Studies on creep and recovery of rheological bodies based upon conventional and fractional formulations and their application on asphalt mixture

Abstract

Traditionally, the time-dependent behaviour of bituminous mixtures has been modelled using linear visco-elastic theory described by creep and relaxation functions. Research, however, has shown that parameter identification for functions with linear time derivatives becomes problematic when the behaviour of asphalt mixtures needs to be matched for both the loading and unloading responses. The research introduced in this paper explored the possibility of using fractional creep functions for modelling. Furthermore, the possibility of using fractional creep functions for various rheological bodies to investigate the fractional time derivatives for strain is discussed. It is shown that, by means of these creep functions, the time-dependent deformation behaviour of bituminous material in terms of the retarded creep during loading and the relaxation behaviour during unloading may be described more realistically than by using time derivatives of integer order. The fractional creep functions allow for the development of non-linear viscous strain during the creep process and to better match the observed behaviour of asphalt mixtures, compared to the use of conventional linear models. This study specifically investigated the retardation and relaxation times in creep and recovery, and examined how these can be influenced by the choice of the fractional derivatives. The constitutive relationships developed in this paper are implemented in a non-linear computational model based on the finite element method. Modelling of the above-mentioned phenomena is presented and discussed with the help of numerical simulations and determination of model parameters with the help of actual test data.

Keywords:

• fractional time derivatives
• relaxation
• retardation
• creep
• recovery
• rheology

Acknowledgements

The authors wish to thank Professor Dr A. Collop and Dr H. Taherkani from the University of Nottingham, UK, for their help in providing the measured creep test data for the study.