Framework of aftershock fragility assessment–case studies: older California reinforced concrete building frames

Current seismic design codes and damage estimation tools neglect the influence of successive events on structures. However, recent earthquakes have demonstrated that structures damaged during an initial event (mainshock) are more vulnerable to severe damage and collapse during a subsequent event (aftershock). This increased vulnerability to damage translates to increased likelihood of loss of use, property, and life. Thus, a reliable risk assessment tool is required that characterizes the risk of the undamaged structure subjected to an initial event and the risk of the damaged structure under subsequent events. In this paper, a framework for development of aftershock fragilities is presented; these aftershock fragilities define the likelihood that a building damaged during a mainshock will exhibit a given damage state following one or more aftershocks. Thus, the framework provides a method for characterizing the risk associated with damage accumulation in the structure. The framework includes the following: (i) creation of a numerical model of the structure; (ii) characterization of building damage states; (iii) generation of a suite of mainshock–aftershocks; (iv) mainshock–aftershock analyses; and (v) development of aftershock fragility curves using probabilistic aftershock demand models, defined as a linear regression of aftershock demand–intensity pairs in a logarithmic space, and damage‐state prediction models. The framework is not limited to a specific structure type but requires numerical models defining structural response and linking structural response with damage. In the current study, non‐ductile RC frames (low‐rise, mid‐rise, and high‐rise) are selected as case studies for the application of the framework. Copyright © 2015 John Wiley & Sons, Ltd.     

Aftershock seismic assessment taking into account postmainshock residual drifts

This paper introduces and evaluates a methodology for the aftershock seismic assessment of buildings taking explicitly into account residual drift demands after the mainshock (i.e., postmainshock residual interstory drifts, RIDR_o). The methodology is applied to a testbed four‐story steel moment‐resisting building designed with modern seismic design provisions when subjected to a set of near‐fault mainshock–aftershock seismic sequences that induce five levels of RIDR_o. Once the postmainshock residual drift is induced to the building model, a postmainshock incremental dynamic analysis is performed under each aftershock to obtain its collapse capacity and its capacity associated to demolition (i.e., the capacity to reach or exceed a 2% residual drift). The effect of additional sources of stiffness and strength (i.e., interior gravity frames and slab contribution) and the polarity of the aftershocks are examined in this study. Results of this investigation show that the collapse potential under aftershocks strongly depends on the modeling approach (i.e., the aftershock collapse potential is modified when additional sources of lateral stiffness and strength are included in the analytical model). Furthermore, it is demonstrated that the aftershock capacity associated to demolition (i.e., the aftershock collapse capacity associated to a residual interstory drift that leads to an imminent demolition) is lower than that of the aftershock collapse capacity, which mean that this parameter should be a better measure of the building residual capacity against aftershocks. Copyright © 2014 John Wiley & Sons, Ltd.     

Effect of seismic sequences in reinforced concrete frame buildings located in soft-soil sites

On September 19 and 20, 1985, two strong subduction interface earthquakes struck Mexico City leading to a large stock of damaged, or even collapsed, reinforced concrete (RC) building structures located in soft soil sites of the former lake-bed zone. The aim of this study is to gain further understanding on the effects of soft-soil seismic sequences on the seismic response of RC framed-buildings. This investigation employed artificial sequences since only two real sequences were gathered during the 1985 earthquakes. The nonlinear response, in terms of peak and residual lateral inter-story drift demands of four RC buildings having 4, 8, 12, and 16 stories, was evaluated. Results show that the relationship of the damaged period of the building (i.e. period of the building after the mainshock) to the predominant period of the aftershock, which is a measure of its frequency content, has a significant impact in the building response.     

Aftershock collapse fragility curves for non‐ductile RC buildings: a scenario‐based assessment

Recent studies have addressed the computation of fragility curves for mainshock (MS)‐damaged buildings. However, aftershock (AS) fragilities are generally conditioned on a range of potential post‐MS damage states that are simulated via static or dynamic analyses performed on an intact building. Moreover, there are very few cases where the behavior of non‐ductile reinforced concrete buildings is analyzed. This paper presents an evaluation of AS collapse fragility conditioned on various return periods of MSs, allowing for the rapid assessment of post‐earthquake safety variations based solely on the intensity of the damaging earthquake event. A refined multi‐degree‐of‐freedom model of a seven‐storey non‐ductile building, which includes brittle failure simulations and the evaluation of a system level collapse, is adopted. Aftershock fragilities are obtained by performing an incremental dynamic analysis for a number of MS–AS ground motion sequences and a variety of MS intensities. The AS fragilities show that the probability of collapse significantly increases for higher return periods for the MS. However, this result is mainly ascribable to collapses occurred during MSs. When collapse cases that occur during a MS are not considered in the assessment of AS collapse probability, a smaller shift in the fragility curves is observed as the MS intensity increases. This result is justified considering the type of model and collapse modes introduced, which strongly depend on the brittle behavior of columns failing in shear or due to axial loads. The analysis of damage that is due to MSs when varying the return period confirms this observation. Copyright © 2017 John Wiley & Sons, Ltd.     

