An improved method to establish continuous relaxation spectrum of asphalt materials

The relaxation spectrum plays a vital role in the study of linear viscoelastic (LVE) properties of asphalt materials; however, the current developed using methods are not accurate enough to characterize the LVE properties of asphalt materials. This paper aims to develop an improved method to determine the continuous relaxation spectrum of asphalt materials. A modified Christensen-Anderson-Marasteanu (CAM) model is first selected as the master curve model of the storage modulus, upon which the master curve model of loss modulus is then established using the numerical form of the exact Kramers-Kronig relation between the storage modulus and loss modulus. According to LVE conversions between the relaxation spectrum and storage modulus, the model of the continuous relaxation spectrum is subsequently derived and finally determined based on the same model pa-rameters of the storage modulus and loss modulus models. This study demonstrates that the relaxation spectrum of both mixtures and binders constructed by the proposed method is compliant with LVE theory and physical causality. The generated relaxation spectrum is verified to be accurate enough to compare the storage modulus and loss modulus values recalculated by the relaxation spectrum and the corresponding values predicted by master curve models. The results also show that the approximate Kramers-Kronig relation between the storage modulus and loss modulus cannot be used to establish the relaxation spectrum of asphalt materials, especially for asphalt binders. In addition, the generated relaxation spectrum was utilized to construct the relaxation modulus of mixtures and to develop the stiffness modulus of binders, respectively. Since the relaxation modulus and creep stiffness are determined from the relaxation spectrum, both are consistent with LVE theory and physical causality.

Automated summary

This study developed an improved method to determine the continuous relaxation spectrum of asphalt materials, demonstrating compliance with LVE theory and physical causality. The generated relaxation spectrum was accurate enough to compare the storage modulus and loss modulus values recalculated by the relaxation spectrum with those predicted by master curve models, highlighting the limitations of the Kramers-Kronig relation for establishing the relaxation spectrum of asphalt materials. Additionally, the generated relaxation spectrum was utilized to construct the relaxation modulus of mixtures and to develop the stiffness modulus of binders, both consistent with LVE theory and physical causality.