Influence of Viscous Coupling in Propagation of Elastic Waves in Saturated Soil
Publication: Journal of Geotechnical Engineering
Volume 121, Issue 9
Abstract
The interactions between the solid and fluid phases of saturated porous media are due to inertial, viscous, and mechanical coupling. In particular, viscous coupling plays a key role because it makes wave propagation dispersive. The effects of viscous coupling on harmonic problems were described in detail by Biot, but the implications in transient problems have not been fully analyzed. Therefore, a detailed analysis is carried out on the effects of viscous coupling on the mechanics of transient wave propagation, by considering the propagation of simple shaped driving pulses (a step pulse, a single sine, and a single triangle), for both constant and frequency-dependent viscous coupling. Particular attention is paid to the interpretation of dynamic soil test measurements, because of their importance in the current practice of soil investigation, both in laboratory and in situ. Results show that it is possible to identify two extreme kinds of transient behavior: in the first, the porous medium behaves as a two-phase medium in which the velocity of propagation corresponds to null viscous coupling; in the second, the behavior corresponds to a one-phase medium with velocity of propagation corresponding to infinite viscous coupling. There is a gradual transition between these two extreme behaviors, but it extends for quite a narrow range of values of travel length and of the coefficient of permeability for a given frequency content of the driving pulse. Such conclusions are very useful in the interpretation of dynamic measurements and should enhance the comprehension of the mechanics of dispersive wave propagation in saturated porous media.
Get full access to this article
View all available purchase options and get full access to this article.
References
1.
Berryman, J. G.(1980). “Confirmation of Biot's theory.”Appl. Phys. Lett., 37(4), 382–384.
2.
Biot, M. A. (1941). “General theory of three dimensional consolidation.”J. Appl. Phys., Vol. 12, 155–164.
3.
Biot, M. A.(1956a). “Theory of propagation of elastic waves in a fluid saturated porous solid. I: Low frequency range.”J. Acust. Soc. of Am., 28(2), 168–178.
4.
Biot, M. A.(1956b). “Theory of propagation of elastic waves in a fluid saturated porous solid. II: Higher frequency range.”J. Acust. Soc. of Am., 28(2), 179–191.
5.
Biot, M. A. (1962a). “Mechanics of deformation and acoustic propagation in porous media.”J. Appl. Phys., Vol. 33, 1482–1498.
6.
Biot, M. A. (1962b). “Generalized theory of acoustic propagation in porous dissipation media.”J. Acust. Soc. of Am., Vol. 34, 1254–1264.
7.
Biot, M. A., and Willis, D. G. (1957). “The elastic coefficients of the theory of consolidations.”J. Appl. Mech., Vol. 24, 594–601.
8.
Burridge, R., and Vargas, C. A. (1979). “The fundamental solution in dynamic poroelasticity.”Geophys. J. R. Astr. Soc., Vol. 58, 61–90.
9.
Chen, J.(1994a). “Time domain fundamental solution to Biot's complete equations of dynamic poroelasticity. Three dimensional solution.”Int. J. Solids Struct., 31(2), 169–202.
10.
Chen, J.(1994b). “Time domain fundamental solution to Biot's complete equations of dynamic poroelasticity. Two dimensional solution.”Int. J. Solids Struct., 31(10), 1447–1490.
11.
Chin, R. C. Y., Berryman, J. G., and Hedstrom, G. W. (1985). “Generalized ray expansion for pulse propagation and attenuation in fluid-saturated porous media.”Wave Motion, Vol. 7, 43–65.
12.
Deresiewicz, H., and Skalak, R. (1963). “On uniqueness in dynamic poroelasticity.”J. Acoust. Soc. Am., Vol. 53, 783–788.
13.
Gaboussi, J., and Wilson, E. L.(1973). “Variational formulation of dynamics of fluid-saturated porous elastic solids.”J. Engrg. Mech., ASCE, 98(4), 947–962.
14.
Gajo, A., and Mongiovì, L. (1994). “The effects of measure accuracy in the interpretation of dynamic tests on saturated soil.”Proc., Int. Symp. on Pre-Failure Deformation Characteristics of Geomaterials, Balkema, Japan, 163–168.
15.
