Uniform fragility spectra for the performance‐based seismic design of structures considering variabilities in structural properties

This paper presents a new methodology based on structural performance to determine uniform fragility design spectra, i.e., spectra with the same probability of exceedance of a performance level for a given seismic intensity. The design spectra calculated with this methodology provide directly the lateral strength, in terms of yield‐ pseudo‐accelerations, associated with the rate of exceedance of a specific ductility characterizing the performance level for which the structures will be designed. This procedure involves the assessment of the seismic hazard using a large enough number of seismic records of several magnitudes; these records are simulated with an improved empirical Green function method. The statistics of the performance of a single degree of freedom system are obtained using Monte Carlo simulation considering the seismic demand, the fundamental period, and the strength of the structure as uncertain variables. With these results, the conditional probability that a structure exceeds a specific performance level is obtained. The authors consider that the proposed procedure is a significant improvement to others considered in the literature and a useful research tool for the further development of uniform fragility spectra that can be used for the performance‐based seismic design and retrofit of structures.     

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.     

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.     

Decision support for conceptual performance‐based design

Performance assessment implies that the structural, non‐structural, and content systems are given and that decision variables, DVs, (e.g. expected annual loss, mean annual frequency of collapse) are computed and compared to specified performance targets. Performance‐based design (PBD) is different by virtue of the fact that the building and its components and systems first have to be created. Good designs are based on concepts that incorporate performance targets up front in the conceptual design process, so that subsequent performance assessment becomes more of a verification process of an efficient design rather than a design improvement process that may require radical changes of the initial design concept. In short, the design approach could consist of (a) specifying performance targets (e.g. tolerable probability of collapse, acceptable dollar losses) and associated seismic hazards, and (b) deriving engineering parameters for system selection, or perhaps better, using the relatively simple design decision support tools discussed in this paper. Copyright © 2005 John Wiley & Sons, Ltd.     

Damage mechanics applied to performance‐based design of reinforced concrete columns

Performance‐based design methodology is based on reaching performance objectives that are associated to certain damage conditions. These performance objectives are related to the seismic hazard and to the performance levels. In actual application, reliable tools are required for capturing the evolution of the damage condition as well as for measuring and locating it. Moreover, it is essential to accurately establish the relationship between the damage and the performance levels. This paper shows the application of damage mechanics to performance‐based design. A layered damage mechanics‐based finite element program is presented with a discussion on modeling for prediction of the response of normal‐strength and high‐strength concrete columns subjected to cyclic flexural loading and various axial load levels. The damage indices derived from these analyses were used to elaborate several damage charts expressed as a function of drift and displacement ductility. This makes it possible to establish a relationship between the damage state and the performance levels. Results have demonstrated the ability of the damage mechanics modeling to accurately predict the behavior of the specimens tested. Copyright © 2017 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.     

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.     

A probabilistic performance‐based approach for mitigating the seismic pounding risk between adjacent buildings

Existing design procedures for determining the separation distance between adjacent buildings subjected to seismic pounding risk are based on approximations of the buildings' peak relative displacement. These procedures are characterized by unknown safety levels and thus are not suitable for use within a performance‐based earthquake engineering framework. This paper introduces an innovative reliability‐based methodology for the design of the separation distance between adjacent buildings. The proposed methodology, which is naturally integrated into modern performance‐based design procedures, provides the value of the separation distance corresponding to a target probability of pounding during the design life of the buildings. It recasts the inverse reliability problem of the determination of the design separation distance as a zero‐finding problem and involves the use of analytical techniques in order to evaluate the statistics of the dynamic response of the buildings. Both uncertainty in the seismic intensity and record‐to‐record variability are taken into account. The proposed methodology is applied to several different buildings modeled as linear elastic single‐degree‐of‐freedom (SDOF) and multi‐degree‐of‐freedom (MDOF) systems, as well as SDOF nonlinear hysteretic systems. The design separation distances obtained are compared with the corresponding estimates that are based on several response combination rules suggested in the seismic design codes and in the literature. In contrast to current seismic code design procedures, the newly proposed methodology provides consistent safety levels for different building properties and different seismic hazard conditions. Copyright © 2012 John Wiley & Sons, Ltd.     

Multiobjective optimization for performance‐based seismic design of steel moment frame structures

The performance‐based seismic design of steel special moment‐resisting frame (SMRF) structures is formulated as a multiobjective optimization problem, in which conflicting design criteria that respectively reflect the present capital investment and the future seismic risk are treated simultaneously as separate objectives other than stringent constraints. Specifically, the initial construction expenses are accounted for by the steel material weight as well as by the number of different standard steel section types, the latter roughly quantifying the degree of design complexity related additional construction cost; the seismic risk is considered in terms of maximum interstory drift demands at two hazard levels with exceedance probabilities being 50% and 2% in 50 years, respectively. The present formulation allows structural engineers to find an optimized design solution by explicitly striving for a desirable compromise between the initial investment and seismic performance. Member sizing for code‐compliant design of a planar five‐story four‐bay SMRF is presented as an application example using the proposed procedure that is automated by a multiobjective genetic algorithm. Copyright © 2004 John Wiley & Sons, Ltd.     

