A Unified Analytical Solution for Seismic Response of a Symmetrical Triangular Hill or Canyon Subjected to SH Waves

ABSTRACT In this study, a unified analytical solution for the seismic response of a symmetrical triangular hill or canyon under SH‐wave incidence is developed using novel coordinate transformations in the complex domain. First, the entire solution domain is divided into two subregions. Wave functions with undetermined coefficients are then constructed in each subregion such that the zero‐stress boundary conditions on the free surface are inherently satisfied. Second, the continuity boundary conditions along the interface are enforced to determine the unknown coefficients in the complex domain. Finally, a parametric study is conducted to investigate the differences in the effects of hills and canyons on SH‐wave scattering. The results indicate that the seismic response characteristics of a symmetrical triangular hill or canyon under SH wave incidence exhibit different patterns. The seismic response of hills shows reduced displacement amplitudes with increasing incidence angle, while that of canyons exhibits opposite trends. Under oblique SH‐wave incidence, peak displacement amplitudes are typically found on the right slope of hills and the left slope of canyons. The height‐to‐span ratio of hills significantly affects peak displacement amplitudes, but the depth‐to‐span ratio of canyons has a negligible effect.