岩石蠕变的非定常分数伯格斯模型

Nonstationary parameter fractional Burgers model of rock creep

典型的伯格斯(Burgers)模型只能描述岩石第3期以前的蠕变规律。分数单元利用分数阶导数定义,是一种介于弹簧和黏壶的力学元件。用分数单元代替伯格斯模型中并联的黏壶,给出分数伯格斯模型。为了描述加速蠕变阶段,把分数伯格斯模型中串联的黏壶看成与时间有关的非定常参数,给出非定常分数伯格斯模型及相应的本构方程和蠕变柔量。串联的非定常黏壶关闭、开启时,模型分别适合描述前两期和包含第3期在内的蠕变规律。用模型拟合不同应力下的蠕变试验数据,都可给出较好的描述,说明非定常分数伯格斯模型能够很好地描述蠕变曲线中的初始衰减蠕变阶段、稳态蠕变阶段和加速蠕变阶段,证明了该模型的正确性和合理性。

The classic Burgers creep model could only describe the behavior of rock material before the third creep-phase.The fractional element,defined by using fractional derivative,is an element between spring and dashpot.Through the substitution of a dashpot by a fractional element,a fractional Burgers model is developed.Moreover let the dashpot acted in series be a nonstationary parameter of time for describing the acceleration stage of rock creep.Their constitutive relation and creep compliance are obtained.When the nonstationary dashpot work or does not work,the model could respectively describe two-phase and three-phase creep.It is shown that the creep testing curves under different conditions are coincident well with the theoretical curves.The model can well describe the variation of creep in the period of attenuation,steady period and the period of acceleration.The validity of the model is verified by the experiment data.