Optimal aggregate testing using Vandermonde polynomials and spectral methods

Abstract

Recycled aggregate (RA) has been used in various construction applications around the world mainly as sub-grade, roadwork and unbound materials, but not in higher-grade applications. The major barrier encountered is the variation of quality within RA, which causes lower strength, and poorer quality. This work studies the relationships among six parameters describing the characteristics of RA: (i) particle size distribution, (ii) particle density, (iii) porosity and absorption, (iv) particle shape, (v) strength and toughness, and (vi) chemical composition. Samples of RA from 10 demolition sites were obtained with service life ranging from 10 to 40 years. One additional set of samples was specifically collected from the Tuen Mun Area 38 Recycling Plant. The characteristics of these eleven sets of samples were then compared with normal aggregate samples. A Vandermonde matrix for interpolation polynomial coefficient estimation is used to give detailed mathematical relationships among pairs of samples, which can be used to work out redundant tests. Different orders of interpolation polynomials are used for comparison, hence the best-fit equations with the lowest fitting errors from different orders of polynomials can be found. Fitting error distributions are then studied by using spectral methods such as power spectra and bispectra. From that, the best equations for result estimations can be obtained. This study reveals that there is strong correlation among test parameters, and by measuring two of them: either “particle density” or “porosity and absorption” or “particle shape” or “strength and toughness”, and “chemical content”, it is sufficient to study RA.