Analysis of wave propagation and soil–structure interaction using a perfectly matched layer model

• PML performance is significantly improved.
• Novel requirement for minimal PML depth is established.
• Frequency dependent attenuation is employed.
• Optimal wave attenuation is proposed in pre-calculation step.

This paper presents an application of a perfectly matched layer as an absorbing condition for solution of linear wave equations for unbounded domains. The perfectly matched layer can be combined with different numerical methods. In this particular case, a frequency dependent finite element formulation has been pursued. What is most significant is that it utilizes a newly established requirement for definition of the perfectly matched layer, which improves the accuracy and efficiency of the method. In this study, different definitions of the attenuation were considered to optimize the performance of the radiation condition. They were verified in comparison with an exact solution of wave propagation in a half-plane. This analysis was used later to establish a requirement for definition of minimum layer depth as an accuracy prerequisite. Similar requirements are presented for the other nonphysical attenuation parameters. The advantages of the proposed model for a rigid foundation over a half-plane are shown in comparison to other solutions from the literature, but also to exact analytical result. The importance of well-defined boundary condition is best demonstrated when compared to a model with viscous damper boundary. In fact, even if a perfectly matched layer is a rigorous boundary condition, it performs much better, reducing the computational time in half by using fewer elements. Moreover, an application of the approach is presented where the kinematic effects of vibrating foundation for different ground conditions are evaluated.