Using experimental data to reduce the single-building sigma of fragility curves: case study of the BRD tower in Bucharest, Romania

The lack of knowledge concerning modelling existing buildings leads to significant variability in fragility curves for single or grouped existing buildings. This study aims to investigate the uncertainties of fragility curves, with special consideration of the single-building sigma. Experimental data and simplified models are applied to the BRD tower in Bucharest, Romania, a RC building with permanent instrumentation. A three-step methodology is applied： （1） adjustment of a linear MDOF model for experimental modal analysis using a Timoshenko beam model and based on Anderson＇s criteria, （2） computation of the structure＇s response to a large set of accelerograms simulated by SIMQKE software, considering twelve ground motion parameters as intensity measurements （IM）, and （3） construction of the fragility curves by comparing numerical interstory drift with the threshold criteria provided by the Hazus methodology for the slight damage state. By introducing experimental data into the model, uncertainty is reduced to 0.02 considering Sd ） as seismic intensity IM and uncertainty related to the model is assessed at 0.03. These values must be compared with the total uncertainty value of around 0.7 provided by the Hazus methodology.     

Development of damage probability matrices based on Greek earthquake damage data

A comprehensive study is presented for empirical seismic vulnerability assessment of typical structural types, representative of the building stock of Southern Europe, based on a large set of damage statistics. The observational database was obtained from post-earthquake surveys carried out in the area struck by the September 7, 1999 Athens earthquake. After analysis of the collected observational data, a unified damage database has been created which comprises 180,945 damaged buildings from/after the near-field area of the earthquake. The damaged buildings are classified in specific structural types, according to the materials, seismic codes and construction techniques in Southern Europe. The seismic demand is described in terms of both the regional macroseismic intensity and the ratio αg/ao, where αg is the maximum peak ground acceleration (PGA) of the earthquake event and ao is the unique value PGA that characterizes each municipality shown on the Greek hazard map. The relative and cumulative frequencies of the different damage states for each structural type and each intensity level are computed in terms of damage ratio. Damage probability matrices (DPMs) and vulnerability curves are obtained for specific structural types. A comparison analysis is fulfilled between the produced and the existing vulnerability models.     

Performance-based methodology for assessing seismic vulnerability and capacity of buildings

This paper presents a performance-based methodology for the assessment of seismic vulnerability and capacity of buildings. The vulnerability assessment methodology is based on the HAZUS methodology and the improved capacity- demand-diagram method. The spectral displacement (Sd) of performance points on a capacity curve is used to estimate the damage level of a building. The relationship between Sd and peak ground acceleration (PGA) is established, and then a new vulnerability function is expressed in terms of PGA. Furthermore, the expected value of the seismic capacity index (SCev) is provided to estimate the seismic capacity of buildings based on the probability distribution of damage levels and the corresponding seismic capacity index. The results indicate that the proposed vulnerability methodology is able to assess seismic damage of a large number of building stock directly and quickly following an earthquake. The SCev provides an effective index to measure the seismic capacity of buildings and illustrate the relationship between the seismic capacity of buildings and seismic action. The estimated result is compared with damage surveys of the cities of Dujiangyan and Jiangyou in the M8.0 Wenchuan earthquake, revealing that the methodology is acceptable for seismic risk assessment and decision making. The primary reasons for discrepancies between the estimated results and the damage surveys are discussed.     

Force and Displacement Based Vulnerability Assessment for Traditional Buildings

Vulnerability assessment for historic buildings is usually carried out using capacity based approaches and prediction of losses is obtained by using normal or lognormal distributions for expected levels of macro seismic intensity or peak ground accelerations. Several authors have outlined the limitations of such approach. The paper presents a method to correlate analysis of seismic vulnerability using a failure mechanisms approach to observed in situ damage. The various aspects of the procedure are highlighted with application to a real case. It is shown how once the typologies within a sample have been identified, fragility curves for each of them can be derived and predictive cumulative damage curve obtained for samples for which direct survey of damage data is lacking. Finally the paper shows how the failure mechanism approach can be used to derive damage scenarios both in terms of spectral acceleration and spectral displacement     

Seismic vulnerability assessment to slight damage based on experimental modal parameters

