Effects of Damage and Fractional Derivative Operator on Creep Model of Fractured Rock

The long-term stability and safety of underground engineering greatly depend on a thorough understanding of the creep characteristics of fractured rock. This paper discusses the potential application of the damage evolution equation and the fractional derivative operator for describing the creep characteristics of fractured rock. By considering the initial damage of the original fracture and the internal damage induced by external loads, coupled damage evolution equations are proposed to account for different failure mechanisms. The introduction of damage and fractional calculus into basic mechanical elements allows for the deduction of creep constitutive relationships for both viscoelastic and viscoplastic bodies. A range of fractional-order damaged creep models is developed based on the Burgers model and the Nishihara model. Parameter sensitivity analysis shows that the inclusion of the damage evolution equation in the creep model is crucial for accurately capturing the accelerated creep deformation characteristics of rock, with the fractional derivative order primarily affecting the steady creep strain rate. By fitting the creep experimental data of fractured Beishan granite, it is evident that the damaged Nishihara model [H-N(D)/H(D)-N(D)/St. V model], which considers only the damage effect, and the fractional damaged Burgers model [H-N(A)-N(D)/H(D) model], which accounts for both the damage effect and the fractional operator, exhibit significant advantages in characterizing the entire process of creep deformation in fractured granite.