Analytical solution to the scattering of SH waves by a step-like slope topography

Abstract

To investigate the amplification effects of slope topography under seismic loading, this study employs the wave function expansion method to derive an exact analytical solution to the scattering of SH waves by a step-like slope. The accuracy and reliability of the solution are verified through systematic convergence tests and model degeneration validation. Through time-domain parametric analyses, the influence of the slope angle and the incident direction of seismic waves on the peak ground acceleration (PGA) and the topographic amplification factor (TAF) is quantitatively examined. The results indicate that the PGA values on the slope surface generally increase with the slope angle β₁ under horizontal and oblique seismic waves, but remain nearly unaffected under vertical incidence. Moreover, the TAF values at various positions generally decrease as the incident angle of the seismic waves increases. These findings not only provide theoretical support for the seismic design and risk assessment of slopes, but also serve as a benchmark for validating numerical simulations.