Earthquake Engineering for Concrete Dams Design, Performance, and Research Needs (1990) / Chapter Skim
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4. Nonlinear Analysis and Response Behavior
4. Nonlinear Analysis and Response Behavior
Pages 61-79
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From page 61... ...
In this chapter the nonlinear behavior important in the earthquake response of concrete dams and the requirements for nonlinear analysis are identified. In addition, recent developments in modeling and analysis of such dams are summarized, and further research needed to improve the seismic safety evaluation is outlined.
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From page 62... ...
For example, assuming a compressive strength of 4,000 psi, nonlinear behavior is important for compressive stresses greater than about 2,000 to 2,400 psi. But linear elastic dynamic analyses of gravity and arch dams show that compressive stresses rarely exceed this range during typical earthquakes; consequently, the nonlinear behavior of concrete in compression, including hysteretic energy dissipation, can generally be neglected in the earthquake response analysis of dams.
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From page 63... ...
Both linear analyses and model studies of arch dams have indicated related failure modes: extensive tensile cracking that results in the formation of a semicircular or rectangular notch near the crest, leading to dynamic instability of the notched portion. Although it is not certain that such a failure can actually develop in an arch dam due to an earthquake, or that crack propagation completely through a dam section necessarily results in instability, the major goal of a safety evaluation is to determine whether unstable response could develop due to credible levels of earthquake ground motion.
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From page 64... ...
On the other hand, the nonlinear behavior of the joints may limit the earthquake response of large (long-period) dams by further lengthening the vibration period, thereby reducing the dynamic amplification that is a function of the vibration properties of the dam and characteristics of the ground motion (3-17~.
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From page 65... ...
For these reasons a realistic safety evaluation based on nonlinear analysis would require a detailed seismotectonic study of a dam site and the development of appropriate site-specific ground motion records. The nonlinear behavior mechanisms mentioned above (tensile cracking of concrete, loss of joint integrity, and foundation failure)
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From page 66... ...
Because of the large amount of computation required to obtain the nonlinear dynamic response of a concrete dam system, it is mandatory to truncate the size of the water and foundation rock domains; however, the boundaries should be modeled in a manner that allows radiation of energy from the system. Methods for reducing the number of generalized coordinates while still representing the nonlinear behavior of a dam system may be explored (4-4~.
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From page 67... ...
Although researchers and practitioners have investigated limited aspects of the nonlinear behavior of concrete dams, a great deal of innovative analytical research must yet be done to develop practical nonlinear response analysis procedures; in addition, the results of such analyses must be verified by careful experimentation before the procedures can be fully accepted for earthquake safety evaluation of concrete dams. CRITERIA FOR SAFETY EVALUATION Although the criteria for evaluating the seismic performance of concrete dams are discussed in detail in Chapter 6, it is pertinent to note here that performance criteria based on nonlinear response evaluations are especially important.
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From page 69... ...
Experimental Research Experimental investigations of the nonlinear behavior and failure mechanisms for concrete dams are discussed in Chapter 5 of this report, but the testing of the materials used in such dams is discussed briefly in the following paragraphs. Most mathematical models for tensile cracking are based on data from direct uniaxial, split-cylinder, and flexural tension tests.
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From page 70... ...
, where it is recommended that the tensile strength be increased by 50 percent to include the effect of strain rates typical in the earthquake response of dams. Models for Concrete Cracking Early work in evaluating the static behavior of reinforced concrete members, including tensile cracking, used the finite element method with predefined cracks modeled by separations between elements (4-16~.
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From page 71... ...
Analytical Research Numerical computation of the nonlinear earthquake response of concrete dams has received more attention than physical testing of models and materials. An early investigation of the nonlinear response of gravity dam monoliths used a biaxial failure model for concrete (4-25~.
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From page 72... ...
Figure 4-3 shows the crack that forms in the same 400-ft-high gravity dam monolith with full reservoir when subjected to horizontal and vertical ground motions with maximum acceleration of 0.50 g and 0.30 g, respectively. The narrow crack zone extends from the stress concentration at the downstream face, turning down near and parallel to the upstream face.
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From page 73... ...
. earthquake analysis of gravity dam monoliths, neglecting interaction with the water and foundation rock (4-31~.
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From page 74... ...
Other applications of fracture mechanics concepts to concrete dams are described in references 4-32 and 4-33. There have been two particularly noteworthy earthquake studies of arch dams that included the nonlinear behavior of construction joints.
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From page 75... ...
During severe ground motion some cantilever blocks lifted off their supports, and large compressive cantilever stresses developed, possibly invalidating the assumption of no joint slip and linear behavior of the concrete in compression. Nonlinear analysis of concrete dams allows for the inclusion of other phenomena that may affect the earthquake response.
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From page 76... ...
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From page 77... ...
Identification of a set of parameters that are predictive of nonlinear dynamic behavior of concrete would be an important advance. The material model should allow multiaxial stress states, including criteria for tensile cracking and propagation of cracks, strain rate effects, and shear stress transfer by aggregate interlock.
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From page 78... ...
Research should identify methods for reducing the computational effort, while still representing the important nonlinear behavior of the system, so that nonlinear analysis can be used for routine design and evaluation of dams. Although the finite element method and time integration of the equations of motion appear to be the most useful techniques for nonlinear dynamic analysis of concrete dams, other discretization methods and procedures for solving nonlinear equations of motion should not be precluded.
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From page 79... ...
Although nonlinear earthquake analysis may not become a standard practice in design offices, design criteria should recognize the tensile strength of concrete and postcracking stability of gravity and arch dams and identify acceptable limits of such behavior. Comparison of the predicted nonlinear response with the more easily calculated linear response would be useful to determine the limits of assessing nonlinear behavior based on the results of linear elastic analysis.
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