Conditional spectrum‐based ground motion selection. Part II: Intensity‐based assessments and evaluation of alternative target spectra

In a companion paper, an overview and problem definition was presented for ground motion selection on the basis of the conditional spectrum (CS), to perform risk‐based assessments (which estimate the annual rate of exceeding a specified structural response amplitude) for a 20‐story reinforced concrete frame structure. Here, the methodology is repeated for intensity‐based assessments (which estimate structural response for ground motions with a specified intensity level) to determine the effect of conditioning period. Additionally, intensity‐based and risk‐based assessments are evaluated for two other possible target spectra, specifically the uniform hazard spectrum (UHS) and the conditional mean spectrum (CMS, without variability).It is demonstrated for the structure considered that the choice of conditioning period in the CS can substantially impact structural response estimates in an intensity‐based assessment. When used for intensity‐based assessments, the UHS typically results in equal or higher median estimates of structural response than the CS; the CMS results in similar median estimates of structural response compared with the CS but exhibits lower dispersion because of the omission of variability. The choice of target spectrum is then evaluated for risk‐based assessments, showing that the UHS results in overestimation of structural response hazard, whereas the CMS results in underestimation. Additional analyses are completed for other structures to confirm the generality of the conclusions here. These findings have potentially important implications both for the intensity‐based seismic assessments using the CS in future building codes and the risk‐based seismic assessments typically used in performance‐based earthquake engineering applications. Copyright © 2013 John Wiley & Sons, Ltd.     

Seismic loss estimation of non‐ductile reinforced concrete buildings

Non‐ductile reinforced concrete buildings represent a prevalent construction type found in many parts of the world. Due to the seismic vulnerability of such buildings, in areas of high seismic activity non‐ductile reinforced concrete buildings pose a significant threat to the safety of the occupants and damage to such structures can result in large financial losses. This paper introduces advanced analytical models that can be used to simulate the nonlinear dynamic response of these structural systems, including collapse. The state‐of‐the‐art loss simulation procedure developed for new buildings is extended to estimate the expected losses of existing non‐ductile concrete buildings considering their vulnerability to collapse. Three criteria for collapse, namely first component failure, side‐sway collapse, and gravity‐load collapse, are considered in determining the probability of collapse and the assessment of financial losses. A detailed example is presented using a seven‐story non‐ductile reinforced concrete frame building located in the Los Angeles, California. Copyright © 2012 John Wiley & Sons, Ltd.     

Aftershock collapse vulnerability assessment of reinforced concrete frame structures

In a seismically active region, structures may be subjected to multiple earthquakes, due to mainshock–aftershock phenomena or other sequences, leaving no time for repair or retrofit between the events. This study quantifies the aftershock vulnerability of four modern ductile reinforced concrete (RC) framed buildings in California by conducting incremental dynamic analysis of nonlinear MDOF analytical models. Based on the nonlinear dynamic analysis results, collapse and damage fragility curves are generated for intact and damaged buildings. If the building is not severely damaged in the mainshock, its collapse capacity is unaffected in the aftershock. However, if the building is extensively damaged in the mainshock, there is a significant reduction in its collapse capacity in the aftershock. For example, if an RC frame experiences 4% or more interstory drift in the mainshock, the median capacity to resist aftershock shaking is reduced by about 40%. The study also evaluates the effectiveness of different measures of physical damage observed in the mainshock‐damaged buildings for predicting the reduction in collapse capacity of the damaged building in subsequent aftershocks. These physical damage indicators for the building are chosen such that they quantify the qualitative red tagging (unsafe for occupation) criteria employed in post‐earthquake evaluation of RC frames. The results indicated that damage indicators related to the drift experienced by the damaged building best predicted the reduced aftershock collapse capacities for these ductile structures. Copyright © 2014 John Wiley & Sons, Ltd.     

