An analytical solution for three-dimensional diffraction of plane P-waves by a hemispherical alluvial valley with saturated soil deposits
Source abstract
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.
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Research context
OpenAlex topics: Geotechnical Engineering and Underground Structures · Seismic Waves and Analysis · Geophysical Methods and Applications
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References (16)
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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.
2. Trifunac, M.D., Scattering of plane SH wave by a semi-cylindrical canyon, Soil Dynamics and Earthquake Engineering, Vol.1, 1973, 267–281.10.1002/eqe.4290010307 ↗
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, 192–200.10.1016/0267-7261(91)90033-V ↗
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, 1389–1408.10.1785/BSSA0640051389 ↗
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, 141–150.10.1016/S0267-7261(09)90013-6 ↗
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, 2035–2056.10.1061/(ASCE)0733-9399(1989)115:9(2035) ↗
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.
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, 122–129.10.1016/0261-7277(82)90003-1 ↗
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, 133–144.10.1016/0261-7277(84)90043-3 ↗
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).10.1002/cjg2.3396 ↗
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).
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, 168–178.10.1121/1.1908239 ↗
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, 599–607.10.1785/BSSA0500040599 ↗
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.
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).
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).