Spatiotemporal seismic hazard and risk assessment of M9.0 megathrust earthquake sequences of wood‐frame houses in Victoria,British Columbia,Canada

Megathrust earthquake sequences, comprising mainshocks and triggered aftershocks along the subduction interface and in the overriding crust, can impact multiple buildings and infrastructure in a city. The time between the mainshocks and aftershocks usually is too short to retrofit the structures; therefore, moderate‐size aftershocks can cause additional damage. To have a better understanding of the impact of aftershocks on city‐wide seismic risk assessment, a new simulation framework of spatiotemporal seismic hazard and risk assessment of future M9.0 sequences in the Cascadia subduction zone is developed. The simulation framework consists of an epidemic‐type aftershock sequence (ETAS) model, ground‐motion model, and state‐dependent seismic fragility model. The spatiotemporal ETAS model is modified to characterise aftershocks of large and anisotropic M9.0 mainshock ruptures. To account for damage accumulation of wood‐frame houses due to aftershocks in Victoria, British Columbia, Canada, state‐dependent fragility curves are implemented. The new simulation framework can be used for quasi‐real‐time aftershock hazard and risk assessments and city‐wide post‐event risk management.     

Adapting earthquake actions in Eurocode 8 for performance‐based seismic design

Performance‐based seismic design (PBSD) can be considered as the coupling of expected levels of ground motion with desired levels of structural performance, with the objective of achieving greater control over earthquake‐induced losses. Eurocode 8 (EC8) already envisages two design levels of motion, for no collapse and damage limitation performance targets, anchored to recommended return periods of 475 and 95 years, respectively. For PBSD the earthquake actions need to be presented in ways that are appropriate to the estimation of inelastic displacements, since these provide an effective control on damage at different limit states. The adequacy of current earthquake actions in EC8 are reviewed from this perspective and areas requiring additional development are identified. The implications of these representations of the seismic loads, in terms of mapping and zonation, are discussed. The current practice of defining the loading levels on the basis of the pre‐selected return periods is challenged, and ideas are discussed for calibrating the loading‐performance levels for design on the basis of quantitative earthquake loss estimation. Copyright © 2005 John Wiley & Sons, Ltd.     

Modelling considerations in probabilistic performance‐based seismic evaluation: case study of the I‐880 viaduct

Limitations associated with deterministic methods to quantify demands and develop rational acceptance criteria have led to the emergence of probabilistic procedures in performance‐based seismic engineering. The Pacific Earthquake Engineering Research performance‐based methodology is one such approach. In this paper, the impact of certain modelling decisions made at different stages of the evaluation process on the performance assessment of a typical multi‐bent viaduct is examined. Modelling, in the context of this paper, covers hazard modelling, structural modelling and loss modelling. The specific application considered in this study is a section of an existing viaduct in California: the I‐880 interstate highway. Several simulation models of the viaduct are developed, a series of nonlinear time‐history analyses are carried out to predict demands, measures of damage are evaluated and the probability of closure of the viaduct is estimated using the specified hazard for the site. It is concluded that the methodology offers several advantages over existing deterministic performance‐based procedures. Results of the investigation indicate that the assessment methodology is particularly sensitive to the reliability of decisions made by bridge inspectors following a seismic event, and to the dispersion in the demand estimation, which in turn is influenced by several factors including soil–structure interaction effects and ground motion scaling procedures. Copyright © 2005 John Wiley & Sons, Ltd.     

Improved risk‐targeted performance‐based seismic design of reinforced concrete frame structures

This paper presents a procedure for seismic design of reinforced concrete structures, in which performance objectives are formulated in terms of maximum accepted mean annual frequency (MAF) of exceedance, for multiple limit states. The procedure is explicitly probabilistic and uses Cornell's like closed‐form equations for the MAFs. A gradient‐based constrained optimization technique is used for obtaining values of structural design variables (members' section size and reinforcement) satisfying multiple objectives in terms of risk levels. The method is practically feasible even for real‐sized structures thanks to the adoption of adaptive equivalent linear models where element‐by‐element stiffness reduction is performed (2 linear analyses per intensity level). General geometric and capacity design constraints are duly accounted for. The procedure is applied to a 15‐storey plane frame building, and validation is conducted against results in terms of drift profiles and MAF of exceedance, obtained by multiple‐stripe analysis with records selected to match conditional spectra. Results show that the method is suitable for performance‐based seismic design of RC structures with explicit targets in terms of desired risk levels.     

