Direct-Finite-Element Method for Nonlinear Earthquake Analysis of Concrete Dams Including Dam–Water–Foundation Rock Interaction
Authors: Lokke Arnkjell , Chopra Anil 
Published: October 2023

Evaluating the seismic performance of concrete dams requires nonlinear dynamic analysis of two- or three-dimensional dam–water–foundation rock systems that include all the factors known to be significant in the earthquake response of dams. Such analyses are greatly complicated by interaction between the structure, the impounded reservoir and the deformable foundation rock that supports it, and the fact that the fluid and foundation domains extend to large distances. Presented in this report is the development of a direct finite-element (FE) method for nonlinear earthquake analysis of two- and three-dimensional dam–water–foundation rock systems. The analysis procedure applies standard viscous-damper absorbing boundaries to model the semi-unbounded fluid and foundation domains, and specifies at these boundaries effective earthquake forces determined from a ground motion defined at a control point on the ground surface. This report is organized in three parts, with a common notation list, references, and appendices at the end of the report. Part I develops the direct FE method for 2D dam–water–foundation rock systems. The underlying analytical framework of treating dam–water–foundation rock interaction as a scattering problem, wherein the dam perturbs an assumed "free-field" state of the system, is presented, and by applying these concepts to a bounded FE model with viscous-damper boundaries to truncate the semi-unbounded domains, the analysis procedure is derived. Step-by-step procedures for computing effective earthquake forces from analysis of two 1D free-field systems are presented, and the procedure is validated by computing frequency response functions and transient response of an idealized dam–water–foundation rock system and comparing against independent benchmark results. This direct FE method is generalized to 3D systems in Part II of this report. While the fundamental concepts of treating interaction as a scattering problem are similar for 2D and 3D systems, the derivation and implementation of the method for 3D systems is much more involved. Effective earthquake forces must now be computed by analyzing a set of 1D and 2D systems derived from the boundaries of the free-field systems, which requires extensive book-keeping and data transfer for large 3D models. To reduce these requirements and facilitate implementation of the direct FE method for 3D systems, convenient simplifications of the procedure are proposed and their effectiveness demonstrated. Part III of the report proposes to use the direct FE method for conducting the large number of nonlinear response history analyses (RHAs) required for performance-based earthquake engineering (PBEE) of concrete dams, and discusses practical modeling considerations for two of the most influential aspects of these analyses: nonlinear mechanisms and energy dissipation (damping). The findings have broad implications for modeling of energy dissipation and calibration of damping values for concrete dam analyses. At the end of Part III, the direct FE method is implemented with a commercial FE program and used to compute the nonlinear response of an actual arch dam. These nonlinear results, although limited in their scope, demonstrate the capabilities and effectiveness of the direct FE method to compute the types of nonlinear engineering response quantities required for PBEE of concrete dams.