The aim of this paper is to adjust behaviour models for each class of structure for vulnerability assessment by using ambient vibration. A simple model based on frequencies, mode shapes and damping, taken from ambient vibrations, allows computation of the response of the structures and comparison of inter‐storey drifts with the limits found in the literature for the slight damage grade, considered here as the limit of elastic behaviour. Two complete methodologies for building fragility curves are proposed: (1) using a multi‐degree of freedom system including higher modes and full seismic ground‐motion and (2) using a single‐degree of freedom model considering the fundamental mode f₀ of the structure and ground‐motion displacement response spectra S_D(f₀). These two methods were applied to the city of Grenoble, where 60 buildings were studied. Fragility curves for slight damage were derived for the various masonry and reinforced concrete classes of buildings. A site‐specific earthquake scenario, taking into account local site conditions, was considered, corresponding to an M_L = 5.5 earthquake at a distance of 15 km. The results show the benefits of using experimental models to reduce variability of the slight damage fragility curve. Moreover, by introducing the experimental modal model of the buildings, it is possible to improve seismic risk assessment at an overall scale (the city) or a local scale (the building) for the first damage grade (slight damage). This level of damage, of great interest for moderate seismic‐prone regions, may contribute to the seismic loss assessment. Copyright © 2011 John Wiley & Sons, Ltd.     

Mainshock-aftershock state-dependent fragility curves: A case of wood-frame houses in British Columbia,Canada

During a mainshock-aftershock (MSAS) sequence, there is no time to retrofit structures that are damaged by a mainshock; therefore, aftershocks could cause additional damage. This study proposes a new approach to develop state-dependent fragility curves using real MSAS records. Specifically, structural responses before and after each event of MSAS sequences are used to obtain statistical relationships among the engineering demand parameter prior to the seismic event (pre-EDP), the intensity measure of the seismic event (IM), and the engineering demand parameter after the seismic event (post-EDP). The developed fragility curves account for damage accumulation, providing the exceeding probability of damage state (DS) given the IM of the event and the DS of the structure prior to the seismic excitation. The UBC-SAWS model, which was developed for wood-frame houses in British Columbia, Canada, is considered as a case study application. Results indicate that for the examined structural typology, state-dependent fragility curves based on residual interstorey drift ratio (pre-EDP), peak ground velocity (IM), and maximum inter-storey drift ratio (post-EDP) are the best choice to characterise the cumulative damage effect. An illustration of the developed fragility curves is provided by considering a hypothetical MSAS scenario of a M_w 9.0 Cascadia mainshock triggering a M_w 6.0 crustal event in the Leech River fault, affecting wooden houses in Victoria, Canada. The MSAS scenario increases Yellow tags (restricted access) by 12.3% and Red tags (no access) by 4.8%.     

Effect of the angle of seismic incidence on the fragility curves of bridges

This study examines the effect of the angle of seismic incidence θ on the fragility curves of bridges. Although currently, fragility curves of bridges are usually expressed only as a function of intensity measure of ground motion (IM) such as peak ground acceleration, peak ground velocity, or S_a(ω₁), in this study they are expressed as a function of IM with θ as a parameter. Lognormal distribution function is used for this purpose with fragility parameters, median c_m and standard deviation ζ to be estimated for each value of θ chosen from 0 < θ < 360°. A nonlinear 3D finite element dynamic analysis is performed, and key response values are calculated as demand on the bridge under a set of acceleration time histories with different IM values representing the seismic hazard in Los Angeles area. This method is applied to typical straight reinforced concrete bridges located in California. The results are validated with existing empirical damage data from the 1994 Northridge earthquake. Even though the sample bridges are regular and symmetric with respect to the longitudinal axis, the results indicate that the weakest direction is neither longitudinal nor transverse. Therefore, if the angle of seismic incidence is not considered, the damageability of a bridge can be underestimated depending on the incidence angle of seismic wave. Because a regional highway transportation network is composed of hundreds or even thousands of bridges, its vulnerability can also be underestimated. Hence, it is prudent to use fragility curves taking the incident angle of seismic waves into consideration as developed here when the seismic performance of a highway network is to be analyzed. Copyright © 2012 John Wiley & Sons, Ltd.     

