Vulnerability assessment of a high‐rise building subjected to mainshock–aftershock sequences

Strong aftershocks have the potential to further aggravate the damage state of structures, and much less attention has been given to the seismic vulnerability of high‐rise buildings than that of low‐ to medium‐rise buildings. This study assesses the seismic vulnerability of a 32‐storey frame–core tube building by performing the incremental dynamic analysis on the material‐based three‐dimensional numerical model. A storey damage model based on the material damage is developed using the weighted average method. Eighteen recorded mainshock–aftershock sequences, whose mainshock records match the target spectrum, are selected. The results indicate that the developed stroey damage model can effectively reflect the additional damage induced by aftershocks. Strong aftershocks have high potential to change the location of weak storeys. Notably, shifts of weak storeys are observed in more than 30% of aftershocks with relative spectral acceleration of 0.8. As the mainshock‐induced damage state becomes more severe, the mainshock‐damaged building becomes increasingly fragile to the aftershock excitation and more sensitive to aftershock intensities. The probability of exceeding severe damage state increases from 35.3% to 62.1% due to the effects of strong aftershocks. The results in this study can provide supports to the seismic resilience assessment of this high‐rise building.     

钢筋混凝土框架结构的损伤状态相关余震易损性分析

一次主震过后通常伴有多次余震发生,由于主、余震间隔时间较短,主震损伤结构通常要遭受进一步的余震作用.为了评估震损结构的余震安全,提出了一种损伤状态相关的余震易损性分析方法.该方法采用有限次整体调幅的主余震序列作为输入,利用Park-Ang指数描述结构在主余震序列作用下的主震损伤和累积损伤,基于logistic回归方法生...     

基于试验的大跨异形钢连廊连体结构地震易损性分析

为研究大跨异形钢连廊连体结构的地震易损性,以某实际工程为研究背景,首先分别定义连体结构中的框架剪力墙结构、橡胶支座端和预埋锚固端的极限状态与损伤指标,并采用有限元软件SAP2000建立分析模型。其次,根据结构所在的场地条件,选取了24条地震动记录,并对结构进行三向地震激励下的增量动力分析。在此基础上,以最大层间位移角、橡胶支座的剪切应变和预埋锚固端的损伤因子作为结构地震需求参数,以地面峰值加速度作为地震动强度参数,根据增量动力分析的结果,得到大跨异形钢连廊连体结构的地震易损性曲线。最后,采用振动台试验对易损性分析结果进行验证。结果表明：在8度罕遇地震时,主楼、附楼I、橡胶支座端及角钢预埋锚固端发生毁坏的超越概率分别为0.8%、0.3%、0及47.7%,整体结构发生毁坏的超越概率上界为48.4%,下界为47.7%。这说明用局部结构的地震易损性来评价整体结构的地震易损性是偏于不安全的。易损性分析结果也显示连体结构易发生损坏的部位依次是预埋锚固端、主楼、附楼I和橡胶支座端,这与振动台试验结果相同。建议在设计中加强连体结构的锚固端,保证其可靠连接。     

Incremental dynamic analysis of steel braced frames designed based on the first,second and third editions of the Iranian seismic code (standard no. 2800)

Incremental dynamic analysis (IDA) is an emerging method in structural analysis which allows evaluation of seismic capacity and demand of structures through a series of nonlinear dynamic analyses using multiple scaled ground motion records. Seismic behaviour of concentrically braced frames designed based on the first, second and third revisions of the Iranian seismic code, standard no. 2800, has been evaluated through IDA in the present paper. Besides, a brief comparison is made between seismic behaviour of these frames, frames with different heights and different bracing types. Seismic capacity and limit states of such structures have been reviewed through the paper. The IDA results imply that frames designed with the first edition are seriously vulnerable and fail before reaching the acceleration levels predicted in the code. On the other hand, frames designed with the second and third editions, although behaving better, need partial reinforcement in some cases. Other results of this study show that chevron braced frames behave seismically better than X‐braced ones. Copyright © 2009 John Wiley & Sons, Ltd.     

