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Diffraction of anti-plane SH waves by a semi-circular cylindrical hill with an inside concentric semi-circular tunnel

Vincent W. Lee1, Luo Hao (罗 昊)2,3 and Liang Jianwen (梁建文)3

1. Dept. of Civil and Environmental Engineering, Univ. of Southern California, Los Angeles, CA 90089-2531, USA

2. Civil Engineering and Architecture Experiment Center, Dept. of Civil Engineering, Shanghai Jiaotong Univ., 800 Dongchuan Rd., Shanghai 200240, China

3. Dept. of Civil Engineering, Tianjin Univ., Tianjin 300072, China

Abstract: A closed-form analytic solution of two-dimensional scattering and diffraction of plane SH waves by a semi-cylindrical hill with a semi-cylindrical concentric tunnel inside an elastic half-space is presented using the cylindrical wave functions expansion method. The solution is reduced to solving a set of infinite linear algebraic equations. Fourier expansion theorem with the form of complex exponential function and cosine function is used. Numerical solutions are obtained by truncation of the infinite equations. The accuracy of the presented numerical results is carefully verified.

Keywords: SH waves; hill; tunnels; close-form analytic solution; amplifications.