A Y-shaped artificial boundary and earthquake input scheme for step-shaped layered site and soil-structure interaction analyses

Conventional methods for seismic soil-structure interaction (SSI) are generally limited to horizontally layered half-space sites. Extending them to non-horizontally layered step-shaped sites is challenging due to the lack of effective approaches for evaluating site seismic responses, which are critical for earthquake input in SSI analysis. This study proposes a high-precision Y-shaped artificial boundary and earthquake input scheme for step-shaped layered sites and SSI analyses. First, a Y-shaped artificial boundary is introduced to enclose the numerical model of the two-dimensional (2D) step-shaped layered site and to truncate the remaining domains, which correspond to portions of two different horizontally layered half-spaces. To simulate the radiation damping of the two truncated domains, two artificial boundary conditions are imposed on the Y-shaped boundary, for which two zigzag-paraxial combined boundaries are adopted. The one-dimensional site responses of the two truncated domains are calculated and transformed into two sets of equivalent nodal forces applied to the Y-shaped artificial boundary to implement earthquake input. Furthermore, we also develop a direct method to evaluate the 3D structures, based on the obtained step-shaped layered site responses and a new artificial boundary condition called as the SBPML. Benchmark examples confirm the accuracy, effectiveness, and robustness of the proposed scheme, while comparisons show that conventional hybrid wave input methods may introduce errors up to 20%. The proposed framework enables reliable SSI evaluation in complex step-shaped site conditions.