Error estimation of closed‐form solution for annual rate of structural collapse

With the increasing emphasis of performance‐based earthquake engineering in the engineering community, several investigations have been presented outlining simplified approaches suitable for performance‐based seismic design (PBSD). Central to most of these PBSD approaches is the use of closed‐form analytical solutions to the probabilistic integral equations representing the rate of exceedance of key performance measures. Situations where such closed‐form solutions are not appropriate primarily relate to the problem of extrapolation outside of the region in which parameters of the closed‐form solution are fit. This study presents a critical review of the closed‐form solution for the annual rate of structural collapse. The closed‐form solution requires the assumptions of lognormality of the collapse fragility and power model form of the ground motion hazard, of which the latter is more significant regarding the error of the closed‐form solution. Via a parametric study, the key variables contributing to the error between the closed‐form solution and solution via numerical integration are illustrated. As these key variables cannot be easily measured, it casts doubt on the use of such closed‐form solutions in future PBSD, especially considering the simple and efficient nature of using direct numerical integration to obtain the solution. Copyright © 2008 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.     

Performance‐based earthquake engineering assessment of a self‐centering,post‐tensioned concrete bridge system

Highway bridges in highly seismic regions can sustain considerable residual displacements in their columns following large earthquakes. These residual displacements are an important measure of post‐earthquake functionality, and often determine whether or not a bridge remains usable following an earthquake. In this study, a self‐centering system is considered that makes use of unbonded, post‐tensioned steel tendons to provide a restoring force to bridge columns to mitigate the problem of residual displacements. To evaluate the proposed system, a code‐conforming, case‐study bridge structure is analyzed both with conventional reinforced concrete columns and with self‐centering, post‐tensioned columns using a formalized performance‐based earthquake engineering (PBEE) framework. The PBEE analysis allows for a quantitative comparison of the relative performance of the two systems in terms of engineering parameters such as peak drift ratio as well as more readily understood metrics such as expected repair costs and downtime. The self‐centering column system is found to undergo similar peak displacements to the conventional system, but sustains lower residual displacements under large earthquakes, resulting in similar expected repair costs but significantly lower expected downtimes. Copyright © 2010 John Wiley & Sons, Ltd.     

Need of performance‐based earthquake engineering in Taiwan: a lesson from the Chichi earthquake

The objectives of seismic engineering are to design and build better and more economic earthquake‐resistant structures. Performance, which is measured as the amount of damage of a facility and the impact of damage to the society after an earthquake, is the main concern. Performance‐based earthquake engineering (PBEE) implies design, evaluation, and construction of engineered facilities whose performance under common and extreme earthquake ground motions responds to the diverse needs and objectives of the owners, users and society. Observations on the performance or damage of structures after strong earthquake ground motions have always served as an effective means to evaluate the current seismic regulations and guidelines and make further improvements afterwards. This paper presents some of the typical damage evidence after the Chichi earthquake occurred recently in Taiwan. Important issues in performance‐based earthquake engineering that need to be considered in future seismic regulations of Taiwan are addressed accordingly. Copyright © 2000 John Wiley & Sons, Ltd.     

Evaluation of displacement‐based vulnerability assessment methodology using observed damage data from Christchurch

On 22 February 2011, Christchurch City experienced a destructive magnitude (Mw) 6.2 aftershock following the main event of magnitude (Mw) 7.1 on the 4 September 2010. Severe damage was inflicted on the building stock, particularly within the central business district (CBD) of Christchurch. The strong motion stations around the CBD region and extensive building damage survey information from the Christchurch City Council provided a unique opportunity to calibrate a theoretical regional vulnerability assessment model developed and refined to be applicable for New Zealand (NZ) buildings. In this study, data from the building safety evaluation survey conducted by Christchurch City Council are synthesised and processed to extract details on building typologies in the CBD region and the colour tagging assigned to each building depending on the degree of damage. A displacement‐based framework is used to carry out vulnerability assessment for Christchurch buildings to estimate damage sustained under the recorded ground motions in the February event. As the damage survey indicators were ‘colour tags’, a mapping scheme has been explored to link the observed colour tagging damage statistics with ‘drift‐based damage limit states’ adopted in the theoretical approach. A sensitivity analysis is carried out to calibrate the mapping scheme, which can provide estimates of proportions of buildings likely to fall in different colour regimes when used in conjunction with the proposed vulnerability assessment methodology. It is shown that the methodology is reasonably robust, thereby increasing the confidence in using this approach to predict seismic vulnerability of building stock in NZ. Copyright © 2014 John Wiley & Sons, Ltd.     

