Development and Validation of the HDI Matrix Method for Fluid–Dam Interaction

Abstract

This paper presents the theoretical development of a practical numerical method for analysis of complex dam-reservoir interaction problems. The proposed approach takes advantage of the combination of boundary and finite element methods (BEM-FEM) for an independent analysis of two physically distinct dam structure and reservoir-foundation domains. It involves the matrix of hydrodynamic influence (HDI) based on the application of the virtual work principle to the fluid (BEM) domain to calculate the hydrodynamic forces (HDF). Equilibrium between hydrodynamic forces and absolute accelerations is obtained by repetitive solution of the dynamic equation for the FEM domain only until the Euclidean norm of the vector of residual errors at the interface nodes becomes smaller than the prescribed tolerance. The method allows effective consideration of compound wave-field of compressive and dilatational waves and wave-scattering effects for a more realistic evaluation of the interaction phenomenon. A validation procedure is presented through comparisons with analytical and numerical solutions of simple two-dimensional (2D) and three-dimensional (3D) problems. A realistic 3D example of a concrete gravity dam subjected to seismic excitation is given at the end. The method yields fast and accurate results without the necessity of time-consuming iterative computation of dependent variables in both domains.