On the design and seismic response of RC frame buildings designed with Eurocode 8

Performance-Based Seismic Design is now widely recognized as the pre-eminent seismic design and assessment methodology for building structures. In recognition of this, seismic codes may require that buildings achieve multiple performance objectives such as withstanding moderate, yet frequently occurring earthquakes with minimal structural and non-structural damage, while withstanding severe, but rare earthquakes without collapse and loss of life. These objectives are presumed to be satisfied by some codes if the force-based design procedures are followed. This paper investigates the efficacy of the Eurocode 8 force-based design provisions with respect to RC frame building design and expected seismic performance. Four, eight, and 16-storey moment frame buildings were designed and analyzed using the code modal response spectrum analysis provisions. Non-linear time-history analyses were subsequently performed to determine the simulated seismic response of the structures and to validate the Eurocode 8 force-based designs. The results indicate the design of flexural members in medium-to-long period structures is not significantly influenced by the choice of effective member stiffness; however, calculated interstorey drift demands are significantly affected. This finding was primarily attributed to the code’s enforcement of a minimum spectral ordinate on the design spectrum. Furthermore, design storey forces and interstorey drift demand estimates (and therefore damage), obtained by application of the code force-based design procedure varied substantially from those found through non-linear time-history analysis. Overall, the results suggest that though the Eurocode 8 may yield life-safe designs, the seismic performance of frame buildings of the same type and ductility class can be highly non-uniform.     

Nonlinear dynamic response of r.c. framed structures subjected to near-fault ground motions

The nonlinear dynamic response of reinforced concrete (r.c.) framed buildings subjected to near-fault ground motions is studied to check the effectiveness of current code provisions with reference to study cases. Three-, six- and twelve-storey r.c. plane frames, representative of symmetric framed buildings, are designed according to the European seismic code (EC8), assuming medium and high ductility classes and stratigraphic profiles A (rock) and D (soft soil) in a high-risk seismic region. The nonlinear seismic analysis is performed using a step-by-step procedure; a bilinear model idealizes the behaviour of the r.c. frame members. Artificially generated motions (matching EC8 response spectra for subsoil classes A and D) and horizontal motions (recorded on rock- and soft soil-site at near-fault areas) are considered. The results indicate that near-fault ground motions may require a special consideration in the code, in particular when designing r.c. framed structures placed on a soft soil-site; particular attention should be paid to the design of the frame members of the lower storeys.     

Fragility functions for masonry infill walls with in‐plane loading

Recent seismic events have provided evidence that damage to masonry infills can lead not only to large economic losses but also to significant injuries and even fatalities. The estimation of damage of such elements and the corresponding consequences within the performance‐based earthquake engineering framework requires the construction of reliable fragility functions. In this paper, drift‐based fragility functions are developed for in‐plane loaded masonry infills, derived from a comprehensive experimental data set gathered from current literature, comprising 152 masonry infills with different geometries and built with different types of masonry blocks, when tested under lateral cyclic loading. Three damage states associated with the structural performance and reparability of masonry infill walls are defined. The effect of mortar compression strength, masonry prism compression strength, and presence of openings is evaluated and incorporated for damage states where their influence is found to be statistically significant. Uncertainty due to specimen‐to‐specimen variability and sample size is quantified and included in the proposed fragility functions. It is concluded that prism strength and mortar strength are better indicators of the fragility of masonry infills than the type of bricks/blocks used, whose influence, in general, is not statistically significant for all damage states. Finally, the presence of openings is also shown to have statistically relevant impact on the level of interstory drift ratio triggering the lower damage states.     

Pseudo‐dynamic seismic response of reinforced concrete frames infilled with non‐structural brick masonry

This paper presents pseudo‐dynamic test results on the in‐plane seismic behaviour of infilled frames. Thirteen single‐storey, single‐bay, half‐size‐scale, reinforced concrete‐frame specimens, most of which infilled with non‐structural masonry made of perforated bricks and cement mortar are tested. The infills are in contact with frames, without any connector; openings are not covered. The frames are different in their strength and details, reinforcement grade, and aspect ratio. Seismic input is the 1976 Tolmezzo (Friuli, Italy) ground acceleration, to which specimens are subjected two times: virgin and damaged by the previous test. The global seismic response of initially virgin infilled specimens considerably differs from that of bare specimens. This follows a dramatic change of properties: compared to a bare frame, the initial stiffness increases by one order of magnitude, and the peak strength more than doubles. The peak drift lessens; however, the displacement ductility demand does not. The energy demand is greater. Nevertheless, the influence of infill decreases as damage proceeds. Displacement time histories of damaged specimens are quite similar. At the local level, infill causes asymmetry and concentration of the frame deformation. Copyright © 2005 John Wiley & Sons, Ltd.     

