Anti-Plane Responses Induced by Circular Cavity beneath Semi-circular Canyon

ABSTRACT

A complicated natural topography, such as a cavity beneath a canyon, can cause considerable ground motion during earthquakes. This phenomenon is referred to as a site effect. An awareness of site effects can help to reduce damage to property and loss of life. However, modeling the highly complex interactions between a cavity and a canyon requires considerable mesh skills. In this study, we developed a novel, systematic approach to meshing this kind of complicated topography, wherein irregularities are meshed via arithmetic progression, the formula of the internal division point, and the transfinite interpolation (TFI) function. We then implemented a hybrid method combining Lamb’s series with the finite element method (FEM) in conjunction with the proposed meshing skill to resolve the problem of anti-plane scattering. The results were verified using two degenerated models: a semi-circular canyon and a cavity beneath a planar surface. We made a detailed account of how the responses of $\left|u_y\right|$ at the surface of the semi-circular canyon and around the surface of the circular cavity were affected by the incident angle of SH waves ($\mathrm{\Theta }$), dimensionless frequency ($\eta$), and variations in the radius of the circular cavity ($a_1$). Interestingly, the responses of $\left|u_y\right|$ were affected by the following site effects: (1) plate-like effects related to the buried depth of the circular cavity, (2) canyon-decay effects due to the existence of the canyon, and (3) creep effects associated with the curvature and size of circular cavity. The patterns of $\left|u_y\right|$ at the free surface and surface of the circular cavity are affected by each of the aforementioned site effects, which all depend profoundly on $\mathrm{\Theta }$, $\eta$ and $a_1$.

KEYWORDS:

• SH Waves
• Canyon
• Cavity
• Hybrid Method
• Site Effects

Acknowledgments

The authors would like to thank the Ministry of Science and Technology, Taiwan R.O.C. for financially supporting this research under Contract No. MOST 106-2221-E-020-007.

Additional information

Funding

This work was supported by the Ministry of Science and Technology, Taiwan, R.O.C. [MOST 106-2221-E-020-007].