Gajo, A., Saetta, A., and Vitaliani, R. (1994). “Evaluation of three and two field finite element methods for the dynamic response of saturated soil.”Int. J. Numer. Methods Engrg., Vol. 37, 1231–1247.
16.
Garg, S. K., Nayfeh, H., and Good, A. J. (1974). “Compressional waves in fluid-saturated elastic porous media.”J. Appl. Phys., Vol. 45, 1968–1974.
17.
Geertsma, J., and Smit, D. C.(1961). “Some aspects of elastic waves propagation in fluid saturated porous solids.”Geophysics., 26(2), 169–181.
18.
Ishihara, K. (1967). “Propagation of compressional waves in a saturated soil.”Proc., Int. Symp. on Wave Propagation and Dynamic Properties of Earth Materials, Albuquerque, N.M., 451–467.
19.
Johnson, D. L., Plona, T. J., Scala, C., Pasierb, F., and Kojima, H.(1982). “Tortuosity and acoustic slow waves.”Phys. Rev Lett., 49(25), 1840–1844.
20.
Johnson, D. L., and Plona, T. J.(1982). “Acoustic slow waves and the consolidation transition.”J. Acust. Soc. of Am., 72(2), 556–565.
21.
Johnson, D. L., Koplik, J., and Dashen, R. (1987). “Theory of dynamic permeability and tortuosity in fluid saturated porous media.”J. Fluid Mech., Vol. 176, 379–402.
22.
Mainardi, F., Servizi, G., and Turchetti, G. (1977). “On the propagation of seismic pulses in a porous elastic solid.”J. Geophys., Vol. 43, 83–94.
23.
McCuen, R. H. (1989). Hydrologic analysis and design . Prentice-Hall, Englewood Cliffs, N.J.
24.
Norris, A. N. (1993). “Low frequency dispersion and attenuation in partially saturated rocks.”J. Acoust. Soc. Am., Vol. 94, 359–370.
25.
Plona, T. J.(1980). “Observation of a second bulk compressional wave in a porous medium at ultrasonic frequencies.”Appl. Phys. Lett., 36(4), 259–261.
26.
Schreyer, H. L. (1983). “Dispersion of semidiscretized and fully discretized systems.”Computational methods for transient analysis, T. Belytschko and T. J. R. Huges, eds., Elsevier Science Publishers, 268–299.
27.
Sen, P. N., Scala, C., and Cohen, M. H.(1981). “A self-similar model for sedimentary rocks with application to the dielectric constant of fused glass beads.”Geophys., 46(5), 781–795.
28.
Simon, B. R., Zienkiewicz, O. C., and Paul, D. K. (1984). “An analytical solution for the transient response of saturated porous elastic solids.”Int. J. Numer. Anal. Methods Geomech., Vol. 8, 381–398.
29.
Simon, B. R., Wu, J. S.-S., Zienkiewicz, O. C., and Paul, D. K. (1986a). “Evaluation of u - w and u -π finite element methods for the dynamic response of saturated porous media using one-dimensional models.”Int. J. Numer. Anal. Methods Geomech., Vol. 10, 461–482.
30.
Simon, B. R., Wu, J. S.-S., Zienkiewicz, O. C., and Paul, D. K. (1986b). “Evaluation of higher order, mixed and Hermitian finite element procedures for dynamic analysis of saturated porous media using one-dimensional models.”Int. J. Numer. Anal. Methods Geomech., Vol. 10, 483–499.
31.
Van der Grinten, J. G. M., Van Dongen, M. E. H., and Van der Kogel, H.(1987). “Strain and pore pressure propagation in a water-saturated porous medium.”J. Appl. Phys., 62, 4682–4687.
32.
Zienkiewicz, O. C., and Shiomi, T. (1984). “Dynamic behaviour of saturated porous media: the generalized Biot formulation and its numerical solution.”Int. J. Numer. Anal. Methods Geomech., Vol. 8, 71–96.
Information & Authors
Information
Published In
Copyright
Copyright © 1995 American Society of Civil Engineers.
History
Published online: Sep 1, 1995
Published in print: Sep 1995
Authors
Metrics & Citations
Metrics
Citations
Download citation
If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download.