Rui Maio, Georgios Tsionis

Review and evaluation of

analytical fragility curves

Seismic fragility curves for the European building stock

2015

EUR 27635 EN

Seismic fragility curves for the European building stock

i

This publication is a Technical report by the Joint Research Centre, the European Commission’s in-house science

service. It aims to provide evidence-based scientific support to the European policy-making process. The scientific

output expressed does not imply a policy position of the European Commission. Neither the European

Commission nor any person acting on behalf of the Commission is responsible for the use that might be made of

this publication.

Contact information

Name: Georgios Tsionis

Address: Joint Research Centre, Via E. Fermi 2749, Ispra (VA) 21027, Italy

E-mail: georgios.tsionis@jrc.ec.europa.eu

Tel.: 39 03 32 78 94 84

JRC Science Hub

https://ec.europa.eu/jrc

JRC99561

EUR 27635 EN

ISBN 978-92-79-54136-0 (PDF)

ISBN 978-92-79-54137-7 (print)

ISSN 1831-9424 (online)

ISSN 1018-5593 (print)

doi:10.2788/586263 (online)

doi:10.2788/798152 (print)

© European Union, 2015

Reproduction is authorised provided the source is acknowledged.

How to cite: Maio R and Tsionis G (2016) Seismic fragility curves for the European building stock: review and

evaluation of analytical fragility curves. EUR 27635 EN. doi:10.2788/586263.

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Table of contents

1. Introduction .................................................................................................... 1

1.1. Background ............................................................................................... 1

1.2. Objectives and motivation ........................................................................... 2

1.3. Outline of the report ................................................................................... 3

2. Overview of existing fragility curves ................................................................... 5

2.1. Analytical approaches ................................................................................. 5

2.2. Empirical approaches .................................................................................. 6

2.3. Expert judgment elicitation approaches ......................................................... 7

2.4. Hybrid approaches ...................................................................................... 8

3. Review of analytical fragility assessment methodologies ..................................... 11

3.1. Structural system ..................................................................................... 14

3.2. Components for response analysis .............................................................. 15

3.3. The selection of the analysis type ............................................................... 17

3.3.1. Nonlinear Dynamic Analysis .................................................................. 17

3.3.2. Nonlinear Static Analysis ...................................................................... 19

3.3.3. Simplified Mechanism Models ............................................................... 20

3.3.3.1. FaMIVE method ............................................................................. 21

3.3.3.2. DBELA method .............................................................................. 22

3.3.3.3. SP-BELA method ........................................................................... 23

3.3.3.4. VULNUS method ............................................................................ 25

3.4. The selection of the model type .................................................................. 25

3.4.1. MDoF models ...................................................................................... 26

3.4.2. Reduced MDoF models ......................................................................... 27

3.4.3. SDoF models ...................................................................................... 27

3.5. Shear failure ............................................................................................ 28

3.6. Out-of-plane response of masonry buildings ................................................ 29

3.7. Horizontal diaphragms in masonry buildings ................................................ 30

3.8. Geometrical irregularities........................................................................... 30

3.9. Seismic demand and site-specific records .................................................... 31

3.10. Definition of EDP values at damage thresholds ............................................. 31

3.11. Form of relation ....................................................................................... 32

3.12. Intensity Measure ..................................................................................... 33

3.13. Sampling method and sample size .............................................................. 33

3.14. Summary table of the reviewed fragility curves ............................................ 35

4. Criteria and evaluation of fragility curves .......................................................... 41

4.1. Capacity .................................................................................................. 42

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4.2. Demand .................................................................................................. 43

4.3. Fragility curve (derivation method) ............................................................. 43

4.4. Treatment of uncertainty ........................................................................... 44

5. Current trends in seismic fragility curves ........................................................... 49

6. Concluding remarks ........................................................................................ 55

v

Acknowledgements

The work herein presented entitled Seismic fragility curves for the European building

stock: review and evaluation of analytical fragility curves, was carried out under the

European Commission traineeship job contract no. 228449 at the European Laboratory

for Structural Assessment of the Joint Research Centre, in the framework of the of the

RESURBAN institutional project, which deals with the resilience of the buildings in urban

areas across the European Union. This was not only a quite challenging but also a very

motivating research topic since seismic fragility assessment has becoming an issue of

growing interest worldwide. However, without the support from many sides it would not

have been possible to accomplish this outcome and therefore I would like to use this

occasion to express my gratitude.

