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基于分数阶微积分岩石的动态变形行为研究

何明明, 李宁, 陈蕴生, 朱才辉

何明明, 李宁, 陈蕴生, 朱才辉. 基于分数阶微积分岩石的动态变形行为研究[J]. 岩土工程学报, 2015, 37(zk1): 178-184. DOI: 10.11779/CJGE2015S1034
引用本文: 何明明, 李宁, 陈蕴生, 朱才辉. 基于分数阶微积分岩石的动态变形行为研究[J]. 岩土工程学报, 2015, 37(zk1): 178-184. DOI: 10.11779/CJGE2015S1034
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HE Ming-ming, LI Ning, CHEN Yun-sheng, ZHU Cai-hui. Dynamic deformation behavior of rock based on fractional order calculus[J]. Chinese Journal of Geotechnical Engineering, 2015, 37(zk1): 178-184. DOI: 10.11779/CJGE2015S1034
Citation: HE Ming-ming, LI Ning, CHEN Yun-sheng, ZHU Cai-hui. Dynamic deformation behavior of rock based on fractional order calculus[J]. Chinese Journal of Geotechnical Engineering, 2015, 37(zk1): 178-184. DOI: 10.11779/CJGE2015S1034
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基于分数阶微积分岩石的动态变形行为研究  English Version

  • 西安理工大学岩土工程研究所,陕西 西安 710048

基金项目: 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）
详细信息
    作者简介:

    何明明(1986- ),男,博士研究生,主要从事岩土工程等方面的研究工作。

Dynamic deformation behavior of rock based on fractional order calculus

  • Institute of Rock and Soil Mechanics,Xi’an University of Technology, Xi’an 710048 China

摘要

    摘要
  • 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 dynamic strain of rock better, lateral-axial strain fractional dashpot and viscoelastic lateral-axial strain combined models are put forward on the basis of viscoelastic stress-strain combined model theory. The fractional lateral-axial strain relationship and the fractional volume strain model are proposed based on the fractional order calculus, and the corresponding equations under dynamic loading and cyclic loading are derived. The analytic solution for the model of lateral-axial strain relationship is given theoretically. Moreover, a multi-functional material testing set-up is employed to measure the lateral-axial strain of a variety of rock, concrete and gypsum samples under the dynamic loading and cyclic loading. The parameters of the lateral-axial strain model are determined by fitting to the experimental results of lateral-axial strain of rock. In addition, a sensitivity study for the analytic solution of the lateral-axial strain model is carried out, showing the effects of confining pressure, strain level, fractional derivative order and model coefficient on axial strain of rock samples. Furthermore, it’s found that the new model can describe the volume strain phenomenon of negative and positive dilatancy and the variation law of deformation under dynamic loading and cyclic loading in rock.
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    • 参考文献(19)
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出版历程
  • 收稿日期:  2015-03-25
  • 发布日期:  2015-07-24

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