Assessing reparability: simple tools for estimation of costs and performance loss of earthquake damaged reinforced concrete buildings

Tools for assessing building reparability via the estimation of expected performance loss (PL) and associated costs for repair of existing RC building classes damaged by an earthquake are presented. The assessment approach relies on the availability of a number of suitably developed: (i) capacity curves for representative building classes; (ii) curves relating global ductility demand μ to the expected PL for the same classes; and (iii) PL–cost for repair relationship calibrated on database collecting cost data of more than 2300 buildings damaged after 2009 L'Aquila earthquake. The tools are developed applying a simplified procedure involving the simulated design of existing building classes, the assumption of predefined collapse mechanism types and the analyses of the seismic behavior of equivalent SDOF systems representative of ‘intact’ and ‘damaged’ structures after an earthquake. The use of these tools may give useful preliminary indications to decision makers for establishing reparability priorities in the aftermath of damaging earthquakes or to insurance companies to value sound insurance premium for existing building classes. Copyright © 2014 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.     

Shaking table tests of 1:4 reduced‐scale models of masonry infilled reinforced concrete frame buildings

Two models of masonry infilled reinforced concrete frame buildings were tested at the shaking table. Models were built in the reduced scale 1:4 using the materials produced in accordance to modelling demands of true replica modelling technique. The first model represented a one‐storey box‐like building and the second one the two‐stories building with plan shaped in the form of a letter H. Models were shaken with the series of horizontal sine dwell motions with gradually increasing amplitude. Masonry infills of tested models were constructed of relatively strong bricks laid in weak mortar. Therefore, typical cracks developed and propagated along mortar beds without cracking of bricks or crushing of infill corners. Data collected from tests will be used in future evaluation, verification and development of computational models for prediction of in‐plane and out‐of‐plane behaviour of masonry infills. The responses of tested models can be well compared with global behaviour of real structures using the modelling rules. The similarity of local behaviour of structural elements, e.g. reinforced concrete joints, is less reliable due to limitations in modelling of steel reinforcement properties. The model responses showed that buildings designed according to Eurocodes are able to sustain relatively high dynamic excitations due to a significant level of structural overstrength. Copyright © 2001 John Wiley & Sons, Ltd.     

Development of seismic fragility surfaces for reinforced concrete buildings by means of nonlinear time‐history analysis

Fragility curves are generally developed using a single parameter to relate the level of shaking to the expected structural damage. The main goal of this work is to use several parameters to characterize the earthquake ground motion. The fragility curves will, therefore, become surfaces when the ground motion is represented by two parameters. To this end, the roles of various strong‐motion parameters on the induced damage in the structure are compared through nonlinear time‐history numerical calculations. A robust structural model that can be used to perform numerous nonlinear dynamic calculations, with an acceptable cost, is adopted. The developed model is based on the use of structural elements with concentrated nonlinear damage mechanics and plasticity‐type behavior. The relations between numerous ground‐motion parameters, characterizing different aspects of the shaking, and the computed damage are analyzed and discussed. Natural and synthetic accelerograms were chosen/computed based on a consideration of the magnitude‐distance ranges of design earthquakes. A complete methodology for building fragility surfaces based on the damage calculation through nonlinear numerical analysis of multi‐degree‐of‐freedom systems is proposed. The fragility surfaces are built to represent the probability that a given damage level is reached (or exceeded) for any given level of ground motion characterized by the two chosen parameters. The results show that an increase from one to two ground‐motion parameters leads to a significant reduction in the scatter in the fragility analysis and allows the uncertainties related to the effect of the second ground‐motion parameter to be accounted for within risk assessments. Copyright © 2009 John Wiley & Sons, Ltd.     

Earthquake‐induced loss assessment of steel frame buildings with special moment frames designed in highly seismic regions

