Abstract
In this contribution an overview of the continuum mechanical modeling of linear elastic partially saturated porous media and the application of such a model to linear wave propagation is given. First the involved microstructural variables are discussed and the construction of the model is presented. The macroscopic parameters used in the model are obtained by micro-macro-transition procedure from the measurable microscopic quantities. The linear elastic wave propagation analysis is demonstrated exemplarily for sandstone, sand and clayey loam. The properties of the four appearing waves – three compressional and one shear wave – are compared. Phase speeds and attenuations of these waves depend both on the frequency and on the degree of saturation.
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References
Albers, B.: Micro-macro transition and linear waves in compact granular materials. In: AIP Conference Proceedings of the IUTAM-ISIMM Symposium on Mathematical Modeling and Physical Instances of Granular Flows (to be published, 2009)
Albers, B.: Linear elastic wave propagation in unsaturated sands, silts, loams and clays. Submitted to Transport in Porous Media (2009)
Albers, B.: Modeling and Numerical Analysis of Wave Propagation in Saturated and Partially Saturated Porous Media, habilitation thesis, Veröffentlichungen des Grundbauinstitutes der Technischen Universität Berlin. Shaker (2010)
Albers, B.: Analysis of the propagation of sound waves in partially saturated soils by means of a macroscopic linear poroelastic model. Transport in Porous Media 80(1), 173–192 (2009)
Albers, B.: Modelling of surface waves in poroelastic saturated materials by means of a two component continuum. In: Lai, C., Wilmanski, K. (eds.) Surface Waves in Geomechanics: Direct and Inverse Modelling for Soils and Rocks, CISM Courses and Lectures, pp. 277–323. Springer, Wien (2005)
Albers, B.: Relaxation analysis and linear stability vs. adsorption in porous materials. Continuum Mech. Thermodyn. 15(1), 73–95 (2003)
Albers, B., Wilmanski, K.: On modeling acoustic waves in saturated poroelastic media. J. Engrg. Mech. 131(9), 974–985 (2005)
Biot, M.A., Willis, D.G.: The Elastic Coefficients of the Theory of Consolidation. J. Appl. Mech. 24, 594–601 (1957)
DIN 4220: Pedologic site assessment – Designation, classification and deduction of soil parameters (normative and nominal scaling). DIN Deutsches Institut für Normung e.V., Beuth Verlag GmbH (draft, in German), German title: Bodenkundliche Standortbeurteilung – Kennzeichnung, Klassifizierung und Ableitung von Bodenkennwerten (normative und nominale Skalierungen) (2005)
Gassmann, F.: Über die Elastizität poröser Medien. Vierteljahresschrift der Naturforschenden Gesellschaft in Zürich 96(1), 1–23 (1951)
Geertsma, J.: The effect of fluid pressure decline on volumetric changes of porous rocks. Trans. AIME 210, 331–340 (1957)
Santos, J., Douglas, J., Corbero, J.: Static and dynamic behaviour of a porous solid saturated by a two-phase fluid. JASA 87(4), 1428–1438 (1990)
Schick, P.: Ein quantitatives Zwei-Komponenten-Modell der Porenwasser-Bindekräfte in teilgesättigten Böden. habilitation-thesis, Universität der Bundeswehr, München (2003); In German, Heft 17, Mitteilungen des Instituts für Bodenmechanik und Grundbau
Tolstoy, I.: Acoustics, Elasticity and Thermodynamics of Porous Media: Twenty-One Papers by Biot, M.A. Acoustical Society of America (1991)
Tuncay, K., Corapcioglu, M.Y.: Body waves in poroelastic media saturated by two immiscible fluids. J. Geophys. Res. 101(B11), 25149–25159 (1996)
Van Genuchten, M.T.: A Closed-form Equation for Predicting the Hydraulic Conductivity of Unsaturated Soils. Soil Sci. Soc. Am. J. 44, 892–898 (1980)
Vanorio, T., Prasad, M., Nur, A.: Elastic properties of dry clay mineral aggregates, suspensions and sandstones. Geophysical Journal International 155(1), 319–326 (2003)
Wei, C., Muraleetharan, K.K.: Acoustical Waves in Unsaturated Porous Media. In: Proceedings 16th Engineering Mechanics Conference, ASCE, Seattle (2003)
White, J.E.: Underground sound. In: Application of seismic waves, Methods in Geochemistry and Geophysics, vol. 18, Elsevier, Amsterdam (1983)
Wilmanski, K.: On microstructural tests for poroelastic materials and corresponding Gassmann-type relations. Geotechnique 54(9), 593–603 (2004)
Wilmanski, K.: Waves in Porous and Granular Materials. In: Hutter, K., Wilmanski, K. (eds.) Kinetic and Continuum Theories of Granular and Porous Media, CISM 400, pp. 131–186. Springer, Wien (1999)
Wilmanski, K.: Thermomechanics of Continua. Springer, Berlin (1998)
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Albers, B. (2010). Linear Wave Propagation in Unsaturated Rocks and Soils. In: Albers, B. (eds) Continuous Media with Microstructure. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-11445-8_17
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DOI: https://doi.org/10.1007/978-3-642-11445-8_17
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