To identify the most accurate approach for constructing of the dynamic modulus master curves for warm mix crumb rubber modified asphalt mixtures and assess the feasibility of predicting the phase angle master curves from the dynamic modulus ones. The SM (Sigmoidal model) and GSM (generalized sigmoidal model) were utilized to construct the dynamic modulus master curve, respectively. Subsequently, the master curve of phase angle could be predicted from the master curve of dynamic modulus in term of the K-K (Kramers–Kronig) relations. The results show that both SM and GSM can predict the dynamic modulus very well, except that the GSM shows a slightly higher correlation coefficient than SM. Therefore, it is recommended to construct the dynamic modulus master curve using GSM and obtain the corresponding phase angle master curve in term of the K-K relations. The Black space diagram and Wicket diagram were utilized to verify the predictions were consistent with the LVE (linear viscoelastic) theory. Then the master curve of storage modulus and loss modulus were also obtained. Finally, the creep compliance and relaxation modulus can be used to represent the creep and relaxation properties of warm-mix crumb rubber-modified asphalt mixtures.

To study the linear viscoelastic (LVE) of crumb rubber-modified asphalt mixtures before and after the warm mix additive was added methods of obtaining the discrete and continuous spectrum are presented. Besides, the relaxation modulus and creep compliance are constructed from the discrete and continuous spectrum, respectively. The discrete spectrum of asphalt mixtures can be obtained from dynamic modulus test results according to the generalized Maxwell model (GMM) and the generalized Kelvin model (GKM). Similarly, the continuous spectrum of asphalt mixtures can be obtained from the dynamic modulus test data via the inverse integral transformation. In this paper, the test procedure for all specimens was ensured to be completed in the LVE range. The results show that the discrete spectrum and the continuous spectrum have similar shapes, but the magnitude and position of the spectrum peaks is different. The continuous spectrum can be considered as the limiting case of the discrete spectrum. The relaxation modulus and creep compliance constructed by the discrete and continuous spectrum are almost indistinguishable in the reduced time range of 10⁻⁵ s–10³ s. However, there are more significant errors outside the time range, and the maximum error is up to 55%.