Acta Mechanica Solida Sinica

, Volume 19, Issue 2, pp 141–151 | Cite as

An analytical solution for three-dimensional diffraction of plane P-waves by a hemispherical alluvial valley with saturated soil deposits

Article

Abstract

An analytical solution for the three-dimensional scattering and diffraction of plane P-waves by a hemispherical alluvial valley with saturated soil deposits is developed by employing Fourier-Bessel series expansion technique. Unlike previous studies, in which the saturated soil deposits were simulated with the single-phase elastic theory, in this paper, they are simulated with Biot’s dynamic theory for saturated porous media, and the half space is assumed as a single-phase elastic medium. The effects of the dimensionless frequency, the incidence angle of P-wave and the porosity of soil deposits on the surface displacement magnifications of the hemispherical alluvial valley are investigated. Numerical results show that the existence of a saturated hemispherical alluvial valley has much influence on the surface displacement magnifications. It is more reasonable to simulate soil deposits with Biot’s dynamic theory when evaluating the displacement responses of a hemispherical alluvial valley with an incidence of P-waves.

Key words

Biot’s dynamic theory three-dimensional scattering hemispherical alluvial valley analytical solution 

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References

  1. [1]
    Singh, S.K., Mena, E. and Castro, R., Some aspects of source characteristics of the 19 September 1985 Michoacan earthquake and ground motion amplification in and near Mexico City from strong motion data, Bulletin of Seismological Society of America, Vol.78, No.2, 1988, 451–477.Google Scholar
  2. [2]
    Trifunac, M.D., Scattering of plane SH wave by a semi-cylindrical canyon, Soil Dynamics and Earthquake Engineering, Vol.1, 1973, 267–281.CrossRefGoogle Scholar
  3. [3]
    Todorovska, M. and Lee, V.W., Surface motion of shallow circular alluvial valleys for incident plane SH waves: analytical solution, Soil Dynamics and Earthquake Engineering, Vol.4, 1991, 192–200.CrossRefGoogle Scholar
  4. [4]
    Wong, H.L. and Trifunac, M.D., Surface motion of semi-elliptical alluvial valley for incident plane SH waves, Bulletin of Seismological Society of America, Vol.64, No.1, 1974, 1389–1408.Google Scholar
  5. [5]
    Cao, H. and Lee, V.W., Scattering and diffraction of plane P waves by circular-cylindrical canyons with variable depth-to-width ratio, Soil Dynamics and Earthquake Engineering, Vol.9, No.3, 1990, 141–150.CrossRefGoogle Scholar
  6. [6]
    Lee, V.W. and Cao, H., Diffraction of SV by circular canyons of various depth, Journal of Engineering Mechanics, ASCE, Vol.115, No.9, 1989, 2035–2056.CrossRefGoogle Scholar
  7. [7]
    Mow, C.C. and Pao, Y.H., The diffraction of elastic waves and dynamics stress concentrations, Rand report, R-482-PR, New York, 1971.Google Scholar
  8. [8]
    Lee, V.W., A note on the scattering of elastic plane waves by a hemispherical canyon, Soil Dynamics and Earthquake Engineering, Vol.1, No.3, 1982, 122–129.CrossRefGoogle Scholar
  9. [9]
    Lee, V.W., Three-dimensional diffraction of plane P, SV and SH waves by a hemispherical alluvial valley, Soil Dynamics and Earthquake Engineering, Vol.3, No.3, 1984, 133–144.CrossRefGoogle Scholar
  10. [10]
    Li, W.H. and Zhao, C.G., An analytical solution for the diffraction of plane P-waves by circular cylindrical canyons in a fluid-saturated porous media half space, Chinese Journal of Geophysics, Vol.46, No.4, 2003, 539–546 (in Chinese).CrossRefGoogle Scholar
  11. [11]
    Li, W.H. and Zhao, C.G., Scattering of plane P waves in alluvial valleys with saturated soil deposits, Chinese Journal of Geotechnical Engineering, Vol.25, No.3, 2003, 346–351 (in Chinese).Google Scholar
  12. [12]
    Biot, M.A., Theory of propagation of elastic wave in fluid-saturated porous soil, Journal of the Acoustical Society of America, Vol.28, No.2, 1956, 168–178.CrossRefGoogle Scholar
  13. [13]
    Deresiewicz, H., and Rice, J.T., The effect of boundaries on wave propagation in a liquid filled porous solid.: Reflection of plane waves at a free plane boundary (non-dissipative case), Bulletin of Seismological Society of America, Vol.50, No.4, 1960, 599–607.MathSciNetGoogle Scholar
  14. [14]
    Lee, V.W., Displacements near a three-dimensional hemispherical canyon subjected to incident plane waves, Report No.CE 78-16, Department of Civil Engineering, University of Southern California, Los Angeles, California, 1978.Google Scholar
  15. [15]
    Dong, J. Study on the three-dimensional scattering and diffraction of plane-waves by irregular local sites with saturated soil, Master Dissertation (Supervisor: Zhao Chenggang), Beijing: Beijing Jiaotong Unversity, 2005 (in Chinese).Google Scholar
  16. [16]
    Li, L. and Zhao, C.G., Equations of wave propagation with mass-coupling effect in fluid-saturated porous media, Acta Mechanica Solida Sinica, Vol.24, No.2, 2003, 243–248 (in Chinese).Google Scholar

Copyright information

© The Chinese Society of Theoretical and Applied Mechanics and Technology 2006

Authors and Affiliations

  1. 1.School of Civil Engineering and ArchitectureBeijing Jiaotong UniversityBeijingChina
  2. 2.Institute of MechanicsChinese Academy of SciencesBeijingChina

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