Exploring the impact of chloride-induced corrosion on seismic damage limit states and residual capacity of reinforced concrete structures

A non-linear finite element (FE) framework for time-dependent capacity assessment of corroded rectangular reinforced concrete (RC) columns is developed. The proposed non-linear FE model includes the impact of corrosion on inelastic buckling and low-cycle fatigue degradation of longitudinal reinforcement. The proposed non-linear FE model is validated against a set of experimental data and then extended to evaluate the impact of corrosion on damage limit states to be used in seismic performance and evaluation of corroded structures. This is done through a parametric study on hypothetical RC columns, varied in axial force ratios, mass loss ratios, cover crack widths and confinement levels. Moreover, the application of the proposed model in seismic collapse capacity assessment of corroded structures is shown through non-linear dynamic analyses of prototype columns. Results show that, depending on the axial force ratio, corrosion changes the failure mechanism of the columns. The results of this study suggest that in seismic fragility analysis of corroded structures, the damage limit states should be considered as time-variant parameters.     

地震作用下钢框架结构抗竖向连续倒塌可靠度分析

为了对偶然荷载作用下结构的抗连续性倒塌进行可靠度研究,采用OpenSEES软件建立钢框架连续倒塌分析数值模型,考虑到钢框架结构材料和荷载的不确定性,使用拉丁超立方抽样方法生成钢框架结构随机样本,并采用随机Pushover算法对钢框架结构进行分析,计算得到X、Y两个方向不同地震水平下各钢柱承载能力及变形能力的可靠度指标,根据抗震可靠度相关理论确定目标可靠度指标,通过比较各柱的可靠度指标和目标可靠度,对结构在地震作用下最可能失效构件进行识别。基于所识别的最可能失效构件,结合所生成的100组钢框架结构随机样本,采用拆除构件法对钢框架结构在单柱失效和多柱失效等工况下进行抗连续倒塌IDA分析,得到随机IDA分析曲线。通过结构连续倒塌极限状态方程,计算得到损伤结构发生连续倒塌的概率及连续倒塌条件可靠度指标。采用基于风险的结构连续倒塌概率表达式,分析地震作用下钢框架结构发生局部破坏后的连续倒塌全概率可靠度,为准确评价钢框架结构在地震作用下的抗连续倒塌能力提供依据。     

Seismic fragility assessment of a tall reinforced concrete chimney

In China, a considerable proportion of reinforced concrete (RC) industrial chimneys in operation was designed and constructed in accordance with less rigorous outdated seismic criteria during the end of 19th and early 20th century. However, few research works have been reported till date on a realistic overall assessment of the seismic performance of these existing aging RC chimney structures. Therefore, in this study, fragilities of existing RC chimney were studied. For this purpose, an existing 240 m tall RC chimney was selected and structurally modeled with a lumped mass beam (stick) model by means of the OpenSees analysis program. In order to capture the uncertainties in ground motion realizations, a series of 21 ground motions are selected from the Next Generation Attenuation database as the input motions. To develop the analytical fragility curves, nonlinear incremental dynamic analysis of the studied RC chimney was then carried out using the selected input motions, which were normalized to different excitation levels. The section curvature ductility ratio was considered as the damage index. Based on material strain and sectional analysis, four limit states (LSs) were defined for five damage state. The seismic responses of the all sections were utilized to evaluate the likelihood of exceeding the LSs. Then the peak ground acceleration (PGA)‐based seismic fragility curves of the structure were constructed assuming a lognormal distribution. Finally, under the light of these fragility curves, the damage risks in existing RC chimney were discussed. The analytical results indicated that for design level earthquake of PGA = 0.1 g (g is the gravitational acceleration) and the maximum considered earthquake of PGA = 0.22 g, the probabilities of exceeding the light damage state were around 1.5% and 44%, respectively, while the exceedance probabilities corresponding to moderate, extensive and complete damage states were approximately zero in both cases. On the other hand, fragility analysis revealed that the RC chimney structure had considerable ductility capacity and was capable to withstand a strong earthquake with some structural damages. Copyright © 2014 John Wiley & Sons, Ltd.     

Fragility assessment of high‐rise reinforced concrete buildings considering the effects of shear wall contributions

The effect of shear wall configurations on seismic responses of high‐rise RC buildings is investigated in this paper using fragility analysis method. Four lower high‐rise RC buildings that have the same plan dimensions and height but are different in configurations in lateral force resisting systems, were firstly designed following the standard code procedure. To consider uncertainties in earthquake motions, 16 real ground motion pairs were selected and scaled, then applied orthogonally to the four RC building models during the Incremental Dynamic Analysis (IDA). Fragility relationships were therefore derived based on the IDA results for the three limit states including slight damage, moderate damage and collapse to show the probabilistic comparison of seismic responses among the four buildings in both x and y‐directions. It was observed that generally adding shear walls will improve buildings' seismic performance at all limit states. However, shear wall configuration also plays a significant role in seismic behavior of the lower high‐rise regular RC buildings' and internal shear walls are generally more effective than external shear walls in improving building's seismic resistance. Copyright © 2016 John Wiley & Sons, Ltd.     

