Development of seismic fragility curves for low-rise masonry infilled reinforced concrete buildings by a coefficient-based method

This study presents a seismic fragility analysis and ultimate spectral displacement assessment of regular low-rise masonry infilled (MI) reinforced concrete (RC) buildings using a coefficient-based method. The coefficient-based method does not require a complicated finite element analysis; instead, it is a simplified procedure for assessing the spectral acceleration and displacement of buildings subjected to earthquakes. A regression analysis was first performed to obtain the best-fitting equations for the inter-story drift ratio (IDR) and period shift factor of low-rise MI RC buildings in response to the peak ground acceleration of earthquakes using published results obtained from shaking table tests. Both spectral acceleration-and spectral displacement-based fragility curves under various damage states (in terms of IDR) were then constructed using the coefficient-based method. Finally, the spectral displacements of low-rise MI RC buildings at the ultimate (or near-collapse) state obtained from this paper and the literature were compared. The simulation results indicate that the fragility curves obtained from this study and other previous work correspond well. Furthermore, most of the spectral displacements of low-rise MI RC buildings at the ultimate state from the literature fall within the bounded spectral displacements predicted by the coefficient-based method.     

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.     

Generation of fragility curves for Turkish masonry buildings considering in‐plane failure modes

This study focuses on the seismic safety evaluation of masonry buildings in Turkey for in‐plane failure modes using fragility curves. Masonry buildings are classified and a set of fragility curves are generated for each class. The major structural parameters in the classification of masonry buildings are considered as the number of stories, load‐bearing wall material, regularity in plan and the arrangement of walls (required length, openings in walls, etc.), in accordance with the observations from previous earthquakes and field databases. The fragility curves are generated by using time history (for demand) and pushover (for capacity) analyses. From the generated sets of fragility curves, it is observed that the damage state probabilities are significantly influenced from the number of stories and wall material strength. In the second stage of the study, the generated fragility curves are employed to estimate the damage of masonry buildings in Dinar after the 1995 earthquake. The estimated damage by fragility information is compared with the inspected visual damage as assessed from the Damage Evaluation Form. For the quantification of fragility‐based damage, a single‐valued index, named as ‘vulnerability score’ (VS), is proposed. There seems to be a fair agreement between the two damage measures. In addition to this, decisions regarding the repair or demolition of masonry buildings in Dinar due to visual damage inspection are on comparable grounds with the relative measure obtained from VS of the same buildings. Hence, the fragility‐based procedure can provide an alternative for the seismic safety evaluation of masonry buildings in Turkey. Copyright © 2007 John Wiley & Sons, Ltd.     

Appropriate viscous damping for nonlinear time‐history analysis of base‐isolated reinforced concrete buildings

There is no consensus at the present time regarding an appropriate approach to model viscous damping in nonlinear time‐history analysis of base‐isolated buildings because of uncertainties associated with quantification of energy dissipation. Therefore, in this study, the effects of modeling viscous damping on the response of base‐isolated reinforced concrete buildings subjected to earthquake ground motions are investigated. The test results of a reduced‐scale three‐story building previously tested on a shaking table are compared with three‐dimensional finite element simulation results. The study is primarily focused on nonlinear direct‐integration time‐history analysis, where many different approaches of modeling viscous damping, developed within the framework of Rayleigh damping are considered. Nonlinear direct‐integration time‐history analysis results reveal that the damping ratio as well as the approach used to model damping has significant effects on the response, and quite importantly, a damping ratio of 1% is more appropriate in simulating the response than a damping ratio of 5%. It is shown that stiffness‐proportional damping, where the coefficient multiplying the stiffness matrix is calculated from the frequency of the base‐isolated building with the post‐elastic stiffness of the isolation system, provides reasonable estimates of the peak response indicators, in addition to being able to capture the frequency content of the response very well. Furthermore, nonlinear modal time‐history analyses using constant as well as frequency‐dependent modal damping are also performed for comparison purposes. It was found that for nonlinear modal time‐history analysis, frequency‐dependent damping, where zero damping is assigned to the frequencies below the fundamental frequency of the superstructure for a fixed‐base condition and 5% damping is assigned to all other frequencies, is more appropriate, than 5% constant damping. Copyright © 2013 John Wiley & Sons, Ltd.     

