Nonlinear Seismic Dam and Foundation Analysis Using Explicit Newmark Integration Method with Static Condensation

Abstract

Engineers use the explicit Newmark integration method to analyze nonlinear dynamic problems. Instead of using computationally expensive global matrix assembly and factorization, the explicit integration method performs computations at element level which is computationally efficient, easily parallelizable, and does not require equilibrium iterations in case of nonlinear analysis. On the other hand, the explicit schema might require much smaller time steps compared to implicit integration alternative especially for models with high stiffness and low mass density. A problem type that might suffer from such a disadvantage is the seismic analysis of dams and their foundation. In these type of problems, the foundation is usually assumed massless in order to model the wave propagation realistically. For this purpose the foundation is modeled with zero or very small mass density which makes the use of explicit integration method almost impossible. Modeling the foundation with zero mass would result in indefinite solutions and modeling the foundation with very small mass density would result in very small time steps, and make the analysis computationally inefficient. In this study, static condensation method is utilized to reduce the full stiffness matrix of the foundation to the degrees of freedom at the dam-foundation interface. This way the foundation can be modeled with zero mass and integrated by the explicit Newmark integration method. Thus, an explicit integration algorithm with static condensation was implemented on a previously developed high performance parallel finite element analysis framework and tested on a 32 cores high performance computing system. The efficiency and accuracy of the proposed approach was examined by performing nonlinear time history analysis on several 3D dam and foundation models with different mesh densities.