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

The master curves of complex shear modulus (Formula presented.) and phase angle (Formula presented.) of asphalt binder provide its important rheological information. Although many studies have been performed to develop prediction models of (Formula presented.), the determination methods often focus on fitting them with experimental data of the modulus. The intrinsic relationships between (Formula presented.), (Formula presented.), relaxation spectrum (Formula presented.) and relaxation modulus (Formula presented.) 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 (Formula presented.), and (Formula presented.) often lead to inconsistent (Formula presented.) deduced from storage modulus (Formula presented.) and loss modulus (Formula presented.), and also inaccurate (Formula presented.) calculated from the resultant (Formula presented.). This study proposes a new method to determine the master curves of (Formula presented.) and (Formula presented.), which uses a joint optimisation to simultaneously minimise errors between the data and the models of (Formula presented.) and (Formula presented.), together with the differences between (Formula presented.) ’s obtained from (Formula presented.) and (Formula presented.) 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.