Closed‐form aftershock reliability of damage‐cumulating elastic‐perfectly‐plastic systems

Major earthquakes (i.e., mainshocks) typically trigger a sequence of lower magnitude events clustered both in time and space. Recent advances of seismic hazard analysis stochastically model aftershock occurrence (given the main event) as a nonhomogeneous Poisson process with rate that decays in time as a negative power law. Risk management in the post‐event emergency phase has to deal with this short‐term seismicity. In fact, because the structural systems of interest might have suffered some damage in the mainshock, possibly worsened by damaging aftershocks, the failure risk may be large until the intensity of the sequence reduces or the structure is repaired. At the state‐of‐the‐art, the quantitative assessment of aftershock risk is aimed at building tagging, that is, to regulate occupancy. The study, on the basis of age‐dependent stochastic processes, derived closed‐form approximations for the aftershock reliability of simple nonevolutionary elastic‐perfectly‐plastic damage‐cumulating systems, conditional on different information about the structure. Results show that, in the case hypotheses apply, the developed models may represent a basis for handy tools enabling risk‐informed tagging by stakeholders and decision makers. Copyright © 2013 John Wiley & Sons, Ltd.     

Life‐cycle reliability of RC bridge piers under seismic and airborne chloride hazards

Over the last two decades, the probabilistic assessment of reinforced concrete (RC) structures under seismic hazard has been developed rapidly. However, little attention has been devoted to the assessment of the seismic reliability of corroded structures. For the life‐cycle assessment of RC structures in a marine environment and earthquake‐prone regions, the effect of corrosion due to airborne chlorides on the seismic capacity needs to be taken into consideration. Also, the effect of the type of corrosive environment on the seismic capacity of RC structures has to be quantified. In this paper, the evaluation of the displacement ductility capacity based on the buckling model of longitudinal rebars in corroded RC bridge piers is established, and a novel computational procedure to integrate the probabilistic hazard associated with airborne chlorides into life‐cycle seismic reliability assessment of these piers is proposed. The seismic demand depends on the results of seismic hazard assessment, whereas the deterioration of seismic capacity depends on the hazard associated with airborne chlorides. In an illustrative example, an RC bridge pier was modeled as single degree of freedom (SDOF). The longitudinal rebars buckling of this pier was considered as the sole limit state when estimating its failure probability. The findings show that the life‐cycle reliability of RC bridge piers depends on both the seismic and airborne chloride hazards, and that the cumulative‐time failure probabilities of RC bridge piers located in seismic zones can be dramatically affected by the effect of airborne chlorides. Copyright © 2011 John Wiley & Sons, Ltd.     

A critical examination of seismic response uncertainty analysis in earthquake engineering

The last decade of performance‐based earthquake engineering (PBEE) research has seen a rapidly increasing emphasis placed on the explicit quantification of uncertainties. This paper examines uncertainty consideration in input ground‐motion and numerical seismic response analyses as part of PBEE, with particular attention given to the physical consistency and completeness of uncertainty consideration. It is argued that the use of the commonly adopted incremental dynamic analysis leads to a biased representation of the seismic intensity and that when considering the number of ground motions to be used in seismic response analyses, attention should be given to both reducing parameter estimation uncertainty and also limiting ground‐motion selection bias. Research into uncertainties in system‐specific numerical seismic response analysis models to date has been largely restricted to the consideration of ‘low‐level’ constitutive model parameter uncertainties. However, ‘high‐level’ constitutive model and model methodology uncertainties are likely significant and therefore represent a key research area in the coming years. It is also argued that the common omission of high‐level seismic response analysis modelling uncertainties leads to a fallacy that ground‐motion uncertainty is more significant than numerical modelling uncertainty. The author's opinion of the role of uncertainty analysis in PBEE is also presented. Copyright © 2013 John Wiley & Sons, Ltd.     

