A nonlinear creep model for transversely isotropic rock based on fractional calculus theory

A nonlinear creep model based on fractional calculus theory is proposed to better describe the creep characteristics of transversely isotropic rock. The model includes a Hooke elastomer, a fractional Abel dashpot, a Kelvin body, and a nonlinear viscoplastic body, which effectively capture the three stages of creep (including the primary, steady-state, and accelerating creep stages) while also reflect the influence of different bedding angles on creep behavior. The parameters of the model are identified by the Levenberg-Marquardt algorithm. Compared to previous models assuming constant Poisson's ratio for transversely isotropic rock, our nonlinear creep model demonstrates improved accuracy and rationality.