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Published in:
01-08-2023
Scattering of shallow asymmetric V-shaped canyon under cylindrical SH waves
Authors: Yongjiu Tang, Zhihui Zhu, Zhenning Ba, Wei Gong
Published in: Journal of Engineering Mathematics | Issue 1/2023
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Abstract
The article delves into the complex phenomenon of seismic wave scattering in shallow asymmetric V-shaped canyons under cylindrical SH waves. It highlights the significance of considering the seismic source location, which can greatly influence the topography amplification effect. The study employs the Wave Function Expansion Method (WFEM) and Graf’s formula to derive a series solution for the wave scattering problem. The research also includes a detailed verification of the model and solution through comparisons with existing literature results. Furthermore, the paper discusses the parametric analysis of near-source topography effects, focusing on the influence of source location, dimensionless frequency, and the width of the asymmetric canyon on surface displacement amplification. The conclusions emphasize the importance of considering near-source effects and the asymmetry of the canyon in seismic studies, providing valuable insights for the design and engineering of structures in seismically active regions.
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Abstract
Previous studies mostly used plane waves as the source input to study the influence of topography effects without considering the source distance. However, the influence of source effect on topography amplification cannot be ignored. This study presents a series solution for the scattering of cylindrical SH waves by a shallow asymmetric V-shaped canyon, and the effect of the location of the source on the topography magnification is investigated. The presented formulations in this paper first divide the asymmetric shallow V-shaped canyon into enclosed and open regions using the region-matching method. The free wavefield of cylindrical SH wave is solved by the image theory, and the wavefield in the enclosed and open regions is obtained based on the separation of variable method. The Graf’s formula is derived to unify the wavefield coordinates of the two regions, and the unknown coefficients of the wavefield are solved by the continuity condition of the boundary. Then, the proposed solution is verified by comparisons with published data for two cases (e.g. those pertaining to the symmetrical V-shaped canyon of cylindrical SH waves and the asymmetric shallow V-shaped canyon of plane SH waves). Finally, the effect of the source position, the width, and the dimensionless frequency of the asymmetric V-shaped canyon on the surface displacement amplification is discussed. It is found that the difference of displacement amplitude between asymmetric canyon and symmetric canyon can reach 270.2% under the cylindrical SH waves, that is, the asymmetric effect of the canyon has a significant influence on the topography amplification. The cylindrical SH waves cannot simply be regarded as plane SH waves unless the source location \({r}_{0}\) exceeds 100 times canyon depth and it is necessary to use cylindrical SH waves to simulate the influence of near-source effects on topography amplification when the source is relatively close. Therefore, the near-source effect should warrant careful engineering attention in the seismic design of large-span structures such as bridges across shallow V-shaped canyons.
