The 3D Nonstationary Creep Constitutive Model of Sandstone Based on Fractional Order

Based on nonlinear creep characteristics of rock, triaxial creep tests were conducted on sandstone by using an MTS812.02 test machine. The creep properties of rocks under different conditions were analyzed. Establishing a creep model that describes parameter degradation is necessary to address the deterioration of rock creep parameters over time. A nonstationary Abel pot was constructed on the basis of laws of damage accumulation and deterioration. Then, the nonstationary creep model was established according to fractional order theory. The parameters of the triaxial creep test curve under different confining pressures were identified on the basis of Levenberg–Marquardt algorithm in Hengda coal mine in Fuxin, China. By comparing the model curve with the experimental curve, we found that the nonlinear model not only accurately reflected the creep characteristics of the decay and steady creep stages but also overcame the limitation of traditional creep model, that is, difficulty in describing the accelerated creep. Finally, the influence of fractional order and nonstationary parameters on rock creep was obtained by parameter sensitivity analysis. Overall, the model had high fitting degree as well as good prediction and analysis for 3D creep test data.