Nonlinear damage creep model based on fractional theory for rock materials

Abstract

In this study, based on the first application of Caputo fractional derivative with respect to the Mittag–Leffler and power functions, two improved time-varying viscoelastic constitutive models are presented. And the Norton power law and damage factor are applied to build a new damage function. Then the new nonlinear damage creep models 1 and 2 with time-varying viscoelasticity and time-dependent damage are proposed to describe the creep mechanical behavior, which are based on the two improved time-varying viscoelastic constitutive models. Then a series of creep experiments are conducted on the sandstone to obtain the creep experimental data. And based on the creep experimental data of sandstone and creep data of salt rock and mudstone obtained from other papers, the applicability of proposed creep models 1 and 2 is verified. The proposed creep model 2 with power function has a higher accuracy than model 1 with Mittag–Leffler function in describing creep mechanical behavior. And the predicted creep from model 2 is in good agreement with experimental data. Finally, it is shown that compared with creep model 1, model 2 needs fewer parameters to depict the creep mechanical behavior.