First of all I would like to thank my traineeship advisor, Georgios Tsionis, for his support

and understanding, and also for his remarkable comments and suggestions throughout

the traineeship, which were definitely decisive to improve the overall quality of this

report. I would like also to thank Luísa Sousa and Artur Pinto for their support and

willingness to help solving whatever situation, either work-related or everyday life

unexpected difficulties, and Professor Serena Cattari, for her interest, expertise and kind

collaboration on writing the foreword of the present report.

I would like to address a special word of thanks to the Board of Studies of my PhD

Program Infrarisk- “Analysis and Mitigation of risks in Infrastructures”, in particular to

Professor Carlos Sousa Oliveira, for his support and receptiveness regarding this

traineeship opportunity at the Joint Research Centre.

I would also like to thank my PhD supervisor, Professor Romeu Vicente, for his

motivation and positivism that keeps me interested following a research career, and also

for his help and support on overcoming all the institutional and bureaucratic hurdles.

Last but not least, I would like to thank all the extraordinary people that I had the

chance to meet here at the Joint Research Centre, namely to Traineeland. Within this

unofficial community of trainees I have met the most highly talented young individuals

who taught me among other things, to be more tolerant, open-minded and to always

think on the positive side of things.

Rui Maio

PhD Student of the Infrarisk- Doctoral Programme

DECivil-UA, Department of Civil Engineering

RISCO – Aveiro Research Centre of Risks and Sustainability in Construction

University of Aveiro

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Foreword

Seismic risk is defined as the potential of negative consequences of hazardous events

that may occur in a specific area and period of time and is obtained by the probabilistic

convolution of three main components, the hazard, vulnerability and exposure. The

concept of negative consequences can belong to different categories such as: physical

damage to buildings, casualties, direct cost of damage, indirect economic impacts (loss

of productivity and business interruption), loss of function in lifelines and critical facilities

and also social, organizational and institutional impacts. In recent years a growing

attention in research has been paid on how to consider all these contributions in an

integrate approach within a seismic loss assessment: this also agrees with the emerging

concept of resilience-based assessment. However, vulnerability still represents a

relevant and crucial component of the chain of the seismic risk analysis.

In this context, the so-called fragility curves provide the essential link between the

seismic hazard at the site and the corresponding effects on any kind of exposed

components and aim to relate a selected intensity measure (IM) to a proper engineering

demand parameter.

Many fragility curves are available in literature for ordinary buildings as derived from

different approaches (i.e. empirical, expert elicitation based, analytical, hybrid), but to

select “the most reliable one for a given application” still represents a very challenging

task and the use of existing fragility functions has to be made very carefully.

First of all, the complexity arises from the wide variety of existing constructions, which

are characterized by very different structural systems, moving through historical periods

and geographical areas. This is particularly true for ancient masonry buildings, since

they were often built by an empirical approach that was strongly affected by the

seismicity of the area and by the constructive details specifically conceived to withstand

the earthquake after the damage observation, but it is also valid for the reinforced

concrete ones, which although more engineered, can be influenced by the code rules in

force at the moment of their design or by specific patents.

From that it follows as the first step of the vulnerability assessment at large scale and of

the most reliable selection of fragility curves consists in the proper classification of the

building stock that cannot ignore a preliminary study of the characteristics of the built

environment under investigation. Depending on the availability and reliability of fragility

curves, the building classification should be more or less detailed. In fact, an excessive

splitting of the built environment into detailed classes, with associated low dispersed

fragility curves, turns out to be specious if their reliability is not robust; in these cases it

is better to reduce the number of buildings classes and ascribe to each one a more

reliable fragility curve, even if defined by a bigger dispersion.

