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Tytuł artykułu
Autorzy
Wybrane pełne teksty z tego czasopisma
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Warianty tytułu
Konferencja
International Conference on Continuous and Discrete Modelling in Mechanics (05-09.09.2005 ; Warsaw ; Poland)
Języki publikacji
Abstrakty
In earlier works it has been shown that linearization of thermodynamical models of poroelastic materials yields a contribution to stresses in the form ......., where ... is the current porosity, ... denotes its value in the thermodynamical equilibrium and ... is a material parameter. It has been also claimed on the basis of rough estimates that this parameter gives only negligible contributions to the properties of acoustic waves. The purpose of this work is twofold. We investigate the influence of ß on the propagation of acoustic waves in more details. We use the full linear model of saturated poroelastic materials in which an additional coupling to porosity changes appears. This results from the presence of a term with the porosity gradient in the momentum sources. Such a model becomes identical with Biot's model without any added mass contribution in the limit if infinite relaxation time of porosity ... and for the parameters ß=0, and N=0, where the latter is describing the above mentioned influence of porosity gradient on the momentum sources. The analysis of influence of the parameter N, i.e. the influence of the porosity gradient on properties of acoustic waves, is the second purpose of this work. We also indicate a correction of the permeability contribution to the momentum source. The permeability coefficient ... is assumed in Biot's model to be dependent on the frequency. This is inconsistent with other temporal contributions to field equations. In order to obtain such a dependence in the Fourier space, one has to assume a viscous effect to enter the momentum source and we do so in the general equations. However, we do not use this general relation in the analysis of monochromatic waves.
Czasopismo
Rocznik
Tom
Strony
313--325
Opis fizyczny
Bibliogr. 17 poz.
Twórcy
autor
autor
- Federal Institute for Geosciences and Natural Resources BGR, Germany, wilmansk@wias-berlin.de
Bibliografia
- 1. K. AKI, P. G. RICHARDS, Quantitative seismology, Second Edition, University Science Books, Sansalito 2002.
- 2. B. ALBERS, On results of the surface wave analyses in poroelastic media by means of the simple mixture model and the Biot model, Soil Dynamics and Earthquake Engineering, 26, 537-547, 2006.
- 3. B. ALBERS, Modelling of surface waves in poroelastic saturated materials by means of a two component continuum [in:] Surface Waves in Geomechanics: Direct and Inverse Modelling for Soils and Rocks, C. LAI, K. WILMANSKI [Eds.], CISM-Course No. 481, 277-323, Springer, Vienna 2005.
- 4. T. BOURBIE, 0. COUSSY, B. ZINSZNER, Acoustics of porous media. Edition Technip, Paris 1987.
- 5. I-SHIH Liu, Continuum mechanics, Springer, Berlin 2002.
- 6. B. ALBERS, K. WILMANSKI, On modeling acoustic waves in saturated poroelastic media J. Engn. Mech., ASCE, 975-985, September 2005.
- 7. B. ALBERS, K. WILMANSKI, Monochromatic surface waves on impermeable boundaries in two-component poroelastic media Continuum Mech. Thermodyn., 17, 3, 269-285, 2005.
- 8. E. RADKEVICH, K. WILMANSKI, On dispersion in the mathematical model of poroelastic materials with the balance equation for porosity Journal of Mathematical Sciences, 114, 4, 1431-1449, 2003.
- 9. K. WILMANSKI, Porous media at finite strains. The new model with the balance equation for porosity, Arch. Mech., 48, 4, 591-628, 1996.
- 10. K. WILMANSKI, Thermomechanics of continua Springer, Berlin 1998.
- 11. K. WILMANSKI, Waves in porous and granular materials [in:] Kinetic and Continuum Theories of Granular and Porous Media, K. HUTTER, K. WILMANSKI [Eds.], 131-185, Springer, Wien New York 1999.
- 12. K. WILMANSKI, Sound and Shock waves in porous and granular materials, [in:] Proceedings "WASCOM 99", Waves and Stability in Continuous Media, V. CIANCIO, A. DONATO, F. OLIVERI, S. RIONERO [Eds.], World Scientific, Singapore, 489-503, 2001.
- 13. K. WILMANSKI, Thermodynamics of multicomponent continua, [in:] Earthquake Thermodynamics and Phase Transformations in the Earth's Interior, J. MAJEWSKI, R. TEISSEYRE [Eds.], 567-655, Academic Press, San Diego 2001.
- 14. K. WILMANSKI, Thermodynamical admissibility of Biot’s model of poroelastic saturated materials, Arch. of Mech., 54, 5-6, 709-736, 2002.
- 15. K. WILMANSKI, On microstructural tests for poroelastic materials and corresponding Gassman-type relations, Gootechnique, 54, 9, 593-603, 2004.
- 16. K. WILMANSKI, Tortuosity and objective relative accelerations in the theory of porous materials, Proc. R. Soc. A, 461, 1533-1561, 2005.
- 17. K. WILMANSKI, A few remarks on Biot's model and linear acoustics of poroelastic saturated materials. Soil Dynamics and Earthquake Engineering, 26, 509-536, 2006.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-article-BAT7-0002-0011