Influence of gradient wave velocity structure of 3–D Gaussian–shaped rocky hills on seismic wave propagation

The seismic response of terrain sites has long been a hot topic in the field of geophysics and earthquake engineering over decades, which plays a critical role in evaluating the seismic safety of major engineering in mountain areas. In current practice, rocky mountain structures are often treated as a homogeneous body for the simulation of seismic wave propagation, with only the topographic effects taken into account. However, the in-situ stress field can introduce spatial heterogeneity in wave velocity in the hilly body, which may have a significant influence on the seismic wave propagation. In this study, a three-dimensional (3-D) finite element model of a homogeneous Gaussian-shaped hill was first constructed and validated against existing simulations using the boundary element method. Then, an empirical model for the hilly body with shear wave velocity varying with depth in gradients is established based on the results of laboratory tests from the literature. Finally, with the validated model and the empirical relationship, the seismic wave propagation of the 3-D Gaussian-shaped rocky hilly body with gradient shear wave velocity was investigated numerically via the finite element method. The results show that: (1) The gradient shear wave velocity structure of hilly body can significantly influence the seismic wave propagation and alter the spatial distribution of seismic motion near the hilly surface; (2) As the gradient of shear wave velocity structure intensifies, the amplification of surface ground motion on hill generally increases, accompanied by a shift of the transfer function toward lower frequencies; (3) For the complex site effects of rocky hilly body, there exists a complicated interaction effect between the topography and the gradient shear wave velocity structure.