This paper discusses an analytical study that quantifies the expected earthquake‐induced losses in typical office steel frame buildings designed with perimeter special moment frames in highly seismic regions. It is shown that for seismic events associated with low probabilities of occurrence, losses due to demolition and collapse may be significantly overestimated when the expected loss computations are based on analytical models that ignore the composite beam effects and the interior gravity framing system of a steel frame building. For frequently occurring seismic events building losses are dominated by non‐structural content repairs. In this case, the choice of the analytical model representation of the steel frame building becomes less important. Losses due to demolition and collapse in steel frame buildings with special moment frames designed with strong‐column/weak‐beam ratio larger than 2.0 are reduced by a factor of two compared with those in the same frames designed with a strong‐column/weak‐beam ratio larger than 1.0 as recommended in ANSI/AISC‐341‐10. The expected annual losses (EALs) of steel frame buildings with SMFs vary from 0.38% to 0.74% over the building life expectancy. The EALs are dominated by repairs of acceleration‐sensitive non‐structural content followed by repairs of drift‐sensitive non‐structural components. It is found that the effect of strong‐column/weak‐beam ratio on EALs is negligible. This is not the case when the present value of life‐cycle costs is selected as a loss‐metric. It is advisable to employ a combination of loss‐metrics to assess the earthquake‐induced losses in steel frame buildings with special moment frames depending on the seismic performance level of interest. Copyright © 2017 John Wiley & Sons, Ltd.     

Composed analytical models for seismic assessment of reinforced concrete bridge columns

This paper presents general composed analytical models to predict the behavior of reinforced concrete (RC) bridge columns. The analytical models were developed in OpenSees to represent the common hysteretic behavior of RC bridge columns. The proposed composed models can accommodate flexure failure, flexure‐shear failure, and pure shear failure, which are observed in existing RC bridge piers. The accuracy of the models was verified using data from the static cyclic‐loading experiments of 16 single columns and one multi‐column bent and dynamical experiment from two pseudo‐dynamic tests. The results showed that the analytical models could simulate the nonlinear behavior until the post‐failure behavior, including the strength degradation, the buckling of the reinforcement, and the pinching effect. Therefore, a global view of the behavior of reinforcement concrete is prescribed as simply as possible from the academic perspective, and these models are expected to provide sufficient accuracy when applied in engineering practice. Copyright © 2014 John Wiley & Sons, Ltd.     

钢筋混凝土框架柱震损程度量化鉴定方法

钢筋混凝土结构震后损伤鉴定中,最常见的方式是鉴定者观察房屋破坏现象,根据经验给出震损等级。该方法直观高效,但对鉴定者的专业经验要求较高,且鉴定结果的主观差异较大。对此以RC框架柱为对象,开展了基于震损现象的震损量化鉴定方法研究:在RC框架柱震损现象量化试验基础上给出基于构件骨架曲线特征阶段的震损分级方法;对7个RC框架柱试件进行了改进Park-Ang损伤指数分析,建立了RC框架柱损伤指数-震损分级-震损现象的对应关系;基于RC框架柱的试验结果及典型震害编制了RC框架柱震损图集,并给出了使用图集进行框架柱震损鉴定的流程及方法。使用该方法对2个实际震害中的RC框架柱进行了震损鉴定,可为更加客观以及准确地开展钢筋混凝土结构的震损鉴定提供参考。     

Shake‐table tests of a reinforced concrete frame designed following modern codes: seismic performance and damage evaluation

This paper presents shake‐table tests conducted on a two‐fifths‐scale reinforced concrete frame representing a conventional construction design under current building code provisions in the Mediterranean area. The structure was subjected to a sequence of dynamic tests including free vibrations and four seismic simulations in which a historical ground motion record was scaled to levels of increasing intensity until collapse. Each seismic simulation was associated with a different level of seismic hazard, representing very frequent, frequent, rare and very rare earthquakes. The structure remained basically undamaged and within the inter‐story drift limits of the ‘immediate occupancy’ performance level for the very frequent and frequent earthquakes. For the rare earthquake, the specimen sustained significant damage with chord rotations of up to 28% of its ultimate capacity and approached the upper bound limit of inter‐story drift associated with ‘life safety’. The specimen collapsed at the beginning of the ‘very rare’ seismic simulation. Besides summarizing the experimental program, this paper evaluates the damage quantitatively at the global and local levels in terms of chord rotation and other damage indexes, together with the energy dissipation demands for each level of seismic hazard. Further, the ratios of column‐to‐beam moment capacity recommended by Eurocode 8 and ACI‐318 to guarantee the formation of a strong column‐weak beam mechanism are examined. Copyright © 2013 John Wiley & Sons, Ltd.     

