Ground Motion of Non-Circular Alluvial Valley for Incident Plane SH-Wave

Abstract:

The seismic ground motions are studied in an infinite half-space with a non-circular alluvial valley under time harmonic incident anti-plane shear waves. Based on the conformal mapping method and Fourier series expansions, the conditions of displacement continuity and stress equilibrium at the interface of alluvial valley are set as semi-circular alluvial valley in conformal plane, then the result is obtained by constructing a set of infinite linear algebraic equations with boundary discretization. The unknown coefficients in the algebraic system can be easily determined. The present method is treated as a semi-analytical solution since error only attributes to the truncation of Fourier series. Earthquake analysis for the site response of alluvial valley or canyon subject to the incident SH-wave is the main concern. Numerical examples for semi-elliptic alluvial valley are given to test our program. The research indicates that great interaction exists between the alluvial valley and the horizontal surface, which will bring on great influence on ground motion. Therefore enough importance must be attached to the existing of subsurface cavity while finishing seismic design.

• Periodical: Applied Mechanics and Materials (Volumes 105-107)
• Pages: 2092-2097
• DOI: https://doi.org/10.4028/www.scientific.net/AMM.105-107.2092
• Online since: September 2011
• Authors: Hui Qi, Gen Chang Zhang, Jing Fu Nan
• Keywords: Conformal Mapping Method, Ground Motion, Non-Circular Alluvial Valley, Sh Wave

References

[1] Trifunac M D. (1971). Surface motion of a semi-cylindrical alluvial valley for incident plane SH waves. Bull Seismol Soc Am 61:6, 1755–1770.

DOI: 10.1785/bssa0610061755

[2] Pao YH, Mow CC. (1972). Diffraction of elastic waves and dynamics stress concentration. Crane, New York.

[3] Lee V W, Chen S, Hsu I R. (1999). Anti-plane diffraction from canyon above subsurface unlined tunnel. Journal of Engineering Mechanics 125:668-674.

DOI: 10.1061/(asce)0733-9399(1999)125:6(668)

[4] Abdul Hayir, Maria I. Todorovska, Mihailo D. Trifunac. (2001). Antiplane response of a dike with flexible soil-structure interface to incident SH waves. Soil Dynamics and Engineering 21:603-613.

DOI: 10.1016/s0267-7261(01)00035-5

[5] Qiu F Q, Liu D K. (2005). Anti-plane response of isosceles triangular hill to incident SH waves. Earthquake Engineering and Engineering Vibration 4:1-10.

[6] Liu D K, Han F. (1990). Scattering of plane SH-waves by cylindrical canyon of arbitrary shapes in anisotropic media. Acta Mechanica Sinica 6:256-266.

DOI: 10.1007/bf02487648

[7] Lee VW, Manoogian ME. (1995). Surface motion above an arbitrary shape underground cavity for incident SH waves. Eur Earthquake Eng 1: 3-11.

[8] Nazaret D, Lee V W, Liang J W. (2003). Anti-plane deformations around arbitrary shaped canyons on a wedge shape half space: moment method solutions. Earthquake Engineering and Engineering Vibration 2:281-287.

DOI: 10.1007/s11803-003-0011-y

[9] Liu D K, Wang G Q. (2006). Anti-plane SH-deformation of a semi-cylindrical hill above a subsurface cavity in half-space. Acta Mechanical Sinica 38:209-218.