Fractional derivative Burgers models describing dynamic viscoelastic properties of asphalt binders

Abstract

The Burgers model is ineffective in the representation of dynamic viscoelastic properties of asphalt binders; the existing fractional derivative Burgers (FDB I) model has limitations in its application and construction concept. Consequently, this study started by deriving the constitutive equations of the FDB I model and proposed a new application idea of Abel dashpot to construct the second fractional derivative Burgers (FDB II) model. Then, dynamic modulus formulas for the FDB II model were derived. On this basis, the frequency sweep tests of base and two polyphosphoric acid (PPA) modified asphalt binders were carried, and the dynamic viscoelastic properties of three different asphalt binders were described using three different models, and in-depth comparisons and analysis are carried out. The results show that both fractional derivative Burgers (FDB) models can simultaneously express the dynamic viscoelastic properties of asphalt binders with a set of parameters. Both FDB models perform better than traditional Burgers model in the representation of dynamic viscoelastic properties, and fitting results of master curves no longer exhibit oscillation properties like the traditional Burgers model. The R2 of FDB models could reach above 0.99, while R2 of traditional Burgers model was only 0.9349 at minimum. Among them, the FDB II model performs best. Five parameters of the FDB II model have relatively clear physical meanings. The new application concept of fractional dashpots was verified its theoretical feasibility and application advantages, which will provide a new idea for further application and development of fractional derivative constitutive models.