考虑非结构构件损伤的钢筋混凝土框架建筑多维地震易损性分析

基于单一指标的传统地震易损性分析忽略了非结构构件损伤对建筑抗震性能的影响。首先基于多维性能极限状态理论建立了三维性能极限状态方程,并对几种特殊情况下的三维阈值曲面进行了讨论。进而以最大层间位移角作为整体结构与位移敏感型非结构构件的性能指标,以峰值楼面加速度作为加速度敏感型非结构构件的性能指标,对建筑的结构损伤和非结构损伤进行描述。考虑各性能指标之间的相关性和各性能指标所对应的极限状态阈值的不确定性,建立了建筑在地震作用下的三维性能极限状态的超越概率函数。最后,采用Open Sees有限元软件对一7层钢筋混凝土框架填充墙建筑进行增量动力分析,得到其各性能水平下的地震易损性曲线。分析结果表明,当忽略非结构构件损伤时,各性能极限状态的超越概率均降低,从而高估了建筑剩余功能水平,进而导致低估建筑的损失。在考虑各性能指标的极限状态阈值的不确定性时,对任一性能极限状态,不同变异系数取值下的易损性曲线会出现交点,在交点之前超越概率随着变异系数的增大而增大,交点之后则随着变异系数的增大而减小。在考虑性能指标间的相关性时,对任一性能极限状态,超越概率随着相关系数的减小而增大。另外,性能指标阈值的不确定性与性能指标间的相关性对地震易损性的影响随着性能水平的提高而逐渐降低,且对低性能水平下建筑地震易损性有明显影响。     

Fragility functions and floor spectra of RC masonry infilled frames: influence of mechanical properties of masonry infills

A wide number of experimental studies conducted in latest years pointed out the high influence of the mechanical properties of masonry units and mortar bed joints on lateral strength and stiffness of masonry panels. This feature significantly modifies the global response of infilled frames under seismic actions as well as the local interaction phenomena. Despite a wide investigation on the influence of the infills on global behaviour of reinforced concrete (RC) frames has already been provided, different features characterizing the seismic performances of buildings suggest the need of accurately evaluating local interaction phenomena as well as the influence of the panel on specific and relevant aspects, as the accelerations transferred to non-structural components. This study provides a parametrical analysis of the influence of shear strength and elastic modulus of masonry infills on the seismic behaviour of RC frames originally designed for gravity loads. Regular buildings with different height were analysed using the Incremental Dynamic Analysis in order to provide fragility curves, investigate on the collapse mechanisms and define the floor spectra depending on the properties of the infills. Results obtained pointed out the high influence of the considered parameters on the fragility of existing RC frames, often characterized by inadequate transversal reinforcement of columns, which may lead to brittle failure due to the interaction with the infills. Floor response spectra are also significantly affected by the influence of masonry infills both in terms of shape and maximum spectral accelerations. Lastly, on the basis of the observed failure mechanisms, a parameter defining the ductility of the frames depending on the properties of the infills was also provided (Capacity Design Factor). The correlation between the mechanical properties of the infills and this parameter suggests its reliability in the simplified vulnerability analysis of existing buildings as well as for the design of new buildings.     

