Abstract
A study of surface wave propagation in a fluid-saturated incompressible porous half-space lying under a uniform layer of liquid is presented. The dispersion relation connecting the phase velocity with wave number is derived. The variation of phase velocity and attenuation coefficients with wave number is presented graphically and discussed. As a particular case, the propagation of Rayleigh type surface waves at the free surface of an incompressible porous half-space is also deduced and discussed.
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References
Achenbach J D (1976) Wave propagation in elastic solids. (Amsterdam: North-Holland Publishing Company)
Auriault J L (1980) Dynamic behaviour of a porous medium saturated by a newtonian fluid. Int. J. Eng. Sci. 18: 775–785
Biot M A (1941) General theory of three dimensional consolidation. J. Appl. Phys. 12: 155–161
Biot M A (1956a) Theory of propagation of elastic waves in a fluid-saturated porous solid — I. Low frequency range. J. Acout. Soc. Am. 28: 168–178
Biot M A (1956b) Theory of propagation of elastic waves in a fluid-saturated porous solid — II. Higher frequency range. J. Acout. Soc. Am. 28: 179–191
Biot M A (1962) Mechanics of deformation and acoustic propagation in porous media. J. Appl. Phys. 33: 1482–1498
Bowen R M (1980) Incompressible porous media models by use of the theory of mixtures. Int. J. Eng. Sci. 18: 1129–1148
de Boer R, Ehlers W (1990) The development of the concept of effective stress theories. Acta Mech. 83: 77–92
de Boer R, Ehlers W (1990) Uplift, friction and capillarity — Three fundamental effects for liquidsaturated porous solids. Int. J. Solids Struct. 26: 43–57
de Boer R, Ehlers W, Liu Z (1993) One-dimensional transient wave propagation in a fluid-saturated incompressible porous media. Arch. Appl. Mech. 63: 59–72
de Boer R, Ehlers W (1988) A historical review of the formulation of porous media theories. Acta Mech. 74: 1–8
de Boer R (2000) Theory of porous media. (New York: Springer-Verleg)
Edelman I (2004) Surface waves at vacuum/porous medium interface: low frequency range. Wave Motion 39: 111–127
Ehlers W (1993) Compressible, incompressible and hybrid two-phase models in porous theories. ASME; AMD 158: 25–38
Ewing W M, Jardetzky W S, Press F (1957) Elastic waves in layered media, (: Mc Graw Hill)
Fillunger P (1933) Der auftrieb in talsperren. osterr. wochenschrift fur den offentl. baudienst [M]. I. Teil 532–552, II. Teil 552–556, III. Teil 567–570.
Kumar R, Miglani A (1996) Effect of pore alignment on surface wave propagation in a liquid-saturated porous layer over a liquid-saturated porous half-space with loosely bonded interface. J. Phys. Earth 44: 1317–1337
Kumar R, Deswal S (1996) Surface wave propagation in liquid-saturated porous layer over a liquid-saturated porous half-space with loosely bonded interface. J. Phys. Earth, 44: 1317–1337
Kumar S, Hundal B S (2002) A Study of spherical and cylindrical wave propagation in a non-homogeneous fluid-saturated incompressible porous medium by method of characteristics. current trends in industrial and applied mathematics. Ed. P Manchanda et al New Delhi: Anamya Publisher 181–194
Kumar R, Hundal B S (2003) Wave propagation in a fluid-saturated incompressible porous medium. Indian J. Pure Appl. Math. 4: 651–665
Kumar R, Hundal B S (2003) One-dimensional wave propagation in a non-homogeneous fluid-saturated incompressible porous medium. Bull. Allahabad Math. Soc. 18: 1–13
Kumar R, Hundal B S (2004) Effect of non-homogeneity on one-dimensional wave propagation in a fluid-saturated incompressible porous medium. Bull. Callif. Math. Soc. 96: 179–188
Kumar R, Hundal B S (2004) Symmetric wave propagation in a fluid-saturated incompressible porous medium. J. Sound Vib. 96: 179–188
Levy T (1979) Propagation of waves in a fluid-saturated porous elastic solids. Int. J. Eng. Sci. 17: 1005–1014
Liu K, Liu Y (2004) Propagation characteristics of rayleigh waves in orthotropic fluid-saturated porous media. J. Sound Vib. 271: 1–13
Prevost J H (1982) Nonlinear transient phenomena in saturated porous media. Comp. Math. Appl. Mech. Eng. 3–18
von Terzaghi K (1923) Die Berechnug der Durchlassigkeit des Tones aus dem Verlauf der hydromechanischen Spannungserscheinungen. Sitzungsber. Akad. Wiss. (Wien), Math. Naturwiss. Kl., Abt. IIa 132: 125–138
von Terzaghi K (1925) Erdbaumechanik auf Bodenphysikalischer Grundlage, p. 399. Leipzig — wien: Franz Deuticke
Zienkiewicz O C, Shiomi T (1984) Dynamic behaviour of saturated porous media — the generalized biot formulation and its numerical solution. Int. J. Numer. Ana. Methods Geomech. 8: 71–96
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Kumar, R., Hundal, B.S. Surface wave propagation in a fluid-saturated incompressible porous medium. Sadhana 32, 155–166 (2007). https://doi.org/10.1007/s12046-007-0014-x
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DOI: https://doi.org/10.1007/s12046-007-0014-x