Multi-scale damage creep model and long-term strength for hard brittle rocks

From the viewpoint of damage accumulation, the subcritical propagation of microcracks under the action of stress dissolution was considered. The evolution of the time-dependent damage was explored on the basis of multi-scale friction damage coupled model. The time-dependent damage was introduced into the friction criterion and an appropriate time-dependent damage criterion was proposed. Moreover, the relationship between the macroscopic inelastic strain and microscopic damage was derived. A multi-scale damage creep model was established to reflect the characteristics of three stages of creep curves. Taking the crack damage stress as the index to reflect the long-term strength of hard brittle rock, the analytical solution of long-term strength and up-scale calibration method for model parameters was presented by combining damage friction coupling analysis and microscopic time-dependent damage evolution law. The proposed multi-scale damage creep model was used to simulate the triaxial compression creep test of Xiangjiaba sandstone, and the accuracy and effectiveness of the model were verified. The results show that the model not only can completely describe each stage of creep behaviour in hard brittle rocks under different stress but also reflect the effect of strain history on the time-dependent damage correctly. In addition, the analytical solution of long-term strength provides a theoretical basis for determining the applied stress in the multi-step creep test. © 2022 Central South University of Technology. All rights reserved.