Simplified estimation of the expected annual loss of reinforced concrete buildings

Performance‐based earthquake engineering procedures have now developed to the point that it is possible to evaluate a range of possible decision variables, including the expected annual monetary loss (EAL). Quantification of the EAL is considered to be particularly useful because it could assist with the identification of effective design and retrofit measures that consider seismic performance over a range of intensity levels. Recognizing, however, that existing procedures for the evaluation of EAL tends to be quite time consuming, this paper builds on a recent proposal to use simplified limit state loss versus intensity relationships to compute EAL via a closed‐form equation, without the need to compile an inventory of damageable components and with freedom in the choice of structural analysis method. Various developments to the simplified approach are made in this paper to allow consideration of loss thresholds, non‐uniform damage distributions and the impact of differences in seismic performance in orthogonal directions. In addition, means of accounting for uncertainties in the simplified EAL assessment are described. The work has focused on the assessment of EAL for reinforced concrete frame buildings with details representative of construction practice adopted in Italy in the 1950s through to the early 1970s. By comparing loss assessment results obtained using a refined methodology with those obtained using the new guidelines developed here for two case study buildings, it is concluded that the simplified approach works well. Future research should therefore aim to further validate the approach and extend it to other building typologies and construction eras. Copyright © 2017 John Wiley & Sons, Ltd.     

Probabilistic economic seismic loss estimation in steel buildings using post‐tensioned moment‐resisting frames and viscous dampers

The potential of post‐tensioned self‐centering moment‐resisting frames (SC‐MRFs) and viscous dampers to reduce the economic seismic losses in steel buildings is evaluated. The evaluation is based on a prototype steel building designed using four different seismic‐resistant frames: (i) conventional moment resisting frames (MRFs); (ii) MRFs with viscous dampers; (iii) SC‐MRFs; or (iv) SC‐MRFs with viscous dampers. All frames are designed according to Eurocode 8 and have the same column/beam cross sections and similar periods of vibration. Viscous dampers are designed to reduce the peak story drift under the design basis earthquake (DBE) from 1.8% to 1.2%. Losses are estimated by developing vulnerability functions according to the FEMA P‐58 methodology, which considers uncertainties in earthquake ground motion, structural response, and repair costs. Both the probability of collapse and the probability of demolition because of excessive residual story drifts are taken into account. Incremental dynamic analyses are conducted using models capable to simulate all limit states up to collapse. A parametric study on the effect of the residual story drift threshold beyond which is less expensive to rebuild a structure than to repair is also conducted. It is shown that viscous dampers are more effective than post‐tensioning for seismic intensities equal or lower than the maximum considered earthquake (MCE). Post‐tensioning is effective in reducing repair costs only for seismic intensities higher than the DBE. The paper also highlights the effectiveness of combining post‐tensioning and supplemental viscous damping by showing that the SC‐MRF with viscous dampers achieves significant repair cost reductions compared to the conventional MRF. Copyright © 2016 John Wiley & Sons, Ltd.     

Determination of column size for displacement‐based design of reinforced concrete frame buildings

This article reports a method to determine the storey‐wise column size for displacement‐based design of reinforced concrete frame buildings with a wide range of storey drift and building plan. The method uses a computer program based algorithm. The basic relation used in the algorithm is formulated by considering the various possible deformation components involved in the overall frame deformation. As a necessity to represent the deformation component due to plastic rotation of beam members, a relation between the beam plastic rotation and the target‐drift is adopted. To control the dynamic amplification of interstorey drift, a target‐drift dependant design‐drift reduction factor is used. The dynamic amplification of column moment is accounted with the help of an approximate conversion of fundamental period of the building from the effective period of the equivalent SDOF system. To avoid the formation of plastic hinge in column members, a design‐drift dependant column–beam moment capacity ratio is used. The method successfully determines the storey‐wise column size for buildings of four plans of different varieties, heights up to 12 storeys and target‐drift up to 3%. Copyright © 2013 John Wiley & Sons, Ltd.     

Evaluation of out‐of‐plane seismic performance of column‐to‐column precast concrete cladding panels in one‐storey industrial buildings

Recent earthquakes in Italy (L'Aquila 2009 and Emilia 2012) highlighted the vulnerability of precast cladding panels, typically associated with a connection system not designed to account for displacement and rotation compatibility between the panels and the supporting structure. Experimental investigations were performed in the past to investigate the in‐plane performance of cladding panels and design recommendations have been made accordingly; however, in the case of out‐of‐plane seismic loads, the load demand is commonly evaluated in the design practice by means of formulations for nonstructural components. This paper summarizes the results obtained from parametric analyses conducted to estimate the out‐of‐plane load demand in column‐to‐column cladding panels typical of one‐storey commercial and industrial buildings. Empirical equations suitable for both new and existing panels are proposed and compared with the design equations given in Eurocode 8 and ASCE 7. The paper also considers the effects of the development of plastic hinges at the column base and of the roof flexibility on the load demand in panel‐to‐column connections. The roof flexibility may generate the torsion of the panels; consequently, an analytical procedure to account for such effects is proposed. Finally, general design recommendations are made.     

