Abstract
The dispersion relation for surface waves on an impermeable boundary of a fully saturated poroelastic medium is investigated numerically over the whole range of applicable frequencies. To this aim a linear simplified model of a two-component poroelastic medium is used. Similarly to the classical Biot’s model, it is a continuum mechanical model but it is much simpler due to the lack of coupling of stresses. However, results for bulk waves following for these two models agree very well indeed which motivates the application of the simplified model in the analysis of surface waves. In the whole range of frequencies there exist two modes of surface waves corresponding to the classical Rayleigh and Stoneley waves. The numerical results for velocities and attenuations of these waves are shown for different values of the bulk permeability coefficient in different ranges of frequencies. In particular, we expose the low and high frequency limits, and demonstrate the existence of the Stoneley wave in the whole range of frequencies as well as the leaky character of the Rayleigh wave.
This is a preview of subscription content, log in via an institution to check access.
References
Owino, J.O., Jacobs, L.J.: Attenuation measurements in cement-based materials using laser ultrasonics. J. Eng. Mech. 125(6), 637–647 (1999)
Kutruff, H.: Ultrasonics, Fundamentals and Applications. Elsevier (1991)
Viktorov, I.A.: Rayleigh and Lamb Waves. Physical Theory and Applications. Plenum Press, NY (1967)
Lai, C.: Simultaneous inversion of Rayleigh phase velocity and attenuation for near-surface site characterization. Ph.D. Thesis. Georgia Inst. of Tech. (1998)
Rix, G.J., Lai, C.G., Foti, S.: Simultaneous measurement of surface wave dispersion and attenuation curves. Geotechnical Test. J. 24(4), 350–358 (2001)
Deresiewicz, H.: The effect of boundaries on wave propagation in a liquid filled porous solid. IV. Surface waves in a half space. Bull. Seismol. Soc. Am. 52, 627–638 (1962)
Biot, M.A.: Acoustics, Elasticity and Thermodynamics of Porous Media: Twenty-one Papers by M.A. Biot. (ed.) I. Tolstoy Am. Inst. of Phys. (1992)
Feng, S., Johnson, D.L.: High-frequency acoustic properties of a fluid/porous solid interface. I. New surface mode. J. Acoust. Soc. Am. 74(3), 906–914 (1983)
Bourbie, T., Coussy, O., Zinszner, B.: Acoustics of Porous Media. Editions Technip, Paris (1987)
Nagy, P.B.: Acoustics and ultrasonics, in methods the physics of porous media. In: Po-zen Wong (ed.) pp.~161–221. Academic Press (1999)
Albers, B.: Monochromatic surface waves at the interface between poroelastic and fluid halfspaces, eingereicht bei {Proc. Royal Soc. (Mathematical, Physical and Engineering Sciences),} 2005; WIAS-Preprint Nr. 1010 (2005)
Wilmanski, K.: Some questions on material objectivity arising in models of porous materials. In: M. Brocato (ed.) pp.149–161, Rational Continua, Classical and New. Springer-Verlag, Italia Srl, Milano (2001)
Albers, B., Wilmanski, K.: On modeling acoustic waves in saturated poroelastic media. {J. Engn. Mech.} September 2005; WIAS-Preprint Nr. 874 (2004)
Edelman, I., Wilmanski, K.: Asymptotic analysis of surface waves at vacuum/porous medium and liquid/porous medium interfaces. Cont. Mech. Thermodyn. 14(1), 25–44 (2002)
Norris, A.N.: Stoneley-wave attenuation and dispersion in permeable formations. Geophysics 54(3), 330–341 (1989)
Wilmanski, K.: Waves in porous and granular materials. In: Hutter, K., Wilmanski, K. (eds.) Kinetic and Continuum Theories of Granular and Porous Media. CISM Courses and Lectures No. 400. pp.~131–186. Springer, Wien NY (1999)
Wilmanski, K.: Propagation of sound and surface waves in porous materials. In: B. Maruszewski (ed.) Structured Media. Poznan University of Technology, pp.~312–326. Poznan (2002)
Wilmanski, K., Albers, B.: Acoustic waves in porous solid-fluid mixtures. In: Hutter, K., Kirchner, N. (eds.) Dynamic Response of Granular and Porous Materials Under Large and Catastrophic Deformations. Lecture Notes in Applied and Computational Mechanics, vol.11, pp.285–314. Springer, Berlin (2003)
Edelman, I.: Bifurcation of the Biot slow wave in a porous medium. J. Acoust. Soc. Am. 114 (1), 90–97 (2003)
Deresiewicz, H., Skalak, R.: On uniqueness in dynamic poroelasticity. Bull. Seismol. Soc. Am. 53, 783–788 (1963)
Wilmanski, K.: Note on weak discontinuity waves in linear poroelastic materials. Part I. Acoustic waves in saturated porous media. WIAS-Preprint No. 730 (2002)
Bear, J.: Dynamics of Fluids in Porous Media. Dover, NY (1988)
Aki, K. Richards, P.: Quantitative Seismology, Theory and Methods. W. H. Freeman and Co. (1980)
Author information
Authors and Affiliations
Additional information
Communicated by W. H. Müller
Rights and permissions
About this article
Cite this article
Albers, B., Wilmański, K. Monochromatic surface waves on impermeable boundaries in two-component poroelastic media. Continuum Mech. Thermodyn. 17, 269–285 (2005). https://doi.org/10.1007/s00161-005-0203-y
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00161-005-0203-y