Earthquake Engineering for Concrete Dams. Anil K. Chopra
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Figure 1.7.2 Arch dam–water–foundation system.
Formulated in the frequency domain, this method is restricted to linear analysis, and requires special purpose computer programs, e.g. EAGD‐84 for two‐dimensional analysis of gravity dams and EACD‐3D‐1996 for three‐dimensional analysis of arch dams. These freely available programs were developed by graduate students at the University of California, Berkeley, as a part of their research for the doctoral degree, not as commercial software programs. Thus, they lack user‐friendly interfaces to facilitate input of data to define the system to be analyzed and to process response results. Despite these limitations, the aforementioned programs have been employed for seismic design of a few new dams and for seismic evaluation of several existing dams.
Figure 1.7.3 Finite‐element model of a dam–water–foundation system with wave‐absorbing boundaries.
Although linear analyses have provided great insight into the earthquake response of concrete dams, it is evident that a reliable estimate of the seismic safety of a dam can be obtained only by a nonlinear analysis if the earthquake damage is expected to be significant. The nonlinear model must recognize the possibility that the reservoir may extend to great distances upstream of the dam and the supporting rock extend to large depths and large distances in horizontal directions (Figures 1.2.1 and 1.2.2). The Direct FEM, presented in Chapter 11, overcomes the limitations of the standard FEM by introducing wave‐absorbing (or non‐reflecting) boundaries at two locations: (i) upstream end of the fluid domain to model its essentially semi‐infinite length; and (ii) the bottom and side boundaries of the foundation domain to model its semi‐unbounded geometry (Figure 1.7.3). The finite‐element model of the fluid domain now includes water compressibility and reservoir bottom sediments, and the finite‐element model of the foundation domain includes mass, stiffness, and material damping appropriate for the rock; water–foundation interaction is also included. Thus, the untenable assumptions of massless rock and incompressible water in the popular FEM are eliminated.
The earthquake excitation also is more realistically defined in the Direct FEM compared to the popular FEM. The excitation defined at the bottom and side boundaries of the foundation domain is determined by deconvolution of the design ground motion, typically specified on level ground at the elevation of the abutments (Figure 1.7.3). The resulting spatially varying motions cannot be input directly at wave‐absorbing boundaries; instead, tractions determined from the motions are specified.
Presented in Chapter 11, the direct FEM has the great advantage over the substructure method in that is it applicable to nonlinear systems, thus permitting modeling of concrete cracking, as well as sliding and separation at contraction joints, lift joints, dam–foundation interface, and fissures in rock; however, it has the disadvantage in that it requires truncation of fluid and foundation domains, thus requiring absorbing boundaries to simulate their semi‐unbounded size. This method has been developed in a form that can be implemented in any commercial finite‐element code; thus, it is applicable to 3D models of all types of concrete dams: gravity, arch, and buttress. Validation of the Direct FEM applied to linear systems against the substructure method is also included in Chapter 11.
1.8 SCOPE AND ORGANIZATION
The primary goals of the book are: (i) develop dynamic analysis procedures to determine the response of concrete dams to ground shaking; (ii) identify factors that must be included in the response analyses; (iii) describe procedures for selecting ground motions for dynamic analyses; and (iv) illustrate application of these procedures to the seismic design of new dams and safety evaluation of existing dams. Ground shaking is the only earthquake hazard that is considered; excluded are hazards such as fault rupture under the dam or its abutments, and landslides around the reservoir that may cause overtopping of the dam.
The book is organized into three parts: I. Gravity Dams: Chapters 2–7; II. Arch Dams: Chapters 8–11; and III. Design and Safety Evaluation: Chapters 12–14. Part I and Part II are developed to address the first two of the above‐stated goals for gravity dams and arch dams, respectively. The various topics covered in Chapters 2–11 were mentioned in the preceding sections.
Part III includes three chapters. In Chapter 12, two levels of design earthquakes are defined and the performance requirements for the dam during each earthquake stated, among other topics. Chapter 13 is concerned with construction of the target design spectrum as well as selection of an ensemble of three‐components of ground motions consistent with this spectrum. The book closes with Chapter 14 where application of modern dynamic analysis procedures to four projects are summarized.
NOTES
1 † The first part of this section is adapted from a National Research Council report (1990).
2 ‡ The word “foundation” denotes the rock that supports the dam.
3 † “Reservoir” is the place of storage, not the fluid itself.
Part I GRAVITY DAMS
2 Fundamental Mode Response of Dams Including Dam–Water Interaction
PREVIEW
The motions of a dam during an earthquake cause dynamic pressures in the impounded water that act on the upstream face of the dam to modify the dam motions, which in turn influence the hydrodynamic pressures. It is this interaction between the dam and water that is the subject of this chapter. Considering only the fundamental mode of vibration of the dam, we first develop