Wave propagation in partial saturated media

Research Area

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 [1] and the mixture theory [2]. 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 [4]). 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 [3]. 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 used here.

Project Topics

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 numerical realisation.
The key points of this project are

• to work on the governing equations for unsaturated poroelastic media,
• 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 continua.

References

[1]

M.A. Biot. 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.

[2]

R. de Boer and W. Ehlers. On the problem of fluid- and gas-filled elasto-plastic solids. Internat. J. Solids Structures, 22(11), 1986.

[3]

M. Schanz. Wave Propagation in Viscoelastic and Poroelastic Continua: A Boundary Element Approach, volume 2 of Lecture Notes in Applied Mechanics. Springer-Verlag, Berlin, Heidelberg, New York, 2001.

[4]

M. Schanz. Poroelastodynamics: Linear models, analytical solutions, and numerical methods. AMR, 62(3), 030803-1--030803-15, 2009.

[5]

B. A. Schrefler and R. Scotta. A fully coupled dynamic model for two-phase fluid flow in deformable porous media. Comput. Methods Appl. Mech. Engrg., 190(24-25), 2001.

[6]

C. F. Wei and K.K. Muraleetharan. Acoustical waves in unsaturated porous media. 16th ASCE Engineering Mechanics Conference, 2003.