建筑结构监测与抗震韧性评估

建筑结构响应是有效反映结构动力特性的最直接参数,开展结构动力响应实时监测可为结构抗震韧性评估提供准确的地震动输入。本文基于非结构构件损失构建结构抗震韧性评估方法,研究确定位移敏感型和加速度敏感型非结构构件的易损性模型。选择某六层钢筋混凝土框架结构进行实时监测系统建设,基于监测数据开展结构抗震韧性评估。通过构建建筑信息模型（BIM）,并在有限元分析软件OpenSees中建立结构弹塑性分析模型,利用实时监测数据实现结构模型更新,直至监测数据与模型分析结果一致。由于实时监测数据峰值较低,结构不会发生塑性变形,因此选择10条双向非脉冲地震动模拟实时监测地震记录。根据层间位移角和楼面加速度分布,开展结构功能损失评估,得到该建筑结构的抗震韧性得分。分析表明,该结构抗震性能较好,在遭受地震破坏后,会发生非结构构件脱落,需要采取有效措施进一步提升建筑抗震韧性水平。     

Prediction of inter-storey drifts for regular RC structures with masonry infills based on bare frame modelling

The traditional construction of masonry infills adjacent to RC structural elements is still widely adopted in European countries, including seismically active regions. Given the repeated field observations from damaging earthquakes, pointing to unacceptably high levels of masonry infill damage, the present study is motivated by the need to improve further the European seismic design approach for new RC structures with masonry infills, in order to exclude the poor seismic behaviour probably caused by deficiencies in the verification procedure. Since the in-plane damage to non-structural panels is commonly controlled through the limitation of inter-storey drifts, the possibility to introduce more effective verification criteria, accounting for structural properties, infill layouts and masonry properties is explored. Therefore, starting from the assumption that analyses and verifications in the design of buildings are commonly accomplished neglecting the presence of infills, results of extensive nonlinear numerical analyses for different building configurations are examined. As a result, a simplified procedure for the prediction of expected inter-storey drifts for infilled structures, based on the corresponding demands of bare configurations, in function of a simple parameter accounting for structural properties and the presence of infills, is introduced. Possible implications of the proposed approach aimed at the improvement of the current design provisions are discussed.     

Multiplication factor for open ground storey buildings–a reliability based evaluation

Open Ground Storey(OGS) framed buildings where the ground storey is kept open without infill walls, mainly to facilitate parking, is increasing commonly in urban areas. However, vulnerability of this type of buildings has been exposed in past earthquakes. OGS buildings are conventionally designed by a bare frame analysis that ignores the stiffness of the infill walls present in the upper storeys, but doing so underestimates the inter-storey drift(ISD) and thereby the force demand in the ground storey columns. Therefore, a multiplication factor(MF) is introduced in various international codes to estimate the design forces(bending moments and shear forces) in the ground storey columns. This study focuses on the seismic performance of typical OGS buildings designed by means of MFs. The probabilistic seismic demand models, fragility curves, reliability and cost indices for various frame models including bare frames and fully infilled frames are developed. It is found that the MF scheme suggested by the Israel code is better than other international codes in terms of reliability and cost.     

Influence of earthquake ground‐motion duration on damage estimation: application to steel moment resisting frames

This paper presents an analytical study evaluating the influence of ground motion duration on structural damage of 3‐story, 9‐story, and 20‐story SAC steel moment resisting frame buildings designed for downtown Seattle, WA, USA, using pre‐Northridge codes. Two‐dimensional nonlinear finite element models of the buildings are used to estimate the damage induced by the ground motions. A set of 44 ground motions is used to study the combined effect of spectral acceleration and ground motion significant duration on drift and damage measures. In addition, 10 spectrally equivalent short‐duration shallow crustal ground motions and long‐duration subduction zone records are selected to isolate duration effect and assess its effect on the response. For each ground motion pair, incremental dynamic analyses are performed at at least 20 intensity levels and response measures such as peak interstory drift ratio and energy dissipated are tracked. These response measures are combined into two damage metrics that account for the ductility and energy dissipation. Results indicate that the duration of the ground motion influences, above all, the combined damage measures, although some effect on drift‐based response measures is also observed for larger levels of drift. These results indicate that because the current assessment methodologies do not capture the effects of ground motion duration, both performance‐based and code‐based assessment methodologies should be revised to consider damage measures that are sensitive to duration. Copyright © 2016 John Wiley & Sons, Ltd     

Convex model-based calculation of robust seismic fragility curves of isolated continuous girder bridge

