一种新的岩石非线性黏弹塑性流变模型

A new nonlinear viscoelasto-plastic rheological model for rocks

借鉴经典元件组合模型的建模思路,将含分数阶微积分的软体元件与弹簧元件串联,结合一个幂函数黏塑性体,提出一种新的四元件非线性黏弹塑性流变模型,并给出该模型的本构方程和蠕变方程,得到在不同应力条件下的蠕变曲线。可以发现,岩石稳定蠕变阶段的非线性渐变过程和加速蠕变阶段蠕变速率的快慢程度可通过调整蠕变参数进行有效地模拟。在较低应力水平时,模型能够有效地刻画岩石的初始蠕变和稳定蠕变;当应力水平超过岩石的长期强度时,能够反映加速蠕变特性。利用该模型对试验数据拟合的结果表明,含有软体元件和幂函数黏塑性体的非线性流变模型能够有效地描述岩石的蠕变特性,减少组合模型中的元件个数和参数数量。

By means of classic element combination modeling ideas,making fractional calculus soft-matter element and spring element in series and combining a visco-plastic body of power function,a new nonlinear viscoelasto-plastic rheological model with four elements is put forward.The constitutive equation and creep equation of the model are given and the creep curves in different stress conditions are obtained.It can be found that nonlinear gradual change process of steady creep phase and creep speed rate of accelerated creep stage of rock can be effectively simulated by adjusting creep parameters.In lower stress level,the model can describe the initial creep and steady creep of rocks.Moreover,if the stress level exceeds the long-term strength of rocks,the model can reflect the accelerated creep characteristics.The fitted results show that the nonlinear rheological model which contains soft-matter element and visco-plastic body of power function can effectively describe the creep properties of rocks and reduce the number of components and parameters of combination model.