A stochastic model and synthesis for near‐fault impulsive ground motions

The orientations of ground motions are paramount when the pulse‐like motions and their unfavorable seismic responses are considered. This paper addresses the stochastic modeling and synthesizing of near‐fault impulsive ground motions with forward directivity effect taking the orientation of the strongest pulses into account. First, a statistical parametric analysis of velocity time histories in the orientation of the strongest pulse with a specified magnitude and various fault distances is performed. A new stochastic model is established consisting of a velocity pulse model with random parameters and a stochastic approach to synthesize high‐frequency velocity time history. The high‐frequency velocity history is achieved by integrating a stochastic high‐frequency accelerogram, which is generated via the modified K‐T spectrum of residual acceleration histories and then modulated by the specific envelope function. Next, the associated parameters of pulse model, envelope function, and power spectral density are estimated by the least‐square fitting. Some chosen parameters in the stochastic model of near‐fault motions based on correlation analysis are regarded as random variables, which are validated to follow the normal or lognormal distribution. Moreover, the number theoretical method is suggested to select efficiently representative points, for generating artificial near‐fault impulsive ground motions with the feature of the strongest pulse, which can be used to the seismic response and reliability analysis of critical structures conveniently. Finally, the simulated ground motions demonstrate that the synthetic ground motions generated by the proposed stochastic model can represent the impulsive characteristic of near‐fault ground motions. Copyright © 2014 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.     

Seismic damage accumulation in multiple mainshock–aftershock sequences

Earthquakes are generally clustered, both in time and space. Conventionally, each cluster is made of foreshocks, the mainshock, and aftershocks. Seismic damage can possibly accumulate because of the effects of multiple earthquakes in one cluster and/or because the structure is unrepaired between different clusters. Typically, the performance-based earthquake engineering (PBEE) framework neglects seismic damage accumulation. This is because (i) probabilistic seismic hazard analysis (PSHA) only refers to mainshocks and (ii) classical fragility curves represent the failure probability in one event, of given intensity, only. However, for life cycle assessment, it can be necessary to account for the build-up of seismic losses because of damage in multiple events. It has been already demonstrated that a Markovian model (i.e., a Markov chain), accounting for damage accumulation in multiple mainshocks, can be calibrated by maintaining PSHA from the classical PBEE framework and replacing structural fragility with a set of state-dependent fragility curves. In fact, the Markov chain also works when damage accumulates in multiple aftershocks from a single mainshock of known magnitude and location, if aftershock PSHA replaces classical PSHA. Herein, this model is extended further, developing a Markovian model that accounts, at the same time, for damage accumulation: (i) within any mainshock–aftershock seismic sequence and (ii) among multiple sequences. The model is illustrated through applications to a series of six-story reinforced concrete moment-resisting frame buildings designed for three sites with different seismic hazard levels in Italy. The time-variant reliability assessment results are compared with the classical PBEE approach and the accumulation model that only considers mainshocks, so as to address the relevance of aftershocks for life cycle assessment.     

Decomposition algorithms for system reliability estimation with applications to interdependent lifeline networks

Reliability and risk assessment of lifeline systems call for efficient methods that integrate hazard and interdependencies. Such methods are computationally challenged when the probabilistic response of systems is tied to multiple events, as performance quantification requires a large catalog of ground motions. Available methods to address this issue use catalog reductions and importance sampling. However, besides comparisons against baseline Monte Carlo trials in select cases, there is no guarantee that such methods will perform or scale well in practice. This paper proposes a new efficient method for reliability assessment of interdependent lifeline systems, termed RAILS, that considers systemic performance and is particularly effective when dealing with large catalogs of events. RAILS uses the state‐space partition method to estimate systemic reliability with theoretical bounds and, for the first time, supports cyclic interdependencies among lifeline systems. Recycling computations across an entire seismic catalog with RAILS considerably reduces the number of system performance evaluations in seismic performance studies. Also, when performance estimate bounds are not tight, we adopt an importance and stratified sampling method that in our computational experiments is various orders of magnitude more efficient than crude Monte Carlo. We assess the efficiency of RAILS using synthetic networks and illustrate its application to quantify the seismic risk of realistic yet streamlined systems hypothetically located in the San Francisco Bay Region.     

