盐岩分数阶三元件本构模型研究

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摘要借助盐岩流变–超声波试验，得出损伤变量随加载时间的函数关系式，并在经典三元件模型的基础上，通过引入分数阶微积分理论及损伤理论，构建基于损伤演化的盐岩分数阶三元件模型，该本构模型具有元件简明、参数较少等优点。基于盐岩单轴流变试验数据，采用最小二乘法拟合获得该本构模型中的参数。由拟合曲线可知，分数阶三元件模型能够很好地描述盐岩流变的3个阶段，且精度较高，克服经典三元件模型不能表征加速流变阶段的缺点，且验证经典三元件模型为分数阶三元件模型的一种特殊形式。

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关键词 ：岩石力学, 损伤变量, 盐岩单轴流变试验, 分数阶三元件模型, 分数阶微积分理论

Abstract：A relationship between the damage variable and the loading time has been obtained from the rheologic-ultrasonic tests of salt rock. On the basis of the classical three elements model，a fractional derivative three elements model for salt rock considering the damage evolution was established employing the theory of fractional calculus and damage. The model is structural concise and has less fitting parameters. The parameters of the model can be determined by the fitting analysis of least-squares using the data from the uniaxial rheological tests. The fractional derivative three elements model can fit the three stages of rheologic of the experimental data of the salt rock with high accuracy and is better than the classical one in characterizing the tertiary rheological stage. Furthermore，it is shown that the classical three elements model is a special case of the new model.

Key words： rock mechanics damage variable uniaxial rheological tests of salt rock fractional derivative three elements model theory of fractional calculus

收稿日期: 2013-06-28

引用本文:

丁靖洋1，周宏伟1，刘迪1，陈琼1，刘建锋2. 盐岩分数阶三元件本构模型研究[J]. 岩石力学与工程学报, 2014, 33(4): 672-678.
DING Jingyang1，ZHOU Hongwei1，LIU Di1，CHEN Qiong1，LIU Jianfeng2. RESEARCH ON FRACTIONAL DERIVATIVE THREE ELEMENTS MODEL OF SALT ROCK. , 2014, 33(4): 672-678.

链接本文:

http://www.rockmech.org/CN/Y2014/V33/I4/672

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