Seismic behavior of concrete gravity dams with penetrated cracks and equivalent impact damping

The seismic behavior of concrete gravity dams with cracks that penetrate the monoliths has rarely been studied. The treatment of dynamic contact conditions at the cracks is the major difficulty. Not only all the sliding, rocking and drifting modes of motion have to be properly handled, but also specific attention should be focused on impact when the crack is closing. This study employs the FEM and adopts the IDCE (incremental displacement constraint equations) model to deal with all the modes of motion along the cracks. For impact, equivalent damping is introduced based on the concept of coefficient of restitution that is used in collision between point masses. After the IDCE damping model is verified in dynamic contact situations for rigid and flexible bodies, a typical concrete gravity dam with full reservoir water and three cases of crack is investigated under El Centro 1940 NS earthquake excitation. Calculations reveal very interesting phenomena, such as occurrence of rocking and jumping, coupling between the direction of residual sliding and the direction of peak rocking, and the large damping effect of multi-cracks on peak residual sliding, rocking and jumping.