Aftershock collapse fragility curves for non‐ductile RC buildings: a scenario‐based assessment

Recent studies have addressed the computation of fragility curves for mainshock (MS)‐damaged buildings. However, aftershock (AS) fragilities are generally conditioned on a range of potential post‐MS damage states that are simulated via static or dynamic analyses performed on an intact building. Moreover, there are very few cases where the behavior of non‐ductile reinforced concrete buildings is analyzed. This paper presents an evaluation of AS collapse fragility conditioned on various return periods of MSs, allowing for the rapid assessment of post‐earthquake safety variations based solely on the intensity of the damaging earthquake event. A refined multi‐degree‐of‐freedom model of a seven‐storey non‐ductile building, which includes brittle failure simulations and the evaluation of a system level collapse, is adopted. Aftershock fragilities are obtained by performing an incremental dynamic analysis for a number of MS–AS ground motion sequences and a variety of MS intensities. The AS fragilities show that the probability of collapse significantly increases for higher return periods for the MS. However, this result is mainly ascribable to collapses occurred during MSs. When collapse cases that occur during a MS are not considered in the assessment of AS collapse probability, a smaller shift in the fragility curves is observed as the MS intensity increases. This result is justified considering the type of model and collapse modes introduced, which strongly depend on the brittle behavior of columns failing in shear or due to axial loads. The analysis of damage that is due to MSs when varying the return period confirms this observation. Copyright © 2017 John Wiley & Sons, Ltd.     

Probabilistic performance assessment of low‐ductility reinforced concrete frames retrofitted with dissipative braces

The paper illustrates a probabilistic methodology for assessing the vulnerability of existing reinforced concrete (RC) buildings with limited ductility capacity retrofitted by means of dissipative braces. The aim is to highlight the most important parameters controlling the capacity of these coupled systems and specific aspects concerning the response uncertainties. The proposed methodology is based on the use of local engineering demand parameters for monitoring the seismic response and on the development of component and system fragility curves before and after the retrofit. In the first part of the paper, the methodology is illustrated by highlighting its advantages with respect to the existing approaches. Then, its capability and effectiveness are tested by considering a benchmark two‐dimensional RC frame designed for gravity‐loads only. The frame is retrofitted by introducing elasto‐plastic dissipative braces designed for different levels of base shear capacity. The obtained results show the effectiveness of the methodology in describing the changes in the response and in the failure modalities before and after the retrofit, for different retrofit levels. Moreover, the retrofit effectiveness is evaluated by introducing proper synthetic parameters describing the fragility curves and by stressing the importance of employing local engineering demand parameters (EDPs) rather than global EDPs in the seismic risk evaluation of coupled systems consisting in low‐ductility RC frames and dissipative braces. Copyright © 2012 John Wiley & Sons, Ltd.     

A rational H∞‐norm–based approach for the optimal design of seismically excited reinforced concrete frames

A rational approach is presented for minimizing the dynamic response of reinforced concrete framed structures forced by a seismic base acceleration. Reference is made to EC8 regulations, but the presented approach may in principle be applied to structures ruled by any regulation code. Governing equations are set in the frequency domain (and not in the periods domain as usual) so as to enable the adoption of sound approaches for analysis and design of dynamic structures that are typical of automatics. Among these, a novel usage of the H_∞‐norm concept is proposed that determines a rational design approach capable to minimize the structural response with reference to any quantity of engineering interest, eg, the overall compliance and the displacement of a specific point or the interstorey drift. A numerical investigation on a 6‐storey 3‐bay frame is performed, and relevant analysis and design results are presented in much detail to validate the theoretical framework.     

Post‐repair effect of column jackets on aftershock fragilities of damaged RC bridges subjected to successive earthquakes

In light of recent earthquakes, structures damaged during an initial seismic event (mainshock) may be more vulnerable to severe damage and collapse during a subsequent event (aftershock). In this paper, a framework for the development of aftershock fragilities is presented; these aftershock fragilities define the likelihood that a bridge damaged during an initial event will exhibit a given damage state following one or more subsequent events. The framework is capable of (i) quantifying the cumulative damage of unrepaired bridges subjected to mainshock–aftershock sequences (effect of multiple earthquakes) and (ii) evaluating the effectiveness of column repair schemes such as steel and fiber‐reinforced‐polymer jackets (post‐repair effect of jackets). To achieve this aim, the numerical model of repaired columns is validated using existing experimental results. A non‐seismically designed bridge is chosen as a case study and is modeled for three numerical bridge models: a damaged (but unrepaired) bridge model, and two bridge models with columns repaired with steel and fiber‐reinforced polymer jackets. A series of back‐to‐back dynamic analyses under successive earthquakes are performed for each level of existing damage. Using simulated results, failure probabilities of components for multiple limit states are computed for each bridge model and then are used to evaluate the relative vulnerability of components associated with cumulative damage and column repair. Copyright © 2016 John Wiley & Sons, Ltd.     

Simplified non‐linear seismic analysis of infilled reinforced concrete frames

The N2 method for simplified non‐linear seismic analysis has been extended in order to make it applicable to infilled reinforced concrete frames. Compared to the simple basic variant of the N2 method, two important differences apply. A multi‐linear idealization of the pushover curve, which takes into account the strength degradation which occurs after the infill fails, has to be made, and specific reduction factors, developed in a companion paper, have to be used for the determination of inelastic spectra. It is shown that the N2 method can also be used for the determination of approximate summarized IDA curves. The proposed method was applied to two test buildings. The results were compared with the results obtained by non‐linear dynamic analyses for three sets of ground motions, and a reasonable accuracy was demonstrated. A similar extension of the N2 method can be made to any structural system, provided that an appropriate specific R–µ–T relation is available. Copyright © 2004 John Wiley & Sons, Ltd.     