主余震作用下塔尔寺中心大塔响应研究

目前对建筑结构进行主余震序列作用下的动力响应研究表明,主震过后的余震往往会造成结构损伤的累积,导致结构裂缝扩展甚至倒塌,但主余震分析在土遗址的分析中却应用较少。以锁阳城塔尔寺中心大塔为研究对象,基于目标谱匹配方法选取6条自然地震动记录调幅,进行单一主震与主余震序列作用下的动力响应分析。结果表明：加速度与位移响应沿佛塔高度的变化趋势在主震作用与余震作用下基本一致,加速度与竖向位移最大值位于佛塔顶点,而水平位移最大值位于覆钵体与塔身结合处;结构在主震作用下产生塑性损伤后,余震会扩大损伤的范围和程度,且损伤严重的部位扩大效果最明显。通过以上分析得到塔尔寺中心大塔的薄弱位置,提出在合适部位进行支护加固等改进措施。     

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 analyses of a RCC building under mainshock–aftershock seismic sequences

A large mainshock may trigger numerous aftershocks within a short period, and nuclear power plant (NPP) structures have the probability to be exposed to mainshock–aftershock seismic sequences. However, the researchers focused on seismic analyses of reinforced concrete containment (RCC) buildings under only mainshocks. The aim of this paper is to thoroughly investigate the dynamic responses of a RCC building under mainshock–aftershock seismic sequences. For that purpose, 10 as-recorded mainshock–aftershock seismic sequences with two horizontal components are considered in this study, and a typical three-dimensional RCC model subjected to the selected as-recorded seismic sequences is established. Peak ground accelerations (PGAs) of mainshocks equal to 0.3 g (safe shutdown earthquake load-SSE load) are considered in this paper. The results indicate that aftershocks have a significant effect on the responses of the RCC in terms of maximum top accelerations, maximum top displacements and accumulated damage. Furthermore, in order to preserve the RCC from large damage under repeated earthquakes, local damage and global damage indices are suggested as limitations under only mainshocks.     

Damage‐dependent vulnerability curves for existing buildings

Seismic behavior of damaged buildings may be expressed as a function of their REsidual Capacity (REC), which is a measure of seismic capacity, reduced by damage. REC can be interpreted as the median value of collapse vulnerability curves. Its variation owing to damage is a useful indication of increased building vulnerability. REC reduction, indicating the lowering of seismic safety after an earthquake (performance loss, PL), represents an effective index for assessing the need of seismic repair/strengthening after earthquakes. The study investigates the applicability of a pushover‐based method in the analysis of damaged structures for the case of existing under‐designed RC buildings. The paper presents a systematization of the procedure in an assessment framework that applies the capacity spectrum method based on inelastic demand spectra; furthermore, the vulnerability variation of a real building is investigated with a detailed case study. The behavior of damaged buildings is simulated with pushover analysis through suitable modification of plastic hinges (in terms of stiffness, strength and residual drift) for damaged elements. The modification of plastic hinges has been calibrated in tests on nonconforming columns. The case study analysis evidenced that, for minor or moderate damages, the original structural displacement capacity was only slightly influenced, but the ductility capacity was significantly reduced (up to 40%) because of the increased structure deformability. This implied performance loss in the range 10%–20%. For severe damages the PL ranged between 41% and 56%. Local mechanism types exhibit PL nearly double with respect to global mechanism types. Copyright © 2012 John Wiley & Sons, Ltd.     

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.     

Loss estimation for non‐ductile reinforced concrete building in Victoria,British Columbia,Canada: effects of mega‐thrust Mw9‐class subduction earthquakes and aftershocks

This paper presents, within the performance‐based earthquake engineering framework, a comprehensive probabilistic seismic loss estimation method that accounts for main sources of uncertainty related to hazard, vulnerability, and loss. The loss assessment rigorously integrates multiple engineering demand parameters (maximum and residual inter‐story drift ratio and peak floor acceleration) with consideration of mainshock–aftershock sequences. A 4‐story non‐ductile reinforced concrete building located in Victoria, British Colombia, Canada, is considered as a case study. For 100 mainshock and mainshock–aftershock earthquake records, incremental dynamic analysis is performed, and the three engineering demand parameters are fitted with a probability distribution and corresponding dependence computed. Finally, with consideration of different demolition limit states, loss assessment is performed. From the results, it can be shown that when seismic vulnerability models are integrated with seismic hazard, the aftershock effects are relatively minor in terms of overall seismic loss (1–4% increase). Moreover, demolition limit state parameters, uncertainties of collapse fragility, and non‐collapse seismic demand prediction models have showed significant contribution to the loss assessment. The seismic loss curves for the reference case and for cases with the varied parameters can differ by as large as about 150%. Copyright © 2015 John Wiley & Sons, Ltd.     

