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Scattering of SH Waves by a Truncated Semi-Elliptic Canyon

Published online by Cambridge University Press:  14 November 2013

M.-S. Hsu  and
D.-H. Tsaur
M.-S. Hsu
Affiliation:
Department of Harbor and River Engineering, National Taiwan Ocean University, Keelung, Taiwan 20224, R.O.C.
D.-H. Tsaur*
Affiliation:
Department of Harbor and River Engineering, National Taiwan Ocean University, Keelung, Taiwan 20224, R.O.C.
*
hretdh@ntou.edu.tw
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Abstract

In this study, the region-point-matching technique (RPMT) is applied to examine the scattering problem of truncated semi-elliptic canyons under plane SH-wave excitation. The partition of the entire analyzed region into two subregions is carried out via an introduction of the elliptic-arc auxiliary boundary. Taking advantage of appropriate wavefunctions in elliptic coordinates, the expression of antiplane motions for each subregion can be obtained. To accomplish the indispensable coordinate shift, the coordinate-transformed relation, intended as a substitute for the addition theorem involving Mathieu functions, is well utilized. Integration of the coordinate-transformed relation into the RPMT brings about the rapid construction of simultaneous equations. Effects of pertinent parameters on steady-state and transient surface motions are demonstrated. Computed results show that, for horizontal incidence, the potential high level of ground shaking may occur near the illuminated upper corner of the canyon. In such a small localized region, due to the occurrence of constructive interference between the reflected waves from the horizontal ground surface and the scattered waves from the corners of the canyon, the peak amplifaction may be at least two times that of free-field response.

Keywords

ScatteringSH wavesMathieu functionTruncated canyon
Type
Research Article
Information
Journal of Mechanics , Volume 30 , Issue 2 , April 2014 , pp. 137 - 144
Copyright
Copyright © The Society of Theoretical and Applied Mechanics, R.O.C. 2013 

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References

REFERENCES

1.Gazetas, G., Kallou, P. V., and Psarropoulos, P.N., “Topography and Soil Effects in the Ms 5.9 Parnitha (Athens) Earthquake: The Case of Adámes,” Natural Hazards, 27, pp. 133–169 (2002).CrossRefGoogle Scholar
2.Pagliaroli, A., Lanzo, G. and D'Elia, B., “Numerical Evaluation of Topographic Effects at the Nicastro Ridge in Southern Italy,” Journal of Earthquake Engineering, 15, pp. 404–432 (2011).CrossRefGoogle Scholar
3.Ansal, A., “Recent Advances in Earthquake Ge-otechnical Engineering and Microzonation,” Geotechnical, Geological and Earthquake Engineering, 1, Kluwer Academic Publishers, Dordrecht (2004).Google Scholar
4.Sánchez-Sesma, F. J., Palencia, V. J., and Luzón, F., “Estimation of Local Site Effects During Earthquakes: An Overview,” ISET Journal of Earthquake Technology, 39, pp. 167–193 (2002).Google Scholar
5.Trifunac, M. D., “Scattering of Plane SH Waves by a Semi-cylindrical Canyon,” Earthquake Engineering & Structural Dynamics, 1, pp. 267–281 (1973).CrossRefGoogle Scholar
6.Wong, H. L. and Trifunac, M. D., “Scattering of Plane SH Waves by a Semi-elliptical Canyon,” Earthquake Engineering & Structural Dynamics, 3, pp. 157–169 (1974).CrossRefGoogle Scholar
7.Aki, K. and Larner, K. L., “Surface Motion of a Layered Medium Having an Irregular Interface due to Incident Plane SH Waves,” Journal Geophysical Research, 75, pp. 933–954 (1970).CrossRefGoogle Scholar
8.Bouchon, M., “Effect of Topography on Surface Motion,” Bulletin of the Seismological Society of America, 63, pp. 615–632 (1973).CrossRefGoogle Scholar
9.Wong, H. L. and Jennings, P. C., “Effects of Canyon Topography on Strong Ground Motion,” Bulletin of the Seismological Society of America, 65, pp. 1239–1257 (1975).Google Scholar
10.Sabina, F. J. and Willis, J. R., “Scattering of SH Waves by a Rough Half-space of Arbitrary Slope,” The Geophysical Journal of the Royal Astronomical Society, 42, pp. 685–703 (1975).CrossRefGoogle Scholar
11.Sánchez-Sesma, F. J. and Rosenblueth, E., “Ground Motion at Canyons of Arbitrary Shape under Incident SH Waves,” Earthquake Engineering & Structural Dynamics, 7, pp. 441–450 (1979).CrossRefGoogle Scholar
12.England, R., Sabina, F. J., and Herrera, I., “Scattering of SH Waves by Surface Cavities of Arbitrary Shape Using Boundary Methods,” Physics of the Earth and Planetary Interiors, 21, pp. 148–157 (1980).CrossRefGoogle Scholar
13.Shah, A. H., Wong, K. C. and Datta, S. K., “Diffraction of Plane SH Waves in a Half-space,” Earthquake Engineering & Structural Dynamics, 10, pp. 519–528 (1982).CrossRefGoogle Scholar
14.Zhang, C. and Zhao, C., “Effects of Canyon Topography and Geological Conditions on Strong Ground Motion,” Earthquake Engineering & Structural Dynamics, 16, pp. 81–97 (1988).Google Scholar
15.Liu, D. K. and Han, F., “Scattering of Plane SH-wave by Cylindrical Canyon of Arbitrary Shape,” Soil Dynamics and Earthquake Engineering, 10, pp. 249–255 (1991).Google Scholar
16.Zhou, H. and Chen, X., “A New Approach to Simulate Scattering of SH Waves by an Irregular Topography,” Geophysical Journal International, 164, pp. 449–459 (2006).CrossRefGoogle Scholar
17.Moczo, P., Kristek, J., Galis, M., Pazak, P. and Balazovjech, M., “The Finite-difference and Finite-element Modeling of Seismic Wave Propagation and Earthquake Motion,” Acta Physica Slovaca, 57, pp. 177–406 (2007).Google Scholar
18.Tsaur, D. H. and Chang, K. H., “An Analytical Approach for the Scattering of SH Waves by a Symmetrical V-shaped Canyon: Shallow Case,” Geophysical Journal International, 174, pp. 255–264 (2008).CrossRefGoogle Scholar
19.Tsaur, D. H. and Chang, K. H., “Scattering of SH Waves by Truncated Semicircular Canyon,” Journal of Engineering Mechanics, ASCE, 135, pp. 862–870 (2009).CrossRefGoogle Scholar
20.Tsaur, D. H., Chang, K. H. and Hsu, M. S., “An Analytical Approach for the Scattering of SH Waves by a Symmetrical V-shaped Canyon: Deep Case,” Geophysical Journal International, 183, pp. 1501–1511 (2010).CrossRefGoogle Scholar
21.Mow, C. C. and Pao, Y. H., The Diffraction of Elastic Waves and Dynamic Stress Concentrations, R-482-PR, U.S. Air Force Project Rand (1971).Google Scholar
22.Abramowitz, M. and Stegun, I. A., Handbook of Mathematical Functions, with Formulas, Graphs, and Mathematical Tables, Dover, New York (1972).Google Scholar
23.Gradshteyn, I. S. and Ryzhik, I. M., Table of Integrals, Series and Products, 7th Edition, Elsevier-Academic Press, Amsterdam (2007).Google Scholar
24.Særmark, K., “A Note on Addition Theorems for Mathieu Functions,” Zeitschrift Für Angewandte Mathematik Und Physik, 10, pp. 426–428 (1959).CrossRefGoogle Scholar