Characterizing three-dimensional creep of Beishan granite by the variable-coefficient Abel dashpot

Accurate description of creep behavior is of great significance to the safety evaluation of high-level radioactive waste disposal in granite. In this study, a fractional derivative constitutive model is proposed to depict the creep process of Beishan granite, based on the conformable derivative. A variable-coefficient Abel dashpot considering the effect of damage evolution on creep properties is introduced to describe the nonlinear dilatancy strain in the accelerating stage. A new model is proposed and further generalized to three-dimensional creep equations by adopting Drucker–Prager criterion, and the analytic solutions are given employing the Laplace transform. The parameters of new creep model are determined based on experimental data and fitting results are compared. The fitting curves present a good agreement with experimental data, indicating that the conformable derivative creep model achieves a good performance in describing all three creep stages. The proposed model is validated by the comparison of different experiments and degradation of fractional derivative model. In addition, a sensitivity analysis is carried out to show the effects of stress level, fractional derivative order, damage exponent, and other parameters.