Absorbing Layers Formed by Distributed Viscous Dashpots

Abstract

The modeling of soil–structure dynamic interaction poses the challenge of properly representing the unbounded nature of the physical medium through absorbing boundary conditions. In recent years, Perfectly Matched Layers (PML) have represented a major breakthrough in this field. Although these boundary conditions are highly effective, they often exhibit numerical instabilities that hinder the time-domain integration of the equations of motion and restrict their application to linear systems. On the other hand, viscous boundaries offer a simple and fully stable alternative, but they show deficiencies in absorbing low-frequency waves, which are typical of seismic events. This work proposes a technique that combines the advantages of both approaches: the viscous boundary constant is distributed over a given length, forming an absorbing layer. The result is an accurate, stable, and easily implementable boundary condition. The proposed method is introduced through a one-dimensional case. Numerical results are validated by comparisons with reference analytical solutions.