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。     

The effect of near-fault directivity on building seismic collapse risk

Forward directivity may cause large velocity pulses in ground motion time histories that are damaging to buildings at sites close to faults, potentially increasing seismic collapse risk. This study quantifies the effects of forward directivity on collapse risk through incremental dynamic analysis of building simulation models that are capable of capturing the key aspects of strength and stiffness degradation associated with structural collapse. The paper also describes a method for incorporating the effects of near-fault directivity in probabilistic assessment of seismic collapse risk. The analysis is based on a suite of RC frame models that represent both past and present building code provisions, subjected to a database of near-fault, pulse-like ground motions with varying pulse periods. Results show that the predicted collapse capacity is strongly influenced by variations in pulse period and building ductility; pulse periods that are longer than the first-mode elastic building period tend to be the most damaging. A detailed assessment of seismic collapse risk shows that the predicted probability of collapse in 50 years for modern concrete buildings at a representative near-fault site is approximately 6%, which is significantly higher than the 1% probability in the far-field region targeted by current seismic design maps in the US. Copyright © 2012 John Wiley & Sons, Ltd.     

Seismic collapse capacity of basic inelastic structures vulnerable to the P‐delta effect

The collapse capacity of earthquake‐excited inelastic nondeteriorating SDOF systems, which are vulnerable to the destabilizing effect of gravity loads (P‐delta effect), is evaluated. In this paper, the collapse capacity of the system subjected to a ground motion is defined as spectral acceleration at its initial structural period, at which the structure becomes unstable. Characteristic structural parameters, which affect the collapse capacity, are identified. Ground motion records of the ATC 63 far‐field set characterize severe earthquake excitation. In extensive incremental dynamic analyses studies, the impact of these parameters and of aleatory uncertainties on the collapse capacity is assessed and quantified. Median and percentile collapse capacities are plotted against the initial structural period leading to collapse capacity spectra. Nonlinear regression analyses are applied to derive analytical expressions of the design collapse capacity spectra and collapse fragility curves. The ultimate objective is to provide collapse capacity spectra for easy application and yet sufficient accurate assessment of the dynamic stability of flexible multistory buildings. Copyright © 2011 John Wiley & Sons, Ltd.     

Effects of vertical irregularity and thickness of unreinforced masonry infill on the robustness of RC framed buildings

Presence of irregularities in reinforced concrete (RC) buildings increases seismic vulnerability. During severe seismic shaking, such buildings may suffer disproportionate damage or even collapse that can be minimized by increasing robustness. Robustness is a desirable property of structural systems that can mitigate susceptible buildings to disproportionate collapse. In this paper, the effects of vertical irregularity and thickness of unreinforced masonry infill on the robustness of a six‐story three‐bay RC frame are quantified. Nonlinear static analysis of the frame is performed, and parametric study is undertaken by considering two parameters: absence of masonry infill at different floors (i.e., vertical irregularities) and infill thickness. Robustness has been quantified in terms of stiffness, base shear, ductility, and energy dissipation capacity of the frame. It was observed that the infill thickness and vertical irregularity have significant influence on the response of RC frame. The response surface method is used to develop a predictive equation for robustness as a function of the two parameters. The predictive equation is validated further using 12 randomly selected computer simulations. Copyright © 2013 John Wiley & Sons, Ltd.     

Sensitivity analysis of the seismic demands of RC moment resisting frames to different aspects of ground motions

A weight vector representing the relative importance of various characteristics of ground motions (GMs) and a conditioning intensity measure (IM) are required to be able to use the generalized conditional IM framework for the purpose of GM selection. An inappropriate weight vector may result in the biased distributions of some important characteristics of GMs and, consequently, the bias in the structural responses. This article aims to provide the analyst with the understanding of which properties of GMs are important in capturing the accurate structural responses, to specifically assign a suitable weight to them and to select an appropriate conditioning IM as well. To this end, 4 reinforced concrete buildings, located at the site in which the seismic hazard is dominated by shallow crustal earthquakes, are considered. The findings reveal that the appropriate weight vectors depend on the characteristics of the employed structural systems. In addition, the role played by each IM in capturing the true structural responses changes over different earthquake intensity levels implying that different weight vectors are required over different earthquake levels. Furthermore, this study shows that, even in case of shorter‐duration GMs from shallow events, GM duration should be incorporated in GM selection as it has effects on the peak‐based structural responses in the earthquake levels beyond the level of 2%‐in‐50‐years. Specifically, the findings reveal that in case of shallow events, unlike large magnitude earthquakes, the shorter the duration of GM the more rapid release of energy and, consequently, the larger the peak‐based structural responses.     