Near‐source seismic hazard and design scenarios

Earthquakes damage engineering structures near, relatively to the rupture's size, to the source. In this region, the fault's dynamics affect ground motion propagation differently from site to site, resulting in systematic spatial variability known as directivity. Although a number of researches recommend that records with directivity‐related velocity pulses should be explicitly taken into account when defining design seismic action on structures, probabilistic seismic hazard analysis (PSHA), in its standard version, seems inadequate for the scope. In the study, it is critically reviewed why, from the structural engineering point of view, hazard assessment should account for near‐source effects (i.e., pulse‐like ground motions), and how this can be carried out adjusting PSHA analytically via introduction of specific terms and empirically calibrated models. Disaggregation analysis and design scenarios for near‐source PSHA are also formulated. The analytical procedures are then applied to develop examples of hazard estimates for sites close to strike–slip or dip–slip faults and to address differences with respect to the ordinary case, that is, when pulse‐like effects are not explicitly accounted for. Significant increase of hazard for selected spectral ordinates is found in all investigated cases; increments depend on the fault‐site configuration. Moreover, to address design scenarios for seismic actions on structures, disaggregation results are also discussed, along with limitations of current design spectra to highlight the pulse‐like effects of structural interest. Finally, an attempt to overcome these, by means of disaggregation‐based scenarios specific for the pulse occurrence case, is presented. Copyright © 2012 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.     

Probabilistic seismic loss assessment of aging bridges using a component‐level cost estimation approach

Deteriorating highway bridges in the United States and worldwide have demonstrated susceptibility to damage in earthquake events, with considerable economic consequences due to repair or replacement. Current seismic loss assessment approaches for these critical elements of the transportation network neglect the effects of aging and degradation on the loss estimate. However, the continued aging and deterioration of bridge infrastructure could not only increase susceptibility to seismic damage, but also have a significant impact on these economic losses. Furthermore, the contribution of individual aging components to system‐level losses, correlations between these components, and uncertainty modeling in the risk assessment and repair modeling are all crucial considerations to enhance the accuracy and confidence in bridge loss estimates. In this paper, a new methodology for seismic loss assessment of aging bridges is introduced based on the non‐homogeneous Poisson process. Statistical moments of seismic losses can be efficiently estimated, such as the expected value and variance. The approach is unique in its account for time‐varying seismic vulnerability, uncertainty in component repair, and the contribution of multiple correlated aging components. A representative case study is presented with two fundamentally distinct highway bridges to demonstrate the effects of corrosion deterioration of different bridge components on the seismic losses. Using the proposed model, a sensitivity study is also conducted to assess the effect of parameter variations on the expected seismic losses. The results reveal that the seismic losses estimated by explicitly considering the effects of deterioration of bridge components is significantly higher than that found by assuming time‐invariant structural reliability. Copyright © 2011 John Wiley & Sons, Ltd.     

Building service life economic loss assessment under sequential seismic events

Aftershocks have been shown to exacerbate earthquake‐induced financial losses by causing further damage to structural and nonstructural components in buildings that have already been affected by a mainshock event and increasing the duration of disrupted functionality. Whereas seismic loss assessment under isolated events has been addressed thoroughly in previous studies, comparatively less has been accomplished in the area of loss assessment under sequences of mainshock‐aftershock ground motions. The main objective of the current study is to formulate a comprehensive framework for quantifying financial losses under sequential seismic events. The proposed framework is capable of accounting for the uncertainties in the state of structure due to accumulation of earthquake‐induced damage, the time‐dependent nature of seismic hazard in the post‐mainshock environment, and the uncertainties in the occurrence of mainshock and aftershock events. Application of the proposed framework to a 4‐story reinforced concrete moment frame shows that consideration of aftershocks could increase lifecycle earthquake‐induced losses by up to 30% compared with mainshock‐only assessments.     

Seismic hazard disaggregation in performance‐based earthquake engineering: occurrence or exceedance?

Seismic hazard disaggregation is commonly used as an aid in ground‐motion selection for the seismic response analysis of structures. This short communication investigates two different approaches to disaggregation related to the exceedance and occurrence of a particular intensity. The impact the different approaches might have on a subsequent structural analysis at a given intensity is explored through the calculation of conditional spectra. It is found that the exceedance approach results in conditional spectra that will be conservative when used as targets for ground‐motion selection. It is however argued that the use of the occurrence disaggregation is more consistent with the objectives of seismic response analyses in the context of performance‐based earthquake engineering. Copyright © 2015 John Wiley & Sons, Ltd.     

