Propagation of Plane P-Waves at the Interface Between an Elastic Solid and an Unsaturated Poroelastic Medium

CHEN Wei-yun; XIA Tang-dai; CHEN Wei; ZHAI Chao-jiao

doi:10.3879/j.issn.1000-0887.2012.07.001

Volume 33 Issue 7

Turn off MathJax

Article Contents

Article Navigation > Applied Mathematics and Mechanics > 2012 > 33(7): 781-795

CHEN Wei-yun, XIA Tang-dai, CHEN Wei, ZHAI Chao-jiao. Propagation of Plane P-Waves at the Interface Between an Elastic Solid and an Unsaturated Poroelastic Medium[J]. Applied Mathematics and Mechanics, 2012, 33(7): 781-795. doi: 10.3879/j.issn.1000-0887.2012.07.001

Citation:

PDF( 3042 KB)

Propagation of Plane P-Waves at the Interface Between an Elastic Solid and an Unsaturated Poroelastic Medium

doi: 10.3879/j.issn.1000-0887.2012.07.001

¹MOE Key Laboratory of Soft Soils and Geoenvironmental Engineering, Zhejiang University, Hangzhou 310058, P.R.China;²Institute of Geotechnical Engineering, Zhejiang University, Hangzhou 310058, P.R.China;³Institute of Geotechnical, TU Bergakademie Freiberg, Freiberg 09599, Germany

Received Date: 2012-01-11
Rev Recd Date: 2012-04-11
Publish Date: 2012-07-15

Abstract

Abstract

A linear viscoporoelastic model was developed to describe the problem of reflection and transmission of an obliquely incident plane Pwave at an interface between an elastic solid and an unsaturated poroelastic medium in which the solid matrix was filled with two weakly coupled fluids (liquid and gas). The expressions for the amplitude reflection coefficients and amplitude transmission coefficients were derived using the potential method. The present derivation was subsequently applied to study the energy conversions among the incident, reflected and transmitted wave modes. It was found that the reflection coefficients and transmission coefficients in the forms of amplitude ratios and energy ratios are functions of incident angle, liquid saturation, frequency of incident wave and elastic constants of the upper and lower media. The numerical computations are performed graphically, and the effects of the incident angle, frequency and liquid saturation on the amplitude and energy reflection and transmission coefficients are respectively discussed. It was verified that during transmission process there was no energy dissipation at the interface.
- wave reflection,
- wave transmission,
- unsaturation,
- poroelasticity,
- wave propagation,
- porous medium

FullText(HTML)

References(28)

