Risk-based mainshock-aftershock performance assessment of SMA braced steel frames
Introduction
Current seismic design methodology of building structures aims to control the seismic response and achieve structural safety considering mainshock events only [1]. However, a number of aftershock earthquakes, varying in magnitude and location, commonly occurs following a mainshock event. Aftershocks may immediately follow the mainshock and can continue over a relatively long period of time. For instance, a moment magnitude Mw of 7.1 earthquake struck Anchorage, Alaska on November 30, 2018, and an aftershock with a magnitude of 5.7 occurred six minutes after the mainshock. A total of 18 aftershocks measured greater than 4.0 occurred in a week, and aftershock with a magnitude of 3.0 or larger is expected to continue for about 300 days after the November 30, 2018 mainshock [2]. Similar sequential seismic events were observed during Wenchuan (China, 2008), Christchurch (New Zealand, 2010–2011), Tohoku (Japan, 2011), Gorkha (Nepal, 2015), and Amatrice (Italy, 2016) earthquakes, and in some of these events, the aftershocks induced additional damage to mainshock damaged buildings and resulted in further disruptions [3], [4], [5], [6], [7]. Therefore, it is important to consider aftershocks in quantifying seismic resilience of building systems.
There has been an increasing interest in performance evaluation of buildings subjected to seismic sequences in recent years. These studies explored the impact of aftershocks on various structural systems including reinforced concrete buildings [8], [9], [10], steel frame buildings [11], [12], [13], [14], and wood frame buildings [15]. Some of earlier studies focused on inelastic spectrum and ductility demand of structures by analyzing nonlinear single-degree-of-freedom systems [16], [17], [18]. Some other studies considered realistic finite element models to study seismic vulnerability of buildings under sequential seismic events and/or explore aftershock fragility and residual capacity of mainshock damaged buildings [19], [20], [21], [22]. However, there have been only a few studies where the aftershock seismic risk assessment was conducted for lateral load resisting systems with bracing or damping systems [23], [24].
To assess aftershock collapse risk, different performance indicators were used to specify damage due to mainshock event. Most studies employed damage states associated to maximum interstory drift thresholds to define post-mainshock damage states [8], [9], [10], [13], [14], [23]. The importance of residual drifts in seismic design was discussed in early work of Pristley [25], but it has been considered as a significant measure of seismic performance assessment only more recently [26], [27], [28]. In particular, with the development of performance-based seismic design approaches, the role of residual drifts in evaluating the performance of multi-story frame buildings has been more closely investigated [29], [30]. FEMA P-58 recommendations use residual drifts to determine post-event condition of buildings and economic feasibility of their repair [31]. Ruiz-Garcia [12], [32] suggested the use of post-mainshock residual drift demand as damage indicator for the prediction of aftershock collapse capacity of steel frame buildings. They argued that peak residual drifts, which can be measured during a structural assessment after a seismic event as opposed to peak interstory drift, can be a better parameter to define mainshock damage levels during seismic assessments under aftershocks.
Shape memory alloy (SMA), a metallic alloy that can recover large nonlinear deformations upon removal of applied load, has been widely explored for seismic applications over the past two decades due to its good energy dissipation capacity and unique self-centering ability [33]. A number of SMA-based passive control devices have been developed to control seismic response of structures while minimizing residual drifts [34], [35], [36], [37], [38], [39]. Most of these devices have relied on the wire form of SMAs and remained to be small-scale devices. A few studies have explored large-scale devices that employ SMA bars. Recently, large-diameter SMA cables that can provide high force capacity similar to SMA bars but have considerably lower cost than SMA bars, have been experimentally characterized [40], [41] and studied for the development of self-centering bracing systems [37], [42]. However, aftershock seismic collapse performance of SMA-based self-centering system has yet to be explored.
The seismic performance of structural frames subjected to mainshock-aftershock sequences can be assessed under a probabilistic framework using the seismic fragility and seismic demand hazard curve methods. In this context, seismic fragility is described as the conditional probability that the engineering demand parameter such as interstory peak or residual drift exceeds a damage state given certain intensity measure. The seismic fragility and ground motion hazard are convolved to generate a seismic demand hazard curve. The seismic demand hazard curve rigorously accounts for the aleatory variability in the intensity measure and the engineering demand parameter. For a direct comparison of structure-dependent intensity measures of different structural systems, e.g. spectral acceleration at the natural period, Sa(T1), seismic demand curves constitute a better option than the seismic fragilities.
