Characterization of asphalt concrete linear viscoelastic behavior utilizing Havriliak–Negami complex modulus model

Abstract

This study proposed a new procedure for characterizing linear viscoelastic (LVE) behavior of asphalt concrete using the Havriliak–Negami (HN) complex modulus model and corresponding continuous relaxation spectrum model. To extend its application to modeling retardation behavior of asphalt concrete, the continuous retardation spectrum was analytically derived from the HN model by performing an inverse Fourier–Laplace transform followed by a variable substitution. The two continuous spectra of the HN model allow the accurate construction of all the modulus and compliance function master curves in time and frequency domains as well as the efficient determination of the high-quality discrete relaxation and retardation spectra. The advantages of the proposed approach over existing ones were demonstrated through two different complex modulus test data sets. Also, a simple and practical numerical interconversion method was presented based on the LVE relations between the continuous relaxation and retardation spectra, which can effectively compute one continuous spectrum from the other for any characterization model. Further, for practical considerations, a two-step method for determining reduced master curves with fewer discrete spectrum lines was suggested.