具有球形空腔饱和土分数导数
黏弹性土的动力特性

›› 2013, Vol. 34 ›› Issue (4): 1001-1008.

具有球形空腔饱和土分数导数黏弹性土的动力特性

闻敏杰¹，杨骁²，高华喜³

1.嘉兴职业技术学院生物与环境分院，浙江嘉兴 314036；2.上海大学土木系，上海 200072； 3.浙江海洋学院船舶与建筑工程学院，浙江舟山 316004

收稿日期:2012-02-15 出版日期:2013-04-10 发布日期:2013-04-16
作者简介:闻敏杰，男，1986年生，硕士, 助教，主要从事饱和多孔介质理论、土动力学的研究
基金资助:
国家自然科学基金资助（No. 10872124）；浙江省自然科学基金资助（No. LY12E09006）；浙江省水利厅重点科研项目资助（No. 20110721003）

Dynamic characteristics of saturated fractional derivative viscoelastic soil with a spherical cavity

WEN Min-jie¹, YANG Xiao², GAO Hua-xi³

1. Department of Biological and Engviromental Engineering, Jiaxing Vocational and Technical College, Jiaxing, Zhejiang 314036, China; 2. Department of Civil Engineering, Shanghai University, Shanghai 200072, China; 3. School of Naval Architecture and Civil Engineering, Zhejiang Ocean University, Zhoushan, Zhejiang 316004, China

Received:2012-02-15 Online:2013-04-10 Published:2013-04-16

摘要/Abstract

摘要： 将土骨架视为具有分数阶导数本构关系的黏弹性体，基于Biot两相饱和介质模型，建立具有球形空腔饱和分数导数黏弹性土体稳态振动的控制方程。通过引入势函数，得到球对称情形下具有球形空腔饱和分数导数黏弹性土体的位移、应力和孔隙流体压力等解析表达式。考察分数导数模型参数和饱和土参数等对土体振动特性的影响，结果表明，流体压缩性对饱和土体的动力特性有显著影响，而土骨架压缩性和流-固耦合系数的影响相对较小；分数导数阶数对土体动力特性的影响与材料参数比的取值有关。同时，边界不排水条件下饱和土体的动力响应大于排水条件下饱和土体的动力响应。

关键词: 饱和黏弹性土, 球空腔, 分数导数, 稳态振动, 解析解

Abstract: Regarding the soil skeleton as a viscoelastic medium with fractional derivative constitutive relation, the governing equations of the steady state vibration of the saturated fractional derivative viscoelastic soil embedded a spherical cavity are established based on the Biot’s theory. The analytical expressions of the displacements, stresses and pore water pressure of the saturated fractional derivative viscoelastic soil with a spherical cavity are obtained with the introduction help of potential functions in case of spherical symmetry. The influences of the parameters of fractional derivative model and saturated soil on the vibration characteristics of the soil are examined; and the numerical results show that the fluid compressibility has a great influence on the dynamic characteristics; while the influences of the soil skeleton compressibility and fluid-solid coupling coefficient are trivial. The influence of the fractional derivative order on the dynamic behavior of the soil depends on the values of material parameter ratio. Furthermore, the dynamic responses of the saturated soil with undrained boundary condition are greater than those with the drained boundary condition.

Key words: saturated viscoelastic soil, spherical cavity, fractional derivative, steady-state vibration, analytical solution

中图分类号:

TU 442

闻敏杰，杨骁，高华喜 . 具有球形空腔饱和土分数导数黏弹性土的动力特性 [J]. , 2013, 34(4): 1001-1008.

WEN Min-jie , YANG Xiao , GAO Hua-xi . Dynamic characteristics of saturated fractional derivative viscoelastic soil with a spherical cavity[J]. , 2013, 34(4): 1001-1008.

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