IM‐based and EDP‐based decision models for the verification of the seismic collapse safety of buildings

Decision models for the verification of seismic collapse safety of buildings are introduced. The derivations are based on the concept of the acceptable (target) annual probability of collapse, whereas the decision making involves comparisons between seismic demand and capacity, which is familiar to engineering practitioners. Seismic demand, which corresponds to the design seismic action associated with a selected return period, can be expressed either in terms of an intensity measure (IM) or an engineering demand parameter (EDP). Seismic capacity, on the other hand, is defined by dividing the near‐collapse limit‐state IM or EDP by an appropriate risk‐targeted safety factor (γ _im or γ _edp ), which is the only safety factor used in the proposed decision model. Consequently, the seismic performance assessment of a building should be based on the best possible estimate. For a case study, it is shown that if the target collapse risk is set to 10^?4 (0.5% over a period of 50 years), and if the seismic demand corresponds to a return period of 475 years (10% over a period of 50 years), then it can be demonstrated that γ _im is approximately equal to 2.5 for very stiff buildings, whereas for buildings with long periods the value of γ _im can increase up to a value of approximately 5. The model using γ _edp is equal to that using γ _im only if it can be assumed that displacements, with consideration of nonlinear behavior, are equal to displacements from linear elastic analysis.     

Seismic performance evaluation of non‐structural components: drywall partitions

As the first part of non‐structural component test series, interior drywall partitions are selected for an experimental program. This test series will cover non‐structural components that are significant in the economic losses in buildings subjected to seismic loading, namely interior drywall partitions, exterior cladding and window glasses, and ceilings. Four full‐scale drywall partitions with light‐gage steel stud framing were tested to observe damage in cyclic loading conditions. Effects of a door and an intersecting wall on the behaviour of drywall partition are studied. Damage was concentrated to perimeter regions where gypsum boards made contacts with ceiling, floor, or columns. Dynamic loading did not amplify the damage on a drywall partition over the damage observed from the quasi‐static test. Damage–repair cost relationships show that the repair cost reaches almost the initial cost under 2% radian interstorey drift. Copyright © 2006 John Wiley & Sons, Ltd.     

Post‐earthquake functionality of highway overpass bridges

Bridges are crucial to the transportation network in a region struck by an earthquake. Collapse of a bridge determines if a road is passable. Ability of a bridge to carry traffic load after an earthquake determines the weight and speed of vehicles that can cross it. Extent of system and component structural damage in bridges determines the cost and time required for repair. Today, post‐earthquake bridge evaluation is qualitative rather than quantitative. The research presented in this paper aims to provide a quantitative engineering basis for quick and reliable evaluation of the ability of a typical highway overpass bridge to function after an earthquake. The Pacific Earthquake Engineering Research (PEER) Center's probabilistic performance‐based evaluation approach provides the framework for post‐earthquake bridge evaluation. An analytical study was performed that linked engineering demand parameters to earthquake intensity measures. The PEER structural performance database and reliability analysis tools were then used to link demand parameters to damage measures. Finally, decision variables were developed to describe three limit states, repair cost, traffic function, and collapse, in terms of induced damage. This paper presents the analytical models used to evaluate post‐earthquake bridge function, decision variables and their correlation to the considered limit states, and fragility curves that represent the probability of exceeding a bridge function limit state given an earthquake intensity. Copyright © 2005 John Wiley & Sons, Ltd.     

Use of the conditional spectrum to incorporate record‐to‐record variability in simplified seismic assessment of RC wall buildings

A procedure for incorporating record‐to‐record variability into the simplified seismic assessment of RC wall buildings is presented. The procedure relies on the use of the conditional spectrum to randomly sample spectral ordinates at relevant periods of vibration. For inelastic response, displacement reduction factors are then used to relate inelastic displacement demand to the spectral displacement at the effective period for single‐degree‐of‐freedom systems. Simple equations are used to convert back and forth between multi‐degree‐of‐freedom RC wall buildings and equivalent single‐degree‐of‐systems so that relevant engineering demand parameters can be obtained. Consideration is also given to higher‐mode effects by adapting existing modal combination rules. The proposed method is applied to several case study buildings, showing promising results in the examination of inter‐storey drift ratio and shear forces. The proposed method captures the variation in the distribution of structural response parameters that occurs with variations in structural configuration, intensity, engineering demand parameter of interest and site characteristics. Discussion is provided on possible ways to improve the accuracy of the procedure and suggestions for additional future work. Copyright © 2015 John Wiley & Sons, Ltd.     