Shaking table tests of 1:4 reduced‐scale models of masonry infilled reinforced concrete frame buildings

Two models of masonry infilled reinforced concrete frame buildings were tested at the shaking table. Models were built in the reduced scale 1:4 using the materials produced in accordance to modelling demands of true replica modelling technique. The first model represented a one‐storey box‐like building and the second one the two‐stories building with plan shaped in the form of a letter H. Models were shaken with the series of horizontal sine dwell motions with gradually increasing amplitude. Masonry infills of tested models were constructed of relatively strong bricks laid in weak mortar. Therefore, typical cracks developed and propagated along mortar beds without cracking of bricks or crushing of infill corners. Data collected from tests will be used in future evaluation, verification and development of computational models for prediction of in‐plane and out‐of‐plane behaviour of masonry infills. The responses of tested models can be well compared with global behaviour of real structures using the modelling rules. The similarity of local behaviour of structural elements, e.g. reinforced concrete joints, is less reliable due to limitations in modelling of steel reinforcement properties. The model responses showed that buildings designed according to Eurocodes are able to sustain relatively high dynamic excitations due to a significant level of structural overstrength. Copyright © 2001 John Wiley & Sons, Ltd.     

Seismic behavior of steel buildings with out‐of‐plumb

A structure that has a permanent offset from a true vertical line is commonly referred to as being ‘out‐of‐plumb’. Out‐of‐plumb may result from construction tolerances or post‐earthquake permanent deformations in steel buildings. This paper quantifies the displacements of buildings with out‐of‐plumb in subsequent seismic events by means of inelastic dynamic time history analysis. Structures considered have different structural heights, force design reduction factors (R), and target inter‐story drifts. It is shown that buildings with greater out of plumb and force design reduction factor have larger normalized peak inter‐story drift ratio and ratio of residual‐to‐peak drift. Also, the ratio of residual‐to‐peak drift was not strongly dependent on structural height or design drift. A design procedure and example provided, based on the results obtained, show how peak and residual inter‐story drift ratio can be estimated. Copyright © 2015 John Wiley & Sons, Ltd.     

Simulation of masonry out‐of‐plane failure modes by multi‐body dynamics

The seismic assessment of the local failure modes in existing masonry buildings is currently based on the identification of the so‐called local mechanisms, often associated with the out‐of‐plane wall behavior, whose stability is evaluated by static force‐based approaches and, more recently, by some displacement‐based proposals. Local mechanisms consist of kinematic chains of masonry portions, often regarded as rigid bodies, with geometric nonlinearity and concentrated nonlinearity in predefined contact regions (unilateral no‐tension behavior, possible sliding with friction). In this work, the dynamic behavior of local mechanisms is simulated through multi‐body dynamics, to obtain the nonlinear response with efficient time history analyses that directly take into account the characteristics of the ground motion. The amplification/filtering effects of the structure are considered within the input motion. The proposed approach is validated with experimental results of two full‐scale shaking‐table tests on stone masonry buildings: a sacco‐stone masonry façade tested at Laboratório Nacional de Engenharia Civil and a two‐storey double‐leaf masonry building tested at European Centre for Training and Research in Earthquake Engineering (EUCENTRE). Copyright © 2015 John Wiley & Sons, Ltd.     

Effects of vertical irregularity and thickness of unreinforced masonry infill on the robustness of RC framed buildings

Presence of irregularities in reinforced concrete (RC) buildings increases seismic vulnerability. During severe seismic shaking, such buildings may suffer disproportionate damage or even collapse that can be minimized by increasing robustness. Robustness is a desirable property of structural systems that can mitigate susceptible buildings to disproportionate collapse. In this paper, the effects of vertical irregularity and thickness of unreinforced masonry infill on the robustness of a six‐story three‐bay RC frame are quantified. Nonlinear static analysis of the frame is performed, and parametric study is undertaken by considering two parameters: absence of masonry infill at different floors (i.e., vertical irregularities) and infill thickness. Robustness has been quantified in terms of stiffness, base shear, ductility, and energy dissipation capacity of the frame. It was observed that the infill thickness and vertical irregularity have significant influence on the response of RC frame. The response surface method is used to develop a predictive equation for robustness as a function of the two parameters. The predictive equation is validated further using 12 randomly selected computer simulations. Copyright © 2013 John Wiley & Sons, Ltd.     

