Overturning of Retrofitted Rocking Structures under Pulse-Type Excitations

Abstract

Numerous existing structures exhibit rocking behavior during earthquakes, and there is a continuing need to retrofit these structures to prevent collapse. In addition, while rocking behavior is typically prevented instead of utilized, an increasing number of structures are being designed or retrofitted to allow rocking motion as a means of seismic isolation. This paper investigates the use of viscous damping to limit the rocking motion by characterizing the fundamental behavior of damped rocking structures through analytical modeling. A single rocking block analytical model is used to determine the viscous damping characteristics, which exploit the beneficial aspects of the rocking motion, while dissipating energy and preventing overturning collapse. To clarify the benefits of damping, overturning envelopes for pulse-type ground accelerations are presented and compared with the pertinent envelopes of the free rocking block. A semianalytical solution to the linearized equations of motion enables rapid generation of collapse diagrams for pulse excitations, which provide insight into the overturning mechanisms of the damped rocking block and the sensitivity of the response to the parameters involved. In addition, through solution of the nonlinear equations of motion, bilateral and unilateral linear viscous dampers are shown to provide similar benefit toward preventing overturning, while nonlinear damping is found to provide relatively little and inconsistent benefit with respect to linear damping.