基于非定常分数阶的岩石时效性蠕变模型  

Time-dependent creep model of rock based on unsteady fractional order

作　　者：刘文博 张树光[1,3] 陈雷 LIU Wenbo;ZHANG Shuguang;CHEN Lei(Guangxi Key Laboratory of Geomechanics and Geotechnical Engineering,Guilin,Guangxi 541004,China;School of Civil Engineering and Transportation,Liaoning Technical University,Fuxin,Liaoning,123000,China;School of Civil Engineering,Guilin University of Technology,Guilin,Guangxi 541004,China)

机构地区：[1]广西岩土力学与工程重点实验室,广西桂林541004 [2]辽宁工程技术大学土木工程学院,辽宁阜新123000 [3]桂林理工大学土木与建筑工程学院,广西桂林541004

出　　处：《采矿与安全工程学报》2021年第2期388-395,共8页Journal of Mining & Safety Engineering

基　　金：国家自然科学基金项目(51274109)。

摘　　要：为了研究砂岩在不同围压作用下的蠕变特性,采用MTS815.02试验机对砂岩进行三轴蠕变试验,进而分析了砂岩在不同围压作用下的蠕变变形规律。将黏壶黏滞系数非定常化来构建非定常Abel黏壶,在此基础上对分数阶阶数进行非定常化,进而建立一种基于非定常分数阶的砂岩时效性蠕变本构模型,使得该模型可以更好地描述岩石的加速蠕变变形规律;通过Levenberg-Marquardt算法对三轴蠕变模型参数进行识别,来验证构建蠕变模型的正确性。结果表明:在时间和应力双重作用影响下,将分数阶阶数γ当做是一个关于应力和时间的函数,构建的非定常分数阶砂岩三维时效性蠕变本构模型可以很好地描述岩石的加速蠕变变形规律;模型曲线和试验曲线拟合均在0.95以上,侧面证明了将分数阶阶数非定常化是可行的。同时,采用单轴蠕变曲线和蠕变模型曲线进行对比,得出试验数据与一维时效性蠕变模型的吻合度也较高,这进一步说明了采用非定常化分数阶阶数建立的一维时效性蠕变模型是可靠的。In order to study creep characteristics of sandstone under different confining pressure,triaxial creep test on sandstone was carried out with the testing machine of MTS 815.02,and the creep deformation of sandstone under different confining pressures was analyzed.An unsteady Abel clay pot was constructed with unsteady viscosity coefficient,based on which the fractional order was sorted in terms of unsteady,and a time-dependent creep constitutive model based on unsteady fractional sandstone was established for better description of accelerated creep deformation law.Finally,parameters of the triaxial creep model was identified with Levenberg-Marquardt algorithm to verify the correctness of the creep model.The results have shown that under dual influence of time and stress,with fractional orderγregarded as a function of stress and time,the three-dimensional time-dependent creep constitutive model of unsteady fractional sandstones constructed well describes the law of accelerated creep deformation of rocks;the model curve and the test curve aggregate above 0.95,which proves that it is feasible to unfraction the fractional order.At the same time,the comparison between uniaxial creep curve and creep model curve has shown that the agreement between test data and one-dimensional creep model is high.This further illustrates the reliability of one-dimensional time-dependent creep model established with unsteady fractional order.

关 键 词：分数阶 非定常化 时效性蠕变本构模型 加速蠕变 参数识别 

分 类 号：TD32[矿业工程—矿井建设]