Seismic fragility and cost analyses of actively controlled structures

Seismic fragility represents the probability that structural response exceeds a given performance limit state due to a specified intensity of ground motion, and it has a direct relationship with the cost of rehabilitating the structural system. In this research, a cost analysis framework based on seismic fragility to quantify the expected loss of the structural system was proposed. Incremental dynamic analysis was used to generate the fragility curves, and plastic strain derived from plastic energy dissipation was used to quantify the structural damage at a local level. Two moment‐resisting steel frames and 100 nonstationary Gaussian earthquake ground motions were simulated, and correlations between local damage states and global performance limit states were performed to facilitate the cost analysis study. The results showed that good correlations exist in seismic fragilities, and therefore, the repair cost of the structural system becomes quantifiable. Active control based on the optimal linear control algorithm was included as an auxiliary study to identify the sensitivity of the correlations. It is observed that significant cost reduction can be achieved for structures with few stories when active control is used but may not be cost‐effective if it is installed in taller structures. Published 2011. This article is a US Government work and is in the public domain in the USA.     

基于增量动力分析的大型地下洞室群性能化地震动力稳定性评估

 基于现有研究成果,将增量动力分析引入大型地下洞室群地震动力稳定性评价领域,形成大型地下洞室群的性能化地震动力稳定性评价方法。首先讨论基于PEER-NGA数据库的强震记录选取方法,根据具体工程的地震地质特性针对性地搜索合适的强震记录,为开展增量动力分析提供最优的输入地震动。然后讨论适用于大型地下洞室群的结构损伤性能参数、地震强度因子的选取,为增量动力分析提供合适的地震强度指标和抗震性能表征。继而立足于现有规范,形成了适用于大型地下洞室群性能化地震动力稳定性评估的2级地震动水平和2级抗震性能水平。最后采用本文的方法及步骤对大岗山水电工程地下洞室群进行地震动力稳定性评估。结果表明,该方法较好地考虑了地震动的随机性,给出洞室群的抗震性能,并可进一步对地震动力稳定性进行概率分析,为大型地下洞室群地震动力灾变失稳提供准则。     

Seismic performance of moment resisting steel frame subjected to earthquake excitations

This study presents static and dynamic assessments on the steel structures. Pushover analysis (POA) and incremental dynamic analysis (IDA) were run on moment resisting steel frames. The IDA study involves successive scaling and application of each accelerogram followed by assessment of the maximum response. Steel frames are subjected to nonlinear inelastic time history analysis for 14 different scaled ground motions, 7 near field and 7 far field. The results obtained from POA on the 3, 6 and 9 storey steel frames show consistent results for both uniform and triangular lateral loading. Uniform loading shows that the steel frames exhibits higher base shear than the triangular loading. The IDA results show that the far field ground motions has caused all steel frame design within the research to collapse while near field ground motion only caused some steel frames to collapse. The POA can be used to estimate the performance-based-seismic-design (PBSD) limit states of the steel frames with consistency while the IDA seems to be quite inconsistent. It is concluded that the POA can be consistently used to estimate the limit states of steel frames while limit state estimations from IDA requires carefully selected ground motions with considerations of important parameters.     

Cross‐level fragility analysis of modularized suspended buildings based on experimentally validated numerical models

Suspended buildings typically have a core as the primary and suspended floors as the secondary structures. These configurations offer visual transparency, smaller vertical components, and seismic attenuation via the primary–secondary structure interaction. Such attenuation is further enhanced by the modularization of the suspended segment which allows large drifts but prevents them from causing damage. Previously conducted shake‐table tests have confirmed these features. However, how the component performance contributes to system performance has not been quantitated. To address this gap, fragility analyses are conducted for 10‐story experimentally validated models with optimized supplemental dampers and inter‐module stiffness. Multiple limit state functions are proposed to provide a full account of damage sources. Additionally, a mapping rule from the component‐level to the system‐level limit states is developed which captures the influence of damage distribution on system‐level limit states. Results for the uncontrolled suspended building indicate that for the PGV of 0.5 m/s, the failure probabilities of the repairable and life safety limit states are 97% and 83%, respectively. These probabilities are 92% and 27% for the frame structure with viscous dampers, 58% and 5% for the passive‐controlled modularized suspended building system (MSBS), and 45% and 3% for MSBS with optimal vertical distributions of modularized secondary structure.     

