分数阶导数黏弹性饱和土体一维固结半解析解

发布时间：2018-09-02 05:42

【摘要】：将分数阶微积分理论引入Kelvin-Voigt本构模型,以描述黏弹性饱和土体的力学行为。对饱和土体一维固结方程和上述分数阶导数Kelvin-Voigt本构方程实施Laplace变换,联立求解得到变换域内有效应力和沉降的解析解。采用Crump方法实现Laplace数值反演,从而获得了物理空间一维固结问题的半解析解,并将其退化到弹性和黏弹性两种经典情形,分析表明,它与经典解析解完全相同,这证明了经典弹性和黏弹性解析解可视为本研究提出分数阶导数黏弹性解的特例。开展了参数研究,即分析了相关各种参数对固结沉降的影响。研究表明,瞬时荷载情形下分数阶导数黏弹性饱和土体一维固结最终沉降量与黏滞系数和分数阶次无关,而不同黏滞系数和分数阶次对固结时间有较大影响。其研究结果有助于深入认识黏弹性饱和土体的固结力学行为。
[Abstract]:The fractional calculus theory is introduced into the Kelvin-Voigt constitutive model to describe the mechanical behavior of viscoelastic saturated soil. The one-dimensional consolidation equation of saturated soil and the above fractional derivative Kelvin-Voigt constitutive equation are transformed by Laplace transformation, and the analytical solutions of effective stress and settlement in the transform domain are obtained by simultaneous solution. Using Crump method to realize Laplace numerical inversion, the semi-analytical solution of one-dimensional consolidation problem in physical space is obtained, and it is reduced to two classical cases of elasticity and viscoelasticity. The analysis shows that it is identical to the classical analytical solution. It is proved that the analytical solutions of classical elasticity and viscoelasticity can be regarded as special cases of fractional derivative viscoelastic solutions in this paper. Parameter study was carried out, that is to say, the influence of various parameters on consolidation settlement was analyzed. The results show that the final settlement of one-dimensional consolidation of fractional derivative viscoelastic saturated soil is independent of viscosity coefficient and fractional order, but different viscosity coefficient and fractional order have great influence on consolidation time. The results are helpful to understand the consolidation behavior of viscoelastic saturated soil.
【作者单位】：上海工程技术大学机械工程学院;上海工程技术大学城市轨道交通学院;上海大学土木工程系;
【基金】：上海工程技术大学研究生创新项目(No.15ky0119)~~
【分类号】：TU43

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