Determination of the master curves of shear modulus and phase angle for asphalt binders with consideration of relaxation spectrum

ABSTRACT

The master curves of complex shear modulus $|G^{\ast }(\omega )|$ and phase angle $\delta (\omega )$ of asphalt binder provide its important rheological information. Although many studies have been performed to develop prediction models of $|G^{\ast }(\omega )|$, the determination methods often focus on fitting them with experimental data of the modulus. The intrinsic relationships between $|G^{\ast }(\omega )|$, $\delta (\omega )$, relaxation spectrum $H(\tau )$ and relaxation modulus $G(t)$ are seldom considered. Consequently, defects of the fitting arise naturally, due to overfitting issues from experimental errors and underfitting issues from bias in the approximation/empirical models. The mismatched master curves of $|G^{\ast }(\omega )|$, and $\delta (\omega )$ often lead to inconsistent $H(\tau )$ deduced from storage modulus $G^{\mathrm{\prime }}(\omega )$ and loss modulus $G^{\mathrm{\prime }\mathrm{\prime }}(\omega )$, and also inaccurate $G(t)$ calculated from the resultant $H(\tau )$. This study proposes a new method to determine the master curves of $|G^{\ast }(\omega )|$ and $\delta (\omega )$, which uses a joint optimisation to simultaneously minimise errors between the data and the models of $|G^{\ast }(\omega )|$ and $\delta (\omega )$, together with the differences between $H(\tau )$’s obtained from $G^{\mathrm{\prime }}(\omega )$ and $G^{\mathrm{\prime }\mathrm{\prime }}(\omega )$ as a penalty of the loss function. Two asphalt binders are used to assess the newly developed method and existing ones. Cross-validation based on stress-relaxation test indicates that the new method is more robust and accurate.

KEYWORDS:

• Asphalt binder
• master curves
• relaxation spectrum
• rheological properties

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

This work was supported by Hong Kong Research Grant Council [grant number PolyU 152568/16E].