Elasto‐Plastic Seismic Response of 3‐D Earth Dams: Theory

Abstract

A simplified cost‐effective analytical‐numerical procedure is developed for the nonlinear hysteretic seismic analysis of three‐dimensional (3‐D) nonhomogeneous, one‐zone earth dams. The procedure can be applied efficiently to problems of the nonlinear dynamic response of soil and/or soil‐structure systems. The procedure is based on a Galerkin formulation of the 3‐D equations of motion in which the solution is expanded using 3‐D eigenmodes of the linearized 3‐D problem. The linear mode shapes are obtained using low‐strain elastic moduli and a variational energy approach utilizing both Hamilton's principle and the Rayleigh‐Ritz method. The nonlinear approach is based on a modal discretization of the spatial domain in which 3‐D linear modes are coupled due to material nonlinearity. The dynamic constitutive behavior of the dam materials is modeled using the concept of multiyield surface incremental plasticity in which a purely kinematic hardening rule is adopted. Spatial integrations are performed using a numerical scheme in which Gaussian quadrature is adopted. The time integration of the resulting semidiscrete matrix equation is performed using the Newmark method. Finally, in the analysis, all three directional input ground motions are considered simultaneously; nonlinear dynamic transient solutions, including permanent deformations, can be obtained at modest computational expenses.