Perfectly matched layers for acoustic and elastic waves: Theory, finite-element implementation and application to earthquake analysis of dam-water-foundation rock systems.

摘要

This dissertation develops the perfectly matched absorbing layer model for the modelling of acoustic and elastic wave propagation on unbounded domains, and applies it to a particular coupled multi-physics scattering problem, the earthquake analysis of dam-water-foundation rock systems.;A perfectly matched layer (PML) is an unphysical absorbing layer model for linear wave equations that absorbs, almost perfectly, outgoing waves of all non-tangential angles-of-incidence and of all non-zero frequencies. This dissertation utilizes insights obtained from electromagnetics PMLs to develop PML models for acoustic and elastic waves for both time-harmonic and transient analysis, and presents novel displacement-based finite-element implementations of these PML models. The PML concept is first explored in the context of a one-dimensional rod on elastic foundation. The ideas thus developed are then used analogously to develop PMLs and corresponding displacement-based finite-element implementations for acoustic and elastic waves in higher dimensions, for both time-harmonic and transient analysis. The time-harmonic FE implementations are symmetric (not Hermitian) and sparse, but intrinsically complex-valued and frequency-dependent. The FE implementations for transient analysis result in linear, sparse, positive-definite systems; the system matrices of the acoustic PML are symmetric whereas those of the elastic PML are not. Numerical results for canonical and classical problems demonstrate the high accuracy achievable by PML models even with small bounded domains.;These PML models are then used to develop an analysis procedure for dam-water-foundation rock systems under earthquake excitation by interpreting it as a scattering problem. The procedure allows modelling of nonlinear and irregular material in and near the dam and permits an arbitrarily-shaped dam, foundation-rock surface, and fluid domain near the dam. The only restrictions on the analysis procedure are the assumptions of linearity in the fluid and foundation-rock domains far from the dam. The analysis procedure accurately accounts for radiation damping, dam-water-foundation rock interaction and spatial variation of ground motion. The use of PML models allows modelling of various unbounded geometries and different (visco-)elastic materials in the foundation rock. The analysis procedure is validated numerically for an idealized system against results from the substructure method, and the capabilites of the analysis procedure are demonstrated by computing the earthquake response of a realistic dam-water-foundation rock system.