Wave propagation in porous media is an important fundamental subject
concerning, e.g., geophysical prospecting, earthquake engineering,
petroleum extraction, water conservancy, and environmental
engineering. For instance, the dynamic response of a dam due to
seismic waves or, more general, the dynamic soil-foundation-structure
interaction has to be mentioned.
Different from the fluid saturated porous media case, wave propagation
in partial saturated porous media are studied in this
project. Therefore, the governing differential equations of
the unsaturated porous media, i.e., a three-phase material, are
derived. Further, a numerical discretization technique,
the Boundary Element Method (BEM) for partially saturated media has to
be developed and implemented. The BEM is chosen due to its suitability
modelling infinite domains correctly. Such domains, e.g., half-space,
appear frequently in wave propagation problems.
State of the Art
For wave propagation in saturated poroelastic media, two theories are
widely used which are Biot's theory  and the mixture
theory . A number of analytical and numerical methods has
been developed not only for the quasi-static case but as well for
dynamics (see the review article ). In the past decades as
well for the unsaturated case various efforts has been made to extend
the theory of poroelasticity (see, e.g., [5,6]). As a
matter of fact, the saturated case and the dry medium becomes a
special case of the more general unsaturated case.
Concerning the BE formulation, there exists one for the saturated case
which is based on the convolution quadrature method . This
technique allows to use the easier obtainable Laplace domain
fundamental solutions instead of the time domain ones. Hence, a time
domain formulation without the knowledge of the time domain
fundamental solutions can be established. This technique can also be
This project intends to extend the research on wave propagation in
saturated poroelastic media to partial saturated media, with respect
to the theoretical development of the governing equations and their
The key points of this project are
- to work on the governing equations for unsaturated poroelastic
- to formulate and implement the Laplace domain fundamental
solutions of the unsaturated poroelastic media,
- to implement and test the boundary element formulations of the
unsaturated porous media,
- to study the wave propagation in unsaturated poroelastic
Theory of propagation of elastic waves in fluid-saturated porous
solid. I/II. Lower/Higher frequency range.
J. Acoust. Soc. Am., 28(2), 168-178/179-191, 1956.
R. de Boer and W. Ehlers.
On the problem of fluid- and gas-filled elasto-plastic solids.
Internat. J. Solids Structures, 22(11), 1986.
Wave Propagation in Viscoelastic and Poroelastic Continua: A
Boundary Element Approach, volume 2 of Lecture Notes in Applied
Springer-Verlag, Berlin, Heidelberg, New York, 2001.
Poroelastodynamics: Linear models, analytical solutions, and
AMR, 62(3), 030803-1--030803-15, 2009.
B. A. Schrefler and R. Scotta.
A fully coupled dynamic model for two-phase fluid flow in deformable
Comput. Methods Appl. Mech. Engrg., 190(24-25), 2001.
C. F. Wei and K.K. Muraleetharan.
Acoustical waves in unsaturated porous media.
16th ASCE Engineering Mechanics Conference, 2003.