Zastosowanie pochodnej ułamkowego rzędu do modelowania mieszanek mineralno-asfaltowych

Asphalt-aggregate mixtures constitute basic component for the road pavements construction. The fundamental problem in the procedure of pavement design is to elaborate an appropriate constitutive model suited for the structural behaviour modelling within a wide range of mechanical and environmental loadings. The paper deals with the identification problem for a model representing constitutive properties of asphalt-aggregate mixtures. The constants characterising such a model should be evaluated based on expe-riments. There were analysed two viscoelastic rheological schemes. The classical Burgers model (Fig. 3a) contains linear elastic and viscous elements, while the Huet-Sayegh model (Fig. 3b) is composed of non-classical viscoelastic elements and its constitutive properties can be described using fractional derivatives. The results of cyclic tests of an asphalt-aggregate mixture were taken from the literature [8]. The experiments were carried out when assuming one-dimensional state of stress within the range of frequencies between 0.5 Hz and 35 Hz. The curve fitting procedure for both models was executed based on its complex moduli evaluation (Eqs. 11a and 11b). The obtained results show that by applying the fractional Huet-Sayegh model one can better fit the experiment in comparison with the classical Burgers model (see Figs. 4 and 5). Further investigations should be focused on description of non-linear effects using fractional and plastic elements. The plasticity phenomenon is important within the range of large intensities of loadings. The work on this area is currently underway by the authors.