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

Based on the Biot theory of porous media, the exact solutions to one- dimensional transient response of incompressible saturated single-layer porous media un- der four types of boundary conditions are developed. In the procedure, a relation between the solid displacement u and the relative displacem...

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Bibliographic Details
Published in:Applied mathematics and mechanics 2013, Vol.34 (1), p.75-84
Main Author: 单振东 凌道盛 丁皓江
Format: Article
Language:English
Subjects:
Applications of Mathematics
Boundary conditions
Classical Mechanics
Computational fluid dynamics
Displacement
Exact solutions
Fluid flow
Fluid- and Aerodynamics
Incompressible flow
Mathematical analysis
Mathematical Modeling and Industrial Mathematics
Mathematics
Mathematics and Statistics
Partial Differential Equations
Porous media
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Summary:Based on the Biot theory of porous media, the exact solutions to one- dimensional transient response of incompressible saturated single-layer porous media un- der 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.
ISSN:0253-4827
1573-2754
DOI:10.1007/s10483-013-1654-7