Fractal-order nonlinear damage creep model of rocks based on equivalent viscoelasticity

The importance of relaxation time in the evolution of rock rheological viscoelasticity is highlighted based on the equivalent viscoelasticity between the fractal order Zener model and the time-varying viscosity Zener model. The damage factor related to relaxation time is established, and the physical meaning of the damage factor in the process of rock rheological deformation is explained. The fractal-order variable-order function is established using relaxation time. On this basis, a variable-order fractal-order damage creep model is constructed, and the model is extended to the 3D stress state. A variable-order fractal damage creep model under 3D stress state is given. Finally, the applicability and rationality of the damage creep model under triaxial state are verified based on the triaxial creep test data of sandstone. Results show that the experimental data exhibit good agreement with the model fitting curve, providing a better description of the mechanical behavior of the entire creep process. The validity of the model fitting parameters is analyzed and verified, increasing the applicability of the model in other complex stress environments.