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.     

考虑残损的古建木结构地震易损性分析

现役古建木结构普遍存在残损现象,这将影响结构的抗震性能。本文以北京故宫的咸福宫西配殿为研究对象,通过简化其屋顶、斗拱、榫卯和柱脚节点建立结构的理想模型,并在此基础上考虑材料老化和节点性能降低等因素建立其残损现状模型。通过地震易损性分析,得到古建木结构的地震易损性曲线并进行理想和残损结构的震害等级及其发生概率对比。研究结果表明:残损现象降低了咸福宫西配殿的刚度和自振频率;相比于理想结构,咸福宫西配殿残损结构在小震作用下发生轻微损坏的概率增大21.1%,在中震作用下发生中等破坏的概率增大3.7%,大震作用下发生严重破坏的概率增大10.6%;咸福宫西配殿在大震作用下发生倒塌的概率很小,体现了木结构具有良好的抗震性能。     

Simulations of non‐stationary frequency content and its importance to seismic assessment of structures

To verify the importance of the non‐stationary frequency characteristic of seismic ground motion, a joint time–frequency analysis technique of time signals, called chirplet‐based signal approximation, is developed to extract the non‐stationary frequency information from the recorded data. The chirplet‐based signal approximation is clear in concept, similar to Fourier Transform in mathematical expressions but with different base functions. Case studies show that the chirplet‐based signal approximation can represent the joint time–frequency variation of seismic ground motion quite well. Both the random models of uniform modulating process and evolutionary process are employed to generate artificial seismic waves. The joint time–frequency modulating function in the random model of evolutionary process is determined by chirplet‐based signal approximation. Finally, non‐linear response analysis of a SODF system and a frame structure is performed based on the generated artificial seismic waves. The results show that the non‐stationary frequency characteristic of seismic ground motion can significantly change the non‐linear response characteristics of structures, particularly when a structure goes into collapse phase under seismic action. It is concluded that non‐stationary frequency characteristic of seismic ground motion should be considered for the assessment of seismic capacity of structures. Copyright © 2002 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.     

Seismic assessment of concrete gravity dams using capacity estimation and damage indexes

A new concept to determine state of the damage in concrete gravity dams is introduced. The Pine Flat concrete gravity dam has been selected for the purpose of the analysis and its structural capacity, assuming no sliding plane and rigid foundation, has been estimated using the two well‐known methods: nonlinear static pushover (SPO) and incremental dynamic analysis (IDA). With the use of these two methods, performance and various limit states of the dam have been determined, and three damage indexes have been proposed on the basis of the comparison of seismic demands and the dam's capacity. It is concluded that the SPO and IDA can be effectively used to develop indexes for seismic performance evaluation and damage assessment of concrete gravity dams. Copyright © 2012 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 reliability assessment and the nonergodicity in the modelling parameter uncertainties

Modelling uncertainty can significantly affect the structural seismic reliability assessment. However, the limit state excursion due to this type of uncertainty may not be described by a Poisson process as it lacks renewal properties with the occurrence of each earthquake event. Furthermore, considering uncertainties related to ground motion representation by employing recorded ground motions together with modelling uncertainties is not a trivial task. Robust fragility assessment, proposed previously by the authors, employs the structural response to recorded ground motion as data in order to update prescribed seismic fragility models. Robust fragility can be extremely efficient for considering also the structural modelling uncertainties by creating a dataset of one-to-one assignments of structural model realizations and as-recorded ground motions. This can reduce the computational effort by more than 1 order of magnitude. However, it should be kept in mind that the fragility concept itself is based on the underlying assumption of Poisson-type renewal. Using the concept of updated robust reliability, considering both the uncertainty in ground motion representation based on as-recorded ground motion and non ergodic modelling uncertainties, the error introduced through structural reliability assessment by using the robust fragility is quantified. It is shown through specific application to an existing RC frame that this error is quite small when the product of the time interval and the standard deviation of failure rate is small and is on the conservative side.     

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.     

