A rock creep model based on Atangana-Baleanu fractional derivative with coupled damage effects of pore water pressure, stress and time

Pore water pressure is an important factor affecting long-term rock failure and instability. On the basis of the assumptions that the rock microunit strength follows Weibull distribution and the rock failure compliances Drucker-Prager criterion, a pore water pressure-stress coupled damage (PSCD) variable is constructed in this paper. Considering the effect of pore water pressure, stress and time (PST), a pore water pressure-stress-time coupled damage (PSTCD) variable is put forward by introducing the damage variable considering time effect. Based on the characteristics and advantages of fractional differential theory in viscoelastic analysis of rock materials, one-dimensional and three-dimensional pore water pressure-stress-time coupled damage fractional (PSTCDF) creep models are proposed by Atangana-Baleanu (AB) fractional derivative. By fitting and analyzing the laboratory experimental data of rock creep under the combined action of PST, the relevant parameters for PSTCDF creep model can be deduced. The analysis of the goodness of fit and the generalization accuracy prove the rationality, validity and generalization of the proposed model. The sensitivity of the PSTCDF model is analyzed by different the stress level, pore water pressure, fractional derivative order and damage variable co-efficient. The results show that the creep model changes flexibly when the model parameters change, and the specific creep state of rock can be reflected by reasonable selection of the model parameters.