任意荷载下分数阶导数黏弹性饱和土体一维固结

发布时间：2018-04-26 03:09

本文选题：任意荷载 + 分数阶导数　；参考：《岩土工程学报》2017年10期

【摘要】：将分数阶导数理论引入Kelvin Voigt模型,来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,获得了任意荷载情况下物理空间内一维固结问题的半解析解。并将指数荷载情况下分数阶导数模型退化到黏弹性情形,结果与已有文献解析解相同,验证了本研究提出任意荷载情况下分数阶导数黏弹性解的可靠性。最后,分析了相关参数对固结沉降的影响。研究表明,任意荷载情形下分数阶导数黏弹性饱和土体一维固结发展过程与黏滞系数和分数阶次有关,分数阶次越大,固结沉降发展越快;黏滞系数越大,固结沉降变化越慢;荷载变化趋势与由荷载参数变化引起的沉降变化规律是一致的,且最终沉降量一致。本研究有助于深入认识分数阶黏弹性饱和土体的固结行为。
[Abstract]:The fractional derivative theory is introduced into the Kelvin Voigt model to describe the mechanical behavior of viscoelastic saturated soil. The one-dimensional consolidation equation of saturated soil and the 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. The Crump method is used to realize the Laplace numerical inversion, and the semi-analytical solution of one-dimensional consolidation problem in physical space under arbitrary loads is obtained. The fractional derivative model under exponential load is reduced to the viscoelastic case, and the result is the same as the analytical solution in previous literatures, which verifies the reliability of the proposed fractional derivative viscoelastic solution under arbitrary loads. Finally, the influence of relevant parameters on consolidation settlement is analyzed. The results show that the development of one-dimensional consolidation of fractional derivative viscoelastic saturated soil under arbitrary loads is related to the viscosity coefficient and fractional order. The larger the fractional order, the faster the consolidation settlement develops, the larger the viscosity coefficient, the slower the consolidation settlement changes. The variation trend of load is consistent with the law of settlement caused by the change of load parameters, and the final settlement is the same. This study is helpful to understand the consolidation behavior of fractional viscoelastic saturated soil.
【作者单位】：上海大学土木工程系;上海工程技术大学城市轨道交通学院;上海工程技术大学机械工程学院;
【基金】：国家自然科学基金项目(11672172)
【分类号】：TU43

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