Seismic resilience of concrete structures under corrosion

A probabilistic approach to lifetime assessment of seismic resilience of deteriorating concrete structures is presented. The effects of environmental damage on the seismic performance are evaluated by means of a methodology for lifetime assessment of concrete structures in aggressive environment under uncertainty. The time‐variant seismic capacity associated with different limit states, from damage limitation up to collapse, is assumed as functionality indicator. The role of the deterioration process on seismic resilience is then investigated over the structural lifetime by evaluating the post‐event residual functionality and recovery of the deteriorating system as a function of the time of occurrence of the seismic event. The proposed approach is applied to a three‐story concrete frame building and a four‐span continuous concrete bridge under corrosion. The results show the combined effects of structural deterioration and seismic damage on the time‐variant system functionality and resilience and indicate the importance of a multi‐hazard life‐cycle‐oriented approach to seismic design of resilient structure and infrastructure systems. Copyright © 2015 John Wiley & Sons, Ltd.     

Probabilistic performance‐based optimum design of seismic isolation for a California high‐speed rail prototype bridge

Previous comparison studies on seismic isolation have demonstrated its beneficial and detrimental effects on the structural performance of high‐speed rail bridges during earthquakes. Striking a balance between these 2 competing effects requires proper tuning of the controlling design parameters in the design of the seismic isolation system. This results in a challenging problem for practical design in performance‐based engineering, particularly when the uncertainty in seismic loading needs to be explicitly accounted for. This problem can be tackled using a novel probabilistic performance‐based optimum seismic design (PPBOSD) framework, which has been previously proposed as an extension of the performance‐based earthquake engineering methodology. For this purpose, a parametric probabilistic demand hazard analysis is performed over a grid in the seismic isolator parameter space, using high‐throughput cloud‐computing resources, for a California high‐speed rail (CHSR) prototype bridge. The derived probabilistic structural demand hazard results conditional on a seismic hazard level and unconditional, i.e., accounting for all seismic hazard levels, are used to define 2 families of risk features, respectively. Various risk features are explored as functions of the key isolator parameters and are used to construct probabilistic objective and constraint functions in defining well‐posed optimization problems. These optimization problems are solved using a grid‐based, brute‐force approach as an application of the PPBOSD framework, seeking optimum seismic isolator parameters for the CHSR prototype bridge. This research shows the promising use of seismic isolation for CHSR bridges, as well as the potential of the versatile PPBOSD framework in solving probabilistic performance‐based real‐world design problems.     

Seismic reliability of V‐braced frames: Influence of design methodologies

According to the most modern trend, performance‐based seismic design is aimed at the evaluation of the seismic structural reliability defined as the mean annual frequency (MAF) of exceeding a threshold level of damage, i.e. a limit state. The methodology for the evaluation of the MAF of exceeding a limit state is herein applied with reference to concentrically ‘V’‐braced steel frames designed according to different criteria. In particular, two design approaches are examined. The first approach corresponds to the provisions suggested by Eurocode 8 (prEN 1998—Eurocode 8: design of structures for earthquake resistance. Part 1: general rules, seismic actions and rules for buildings), while the second approach is based on a rigorous application of capacity design criteria aiming at the control of the failure mode (J. Earthquake Eng. 2008; 12 :1246–1266; J. Earthquake Eng. 2008; 12 :728–759). The aim of the presented work is to focus on the seismic reliability obtained through these design methodologies. The probabilistic performance evaluation is based on an appropriate combination of probabilistic seismic hazard analysis, probabilistic seismic demand analysis (PSDA) and probabilistic seismic capacity analysis. Regarding PSDA, nonlinear dynamic analyses have been carried out in order to obtain the parameters describing the probability distribution laws of demand, conditioned to given values of the earthquake intensity measure. Copyright © 2009 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.     

A probabilistic framework for correlated seismic downtime and repair cost estimation of geo‐structures

An important component of probabilistic risk assessment methods is the development of models to quantify the direct consequences of damage to geo‐structural components for a given intensity of the hazard. This paper presents a general probabilistic framework for correlated repair cost and downtime estimation of geo‐structures exposed to seismic hazards. The framework uses as input the results of nonlinear time‐history analysis of geo‐structures for the set of earthquake records that are representative of the seismic hazard models for the region of interest. The repair cost and downtime are estimated for individual earthquakes probabilistically considering the uncertainties associated with damage states. In addition, the formulation of the repair cost and downtime accounts for the reduction in the repair requirements as the number of damaged components in the given damage state increases. An analytical linear and two bilinear regression models are proposed for conditional correlated seismic repair cost and downtime estimation of geo‐structures given the intensity measure. The proposed framework is demonstrated by developing seismic repair models of a typical pile‐supported wharf structure on the west coast of the United States. The presented framework is general and can be applied to other types of geo‐structures and hazards and can include other decision variables such as loss of life as well. Copyright © 2013 John Wiley & Sons, Ltd.     

