单层非饱和多孔介质一维瞬态响应半解析解

›› 2014, Vol. 35 ›› Issue (1): 25-34.

单层非饱和多孔介质一维瞬态响应半解析解

凌道盛^{1, 2}，王筠^{1, 2}，单振东³，丁皓江^{1, 2}

1. 浙江大学软弱土与环境土工教育部重点实验室，杭州 310058；2. 浙江大学岩土工程研究所，杭州 310058； 3. 中国地震局工程力学研究所，哈尔滨 150080）

收稿日期:2012-10-09 出版日期:2014-01-10 发布日期:2014-01-14
作者简介:凌道盛，男，1968年生，博士，教授，博士生导师，主要从事土动力学、基础工程和地基处理方面的教学和科研工作。
基金资助:
国家自然科学基金(No. 51278451)；浙江省自然科学基金重点项目(No. LZ12E09001)。

A semi-analytical solution for one-dimensional transient response of single-layer unsaturated porous media

LING Dao-sheng^{1, 2}，WANG Yun^{1, 2}，SHAN Zhen-dong³，DING Hao-jiang^{1, 2}

1. Key Laboratory of Soft Soils and Geoenvironmental Engineering of Ministry of Education, Zhejiang University, Hangzhou 310058, China; 2. Institute of Geotechnical Engineering, Zhejiang University, Hangzhou 310058, China; 3. Institute of Engineering Mechanics, China Earthquake Administration, Harbin 150080, China

Received:2012-10-09 Online:2014-01-10 Published:2014-01-14

摘要/Abstract

摘要： 基于Zienkiewicz提出的非饱和多孔介质波动理论，考虑两相流体和固体颗粒的压缩性以及惯性、黏滞和机械耦合作用，采用半解析的方法获得了一类典型边界条件下单层非饱和多孔介质一维瞬态响应解。首先推导出无量纲化后以位移表示的控制方程，并将其写成矩阵形式；然后，将边界条件齐次化，求解控制方程所对应的特征值问题，得到了满足齐次边界条件的特征值和相对应的特征函数。根据变异系数法并利用特征函数的正交性，得到了一系列仅黏滞耦合的关于时间的二阶常微分方程及相应的初始条件。在此基础上，运用精细时程积分法给出了常微分方程组的数值解。最后，通过若干算例验证了结果的正确性并探讨了单层非饱和多孔介质一维瞬态动力响应的特点。该方法可推广应用于其他典型的边界条件。

关键词: 非饱和多孔介质, 瞬态响应, 半解析解, 精细时程积分

Abstract: Based on the theory of unsaturated porous media proposed by Zienkiewicz, considering the inertia, viscous and mechanical couplings and the compressibility of fluid and solid particles, semi-analytical solutions for one-dimensional transient response of single-layer unsaturated porous media are obtained with the example of a typical boundary condition problem. During the solution procedure, the dimensionless displacement governing equations in matrix form are derived firstly. Then the the nonhomogeneous boundary conditions are transformed into homogeneous boundary conditions and the eigenvalue problems of the governing equations are solved. After that, the variation coefficient method and the orthogonality of the characteristics functions are utilized to obtain a series of ordinary differential equations with their initial conditions. Applying the precise time-integration method, the semi-analytical solutions of the ordinary differential equations are developed. Finally, several numerical examples are provided to prove the correctness of the present solution and investigate the features of one-dimensional transient response of unsaturated single-layer porous media. This method can be extended to any other boundary conditions.

Key words: unsaturated porous media, transient response, semi-analytical solution, precise time-integration method

中图分类号:

TU 435

凌道盛，王筠，单振东，丁皓江 , . 单层非饱和多孔介质一维瞬态响应半解析解[J]. , 2014, 35(1): 25-34.

LING Dao-sheng ，WANG Yun , 2，SHAN Zhen-dong ，DING Hao-jiang , . A semi-analytical solution for one-dimensional transient response of single-layer unsaturated porous media[J]. , 2014, 35(1): 25-34.

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