Exact solutions to one-dimensional transient response of incompressible fluid-saturated single-layer porous media

SHAN Zhen-Dong;LING Dao-Cheng;DING Hao-Jiang

doi:10.1007/s10483-013-1654-7

Applied Mathematics and Mechanics >

2013 , Vol. 34 >Issue 1: 75 - 84

DOI: https://doi.org/10.1007/s10483-013-1654-7

Articles

Exact solutions to one-dimensional transient response of incompressible fluid-saturated single-layer porous media

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

Received date: 2011-11-12

Revised date: 2012-11-11

Online published: 2013-01-03

Supported by

the Earthquake Administration Foundation for Seismological Researches of China (No. 200808022), the National Natural Science Foundation of China (Nos. 50778163 and 50708095), and the National Basic Research Program of China (No. 2007CB714200)

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Abstract

Based on the Biot theory of porous media, the exact solutions to one dimensional transient response of incompressible saturated single-layer porous media under four types of boundary conditions are developed. In the procedure, a relation between the solid displacement u and the relative displacement w is derived, and the well-posed initial conditions and boundary conditions are proposed. The derivation of the solution for one type of boundary condition is then illustrated in detail. The exact solutions for the other three types of boundary conditions are given directly. The propagation of the compressional wave is investigated through numerical examples. It is verified that only one type of compressional wave exists in the incompressible saturated porous media.

Key words： transient response; incompressible porous medium; exact solution; saturated; nonlinear system; random vibration; equivalent nonlinearization method; mean square response

Cite this article

SHAN Zhen-Dong;LING Dao-Cheng;DING Hao-Jiang . Exact solutions to one-dimensional transient response of incompressible fluid-saturated single-layer porous media[J]. Applied Mathematics and Mechanics, 2013 , 34(1) : 75 -84 . DOI: 10.1007/s10483-013-1654-7

References

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