The convex model approach is applied to derive the robust seismic fragility curves of a five-span isolated continuous girder bridge with lead rubber bearings (LRB) in China. The uncertainty of structure parameters (the yield force and the post-yield stiffness of LRB, the yield strength of steel bars, etc.) are considered in the convex model, and the uncertainty of earthquake ground motions is also taken into account by selecting 40 earthquake excitations of peak ground acceleration magnitudes ranging from 0.125 to 1.126 g. A 3-D finite element model is employed using the software package OpenSees by considering the nonlinearity in the bridge piers and the isolation bearings. Section ductility of piers and shearing strain isolation bearings are treated as damage indices. The cloud method and convex model approach are used to construct the seismic fragility curves of the bridge components (LRB and bridge piers) and the bridge system, respectively. The numerical results indicate that seismic fragility of the bridge system and bridge components will be underestimated without considering the uncertainty of structural parameters. Therefore, the failure probability P _f,max had better be served as the seismic fragility, especially, the fragility of the bridge system is largely dictated by the fragility of LRB. Finally, the probabilistic seismic performance evaluation of the bridge is carried out according to the structural seismic risk estimate method.     

基于IDA方法的框架结构震害风险评估

为了评估不同抗震设防烈度区建筑结构震害风险,即场地地震危险性与结构地震易损性的卷积,本文以典型框架结构为例,对其震害风险进行研究。依据抗震设计规范,分别按照6度、7度和8度设计3个3跨10层框架结构模型,采用动力增量分析方法（Incremental Dynamic Analysis,IDA）对其进行地震易损性分析。同时,基于我国地震烈度概率分布特点,应用MATLAB软件生成符合极值Ⅲ型分布的地震烈度,并将其转化为地震加速度峰值,联合地震易损性结果评估模型震害风险。通过划分震害风险等级,为建筑结构抗震防灾对策的制定提供借鉴。     

Influence of infill distribution and design typology on seismic performance of low- and mid-rise RC buildings

A growing attention has been addressed to the influence of infills on the seismic behavior of Reinforced Concrete buildings, also supported by the observation of damage to infilled RC buildings after severe earthquakes (e.g. L’Aquila 2009, Lorca 2011). In this paper, a numerical investigation on the influence of infills on the seismic behavior of four different case study buildings is carried out: four- and eight-storey buildings, designed for seismic loads according to the current Italian technical code or for gravity loads only according to an obsolete technical code, are considered. Seismic capacity at two Limit States (Damage Limitation and Near Collapse) is assessed through static push-over analyses, within the N2 spectral assessment framework. Different infill configurations are considered (Bare, Uniformly Infilled, Pilotis), and a sensitivity analysis is carried out, thus evaluating the influence of main material and capacity parameters on seismic response, depending on the number of storeys and the design typology. Fragility curves are obtained, through the application of a Response Surface Method. Seismic performance is also expressed in terms of failure probability, given a reference time period.     

Shake table tests on RC frame infilled by slitted masonry panels

Unreinforced masonry infill walls are widely used as non-structural partitions in RC frames. The effects of infills on the structural responses are often ignored in the design process since they are generally considered as expendable elements. However, recent studies have shown that not only shear damage can be inflicted to the columns braced by the infill walls, but also that the structural stability can be jeopardised by the fall-off of the infills. This paper presents the development of new detailing methods for the infill walls, which features slit panels, isolation gaps between the infills and columns, and anchorage of the infills. The proposed detailing methods were tested and verified experimentally using shake-table tests on five 1/3-scale infilled RC frame specimens with different combinations of the features stated above. The design and construction of the shake-table test specimens have taken into account the similitude requirements. The test results indicate that the proposed detailing method effectively reduced the undesirable interaction between column and infill walls. And the use of proper anchorage could prevent the fall off of infills from the bounding frame. Furthermore, the specimens with slit infill walls displayed better seismic performances, which could be attributed to the rocking behaviour of the sub-panels with increased aspect ratios.     

