Legendre spectral element method for seismic analysis of dam-reservoir interaction

Abstract

It is well-known that dam-reservoir interaction has significant effects on the response of dams to the earthquakes. This phenomenon should be considered more exactly in the seismic design of dams with a rational and reliable dynamic analysis method. In this research, seismic analysis of the dam-reservoir is studied as a wave propagation problem by using Legendre Spectral element method (SEM). The special FEM and SEM codes are developed to carry out the seismic analysis of the damreservoir interaction system. The results of both SEM and FEM models are compared considering the accuracy and the time consumption of the analysis. Attractive spectral convergence of SEM is obtained either by increasing the degree of the polynomials in the reservoir or by the number of elements of dam. It is shown that all boundary conditions of the reservoir domain in the SEM are evaluated by the exact diagonal matrices. The SEM leads to the diagonal mass matrix for both dam and reservoir domains. The stiffness matrices obtained from the SEM are more sparse than the corresponding stiffness matrices in the FEM consequently the SEM needs a significant less time consumption of the analysis.