Deriving fragility functions from bilinearized capacity curves for earthquake scenario modelling using the conditional spectrum

The development of fragility curves to perform seismic scenario-based risk assessment requires a fully probabilistic procedure in order to account for uncertainties at each step of the computation. This is especially true when developing fragility curves conditional on an Intensity Measure that is directly available from a ground-motion prediction equation. In this study, we propose a new derivation method that uses realistic spectra instead of design spectral shapes or uniform hazard spectra and allows one to easily account for the features of the site-specific hazard that influences the fragility, without using non-linear dynamic analysis. The proposed method has been applied to typical school building types in the city of Basel (Switzerland) and the results have been compared to the standard practice in Europe. The results confirm that fragility curves are scenario dependent and are particularly sensitive to the magnitude of the earthquake scenario. The same background theory used for the derivation of the fragility curves has allowed an innovative method to be proposed for the conversion of fragility curves to a common IM (i.e. spectral acceleration or PGA). This conversion is the only way direct comparisons of fragility curves can be made and is useful when inter-period correlation cannot be used in scenario loss assessment. Moreover, such conversion is necessary to compare and verify newly developed curves against those from previous studies. Conversion to macroseismic intensity is also relevant for the comparison between mechanical-based and empirical fragility curves, in order to detect possible biases.     

Processing Italian damage data to derive typological fragility curves

Typological fragility curves have been derived from post-earthquake survey data on building damage, collected in the areas affected by the most relevant Italian earthquakes of the last three decades. A complex and time consuming codification and reinterpretation work has been done on a set of about 150,000 survey building records, in order to define empirical damage probability matrices for several building typologies, characteristic of the Italian building stock. The obtained data have then been processed by advanced nonlinear regression methods in order to derive typological fragility curves. These curves, organised in five damage levels, provide useful information both for relative comparisons among typologies and for seismic risk analyses at different scales. By combining hazard definitions, fragility curves and inventory data, complete earthquake risk scenario studies can be performed, but even the single convolution of hazard and fragility allows to obtain typological risk maps, both for single damage state definitions and for concise average loss parameters. The very high potential of these results is shown by some applications reported in the paper.     

On the vulnerability assessment of monumental buildings

In all European countries the will to conserve the building heritage is very strong. Unfortunately, large areas in Europe are characterised by a high level of seismic hazard and the vulnerability of ancient masonry structures is often relevant. The large number of monumental buildings in urban areas requires facing the problem with a methodology that can be applied at territorial scale, with simplified models which need little easily obtainable, data. Within the Risk-UE project, a new methodology has been stated for the seismic vulnerability assessment of monumental buildings, which considers two different approaches: a macroseismic model, to be used with macroseismic intensity hazard maps, and a mechanical based model, to be applied when the hazard is provided in terms of peak ground accelerations and spectral values. Both models can be used with data of different reliability and depth. This paper illustrates the theoretical basis and defines the parameters of the two models. An application to an important church is presented.     

Deriving vulnerability curves using Italian earthquake damage data

The concerted effort to collect earthquake damage data in Italy over the past 30 years has led to the development of an extensive database from which vulnerability predictions for the Italian building stock can be derived. A methodology to derive empirical vulnerability curves with the aforementioned data is presented herein and the resulting curves have been directly compared with mechanics-based vulnerability curves. However, it has been found that a valid comparison between the empirical and analytical vulnerability curves is not possible mainly due to a number of shortcomings in the database of surveyed buildings. A detailed discussion of the difficulties in deriving vulnerability curves from the current observed damage database is thus also presented.     

Seismic vulnerability of roof systems combining URM gable walls and timber diaphragms

Typical low-rise masonry buildings consist of unreinforced masonry (URM) walls covered with various timber roof configurations generally supported or finished by masonry gables. Post-earthquake observations and experimental outcomes highlighted the large vulnerability of the URM gables to the development of overturning mechanisms, both because of the inertial out-of-plane excitation and the in-plane timber diaphragm deformability. This paper presents the static and dynamic experimental seismic performance of three full-scale roofs tested via quasi-static cyclic and shake table tests. Two of them were tested as part of a whole full scale one-storey and two-storey building. A single-degree-of-freedom (SDOF) numerical model is calibrated against experimental data and proposed for the analysis of this roof typology's dynamic behaviour. Several sets of analyses were conducted to assess the vulnerability of these structural components and to study the effect of the whole building's characteristics (eg, number of storeys and structural stiffness and strength) on the seismic performance of this roof typology.     

