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Energy flux characteristics of seismic waves at the interface between soil layers with different saturations

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Abstract

Based on the multiphase poroelasticity theory describing the propagation of waves in the unsaturated fluid-saturated porous medium, the reflection and transmission coefficients of the seismic waves at the interface between soil layers with different saturations are obtained. Our unsaturated model consists of a deformable skeleton in which two compressible and viscous fluids (i.e., water and gas) flow in the interstices. Three compressional waves (i.e., P1, P2, and P3 waves) and one shear (i.e., S wave) wave exist in the unsaturated soils. The expressions for the energy ratios of the various reflected and transmitted waves at the interface during the transmission and reflection processes are presented in explicit forms accordingly. At last, numerical computations are performed and the results obtained are respectively depicted graphically. The variation of the energy ratios with the incident angle, wave frequency and saturation degrees of the upper and lower soil layers is illustrated in detail. The calculation results show that the allocation of incident seismic waves at the interface is influenced not only by the angle and frequency of the incident seismic waves, but also by the saturations of the upper and lower soil layers. It is also verified that, at the interface, the sum of energy ratios of the reflected and transmitted waves is approximately equal to unity as was expected. This study is of importance to several fields such as geotechnical engineering, seismology, and geophysics.

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References

  1. Biot M A. Theory of propagation of elastic waves in a fluid saturated porous solid. J Acoust Soc Am, 1956, 28(2): 168–191

    Article  MathSciNet  Google Scholar 

  2. Deresiewicz H, Rice J T. The effect of boundaries on wave propagation in a liquid-filled porous solid V. Transmission across a plane interface. B Seismol Soc Am, 1964, 54: 409–416

    Google Scholar 

  3. Stoll R D, Kan T K. Reflection of acoustic wave at a water-sediment interface. J Acoust Soc Am, 1981, 70(1): 149–156

    Article  MATH  Google Scholar 

  4. Dutta N C, Ode H. Seismic reflections from a gas water contact. Geophysics, 1983, 48(2): 148–162

    Article  Google Scholar 

  5. 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, 1995, 97(2): 822–830

    Article  Google Scholar 

  6. Yang J, Wu S M. Reflection and transmission of seismic waves at an interface between two saturated soils. Acta Seismol Sin, 1997, 10(1): 35–42

    Article  MATH  Google Scholar 

  7. Wei C, Muraleetharan K K. A continuum theory of porous media saturated by multiple immiscible fluids: I. Linear poroelasticity. Int J Eng Sci, 2002, 40(16): 1807–1833

    Article  MathSciNet  MATH  Google Scholar 

  8. Lo W C, Majer E, Sposito G. Wave propagation through elastic porous media containing two immiscible fluids. Water Resour Res, 2005, 41(2): 1–20

    Google Scholar 

  9. Lu J F, Hanyga A. Linear dynamic model for porous media saturated by two immiscible fluids. Int J Solids Struct, 2005, 42(9–10): 2689–2709

    Article  MATH  Google Scholar 

  10. Albers B. Analysis of the propagation of sound waves in partially saturated soils by means of a macroscopic linear poroelastic model. Transport Porous Med, 2009, 80(1): 173–192

    Article  Google Scholar 

  11. Chen W Y, Xia T D, Chen W, et al. Propagation of plane P-waves at the interface between an elastic solid and an unsaturated poroelastic medium. Appl Math Mech, 2012, 33(7): 829–844

    Article  MathSciNet  Google Scholar 

  12. Chen W Y, Xia T D, Sun M M, et al. Transverse wave at a plane interface between isotropic elastic and unsaturated porous elastic solid half-spaces. Transport Porous Med, 2012, 94(1): 417–436

    Article  MathSciNet  Google Scholar 

  13. 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 Met, 1999, 23(13): 1579–1608

    Article  MATH  Google Scholar 

  14. 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, 2011, 48(46–17): 2402–2412

    Article  Google Scholar 

  15. Berryman J G, Thigpen L, Chin R C Y. Bulk elastic wave propagation in partially saturated porous solids. J Acoust Soc Am, 1988, 84(1): 360–373

    Article  Google Scholar 

  16. Coussy O. Poromechanics. 2ed. John Wiley and Sons, Chichester, 2004

    Google Scholar 

  17. Van Genuchten M T. A closed-form equation for predicting the hydraulic conductivity of unsaturated soils. Soil Sci Soc Am J, 1980, 44(5): 892–898

    Article  Google Scholar 

  18. 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, 2006, 120(5): 2425–2436

    Article  Google Scholar 

  19. Murphy W F. Effects of partial water saturation on attenuation in massilon sandstone and vycor porous glass. J Acoust Soc Am, 1982, 71(6): 1458–1468

    Article  Google Scholar 

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Correspondence to WeiYun Chen.

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Chen, W., Chen, G., Xia, T. et al. Energy flux characteristics of seismic waves at the interface between soil layers with different saturations. Sci. China Technol. Sci. 57, 2062–2069 (2014). https://doi.org/10.1007/s11431-014-5625-y

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  • DOI: https://doi.org/10.1007/s11431-014-5625-y

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