Analytical fragility assessment using unscaled ground motion records

It is desirable that nonlinear dynamic analyses for structural fragility assessment are performed using unscaled ground motions. The widespread use of a simple dynamic analysis procedure known as Cloud Analysis, which uses unscaled records and linear regression, has been impeded by its alleged inaccuracies. This paper investigates fragility assessment based on Cloud Analysis by adopting, as the performance variable, a scalar demand to capacity ratio that is equal to unity at the onset of limit state. It is shown that the Cloud Analysis, performed based on a careful choice of records, leads to reasonable and efficient fragility estimates. There are 2 main rules to keep in mind for record selection: to make sure that a good portion of the records leads to a demand to capacity ratio greater than unity and that the dispersion in records' seismic intensity is considerable. An inevitable consequence of implementing these rules is that one often needs to deal with the so‐called collapse cases. To formally consider the collapse cases, a 5‐parameter fragility model is proposed that mixes the simple regression in the logarithmic scale with logistic regression. The joint distribution of fragility parameters can be obtained by adopting a Markov Chain Monte Carlo simulation scheme leading directly to the fragility and its confidence intervals. The resulting fragility curves compare reasonably with those obtained from the Incremental Dynamic Analysis and Multiple Stripe Analysis with (variable) conditional spectrum–compatible suites of records at different intensity levels for 3 older reinforced concrete frames with shear‐, shear‐flexure‐, and flexure‐dominant behavior.     

Evaluation of collapse resistance of RC frame structures for Chinese schools in seismic design categories B and C

According to the Code for Seismic Design of Buildings (GB50011-2001), ten typical reinforced concrete (RC) frame structures, used as school classroom buildings, are designed with different seismic fortification intensities (SFIs) (SFI=6 to 8.5) and different seismic design categories (SDCs) (SDC=B and C). The collapse resistance of the frames with SDC=B and C in terms of collapse fragility curves are quantitatively evaluated and compared via incremental dynamic analysis (IDA). The results show that the coll...     

A novel structural detailing for the improvement of seismic and progressive collapse performances of RC frames

Earthquake-induced building collapse and progressive collapse due to accidental local failure of vertical components are the two most common failure modes of reinforced concrete (RC) frame structures. Conventional design methods usually focus on the design requirements of a specific hazard but neglect the interactions between different designs. For example, the progressive collapse design of an RC frame often yields increased reinforcement and flexural strength of the beams. As a result, the seismic design principle of “strong-column-weak-beam” may be violated, which may lead to unfavorable failure modes and weaken the seismic performance. To avoid these adverse effects of the progressive collapse design on the seismic resistance of RC frames, a novel structural detailing is proposed in this study. The proposed detailing technique intends to concurrently improve the seismic and progressive collapse performances of an RC frame by changing the layout of the newly added longitudinal reinforcement against progressive collapse without introducing any additional reinforcement. A six-story RC frame is used as the prototype building for this investigation. Both cyclic and progressive collapse tests are conducted to validate the performance of the proposed structural detailing. Based on the experimental results, detailed finite element (FE) models of the RC frame with different reinforcement layouts are established. The seismic and progressive collapse resistances of different models are compared based on the incremental dynamic analysis (IDA) and nonlinear dynamic alternate path (AP) methods, respectively. The results indicate that the proposed structural detailing can effectively resolve the conflict between the seismic and progressive collapse designs.     

