长江科学院院报 ›› 2018, Vol. 35 ›› Issue (2): 109-115.DOI: 10.11988/ckyyb.20170454

• 岩土工程 • 上一篇    下一篇

低动应力下岩石分数阶Burgers本构模型

浦少云1,黄质宏1,饶军应1,穆 锐1,郑红超1,王田龙1,刘小浪2,李 磊1,王义红1   

  1. 1.贵州大学 土木工程学院,贵阳 550025;
    2 中国地质大学武汉 工程学院, 武汉 430074
  • 收稿日期:2017-04-21 出版日期:2018-02-01 发布日期:2018-03-01
  • 作者简介:浦少云(1993-),男,贵州威宁人,硕士研究生,主要从事岩土工程相关方面研究。E-mail:2290605640@qq.com
  • 基金资助:
    国家自然科学基金项目(51608141);贵州大学引进人才科研项目(贵大人基合字(2015)16)

Fractional order Burgers Constitutive Model for Rock under Low Dynamic Stress

PU Shao yun1, HUANG Zhi hong1, RAO Jun ying1, MU Rui1, ZHENG Hong chao1, WANG Tian long1, LIU Xiao lang2, LI Lei1, WANG Yi hong1   

  1. 1.College of Civil Engineering, Guizhou University, Guiyang 550025, China;
    2.Faculty of Engineering, China University of Geosciences, Wuhan 430074, China
  • Received:2017-04-21 Online:2018-02-01 Published:2018-03-01

摘要: 动荷载下岩石变形特性是岩土工程界的常见问题之一。为研究岩石低动应力下变形特性,基于分数阶微积分构建分数阶黏壶,将分数阶黏壶替换Burgers模型中Maxwell常值黏壶,建立了可反映低动应力荷载作用下岩石变形规律的分数阶Burgers模型(Fractional-order Burgers Model,FBM)。将动荷载分解为一个静力荷载和一个平均应力值为0的循环荷载,基于流变力学理论给出了静力作用下基于分数阶Burgers模型的岩石流变本构方程,再根据黏弹性力学理论,考虑岩石损伤、裂隙及塑性变形对动荷载下岩石储能柔量和耗能柔量造成的影响,引入储能和耗能柔量变化量,构建了循环荷载下基于分数阶Burgers模型的岩石动态响应本构方程式,最后将已获得的岩石流变本构方程式与动态响应本构方程式叠加,即得到一种新的岩石本构方程。与已有的试验结果相比,改进Burgers模型可较好地描述低动应力状态下岩石减速、等速2个阶段的变形特征,且模型参数可运用数值方法简便得到。

关键词: 岩石动力学, 低动应力, 分数阶黏壶, 分数阶Burgers模型, 流变力学

Abstract: The deformation characteristics of rock under dynamic loading is a common problem in geotechnical engineering. In this article, a Fractional order Burgers Model (FBM) which reflects the deformation characteristics of rock under low dynamic stress is established by replacing constant Maxwell dashpot of Burgers model with fractional order dashpot based on fractional calculus. The dynamic loading is decomposed into a static loading and a cyclic loading with an zero average stress by stress decomposition method. According to rheological mechanics theory, the rheology constitutive equation for rock based on FBM is given under the static loading; and meanwhile according to viscoelastic mechanics theory, the dynamic response constitutive equation of rock based on FBM is deduced under the cyclic loading in consideration of the influence of rock damage, fracture and plastic deformation on energy storage and energy dissipation compliance. Furthermore, a new constitutive equation for rock is obtained by superimposing the constitutive equations under the two stress conditions. Compared with existing test results of rock under dynamic loading, the FBM could better describe the deformation characteristics of rock under low dynamic stress in deceleration stage and constant velocity stage; moreover the FBM parameters can be obtained conveniently by numerical methods.

Key words: rock dynamic mechanics, low dynamic stress, fractional order dashpot, Fractional order Burgers Model (FBM), rheological mechanics

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