As far as the different approaches available to define the fragility curves concern, those

obtained from observed damage after the occurrence of an earthquake (empirical

approach) are surely valuable, because they are directly correlated to the actual seismic

behaviour of buildings and can be very useful for validation of analytical methods and

calibration of hybrid fragility curves. However, empirical fragility curves are strongly

influenced by the reliability of the damage assessment, which is often made by a quick

survey aimed to other scopes, as the building tagging for use and occupancy. Moreover,

they usually refer to the macroseismic intensity, which is not an instrumental measure

but is based on a subjective evaluation. Then, for more accurate loss estimation, it is

often necessary to convert macroseismic intensity into an instrumental intensity

measure, introducing important approximation and normally huge uncertainties. Finally,

it is important to take into account they are obviously affected also by the “local seismic

culture” of the area and by the specific constructive details which characterize the

building stock, thus their extrapolation to other geographic areas have to be made

carefully.

viii

The use of the analytical fragility curves looks quite attractive in moving towards a more

versatile approach since presents the following main advantages: a) fully employ all

results of Probabilistic Seismic Hazard Analysis (instrumental IMs, seismic input in the

spectral form); b) explicitly keep into account the various parameters that determine the

structural response; c) accurately evaluate the uncertainty propagation. Within this

context, fragility curves may be based on nonlinear static approaches through simplified

and detailed models or based on linear dynamic approaches. Although the reliability of

the vulnerability assessment is affected by the capability of the model to simulate the

actual seismic response of the examined class, the use of the nonlinear static approach

through simplified mechanical based models certainly aims to find a compromise among

the different needs to limit the computational effort, to limit the number of parameters

to be acquired for the building stock at large scale, and provide an adequate versatility

to capture different structural responses.

Therefore, within such context and focusing in particular on the analytical approach, this

report aims to contribute in providing useful and effective tools for supporting the

selection of fragility curves available in literature.

Serena Cattari

Assistant Professor

DICCA - Department of Civil, Chemical and Environmental Engineering

University of Genova

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Abstract

Earthquakes continue to represent a serious threat for some European countries,

particularly for Mediterranean bordering countries, where these events have been

triggering significant destruction and loss over the last decades. Despite the

unpredictable nature of earthquakes, seismic risk assessment should be addressed

having in mind the main cause of damage, which is related to the inadequate seismic

resistance of the existing structures such as residential, industrial or cultural heritage

buildings.

A literature review on the existing methodologies for deriving fragility curves suitable to

the European building stock is herein presented. Even though a brief overview of all the

existing approaches for deriving fragility curves is made, this report focuses on analytical

fragility curves and discusses the most relevant features inherently associated with the

computation of these curves. Additionally, these methodologies are qualitatively

evaluated by means of different sets of criteria.

With this report it is intended to provide a clear insight about the main differences

between existing analytical methodologies for deriving fragility curves, highlighting as

well some of their most important advantages and drawbacks. The proposed evaluation

criteria can be used further on to help not only on the selection of the most suitable

fragility curves for a given geographical location and structural typology, but also for the

further comparison and validation of fragility curves.

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1

1. Introduction

1.1. Background

Earthquakes continue to represent a serious threat for some European countries,

particularly for Mediterranean bordering countries, where these events have been

triggering significant destruction and loss over the last decades. Despite the

unpredictable nature of earthquakes, seismic risk assessment should be addressed

having in mind the main cause of damage, which is related to the inadequate seismic

resistance of the existing structures such as residential, industrial or cultural heritage

buildings.

The causes and consequences associated to seismic risk have been acknowledged by the

European Union, which has expressed great concern about this issue, either by

supporting the development and implementation of Eurocodes, supplementary

coordination of Civil Protection bodies, or even funding numerous research programmes

in this particular field. However, there is still much to be done as regards seismic risk

assessment and mitigation, particularly regarding the oldest and most vulnerable

buildings erected without anti-seismic provisions.

