A creep constitutive model for salt rock based on fractional derivatives

By replacing a Newtonian dashpot in the classical Nishihara model with the fractional derivative Abel dashpot, a new creep constitutive model is proposed on the basis of time-based fractional derivative. The analytic solution for the fractional derivative time-dependent constitutive model is given. The parameters of the fractional derivative model and the Nishihara model are determined by fitting to existing experimental results of time-dependent deformation of salt rock. The results estimated by the fractional derivative model proposed in the paper are in better agreement with the experimental data than the results estimated by the Nishihara model. A sensitivity study for the analytic solution of the time-based fractional derivative model is carried out, showing the effects of fractional derivative order and stress level on creep strain of salt rock. It is shown that the time-based fractional derivative model can be simplified to the Nishihara model for the special case of fractional derivative order equal to 1.0.