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.     

Simplified design procedure for frame buildings with viscoelastic or elastomeric structural dampers

A simplified design procedure (SDP) for preliminary seismic design of frame buildings with structural dampers is presented. The SDP uses elastic‐static analysis and is applicable to structural dampers made from viscoelastic (VE) or high‐damping elastomeric materials. The behaviour of typical VE materials and high‐damping elastomeric materials is often non‐linear, and the SDP idealizes these materials as linear VE materials. With this idealization, structures with VE or high‐damping elastomeric dampers can be designed and analysed using methods based on linear VE theory. As an example, a retrofit design for a typical non‐ductile reinforced concrete (RC) frame building using high‐damping elastomeric dampers is developed using the SDP. To validate the SDP, results from non‐linear dynamic time history analyses (NDTHA) are presented. Results from NDTHA demonstrate that the SDP estimates the seismic response with sufficient accuracy for design. It is shown that a non‐ductile RC frame building can be retrofit with high‐damping elastomeric dampers to remain essentially elastic under the design basis earthquake (DBE). Copyright © 2005 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.     

损失分布和非结构损失对房屋建筑地易损性的影响

房屋建筑的地震易损性是地震损失评估和地震巨灾风险模型的基础。作为房屋建筑的重要组成部分,各类非结构构件的损失在现有的易损性模型中并未得到足够重视。本文以一栋典型钢筋混凝土框架结构教学楼为对象,通过将房屋建筑中的各类构件划分为具有不同地震损伤特性和损失后果的易损性组,考察建筑内的损失分布和非结构损失对房屋建筑地震易损性的影响。分析结果表明:由于许多非结构构件在中小地震作用下即可能发生较严重的破坏,房屋建筑在中小地震下的易损性主要受非结构损失控制;随着地震动强度等级的不断提高,结构损伤渐趋严重,结构损失对整体建筑易损性的影响不断增大;在结构进入震后不可修状态之前,建筑不同楼层的损失分布是评估建筑地震损失时不可忽略的因素。     

Incremental dynamic analysis of woodframe buildings

The collapse of wood buildings was one of the main contributors to the heavy death toll and economic losses during the 1995 Hyogo‐ken Nanbu (Kobe) earthquake in Japan. In California, half of the property loss from the 1994 Northridge earthquake was attributed to wood construction. Based on damage observed in recent earthquakes, the seismic vulnerability of existing wood buildings under maximum credible seismic events is uncertain. The main objective of this study is to quantify the seismic collapse fragilities and collapse mechanisms of a two‐story townhouse and three‐story woodframe apartment building through numerical analyses. Three construction quality variants (poor, typical and superior) were considered for each building in order to assess the effects of construction qualities on seismic collapse fragilities. The buildings were also re‐designed according to the 2006 edition of the International Building Code to quantify the seismic fragilities of modern woodframe construction. The results obtained suggest that the construction quality, excitation direction and wall finish materials can influence significantly the collapse fragilities of woodframe buildings. Copyright © 2008 John Wiley & Sons, Ltd.     

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。     

汶川地区震后钢筋混凝土框架结构的地震易损性研究

以汶川地震为研究背景,针对震后典型钢筋混凝土框架结构进行地震易损性研究。基于Cornell理论框架结合汶川地质资料,拟合出考虑场地特点的地震危险性模型,同时定义损伤水平状态及限值指标,以概率解析易损性研究方法为基础,运用考虑地震动参数的解析易损性评估方法绘制汶川地区钢筋混凝土框架建筑的地震易损性曲线。研究结果表明:考虑地震动参数的概率解析易损性研究方法是一种有效的地震易损性评估方法;以PGA作为地震强度输入指标的结构反应,随自振周期的增大体系最大响应的相关性降低,结构各个损伤状态的失效概率均随之增大。     

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.     

