基于分数阶导数的非定常蠕变本构模型研究

针对锦屏二级水电站深埋长大隧洞围岩在开挖过程中呈现明显的流变劣化特征，基于分数阶微积分理论，用Abel黏壶替换西原模型中的牛顿黏壶，推导出基于分数阶导数的蠕变本构方程，同时考虑岩石在蠕变过程中，尤其是所受应力超过其长期强度时，蠕变参数是非定常的特征，把蠕变参数的非定常性引入本构方程中，建立了基于分数阶导数的非定常蠕变本构模型。结合锦屏二级水电站引水隧洞主要围岩之一的大理岩的室内剪切蠕变试验的结果，对模型中的参数进行反演，结果表明，基于分数阶导数的非定常蠕变本构模型能够在蠕变初期和拐点处与试验结果很好地吻合，并且可以克服西原模型不能反映蠕变第3阶段的不足。通过对模型中参数的敏感性进行分析，得出分数阶阶数、非定常参数对岩石蠕变的影响规律。研究结果表明，提出的基于分数阶导数的非定常蠕变模型能够很好地反映大理岩的蠕变全过程。

An unsteady creep constitutive model based on fractional order derivatives

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.