Fractional derivative triaxial creep model of Beishan granite considering probabilistic damage evolution

It is helpful to study the creep process of rock by modeling the process of damage evolution in triaxial creep test. Based on the statistical distribution of strength of representative element, a dynamic damage model suitable for the initial loading stage is established. From the perspective of strength deterioration of representative element, the similarity of damage characteristics between characteristic representative element and rock sample during creep is found, and a time-dependent damage model suitable for the constant loading stage is also obtained. And the quantitative identification of parameters in the damage model is realized based on the cumulative acoustic emission (AE) count, which reveals the whole process of damage evolution in triaxial creep test. In addition, the power-law dashpot suitable for the accelerated creep stage is proposed, and the fractional non-Newtonian creep model considering the damage evolution is further established. The parameters of creep model are also identified by the stepwise least square fitting (LSF), and the applicability and superiority of the models are verified.