Diffraction of SH-Waves by Subsurface Inclusions of Arbitrary Shape
Publication: Journal of Engineering Mechanics
Volume 122, Issue 2
Abstract
The weighted residual method was applied to the problem of scattering and diffraction of plane SH-waves by an underground inclusion of a different elastic medium and of arbitrary shape in a two-dimensional half-space. Results from the application of the weighted residual approach to the case of an underground circular inclusion closely approximate those obtained using the closed-form solution for underground inclusions. To demonstrate the versatility of the method, it was applied to inclusions of elliptical and square shape. It was shown that significant ground-motion amplification, with respect to the amplitude of the incident waves, occurred due to the presence of an inclusion or cavity. Amplifications were dependent on the size, shape, and depth of the inclusion as well as the frequency and angle of incidence of the incident waves. Amplification profiles for the lower-frequency incident waves were simple with peak values that did not differ significantly from 2, the value expected on the surface of a uniform half-space. As the frequency is increased, amplification profiles become more complicated with worst-case values exceeding 7 for elliptical-shaped inclusions.
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References
1.
Abramowitz, M., and Stegun, I. A. (1972). Handbook of mathematical functions, with formulas, graphs, and mathematical tables. Dover Publications, Inc. (0-486-61272-4), New York, N.Y.
2.
Datta, S. K.(1978). “Scattering of elastic waves.”Mech. Today, 4, 149–208.
3.
Dravinski, M.(1983). “Ground motion amplification due to elastic inclusions in a half-space.”Int. J. Earthquake Engrg. and Struct. Dynamics, 11, 313–335.
4.
Fenlon, F. H. (1969). “Calculation of the acoustic radiation field at the surface of a finite cylinder by the method of weighted residuals.”Proc., IEEE, 57(3).
5.
Gregory, R. D.(1967). “An expansion theorem applicable to problems of wave propagation in an elastic half-space.”Proc., Camb. Philos. Soc., 63, 1341–1367.
6.
Gregory, R. D.(1970). “The propagation of waves in an elastic half-space containing a circular cylindrical cavity.”Proc., Camb. Philos. Soc., 67, 689–710.
7.
Harrington, R. F.(1967). “Matrix methods for field problems.”Proc., IEEE, 55(2), 136–149.
8.
Harrington, R. F. (1968). Field computation by method of moments . The MacMillan Co., New York, N.Y.
9.
Lee, V. W. (1977). “On deformations near a circular underground cavity subjected to incident plane Sh-waves.”Proc., Application of Comp. Methods in Engrg. Conf., Vol. II, Univ. of Southern California, Los Angeles, Calif., 951–962.
10.
Lee, V. W.(1988). “Three-dimensional diffraction of elastic waves by a spherical cavity in an elastic half-space. I: Closed-form solutions.”Int. J. of Soil Dynamics and Earthquake Engrg., 7(3), 149–161.
11.
Lee, V. W., and Trifunac, M. D.(1979). “Response of tunnels to incident Sh-waves.”Engrg. Mech. Div., ASCE, 105, 643–659.
12.
Lee, V. W., and Wu, X.(1994a). “Application of the weighted residues (moment) method to scattering by 2-D canyons of arbitrary shape: I. Incident Sh-waves.”Int. J. Soil Dynamics and Earthquake Engrg., 13(5), 355–364.
13.
Lee, V. W., and Wu, X.(1994b). “Application of the weighted residues (moment) method to scattering by 2-D canyons of arbitrary shape: II. Incident P, SV, and Rayleigh waves.”Int. J. Soil Dynamics and Earthquake Engrg., 13(5), 265–273.
14.
Manoogian, M. E. (1992). “Scattering and diffraction of plane SH-waves by surface and sub-surface discontinuities,” PhD dissertation, Univ. of Southern California, Los Angeles, Calif.
15.
Pao, Y. H., and Mao, C. C. (1973). Diffraction of elastic waves and dynamic stress concentrations. Crane, Russak and Co., Inc., New York, N.Y.
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Copyright © 1996 American Society of Civil Engineers.
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Published online: Feb 1, 1996
Published in print: Feb 1996
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