A nonlinear damage creep model for sandstone based on fractional theory

In this study, an improved viscoelastic model is proposed, which is based on the application of Caputo fractional derivatives of one function in regard to exponential function. This new mathematical way is effective in the construction of viscoelastic model with time dependence. And based on the type of Norton power law and damage factor, we propose a new damage model. By combining the improved viscoelastic model and proposed damage model, a nonlinear fractional damage creep model is presented to describe the creep mechanical behavior of sandstone. A series of creep experiments were conducted on the sandstone by the step loading way. The decaying, steady, and accelerating creep stage all appear in the experiments. Based on those experimental data, the fitting curves of the presented creep model are in well agreement with those of the experimental data. And the reasonability of fitting parameters also has been analyzed in detail.