A unified procedure for rapidly determining asphalt concrete discrete relaxation and retardation spectra

This paper presents a unified procedure that can rapidly determine the discrete relaxation and retardation spectra of asphalt concrete. The new procedure involves three consecutive steps: (1) pre-smoothing the complex modulus data with the Havriliak-Negami (HN) model, (2) identifying the discrete relaxation spectrum from the smoothed data with a modified windowing method (MWM) and (3) converting the obtained spectrum into the corresponding discrete retardation spectrum. The HN model adopted furnishes reasonable analytical representations for all the complex modulus components and allows an asymmetrical inflection point for the dynamic modulus and storage modulus master curves on the log-log scale, effectively overcoming the drawbacks of the conventional sigmoidal function in characterizing the asphalt concrete linear viscoelastic (LVE) behavior. Also, the HN model can well predict the phase angle from the dynamic modulus data, substantially extending the application of the old data lacking the phase angle information in the LVE analysis. Additionally, the MWM offers a more appropriate estimation approach for the glassy modulus, successfully avoiding the undesirable spectrum oscillations and negative spectrum lines. A distribution of the time constants with 0.5 decade intervals was implemented in this procedure, completely excluding the waviness in the bell-shaped master curves of the generalized Maxwell (GM) and generalized Voigt (GV) models. Very few parameters are required for the initial inputs in the procedure and no empirical adjustments or selections are required for the GM or GV model constants during the whole computation process. The convergence of the iterations for determining the discrete spectra proved to be very fast.