Modeling of the viscoelastic behavior of paving bitumen using fractional derivatives

The paving grade bitumen used in the production of asphalt mixtures for roadconstruction is significantly able to affect the in-service performances of flexible roadpavements. It has been proved that, when subjected to loading conditions comparable withmost pavement operating conditions, bituminous binders behave as linear visco-elasticmaterials. The aim of this paper is to propose a model based on fractional differentialequations which is able to describe the behavior of bituminous binders in the linear viscoelasticrange.Shear creep testing and creep recovery testing were carried out over a range of temperaturesand by applying a stress level which makes it possible to maintain the response of the studiedbitumens within the linear visco-elastic region. It is shown that creep tests follow a powerdecay law, rather than an exponential one: it follows that the most appropriate operator fordescribing the constitutive law for bitumen is a fractional operator. The procedures used todetermine the model’s parameters from the experimental data are discussed.