Seismic performance of viaducts with probabilistic method

Due to the uncertainty of both ground motions and structural capacity, it is necessary to consider the seismic performance of viaduct structures using the probabilistic method. The risk is quantified by a procedure on the basis of a numerical determination of the fragility curves. A group of ground motions, Large Magnitude-Short Distance Bin (LMSR-N), selected specially due to its response spectra, is accorded well with the corresponding spectra of the Chinese code for seismic design. The characteristic values of the curvature ductility factors for the serviceability and the damage control limit states are obtained, and two equations for estimating the characteristic values of the curvature ductility factors are developed through regression analysis. Then, the serviceability and damage control limit states were proposed. Three damage states were constituted according the results of the experiment by Pacific Earthquake Engineering Research (PEER) Center. The analytical fragility curves were obtained specifically, using both Capacity Spectrum Method (CSM) (non-linear static) analysis and Ineremental Dynamic Method (IDM) (non-linear dynamic) analysis, respectively, in this paper. The structural fragility curves developed by CSM method can help make the structural analysis simple and quick, avoiding the implementation of the dynamic response history analysis (RHA). Although the dynamic RHA requires a lot of complicated analysis for the structure, the results from RHA are reliable and accurate. Fragility curves are powerful tools for use in performance-based seismic bridge design.     

Seismic design requirements for reinforced concrete piers considering aftershock-induced seismic hazard

The main purpose of this study is to develop an estimation procedure of seismic design level setting for reinforced concrete (RC) piers considering aftershock-induced seismic hazards. This work develops an assessment method of the seismic hazards induced by aftershocks and takes an example of the Chi–Chi Earthquake in Taiwan. The number of aftershocks is assumed to follow the modified Gutenberg–Richter law with lower and upper bounds when analysing the cumulative density function of the magnitude of the aftershock within a specified post-mainshock period for the earthquake. Additionally, this work considers the spatial uncertainty in the hypocentres of aftershocks to assess the aftershock-induced seismic hazards. Fragility curves and residual factors of damaged RC piers are used in the transition probability matrix of Markov Chain model for considering the cumulative damage induced by aftershocks by incorporating uncertainty into aftershock events, as well as into structural capacity and residual factors corresponding to a specified damage state, the exceedance probabilities for various damage states can be estimated using Markov Chain model and Monte Carlo Simulation. Finally, in the case study, the proposed procedure is used to determine the important factor in the preliminary seismic design of typical RC piers for the Chi–Chi Earthquake in Taiwan.     

考虑多维地震作用的高耸钢筋混凝土烟囱结构易损性分析

竖向地震作用对高耸烟囱结构动力响应有不可忽略的影响。选用240m高的某钢筋混凝土烟囱作为研究对象,考虑结构损伤,通过有限元软件ABAQUS,采用复合壳单元建立相应的非线性有限元分析模型。为考虑地震动的不确定性,根据谱相容性原则,选择20条合理地震动记录,进行增量动力分析。输入的地震动分别为一维、二维、三维。分别以材料应变和地面峰值加速度作为结构地震需求参数和地震动强度参数,结合增量动力分析获得的结构地震响应,采用能力需求比模型的曲线拟合法计算易损性曲线。通过钢筋和混凝土的材料应变定义四个损伤状态限值,最终得到在不同维数地震动输入时高耸钢筋混凝土烟囱结构的地震易损性曲线和倒塌概率曲线。研究结果表明,考虑多维地震作用比只考虑一维地震作用时高耸烟囱的结构易损性和倒塌概率增大。     

Building life-cycle cost analysis due to mainshock and aftershock occurrences

The objective of this paper is to develop formal stochastic expected financial loss estimation models over the lifetime of the building due to mainshocks and their subsequent aftershock sequences. Mainshocks are typically modeled as a homogeneous Poisson process with constant mean rate of occurrence, while the resulting aftershocks are modeled as a nonhomogeneous Poisson process with random magnitudes which has parameters (mainshock magnitude, m_m, and location) that are conditional on the random mainshock. The initial model to compute expected losses is the simplified homogeneous Poisson mainshock process and nonhomogeneous Poisson aftershock process with “immediate” repair of the building to the initial building state. We then develop a more general Markov and semi-Markov framework where we consider both Poisson and renewal processes for modeling mainshock occurrences with various building damage progression scenarios. Finally, we will incorporate the random aftershock losses into pre-mainshock financial loss estimation. The ability to compute the expected building life-cycle cost due to both mainshocks and aftershocks will be useful as an input to seismic decision making (both post- and pre-mainshock).     

