Short communicationEffects of multiple earthquakes on inelastic structural response
Introduction
There is substantial field evidence showing that the sequence of seismic events characterized by an earthquake with moderate intensity, followed by aftershocks with comparable or even higher magnitude, may occur in several hazard-prone regions world-wide ([7], [8], among others), e.g. in California (Mammoth Lakes, 1980; Coalinga, 1983; Whittier Narrows, 1987; Northridge 1994), Italy (Friuli, 1976; Irpinia, 1980; Umbria-Marche, 1997; L’Aquila, 2009), Japan (Kobe, 1995; Niigata, 2004; Tohoku, 2011), New Zealand (Darfield, 2010; Christchurch, 2011) and Turkey (2011 Van Earthquakes,), among many others. Although researchers have yet to agree on the fundamental differences in characteristics between a main shock and major afore- and after-shocks [17], there is a renewed interest in assessing the effects of seismic sequences on the structural response of new and existing buildings and bridges. Early analytical investigations carried out by Mahin [18] showed that the displacement ductility demand of elastic–perfectly plastic single-degree-of-freedom (SDOF) systems may slightly increase at the end of the aftershock with respect to the main shock. Similar results were found by Aschheim and Black [4]. They examined the effects of prior earthquake damage on SDOF stiffness degrading structures and concluded that prior ductility demand has a very minor influence on peak displacement response. It was, however, assumed that prior displacement demands were less than those that would result if the structure was initially undamaged. Elnashai et al. [10], assessing an updated database of seismic records from Europe, California and Japan, observed that the ductility demand required by multiple earthquake ground motions can be remarkably higher than that required by a single event. This finding has been confirmed lately by extensive analytical work on SDOF systems and multi-storey steel buildings [3], [12]. However, the latter numerical studies were neither exhaustive nor conclusive, since they examined only one natural and two artificial far-fault ground motions. More recently, extensive inelastic analyses have been carried out on a large ensemble of as-recorded main- and after-shocks to investigate the effects of repeated earthquakes on inelastic displacement ratios [16], [14], [15]. Nevertheless, hysteretic elastic plastic (bilinear) models were utilized for such nonlinear analyses. It is worth noting that the previous work focused primarily on idealized SDOF systems; additionally it was clearly stated that real sequential earthquakes were not examined as they were considered to render the numerical analyses extremely complex and not leading to transpicuous and practically conclusions, thus highlighting the limitation of the research targets.
The present study discusses the results of an ongoing research aimed at investigating the effects of as-recorded multiple earthquakes on the inelastic response of structural systems. Advanced hysteretic models with stiffness and/or strength degradation were considered to reliably simulate the seismic response of reinforced concrete (RC) structures under earthquake loadings. Inelastic constant ductility spectra are examined, alongside force reduction factor spectra. The results of the inelastic response for a sample RC frame subjected to a suite of multiple natural records are also presented to emphasize the lack of conservatism of the modern seismic codes. The results discussed hereafter are the outcomes of the preliminary analyses carried out on the effects of multiple earthquakes; such results provide some first insight of the inelastic behavior of structural systems that exhibit stiffness deterioration and strength degradation, e.g. existing non-ductile RC buildings.
Section snippets
Earthquake input
The Tohoku earthquake was a magnitude Mw = 9.0 undersea mega-thrust earthquake that occurred on 11 March 2011 off the coast of Japan. The epicenter was approximately 70 km s East of the Oshika Peninsula of Tohoku and the hypocenter at an underwater depth of approximately 32 km s (e.g. [22]). Following the main quake of March 11, there has been a large number (about 1000 up to now!) of moderate-to-high magnitude after-shocks. Five seismic stations are selected to represent a set of sites subjected to
Hysteretic models
Three piecewise hysteretic models were considered to evaluate the inelastic response spectra: the elastic–perfectly plastic, the elastic plastic with linear hardening and the modified Clough model. The elastic plastic model is the simplest hysteretic model and can be employed to simulate the response of framed systems in which the plastic collapse is caused by the simultaneous onset (elastic–perfectly plastic) or the progressive formation (elastic plastic with hardening) of plastic hinges.
Model description
The case study structure consists of a two-storey two-bay RC frame designed for gravity loads. The two bays are 2.55 m long; the interstorey heights are 3.5 m and 3.44 m for the first and second levels, respectively; the roof height is 7.65 m. The frame has deep beams, 0.3 m wide and 0.5 m deep; the columns have square cross-sections (0.3 × 0.3 m). The compressive cylinder strength of concrete is 19.42 MPa. The steel yield strength is 330 MPa. The design uniformly distributed loads are 20.33 kN/m and 13.58
Conclusions
This technical note was aimed at investigating the effects of multiple earthquakes on structures. Inelastic constant ductility acceleration, displacement and force reduction factor spectra were derived for a set of strong motions registered at five stations during the 2011 Tohoku (Japan) earthquake and embracing different magnitudes and source-to-site distances. Comprehensive parametric response spectra were evaluated with degrading (stiffness and/or strength) and non-degrading hysteretic
Acknowledgments
This work was financially supported by the Italian Consortium of Laboratories RELUIS (Project 2010–2013 – Task 1.1.2 – Reinforced and Precast Concrete Structures). Any opinions, findings and conclusions or recommendations expressed in this paper are those of the author and do not necessarily reflect those of the Consortium RELUIS. The author would also like to express his gratitude to the anonymous reviewers who provided insightful comments that have contributed to improve significantly the
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