# A numerical approach applied to three-dimensional wave scattering problems subjected to obliquely propagating incident waves

## TL;DR

This paper introduces a numerical method to model 3D seismic wave scattering for oblique wave directions, improving accuracy in semi-infinite domains.

## Contribution

A novel method for handling arbitrary incident directions in 3D seismic wave scattering using viscoelastic boundaries and coordinate transformations.

## Key findings

- The method enables accurate modeling of oblique seismic wave inputs in three-dimensional scenarios.
- The implementation of transmitting boundary conditions and wave inputs supports scattering problems at any incident angle.
- Comparative analysis shows the method's effectiveness in assessing soil-structure dynamic interactions under oblique seismic waves.

## Abstract

Accurately modeling artificial boundary conditions and wave inputs is paramount for numerical simulations of wave scattering in semi-infinite domains within seismic engineering. Traditionally, analysts focused on one- or two-dimensional free-field problems to determine wave inputs, primarily for vertically incident plane waves or obliquely incident waves parallel to two axes. However, these methods were inadequate for handling arbitrary incident directions in three-dimensional scenarios. This paper proposes a method for modeling seismic wave incidents in arbitrary directions. The basic theory of viscoelastic boundaries is leveraged, and a plane containing an arbitrary incident direction and the vertical coordinate axis is selected to establish a two-dimensional plane coordinate system. The two-dimensional free-field problem in this coordinate system is derived using the transfer matrix method. Subsequently, displacement, velocity, and stress are converted into the coordinate system where the three-dimensional calculation model is located, providing input for the three-dimensional scattering problem. Furthermore, the implementation of transmitting boundary conditions and viscoelastic boundary wave inputs is presented to enable incident wave scattering problems at any angle of the plane. The effect of oblique-incidence soil-structure dynamic interaction is also discussed, focusing on the parallel technology method adopted in this paper. With the relatively mature technology route and method, together with nuclear power systems and large-span deep-water bridge models, through examples of comparative analysis, qualitative and quantitative analyses are made on the impact on the soil mass, foundation, and structure when the seismic wave is an oblique incident.