношения воды и вяжущего. Приведены сведения о производстве сухих строительных смесей для декоративной штукатурки на основе местных наполнителей, использовании пластификатора в их составе и его влиянии. Изучались химические, физико-химические и физико-механические свойства сухих строительных смесей в соответствии с требованиями ГОСТ. На основании результатов исследований разработано универсальное математическое уравнение, выражающее соотношение пластификатора и других компонентов, необходимое для получения смеси требуемого состава.

Keywords: cement, dry building mix, plasticizer, quartz, mathematical modeling.

Ключевые слова: цемент, сухая строительная смесь, пластификатор, кварц, математическое моделирование.

Introduction

In the field of dry building mixtures, one of the important issues is the production of materials with improved properties using various chemical reagents. Chemical modifiers used in the mixture,  even though they are introduced into the mixture in small quantities (0.1-2%), have a significant effect on their properties, and also lead to an increase in the cost of the product.

There are many types of such chemical additives according to their properties. Among such chemical additives, plasticizers occupy a special place.

Plasticizers  have the properties of reducing water consumption and increasing the strength of artificial stone; they are stabilizing, mobility-preserving and porosity-providing components [1].

The most promising superplasticizers (water reducers) based on industrially produced substances are polycondensation products of naphthalene sulfonic acid and formaldehyde. They are produced based on oligomeric compositions (superplasticizer C-3 and its analogues, used in many mixtures in powder form), as well as melamine-formaldehyde resins (MF-AR, 10-03 and their analogues). Superplasticizers increase the compressive strength of concrete by an average of 18-40%, the mobility of the mixture by 2-3 times, and reduce cement consumption by 10-12% [1-3].

Method

It is possible to produce dry building mixtures that meet the above requirements based on international and national standards. Dry building mixtures are produced in accordance with the requirements of the State Standard for the Construction, Reconstruction and Repair of Buildings and Structures (GOST 31189-2015). These mixtures differ from each other in their function and purpose.

Cement-based mixtures are produced in accordance with the international regulatory document GOST 31357-2007 ‘Dry building mixtures based on cement binders. General technical conditions’ and meet these requirements. This document is aimed at ensuring a guaranteed level of quality in the production of dry mixtures, their transportation, storage and use at construction sites.

The regulatory document GOST 28013-98 establishes standards for mixtures, components, technological processes, and preparation of mixtures [4]. The application of chemical reagents to the components of the mixture (GOST 24211-2003) is carried out  based on standards for influencing the properties of the mixture.

The study was conducted by adding a plasticizer to a 1:3 (2000:6000 (gr)) mixture of local quartz with GOST (31108-2020, 30515-2013) 450 grade cements. The dry powder additive superplasticizer C-3, which meets the requirements of GOST 24211-2008, was used as a modifier [5]. The mobility of this plaster mixture was determined in the range of 10-11 cm according to the recommended cone slump (GOST 28013-98). The mixture was poured into 4x4x16 (cm) molds, and the samples taken from the molds were stored under the required conditions for 28 days and the compressive strength was determined [6,7].

Mixtures prepared in accordance with the technical requirements of GOST 31356-2007 for the preparation of mixtures for decorative plaster works according to GOST 33083-2014 were tested in accordance with GOST (31356-2007, 5802-86), [8-11].

Sample preparation and testing, i.e., measurement work, were carried out at a humidity of 62% and a room temperature of 22℃ in accordance with the requirements of the above regulatory documents. The forms are made of metal. Samples measuring 4x4x16 (cm) were prepared from dry building mixtures mixed with water and tested after 28 days. The compressive and bending strengths of these samples were determined using the Alfa Test 050X equipment (figure 1).

Figure 1. 4x4x16 samples, (b) the obtained analysis result, (c) a picture of the Alfa Test X050 test equipment

Results And Discussion

The results of the study are presented in Table 1 below. Here z is the 28-day compressive strength of artificial stone (kN), x is the amount of plasticizer - C-3 (%), y is the amount of water (kg).

Table 1.