The authors presented a probabilistic framework for the seismic performance of steel frame buildings designed with SMA bracing system in a previous work [42]. In particular, they carried out a probabilistic performance assessment to determine the maximum interstory and residual drift hazard curves by incorporating uncertainties in seismic excitation as well as in seismic responses of the evaluated structures. However, these empirical models were developed using recorded motions from active tectonic regions and did not accompany aftershock records. In essence, there is a knowledge gap regarding the effects of aftershocks on ground motions parameters. Aftershock ground motions typically have smaller magnitudes; but, some of their other characteristics such as duration and intensity can be greater than the mainshock records.
The objective of this study is to develop seismic demand hazard curves for the steel moment resisting frames (SMRF) designed with and without SMA cable bracing system and subjected to mainshock – aftershock sequence. To this end, first mainshock incremental dynamic analyses were conducted to determine spectral acceleration demands corresponding to specific mainshock damage states that were defined using both peak interstory drift and residual drift ratios. Then, aftershock incremental dynamic analyses were carried out on the post-mainshock SMRF and SMA frames at three damage states. Seismic demand curves were generated to predict the annual rate of exceedance of different levels of engineering demand parameters. The developed demand curves provide a robust seismic risk evaluation approach in a multi-hazard environment.
Section snippets
Mainshock-aftershock ground motions
Various protocols for selecting ground motion records have been followed in previous studies on aftershock seismic performance assessment [14], [15], [43], [44]. These protocols include but not limited to the use of the same record as both mainshock and aftershock, the use of historical mainshock-aftershock records, or the use of different seismic records as mainshock and aftershock ground motions. Although conflicting results have been reported in the literature regarding the effects of ground
Building description
A four-story steel moment resisting frame (SMRF) building was selected as a case-study structure in this investigation. This building was designed by Lignos [46] to examine the collapse performance of modern steel building frames, and satisfies the design provisions of IBC [47], SEI/ASCE 7 [48] as well as AISC 341 [49]. Note that a 1:8 scale model of the frame was built and tested until collapse on a shake table and the relevant data can be accessed in NEEShub website. The perimeter
Post-mainshock damage states
The seismic and collapse performance of the frame under aftershocks depend on the intensity of the aftershock as well as the damage level of the building subjected to mainshock. In this study, both maximum interstory drift ratio (IDR) and maximum residual interstory drift ratio (RIDR) were utilized to define the initial mainshock damage states. First, three post-mainshock damage states (DSi, i = 1–3) were selected based on maximum RIDR (0.2%, 0.5%, and 1%). Note that FEMA P-58 indicated that
Seismic response of frames under mainshock-aftershock sequences
The characteristics of aftershock ground motion have strong impact on the aftershock performance of the buildings. Fig. 12(a) shows the third floor interstory drift time-history response of SMRF subjected to first a mainshock record GM2 (Northridge/LOS000) to induce DS2 (i.e. 2.5% IDR) and then an aftershock record GM21 (San Fernando/PEL090) at increasing intensities. While the aftershock record is scaled to 0.2 g or 0.6 g, no considerable further damage is observed in the building but when it
Development of seismic demand models
The mainshock and aftershock ground motion characteristics can be remarkably different than each other. Aftershocks typically are smaller in magnitude but they may have greater ground motion characteristics (e.g., higher intensity, longer duration, higher frequency) as compared to mainshocks due to changes in site location and earthquake mechanism. Engineering demand parameters are sensitive to strong motion record features and structure specific parameters including the damping ratio and frame
Conclusions
In this study, the seismic collapse performance of steel moment resisting frames with and without SMA bracing system under mainshock-aftershock sequences were evaluated through a probabilistic hazard framework. A total of 484 artificial mainshock-aftershock sequences were generated using 22 historical far field ground motion records. Two steel frame buildings, a steel moment resisting frame and a steel frame with SMA braces, were designed and modeled in OpenSees. Mainshock and aftershock
CRediT authorship contribution statement
Fei Shi: Writing - original draft, Methodology, Software, Visualization, Formal analysis. Gokhan Saygili: Writing - original draft, Software, Formal analysis. Osman E. Ozbulut: Conceptualization, Writing - review & editing, Supervision. Yun Zhou: Supervision, Funding acquisition.
Declaration of Competing Interest
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
Acknowledgement
The research described in the paper was supported by the Natural Science Foundation of China under grant No. 51878195.
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