Seismic partitioned fragility analysis for high‐rise RC chimney considering multidimensional ground motion

In order to identify the vulnerable parts and areas of the high‐rise reinforced concrete chimney, this paper presents an effective method, which called partitioned fragility analysis. One 240‐m‐high reinforced concrete chimney was selected as the practical project, and its analytical model was created with ABAQUS software. The selected high‐rise chimney structure was divided into 17 parts, and then the damage probability of each part in different damage states was obtained with the fragility analysis considering multidimensional ground motions. Twenty ground motion records were taken from the Next Generation Attenuation database as the input motions, and the peak ground acceleration was selected as the intensity measure. The response of the chimney structure under multidimensional ground motions was obtained based on incremental dynamic analysis. The maximum strains of concrete and steel bars were defined as the damage limit states of the chimney structure. The fragility curves and surfaces obtained from this analysis showed that the vulnerable areas of the chimney structure appear at 0–20 m, 90–130 m, and 150–200 m along the height of the chimney respectively. Based analytical results, these vulnerable parts can be retrofitted to enhance the seismic resistance of existing chimney structures. And the partitioned fragility analysis method can also be used to improve the design of new chimney structures.     

考虑倒塌概率修正的钢筋混凝土框架结构地震易损性分析

为研究倒塌概率对非倒塌极限状态的影响,提出了考虑倒塌概率修正的结构地震易损性分析方法。基于全概率定理,将结构极限状态划分为倒塌状态和非倒塌状态两类,若结构发生倒塌则认为结构发生非倒塌极限状态破坏的概率为100%。考虑倒塌概率修正的地震易损性分析方法包含直接方法和间接方法,其中,直接方法是直接对传统地震易损性函数进行修正,而间接方法仅修正地震易损性函数中的概率地震需求参数。以4榀不同高度不同设防烈度的钢筋混凝土平面框架结构作为研究对象,选择100条实际地震动记录作为输入,分别采用直接方法和间接方法开展考虑倒塌概率修正的地震易损性分析。结果表明：倒塌概率对轻微破坏和中等破坏极限状态的影响较小,而对严重破坏极限状态的影响较大;在地震动强度较小时,两种方法对地震易损性的修正结果相差较小;随着地震动强度的提高,两种方法对地震易损性修正结果的差距逐渐增大。     

单层柱面铝合金网壳结构强震失效机理及地震易损性

通过有限元分析软件ABAQUS建立了单层柱面铝合金网壳结构的有限元分析模型,利用增量动力分析方法（IDA）对网壳结构进行强震作用下动力响应全过程分析,获得了单层柱面铝合金网壳结构强震失效模式。基于模糊数学理论提出单层柱面铝合金网壳结构强震失效判别方法,结合结构损伤理论拟合网壳结构强震损伤因子,通过大规模参数分析定义适用于铝合金网壳结构的损伤程度分级,对铝合金网壳结构不同损伤状态进行划分。通过随机抽样选取一定数量的结构-地震样本,对铝合金网壳结构开展地震易损性分析,通过回归分析建立地震易损性函数,获得单层柱面铝合金网壳结构的概率地震易损性曲线。结果表明：通过结构地震易损性分析可以看出铝合金网壳结构具有良好的抗震性能,在强震作用下保持基本完好或仅有轻微破坏的概率较大。     

Seismic vulnerability assessment of tilt-up concrete structures

This paper focuses on seismic vulnerability assessment for one-story tilt-up concrete structures. To capture the potential failure mechanisms, an analytical modelling approach using nonlinear properties is developed and verified with measured data from a shake table test documented in the literature. Nonlinear dynamic analyses using synthetic ground motions for Memphis, Tennessee, are performed to assess dynamic behaviour of the buildings. Then, probabilistic demand models for multiple limit states that represent potential failure mechanisms are developed with a Bayesian updating approach. These demand models are used in conjunction with appropriate capacity limits to develop fragility curves that provide a probabilistic measure of the seismic vulnerability of typical tilt-up concrete buildings. This study shows that the vulnerability of typical tilt-up structures in Mid-America is significant when seismic hazards are high. In addition, it is found that the aspect ratio of building geometry has a significant impact on the seismic performance and fragility estimates of tilt-up buildings.