Evaluation of a recently proposed record selection and scaling procedure for low‐rise to mid‐rise reinforced concrete buildings and its use for probabilistic risk assessment studies

This paper evaluates a recent record selection and scaling procedure of the authors that can determine the probabilistic structural response of buildings behaving either in the elastic or post‐elastic range. This feature marks a significant strength on the procedure as the probabilistic structural response distribution conveys important information on probability‐based damage assessment. The paper presents case studies that show the utilization of the proposed record selection and scaling procedure as a tool for the estimation of damage states and derivation of site‐specific and region‐specific fragility functions. The method can be used to describe exceedance probabilities of damage limits under a certain target hazard level with known annual exceedance rate (via probabilistic seismic hazard assessment). Thus, the resulting fragility models can relate the seismicity of the region (or a site) with the resulting building performance in a more accurate manner. Under this context, this simple and computationally efficient record selection and scaling procedure can be benefitted significantly by probability‐based risk assessment methods that have started to be considered as indispensable for developing robust earthquake loss models. Copyright © 2013 John Wiley & Sons, Ltd.     

Evaluation of fundamental period of low‐rise and mid‐rise reinforced concrete buildings

Fundamental period of vibration appears to be one of the most critical parameter for the seismic design of buildings because this period strongly affects the magnitude of seismic forces. In this paper, an empirical formula for estimating the fundamental period of reinforced concrete structures is recommended, on the basis of the vibration analysis of 20 different real building configurations. These structures have already been constructed in Greece, and they are analyzed by using in detail 3‐D finite element models and modal eigenvalue analysis. These models take into account the presence of external and internal infill walls, which are usually ignored as nonstructural elements. This neglect leads to unreliable evaluation of period because the infill walls' contribution to the lateral stiffness and therefore to the fundamental period of vibration is also ignored. Furthermore, taking into account that the flexibility of soil elongates the fundamental period, the soil–structure interaction effect is also considered. To achieve a unique, simple, and effective empirical expression for the fundamental period of vibration, a comprehensive nonlinear regression analysis is applied for the datasets of buildings under consideration. This empirical expression is also compared with the similar expressions from the pertinent literature. Copyright © 2013 John Wiley & Sons, Ltd.     

A study on the seismic performance of steel‐reinforced concrete frame‐concrete core wall high‐rise mixed structure by large‐scale shaking table tests and numerical simulations

This paper reports a study for the seismic performance of one large‐scaled (1/15) model of 30‐story steel‐reinforced concrete frame‐concrete core wall mixed structure. The study was implemented by both shaking table tests, in which the similarity ratio for lateral and gravitational accelerations was kept to 1:1, and numerical nonlinear dynamic analysis. The test observations presented herein include story displacement, interstory drift, natural vibration periods, and final failure mode. The numerical analysis was performed to simulate the shaking table test procedure, and the numerically obtained responses were verified by the test results. On the basis of the numerical results, the progressions of structural stiffness, base shear, and overturning moment were investigated, and the distributions of base shear and overturning moment between frame and core wall were also discussed. The test demonstrates the seismic performance of the steel‐reinforced concrete frame‐core wall mixed structure and reveals the potential overturning failure mode for high rise structures. The nonlinear analysis results indicate that the peripheral frames could take more shear forces after core wall damaged under severe earthquakes. Copyright © 2013 John Wiley & Sons, Ltd.     

Development of seismic fragility surfaces for reinforced concrete buildings by means of nonlinear time‐history analysis

