基于分数阶微积分理论的泥岩蠕变损伤本构模型

Damage Constitutive Model of Mudstone Creep Based on Theory of Fractional Calculus

泥岩在吸水膨胀时,其各力学参数均会发生明显变化。建立泥岩分数阶损伤蠕变模型结构图,引入描述岩石损伤程度的损伤变量,当应力水平超过岩石的长期强度时,在泥岩加速应变率加载情况下,建立基于分数阶微积分理论的非线性蠕变损伤模型,基于蠕变模型建立加速应变率加载情况下的泥岩蠕变本构模型。通过本构模型得到,在加速蠕变阶段,应变与时间呈指数函数关系。利用蠕变试验数据对所提出的模型进行验证,结果表明,分数阶β为岩体固有参数并且能够反映岩体硬度,在加速蠕变阶段,分数阶损伤蠕变本构模型能够较好地描述泥岩蠕变的应力—应变关系。

When swelling mudstone,its various mechanical parameters will change significantly. Establishing mudstone＇s fractional cal- culus creep damage model structure diagram ,which describes the extent of damage in rock damage variable. Assumed that the stress lev- el of rock exceeded its the long-term strength and under the condition of mudstone accelerated strain rate loading, nonlinear damage model based on fractional calculus theory was established. Therefore mudstone creep constitutive model considering the accelerated strain rate loading conditions was obtained. The results of constitutive model showed that, there appears to be an exponential function be- tween strain and time in the accelerated creep stage. The creep test data were used to verify the proposed model and the results sugges- ted that the fractional order βwas the intrinsic parameters of rock mass which could reflect its hardness. During the accelerated creep stage, fractional creep damage constitutive model could describe the stress-strain relationship well.