Multi-stepped creep constitutive model based on asymptotic damage evolution behavior of sandstone

Under prolonged stress conditions, the tunnel surrounding rock produces a time-varying mechanical response, which poses a serious threat to the life cycle of the tunnel project. In this paper, a series of uniaxial compression tests were carried out on tunnel sandstone from Jiulongpo District using a self-developed rock servo instrument and acoustic emission (AE) testing system. Then, based on the theory of asymptotic damage evolution behaviour, different stress levels were set and multi-stage creep tests were conducted. The results show that the sandstone creep only exhibits a decelerated creep phase and a stabilised creep phase at the first three stress levels, while the accelerated creep phase is extremely obvious at the fourth stress level. The total number of acoustic emission events and total energy remained relatively constant in the stable creep stage, increased slightly in the decelerated creep stage, and increased significantly in the accelerated creep stage, and the distribution characteristics of the absolute energy of acoustic emission in different creep stages differed significantly. The probability density algorithm of the RA-AF scatterplot indicated that tensile cracks accounted for a larger proportion than shear cracks during the whole creep process. Finally, the constant parameters in the Burgers model were replaced by power-law functions with time-varying characteristics, and a nonlinear viscoplastic unit was introduced into the Burgers model to construct a nonlinear creep constitutive model that can describe the whole creep stage and has time-varying characteristics. The new model can quantitatively describe and predict the whole process of sandstone creep with high accuracy. The results are of great significance for monitoring and predicting the time-varying characteristics of tunnels and understanding the microscopic damage of sandstone.