Equivalent fatigue stress and non-linear constitutive model for fatigue of rock

The traditional damage model is insensitive to cycles of loading and unloading, and it is obviously inadequate for the characterization of fatigue deformation and failure of rock. Based on the creep and fatigue tests, the "homology" hypothesis of the two kinds of deformation is verified by normalizing the time (cycle number) and deformation of rock creep and fatigue. The rheological theory is used to describe the whole process of fatigue deformation of rock under fatigue loads, and susequently the improved fatigue stress equivalence is put forward based on the equal life curve equation, Gerber and Goodman linear equation. The Kelvin visco-elastomer is replaced by the Murayama visco-elastomer, and the switch function and rock integrity parameters are added to non-linear treatment of Bingham viscoplastic body to establish a 7-parameter non-linear fatigue model for rock. The results show that the model can characterize the whole process of rock deceleration, constant velocity and accelerated fatigue deformation under the fatigue loads. The integrity parameter decreases as the number of cycles, N, increases, and this trend reflects the sensitivity of the fatigue damage to factors of loading and unloading times. The research put a foundation for the long-term deformation prediction of engineering rock mass.