Space–time finite element method with domain reduction techniques for dynamic soil–structure interaction problems

Design of earth structures, such as dams, tunnels, and embankments, against the vibrational loading caused by high-speed trains, road traffic, underground explosions, and, more importantly, earthquake motion, demands solutions of the dynamic soil–structure Interaction (SSI) problem. This paper presents a velocity-based space–time finite element procedure, v-ST/finite element method (FEM), to solve dynamic SSI problems. The main goal of this study is to present the computation details of implementing viscous boundary conditions of Lysmer–Kuhlemeyer to truncate the unbounded soil domain. Furthermore, additional time-dependent boundary conditions, in terms of the free-field response, are included to facilitate energy flow from the far field to the computation domain at the vertical truncated boundaries. In the FEM, seismic input motion is applied to an effective nodal force vector, which can be obtained explicitly in the numerical simulations. Finally, the response of a concrete gravity dam resting on an elastic half-space to the horizontal component of earthquake motion is computed and successfully compared with the results of semidiscrete FEM using the Newmark-$$ method.