周期荷载下岩石分数阶黏弹塑性本构模型研究

为研究周期荷载下岩石疲劳变形特性,基于分数阶微积分构建分数阶黏壶,将分数阶黏壶替换西原模型黏塑性体中的一般黏壶,并在西原模型中串联一个黏性元件,分别建立了可描述周期荷载下岩石变形规律的一维和三维分数阶黏弹塑性本构模型。在高动应力状态下,模型为反映岩石减速、等速、加速3个变形阶段变形规律的岩石分数阶黏弹塑性疲劳本构模型;反之,则为反映岩石减速、加速变形规律的Burgers模型。对既有的岩石疲劳试验结果拟合表明:基于分数阶黏弹塑性模型所建立的岩石疲劳本构方程可较好地描述周期荷载下岩石各种变形特征,拟合系数在0.96以上。研究成果可丰富岩石力学理论,为相关研究提供参考。

Fractional-order Visco-elasto-plastic Constitutive Model forRock under Cyclic Loading

In order to study the fatigue deformation characteristics of rock under cyclic loading, we established one-dimensional and three-dimensional Fractional-order Visco-Elasto-Plastic Constitutive Model (FVEPCM) by replacing the common dashpot in viscoplastic body of Nishihara’s model with the fractional-order dashpot and connecting a viscous element in series in Nishihara’s model. Under high dynamic stress, the model is a FVEPCM reflecting the three states of rock fatigue deformation: deceleration stage, constant velocity stage, and acceleration stage; otherwise, it is a Burgers Model which reflects the two states of rock fatigue deformation: deceleration, and constant velocity stage. Fitting of the existing rock fatigue test results shows that the fatigue constitutive equation for rock based on FVEPCM can be used to better describe different deformation characteristics of rock under cyclic loading, and the effect of fitting to various types of deformation curves of rock is good, with the fitted correlation coefficients above 0.96.