Seismic vulnerability of reinforced concrete buildings with discontinuity in columns

Irregular reinforced concrete (RC) buildings constitute a significant portion of the existing housing stock. A common type of irregularity is in the form of discontinuity in the vertical framing elements, which can exacerbate their seismic vulnerability. The design guidelines available in seismic design codes essentially cater to only regular buildings, and the safety of such buildings, even when the other guidelines of the codes are followed, is doubtful. This article evaluates the vulnerability of RC frame buildings with discontinuity in columns designed for modern seismic codes, in the form of seismic collapse capacity, collapse resistance against maximum earthquake demand level, and failure mechanism. The adequacy and limitations of the provisions of the seismic design codes are evaluated for such buildings. Analysis results show that the sequential analysis of buildings considering the construction staged effects, considerably affects the design and hence the collapse failure mechanism of even low- and mid-rise buildings. The results also underline the importance of strong column–weak beam design in the seismic performance of the floating column buildings. The vertical component of ground motion is also observed to be relatively more crucial in floating column buildings.     

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.     

Alternative non‐linear demand estimation methods for probability‐based seismic assessments

Alternative non‐linear dynamic analysis procedures, using real ground motion records, can be used to make probability‐based seismic assessments. These procedures can be used both to obtain parameter estimates for specific probabilistic assessment criteria such as demand and capacity factored design and also to make direct probabilistic performance assessments using numerical methods. Multiple‐stripe analysis is a non‐linear dynamic analysis method that can be used for performance‐based assessments for a wide range of ground motion intensities and multiple performance objectives from onset of damage through global collapse. Alternatively, the amount of analysis effort needed in the performance assessments can be reduced by performing the structural analyses and estimating the main parameters in the region of ground motion intensity levels of interest. In particular, single‐stripe and double‐stripe analysis can provide local probabilistic demand assessments using minimal number of structural analyses (around 20 to 40). As a case study, the displacement‐based seismic performance of an older reinforced concrete frame structure, which is known to have suffered shear failure in its columns during the 1994 Northridge Earthquake, is evaluated. Copyright © 2008 John Wiley & Sons, Ltd.     

Seismic vulnerability evaluation of RC moment frame buildings in moderate seismic zones

A multi‐level seismic vulnerability assessment of reinforced concrete moment frame buildings located in moderate seismic zones (0.25g) is performed on a set of ductile versions of low‐ to mid‐rise two‐dimensional moment frames. The study is illustrated through application to comparative trial designs of two (4‐ and 8‐story) buildings adopting both space‐ and perimeter‐framed approaches. All frames are dimensioned as per the emerging version of the seismic design code in Egypt. These new seismic provisions are in line with current European norms for seismic design of buildings. Code‐compliant designs (CCD), as well as a proposed modified code design relaxing design drift demands for the investigated buildings, are examined to test their effectiveness and reliability. Applying nonlinear inelastic incremental dynamic analyses, fragility curves (FC) for the frames are developed corresponding to various code‐specified performance levels. Code preset lower and upper bounds on design acceleration and drift, respectively, are also addressed along with their implications, if imposed, on the frames seismic performance and vulnerability. Annual spectral acceleration hazard curves for the case study frames are also generated. Estimates for mean annual frequency (MAF) of exceeding various performance levels are then computed through an integration process of the data resulting from the FC with the site hazard curves. The study demonstrates that the proposed design procedure relaxing design drift demands delivers more economic building designs relative to CCDs, yet without risking the global safety of the structure. The relaxed design technique suggested herein, even though scoring higher, as expected by intuition, MAF of exceeding various code‐limiting performance levels expressed in terms of interstory drift ratios, still guarantees a reasonably acceptable actual margin against violating code limits for such levels. Copyright © 2010 John Wiley & Sons, Ltd.     