A numerical study on the cumulative out‐of‐plane damage to church masonry façades due to a sequence of strong ground motions

Seismic shocks occur sometimes as a sequence, close in space and time, of destructive events of comparable intensity. In these cases, a significant portion of the damage to historical buildings can be related with the cumulated damage on structures that become progressively more vulnerable. This research investigates the specific increase of damage determined by a sequence of strong ground motions, focusing the interest on the out‐of‐plane response of 2 church masonry façades. The dynamic analyses were performed by a specific rigid body and spring model RBSM, which only accounts for out‐of‐plane damage mechanisms. Two idealized models of façade, each made of 2 different masonry bonds, have been studied by applying various sequences of recorded accelerograms. The results highlighted a complex relationship between the spectral content of the seismic shocks and the characteristics of the structures that change in the course of the loading sequence due to the development of damage. The Housner spectral intensity proved to be a reliable scalar measure of the ground motion destructiveness for these façades. Moreover, when considering a design‐consistent accelerogram that causes a relevant damage pattern, ie, with a significant elongation of the effective first period of vibration, the numerical results indicated a possible spectral intensity threshold below which the occurrence of repeated seismic shocks, both before and after the reference design shock, can be considered as irrelevant. On the other hand, a catastrophic increase of damage should be expected when this threshold is overcome.     

Integrating visual damage simulation,virtual inspection,and collapse capacity to evaluate post‐earthquake structural safety of buildings

A methodology is introduced to assess the post‐earthquake structural safety of damaged buildings using a quantitative relationship between observable structural component damage and the change in collapse vulnerability. The proposed framework integrates component‐level damage simulation, virtual inspection, and structural collapse performance assessment. Engineering demand parameters from nonlinear response history analyses are used in conjunction with component‐level damage simulation to generate multiple realizations of damage to key structural elements. Triggering damage state ratios, which describe the fraction of components within a damage state that results in an unsafe placard assignment, are explicitly linked to the increased collapse vulnerability of the damaged building. A case study is presented in which the framework is applied to a 4‐story reinforced concrete frame building with masonry infills. The results show that when subjected to maximum considered earthquake level ground motions, the probability of experiencing enough structural damage to trigger an unsafe placard, leading to building closure, is more than 2 orders of magnitude higher than the risk of collapse.     

基于耐震时程法的钢筋混凝土框架弹塑性地震响应及损伤发展

耐震时程法（ETA）仅需少量的非线性时程分析,便可以掌握结构倒塌破坏的全过程。但是,此方法目前较少应用于结构倒塌失效分析。本文探讨了耐震时程曲线的特性及拟合思路,以钢筋混凝土框架为研究对象,应用ETA方法分析了钢筋混凝土框架的地震响应及损伤发展。研究结果:（1）混凝土框架结构的地震响应分析结果表明:采用ETA方法分析时结构顶点位移和层间位移角与采用IDA方法分析时接近,而最大基底剪力会略大;但是,两种方法的结果相关系数均接近于1。（2）强震下的结构倒塌分析结果表明:ETA方法能较为准确的预测结构的塑性铰分布、塑性铰出现概率及塑性铰发展顺序。当采用多条耐震时程加速度曲线作为输入时,评估结果准确性更高。由于ETA方法仅需进行少量几条耐震时程分析且计算高效,因此ETA方法可以成为预测结构失效模式的高效方法。     

Cloud to IDA: Efficient fragility assessment with limited scaling

Incremental dynamic analysis (IDA) leads to curves expressed in terms of structural response versus intensity, commonly known as the IDA curves. It is known that implementation of IDA usually involves significant computational effort and most often significant scaling of the original records to various intensity levels. Employing as the performance variable the critical demand to capacity ratio (DCR) throughout the structure, which is equal to unity at the onset of the limit state, facilitates the identification of the intensity values at the onset of a desired limit state and hence the implementation of the IDA procedure. Employing the structural response to un‐scaled records and the corresponding regression‐based response predictions (a.k.a., the “Cloud Analysis”) helps in identifying the range of intensity values corresponding to demand to capacity ratio values in the vicinity of unity. The Cloud to IDA procedure for structural fragility assessment is proposed on the premise of exploiting the Cloud Analysis results to obtain the IDA curves both with minimum number of analyses and minimum amount of scaling. The transverse frame of a shear‐critical 7‐story older RC building in Van Nuys, CA, which is modeled in Opensees with fiber‐section considering the flexural‐shear‐axial interactions and the bar slip, is employed as a case study. It is demonstrated, by comparing the results to IDA and other state of the art non‐linear dynamic procedures based on no scaling or spectral‐shape‐compatible scaling, that the Cloud to IDA procedure leads to reliable results in terms of structural fragility and risk for the prescribed limit state.     

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.     

