岩石分数阶黏弹塑性损伤蠕变模型研究

Viscoelastic-plastic damage creep model of rock based on fractional order

为了准确描述岩石蠕变变形破坏的全过程特征,基于分数阶微积分理论,提出了一种用于描述岩石初始非线性衰减蠕变阶段蠕变变形特征的非定常Abel黏壶;进而根据连续损伤力学理论,建立了考虑蠕变损伤的分数阶非线性损伤黏塑性体,以描述加速蠕变阶段的蠕变力学行为。将非定常Abel黏壶和分数阶非线性损伤黏塑性体与胡克体、黏性体进行串联,建立了一种新的岩石分数阶黏弹塑性损伤蠕变模型,并结合广义胡克定律及Perzyna黏塑性理论推导出三维应力状态下的蠕变方程。最后,利用相关蠕变试验数据反演拟合,对比分析试验数据与模型曲线的相关性。结果表明:由该模型导出的蠕变方程不仅可以准确描述岩石在低应力水平下稳态蠕变阶段的非线特征,而且能够反映岩石在高应力状态下的加速蠕变特征,相关系数均在0.96以上,实现了对岩石蠕变过程3阶段的模拟。

To accurately characterize the entire process of rock creep deformation and damage,based on the theory of fractional-order calculus,a non-constant Abel viscous element was proposed for characterizing the creep deformation of rocks in the initial nonlinear decay creep stage;furthermore,according to the theory of continuum damage mechanics,a fractional-order nonlinear damage visco-plasticity model that takes account of creep damage was developed to characterize the mechanical behavior during the accelerated creep stage.By connecting the non-constant Abel viscous element and the fractional-order nonlinear damage visco-plasticity model in series with the Hookean body and a viscous element,a new fractional-order viscoelastic-plastic damage creep model for rock was established,and the creep equations in three-dimensional stress state were derived by combining the generalized Hooke′s law and Perzyna′s theory of viscoplasticity.Finally,the correlation between the experimental data and the model curves was comparatively analyzed through inverse fitting using relevant creep test data.The results show that the model-derived creep equations can not only accurately describe the nonlinear characteristics of the steady-state creep phase of the rock at low stress levels,but also reflect the accelerated creep characteristics of the rock at high stress levels,with correlation coefficients all exceeding 0.96,thus achieving simulation of the rock′s three-stage creep process.