Development of master curve models complying with linear viscoelastic theory for complex moduli of asphalt mixtures with improved accuracy

Approximate Kramers-Kronig relations have shown success in constructing master curves in compliance with the linear viscoelastic theory for the magnitude and phase angle of the complex modulus of an asphalt mixture. However, their applications have been limited to either shifting test data without model construction or constructing master curve models without addressing possible asymmetry of the master curves. Taking advantage of the Kramers-Kronig relations, this paper developed two approaches to establish the master curve models of four viscoelastic parameters of asphalt mixtures, including the magnitude and phase angle of the complex modulus as well as the storage modulus and loss modulus. In each approach, the four viscoelastic parameters shared the same time-temperature shift factor equation with exactly the same fitting parameters. Master curves of the viscoelastic parameters were constructed and were identified to have asymmetric shapes. These master curves were further verified to be compliant with the linear viscoelastic theory using black space diagrams and wicket plots, respectively. It was found that the developed two approaches established master curve models with approximately the same accuracy level with R-2 values larger than 0.96. The two approaches also produced about the same time-temperature shift factor at each temperature. Therefore, either approach could be selected to accurately construct master curves of the four viscoelastic parameters in a wide frequency range. (C) 2017 Elsevier Ltd. All rights reserved.