Performance‐based seismic assessment of conventional and base‐isolated steel buildings including environmental impact and resilience

Sustainability and resilience are issues that are recognized worldwide, and increased attention should be placed on strategies to design and maintain infrastructure systems that are hazard resilient, damage tolerant, and sustainable. In this paper, a methodology to evaluate the seismic sustainability and resilience of both conventional and base‐isolated steel buildings is presented. Furthermore, the proposed approach is used to explore the difference between the performance associated with these buildings by considering the three pillars of sustainability: economic, social, and environmental. Sustainability and resilience are both considered to cover a comprehensive performance‐based assessment content. The uncertainties associated with performance and consequence evaluation of structural and non‐structural components are incorporated within the assessment process. The proposed performance‐based assessment approach is illustrated on conventional and base‐isolated steel buildings under given seismic scenarios. Copyright © 2015 John Wiley & Sons, Ltd.     

Performance‐based design with semi‐active structural control technique

The recent spate of large earthquakes has triggered diverse performance requirements for structures. This has led to increasing worldwide interest in performance‐based design methods. To establish such methods, however, it is necessary to evaluate structure conditions after defining the loads, and this is difficult to accomplish. On the other hand, there has been steady progress on research and development of structural control techniques for improving structural performance. These technological innovations need to be rationally incorporated into structural design. In particular, semi‐active structural control techniques are effective in improving structural performance during large earthquakes. By effectively incorporating them into the design, it is possible to meet the various structural performance requirements. This paper first outlines the various structural control methods and focuses on the semi‐active structural control technique as the main topic. It then describes an example to verify the effectiveness of the semi‐active structural control technique in high‐rise buildings. Copyright © 2001 John Wiley & Sons, Ltd.     

Post‐earthquake bridge repair cost and repair time estimation methodology

While structural engineers have traditionally focused on individual components (bridges, for example) of transportation networks for design, retrofit, and analysis, it has become increasingly apparent that the economic costs to society after extreme earthquake events are caused at least as much from indirect costs as direct costs due to individual structures. This paper describes an improved methodology for developing probabilistic estimates of repair costs and repair times that can be used for evaluating the performance of new bridge design options and existing bridges in preparation for the next major earthquake. The proposed approach in this paper is an improvement on previous bridge loss modeling studies—it is based on the local linearization of the dependence between repair quantities and damage states so that the resulting model follows a linear relationship between damage states and repair points. The methodology uses the concept of performance groups (PGs) that account for damage and repair of individual bridge components and subassemblies. The method is validated using two simple examples that compare the proposed method to simulation and previous methods based on loss models using a power–law relationship between repair quantities and damage. In addition, an illustration of the method is provided for a complete study on the performance of a common five‐span overpass bridge structure in California. Intensity‐dependent repair cost ratios (RCRs) and repair times are calculated using the proposed approach, as well as plots that show the disaggregation of repair cost by repair quantity and by PG. This provides the decision maker with a higher fidelity of data when evaluating the contribution of different bridge components to the performance of the bridge system, where performance is evaluated in terms of repair costs and repair times rather than traditional engineering quantities such as displacements and stresses. Copyright © 2009 John Wiley & Sons, Ltd.     

Accounting for directionality as a function of structural typology in performance‐based earthquake engineering design

For the seismic design of a structure, horizontal ground shaking is usually considered in two perpendicular directions, even though real horizontal ground motions are complex two‐dimensional phenomena that impose different demands at different orientations. While the issue of ground motion dependence on the orientation of the recording devices has been the focus of many significant developments during the last decade, the effects of directionality on the characteristics of the structure have received less attention. This work presents a proposal to calculate the probability of exceedance of elastic spectral displacements accounting for structural typology and illustrates its relevance by means of its application to two case‐study buildings. In order to ease its implementation in seismic design codes, a simplification is developed by means of a detailed statistical analysis of the results obtained using four sets of real hazard curves. The framework presented herein is considered to represent an important contribution to the field of performance‐based earthquake engineering, permitting improved treatment of directionality effects within seismic risk design and assessment. Copyright © 2016 John Wiley & Sons, Ltd.     

