Three-degree-of-freedom rigid model for seismic analysis of cracked concrete gravity dams

A rigid model with three-degrees-of-freedom is proposed for the purpose of seismic analysis of cracked concrete gravity dams. The model considers the geometry of the dam and all its possible modes of motion: sliding, rocking, rock-sliding, and drifting. The governing equations for all the modes are derived with the Mohr-Coulomb friction assumption at the crack, and corresponding conditions to initiate and maintain the modes are also given. For impact that follows rocking and drifting modes, postimpact velocities of the model are explicitly determined according to the momentum principle and the concept of restitution from classical point collision. Studies with the proposed model on rectangular blocks demonstrate two different types of rocking according to the slenderness. Applications to dams indicate that a large coefficient of friction does not necessarily prevent sliding, and rocking and drifting modes should not be neglected in estimating the stability of concrete gravity dams cracked at the base or at a height.