Practical Methods to Construct Asphalt Binder Master Curves and Calculate Christensen–Anderson Model Parameters

Abstract

Asphalt binder master curves are applied to describe the rheological behavior of asphalt binders. A standard for constructing asphalt binder master curves and fitting a model to the results does not presently exist. In this study, a pairwise interpolation is established for free shifting of isotherms. The pairwise interpolation method yields time–temperature shift factors that are in good agreement with the Gordon and Shaw method and can be more easily implemented without sophisticated software. Subsequently, practical methods to calculate the Christensen–Anderson (CA) model crossover frequency and R parameters are compared. The relationship between reduced frequency and the tangent of the phase angle in logarithmic space is generally linear over the tangent of phase angle values spanning from 0.2 to 0.5 and can be used to determine the crossover frequency. Two approaches that generally yielded acceptable model accuracy were identified for calculating the CA model R value: (1) least squares optimization to minimize the sum of squared errors for storage and loss moduli; and (2) fitting a line to log (log dynamic shear modulus) versus the tangent of the phase angle over the tangent of the phase angle values spanning between 0.5 and 2. Based on the asphalt binders evaluated in this study, the CA model can accurately reflect asphalt binder rheological behavior when the dynamic shear modulus exceeds 10⁵ Pa and the phase angle is less than 70° for unmodified asphalts or less than 60° for polymer-modified asphalts.