Abstract: Based on the equivalent viscoelasticity between the fractional Zener model and the time-varying viscosity Zener model, the significance of the relaxation time in the evolution of rock rheological viscoelasticity is highlighted. As the relaxation time approaches infinity, the evolution of viscosity during creep is equivalent to that during relaxation. Accordingly, the damage factor related to relaxation time is established to explain the physical significance of damage factor in rock rheological deformation. In specific, the function of variable order is constructed by using relaxation time and the variable-order fractional damage creep model is introduced. Furthermore, the variable-order fractional damage creep model is extended to the triaxial status. Based on the triaxial sandstone creep experimental data, the applicability and rationality of the variable-order fractional damage creep model in the triaxial state are verified. The results show that the developed variable-order fractional damage creep model and the creep experimental data are in good agreement, indicating that the damage creep model can be used to describe the nonlinear mechanical behavior of complete creep process. The effectiveness of the model fitting parameters is analyzed and verified, which encourages the applicability of the introduced model in other complex stress issues.

Key words: rock rheology, equivalent viscoelasticity, relaxation time, evolution of damage, variable-order fractional damage creep model