References

[1]	Biot M A. The theory of propagation of elastic waves in a fluid-saturated porous solid—Ⅰ: low frequency range; Ⅱ: higher frequency range[J]. Journal of the Acoustical Society of America, 1956, 28(2): 168-191.
[2]	Plona T J. Observation of a second bulk compressional wave in a porous medium at ultrasonic frequencies[J]. Applied Physics Letters, 1980, 36(4): 259-261.
[3]	Deresiewicz H, Rice J T. The effect of boundaries on wave propagation in a liquid-filled porous solid—Ⅰ: Reflection of plane waves at a true plane boundary[J]. Bulletin of the Seismological Society of America, 1960, 50(4): 599-607.
[4]	Deresiewicz H, Rice J T. The effect of boundaries on wave propagation in a liquid-filled porous solid V. Transmission across a plane interface[J]. Bulletin of the Seismological Society of America, 1964, 54(1): 409-416.
[5]	Stoll R D, Kan T K. Reflection of acoustic wave at a water-sediment interface[J]. Journal of the Acoustical Society of America, 1981, 70(1): 149-156.
[6]	Dutta N C, Ode H. Seismic reflections from a gas water contact[J]. Geophysics, 1983, 48(2): 148-162.
[7]	Wu K Y, Xue Q, Adler L. Reflection and transmission of elastic waves from a fluid-saturated porous solid boundary[J]. Journal of the Acoustical Society of America, 1990, 87(6): 2349-2358.
[8]	Santos J E. Reflection and transmission coefficients in fluid-saturated porous media[J]. Journal of the Acoustical Society of America, 1992, 91(4): 1911-1923.
[9]	Tomar S K, Gogna M L. Reflection and refraction of longitudinal wave at an interface between two micropolar elastic solids in welded contact[J]. Journal of the Acoustical Society of America, 1995, 97(2): 822-830.
[10]	Dai Z J, Kuang Z B, Zhao S X. Reflection and transmission of elastic waves at the interface between an elastic solid and a double porosity medium[J]. International Journal of Rock Mechanics and Mining Sciences, 2006, 43: 961-971.
[11]	Brutsaert W. The propagation of elastic waves in unconsolidated unsaturated granular mediums[J]. Journal of Geophysical Research, 1964, 69(2): 360-373.
[12]	Berryman J G, Thigpen L, Chin R C Y. Bulk elastic wave propagation in partially saturated porous solids[J]. Journal of the Acoustical Society of America, 1988, 84(1): 360-373.
[13]	Gray W G. Thermodynamics and constitutive theory for multiphase porous-media flow considering internal geometric constraints[J]. Advances in Water Resources, 1999, 22(5): 521-547.
[14]	Muraleetharan K K, Wei C. Dynamic behaviour of unsaturated porous media: governing equations using the theory of mixtures with interfaces (TMI)[J]. International Journal for Numerical and Analytical Methods in Geomechanics, 1999, 23(13): 1579-1608.
[15]	Wei C, Muraleetharan K K. A continuum theory of porous media saturated by multiple immiscible fluids—Ⅰ：linear poroelasticity[J]. International Journal of Engineering Science, 2002, 40(16): 1807-1833.
[16]	Lo W C, Majer E, Sposito G.Wave propagation through elastic porous media containing two immiscible fluids[J]. Water Resources Research, 2005, 41(2): 1-20.
[17]	Lu J F, Hanyga A. Linear dynamic model for porous media saturated by two immiscible fluids[J]. International Journal of Solids and Structures, 2005, 42(9/10): 2689-2709.
[18]	Bowen R M. Compressible porous media models by use of theory of mixtures[J]. International Journal of Engineering Science, 1982, 20(6): 697-735.
[19]	Albers B. Analysis of the propagation of sound waves in partially saturated soils by means of a macroscopic linear poroelastic model[J].Transport in Porous Media, 2009, 80(1): 173-192.
[20]	Chen W Y, Xia T D, Hu W T. A mixture theory analysis for the surface-wave propagation in an unsaturated porous medium[J]. International Journal of Solids and Structures, 2011, 48(16/17): 2402-2412.
[21]	Tomar S K, Arora A. Reflection and transmission of elastic waves at an elastic/porous solid saturated by two immiscible fluids[J]. International Journal of Solids and Structures, 2006, 43(7/8): 1991-2013.
[22]	Arora A, Tomar S K. Elastic waves at porous/porous elastic half-spaces saturated by two immiscible fluids[J]. Journal of Porous Media, 2007, 8(10): 751-768.
[23]	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]. Journal of Hydrology, 2010, 395(1/2): 91-102.
[24]	Johnson D L, Koplik J, Dashen R. Theory of dynamic permeability and tortuosity in fluid-saturated porous-media[J]. Journal of Fluid Mechanics, 1987, 176: 379-402.
[25]	Lo W C, Sposito G, Majer E. Low-frequency dilatational wave propagation through unsaturated porous media containing two immiscible fluids[J]. Transport in Porous Media, 2007, 68(1): 91-105.
[26]	Dullien F A L. Porous Media Fluid Transport and Pore Structure[M]. San Diego: Academic Press, 1992.
[27]	Coussy O. Poromechanics[M]. 2nd ed. Chichester: John Wiley and Sons, 2004.
[28]	van Genuchten M T. A closed-form equation for predicting the hydraulic conductivity of unsaturated soils[J]. Soil Science Society of America Journal, 1980, 44(5): 892-898.