In seismic risk assessment, vulnerability curves are commonly used to express the

likelihood that assets at risk will sustain different degrees of loss over a range of

earthquake ground motion intensities. These vulnerability curves are based on the

statistical analysis of loss values recorded in past earthquakes, simulated in analytical or

numerical methodologies, assumed through expert judgement elicitations, or on a

combination of these methodologies. They can be constructed either by direct or indirect

procedures. While direct procedures usually correlate loss (cost of the physical damage

to buildings, associated casualties and downtime) with a measure of the ground motion

intensity, indirect procedures are usually two-step techniques. In the first step, the

fragility assessment is carried out correlating the physical damage with a measure of the

ground motion intensity. Then, in a second step, fragility curves are transformed in

vulnerability curves through appropriate damage-to-loss functions (D’Ayala et al. 2014).

With very limited exceptions, analytical vulnerability curves make use of indirect

procedures, as they are based on numerical modelling of differing complexity to simulate

the physical phenomenon of seismic damage of the type of structure under analysis. In

Rossetto et al. (2013) and D’Ayala et al. (2014), a discussion concerning the conversion

from physical damage to economic loss and the choice of appropriate damage to loss

functions in relation to the different vulnerability models adopted is made.

It is within this context that fragility curves are becoming more and more important as a

valuable tool for the seismic risk assessment, establishing the link between the seismic

hazard at a site and the effects of the predicted ground motions on the built

environment. By definition, fragility curves express continuous relationships between the

probabilities associated to an asset or class of assets, of reaching or exceeding

predefined damage states for a range of earthquake ground motion intensities.

As reported in literature, fragility curves can be estimated through empirical, analytical,

expert judgment elicitation or hybrid approaches (see Chapter 2). In this report, only

analytically-derived fragility curves were considered, giving particular emphasis on the

variety of methodologies used for their construction, and the corresponding implications

on robustness and reliability aspects that lead to a more systematic qualitative

assessment. According to Calvi et al. (2006), analytical methodologies produce slightly

more detailed and transparent assessment algorithms with direct physical meaning, that

not only allow detailed sensitivity studies to be undertaken, but also cater for the

straightforward calibration to various characteristics of the building stock and hazard. As

one can perceive by the plentiful references made in the present report, several studies

2

have been carried out over the last decades in multiple countries in the field of fragility

assessment for different building typologies.

However, the employment of these existing models in seismic risk analysis may

represent a challenging task due to the fact that the different approaches and

methodologies are spread across scientific journals, conference proceedings, technical

reports and software manuals, hindering the creation of an integrated framework that

could allow the visualization, acquisition and comparison between all the existing curves.

Another important issue stressed out by many researchers is related to the way in which

these curves are defined and presented. The statistical parameters employed to

characterize each curve can vary considerably among different approaches and

methodologies, and in some cases only plots of the final results are provided, instead of

the actual numerical values and respective calculation processes. Finally, it is also worth

referring that it is not often clear what were the methodologies and assumptions

followed in the derivation of the curves, which hinders the adequate evaluation of the

reliability, accuracy and overall quality of the resulting model.

As a response to these concerns, the Global Earthquake Model (GEM) Foundation has

supported the development of an online platform to store, visualize and explore a

multitude of models required to characterize the physical vulnerability of assets. In

addition to the fragility and vulnerability curves, it is also possible to explore damage-to-

loss models and capacity curves. The development of this database relied strongly on

the outcomes of the Global Vulnerability Consortium (GVC) project (Porter et al. 2012)

launched by GEM, which includes the guidelines for developing analytical (D’Ayala et al.

2014; Porter et al. 2014) and empirical (Rossetto et al. 2014) fragility and vulnerability

curves, as well as recommendations for selecting existing empirical and analytical

fragility curves (D’Ayala and Meslem 2012; Rossetto et al. 2013). The fragility models

collected within the European collaborative research project SYNER-G funded by

European Commission (Pitilakis et al. 2014) were also considered for the creation of this

database, which together with the respective recommendations were the starting point

for developing this report that reviews additional methodologies for deriving fragility

curves and applies the selection criteria with a number of modifications.

1.2. Objectives and motivation

Keeping this background in mind, the current report aims to provide additional insight

regarding the following central question: how can one select suitable (sets of) fragility

curves for a given building typology and location from the literature?

