An intrinsic model of rock damage creep based on the derivative order of variable fractals

To better characterize the rheological properties of rock nonlinearities, a modified fractal dashpot is used instead of the conventional Abel dashpot and Newton dashpot with fractional order derivatives. The fractal derivative order of a fractal dashpot is constructed as a function of time by treating the fractal derivative order as a function of time. In turn, a creep model is developed for the fractal derivative order to time degradation. The validation results of the test data under different stress levels show that the proposed fractal damage creep model has wide applicability for describing the primary creep and steady-state creep deformation of rocks based on triaxial creep tests and can well characterize the viscoelastic-plastic creep properties of rocks. At the same time, it also compensates for the shortcomings of the traditional model that cannot describe the accelerated creep. Through the comparison and analysis with the classical component model, it is found that the fractal damage creep model has the advantages of few parameters, high accuracy, and high computational efficiency. The conclusions of the study can provide a reference for the prediction of surrounding rock deformation in practical engineering.