Scattering of SH waves by a non-symmetrical V-shaped canyon with a shallow cavity in half-space

Abstract

Both surface motion and hole stress concentration have always been concerned in engineering design. In this paper, a theoretical approach is used to study the scattering problem of circular cavities under a non-symmetrical V-shaped canyon. The wave displacement function is obtained by solving the Helmholtz equation that meets the zero-stress boundary conditions by adopting the method of separation of variables and the symmetric method. Based on the complex function method, multi-polar coordinate method and region-matching technique, algebraic equations are established at relevant conditions, which include auxiliary and free boundary conditions. Then, according to sample statistics, a least-square method is used instead of the Fourier expansion method to solve the undetermined coefficients of the algebraic equations by discrete boundary. Numerical results show that the theoretical method is verified valid by the finite element method and the reduced model, and the displacement of the free surface and the stress of the circular cavity are related to the shape of the canyon, the position of the circular cavity, the direction of the incident wave and the frequency content of the excitation.

KEYWORDS:

• Earthquake ground motions
• theoretical seismology
• wave scattering and diffraction
• wave propagation
• earthquake dynamics
• transient deformation
• least square method

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

This work is supported by the National Key Research and Development Program of China (grant number 2019YFC1509301), the National Natural Science Foundation of China (grant number 11872156), the Fundamental Research Funds for the Central Universities and the program for Innovative Research Team in China Earthquake Administration.