Viscoelastic-plastic constitutive model with non-constant parameters for brittle rock under high stress conditions

Under the long-term effect of high stress, the stability problem caused by the time-dependent deformation of brittle surrounding rock in deep engineering is becoming more and more prominent. The accurate description of the effectiveness of brittle rock is an important basis for the prediction of mechanical response and the stability evaluation of surrounding rock in deep engineering. To describe the accelerated time-dependent deformation behavior of brittle rock, a Newtonian body with non-constant parameters considering the effects of stress state is proposed. Combined with the improved Burgers model, a viscoelastic model with non-constant parameters of brittle rock is developed. The effects of time, delay coefficient, and stress level on the viscosity coefficient, as well as the influence of delay coefficient and initial viscosity coefficient on the accelerated time-dependent deformation, are examined. The results show that (1) the viscosity coefficient decreases with time and increases with the delay coefficient, while the attenuation rate increases; (2) the viscosity coefficient decreases with increasing stress level, and its attenuation rate increases with time; (3) with the increase of the delay coefficient, the nonlinear characteristics of the accelerated phase of the rock time-dependent deformation curve become more and more obvious; and (4) as the initial viscosity coefficient increases, the nonlinear characteristics of the accelerated phase of the time-dependent deformation curve become less and less obvious. The above laws fully reflect the evolutionary law of the nonlinear time-dependent deformation of rock. By comparing the results of the marble creep test with theoretical predictions, we found that when the stress limit is exceeded, the established model can well describe the initial attenuation, steady state, and accelerated characteristics of the rock time-dependent deformation curve, thus verifying the ability of the proposed model to describe the accelerated creep behavior, as well as the overall rationality of the model.