Semi-analytical method for solving the anti-plane seismic dynamic response of steep slope site in a layered half-space

Abstract

In order to calculate the anti-plane seismic dynamic response of steep slope in a layered site, a semi-analytical method is proposed. The total wave fields are decomposed into known free-field waves with regular boundary conditions and scattered wave fields caused by the known wave fields acting at the irregular boundary of the steep slope. The problem of solving scattering fields is then transformed from the external input problem of the seismic waves to the internal radiation problem by applying the equivalent seismic loads on the irregular boundary of a steep slope site. Then, a modified scaled boundary finite element method (SBFEM) using splicing lines rather than a point as scaling center to computer the internal radiation problem of the steep slope site analytically along the radial direction and numerically along the curvilinear direction. Numerical examples are used to verify the accuracy, effectiveness, and convergence of this method. Finally, a parametric study of the seismic response of a steep slope in a layered half-space is performed in frequency domain. The results show that the amplification peak occurs at the incident wave angle is 30° for vertical slope. For non-vertical slope, the maximum displacement all occur at the position away from one times slope height form the crest of the slope. Moreover, compared with vertical slope, the topography effect of inclined steep slope is more obvious, and this effect tends to decrease with the increase of the slope angle. Therefore, it can be concluded that the angle of the incident wave and slope angle have a significant effect on the dynamic response of the steep slope.