Seismic response of stratified rock slopes due to incident P and SV waves using a semi-analytical approach

Abstract

Based on the theory of elastodynamics and the concept of wave-field separation, a semi-analytical method for the scattering and diffraction of P-SV waves by stratified rock slopes is proposed in this study. The total wave fields are decomposed into the free field with no irregularity and the scattered wave field generated by slope topography. The former is solved directly with the aid of a dynamic stiffness matrix, and the latter is modeled by applying the inclined and horizontal fictitious distributed loads on the corresponding boundaries. Since the methodology is derived from the exact wave equations and the non-singular frequency-domain Green's functions, it can be applied to seismic dynamic response problems for layered slopes with arbitrary incident waves and layer thicknesses, and the presented solutions are high-precision and well-converged. Using a Ricker wavelet as input, the accuracy and effectiveness of the proposed method for both vertically and obliquely incident P and SV waves are fully verified. Taking three actual earthquake records including Taft wave, El Centro wave, and Loma Prieta wave as inputs, several analysis examples are presented. The parametric studies demonstrate that a significant elevation amplification effect can be seen in the ground motion of rock slopes due to the interaction of the upper slope feature with the underlying bedrock half-space. The PGA amplification factor, Fourier spectrum and standard spectral ratio of rock slopes are evidently affected by the slope height, slope angle and shear velocity of the medium. Subsequently, sensitivity analyses are performed on model slopes with varying incident wave frequencies and incident angles to illustrate the broad applicability of the proposed method. Finally, a case study is presented to evaluate the practicality of the presented procedure and highlight the benefits of performing a rapid semi-analytical solution to assess potential hazards of earthquake-induced rock slides.