Fragility curves are generally developed using a single parameter to relate the level of shaking to the expected structural damage. The main goal of this work is to use several parameters to characterize the earthquake ground motion. The fragility curves will, therefore, become surfaces when the ground motion is represented by two parameters. To this end, the roles of various strong‐motion parameters on the induced damage in the structure are compared through nonlinear time‐history numerical calculations. A robust structural model that can be used to perform numerous nonlinear dynamic calculations, with an acceptable cost, is adopted. The developed model is based on the use of structural elements with concentrated nonlinear damage mechanics and plasticity‐type behavior. The relations between numerous ground‐motion parameters, characterizing different aspects of the shaking, and the computed damage are analyzed and discussed. Natural and synthetic accelerograms were chosen/computed based on a consideration of the magnitude‐distance ranges of design earthquakes. A complete methodology for building fragility surfaces based on the damage calculation through nonlinear numerical analysis of multi‐degree‐of‐freedom systems is proposed. The fragility surfaces are built to represent the probability that a given damage level is reached (or exceeded) for any given level of ground motion characterized by the two chosen parameters. The results show that an increase from one to two ground‐motion parameters leads to a significant reduction in the scatter in the fragility analysis and allows the uncertainties related to the effect of the second ground‐motion parameter to be accounted for within risk assessments. Copyright © 2009 John Wiley & Sons, Ltd.     

Shaking‐table tests of a full‐scale single‐story masonry veneer wood‐frame structure

This paper presents the findings of shaking‐table experiments conducted to examine the seismic performance of a full‐scale, one‐story, wood‐framed structure with masonry veneer. The structure was designed and constructed in accordance with current U.S. code provisions. The veneer was attached to the wood backing with two kinds of metal anchors, corrugated ties fastened with 8d nails and rigid ties fastened with #8 screws. The tests have shown that the use of nails to fasten veneer anchors to the wood studs is highly unreliable due to the high variation of the nail extraction capacity, which can be influenced by the moisture content of the wood. Other than this, both the wood frame and the masonry veneer performed well under severe ground motions far exceeding a design level earthquake for Seismic Design Category D. Good performance was observed for the rigid veneer ties, which were attached to the wood studs with screws. The results have shown that the veneer walls parallel to the direction of shaking helped to restrain the motion of the wood structure and therefore should not be simply treated as added mass. The detailing of wood roof diaphragms requires special attention in consideration of the out‐of‐plane inertia force of the veneer that can be transmitted through the top plate of the wood‐stud wall to the rim joist. Copyright © 2010 John Wiley & Sons, Ltd.     

Shake‐table tests of a three‐story reinforced concrete frame with masonry infill walls

This paper presents the shake‐table tests of a 2/3‐scale, three‐story, two‐bay, reinforced concrete frame infilled with unreinforced masonry walls. The specimen is representative of the construction practice in California in the 1920s. The reinforced concrete frame had nonductile reinforcement details and it was infilled with solid masonry walls in one bay and infill walls with window openings in the other bay. The structure was subjected to a sequence of dynamic tests including white‐noise base excitations and 14 scaled historical earthquake ground motion records of increasing intensity. The performance of the structure was satisfactory considering the seismic loads it was subjected to. The paper summarizes the design of the specimen and the major findings from the shake‐table tests, including the dynamic response, the load resistance, the evolution of damage, and the final failure mechanism. Copyright © 2011 John Wiley & Sons, Ltd.     

Shake table testing of un‐reinforced brick masonry building test model isolated by U‐FREI

This paper presents a detailed study on feasibility of un‐bonded fiber reinforced elastomeric isolator (U‐FREI) as an alternative to steel reinforced elastomeric isolator (SREI) for seismic isolation of un‐reinforced masonry buildings. Un‐reinforced masonry buildings are inherently vulnerable under seismic excitation, and U‐FREIs are used for seismic isolation of such buildings in the present study. Shake table testing of a base isolated two storey un‐reinforced masonry building model subjected to four prescribed input excitations is carried out to ascertain its effectiveness in controlling seismic response. To compare the performance of U‐FREI, same building is placed directly on the shake table without isolator, and fixed base (FB) condition is simulated by restraining the base of the building with the shake table. Dynamic response characteristic of base isolated (BI) masonry building subjected to different intensities of input earthquakes is compared with the response of the same building without base isolation system. Acceleration response amplification and peak response values of test model with and without base isolation system are compared for different intensities of table acceleration. Distribution of shear forces and moment along the height of the structure and response time histories indicates significant reduction of dynamic responses of the structure with U‐FREI system. This study clearly demonstrates the improved seismic performance of un‐reinforced masonry building model supported on U‐FREIs under the action of considered ground motions. Copyright © 2015 John Wiley & Sons, Ltd.     