Modelling exterior unreinforced beam‐column joints in seismic analysis of non‐ductile RC frames

The seismic response of non‐ductile reinforced concrete (RC) buildings can be affected by the behaviour of beam‐column joints involved in the failure mechanism, especially in typical existing buildings. Conventional modelling approaches consider only beam and column flexibility, although joints can provide a significant contribution also to the overall frame deformability. In this study, the attention is focused on exterior joints without transverse reinforcement, and a possible approach to their modelling in nonlinear seismic analysis of RC frames is proposed. First, experimental tests performed by the authors are briefly presented, and their results are discussed. Second, these tests, together with other tests with similar features from literature, are employed to calibrate the joint panel deformability contribution in order to reproduce numerically the experimental joint shear stress–strain behaviour under cyclic loading. After a validation phase of this proposal, a numerical investigation of the influence of joints on the seismic behaviour of a case study RC frame – designed for gravity loads only – is performed. The preliminary failure mode classification of the joints within the analysed frame is carried out. Structural models that (i) explicitly include nonlinear behaviour of beam‐column joints exhibiting shear or anchorage failure or (ii) model joints as elements with infinite strength and stiffness are built and their seismic performance are assessed and compared. A probabilistic assessment based on nonlinear dynamic simulations is performed by means of a scaling approach to evaluate the seismic response at different damage states accounting for uncertainties in ground‐motion records. Copyright © 2016 John Wiley & Sons, Ltd.     

Development and assessment of damage‐to‐loss models for moment‐frame reinforced concrete buildings

The assessment of earthquake loss often requires the definition of a relation between a measure of damage and a quantity of loss, usually achieved through the employment of a damage‐to‐loss model. These models are frequently characterized by a large variability, which inevitably increases the uncertainty in the vulnerability assessment and earthquake loss estimation. This study provides an insight on the development of damage‐to‐loss functions for moment‐frame reinforced concrete buildings through an analytical methodology. Tri‐dimensional finite element models of existing reinforced concrete buildings were subjected to a number of ground motion records compatible with the seismicity in the region of interest, through nonlinear dynamic analysis. These results were used to assess, for a number of damage states, the probability distribution of loss ratio, taking into consideration member damage and different repair techniques, as well as to derive sets of fragility functions. Then, a vulnerability model (in terms of the ratio of cost of repair to cost of replacement, conditional on the level of ground shaking intensity) was derived and compared with the vulnerability functions obtained through the combination of various damage‐to‐loss models with the set of fragility functions developed herein. In order to provide realistic estimates of economic losses due to seismic action, a comprehensive study on repair costs using current Portuguese market values was also carried out. The results of this study highlight important issues in the derivation of vulnerability functions, which are a fundamental component for an adequate seismic risk assessment. © 2015 The Authors. Earthquake Engineering & Structural Dynamics published by John Wiley & Sons Ltd.     

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.     

Risk‐based seismic design for collapse safety

Risk‐based seismic design, as introduced in this paper, involves the use of different types of analysis in order to satisfy a risk‐based performance objective with a reasonable utilization rate and sufficient reliability. Differentiation of the reliability of design can be achieved by defining different design algorithms depending on the importance of a structure. In general, the proposed design is iterative, where the adjustment of a structure during iterations is the most challenging task. Rather than using automated design algorithms, an attempt has been made to introduce three simple guidelines for adjusting reinforced concrete frames in order to increase their strength and deformation capacity. It is shown that an engineer can design a reinforced concrete frame in a few iterations, for example, by adjusting the structure on the basis of pushover analysis and checking the final design by means of nonlinear dynamic analysis. A possible variant of the risk‐based design algorithm for the collapse safety of reinforced concrete frame buildings is proposed, and its application is demonstrated by means of an example of an eight‐storey reinforced concrete building. Four iterations were required in order to achieve the risk‐based performance objective with a reasonable utilization rate. Copyright © 2016 John Wiley & Sons, Ltd.     

