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This work aims to determine the dynamic response of dam–reservoir–foundation systems subjected to asynchronous ground motion. To this end, two-dimensional variable-noded solid and fluid finite elements based on a Lagrangian approach were implemented as subroutines in Fortran 77. These subroutines were incorporated into the program MULSAP, which performs asynchronous dynamic analyses of structural systems; MULSAP, extended for fluid–solid systems, was used to model dam–reservoir–foundation interactions. For comparison, the subroutines were also integrated into SAP IV to perform classical (synchronous) dynamic analyses and to examine the infinite-velocity case. This PhD study comprises five chapters. Chapter 1 introduces the problem, reviews previous work on uniform and asynchronous ground motion effects on dams, and defines the scope of the research. Chapter 2 derives the basic displacement-based (Lagrangian) relations for fluid behavior and, using these relations, develops the finite element formulation for fluid systems; it then presents the dynamic formulation for coupled fluid–solid systems under asynchronous ground motion. Compressibility of the fluid and free-surface sloshing motions are included in the fluid formulations. Chapter 3 describes baseline correction and integration procedures for strong-motion acceleration records and presents numerical applications using various recorded accelerograms. Chapter 4 applies the formulations of Chapter 2 to a sample concrete gravity dam. Using the dam data, modal analyses and asynchronous dynamic analyses were performed for several wave-propagation velocities. In the modal analysis section, Eulerian and Lagrangian solutions, MULSAP and SAP IV results, foundation models with and without mass, and full/empty reservoir conditions are compared; the first 30 mode shapes of the coupled system are also presented. In the asynchronous dynamic analysis section, horizontal and vertical ground displacement shape vectors (r-vectors) are computed. MULSAP results for the infinite-velocity case are compared with SAP IV results, and the effects of asynchronous horizontal and vertical ground motion on the frequency content, stress amplitudes, and hydrodynamic pressures are investigated. The impacts of ground displacement, reservoir presence, and foundation mass on the response are also examined. Chapter 5 summarizes the conclusions and provides detailed recommendations based on the study.
In this study, the dam–water–foundation interaction is described in a combined mathematical model. The static and dynamic analyses of concrete gravity dams were carried out by the finite element method. It was assumed that materials are linear elastic. A dam with a foundation 242 meters in length and 48 meters in depth was considered. The effect of the co-vibrating soil mass on the natural frequencies was studied. In the added mass approach, effects of the fluid on the dynamic properties of the structure are modeled as an apparent fluid mass added to the structural mass. The structure is therefore solved without the fluid, but the structural mass matrix is modified to include the added mass due to the fluid. The study consists of eight chapters. The first chapter outlines the study. The second chapter provides general considerations in designing concrete gravity dams. The third chapter presents the theoretical investigation of the static and dynamic analyses of concrete gravity dams. The fourth chapter gives general information about the finite element and shear beam methods. The fifth chapter presents static analyses of concrete gravity dams by the finite element method for the following cases: full dam — flexible foundation, full dam — fixed foundation, empty dam — flexible foundation, and empty dam — fixed foundation. The sixth chapter covers the dynamic analyses by the finite element method for the same cases. Additionally, dynamic analyses using the shear beam method (assuming a fixed foundation) were performed for both full and empty dam cases. In the seventh chapter, results of the static and dynamic analyses are compared. In the dynamic analysis, taking into account the 0.33 g maximum ground acceleration of the north–south component of the El Centro earthquake (1940), the design spectrum developed by Housner was considered. The results obtained from these studies are summarized in the eighth chapter.