Abstract
An analytical solution to the three-dimensional scattering and diffraction of plane SV-waves by a saturated hemispherical alluvial valley in elastic half-space is obtained by using Fourier–Bessel series expansion technique. The hemispherical alluvial valley with saturated soil deposits is simulated with Biot’s dynamic theory for saturated porous media. The following conclusions based on numerical results can be drawn: (1) there are a significant differences in the seismic response simulation between the previous single-phase models and the present two-phase model; (2) the normalized displacements on the free surface of the alluvial valley depend mainly on the incident wave angles, the dimensionless frequency of the incident SV waves and the porosity of sediments; (3) with the increase of the incident angle, the displacement distributions become more complicated; and the displacements on the free surface of the alluvial valley increase as the porosity of sediments increases.
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Anderson J.G., Bodin P., Brune J.N., Prince J., Singh S.K., Quaas R., Onate M. (1986) Strong ground motion from the Michoacan, Mexico, earthquake. Science 233(4768): 1043–1049
Zahardnik J., Hron F. (1987) Seismic ground motion of sedimentary valley examples La Molina, Lima Peru. J. Geophys. 62, 31–37
Trifunac M.D. (1973) Scattering of plane SH wave by a semi-cylindrical canyon. Earthq. Eng. Struct. Dyn. 1, 267–281
Cao H., Lee V.W. (1990) Scattering and diffraction of plane P wave by circular-cylindrical canyons with variable depth-to-width ratio. Soil Dyn. Earthq. Eng. 9(3): 141–150
Lee V.W., Cao H. (1989) Diffraction of SV wave by circular canyons of various depths. J. Eng. Mech. ASCE 115(9): 2035–2056
Todorovska M., Lee V.W. (1991) Surface motion of shallow circular alluvial valleys for incident plane SH waves: analytical solution. Soil Dyn. Earthq. Eng. 4, 192–200
Wong H.L., Trifunac M.D. (1974) Surface motion of semi-elliptical alluvial valley for incident plane SH waves. Bull. Seism. Soc. Am. 61: 1389–1408
Zhao C., Valliappan S. (1993) Seismic wave scattering effects under different canyon topographic and geologic conditions. Soil Dyn. Earthq. Eng. 12, 129–143
Fishman K.L., Ahmad S. (1995) Seismic response for alluvial valleys subjected to SH, P and SV waves. Soil Dyn. Earthq. Eng. 14, 249-258
Lee V.W.: Displacement near a three-dimensional hemi-spherical canyon subjected to incident plane wave. Department of Civil Engineering, University of Southern California, Report no. CE 78–16 (1978)
Lee V.W. (1982) A note on the scattering of elastic plane wave by a hemispherical canyon. Soil Dyn. Earthq. Eng. 1(3): 122–129
Lee V.W. (1984) Three-dimensional diffraction of plane P, SV, SH waves by a hemispherical alluvial valley. Soil Dyn. Earthq. Eng. 3(3): 133–144
Mow C.C., Pao Y.H.: Diffraction of elastic waves and dynamic stress concentration. Rand Report, R-482-PR, New York (1971)
Li W.H., Zhao C.G. (2003) An analytical solution for the diffraction of plane P-waves by circular cylindrical canyons in a fluid-saturated porous media half space (in Chinese). Chin. J. Geophys. 46(4): 539–546
Li W.H., Zhao C.G. (2003) Scattering of plane P-waves in alluvial valleys with saturated soil deposits (in Chinese). Chin. J. Geotechn. Eng. 25(3): 346–351
Biot M.A. (1956) Theory of propagation of elastic waves in a fluid-saturated porous soil. J. Acoust. Soc. Am. 28(2): 168–178
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The project was supported by the National Natural Science Foundation of China (50478062 and 10532070) and Open Fund at the Key Laboratory of Urban Security and Disaster Engineering (Beijing University of Technology), Chinese Ministry of Education. The English text was polished by Keren Wang.
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Zhao, C., Dong, J., Gao, F. et al. Seismic responses of a hemispherical alluvial valley to SV waves: a three-dimensional analytical approximation. Acta Mech Sin 22, 547–557 (2006). https://doi.org/10.1007/s10409-006-0039-0
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DOI: https://doi.org/10.1007/s10409-006-0039-0