3-D Constitutive Model for Asphalt on the Basis of Fractional Creep Functions

In this paper an improved method for modelling the time-dependent behaviour of asphalt using fractional time derivatives of strains is presented. The corresponding fractional creep functions for the KELVIN and MAXWELL body are derived. By means of these creep functions it is shown that the time-dependent deformation behaviour of asphalt (especially the degressive creep behaviour at the beginning of loading and the progressive behaviour for long load duration) may be described more realistically than by time derivatives of integer order. In order to account for arbitrary loading processes, the fractional creep functions are approximated using DIRICHLET series and converted into so-called hereditary integrals. In order to solve the hereditary integrals it is necessary to subdivide the loading process into increments. If the creep functions are independent of stress, the hereditary integrals may be solved analytically within an increment. If stress dependencies exist, the integrals are solved numerically. An efficient numerical solution algorithm is developed for this purpose. The load history enters this algorithm via series formulations with internal variables. The material model is developed in a onedimensional form and modified for the three-dimensional stress-strain space. This involves a consideration of the description of orthotropic material behaviour, plastic compression and dilation.