Assessment indices for the seismic vulnerability of existing R.C. buildings

The seismic vulnerability of old multi‐storey reinforced concrete (R.C.) buildings reinforced with substandard details is assessed as a function of interstorey drift demand imposed by the design earthquake while considering brittle termination of elastic response of the critical members of the structure due to a premature shear failure. Interstorey drift demand is related to column and wall translational stiffnesses which are expressed through analytical derivations in terms of the floor area ratios of gravity and lateral load bearing members in the critical floor. Interstorey drift capacity is related to the available transverse reinforcement and the axial load ratio of the vertical members. The significance of the area ratio of vertical members in the typical floor as an index of vulnerability is explored with reference to the limitations in the value of axial load ratio used in R.C. design in order to secure ductile flexural behavior, and also with reference to the stability index of gravity load bearing members. Interstorey Drift Spectra are derived for the existing R.C. buildings suitable for rapid seismic vulnerability screening but also as a guide for rehabilitation of the existing structures. Lightly reinforced or substandard reinforced concrete buildings that reportedly collapsed during previous earthquakes are used as example case studies in order to calibrate the proposed methodology. Copyright © 2010 John Wiley & Sons, Ltd.     

Seismic fragility assessment of RC frame structure designed according to modern Chinese code for seismic design of buildings

Following several damaging earthquakes in China,research has been devoted to find the causes of the collapse of reinforced concrete(RC) building sand studying the vulnerability of existing buildings.The Chinese Code for Seismic Design of Buildings(CCSDB) has evolved over time,however,there is still reported earthquake induced damage of newly designed RC buildings.Thus,to investigate modern Chinese seismic design code,three low-,mid-and high-rise RC frames were designed according to the 2010 CCSDB and the corresponding vulnerability curves were derived by computing a probabilistic seismic demand model(PSDM).The PSDM was computed by carrying out nonlinear time history analysis using thirty ground motions obtained from the Pacific Earthquake Engineering Research Center.Finally,the PSDM was used to generate fragility curves for immediate occupancy,significant damage,and collapse prevention damage levels.Results of the vulnerability assessment indicate that the seismic demands on the three different frames designed according to the 2010 CCSDB meet the seismic requirements and are almost in the same safety level.     

Near‐collapse response of existing RC building under severe pulse‐type ground motion using hybrid simulation

Column shear‐axial failure is a complex response, which lends itself to physical experimentation. Reinforced concrete structures built prior to the mid‐1970s are particularly susceptible to such failure. Shear‐axial column failure has been examined and studied at the element level, but current rehabilitation practice equates such a column failure with structural collapse, neglecting the collapse resistance of the full structural system following column failure. This system‐level response can prevent a column failure from leading to progressive collapse of the entire structure. In this study, a hybrid simulation was conducted on a representative pre‐1970s reinforced concrete frame structure under severe seismic ground motion, in which three full‐scale reinforced concrete columns were tested at the University of Illinois at Urbana Champaign. The analytical portion of the model was represented in the computer program OpenSees. Failure occurred in multiple physical specimens as a result of the ground motion, and the hybrid nature of the test allowed for observation of the system‐level response of the tested columns and the remaining structural system. The behavior of the system accounting for multiple column shear‐axial failure is discussed and characterized. Copyright © 2016 John Wiley & Sons, Ltd.     

Seismic steel jacketing of rectangular RC bridge columns for the mitigation of lap‐splice failures

This paper investigated the use of external steel jacketing for seismic retrofit of non‐ductile reinforced concrete (RC) bridge columns to prevent lap‐splice failure. Three 1/2.5‐scale specimens were tested under cyclic loads. The effectiveness of two types of steel jackets for improving the ductility and strength of specimens using inadequate transverse reinforcing and lap‐splice details were examined. An octagonal steel jacketing scheme for the seismic retrofitting of rectangular RC bridge columns was proposed. In addition, the methods for seismic retrofitting rectangular columns using elliptical steel jacketing were also critically tested. The test results indicated that the octagonal steel jackets can effectively provide confinement thereby mitigating failures as a result of inadequate transverse reinforcing and inadequate lap‐splices. Tests also confirmed that the ductility performance and the energy dissipation capacity of the specimens can be significantly improved by the octagonal steel jacket. Copyright © 2010 John Wiley & Sons, Ltd.