TY - JOUR
T1 - Response of an elastic half-plane with an embedded circular cavity subject to a harmonic anti-plane shear wave
T2 - A comparison of methods
AU - Zhao, Mingjuan
AU - de Oliveira Barbosa, João Manuel
AU - Metrikine, Andrei V.
AU - van Dalen, Karel N.
PY - 2025
Y1 - 2025
N2 - In this paper, we investigate the response of a cavity embedded in an elastic half-plane (2D) subjected to a harmonic SH wave. In previous work, the method of conformal mapping and the indirect boundary element method (indirect BEM) were employed to solve the 3D wave scattering from a cylindrical tunnel embedded in a half-space. Inaccurate results were obtained particularly at high frequencies (method of conformal mapping). Therefore, in this study we focus on a comparison of the two methods with the method of images, which serves as a benchmark solution. Through a systematic evaluation, we confirm that the two methods accurately work within the complete considered ranges of the dimensionless frequency and the embedded cavity depth. This suggests that representing the waves scattered from the free surface by cylindrical waves in the method of conformal mapping is the cause of the inaccuracies at high frequency in the 3D problem; the cylindrical waves are probably not able to fully capture all wave conversions taking place at the free surface. The presented results reveal significant effects of the system parameters on the responses. The system's response curves display nearly equally spaced resonances, which is in line with those of the 1D shear layer subject to bedrock motion, while similar response curves for the 3D case do not have this feature.
AB - In this paper, we investigate the response of a cavity embedded in an elastic half-plane (2D) subjected to a harmonic SH wave. In previous work, the method of conformal mapping and the indirect boundary element method (indirect BEM) were employed to solve the 3D wave scattering from a cylindrical tunnel embedded in a half-space. Inaccurate results were obtained particularly at high frequencies (method of conformal mapping). Therefore, in this study we focus on a comparison of the two methods with the method of images, which serves as a benchmark solution. Through a systematic evaluation, we confirm that the two methods accurately work within the complete considered ranges of the dimensionless frequency and the embedded cavity depth. This suggests that representing the waves scattered from the free surface by cylindrical waves in the method of conformal mapping is the cause of the inaccuracies at high frequency in the 3D problem; the cylindrical waves are probably not able to fully capture all wave conversions taking place at the free surface. The presented results reveal significant effects of the system parameters on the responses. The system's response curves display nearly equally spaced resonances, which is in line with those of the 1D shear layer subject to bedrock motion, while similar response curves for the 3D case do not have this feature.
KW - Cavity in half-plane
KW - Comparison study
KW - Indirect BEM
KW - Method of conformal mapping
KW - Method of images
KW - SH wave
UR - http://www.scopus.com/inward/record.url?scp=85212429842&partnerID=8YFLogxK
U2 - 10.1016/j.soildyn.2024.109162
DO - 10.1016/j.soildyn.2024.109162
M3 - Article
AN - SCOPUS:85212429842
SN - 0267-7261
VL - 190
JO - Soil Dynamics and Earthquake Engineering
JF - Soil Dynamics and Earthquake Engineering
M1 - 109162
ER -