Seismic response analysis of reinforced concrete frames using inelasticity‐separated fiber beam‐column model

Evaluating the inelastic seismic response of structures accurately is of great importance in earthquake engineering and generally requires refined simulation, which is a time‐consuming process. Because the material nonlinearity generally occurs in a small part of the whole structure, many researches focus on taking advantage of this characteristic to improve the computational efficiency and the inelasticity‐separated finite element method (IS‐FEM) proposed recently provide a generic finite element formulation for solving this kind of problems efficiently. Although the fiber beam‐column element is widely used for the simulation of reinforced concrete (RC) framed structures, the inelastic deformation is often detected in a large part of the numerical model under earthquake excitation so that it is hard to achieve high efficient computation when applying the IS‐FEM to the inelastic response analysis of RC fiber models directly. In this paper, a new numerical scheme for seismic response analysis of RC framed structures model by fiber beam‐column element is proposed based on the IS‐FEM. To implement the RC fiber model for use in IS‐FEM and improve the computational performance of proposed scheme, a method of identifying the local domains with severe section inelasticity level is proposed and a modified Kent‐Park concrete material model is developed. Because the Woodbury formula is adopted as the solver, the global stiffness matrix can keep unchanged throughout the analysis and the main computational effort is only invested on a small matrix representing local inelastic behavior. The numerical examples demonstrate the validity and efficiency of the proposed scheme.     

Seismic assessment of damaged piloti‐type RC building subjected to successive earthquakes

Building structures damaged by a seismic event may be exposed to the risk of aftershocks or another event within a certain period. In this paper, the seismic assessment of damaged piloti‐type RC buildings was carried out to evaluate probabilistic retrofitting effects under successive earthquakes. First, a framework to evaluate the effectiveness of retrofitting was proposed, and then the proposed methodology was demonstrated with a structure retrofitted with buckling‐restrained braces (BRBs). For consideration of realistic successive earthquakes, past records measured at the same station were combined. Within the framework, a series of nonlinear time history analyses were performed for an as‐is model subjected to single earthquake, a damaged model subjected to successive earthquakes, and a damaged model retrofitted with BRBs subjected to successive earthquakes. In addition, fragility analysis was systematically applied in the framework for evaluation of effectiveness of the retrofitting strategy. The proposed framework was capable of quantifying the influence of successive earthquakes and evaluating the effectiveness of BRB retrofitting by considering the severity of the first earthquake damage and the hysteresis behavior of the retrofit element. Copyright © 2014 John Wiley & Sons, Ltd.     

An efficient three‐dimensional solid finite element dynamic analysis of reinforced concrete structures

Most of the finite element analyses of reinforced concrete structures are restricted to two‐dimensional elements. Three‐dimensional solid elements have rarely been used although nearly all reinforced concrete structures are under a triaxial stress state. In this work, a three‐dimensional solid element based on a smeared fixed crack model that has been used in the past mainly for monotonic static loading analysis is extended to cater for dynamic analysis. The only material parameter that needs to be input for this model is the uniaxial compressive strength of concrete. Steel bars are modelled as uniaxial elements and an embedded formulation allows them to have any orientation inside the concrete elements. The proposed strategy for loading or unloading renders a numerical procedure which is stable and efficient. The whole process is applied to two RC frames and compared against existing experiments in the literature. Results show that the proposed approach may adequately be used to predict the dynamic response of a structure. Copyright © 2005 John Wiley & Sons, Ltd.     

Towards a direct collapse–load method of design for concrete frames subjected to severe ground motions

Most current methods of design for concrete structures under earthquake loads rely on highly idealized ‘equivalent’ static representations of the seismic loads and linear‐elastic methods of structural analysis. With the continuing development of non‐linear methods of dynamic analysis for the overload behaviour and collapse of complete concrete structures, a more direct and more accurate design procedure becomes possible which considers conditions at system collapse. This paper describes an evaluation procedure that uses non‐linear dynamic collapse–load analysis together with global safety coefficients. A back‐calibration procedure for evaluating the global safety coefficients is also described. The aim of this paper is to open up discussion of alternative methods of design with improved accuracy which are necessary to move towards a direct collapse–load method of design. Copyright © 2002 John Wiley & Sons, Ltd.     

Loss estimation for non‐ductile reinforced concrete building in Victoria,British Columbia,Canada: effects of mega‐thrust Mw9‐class subduction earthquakes and aftershocks

This paper presents, within the performance‐based earthquake engineering framework, a comprehensive probabilistic seismic loss estimation method that accounts for main sources of uncertainty related to hazard, vulnerability, and loss. The loss assessment rigorously integrates multiple engineering demand parameters (maximum and residual inter‐story drift ratio and peak floor acceleration) with consideration of mainshock–aftershock sequences. A 4‐story non‐ductile reinforced concrete building located in Victoria, British Colombia, Canada, is considered as a case study. For 100 mainshock and mainshock–aftershock earthquake records, incremental dynamic analysis is performed, and the three engineering demand parameters are fitted with a probability distribution and corresponding dependence computed. Finally, with consideration of different demolition limit states, loss assessment is performed. From the results, it can be shown that when seismic vulnerability models are integrated with seismic hazard, the aftershock effects are relatively minor in terms of overall seismic loss (1–4% increase). Moreover, demolition limit state parameters, uncertainties of collapse fragility, and non‐collapse seismic demand prediction models have showed significant contribution to the loss assessment. The seismic loss curves for the reference case and for cases with the varied parameters can differ by as large as about 150%. Copyright © 2015 John Wiley & Sons, Ltd.