Seismic vulnerability of offshore wind turbines to pulse and non-pulse records

The increasing number of wind turbines in active tectonic regions has attracted scientific interest to evaluate the seismic vulnerability of offshore wind turbines (OWTs). This study aims at assessing the deformation and collapse susceptibility of 2MW and 5MW OWTs subjected to shallow-crustal pulse-like ground motions, which has not been particularly addressed to date. A cloud-based fragility assessment is performed to quantify the seismic response for a given intensity measure and to assess the failure probabilities for pulse-like and non-pulse-like ground motions. The first-mode spectral acceleration S_a(T₁) is found to be an efficient response predictor for OWTs, exhibiting prominent higher-mode behavior, at the serviceability and ultimate conditions. Regardless of earthquake type, it is shown that records with strong vertical components may induce nonlinearity in the supporting tower, leading to potential failure by buckling in three different patterns: (i) at tower base near platform level, (ii) close to tower top, and (iii) between the upper half of the main tower and its top. Type and extent of the damage are related to the coupled excitation of vertical and lateral higher modes, for which tower top acceleration response spectra S_a,i(Top) is an effective identifier. It is also observed that tower's slenderness ratio (l/d), the diameter-to-thickness ratio (d/t), and the rotor-nacelle-assembly mass (m_RNA) are precursors for evaluating the damage mode and vulnerability of OWTs under both pulse-like and non-pulse-like ground motion records.     

Seismic capacity of irregular unreinforced masonry walls with openings

Masonry buildings are often characterized by geometric irregularities. In many cases, such buildings meet global regularity requirements provided by seismic codes, but they are composed by irregular walls with openings. The latter are masonry walls characterized by (i) openings of different sizes, (ii) openings misaligned in the horizontal and/or vertical direction, or (iii) a variable number of openings per story. An irregular layout of openings can induce not only a nonuniform distribution of gravity loads among masonry piers but also unfavorable damage localizations resulting in a premature collapse of the wall and hence a higher seismic vulnerability. This paper is aimed at providing a simplified methodology to assess the effects of irregularities on the in‐plane seismic capacity of unreinforced masonry (URM) walls with openings. To this end, a macroelement method was developed and validated through experimental results available in the literature. The proposed methodology was based on the quantification of wall irregularities by means of geometric indices and their effects on seismic capacity of URM walls with openings through both sensitivity and regression analyses. Sensitivity analysis was based on a high number of static pushover analyses and allowed to assess variations in key seismic capacity parameters. Regression analysis let to describe each capacity parameter under varying irregularity index, providing empirical models for seismic assessment of irregular URM walls with openings. The in‐plane seismic capacity was found to be significantly affected by wall irregularities, especially in the case of openings with different heights. Copyright © 2012 John Wiley & Sons, Ltd.     

Intensity measure conversion of fragility curves

In seismic risk assessment of structures, fragility functions are the probabilistic characterization of vulnerability at the component and/or structural level, expressing the probability of failure as a function of a ground motion intensity measure (IM). Fragility curves, in general, are structure- and site-specific, thus a comparison of fragility curves, then of vulnerability, is not straightforward across multiple structures. Also, it could be the case that hazard at a site of interest is not available for the IM originally considered in the fragility assessment. These situations require to convert fragility curves from an original IM to a target one. The present study addresses a hazard-consistent probabilistic framework for converting spectral acceleration-based IMs from an original IM to a target IM at a given site. In particular, three conversion cases, under different assumptions on the explanatory power of the involved IMs with respect to structural failure, are discussed: (a) a vector-valued IM consisting of the original and target IMs, magnitude, and source-to-site distance; (b) a vector-valued IM consisting of the original and target IMs; and (c) the original (scalar) IM only, assuming that structural response, given the IM, is statistically independent of the other ground motion variables. In this framework, the original fragility functions are characterized using the state-of-the-art methods in performance-based earthquake engineering, then the fragility curves as a function of the target IM are evaluated through applications of the probability calculus rules, ensuring consistency with the seismic hazard at the site of interest. The conversion strategy is illustrated through the applications to three-, six-, and nine-story Italian code-conforming reinforced concrete buildings designed for a high-hazard site in Italy. The study shows that, in most of the cases, the converted fragility curves have agreement with the reference curves directly developed in terms of the target IM. Cases in which least agreement was found are likely due to the models used to obtain the terms required by the conversion equations.     

