Three dimensional responses of a hill in a layered half-space for obliquely incident Rayleigh waves

Abstract

An indirect boundary element method (IBEM) is presented to study the three dimensional responses of a hill in a layered half-space for obliquely incident Rayleigh waves. The presented IBEM yields very accurate results and is very convenient to deal with complex boundaries, for the Greens functions of moving distributed loads acting on inclined lines in a layered half-space are used as fundamental solutions to overcome the problem of singularity of the traditional IBEM, and the exact three dimensional dynamic stiffness of layered site is used to avoid discretization of the layer interfaces. The accuracy of the method is verified by comparing its results with published ones. Numerical calculations are performed both in the frequency and time domains by taking a hill in a homogenous and layered half-space as examples, and the effects of the obliquely incident angles, incident frequencies, cross section of the hill, height of the hill, and characteristics of the multi-modal and dispersion of Rayleigh waves propagating in a layered half-space are discussed in detail. Numerical results show that the amplification can be very different between the layered half-space and homogenous half-space for the multi-modal and dispersion characteristics of Rayleigh waves in a layered site. The amplification spectra of the higher modals (second and higher order modes) are very different from those of the first modal, which shows that the amplification spectra are narrowband, the displacement amplitudes near the top of the hill is extremely high at the peak frequencies and the peak frequencies are consistent with those of the effective damping ratio.