The indirect boundary integral equation method for the broadband scattering of plane P, SV and Rayleigh waves by a hill topography

摘要

The indirect boundary integral equation method (IBIEM) is developed to solve the broadband scattering of plane P, SV and Rayleigh waves by a hill topography, incorporated with the technique of domain-partition construction. It illustrates that the semi-analytical IBIEM can accurately and steadily solve the wave scattering around a steep or a gentle hill both for low and high frequency waves. Numerical results indicate that the seismic response characteristics of a hill strongly depend on the incident angle, wave frequency, the medium stiffness and height-width ratio of the hill. In general, the steep hill has more significant amplification effect on the surface displacement amplitude of the hill, and the displacement peak usually located at the top of the hill for vertically incident SV waves but can also appear near the hill bottom for high-frequency P waves. Multiple standing wave points can be observed for high-frequency wave and steep hill due to the interface effect of scattered waves. Moreover, the high hill has significant shielding effect on the Rayleigh waves. In practice, the notable amplification effect and obvious spatial variation of ground motion must be taken into account in the anti-seismic design of engineering structures in mountainous area.