关键词: 分数阶微积分, 非定常参数, 岩石蠕变模型

Abstract: The surrounding rock of the deep and long tunnels at Jinping II hydropower station shows pronounced rheological deterioration during excavation. According to the fractional calculus theory, a fractional order derivative constitutive model for rock creep is developed by replacing the traditional Newton dashpot with Abel dashpot in the classical Nishihara model. To address the unsteady nature of a creep process, especially when the suffered stress becomes larger than the long-term rock strength, an unsteady creep constitutive model is developed based on the fractional order derivative by introducing the unsteady feature of creep parameters into the constitutive equation. Based on the results of shear creep tests on marble, which is one of the main rock types at Jinping II hydropower station diversion tunnel, the material parameters can be determined by fitting the experiment results. It is shown that the unsteady creep constitutive model based on the fractional order derivative can describe the experimental results very well at the beginning of the creep and the turning points, overcoming the deficiency that Nishihara model cannot describe the third stage of the creep process. The parametric analysis clearly demonstrates the effect of fractional derivative order and unsteady parameters on a creep strain. The proposed model can reflect the whole creep process very well.

Key words: fractional calculus, unsteady parameters, creep model of rock