Determining concrete properties for different optimized combined concrete mixtures: Novel mathematical approach

Abstract

Gradation of the granular skeleton significantly influences almost all of the concrete performances. The main purpose of this research work is to develop a mathematical model to characterize the properties of various dry concrete mixtures. The starting point of this work is to propose a single equation to describe continuous aggregate gradations, by combining several ideal grading curves used to design different concrete mixtures, to achieve higher freedom in optimizing the particle-size distribution (PSD) of a concrete mixture. At the design procedure stage, the concrete constituents are selected so that the overall grading of the mix closely follows a given ideal grading curve for specific properties. Using the gradation equation afore-mentioned, a mathematical framework is established to outline several intrinsic factors in the optimized granular skeleton of concrete, characterized by a wide range of particle sizes. The factors developed, directly measured based on the PSD, include the specific surface area and the fineness modulus of the combined grading of the concrete mix particles, as well as the ratio between the granular fractions determined either by area or by weight, and the surface area of the total concrete mixture. The resulting model expressions relate the characteristics of the size distribution of the concrete skeleton, to the parameters in the proposed gradation equation, in particular the distribution exponent. The proposed model could be implemented in the study of the solid phase of concrete, design aggregate gradation to meet certain requirements, or even predict some attributes of the dry concrete mixture. • A unified equation of well-known optimal particle size distributions is developed. • A model is proposed to accurately calculate some properties of the concrete mixes. • The distribution exponent in the proposed equation is the most relevant parameter. • Optimal PSDs are fractal and converge mathematically to the Fung & Dinger model. • The proposed model is suitable for systems with a wide range of particle sizes.