Rocking Response of Seismically-Isolated Rigid Blocks Under Simple Acceleration Pulses and Earthquake Excitations

Background: Although the dynamic response of rigid block-like structures standing free on a rigid foundation has been extensively studied to date, only a limited number of studies have focused on the dynamics of such systems when seismically isolated. Objective: This paper presents a comprehensive investigation on the dynamic response of base-isolated rigid blocks subjected to pulse-type base excitation, with the aim of identifying potential trends in the response and stability of the system. Method: The model adopted in this study consists of a rectangular-prismatic rigid block standing free on a seismically-isolated base, which, on the assumption of sufficiently-large friction, can be set into rocking on top of the moving base under dynamic excitation. The study examines in depth the motion of the block/base system with a large-displacement formulation that combines the nonlinear equations of motion with a rigorous model governing impact. Two isolation-system models are utilized in the analysis, a linear viscoelastic model and a bilinear hysteretic model. Results: An extensive numerical investigation was performed to calculate the rocking response of the block under simple acceleration pulses and recorded pulse-type earthquake motions of various amplitudes and frequency content. Response-regime spectra for non-isolated and isolated blocks of varying geometric characteristics have been constructed to evaluate the system performance with respect to the rocking initiation and overturning of the block. Conclusion: The study showed that, regardless of block size and excitation period, seismic isolation increases the acceleration required to initiate rocking, a benefit that increases as the isolation period increases. In regard to the stability of the rocking block, the use of isolation yields a better system performance for smaller-sized blocks both for short- and mid-period excitations, provided that the isolation system is suitably designed. On the contrary, for long-period pulses, the use of isolation is practically not beneficial in improving the stability of the rocking block, irrespective of its size.

Closed-form rocking overturning conditions for a family of pulse ground motions

This paper characterizes the stability of a rigid rocking block subjected to a family of multi-lobe pulse ground motions. It unveils a counter to intuition plurality of overturning (OT) modes despite the short duration and bounded energy of the examined ground motions. Accordingly, it describes with original closed-form expressions the critical conditions of all OT modes involving a finite number of impacts. It also proposes pertinent semi-analytical, exact analytical and approximate analytical solutions with respect to the determination of the (unknown) times of impact, as appropriate. The analysis reveals that the first , or lower bound , critical OT mode is in most cases toppling during free rocking after one impact specifically before the end of the pulse. For this case, it elucidates the physical mechanism behind the timing of impact that produces minimum amplitude and maximum amplitude critical OT, respectively, and proposes pertinent closed-form approximations. Finally, the study derives, in ‘universal’ terms, global ‘safety walls’ against rocking OT considering a large number of different pulse shapes.

Oscillations Control of Rocking-Block-Type Buildings by the Addition of a Tuned Pendulum

This study deals with the dynamical evolutions exhibited by a simple mechanical model of building, comprising a parallelepiped standing on a horizontal plane. The main goal is the introduction of a pendulum in order to reduce oscillations. The theoretical part of the work consists of a Lagrange formulation and Galerkin approximation method, and dry friction has also been considered. From the analytical/numerical simulations, we derive some important conclusions, providing us with the tools suitable for the design of absorbers in practical cases.