Theory and implementation of switch‐based hybrid simulation technology for earthquake engineering applications

Hybrid simulation (HS) is a novel technique to combine analytical and experimental sub‐assemblies to examine the dynamic responses of a structure during an earthquake shaking. Traditionally, HS uses displacement‐based control where the finite element program calculates trial displacements and applies them to both the analytical and experimental sub‐assemblies. Displacement‐based HS (DHS) has been proven to work well for most structural sub‐assemblies. However, for specimens with high stiffness, traditional DHS does not work because it is difficult to precisely control hydraulic actuators in small displacement. A small control error in displacement will result in large force response fluctuations for stiff specimens. This paper resolves this challenge by proposing a force‐based HS (FHS) algorithm that directly calculates trial forces instead of trial displacements. The proposed FHS is finite element based and applicable to both linear and nonlinear systems. For specimens with drastic changes in stiffness, such as yielding, a switch‐based HS (SHS) algorithm is proposed. A stiffness‐based switching criterion between the DHS and FHS algorithms is presented in this paper. All the developed algorithms are applied to a simple one‐story one‐bay concentrically braced moment frame. The result shows that SHS outperforms DHS and FHS. SHS is then utilized to validate the seismic performance of an innovative earthquake resilient fused structure. The result shows that SHS works in switching between the DHS and FHS modes for a highly nonlinear and highly indeterminate structural system. Copyright © 2017 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.     

A performance‐based framework for adaptive seismic aftershock risk assessment

Operative seismic aftershock risk forecasting can be particularly useful for rapid decision‐making in the presence of an ongoing sequence. In such a context, limit state first‐excursion probabilities (risk) for the forecasting interval (a day) can represent the potential for progressive state of damage in a structure. This work lays out a performance‐based framework for adaptive aftershock risk assessment in the immediate post‐mainshock environment. A time‐dependent structural performance variable is adopted in order to measure the cumulative damage in a structure. A set of event‐dependent fragility curves as a function of the first‐mode spectral acceleration for a prescribed limit state is calculated by employing back‐to‐back nonlinear dynamic analyses. An epidemic‐type aftershock sequence model is employed for estimating the spatio‐temporal evolution of aftershocks. The event‐dependent fragility curves for a given limit state are then integrated together with the probability distribution of aftershock spectral acceleration based on the epidemic‐type aftershock sequence aftershock hazard. The daily probability of limit state first‐excursion is finally calculated as a weighted combination of the sequence of limit state probabilities conditioned on the number of aftershocks. As a numerical example, daily aftershock risk is calculated for the L'Aquila 2009 aftershock sequence (central Italy). A representative three‐story reinforced concrete frame with infill panels, which has cyclic strength and stiffness degradation, is used in order to evaluate the progressive damage. It is observed that the proposed framework leads to a sound forecasting of limit state first‐excursion in the structure for two limit states of significant damage and near collapse. Copyright © 2014 John Wiley & Sons, Ltd.     

Expected loss‐based alarm threshold set for earthquake early warning systems

Earthquake early warning systems (EEWS) seem to have potential as tools for real‐time seismic risk management and mitigation. In fact, although the evacuation of buildings requires warning time not available in many urbanized areas threatened by seismic hazard, they may still be used for the real‐time protection of critical facilities using automatic systems in order to reduce the losses subsequent to a catastrophic event. This is possible due to the real‐time seismology, which consists of methods and procedures for the rapid estimation of earthquake features, as magnitude and location, based on measurements made on the first seconds of the P‐waves. An earthquake engineering application of earthquake early warning (EEW) may be intended as a system able to issue the alarm, if some recorded parameter exceeds a given threshold, to activate risk mitigation actions before the quake strikes at a site of interest. Feasibility analysis and design of such EEWS require the assessment of the expected loss reduction due to the security action and set of the alarm threshold. In this paper a procedure to carry out these tasks in the performance‐based earthquake engineering probabilistic framework is proposed. A merely illustrative example refers to a simple structure assumed to be a classroom. Structural damage and non‐structural collapses are considered; the security action is to shelter occupants below the desks. The cost due to a false alarm is assumed to be related to the interruption of didactic activities. Results show how the comparison of the expected losses, for the alarm‐issuance and non‐issuance cases, allows setting the alarm threshold on a quantitative and consistent basis, and how it may be a tool for the design of engineering applications of EEW. Copyright © 2007 John Wiley & Sons, Ltd.     

Alternative closed‐form solutions for the mean rate of exceedance of structural limit states

Two new closed‐form expressions representing the mean rate of exceedance of a given limit state are presented herein. These proposals overcome limitations that were identified with the original formulation of the well‐known SAC/FEMA approach. The new expressions involve new parametric functions for the modeling of the seismic hazard data and for the demand evolution for increasing values of the earthquake intensity measure. Given the carefully selected parametric form of these functions, mathematical tractability is able to be maintained to establish two new closed‐form solutions representing the mean rate of exceedance of a given limit state. The function proposed for the hazard exhibits nonlinear behavior in log‐log space and is able to represent the actual hazard data over a wider range of earthquake intensity levels. The function proposed for the demand evolution addresses issues related to the inadequate performance of the SAC/FEMA approach when force‐based demand parameters such as the shear force are considered. To illustrate the applicability of the new closed‐form solutions, the probability of occurrence of several limit states is determined for a reinforced concrete structure. Copyright © 2013 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.