Transient Analysis of Dam–Reservoir Interaction Using a High-Order Doubly Asymptotic Open Boundary

Abstract

A high-order doubly asymptotic open boundary (DAOB) for the modeling of a semi-infinite reservoir with constant cross section is developed, in which the compressibility of water and the absorption characteristic of a reservoir bottom are considered. The dynamic stiffness matrix is approximated by a doubly asymptotic continued fraction solution with an additional factor matrix to improve its numerical robustness. The continued fraction solution converges throughout the entire frequency range quickly as the increasing orders of approximation and is verified by a rigid dam example. Introducing the auxiliary variables, a temporally local high-order DAOB is formulated. Coupling the high-order DAOB with the finite-element method (FEM) straightforwardly, an efficient procedure for the transient analysis of dam–reservoir interaction is developed and implemented in an open-source finite-element software OpenSees. Gravity dam and arch dam examples subject to dynamic loading conditions including the dam–reservoir interaction are analyzed. It is demonstrated that this proposed procedure is of high accuracy and computational efficiency.