Effects of aftershocks on peak ductility demand due to strong ground motion records from shallow crustal earthquakes

Aftershocks induced by a large mainshock can cause additional damage to structures and infrastructure, hampering building reoccupation and restoration activities in a post‐disaster situation. To assess the nonlinear damage potential due to aftershocks, this study investigates the effects of aftershocks by using real as well as artificially generated mainshock–aftershock sequences. The real mainshock–aftershock sequences are constructed from the Pacific Earthquake Engineering Research Center—Next Generation Attenuation database for worldwide shallow crustal earthquakes; however, they are deemed to be incomplete because of missing records. To supplement incomplete real dataset, artificial sequences are generated on the basis of the generalized Omori's law, and a suitable aftershock record selection procedure is then devised to simulate time‐series data for mainshock–aftershock sequences. The results from nonlinear dynamic analysis of inelastic single‐degree‐of‐freedom systems using real and artificial sequences indicate that the incremental effects of aftershocks on peak ductility demand using the real sequences are relatively minor and that peak ductility demand estimates based on the generalized Omori's law are greater, particularly in the upper tail, than those for the real sequences. The results based on the generalized Omori's law also suggest that the aftershock effects based on the real sequences might underestimate the aftershock impact because of the incompleteness of the real dataset. Copyright © 2012 John Wiley & Sons, Ltd.     

汶川8.0级地震中汶川县城房屋震害及其加固情况分析

依据5.12汶川地震中汶川县城(威远镇)11个区域共522栋房屋的房屋安全鉴定报告,深入统计分析房屋的震害情况及特点。结果表明,县城房屋倒塌较少,但破坏程度较重。破坏多集中在低层房屋以及砌体结构和木结构,而钢筋混凝土框架及高层房屋破坏较轻。结合房屋的破坏情况,对县城房屋的维修和加固情况进行分类统计,分析维修加固中出现的问题,并提出了相应建议。     

Inelastic response analysis of reinforced concrete structures using modified force analogy method

A modified force analogy method (MFAM) is developed to simulate the nonlinear inelastic response of reinforced concrete (RC) structures. Beam–column elements with three different plastic mechanisms are utilized to simulate inelastic response caused by moment and shear force. A multi‐linear hysteretic model is implemented to simulate the nonlinear inelastic response of RC member. The P‐Δ effect of the structure is also addressed in MFAM. Static and dynamic inelastic response of structure, damage condition and failure type for structural element, structural limit state and collapse time can also be simulated using MFAM. Compared with the general algorithm, the MFAM provides less computational time especially in the case of large structural system. It is also easier to be written as computer program. Three test data groups, which include cyclic loading test data of a non‐ductile RC bridge column, a two‐storey RC frame, and dynamic collapse test data of a non‐ductile RC portal frame, are selected to confirm the effectiveness of applying MFAM to simulate the inelastic behaviour of structures. Copyright © 2007 John Wiley & Sons, Ltd.     

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.     

Cumulative damage effects of mainshock-aftershock sequences on RC-frame structures

Frequent aftershocks often follow a strong mainshock. They can significantly increase cumulative damage to a structure. A model of a five-story reinforced concrete frame structure was designed and a nonlinear mathematical model of the structure was developed to investigate the damage states resulting from different mainshock-aftershock sequences. Mainshock-aftershock sequences consisting of one of three recorded mainshocks combined with one of five recorded aftershocks were created for input to the mathematical model. Inelastic energy dissipation and the Park-Ang damage index were used as measures of cumulative damage to the structure. The results demonstrate that consideration of only the single mainshock ground motion in seismic building design can result in the design and construction of unsafe buildings. Total cumulative damage to a structure is caused by the combination of damage states resulting from the mainshock and the aftershock(s).     

