Fractional Order Analysis of Creep Characteristics of Sandstone with Multiscale Damage

Deep mining is often accompanied by complex geological conditions, which can cause damage to the coal seam roof surrounding rock, thereby reducing its safety and stability. Therefore, analyzing the long-term mechanical behavior of multiscale damaged sandstone under deep mining conditions is of great significance. To describe the long-term deformation and damage evolution of multiscale damaged sandstone under deep mining conditions, this work establishes a fractional-order multiscale damage creep model by incorporating fractional calculus and damage mechanics theory into the Nishihara model. The model parameters were determined by fitting the creep data of damaged sandstone using the least squares method. The results demonstrate that the proposed model can accurately simulate the complete creep process, including the decelerated, steady-state, and accelerated stages. Compared with the classical integer-order multiscale damage creep model, the fractional-order model can better capture the time-dependent behavior of materials and thus shows superior performance in characterizing the nonlinear features of the accelerated creep stage. Furthermore, through sensitivity analysis of the parameters reveals the influence of key parameters on different creep stages, thereby validating the model’s effectiveness and reliability. This model provides a solid theoretical foundation for evaluating the long-term stability of coal mine roof strata in deep mining environments.