Use of Kramers–Kronig relations to construct the master curves of asphalt materials

Abstract

Kramers–Kronig (K–K) relations have been widely used to construct the master curves of asphalt materials that satisfy the linear viscoelastic (LVE) theory. However, existing methods utilize approximate K–K relations to develop the master curves of viscoelastic variables, which lead to the inaccuracy of master curves. In addition, the resulting master curves cannot fully comply with physical causality. To overcome these deficiencies, this paper proposes two approaches to construct the master curves by using these exact K–K relations: (1) the exact K–K relations between the dynamic modulus and the phase angle, and (2) the exact K–Krelations between the storage modulus and loss modulus. By applying the trapezoid integral rule, the numerical form of the K–K relations between the dynamic modulus and phase angle and between the storage modulus and loss modulus is established, and the master curves of four viscoelastic variables are subsequently constructed. The results indicate that both of the developed methods are accurate in establishing master curves. The fitting errors of each viscoelastic variable are below 2.64%, and the $$R^{{2}}$$ value is larger than 0.96. More important, the developed master curves fully comply with the LVE theory and physical causality. Therefore, the two presented methods apply to developing the master curves of asphalt binders, asphalt mixtures, and even other viscoelastic materials.