Introducing a stress-dependent fractional nonlinear viscoelastic model for modified asphalt binders

Asphalt binders generally behave in a linear viscoelastic manner under conventional stress and strain level. There are several researches and technical protocols consistent with linear viscoelastic theorem. However, two main reasons can affect this well-known behavior of asphalt binders: 1) modification of asphalt binder with some additives causing a change in its microstructure and 2) higher order stress and strain level induced to asphalt binder under heavy traffic or climate loading. It is important to consider non-linear viscoelastic behavior of asphalt binder and its effect on conventional characteristics of asphalt especially two constitutive functions of creep compliance and relaxation modulus. In this research, nonlinear viscoelastic properties of asphalt binders modified with crumb rubber, styrene-butadiene-styrene and polyphosphoric acid are investigated to evaluate the variation in non-linear viscoelastic parameters due to addition of these modifiers. For this purpose, a specified research program was defined to consider non-linear behavior of one neat asphalt binder as well as nine modified ones. Based on a robust literature review and some prior experiences, three different extents selected for each modifier and then specimens were made. Implementing a simple creep-recovery test with creep loading time of 1 s and 100 s and 999 s unloading to simulate traffic load by using a dynamic shear rheometer at different stress levels of 0.1, 1, 10, 20 and 30 kPa, non-linear viscoelastic behavior of neat and modified asphalt binder was captured. The generalized fractional nonlinear viscoelastic model is introduced and successfully implemented to simulate creep and recovery behavior of neat and modified asphalt binders. Addition of all modifiers to the neat asphalt binder alters its non-linear viscoelastic behavior and properties. For short time creep loading, crumb rubber and polyphosphoric acid amplify non-linear behavior while SBS control it and for long creep loading time all asphalt modifiers increases non-linearity of asphalt binder's viscoelastic behavior.