Determination of the master curves of shear modulus and phase angle for asphalt binders with consideration of relaxation spectrum
Kin Ming Chan, Yuhong Wang
Abstract
The master curves of complex shear modulus |G∗(ω)| and phase angle δ(ω) of asphalt binder provide its important rheological information. Although many studies have been performed to develop prediction models of |G∗(ω)|, the determination methods often focus on fitting them with experimental data of the modulus. The intrinsic relationships between |G∗(ω)|, δ(ω), relaxation spectrum H(τ) 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∗(ω)|, and δ(ω) often lead to inconsistent H(τ) deduced from storage modulus G′(ω) and loss modulus G′′(ω), and also inaccurate G(t) calculated from the resultant H(τ). This study proposes a new method to determine the master curves of |G∗(ω)| and δ(ω), which uses a joint optimisation to simultaneously minimise errors between the data and the models of |G∗(ω)| and δ(ω), together with the differences between H(τ)’s obtained from G′(ω) and G′′(ω) 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.