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

Panayiotis C. Roussis*, Spyroulla Odysseos
Department of Civil and Environmental Engineering, University of Cyprus, Nicosia, CY-1678, Cyprus

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© 2017 Roussis and Odysseos.

open-access license: This is an open access article distributed under the terms of the Creative Commons Attribution 4.0 International Public License (CC-BY 4.0), a copy of which is available at: This license permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.

* Address correspondence to this author at the Department of Civil & Environmental Engineering, University of Cyprus, Nicosia, 1 Panepistimiou Avenue, 2109 Nicosia, Cyprus; Tel: +357 22892210, E-mail:



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.


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.


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.


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.


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.

Keywords: Seismic isolation, Rigid block, Rocking, Impact, Overturning, Pulse-type base excitation.