Mathematical model for assigning high-effective concrete mix using ground granulated blast-furnace slag

The selection of materials that increase the efficiency of concrete is made, an approach to the optimal use of ground granulated blast-furnace slag is proposed. In order to achieve a high economic effect, the concrete composition is optimized considering the dynamics of its strength set, for which simplified equations of concrete hardening, which are the core of the developed mathematical model, are derived. Quality control of accepted materials, testing of concrete mixtures for flowability and strength of concrete samples are carried out in accordance with the current standards of Russia. Processing of the obtained data is performed in Microsoft Excel software, and obtaining equations and graphs of response surfaces is carried out in StatSoft STATISTICA. A planned experiment is carried out, in which the variable factors are cement consumption (from 280 to 440 kg per cubic meter of concrete) and slag content in cement (from 24 to 76 %). At each point of the plan, an experimental selection of the parameters of the concrete composition is made, the equations and graphs of the response surfaces for these parameters are obtained. Tests of concrete specimens for strength under normal hardening conditions were aimed to be performed in the 3rd, 7th, and 28th days, and during hardening after heat treatment (7 hours, 70 °C) - in the 1st, 7th and 28th days. The hardening equations are determined from the average strength values at the actual test times for all the compositions obtained, from which the strength is calculated at exactly in the 1st and 28th days for all points of the plan, and then the equations for the strength response surfaces are obtained. The latter are necessary for calculating the strength of the concrete by a set time using previously derived simplified hardening equations. These and other obtained equations are combined into a mathematical model consisting of blocks: input parameters, strength calculation, calculation of concrete composition parameters, calculation of component consumption and cost estimation. The mathematical model presented in the article, through the developed widgets in Excel, allows to quickly and accurately solve the optimization problem - to assign a concrete mix proportion for the selected hardening conditions with a minimum cost and a condition for ensuring the required strength by the specified time.