Modeling of the viscoelastic behavior of paving bitumen using fractional derivatives

The paving grade bitumen used in the production of asphalt mixtures for road construction is significantly able to affect the in-service performances of flexible road pavements. It has been proved that, when subjected to loading conditions comparable with most pavement operating conditions, bituminous binders behave as linear visco-elastic materials. The aim of this paper is to propose a model based on fractional differential equations which is able to describe the behavior of bituminous binders in the linear viscoelastic range. Shear creep testing and creep recovery testing were carried out over a range of temperatures and by applying a stress level which makes it possible to maintain the response of the studied bitumens within the linear visco-elastic region. It is shown that creep tests follow a power decay law, rather than an exponential one: it follows that the most appropriate operator for describing the constitutive law for bitumen is a fractional operator. The procedures used to determine the model’s parameters from the experimental data are discussed.