基于耐震时程法的进水塔结构抗震性能分析

进水塔结构作为水电站的进水建筑物,其抗震性能对水电站的安全运行有重要意义.以沙牌水电站的高耸独立进水塔结构为研究对象,应用3条耐震时程曲线对其进行抗震性能分析与评估,并将计算结果与天然地震动下的增量动力分析结果进行比较,对比分析进水塔塔顶位移、基底剪力及地震损伤历程.实例研究表明:耐震时程法可以较好地分析结构的抗震响应...     

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.     

Seismic response analysis using characteristic ground motion records for risk‐based decision‐making (3R method)

The concept of intensity‐based assessment for risk‐based decision‐making is introduced. It is realized by means of the so‐called 3R method (response analysis, record selection and risk‐based decision‐making), which can be used to check the adequacy of design of a new building or of the strengthening of an existing building by performing conventional pushover analysis and dynamic analysis for only a few ground motions, which are termed characteristic ground motions. Because the objective of the method is not a precise assessment of the seismic risk, a simple decision model for risk acceptability can be introduced. The engineer can decide that the reliability of a no‐collapse requirement is sufficient when collapse is observed in the case of less than half of, for example, seven characteristic ground motions. From the theoretical point of view, it is shown that the accuracy of the method is acceptable if the non‐linear response history analyses are performed at a low percentile of limit‐state intensity, which is also proven by means of several examples of multi‐storey reinforced concrete frame buildings. The 3R method represents a compromise between the exclusive use of either pushover analysis or dynamic analysis and can be easily introduced into building codes provided that its applicability is further investigated (e.g. asymmetric structures and other performance objectives) and that the procedure for the selection of characteristic ground motions is automated and readily available to engineers (www.smartengineering.si).     

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

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

Comparing the adequacy of alternative ground motion intensity measures for the estimation of structural responses

Practical methods for the probability‐based seismic assessment of structures make use of estimates of demands produced by earthquakes of different intensities. The uncertainties associated with these estimates are highly dependent on the variable adopted as the intensity measure (IM, e.g., PGA, spectral acceleration, etc.). This generates the need to compare the efficiency of an originally adopted IMwith that of a new candidate. This implies comparing the dispersion of the demand measure (DM, e.g., maximum interstorey drift ratio, ductility demand, etc.) conditional to each of the two IMs. In order to obtain the demand estimates in a conventional way, a full set of dynamic response analyses should be performed for each IM under scrutiny, i.e., multiple records scaled at several fixed values of each IM. The procedure developed here serves to accelerate this comparison avoiding the effort required to evaluate the dynamic responses of the structure for all the ground motion time histories considered every time that a new IM is adopted. For this purpose, use is made of available results of analyses performed for a different (i.e., the original) IM. Two methods are proposed: the direct method involves performing a regression of the results obtained from the original analyses, taking the candidate IM as the independent variable. The indirect method involves rebuilding the probability density function of the DM given a defined value of the candidate IM by means of the total probability theorem, using the results of the original analyses and certain data relating the two IMs. The proposed methods have been tested by application to several SDOF systems with different periods and different cyclic‐response backbone curves. The conditions affecting their approximation are explored, and some criteria to improve them are identified. The procedure can also be used to determine the optimum value of a parameter to be used in a parameter‐based IM. Copyright © 2004 John Wiley & Sons, Ltd.     

Evaluation of the influence of vertical irregularities on the seismic performance of a nine‐storey steel frame

A methodology based on incremental dynamic analysis (IDA) is presented for the evaluation of structures with vertical irregularities. Four types of storey‐irregularities are considered: stiffness, strength, combined stiffness and strength, and mass irregularities. Using the well‐known nine‐storey LA9 steel frame as a base, the objective is to quantify the effect of irregularities, both for individual and for combinations of stories, on its response. In this context a rational methodology for comparing the seismic performance of different structural configurations is proposed by means of IDA. This entails performing non‐linear time history analyses for a suite of ground motion records scaled to several intensity levels and suitably interpolating the results to calculate capacities for a number of limit‐states, from elasticity to final global instability. By expressing all limit‐state capacities with a common intensity measure, the reference and each modified structure can be naturally compared without needing to have the same period or yield base shear. Using the bootstrap method to construct appropriate confidence intervals, it becomes possible to isolate the effect of irregularities from the record‐to‐record variability. Thus, the proposed methodology enables a full‐range performance evaluation using a highly accurate analysis method that pinpoints the effect of any source of irregularity for each limit‐state. Copyright © 2006 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.