基于分数阶微积分岩石的动态变形行为研究

发布时间：2018-05-17 14:25

本文选题：分数阶微积分 + 分数阶黏壶　；参考：《岩土工程学报》2015年S1期

【摘要】：为了更合理地描述岩石环向与轴向动态变形之间的关系,从分数阶微积分出发,在黏弹性应力应变组合模型理论基础上,提出环向轴向应变分数阶黏壶及环向轴向应变关系的黏弹性组合模型,构建了基于分数阶微积分的岩石在静动态压缩及循环荷载条件下环向轴向应变关系模型,并给出了模型的解析解,从而得到的分数阶体积应变公式可以作为体积应变求解的新方法。基于多种岩石、混凝土及石膏的实验数据,对分数阶微积分环向轴向应变关系模型的参数进行拟合分析,对模型参数进行了敏感性分析,揭示了围压、应变水平、分数阶导数阶数及模型参数对环向应变的影响规律。结果表明环向轴向应变关系模型不仅可以更好地反映岩石体积变形的减缩减胀特性,而且能够描述岩石在循环荷载及动态压缩条件下变形规律。
[Abstract]:In order to describe the relationship between the toroidal and axial dynamic deformation of rock more reasonably, based on the theory of viscoelastic stress-strain combination model, the fractional calculus is used. A viscoelastic combined model for the relationship between the fractional strain and the axial strain of the circumferential strain is proposed. The model of the axial strain relationship of rock under static and dynamic compression and cyclic loading is constructed based on fractional calculus. The analytical solution of the model is given, and the fractional volume strain formula can be used as a new method to solve the volume strain. Based on the experimental data of various rocks, concrete and gypsum, the parameters of the fractional calculus ring-direction axial strain relationship model are fitted and analyzed. The sensitivity of the model parameters is analyzed, and the confining pressure and strain level are revealed. The influence of fractional derivative order and model parameters on the circumferential strain. The results show that the circumferential axial strain relationship model can not only better reflect the reduced dilatation characteristics of rock volume deformation, but also describe the deformation law of rock under cyclic load and dynamic compression.
【作者单位】：西安理工大学岩土工程研究所;
【基金】：国家自然科学基金项目(51179153);国家自然科学基金青年科学基金项目(51308456)
【分类号】：TU45

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