The Joint Research Centre (JRC) by means of the European Laboratory for Structural

Assessment (ELSA) has been collaborating and carrying out several research projects

addressing this issue, as for instance the aforementioned SYNER-G project (Pitilakis et

al. 2013). In that project, an integrated methodology for the systemic seismic

vulnerability and risk analysis of buildings, transportation and utility networks and

critical facilities, considering the interactions between different components and systems,

was developed, together with the development of inventory datasets through remote

sensing and direct observation data for earthquake loss estimation, guidelines for

typology definition of European physical assets for seismic risk assessment, among other

issues (Franchin 2013; Hancilar and Taucer 2013; Kaynia 2013; Pitilakis et al. 2013).

Moreover, acknowledging the sustainable development as one of the fundamental

objectives of the European Union, a research project concerning the seismic performance

assessment addressing sustainability and energy efficiency was carried out within the

European Laboratory for Structural Assessment (Tsimplokoukou et al. 2014).

Furthermore, the seismic strengthening of RC buildings and the proposal of new

European technical rules for the assessment and retrofitting of existing structures from

support to the implementation, harmonization and further development of the

3

Eurocodes, have been also addressed in recent years, through the work developed by

Tsionis et al. (2014) and Luechinger and Fischer (2015), respectively.

The work presented herein was carried out in the framework of the RESURBAN

institutional project, which deals with the resilience of the buildings in urban areas

across the European Union (EU), lending continuity to the research developed in recent

years. It relates to the European strategy for disaster management and to the European

Urban Agenda. The work builds on the experience acquired in the field of vulnerability

assessment of buildings through previous experimental and numerical research at the

JRC and aims to provide scientific support for decision-making as regards the seismic

retrofit of existing buildings in the EU and the consequent reduction of losses due to

natural hazards. The report is focussed on the vulnerability of exposed assets, which

constitutes one of the three main components of seismic risk assessment. The fragility

curves reviewed in this work will be used in a probabilistic risk assessment method,

together with the most up-to-date seismic hazard map and an appropriate databank of

the building stock. Different retrofit scenarios will be examined at a later stage,

considering synergies and conflicts with energy retrofitting of buildings.

Aiming to leverage upon the wealth of existing approaches and methodologies that have

been developed in the last decades by dozens of scientists and practitioners, this report

provides a clear insight on the existing literature concerning the derivation of analytical

fragility curves applicable to the European building stock. Furthermore, this report aims

not only to aid the selection among existing fragility curves available for a given

geographic location, structural typology and level of expected hazard, but also to

contribute for the comparison and validation of new fragility curves proposals.

1.3. Outline of the report

This introductory Chapter 1 presents the background and motivations that served as

basis for this report, pointing out the issues to be addressed, highlighting the main

opportunities associated to its development and summarising the most relevant and

recently developed methodologies. Moreover, the general and specific objectives of the

RESURBAN research project are discussed.

In Chapter 2, an overall review of existing fragility curves is carried out, covering the

most common approaches usually employed for the generation of fragility curves

worldwide: empirical; analytical; expert judgment elicitation, and hybrid approaches.

Chapter 3 provides a comprehensive review of the analytical methodologies for fragility

assessment that are available in literature and are applicable to the European and

Mediterranean building stock.

In turn, in Chapter 4 it is proposed a qualitative evaluation criteria based on four main

categories. These criteria are then applied to all fragility curve methodologies herein

reviewed.

In Chapter 5, the main trends of existing analytical methodologies for deriving fragility

curves are identified through statistical analysis of the main factors influencing the

reviewed methodologies and the respective outputs from the qualitative evaluation

carried out in the previous Chapter 4.

Finally, Chapter 6 presents a general overview of the work developed throughout this

traineeship and summarises the key conclusions that have been pointed out in the

previous chapters of the report. To conclude, possible future research lines are also

outlined and discussed.

4

5

2. Overview of existing fragility curves

In this Chapter, an overall review of existing fragility curves will be carried out, aiming to

cover all of the approaches usually employed for the generation of fragility curves

worldwide.

