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Investigation Progresses and Applications of Fractional Derivative Model in Geotechnical Engineering

机译：分数阶导数模型在岩土工程中的研究进展与应用

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摘要

Over the past couple of decades, as a new mathematical tool for addressing a number of tough problems, fractional calculus has been gaining a continually increasing interest in diverse scientific fields, including geotechnical engineering due primarily to geotechnical rheology phenomenon. Unlike the classical constitutive models in which simulation analysis gradually fails to meet the reasonable accuracy of requirement, the fractional derivative models have shown the merits of hereditary phenomena with long memory. Additionally, it is traced that the fractional derivative model is one of the most effective and accurate approaches to describe the rheology phenomenon. In relation to this, an overview aimed first at model structure and parameter determination in combination with application cases based on fractional calculus was provided. Furthermore, this review paper shed light on the practical application aspects of deformation analysis of circular tunnel, rheological settlement of subgrade, and relevant loess researches subjected to the achievements acquired in geotechnical engineering. Finally, concluding remarks and important future investigation directions were pointed out.
机译：在过去的几十年中，分数阶微积分作为解决许多难题的一种新的数学工具，在各种科学领域，包括岩土工程中，主要是由于岩土流变现象引起的兴趣不断增长。与经典本构模型不同，在经典本构模型中，仿真分析逐渐无法满足要求的合理精度，分数导数模型显示出具有长记忆的遗传现象的优点。此外，可以追溯到分数导数模型是描述流变现象的最有效，最准确的方法之一。与此相关的是，首先提供了针对模型结构和参数确定的概述，并结合了基于分数演算的应用案例。此外，这篇综述文章还介绍了圆形隧道的变形分析，路基的流变沉降以及基于工程技术成果的黄土研究的实际应用方面。最后，指出结论和重要的未来研究方向。

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  • 来源
    《Mathematical Problems in Engineering》 |2016年第4期|9183296.1-9183296.15|共15页
  • 作者

    Lai Jinxing; Mao Sheng; Qiu Junling; Fan Haobo; Zhang Qian; Hu Zhinan; Chen Jianxun;

  • 作者单位

    Changan Univ, Sch Highway, Xian 710064, Peoples R China;

    Changan Univ, Sch Highway, Xian 710064, Peoples R China;

    Changan Univ, Sch Highway, Xian 710064, Peoples R China;

    Changan Univ, Sch Highway, Xian 710064, Peoples R China;

    Shijiazhuang Tiedao Univ, Sch Civil Engn, Shijiazhuang 050043, Peoples R China;

    Shijiazhuang Tiedao Univ, Sch Civil Engn, Shijiazhuang 050043, Peoples R China;

    Changan Univ, Sch Highway, Xian 710064, Peoples R China;

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