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

The article focuses on developing and validating a novel rock creep model based on fractal derivative theory and damage mechanics to better characterize the nonlinear rheological properties of rocks, particularly sandstone. This variable fractal derivative order damage creep model incorporates time-dependent degradation and improves upon traditional models by accurately describing primary, steady-state, and accelerated creep deformation under different stress levels and temperatures. Validation through triaxial creep tests and comparisons with classical models and literature data demonstrate the model’s high accuracy, fewer parameters, and broad applicability, including extension to three-dimensional and radial stress states. The study highlights the model’s potential for predicting long-term deformation of surrounding rock in deep underground engineering and its suitability for numerical simulation in practical engineering contexts.