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.     

Case studies of damage to 19‐storey irregular steel moment‐frame buildings under near‐source ground motion

This paper describes the three‐dimensional nonlinear analysis of six 19‐storey steel moment‐frame buildings, designed per the 1997 Uniform Building Code, under strong ground motion records from near‐source earthquakes with magnitudes in the range of 6.7–7.3. Three of these buildings possess a reentrant corner irregularity, while the remaining three possess a torsional plan irregularity. The records create drift demands of the order of 0.05 and plastic rotation demands of the order of 4–5% of a radian in the buildings with reentrant corners. These values point to performance at or near ‘Collapse Prevention’. Twisting in the torsionally sensitive buildings causes the plastic rotations on the moment frame on one face of the building (4–5% of a radian) to be as high as twice of that on the opposite face (2–3% of a radian). The asymmetric yield pattern implies a lower redundancy in the lateral force‐resisting system as the failure of the heavily loaded frame could result in a total loss of resistance to torsion. Copyright © 2006 John Wiley & Sons, Ltd.     

Tests and model calibration of high‐strength steel tubular beam‐to‐column and column‐base composite joints for moment‐resisting structures

Performance‐based engineering (PBE) methodologies allow for the design of more reliable earthquake‐resistant structures. Nonetheless, to implement PBE techniques, accurate finite element models of critical components are needed. With these objectives in mind, initially, we describe an experimental study on the seismic behaviour of both beam‐to‐column (BTC) and column‐base (CB) joints made of high‐strength steel S590 circular columns filled with concrete. These joints belonged to moment‐resisting frames (MRFs) that constituted the lateral‐force‐resisting system of an office building. BTC joints were conceived as rigid and of partial strength, whereas CB joints were designed as rigid and of full strength. Tests on a BTC joint composed of an S275 steel composite beam and high‐strength steel concrete‐filled tubes were carried out. Moreover, two seismic CB joints were tested with stiffeners welded to the base plate and anchor bolts embedded in the concrete foundation as well as where part of a column was embedded in the foundation with no stiffeners. A test programme was carried out with the aim of characterising these joints under monotonic, cyclic and random loads. Experimental results are presented by means of both force–interstory drift ratio and moment–rotation relationships. The outcomes demonstrated the adequacy of these joints to be used for MRFs of medium ductility class located in zones of moderate seismic hazard. Then, a numerical calibration of the whole joint subassemblies was successfully accomplished. Finally, non‐linear time‐history analyses performed on 2D MRFs provided useful information on the seismic behaviour of relevant MRFs. Copyright © 2015 John Wiley & Sons, Ltd.     

Dispersions for the pushover‐based risk assessment of reinforced concrete frames and cantilever walls

The paper presents the results of an investigation into the dispersion values, expressed in terms of limit‐state spectral accelerations, which could be used for the pushover‐based risk assessment of low‐height to mid‐height reinforced concrete frames and cantilever walls. The results of an extensive parametric study of a portfolio of test structures indicated that the dispersion values due to record‐to‐record variability and modelling uncertainty (β_LS,RU) are within the range from 0.3 to 0.55 for the near collapse limit state, and between 0.35 and 0.60 for the collapse limit state. The dispersions β_LS,RU proposed for the code‐conforming and the majority of old (non code‐conforming) frames are in between these values. On the other hand, the dispersions proposed for the old frames with a soft storey and an invariant plastic mechanism, and for the code‐conforming cantilever walls, are at the lower and upper bounds of the presented values, respectively. The structural parameters that influence these dispersions were identified, and the influence of different ground motion sets, and of the models used for the calculation of the rotation capacities of the columns, on the calculated fragility parameters was examined and quantified. The proposed dispersion values were employed in a practice‐oriented pushover‐based method for the estimation of failure probability for eight selected examples. The pushover‐based risk assessment method, although extremely simple and economical when compared with more rigorous probabilistic methods, was able to predict seismic risk with reasonable accuracy, thus showing it to be a practical tool for engineers. Copyright © 2016 John Wiley & Sons, Ltd.     

