Time to failure prediction and model of Beishan granite under true triaxial stresses

The characteristics of creep deformation and time to failure of deep hard rock are important for predict time-dependent disasters. Based on the short-term compression and long-term single-stage creep tests under true triaxial stresses, the characteristics of creep deformation and time to failure of Beishan granite subjected to different intermediate principal stress (\(\sigma _{2}\)) and deviatoric stress (\(\sigma _{1}\)-\(\sigma _{3}\)) were studied. The prediction formula of time to failure was established for hard rock, considering the effect of \(\sigma _{2}\). The test results show that the time to failure of rock samples increases with the decrease of the stress-strength ratio (SSR = (\(\sigma _{1}\)-\(\sigma _{3}\))/(\(\sigma _{\mathrm{p}}\)-\(\sigma _{3}\))) under the same \(\sigma _{2}\) and \(\sigma _{3}\) conditions. In addition, the steady creep rate of rock sample is affected by the stress-strength ratio of the over-stress (\(\Delta\)SSR = (\(\sigma _{1}\)-\(\sigma \)_cd)/(\(\sigma _{\mathrm{p}}\)-\(\sigma _{3}\))). With the increase of the \(\Delta \)SSR, the steady creep rate of rock samples increases. With the increase of \(\sigma _{2}\), the \(\Delta \)SSR of rock samples decreases under the same SSR, therefore, high \(\sigma _{2}\) increases the time to failure of rock samples. Based on the scientific understanding of the characteristics of small deformation and time to failure of Beishan granite, a 3D Nonlinear Creep Model of Beishan Granite under true triaxial stress is proposed. The model can reflect the viscoelastic-plastic characteristic and damage-accelerated creep process of Beishan granite under true triaxial stress. The applicability of the proposed model is verified by comparing with the creep test data.