任鹏, 王鹏, 张华, 唐印. 黏土蠕变非线性特性及其分数阶导数蠕变模型[J]. 工程力学, 2020, 37(9): 153-160, 207. DOI: 10.6052/j.issn.1000-4750.2019.10.0624
引用本文: 任鹏, 王鹏, 张华, 唐印. 黏土蠕变非线性特性及其分数阶导数蠕变模型[J]. 工程力学, 2020, 37(9): 153-160, 207. DOI: 10.6052/j.issn.1000-4750.2019.10.0624
REN Peng, WANG Peng, ZHANG Hua, TANG Yin. NONLINEAR BEHAVIOR OF CLAY CREEP AND ITS FRACTIONAL DERIVATIVE CREEP MODEL[J]. Engineering Mechanics, 2020, 37(9): 153-160, 207. DOI: 10.6052/j.issn.1000-4750.2019.10.0624
Citation: REN Peng, WANG Peng, ZHANG Hua, TANG Yin. NONLINEAR BEHAVIOR OF CLAY CREEP AND ITS FRACTIONAL DERIVATIVE CREEP MODEL[J]. Engineering Mechanics, 2020, 37(9): 153-160, 207. DOI: 10.6052/j.issn.1000-4750.2019.10.0624

黏土蠕变非线性特性及其分数阶导数蠕变模型

NONLINEAR BEHAVIOR OF CLAY CREEP AND ITS FRACTIONAL DERIVATIVE CREEP MODEL

  • 摘要: 针对黏土蠕变的非线性性质,以成都黏土为研究对象展开蠕变试验,发现黏土变形包括瞬时弹性变形、衰减蠕变变形、稳态蠕变变形和加速蠕变变形;黏土长期弹性模量随时间和应力的增加非线性软化;黏滞系数随应力的增加非线性软化,随时间的增加非线性硬化。基于流变学理论、分数阶微积分理论和Harris衰减函数,分别构建了分数阶导数元件、非线性弹性元件和非线性黏滞元件,从而建立了形式简单、参数较少和概念清晰的非线性分数阶导数蠕变模型。将非线性分数阶导数蠕变模型和Burgers蠕变模型进行对比拟合分析,发现非线性分数阶导数蠕变模型各阶段的拟合结果更好,对黏土非线性蠕变的描述更合理,可准确地反映黏土蠕变全过程,表明了所建立非线性分数阶导数蠕变模型的科学合理性。

     

    Abstract: Creep test is performed on Chengdu clay to study the nonlinear property of clay creep. It is found that instantaneous elastic deformation, attenuated creep deformation, steady creep deformation, and accelerated creep deformation are included in clay deformation. The long-term elastic modulus of clay is nonlinear softening with the increase of time and stress. The viscosity coefficient is nonlinear softening with the increase of stress and nonlinear hardening with the increase of time. Based on the rheology theory, fractional calculus theory and Harris attenuation function, fractional derivative components, nonlinear elastic components and nonlinear viscous components are established, respectively. A nonlinear fractional derivative creep model with simple form, few parameters and clear concept is established. Then, the nonlinear fractional derivative creep model and Burgers creep model are compared. It is found that the fitting effect of nonlinear fractional derivative creep model is better in each stage, and can give more reasonable description of the nonlinear creep of clay, and can accurately reflect the whole process of clay creep. The scientific rationality of the nonlinear fractional derivative creep model is proved.

     

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