Although several pioneering methodologies for the construction of fragility curves have

been developed worldwide, namely in Japan and in the United States of America, special

care should be given when assigning default curves to represent the seismic

performance of the structure under study or the variability of features determining the

corresponding fragility curves. For instance, the existing HAZUS capacity curves (FEMA

2003a) derived for buildings in the USA, have been widely used to generate fragility

curves of buildings located in different regions of the world, which are designed and built

according to very different standards and construction techniques. Some of these cases

can be found in Lourdes et al. (2007) or Vacareanu et al. (2007), for example. This is

particularly recurrent when studies are conducted for large portions of the building stock

and resources for direct survey and data acquisition are modest. In fact, differences in

construction techniques and detailing between different countries can be significant,

even when buildings are nominally designed to the same code standards (D’Ayala and

Meslem 2013). Such detailing can substantially affect both fragility and vulnerability

curves, being therefore recommended that capacity curves can be derived based on

directly acquired data on local building stock, using available nonlinear commercial

analysis programmes (D’Ayala and Meslem 2013).

Moreover, one of the current challenges of this research topic is the harmonisation of

fragility curves, for the purpose of comparing different existing methodologies and

resulting curves. The harmonisation of fragility curves was addressed in the previously

mentioned SYNER-G project (Pitilakis et al. 2014), by means of a tool developed for the

storage and management of fragility curves. In order to accomplish this harmonisation,

the same intensity measure types, the same number of limit states and the same

building typology are needed.

Bearing in mind the exposed and for the sake of simplicity, the literature review herein

presented include the most relevant methodologies and respective fragility curves

developed within the European context, with particular focus to those developed for the

Mediterranean bordering countries. As already mentioned, these methodologies can be

grouped in four main approaches: analytical; empirical; expert judgment elicitation, and

hybrid approaches. In the following sections a very brief overview of each one of these

approaches is given, as the focus of this report are the analytical approaches, which will

be further detailed in the next Chapter 3.

2.1. Analytical approaches

Analytical approaches are commonly used for the construction of fragility curves due to

the way they address the problem of seismic vulnerability in structural engineering

terms, defining a direct relationship between construction characteristics, structural

response to the seismic action and damage effects (Rossetto et al. 2013). Within this

approach, most of the methodologies available in literature rest on two main and distinct

procedures: the correlation between acceleration or displacement capacity curves and

spectral response curves, as the well-known HAZUS or N2 methods (FEMA 2003a; Fajfar

2000), and the correlation between capacity curves and acceleration time histories, as

proposed in Rossetto and Elnashai (2005).

One of the first steps when conducting studies based on analytical approaches is the

definition of the sample or population of buildings that a given fragility curve will

represent. In this sense, the GEM Foundation has proposed a new building taxonomy

(Brzev et al. 2013) that includes information not only concerning the material and the

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lateral load-resisting system itself, but also roof and floor systems, height, date of

construction, structural irregularity and occupancy class. This initiative is seen as a first

step towards the standardisation and harmonisation of building typologies that will

facilitate the comparison of fragility curves derived with different methodologies or to

different regions across the globe.

According to the scheme presented in Figure 1, the procedure for deriving analytical

fragility curves should follow the following path: defining of index buildings; defining of

components for response analysis and loss or repair cost estimation; selecting of the

model type; defining of the damage states at element and global level and defining the

analysis type and calculation of engineering demand parameters (EDPs) thresholds

between damage states, respectively from (A) to (E). Following this path one will be able

to run analysis and derive fragility curves (F), from which subsequently vulnerability

curves (G) can be generated by means of implementing appropriate damage-to-loss

functions.

Figure 1. Flow diagram for deriving analytical fragility curves.

Even though analytical methodologies involve the use of numerical or mechanical models

to evaluate the structural performance of buildings, allowing to take into account many

characteristics of the building stock in a direct, transparent, and detailed way, and also

to explicitly account for the uncertainties involved in the assessment procedure, they

naturally require a larger amount of detailed input data and a higher computational

effort, when compared with empirical methodologies (Del Gaudio et al. 2015). The most

relevant methodologies concerning the use of analytical methodologies for deriving

fragility curves are described and discussed in Chapter 3.

