Nonlinear earthquake response of concrete gravity dam systems

Abstract

The earthquake response of concrete gravity dam systems is investigated with emphasis on the nonlinear behavior associated with tensile concrete cracking and water cavitation. A single dam-monolith is considered and is assumed to respond independently as a two-dimensional system under plane stress conditions. The two-dimensional assumption is also extended to model the compressible water body impounded upstream of the dam. Standard displacement-based finite element techniques are used to spatially discretize the field equations and produce a single symmetric matrix equation for the dam-water system. Energy dissipation in the reservoir, through radiation in the infinite upstream direction and absorption at the bottom, is approximately accounted for, and a set of numerical examples is presented to demonstrate the accuracy of the present formulation in modeling the linear earthquake response of infinite reservoirs. An approximate procedure to account for dam-foundation interaction is incorporated based on the response of a rigid plate attached to a three-dimensional viscoelastic halfspace. Water cavitation is modeled by a smeared approach which uses a bilinear pressure-strain relation. It is shown that the water response becomes dominated by spurious high frequency oscillations upon closure of cavitated regions, and improved results can be obtained by using some stiffness-proportional damping in the water reservoir. As demonstrated in an example analysis of Pine Flat Dam (linear dam), cavitation occurs in the upper part of the reservoir along the dam face, unlike other investigations which show cavitated regions at considerable distances from the dam, and both the tensile pressure cutoffs and compressive impacts have a minor effect on the dam response. Tensile cracks are incorporated using the smeared crack approach, and sliding along closed cracks is allowed. Coupling effects inherent in the finite element formulation are explained, and their influence on open and closed cracks is investigated. Propagation of cracks is monitored in an interactive environment which uses an equivalent strength criterion and allows for user input; remeshing is avoided. The algorithm adopted here produces narrow cracks, unlike many other investigations which show large zones of cracking. An extensive numerical study of Pine Flat Dam demonstrates some interesting features of the nonlinear response of the system, identifies potential failure mechanisms, and reveals a number of difficulties that the analysis encounters. Although no instability of the dam occurs, the numerical difficulties will have to be overcome before definite conclusions regarding stability can be made. It is shown that cracking reduces the hydrodynamic pressures in the reservoir and, hence, reduces water cavitation.

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