Evaluation of the exact conditional spectrum and generalized conditional intensity measure methods for ground motion selection

Two existing, contemporary ground motion selection and modification procedures – (i) exact conditional spectrum (CS‐exact) and (ii) generalized conditional intensity measure (GCIM) – are evaluated in their ability to accurately estimate seismic demand hazard curves (SDHCs) of a given structure at a specified site. The amount of effort involved in implementing these procedures to compute a single SDHC is studied, and a case study is chosen where rigorous benchmark SDHCs can be determined for evaluation purposes. By comparing estimates from ground motion selection and modification procedures with the benchmark, we conclude that estimates from CS‐exact are unbiased in many of the cases considered. The estimates from GCIM are even more accurate, as they are unbiased for most – but not all – of the cases where estimates from CS‐exact are biased. We find that it is possible to obtain biased SDHCs from GCIM, even after employing a very diverse collection of intensity measures to select ground motions and implementing its bias‐checking feature, because it is usually difficult to identify intensity measures that are truly ‘sufficient’ for the response of a complex, multi‐degree‐of‐freedom system. Copyright © 2015 John Wiley & Sons, Ltd.     

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.     

Collapse simulation of reinforced concrete high‐rise building induced by extreme earthquakes

Collapse resistance of high‐rise buildings has become a research focus because of the frequent occurrence of strong earthquakes and terrorist attacks in recent years. Research development has demonstrated that numerical simulation is becoming one of the most powerful tools for collapse analysis in addition to the conventional laboratory model tests and post‐earthquake investigations. In this paper, a finite element method based numerical model encompassing fiber‐beam element model, multilayer shell model, and elemental deactivation technique is proposed to predict the collapse process of high‐rise buildings subjected to extreme earthquake. The potential collapse processes are simulated for a simple 10‐story RC frame and two existing RC high‐rise buildings of 18‐story and 20‐story frame–core tube systems. The influences of different failure criteria used are discussed in some detail. The analysis results indicate that the proposed numerical model is capable of simulating the collapse process of existing high‐rise buildings by identifying potentially weak components of the structure that may induce collapse. The study outcome will be beneficial to aid further development of optimal design philosophy. Copyright © 2012 John Wiley & Sons, Ltd.     

Incremental dynamic analysis of wood-frame houses in Canada: Effects of dominant earthquake scenarios on seismic fragility

Seismic fragility can be assessed by conducting incremental dynamic analysis (IDA). This study extends the current conditional mean spectrum (CMS)-based record selection approach for IDA by taking into account detailed seismic hazard information. The proposed method is applied to conventional wood-frame houses in Canada, across which dominant earthquake scenarios and associated hazard levels vary significantly. Effects due to different seismic environments, site conditions, CMS-based record selection methods, and house models are investigated by comparing various seismic fragility models. Moreover, relative impact of the key characteristics is evaluated in terms of seismic loss curve for a group of wood-frame houses. Importantly, a close examination of regional seismic hazard characteristics using seismic hazard curve and seismic deaggregation facilitates the deeper understanding of the impact of ground motion characteristics on seismic fragility. A comprehensive and systematic assessment of key uncertainties associated with seismic fragility is provided.     

Effect of gravity framing on the overstrength and collapse capacity of steel frame buildings with perimeter special moment frames

This paper investigates the effect of the gravity framing system on the overstrength and collapse risk of steel frame buildings with perimeter special moment frames (SMFs) designed in North America. A nonlinear analytical model that simulates the pinched hysteretic response of typical shear tab connections is calibrated with past experimental data. The proposed modeling approach is implemented into nonlinear analytical models of archetype steel buildings with different heights. It is found that when the gravity framing is considered as part of the analytical model, the overall base shear strength of steel frame buildings with perimeter SMFs could be 50% larger than that of the bare SMFs. This is attributed to the gravity framing as well as the composite action provided by the concrete slab. The same analytical models (i) achieve a static overstrength factor, Ω_s larger than 3.0 and (ii) pass the collapse risk evaluation criteria by FEMA P695 regardless of the assigned total system uncertainty. However, when more precise collapse metrics are considered for collapse risk assessment of steel frame buildings with perimeter SMFs, a tolerable probability of collapse is only achieved in a return period of 50 years when the perimeter SMFs of mid‐rise steel buildings are designed with a strong‐column/weak‐beam ratio larger than 1.5. The concept of the dynamic overstrength, Ω_d is introduced that captures the inelastic force redistribution due to dynamic loading. Steel frame buildings with perimeter SMFs achieve a Ω_d > 3 regardless if the gravity framing is considered as part of the nonlinear analytical model representation. Copyright © 2014 John Wiley & Sons, Ltd.     

