Numerical Modelling of Radiating Boundary Conditions Combined with Modified Absorbing Boundary Condition for Viscoelastic Wave Propagation

Abstract

Modelling the Sommerfeld radiating boundary is a major challenge appearing in the study of many engineering problems involving elastic wave propagation [1]. Particularly, in the finite element analysis of Structure-Soil-Structure-Interaction (SSSI) problems, where the soil modelling has to be truncated at a finite distance. This truncation of the model at finite boundary leads to reflection of radiating elastic waves. The reflected waves from the boundary will affect the solution and may lead to instabilities in the numerical analysis. Therefore, it is necessary to provide an artificial boundary condition that will transmit the outward propagating waves with minimum or negligible reflections. To address the radiating boundary condition problem, researchers have developed various kinds of formulations over few decades, such as: a). Local Absorbing Boundary Conditions (ABC) [2], b). Absorbing Layers techniques which includes Perfectly Matched Layers [3-4], Caughey Absorbing Layer Method (CALM) [5], Absorbing Layers by Increasing Damping (ALID) [6] c). Boundary element method [7], and d). Infinite elements [8-10]. ABC corresponds to the situation where the boundary is supported on infinitesimal dash-pots oriented normal and tangential to the boundary. Though these boundary conditions are very simple, the major drawback is they are inefficient when the wave impinges the boundary in inclined direction. The key property of a PML that distinguishes it from an ordinary absorbing material is that it is designed such that the propagating waves incident upon the PML from a bulk medium do not reflect on the interface. The CALM consists of defining the absorbing layers at the boundaries of the elastic medium under consideration but requires many absorbing layers which requires much computational time. The objective of this study is to present a method for radiating boundary conditions by using modified ABC to take the effect of viscous damping combining with ALID.