DISCLAIMERThis is the pre-peer reviewed version of the following article: "Løkke, A., and Chopra, AK. (2017) Direct finite element method for nonlinear analysis of semi-unbounded dam-waterfoundation rock systems. Earthquake Engineering and Structural Dynamics, 46: 1267-1285 SUMMARYA direct finite element method is presented for nonlinear earthquake analysis of interacting damwater-foundation rock systems. The analysis procedure applies viscous damper absorbing boundaries to truncate the semi-unbounded fluid and foundation-rock domains, and specifies at these boundaries effective earthquake forces determined from the design ground motion defined at a control point on the free surface. The analysis procedure is validated numerically by computing the frequency response functions and transient response of an idealized dam-waterfoundation rock system and comparing against results from the substructure method. Because the analysis procedure is applicable to nonlinear systems, it allows for modeling of concrete cracking, as well as sliding and separation at construction joints, lift joints, and at concrete-rock interfaces. Implementation of the procedure is facilitated by commercial finite element software with nonlinear material models that permit modeling of viscous damper boundaries and specification of effective earthquake forces at these boundaries.

Summary 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.

A response spectrum analysis (RSA) procedure, which estimates the peak response directly from the earthquake design spectrum, was developed in 1986 for the preliminary phase of design and safety evaluation of concrete gravity dams. The analysis procedure includes the effects of damwater-foundation interaction, known to be important in the earthquake response of dams.This report presents a comprehensive evaluation of the accuracy of the RSA procedure by comparing its results with those obtained from response history analysis (RHA) of the dam modeled as a finite element system, including dam-water-foundation interaction. The earthquake response of an actual dam to an ensemble of 58 ground motions, selected and scaled to be consistent with a target spectrum determined from a probabilistic seismic hazard analysis for the dam site, was determined by the RHA procedure. The median of the peak responses of the dam to 58 ground motions provided the benchmark result. The peak response was also estimated by the RSA procedure directly from the median response spectrum. Comparison of the two sets of results demonstrated that the RSA procedure estimates stresses to a degree of accuracy that is satisfactory for the preliminary phase in the design of new dams and in the safety evaluation of existing dams. The accuracy achieved in the RSA procedure is noteworthy, especially considering the complicated effects of dam-water-foundation interaction and reservoir bottom absorption on the dynamics of the system, and the number of approximations necessary to develop the procedure.Also developed in the report is a more complete set of data for the parameters that characterize dam-foundation interaction in the RSA procedure. Availability of these data should provide sufficient control over the overall damping in the dam-water-foundation system to ensure consistency with damping measured from motions of dams recorded during forced vibration tests and earthquakes.iv v ACKNOWLEDGMENTSWe are grateful to several individuals who helped in this research: Professor Gautam Dasgupta at Columbia University provided the computer program to compute new compliance data for a viscoelastic half-plane.

Summary A direct finite element (FE) method for nonlinear response history analysis of semi‐unbounded dam‐water‐foundation systems has recently been presented. The analysis procedure employs standard viscous‐damper absorbing boundaries to model the semi‐unbounded foundation and fluid domains and specifies the seismic input as effective earthquake forces—determined from a control motion defined at the foundation surface—at these boundaries. Presented in this paper are several simplifications to this direct FE method that greatly facilitates its implementation in commercial FE software. Also addressed is the modeling of the principal nonlinear mechanisms for concrete dams, calibration of damping in the numerical model to ensure consistency with values measured at actual dams, and practical procedures for implementation of the direct FE method with a commercial FE program.

No abstract