Improved performance‐based seismic assessment of buildings by utilizing Bayesian statistics

This paper addresses two important issues of concern to practicing engineers and researchers alike in application of performance‐based seismic assessment (PBSA) methodology on buildings: (i) the number of ground motion records required to exercise PBSA—current practice (FEMA P‐58‐1) requires eleven or more pairs of motions for this purpose, and (ii) the time and effort associated with performing the number of nonlinear response history analyses required to exercise PBSA. We present a method for exercising of PBSA that employs classical linear modal analysis to develop a first estimate (i.e., a priori) of probability distribution of loss, followed by utilizing Bayesian statistics to update this estimate using estimates of loss obtained by utilizing a small number of nonlinear response history analyses of a detailed model of the building (i.e., posterior). The proposed technique is used to assess the distribution of monetary loss of two case studies, a 4‐story reinforced concrete moment‐resisting frame building and a 20‐story steel moment‐resisting frame building, both located in Los Angeles, for a ground motion hazard with 10% probability of exceedance in 50 years. The efficiency of the proposed PBSA method is demonstrated by showing the similarity between the distribution of monetary loss at each story of case study buildings obtained from the traditional/sophisticated PBSA methodology and the proposed PBSA method in this study. Copyright © 2015 John Wiley & Sons, Ltd.     

Development of fragility functions as a damage classification/prediction method for steel moment‐resisting frames using a wavelet‐based damage sensitive feature

Fragility functions are commonly used in performance‐based earthquake engineering for predicting the damage state of a structure subjected to an earthquake. This process often involves estimating the structural damage as a function of structural response, such as the story drift ratio and the peak floor absolute acceleration. In this paper, a new framework is proposed to develop fragility functions to be used as a damage classification/prediction method for steel structures based on a wavelet‐based damage sensitive feature (DSF). DSFs are often used in structural health monitoring as an indicator of the damage state of the structure, and they are easily estimated from recorded structural responses. The proposed framework for damage classification of steel structures subjected to earthquakes is demonstrated and validated with a set of numerically simulated data for a four‐story steel moment‐resisting frame designed based on current seismic provisions. It is shown that the damage state of the frame is predicted with less variance using the fragility functions derived from the wavelet‐based DSF than it is with fragility functions derived from an alternate acceleration‐based measure, the spectral acceleration at the first mode period of the structure. Therefore, the fragility functions derived from the wavelet‐based DSF can be used as a probabilistic damage classification model in the field of structural health monitoring and an alternative damage prediction model in the field of performance‐based earthquake engineering. Copyright © 2011 John Wiley & Sons, Ltd.     

芦山地震农村房屋震害调查与分析

“4·20”芦山地震给灾区农村房屋造成严重破坏.本文根据实地调查,对灾区农房总体震害做了简要介绍,并重点对不同烈度区三种主要农房结构的震害现象进行了分类描述,对房屋损伤原因做了初步分析.震害调查表明:倒塌或严重破坏的农房绝大多数为原来的危旧房屋;汶川地震后新建的部分农房由于采取了一定抗震构造措施,在本次地震中表现较好;但总体上由于农村自建房尚未纳入国家监管体系,农房抗震防灾工作依然任重道远.     

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.     

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.     

Experimental multi‐level seismic performance assessment of 3D RC frame designed for damage avoidance

This paper experimentally investigates the application of damage avoidance design (DAD) philosophy to moment‐resisting frames with particular emphasis on detailing of rocking interfaces. An 80% scale three‐dimensional rocking beam–column joint sub‐assembly designed and detailed based on damage avoidance principles is constructed and tested. Incremental dynamic analysis is used for selecting ground motion records to be applied to the sub‐assembly for conducting a multi‐level seismic performance assessment (MSPA). Analyses are conducted to obtain displacement demands due to the selected near‐ and medium‐field ground motions that represent different levels of seismic hazard. Thus, predicted displacement time histories are applied to the sub‐assembly for conducting quasi‐earthquake displacement tests. The sub‐assembly performed well reaching drifts up to 4.7% with only minor spalling occurring at rocking beam interfaces and minor flexural cracks in beams. Yielding of post‐tensioning threaded bars occurred, but the sub‐assembly did not collapse. The externally attached energy dissipators provided large hysteretic dissipation during large drift cycles. The sub‐assembly satisfied all three seismic performance requirements, thereby verifying the superior performance of the DAD philosophy. Copyright © 2007 John Wiley & Sons, Ltd.