关键词: 层状岩石, 横观各向同性, 蠕变, 本构方程, 分数阶

Abstract: Deep-buried tunnels in the central and western China pass through a large number of layered rock masses. Under the action of high in-situ stress, the layered rocks exhibit transversely isotropic properties and significant creep phenomena, which are highly likely to trigger engineering disasters such as tunnel face collapses and support structure failures. To accurately characterize the impact of bedding angles and time effects on the mechanical properties of layered rocks, based on the fractional calculus theory and the creep compliance substitution method, taking the component combination model as the foundation, this study established a transversely isotropic nonlinear creep model (T model) that takes into account damage and rock layer angles, and derived the one- dimensional and three-dimensional creep constitutive equations. The T model uses the fractional-order Kelvin model to describe the characteristics of the decelerating creep stage, the Abel dashpot for the steady-state creep stage, and connects the instantaneous plastic element and the fractional-order nonlinear damage dashpot in parallel to reflect the characteristics of the accelerating creep stage. Based on the creep test data of carbonaceous slate, the least square method was used to identify the parameters of the creep constitutive equations. Through the error analysis of RMSE (root mean square error), MAE (mean absolute error) and R² (coefficient of determination), as well as the comparison with the existing transversely isotropic creep models, the fitting effect of the constitutive equation of the T model was verified, which indicates that the T model can describe the characteristics of each creep stage of layered rocks more accurately. The research results provide a theoretical basis for the long-term stability analysis of the surrounding rock of layered rock tunnels.

Key words: layered rock, transverse isotropy, creep, constitutive model, fractional order