Performance of non-structural elements in RC buildings during the L��Aquila, 2009 earthquake

In Italy infills and partitions (non-structural elements) are typically made up of hollow brick masonry, disposed in one or two parallel vertical walls. Many studies have analysed their role on the seismic behaviour of moment resisting framed RC buildings and many seismic codes, all over the world, have provided specific additional measures for them. During the Abruzzo seismic sequence, non-structural damage in RC buildings, both private and public, was extensive, varying from small cracks to collapse, along with minor or no damage to structural elements. This damage involved a number of buildings, both old and recently completed, determining heavy socio-economic consequences, including human casualties, loss of building functionality (particularly important in case of strategic constructions), and unusable buildings. In this paper a review of the most frequent damage patterns is performed, aimed at identifying the main causes of damage and linking them to commonly adopted construction rules. For this purpose, local and global structural configurations frequently exhibiting non-structural damage are described, aside from out-of-plane and in-plane failures. Furthermore, a review of code provisions on non structural elements has been performed in the paper making reference to the most prominent current seismic codes and, finally, some design and construction rules are suggested.     

Seismic reliability of steel moment resisting framed buildings retrofitted with buckling restrained braces

The present paper investigates the seismic reliability of the application of buckling restrained braces (BRBs) for seismic retrofitting of steel moment resisting framed buildings through fragility analysis. Samples of regular three‐storey and eight‐storey steel moment resisting frames were designed with lateral stiffness insufficient to comply with the code drift limitations imposed for steel moment resisting frame systems in earthquake‐prone regions. The frames were then retrofitted with concentrically chevron conventional braces and BRBs. To obtain robust estimators of the seismic reliability, a database including a wide range of natural earthquake ground motion records with markedly different characteristics was used in the fragility analysis. Nonlinear time history analyses were utilized to analyze the structures subjected to these earthquake records. The improvement of seismic reliability achieved through the use of conventional braces and BRBs was evaluated by comparing the fragility curves of the three‐storey and eight‐storey model frames before and after retrofits, considering the probabilities of four distinct damage states. Moreover, the feasibility of mitigating the seismic response of moment resisting steel structures by using conventional braces and BRBs was determined through seismic risk analysis. The results obtained indicate that both conventional braces and especially BRBs improve significantly the seismic behavior of the original building by increasing the median values of the structural fragility curves and reducing the probabilities of exceedance of each damage state. Copyright © 2011 John Wiley & Sons, Ltd.     

斜交连续刚构桥桥墩地震易损性分析

以美国西部地区某斜交公路连续刚构桥为研究对象，研究其不等高墩易损性差异以及斜交角的改变对桥墩地震易损性的影响。考虑桥梁结构参数和地震动的不确定性，选取100条地震动，沿纵桥向输入，生成"结构-地震动"样本库，以地震动峰值加速度（PGA）为强度指标（IM），利用OpenSees软件对结构进行非线性时程分析得到桥墩动力响应，而后以桥墩曲率延性比衡量桥梁破坏状态，在确定桥墩损伤指标的基础上，采用可靠度理论得到各桥墩的地震易损性曲线，判断桥墩的损伤模式、损伤特点。在此基础上，改变桥梁斜交角度进行易损性分析，得到斜交角变化对桥墩地震易损性的影响。研究表明：该桥最矮墩发生损伤的概率大于其他桥墩，桥墩最先进入塑性的是墩顶和墩底区域；不同斜交角对桥墩的地震响应影响显著，各墩损伤破坏排序与斜交桥结构构造特点有关，同一排架墩的两侧墩柱易损性呈现与角度变化趋势相反的排列，损伤越严重，趋势越明显；对于此不等高的斜交刚构桥，最矮墩为其抗震薄弱环节，斜交角越大，越应该关注钝角处矮墩的损伤情况，并提高其设计标准，在进行斜交刚构桥抗震设计中应予以重视。     

Procedures for calibration of linear models for damage limitation in design of masonry‐infilled RC frames

Recent earthquakes have confirmed the role played by infills in the seismic response of reinforced concrete buildings. The control and limitation of damage to such nonstructural elements is a key issue in performance‐based earthquake engineering. The present work is focused on modeling and analysis of damage to infill panels, and, in particular, it is aimed towards linear analysis procedures for assessing the damage limitation limit state of infilled reinforced concrete frames. First, code provisions on infill modeling and acceptance criteria at the damage limitation limit state are reviewed. Literature contributions on damage to unreinforced masonry infill panels and corresponding displacement capacity are reported and discussed. Two procedures are then proposed aiming at a twofold goal: (i) the determination of ‘equivalent’ interstory drift ratio limits for a bare frame model and (ii) the estimation of the stiffness of equivalent struts representing infill walls in a linear model. These two quantities are determined such that a linear model ensures a reliable estimation of seismic capacity at the damage limitation limit state, providing the same intensity level as that obtained from nonlinear analyses carried out on structural models with infills. Finally, the proposed procedures are applied to four‐story and eight‐story case study‐infilled frames, designed for seismic loads according to current technical codes. The results of these application examples are presented and discussed. Copyright © 2016 John Wiley & Sons, Ltd.     