Global sensitivity analysis for stochastic ground motion modeling in seismic-risk assessment

Seismic risk assessment requires adoption of appropriate models for the earthquake hazard, the structural system and for its performance, and quantification of the uncertainties involved in these models through appropriate probability distributions. Characterization of the seismic hazard comprises undoubtedly the most critical component of this process, the one associated with the largest amount of uncertainty. For applications involving dynamic analysis this hazard is frequently characterized through stochastic ground motion models. This paper discusses a novel, global sensitivity analysis for the seismic risk with emphasis on such a stochastic ground motion modeling. This analysis aims to identify the overall (i.e. global) importance of each of the uncertain model parameters, or of groups of them, towards the total risk. The methodology is based on definition of an auxiliary density (distribution) function, proportional to the integrand of the integral quantifying seismic risk, and on comparison of this density to the initial probability distribution for the model parameters of interest. Uncertainty in the rest of the model parameters is explicitly addressed through integration of their joint auxiliary distribution to calculate the corresponding marginal distributions. The relative information entropy is used to quantify the difference between the compared density functions and an efficient approach based on stochastic sampling is introduced for estimating this entropy for all quantities of interest. The framework is illustrated in an example that adopts a source-based stochastic ground motion model, and valuable insight is provided for its implementation within structural engineering applications.     

Seismic risk assessment considering cumulative damage due to aftershocks

Calculating the limit state (LS) exceedance probability for a structure considering the main seismic event and the triggered aftershocks (AS) is complicated both by the time‐dependent rate of aftershock occurrence and also by the cumulative damage caused by the sequence of events. Taking advantage of a methodology developed previously by the authors for post‐mainshock (MS) risk assessment, the LS probability due to a sequence of mainshock and the triggered aftershocks is calculated for a given aftershock forecasting time window. The proposed formulation takes into account both the time‐dependent rate of aftershock occurrence and also the damage accumulation due to the triggered aftershocks. It is demonstrated that an existing reinforced concrete moment‐resisting frame with infills subjected to the main event and the triggered sequence exceeds the near‐collapse LS. On the other hand, the structure does not reach the onset of near‐collapse LS when the effect of triggered aftershocks is not considered. It is shown, based on simplifying assumptions, that the derived formulation yields asymptotically to the same Poisson‐type functional form used when the cumulative damage is not being considered. This leads to a range of approximate solutions by substituting the fragilities calculated for intact, MS‐damaged, and MS‐plus‐one‐AS‐damaged structures in the asymptotic simplified formulation. The latter two approximate solutions provide good agreement with the derived formulation. Even when the fragility of intact structure is employed, the approximate solution (considering only the time‐dependent rate of aftershock occurrence) leads to higher risk estimates compared with those obtained based on only the mainshock. Copyright © 2016 John Wiley & Sons, Ltd.     

Seismic hazard analysis for engineering sites based on the stochastic finite-fault method

Seismic hazard analyses are mainly performed using either deterministic or probabilistic methods. However, there are still some defects in these statistical model-based approaches for regional seismic risk assessment affected by the near-field of large earthquakes. Therefore, we established a deterministic seismic hazard analysis method that can characterize the entire process of ground motion propagation based on stochastic finite-fault simulation, and we chose the site of the Xiluodu dam to demonstrate the method. This method can characterize earthquake source properties more realistically than other methods and consider factors such as the path and site attenuation of seismic waves. It also has high computational efficiency and is convenient for engineering applications. We first analyzed the complexity of seismogenic structures in the Xiluodu dam site area, and then an evaluation system for ground motion parameters that considers various uncertainties is constructed based on a stochastic finite-fault simulation. Finally, we assessed the seismic hazard of the dam site area comprehensively. The proposed method was able to take into account the complexity of the seismogenic structures affecting the dam site and provide multi-level parameter evaluation results corresponding to different risk levels. These results can be used to construct a dam safety assessment system of an earthquake in advance that provides technical support for rapidly and accurately assessing the post-earthquake damage state of a dam, thus determining the influence of an earthquake on dam safety and mitigating the risk of potential secondary disasters.