基于分数阶微积分的岩石非定常蠕变本构模型

Non-steady State Creep Constitutive Model of Rock Based on Fractional Calculus

基于分数阶微积分理论,对岩石蠕变本构模型中常用的Abel黏壶元件进行改进,得到表征损伤阀值效应的非定常性元件模型,并论证该模型可以良好适用于岩石加速蠕变阶段。基于经典元件组合理论,通过弹性体、Abel黏壶体以及改进后的损伤阀值触发的Abel黏壶元件体建立了新的岩石蠕变本构模型。基于实验数据反演拟合,结果表明,该岩石蠕变本构模型能良好的表征岩石蠕变三阶段,特别是非线性加速蠕变阶段,与实验数据相关程度高,误差较小,且该模型考虑的损伤阈值触发作用情况更贴切岩石蠕变行为。通过对本构模型中加载应力及求导阶数敏感度分析,获得了影响蠕变应变量的参数为加载应力,影响蠕变速率的为求导阶数,从本构模型上揭示了影响岩石蠕变行为特性的基本参数。

Based on fractional calculus theory,the commonly used Abel clay pot element in rock creep constitutive model is improved,and the unsteady element model representing damage threshold effect is obtained.It is proved that the model can be well applied to rock creep stage.Based on the classical component combination theory,a new constitutive model of rock creep is established by using elastomer,Abel clay pot and Abel clay pot element triggered by improved damage threshold.Based on the inversion and fitting of experimental data,the results show that the creep constitutive model can well characterize the three stages of rock creep,especially the non-linear accelerated creep stage.It has high correlation with experimental data and small error.Moreover,the damage threshold triggering effect considered by the model is more suitable for rock creep behavior.Through the sensitivity analysis of loading stress and derivative order in the constitutive model,the parameters affecting creep strain are obtained as loading stress and creep rate as derivative order.The basic parameters affecting creep behavior of rock are revealed from the constitutive model.