Seismic Response of a Shallow Asymmetrical V-Shaped Canyon with Cliffs under SH Waves Propagation
Publication: International Journal of Geomechanics
Volume 24, Issue 11
Abstract
Irregular topographies are widely distributed in nature, particularly in mountainous areas. The cliff on the canyon top forming over long periods of geological evolution significantly influences the amplification or reduction of ground motion. In this study adopting the wave function expansion method, a comprehensive analytical solution is formulated to address the scattering issue under shear horizontal (SH) waves induced by a shallow asymmetrical V-shaped canyon with cliffs. In general, employing the appropriate Graf’s addition formula, wave function expressions in different polar coordinate systems can be unified. According to continuity conditions of stress and displacement on the auxiliary boundary, the region-matching technique (RMT) has also been adopted to determine the unknown coefficients in the algebraic equation. Further, by comparing the results obtained in this study with those from previous studies, the correctness and applicability of the proposed theoretical model and analytical solution have been verified. A significant finding indicates that the maximum difference in peak displacement under a canyon with cliffs (d1/a = 0.4) can reach 1.81 times that without cliffs (d1/a = 0). Meanwhile, the asymmetric effect in this study is mainly concentrated on the ground motion of the canyon inner surface (−1 ≤ x/a ≤ 1), as opposed to a symmetrical V-shaped canyon with cliffs and an asymmetrical V-shaped canyon without cliffs. The proposed analytical solution not only enriches the category of well-known canyon problems related to SH-waves scattering, but also can serve as a reference for numerical verification and engineering practice.
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Data Availability Statement
All data generated or analyzed during this study are included within the article.
Acknowledgments
The research reported in this paper was supported by the National Key R&D Program of China (No. 2023YFC3008302), the National Natural Science Foundation of China (No. 42277183), and the Chongqing Natural Science Innovation and Development Foundation (No. CSTB2022NSCQ-LZX0044).
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Information & Authors
Information
Published In
International Journal of Geomechanics
Volume 24 • Issue 11 • November 2024
Copyright
© 2024 American Society of Civil Engineers.
History
Received: Oct 12, 2023
Accepted: May 7, 2024
Published online: Aug 20, 2024
Published in print: Nov 1, 2024
Discussion open until: Jan 20, 2025
ASCE Technical Topics:
- Asymmetry
- Canyons
- Cliffs
- Continuum mechanics
- Dynamics (solid mechanics)
- Engineering fundamentals
- Engineering mechanics
- Geology
- Geomatics
- Geotechnical engineering
- Geotechnical investigation
- Ground motion
- Mathematics
- Seismic tests
- Seismic waves
- Solid mechanics
- Surveying methods
- Symmetry
- Tests (by type)
- Topography
- Waves (mechanics)
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