A probabilistic framework for quantification of aftershock ground‐motion hazard in California: Methodology and parametric study

This paper presents a proposed method of aftershock probabilistic seismic hazard analysis (APSHA) similar to conventional ‘mainshock’ PSHA in that it estimates the likelihoods of ground motion intensity (in terms of peak ground accelerations, spectral accelerations or other ground motion intensity measures) due to aftershocks following a mainshock occurrence. This proposed methodology differs from the conventional mainshock PSHA in that mainshock occurrence rates remain constant for a conventional (homogeneous Poisson) earthquake occurrence model, whereas aftershock occurrence rates decrease with increased elapsed time from the initial occurrence of the mainshock. In addition, the aftershock ground motion hazard at a site depends on the magnitude and location of the causative mainshock, and the location of aftershocks is limited to an aftershock zone, which is also dependent on the location and magnitude of the initial mainshock. APSHA is useful for post‐earthquake safety evaluation where there is a need to quantify the rates of occurrence of ground motions caused by aftershocks following the initial rupture. This knowledge will permit, for example, more informed decisions to be made for building tagging and entry of damaged buildings for rescue, repair or normal occupancy. Copyright © 2008 John Wiley & Sons, Ltd.     

Seismic behavior of asymmetric RC wall buildings: principles and new deformation‐based design method

The seismic design of multi‐story buildings asymmetric in plan yet regular in elevation and stiffened with ductile RC structural walls is addressed. A realistic modeling of the non‐linear ductile behavior of the RC walls is considered in combination with the characteristics of the dynamic torsional response of asymmetric buildings. Design criteria such as the determination of the system ductility, taking into account the location and ductility demand of the RC walls, the story‐drift demand at the softer (most displaced) edge of the building under the design earthquake, the allowable ductility (ultimate limit state) and the allowable story‐drift (performance goals) are discussed. The definition of an eccentricity of the earthquake‐equivalent lateral force is proposed and used to determine the effective displacement profile of the building yet not the strength distribution under the design earthquake. Furthermore, an appropriate procedure is proposed to calculate the fundamental frequency and the earthquake‐equivalent lateral force. A new deformation‐based seismic design method taking into account the characteristics of the dynamic torsional response, the ductility of the RC walls, the system ductility and the story‐drift at the softer (most displaced) edge of the building is presented and illustrated with an example of seismic design of a multi‐story asymmetric RC wall building. Copyright © 2005 John Wiley & Sons, Ltd.     

Seismic fragility assessment on the post-mainshock damaged shield building considering aftershock duration and damage ratio

In general, historical earthquake events have shown that a strong mainshock might trigger several aftershocks, which can cause additional damage and seismic risk to the structures. This work tries to investigate the aftershock duration on seismic fragility of the shield building in consideration of initial damage. For this purpose, a three-dimensional finite element model of shield building is established using a concrete damage plastic model. A series of mainshock-aftershock sequences with different durations are selected and scaled to match the target spectrum. A damage ratio of tensile damage is developed to evaluate the additional damage caused by mainshock and aftershocks. Aftershocks with three durations, namely, 20 s, 40 s, and 60 s, are used to study the effect of initial damage levels and aftershock durations on the accumulative damage and seismic fragility of the shield building. The results indicate that those aftershocks with longer durations may wreak more worse cumulative damage to the post-mainshock damaged structure and significantly affect the probability of exceedance. It is also indicated that the initial damage levels have a significant impact on the fragility curves of the shield building. This work can directly incorporate the influence of mainshock-damaged states into the fragility assessment for Nuclear Power Plant.

     

基于性能的既有钢筋混凝土建筑结构抗震评估与加固技术研究

根据我国现行的建筑结构抗震规范,无论是新建建筑结构的抗震设计还是既有建筑结构的抗震评估与加固,均通过小震弹性承载力计算 抗震延性构造措施来达到"小震不坏、中震可修、大震不倒"的抗震设防目标(对于不规则且具有明显薄弱部位的建筑结构还需要进行罕遇地震作用下的弹塑性层间变形验算)。对于抗震延性构造措施不满足现行规范的既有建筑结构的评估、改建、扩建,如果仅通过小震弹性的承载力计算,显然无法达到"大震不倒"的目标。本文通过引入国际上先进的基于性能的结构抗震思想,以结构层间位移和结构构件变形作为性能目标,从定量上解决了既有钢筋混凝土建筑结构的抗震评估与加固问题。     

按现行规范设计的Ⅷ度区RC框架结构的倒塌性能评估

选取按照现行规范设计的既有建筑进行有限元建模,考虑地震动的不确定性对其进行大量增量动力分析(IDA),得到模型的IDA曲线簇。在此基础上对其进行地震需求概率分析和概率抗震能力分析,拟合得到结构的易损性曲线,据此对结构的倒塌概率进行定量评估,并比较基于非线性分析与性能评估软件PERFORM-3D的纤维模型和塑性铰模型的分析结果。结果表明:按照我国现行规范设计的钢筋混凝土(RC)框架结构,在预期的罕遇地震作用下倒塌概率较小,可满足"大震不倒"的要求;基于PERFORM-3D的截面纤维模型所得的RC框架结构,经非线性分析所得的倒塌概率相对保守,安全储备更高。