# Seismic behavior of cracked concrete gravity dams

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## Abstract

Two models are proposed to analyze the seismic behavior of cracked concrete gravity dams in order to assess the safety against sliding and overturning. A proposed rigid model first designed for cracked concrete dams considers the geometry of the cracked dam and includes all possible modes of motion with 3 degrees-of-freedom. The other model proposed is a flexible finite element model, which represents a penalty approach, based on the incremental displacement constraint equations between the nodes on both sides of the crack. All governing equations and corresponding conditions for every mode of motion are derived for the rigid model. Verifications show that this simple rigid model is effective in the prediction of the seismic response of cracked dams. Its applications to the cracked Koyna Dam and a typical dam cracked at the base demonstrate its advantages of simplicity, accuracy and ability to reveal the important features of seismic behavior of cracked concrete dams. The flexible model is verified with available solutions, showing its very good applicability in estimation of the dynamic response of cracked concrete dams, owing to its adequate treatment of contact conditions at the crack. Its applications to Koyna Dam and a typical dam prove its adequacy to the cases of cracks at both the base and at a height. Computations with both proposed models show that the cracked Koyna Dam and the cracked typical dam are safe under the earthquakes considered provided the effective coefficient of friction is sufficient large. However, both models suggest that the rocking mode must be considered since it affects the sliding displacement even if the rocking itself is very small. The partial dam above the crack might experience drifting if severe impact occurs. Therefore even a large coefficient of friction cannot prevent sliding. The residual sliding displacement along the crack for a specific cracked dam depends on factors such as coefficient of friction, water level, peak acceleration of earthquake and its details. The consistency of two proposed models is noted when increasing the stiffness in the flexible model. This suggests that the rigid model is applicable to the case when the upper part of the cracked dam is very stiff, while the flexible model is capable of revealing more details of the seismic behavior of cracked dams.

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