Component statistics table

To model the above problem, we construct a linear regression equation using the least squares method based on the data in Table 1.

Next, we find the matrix of pairwise correlation coefficients of the relationships between the factors z, x, and y using MS Excel:

Table 2.

Matrix of pairwise correlation coefficients between factors z,x,y

As can be seen from this table, as the amount of plasticizer increases, the compressive strength first increases and then decreases, leading to a decrease in the amount of water.

It is known from the literature that the multivariate linear regression equation is expressed in the following form:

                                                  (1)

To estimate the unknown parameters in this equation, we find the minimum value of the following sum in terms of :

To find the minimum value of the above function, we set the partial derivatives with respect to the parameters  to zero and form the following system of normal equations:

Based on the data in Table 1 above, we construct the following auxiliary table and, using the system of normal linear equations (3), we form a system of linear equations in terms of unknown parameters : (Table 3)

Table 3.

Auxiliary data table built based on z,x,y factors

Based on the above Table 3 and the system of normal equations (3),

                             (4)

By calculating this system of equations using the inverse matrix method using the Mathcad program, we obtain the following results [6].

 ,       

 ,      

According to the last matrix, the parameter values

. According to the above results, if we substitute the corresponding values of the parameters of the multivariate linear regression equation in the form (1),

                     (5)

(5) we get the shape function. We calculate the discounts by substituting the values of the relevant factors in the Table (1) in this function and use the relative deviations for each observation to determine the average estimated error to get a general idea of the quality of the model. To do this, we construct the following Table 4.

Table 4.

Table of relative errors of discounts calculated based on the z,x,y factors and the z(x,y) regression equation

Based on the above statistical data, we plot the graph of function (5) (Figure 2) [12].

Figure 2. The experimental results and the linear regression equation of the model are plotted

From the average relative error and the graph above,  the multivariate regression equation (5) represents the process under study with an error of 7.529238%.

Conclusion

Domestic manufacturers of dry building mixtures can expand production, given the sufficient availability of the existing raw material base. From the study, it can be concluded that products of any composition, that is, depending on demand, chemical plasticizers and modifiers, types of dry building mixtures for plaster can be produced with the required consistency. The developed mathematical expression allows you to pre-calculate the quantitative composition of the components. This, of course, leads to a reduction in additional time and additional costs.

References:

1. Bumakov M. G. Influence of superplasticizers on the main properties of concrete in structures / M. G. Bumakov // Chemical additives for concrete. - Mosccow: NIIZHB, 1987. - PP. 30-40.
2. K. F. Powers, N. A. Shapovalov, V. A. Lomachenko, A. A. Smosar / The influence of superplasticizers SB-3 on the mobility of concrete mix and the strength of concrete // News of the universities. Series Construction and architecture, 1986. - No. 11. - PP. 52-5.
3. Simonenko L. I. Superplasticizer based on polyelectrolyte complexes / L. I. Simonenko, V. I. Stambulko // Concrete and reinforced concrete, 1991. - No. 11. - PP. 18-20.
4. GOST 28013-98 Construction solutions. General specifications. Date of introduction – July 1, 1999.
5. Zokirov X., Abdullaev O. Preparation of Dry Building Mixtures Based on Local Raw Materials for Plaster Works According to Standards // AIP Conference Proceedings. – AIP Publishing, 2024. Vol. 3244. No. 1.
6. GOST 28013-98 Construction solutions. General specifications. Date of introduction 1999-07-01
7. GOST 31357-2007 Dry building mixtures on cement binder. General specifications
8. Interstate standard GOST 33083-2014 ‘Dry building mixtures on cement binder for plastering works. Technical conditions.’ Date of introduction - July 1, 2015. Introduced for the first time.
9. GOST 31356-2007 Dry building mixtures on cement binder. Test methods.
10. GOST 5802-86 Construction solutions. Test methods.
11. Shterenzon V.A. Modeling of technological processes: lecture notes / Ekaterinburg: Publishing house of RSPPU, 2010. – PP. 66.
12. [Electronic resource] URL: https://www.formpark.ru/upload/Plastificator_C3.pdf