Abstract
Based on the poroelasticity theory, this article investigates the reflection and transmission characteristics of an incident plane transverse wave at a plane interface between an isotropic elastic half-space and an unsaturated poroelastic solid half-space. For this purpose, the effect of the saturation degree and frequency on the properties of the four bulk waves in unsaturated porous medium, i.e., three longitudinal waves and one transverse wave, are discussed at first. Two general cases of mode conversion are considered: (i) The initial transverse wave is incident from an unsaturated poroelastic half-space to the interface, and (ii) the initial transverse wave is incident from an elastic solid half-space to the interface. The expressions for the partition of energy at the interface during transmission and reflection process of waves are presented in explicit forms. At last, numerical computations are performed for these two cases and the results obtained are depicted, respectively. The variation of the amplitude ratios and energy ratios with the saturation degree and incident angle is illustrated in detail. It is also verified that, at the interface, the sum of energy ratios is approximately equal to unity as expected.
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References
Albers B.: Analysis of the propagation of sound waves in partially saturated soils by means of a macroscopic linear poroelastic model. Transp. Porous Media 80, 173–192 (2009)
Arora A., Tomar S.K.: Elastic waves at porous/porous elastic half-spaces saturated by two immiscible fluids. J. Porous Media 10, 751–768 (2007)
Berryman J.G.: Confirmation of Biot’s theory. Appl. Phys. Lett. 37, 382–384 (1980)
Berryman J.G., Thigpen L., Chin R.C.Y.: Bulk elastic wave propagation in partially saturated porous solids. J. Acoust. Soc. Am. 84, 360–373 (1988)
Biot M.A.: Theory of propagation of elastic waves in a fluid saturated porous solid. J. Acoust. Soc. Am. 28, 168–191 (1956)
Brutsaert W.: The propagation of elastic waves in unconsolidated unsaturated granular mediums. J. Geophys. Res. 69, 243–257 (1964)
Chen W.Y., Xia T.D., Hu W.T.: A mixture theory analysis for the surface-wave propagation in an unsaturated porous medium. Int. J. Solids Struct. 48, 2402–2412 (2011)
Coussy O.: Poromechanics. 2nd edn. Wiley, Chichester (2004)
Dai Z.J., Kuang Z.B.: Reflection and transmission of elastic waves at the interface between an elastic solid and a double porosity medium. Int. J. Rock Mech. Min. Sci. 43, 961–971 (2006)
Deresiewicz H., Rice J.T.: The effect of boundaries on wave propagation in a liquid-filled porous solid V. Transmission across a plane interface. Bull. Seism. Soc. Am. 54, 409–416 (1964)
Dullien F.A.L.: Porous media fluid transport and pore structure. Academic Press, San Diego (1992)
Dutta N.C., Ode H.: Seismic reflections from a gas water contact. Geophysics 48, 148–162 (1983)
Garg S.K., Nayfeh A.H.: Compressional wave propagation in liquid and or gas saturated elastic porous media. J. Appl. Phys. 60, 3045–3055 (1986)
Gray W.G.: Thermodynamics and constitutive theory for multiphase porous-media flow considering internal geometric constraints. Adv. Water Resour. 22, 521–547 (1999)
Lo W.C., Majer E., Sposito G.: Wave propagation through elastic porous media containing two immiscible fluids. Water Resour. Res. 41, 1–20 (2005)
Lo W.C., Sposito G., Majer E.: Low-frequency dilatational wave propagation through unsaturated porous media containing two immiscible fluids. Transp. Porous Media 68, 91–105 (2007)
Lu J.F., Hanyga A.: Linear dynamic model for porous media saturated by two immiscible fluids. Int. J. Solids Struct. 42, 2689–2709 (2005)
Muraleetharan K.K., Wei C.: Dynamic behaviour of unsaturated porous media: Governing equations using the theory of mixtures with interfaces (TMI). Int. J. Numer. Anal. Methods Geomech. 23, 1579–1608 (1999)
Plona T.J.: Observation of a second bulk compressional wave in a porous medium at ultrasonic frequencies. Appl. Phys. Lett. 36, 259–261 (1980)
Rubino J.G., Ravazzoli C.L., Santos J.E.: Reflection and transmission of waves in composite porous media: A quantification of energy conversions involving slow waves. J. Acoust. Soc. Am. 120, 2425–2436 (2006)
Stoll R.D., Kan T.K.: Reflection of acoustic wave at a water–sediment interface. J. Acoust. Soc. Am. 70, 149–156 (1981)
Tomar S.K., Gogna M.L.: Reflection and refraction of longitudinal waves at an interface between two micropolar elastic media in welded contact. J. Acoust. Soc. Am. 97, 822–830 (1995)
Tomar S.K., Arora A.: Reflection and transmission of elastic waves at an elastic/porous solid saturated by two immiscible fluids. Int. J. Solids Struct. 43, 1991–2013 (2006)
Tomar, S.K., Arora, A.: Erratum to “Reflection and transmission of elastic waves at an elastic/porous solid saturated by two immiscible fluids” [Int. J. Solids Struct. 43(2006) 1991–2013]. Int. J. Solids Struct. 44, 5796–5800 (2007)
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)
Wei C., Muraleetharan K.K.: A continuum theory of porous media saturated by multiple immiscible fluids: I. Linear poroelasticity. Int. J. Eng. Sci. 40, 1807–1833 (2002)
Yeh C.L., Lo W.C., Jan C.D., Yang C.C.: Reflection and refraction of obliquely incident elastic waves upon the interface between two porous elastic half-spaces saturated by different fluid mixtures. J. Hydrol. 395, 91–102 (2010)
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Chen, Wy., Xia, Td., Sun, Mm. et al. Transverse wave at a plane interface between isotropic elastic and unsaturated porous elastic solid half-spaces. Transp Porous Med 94, 417–436 (2012). https://doi.org/10.1007/s11242-012-0012-2
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DOI: https://doi.org/10.1007/s11242-012-0012-2