Occurrence of negative epsilon in seismic hazard analysis deaggregation,and its impact on target spectra computation

This paper investigates circumstances behind the occurrence of negative ε (the normalized difference between the spectral acceleration of a recorded ground motion and the median response predicted by a ground motion prediction equation) in probabilistic seismic hazard deaggregation. Negative ε values are of engineering interest because of their impact on the conditional mean spectrum (CMS), which is a proposed alternative to the uniform hazard spectrum (UHS) as a target spectrum for ground motion selection. In the case where target ε values from deaggregation are positive, the CMS calculation produces relatively lower response spectra than the UHS. Positive target ε values occur almost universally in active seismic regions at long return periods of engineering interest, but the possibility of negative target ε values is important because in the case of negative target ε, some relationships between the CMS and UHS would reverse. This paper describes the calculation of target ε, performs parametric studies to determine when negative ε values occur in deaggregation, and investigates the potential impact on target spectrum calculation and ground motion selection. The case studies indicate that special seismicity models and certain ground motion prediction equations have the most significant effect on ε values and a combination of these characteristics in Eastern North America creates the most likely situation for negative target ε to occur. CMS results are nonintuitive when the target ε is negative, but it is not clear that this is a common practical concern because negative target ε occurs only in well‐constrained areas. Copyright © 2011 John Wiley & Sons, Ltd.     

基于条件Newmark-Hall三联谱的时程分析选波方法

条件均值谱（CMS）已成为目前国内外广受关注及认可的结构抗震时程分析选波的目标谱,但其无法同时兼顾多个周期点谱加速度具有相同的地震危险水平,对于须考虑多阶振型影响的长周期结构尚存局限。Newmark-Hall三联谱是基于加速度峰值（PGA）、速度峰值（PGV）和位移峰值（PGD）并联合短、中、长周期相关放大系数建立的反应谱,与短、中、长周期结构均具有天然良好的相关性,其与概率地震危险性分析（PSHA）结合较弱及具有经验化特征。将两种反应谱的优势相结合,即将CMS的“条件分布”理念引入Newmark-Hall三联谱,建立了条件Newmark-Hall三联谱（即CN-H）,并提出了以CN-H为目标谱的选波方法（即CN-H方法）。以美国SAC计划设计的3层和9层抗弯钢框架结构为例,将CN-H方法与以CMS为目标谱的选波方法所得结果进行了对比。CN-H方法对于结构反应均值的估计与CMS方法具有一致的准确性,且所得结构反应的离散性也较低,可见CN-H方法对于结构弹塑性时程分析选波具有良好的适用性。     

A generalized conditional intensity measure approach and holistic ground‐motion selection

A generalized conditional intensity measure (GCIM) approach is proposed for use in the holistic selection of ground motions for any form of seismic response analysis. The essence of the method is the construction of the multivariate distribution of any set of ground‐motion intensity measures conditioned on the occurrence of a specific ground‐motion intensity measure (commonly obtained from probabilistic seismic hazard analysis). The approach therefore allows any number of ground‐motion intensity measures identified as important in a particular seismic response problem to be considered. A holistic method of ground‐motion selection is also proposed based on the statistical comparison, for each intensity measure, of the empirical distribution of the ground‐motion suite with the ‘target’ GCIM distribution. A simple procedure to estimate the magnitude of potential bias in the results of seismic response analyses when the ground‐motion suite does not conform to the GCIM distribution is also demonstrated. The combination of these three features of the approach make it entirely holistic in that: any level of complexity in ground‐motion selection for any seismic response analysis can be exercised; users explicitly understand the simplifications made in the selected suite of ground motions; and an approximate estimate of any bias associated with such simplifications is obtained. Copyright © 2010 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.