Vulnerability and risk analysis of monuments in Málaga city’s historical centre (Southern Spain)

A vulnerability analysis of some historical and monumental buildings in the city of Málaga is presented in this paper. More than twenty of these monuments were severely damaged or completely destroyed due to the large earthquake (I _max = VIII–IX) occurred in the Málaga region in October 1680. The vulnerability index methodology has been used in this paper. This technique is based on statistical data from seismic damage caused to Italian monuments for the past 30?years. For each building, vulnerability curves have been obtained and damage grades have been estimated. A comparison has been carried out between the expected damage grades and the damage observed from past earthquakes, in order to check the feasibility of applying this methodology to Spanish monuments. This comparison has been possible due to the fact that detailed seismic damage information exists for monuments in the city of Málaga that still exist today, which is a very uncommon case in Spain. Results show a good consistency between expected and observed damage, especially for the churches type. Two seismic scenarios have been proposed for the city centre, one deterministic and one probabilistic, where 54 historical and modern buildings have been analyzed. Both scenarios show worrying results, especially for the types of churches, chapels and towers, where expected high probabilities of suffering very heavy damage or even collapse have been obtained. It is highly recommended to take the necessary measures, in the hope of trying to avoid the possible damage that can be expected from future earthquakes.     

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.     

On the treatment of uncertainty in seismic vulnerability and portfolio risk assessment

In a related study developed by the authors, building fragility is represented by intensity‐specific distributions of damage exceedance probability of various damage states. The contribution of the latter has been demonstrated in the context of loss estimation of building portfolios, where it is shown that the proposed concept of conditional fragility functions provides the link between seismic intensity and the uncertainty in damage exceedance probabilities. In the present study, this methodology is extended to the definition of building vulnerability, whereby vulnerability functions are characterized by hazard‐consistent distributions of damage ratio per level of primary seismic intensity parameter—Sa(T₁). The latter is further included in a loss assessment framework, in which the impact of variability and spatial correlation of damage ratio in the probabilistic evaluation of seismic loss is accounted for, using test‐bed portfolios of 2, 5, and 8‐story precode reinforced concrete buildings located in the district of Lisbon, Portugal. This methodology is evaluated in comparison with current state‐of‐the‐art methods of vulnerability and loss calculation, highlighting the discrepancies that can arise in loss estimates when the variability and spatial distributions of damage ratio, influenced by ground motion properties other than the considered primary intensity measure, are not taken into account.     

Assessing the impact of ground-motion variability and uncertainty on empirical fragility curves

Empirical fragility curves, constructed from databases of thousands of building-damage observations, are commonly used for earthquake risk assessments, particularly in Europe and Japan, where building stocks are often difficult to model analytically (e.g. old masonry structures or timber dwellings). Curves from different studies, however, display considerable differences, which lead to high uncertainty in the assessed seismic risk. One potential reason for this dispersion is the almost universal neglect of the spatial variability in ground motions and the epistemic uncertainty in ground-motion prediction. In this paper, databases of building damage are simulated using ground-motion fields that take account of spatial variability and a known fragility curve. These databases are then inverted, applying a standard approach for the derivation of empirical fragility curves, and the difference with the known curve is studied. A parametric analysis is conducted to investigate the impact of various assumptions on the results. By this approach, it is concluded that ground-motion variability leads to flatter fragility curves and that the epistemic uncertainty in the ground-motion prediction equation used can have a dramatic impact on the derived curves. Without dense ground-motion recording networks in the epicentral area empirical curves will remain highly uncertain. Moreover, the use of aggregated damage observations appears to substantially increase uncertainty in the empirical fragility assessment. In contrast, the use of limited randomly-chosen un-aggregated samples in the affected area can result in good predictions of fragility.     

Effect of URM infills on seismic vulnerability of Indian code designed RC frame buildings

Unreinforced Masonry(URM) is the most common partitioning material in framed buildings in India and many other countries.Although it is well-known that under lateral loading the behavior and modes of failure of the frame buildings change significantly due to infill-frame interaction,the general design practice is to treat infills as nonstructural elements and their stiffness,strength and interaction with the frame is often ignored,primarily because of difficulties in simulation and lack of modeling guidelines in design codes.The Indian Standard,like many other national codes,does not provide explicit insight into the anticipated performance and associated vulnerability of infilled frames.This paper presents an analytical study on the seismic performance and fragility analysis of Indian code-designed RC frame buildings with and without URM infills.Infills are modeled as diagonal struts as per ASCE 41 guidelines and various modes of failure are considered.HAZUS methodology along with nonlinear static analysis is used to compare the seismic vulnerability of bare and infilled frames.The comparative study suggests that URM infills result in a significant increase in the seismic vulnerability of RC frames and their effect needs to be properly incorporated in design codes.