Seismic loss estimation of non‐ductile reinforced concrete buildings

Non‐ductile reinforced concrete buildings represent a prevalent construction type found in many parts of the world. Due to the seismic vulnerability of such buildings, in areas of high seismic activity non‐ductile reinforced concrete buildings pose a significant threat to the safety of the occupants and damage to such structures can result in large financial losses. This paper introduces advanced analytical models that can be used to simulate the nonlinear dynamic response of these structural systems, including collapse. The state‐of‐the‐art loss simulation procedure developed for new buildings is extended to estimate the expected losses of existing non‐ductile concrete buildings considering their vulnerability to collapse. Three criteria for collapse, namely first component failure, side‐sway collapse, and gravity‐load collapse, are considered in determining the probability of collapse and the assessment of financial losses. A detailed example is presented using a seven‐story non‐ductile reinforced concrete frame building located in the Los Angeles, California. Copyright © 2012 John Wiley & Sons, Ltd.     

Out‐of‐plane behaviour of a full scale stone masonry façade. Part 1: specimen and ground motion selection

The out‐of‐plane response of walls in existing stone masonry buildings is one of the major causes of vulnerability commonly observed in post‐earthquake damage surveys. In this context, a shaking table (ST) test campaign was carried out on a full‐scale masonry façade mainly focusing on the characterization of its out‐of‐plane overturning behaviour. The structure tested on the ST is a partial reproduction of an existing building from Azores, damaged during the 9 July 1998 Faial earthquake. The definition of the tested specimen as well as the selection of the input ground motion is reported in this paper. A specific emphasis is given to the definition of the time‐history to be applied during the tests because it was felt as an essential and crucial part of the work to obtain the desired overturning behaviour. The accelerogram to be imposed was selected from a large set of accelerograms (74) by means of a step‐by‐step procedure on the basis of several numerical analyses resorting to the rocking response of rigid blocks. A companion paper (Part 2) focuses on the ST test results and detailed data interpretation. Copyright © 2013 John Wiley & Sons, Ltd.     

Performance of clay masonry veneer in wood‐stud walls subjected to out‐of‐plane seismic loads

This paper presents the findings of shaking‐table experiments conducted to examine the out‐of‐plane seismic performance of masonry veneer walls. Seven wall assemblies were tested, each consisting of a clay masonry veneer anchored to a wood‐stud backing. Design variables include the type of veneer ties, tie spacing, and presence or absence of mortar joint reinforcement and window opening. The walls were designed and constructed in accordance with current US code provisions. Results of the experiments show that failure of the corrugated ties is governed by pullout of the nails from the wood studs, while failure of the rigid ties is governed by detachment from the mortar joints or pull‐through of the screw heads through fastener holes. Both types of ties show satisfactory performance under ground motions corresponding to Design Basis and Maximum Considered Earthquakes representative of Seismic Design Category E. Although the rigid ties were stronger than the corrugated ties, they had wider vertical spacing and failed at a slightly higher seismic load. Observed extraction capacities of the nails show high variability, which merits attention. Joint reinforcement did not show any noticeable effect on the out‐of‐plane behavior of the veneer. Results of an analytical study have shown that the detachment of a veneer from the backing system is preceded by veneer cracking, which influences the distribution of tie forces, and that the vertical tie spacing influences the cracking load for the veneer. Copyright © 2010 John Wiley & Sons, Ltd.     

Non‐linear seismic analysis and vulnerability evaluation of a masonry building by means of the SAP2000 V.10 code

The aim of the paper is to explore the possibilities offered by SAP2000^® v.10, a software package with user‐friendly interface widely used by practising engineers, for seismic analyses of masonry buildings. The reliability of the code was first investigated by carrying out static push‐over (SPO) analyses of two walls, already analysed by other researchers using advanced programs. The equivalent frame modelling was employed in all analyses carried out. The code was then used to investigate the seismic performance of an existing two‐storey building typical of the north‐east of Italy, with the walls being made of roughly squared stones. An SPO analysis was performed first on the most significant wall, followed by a number of time‐history analyses aimed to evaluate the dynamic push‐over curves. Finally, the seismic fragility curves were derived, considering the seismic input as a random variable. Copyright © 2007 John Wiley & Sons, Ltd.