Correlations between Energy and Displacement Demands for Performance-Based Seismic Engineering

The development of a scientific framework for performance-based seismic engineering requires, among other steps, the evaluation of ground motion intensity measures at a site and the characterization of their relationship with suitable engineering demand parameters (EDPs) which describe the performance of a structure. In order to be able to predict the damage resulting from earthquake ground motions in a structural system, it is first necessary to properly identify ground motion parameters that are well correlated with structural response and, in turn, with damage. Since structural damage during an earthquake ground motion may be due to excessive deformation or to cumulative cyclic damage, reliable methods for estimating displacement demands on structures are needed. Even though the seismic performance is directly related to the global and local deformations of the structure, energy-based methodologies appear more helpful in concept, as they permit a rational assessment of the energy absorption and dissipation mechanisms that can be effectively accomplished to balance the energy imparted to the structure. Moreover, energy-based parameters are directly related to cycles of response of the structure and, therefore, they can implicitly capture the effect of ground motion duration, which is ignored by conventional spectral parameters. Therefore, the identification of reliable relationships between energy and displacement demands represents a fundamental issue in both the development of more reliable seismic code provisions and the evaluation of seismic vulnerability aimed at the upgrading of existing hazardous facilities. As these two aspects could become consistently integrated within a performance-based seismic design methodology, understanding how input and dissipated energy are correlated with displacement demands emerges as a decisive prerequisite. The aim of the present study is the establishment of functional relationships between input and dissipated energy (that can be considered as parameters representative of the amplitude, frequency content and duration of earthquake ground motions) and displacement-based response measures that are well correlated to structural and non-structural damage. For the purpose of quantifying the EDPs to be related to the energy measures, for comprehensive range of ground motion and structural characteristics, both simplified and more accurate numerical models will be used in this study for the estimation of local and global displacement and energy demands. Parametric linear and nonlinear time-history analyses will be performed on elastic and inelastic SDOF and MDOF systems, in order to assume information on the seismic response of a wide range of current structures. Hysteretic models typical of frame force/displacement behavior will be assumed for the local inelastic cyclic response of the systems. A wide range of vibration periods will be taken into account so as to define displacement, interstory drift and energy spectra for MDOF systems. Various scalar measures related to the deformation demand will be used in this research. These include the spectral displacements, the peak roof drift ratio, and the peak interstory drift ratio. A total of about 900 recorded ground motions covering a broad variety of condition in terms of frequency content, duration and amplitude will be used as input in the dynamic analyses. The records are obtained from 40 earthquakes and grouped as a function of magnitude of the event, source-to-site condition and site soil condition. In addition, in the data-set of records a considerable number of near-fault signals is included, in recognition of the particular significance of pulse-like time histories in causing large seismic demands to the structures.     

An earthquake-source-based metric for seismic fragility analysis

The seismic fragility of a system is the probability that the system enters a damage state under seismic ground motions with specified characteristics. Plots of the seismic fragilities with respect to scalar ground motion intensity measures are called fragility curves. Recent studies show that fragility curves may not be satisfactory measures for structural seismic performance, since scalar intensity measures cannot comprehensively characterize site seismicity. The limitations of traditional seismic intensity measures, e.g., peak ground acceleration or pseudo-spectral acceleration, are shown and discussed in detail. A bivariate vector with coordinates moment magnitude m and source-to-site distance r is proposed as an alternative seismic intensity measure. Implicitly, fragility surfaces in the (m, r)-space could be used as graphical representations of seismic fragility. Unlike fragility curves, which are functions of scalar intensity measures, fragility surfaces are characterized by two earthquake-hazard parameters, (m, r). The calculation of fragility surfaces may be computationally expensive for complex systems. Thus, as solutions to this issue, a bi-variate log-normal parametric model and an efficient calculation method, based on stochastic-reduced-order models, for fragility surfaces are proposed.