Seismic performance and damage evaluation of a reinforced concrete frame with hysteretic dampers through shake‐table tests

Passive energy dissipation devices are increasingly implemented in frame structures to improve their performance under seismic loading. Most guidelines for designing this type of system retain the requirements applicable to frames without dampers, and this hinders taking full advantage of the benefits of implementing dampers. Further, assessing the extent of damage suffered by the frame and by the dampers for different levels of seismic hazard is of paramount importance in the framework of performance‐based design. This paper presents an experimental investigation whose objectives are to provide empirical data on the response of reinforced concrete (RC) frames equipped with hysteretic dampers (dynamic response and damage) and to evaluate the need for the frame to form a strong column‐weak beam mechanism and dissipate large amounts of plastic strain energy. To this end, shake‐table tests were conducted on a 2/5‐scale RC frame with hysteretic dampers. The frame was designed only for gravitational loads. The dampers provided lateral strength and stiffness, respectively, three and 12 times greater than those of the frame. The test structure was subjected to a sequence of seismic simulations that represented different levels of seismic hazard. The RC frame showed a performance level of ‘immediate occupancy’, with maximum rotation demands below 20% of the ultimate capacity. The dampers dissipated most of the energy input by the earthquake. It is shown that combining hysteretic dampers with flexible reinforced concrete frames leads to structures with improved seismic performance and that requirements of conventional RC frames (without dampers) can be relieved. Copyright © 2014 John Wiley & Sons, Ltd.     

高强混凝土框架柱的地震损伤模型

本文首先讨论了现有的几种地震损伤模型及其特点,然后计算出试验框架柱累积滞回耗能随加载循环水平的变化,分析和讨论了轴压比、箍筋形式、配箍率、纵向配筋率、混凝土强度等级以及剪跨比对累积滞回耗能的影响。根据现有的损伤模型,对试验框架柱的损伤指数进行了分析比较,给出了符合高强混凝土框架柱和普通混凝土框架柱的地震损伤模型。根据损伤指数随加载循环水平的变化规律,分析和讨论了剪跨比、轴压比以及配箍率对损伤的影响。最后通过对各地震损伤模型的比较分析,提出了高强混凝土框架柱的地震损伤模型。     

既有钢筋混凝土框架结构的多指标云模型地震损伤评估

目前的既有钢混结构地震损伤研究没有同时考虑不同抗震设计规范差异和耐久性两个因素对结构抗震性能的影响,且损伤指标较简单,在动力损伤分析中也存在局限。基于云模型的特点,提出了包括弹塑性耗能差率、刚度损伤指数、层间位移角和顶点位移角的多元结构损伤状态综合评估方法,能够同时考虑结构各损伤指数的随机性和模糊性。考虑不同版本抗震设计规范造成的结构性能差异和耐久性下降对结构性能的影响,设计3个典型五层钢混框架结构,进行增量动力分析,验证损伤评估方法的准确性。结果表明：随着抗震规范版本的更新,结构的损伤程度有适当减轻;同一结构的损伤程度因混凝土碳化作用先减轻后加重;采用弹塑性耗能差率表征既有结构的地震损伤效果优于刚度损伤指数;基于多指标云模型损伤评估方法获得的云模型综合隶属度和综合损伤值能够更加细化和精确地描述结构损伤状态。     

Probabilistic performance assessment of low‐ductility reinforced concrete frames retrofitted with dissipative braces

The paper illustrates a probabilistic methodology for assessing the vulnerability of existing reinforced concrete (RC) buildings with limited ductility capacity retrofitted by means of dissipative braces. The aim is to highlight the most important parameters controlling the capacity of these coupled systems and specific aspects concerning the response uncertainties. The proposed methodology is based on the use of local engineering demand parameters for monitoring the seismic response and on the development of component and system fragility curves before and after the retrofit. In the first part of the paper, the methodology is illustrated by highlighting its advantages with respect to the existing approaches. Then, its capability and effectiveness are tested by considering a benchmark two‐dimensional RC frame designed for gravity‐loads only. The frame is retrofitted by introducing elasto‐plastic dissipative braces designed for different levels of base shear capacity. The obtained results show the effectiveness of the methodology in describing the changes in the response and in the failure modalities before and after the retrofit, for different retrofit levels. Moreover, the retrofit effectiveness is evaluated by introducing proper synthetic parameters describing the fragility curves and by stressing the importance of employing local engineering demand parameters (EDPs) rather than global EDPs in the seismic risk evaluation of coupled systems consisting in low‐ductility RC frames and dissipative braces. Copyright © 2012 John Wiley & Sons, Ltd.