Direct finite element method for nonlinear earthquake analysis of 3-dimensional semi-unbounded dam-water-foundation rock systems

A direct finite element method for nonlinear earthquake analysis of 2-dimensional dam-water-foundation rock systems has recently been presented. The analysis procedure uses standard viscous-damper absorbing boundaries to model the semi-unbounded foundation-rock and fluid domains and specifies the seismic input as effective earthquake forces at these boundaries. Presented in this paper is a generalization of the direct finite element method with viscous-damper boundaries to 3-dimensional dam-water-foundation rock systems. Step-by-step procedures for determining the effective earthquake forces starting from a ground motion specified at a control point on the foundation-rock surface is developed, and several numerical examples are computed and compared with independent benchmark solutions to demonstrate the effectiveness of the analysis procedure for modeling 3-dimensional systems.