A Fractional Nonlinear Creep Damage Model for Transversely Isotropic Rock

Transversely isotropic layered rock is widely distributed in nature. To better describe the time-dependent entire creep characteristics for transversely isotropic rock, a simple nonlinear damage creep model is derived based on fractional order theory, which consists of a Hooke elastomer, a fractional Abel dashpot, a fractional nonlinear damage dashpot, and can effectively describe the characteristics of primary creep, steady-state creep and accelerating damage creep. Assuming that Poisson's ratio is constant, the creep equation of isotropic rock is extended to transversely isotropic rock, and the nonlinear damage creep model for transversely isotropic rock is established. Step-wise loading triaxial creep tests of phyllite specimens with three kinds of bedding angles (0 degrees, 45 degrees and 90 degrees) are carried out, and it is found that there are significant differences in creep deformation and failure characteristics under different bedding angles. The parameters of the creep model at each bedding angle are identified using the Universal Global Optimization method. By comparing the Nishihara model, the modified Nishihara model and experimental data, it shows that the creep model in this paper are highly consistent with the experimental data under different bedding angles, load levels and creep stages, and the accuracy and rationality of the model are verified.