2.2. Empirical approaches

The seismic vulnerability assessment of buildings at large geographical scales has been

first carried out in the early 70’s, through the employment of empirical methodologies

initially developed and calibrated as a function of macroseismic intensities. This came as

a result of the fact that, at the time, hazard maps were, in their vast majority, defined in

terms of these discrete damage scales (Calvi et al. 2006). Therefore, empirical

approaches constituted for many years, the only reasonable and possible means of

developing seismic risk analyses at a large scale of assessment, based on the treatment

of post-earthquake damage observation data. The main drawbacks of this approach lies

precisely in the subjectivity on allocating each building to a damage state or in the lack

of accuracy in the determination of the ground motion affecting the region. Furthermore,

there are only a few dozen regions in the world where post-earthquake damage and

repair cost data has been collected from a number of buildings large enough to allow the

development of reliable fragility curves. The interdependency between macroseismic

intensity and damage and the limited or not homogeneous empirical data are commonly

identified as the main difficulties to overcome on the calibration process of empirical

approaches (Del Gaudio et al. 2015).

From the above, one can easily understand the need for treating uncertainty also when

dealing with this type of approaches. On one hand, aleatory uncertainty is introduced by

the characteristics of earthquakes and the resulting ground shaking and by the variation

7

of the seismic response of the buildings of a given typology. On the other hand,

epistemic uncertainty is introduced not only by small databases of often poor quality,

typically associated with errors introduced by missing data, biased sampling techniques,

misclassification errors or even data aggregated over large areas, but also by the

inability to account for the complete characteristics of the ground shaking in the

selection of measures of the ground motion intensity (Rossetto et al. 2013) as well as

the measurement error in the intensity measure levels at the required locations

(Rossetto et al. 2014).

The results of empirical methodologies are usually given in two different types: damage-

motion relationships such as damage probability matrices (DPM), and fragility curves.

While in the first type the conditional probability of obtaining a damage level due to a

ground motion of a given intensity is expressed in a discrete form, in the second

category, the probability of exceeding a given damage state is expressed as a

continuous function of the earthquake intensity.

2.3. Expert judgment elicitation approaches

Resorting to expert judgment becomes often inevitable in regions where there are no

empirical data or where the assets are difficult to model. Several authors contributed to

the establishment of a systematic approach to eliciting expert opinion (Winkler et al.

1992; von Winterfeld 1989). Cooke and Goossens (2000), for instance, provided formal

protocols, comprehensive procedures and guidelines on the elicitation process and

handling of such data in uncertainty analysis (Ouchi 2004). A common feature inherent

to expert judgment elicitation-based methodologies is the selection of a panel of experts,

which are recruited and trained for each particular study (Jaiswal et al. 2012). These

methodologies can differ significantly one from another on the collection of the expert

elicitation data process and its combination, but in general terms, those adopted in the

fragility literature, can be grouped into two main categories: mathematical and

behavioural methodologies (Clemen and Winkler 1999). In general, mathematical

methodologies to expert judgment elicitation are regarded to be more reliable,

reproducible and fair in aggregating expert opinions than behavioural methodologies

(Cooke 1991; Clemen and Winkler 1999; Jaiswal et al. 2012; Rossetto et al. 2014).

In mathematical methodologies, experts provide their estimate of an uncertain quantity

as a subjective probability without interacting among each other. Thus, after the

elicitation the estimates of the unknown quantity provided by each expert are combined

mathematically, typically using either a technique for weighting each expert’s estimates,

as in the case of Cooke (1991), or through the use of Bayesian statistics, as in the case

of Morris (1997). Such methodologies have been adopted in various financial and

environmental risk assessment exercises, for example in the estimation of volcanic risk

(Aspinall and Cooke 1998) or in seismic hazard estimation (Klügel 2011). Within the

fragility literature, Cooke’s classical method (Cooke 1991) was used by Jaiswal et al.

(2012) for the construction of fragility curves for the collapse limit state of reinforced

concrete (RC) and unreinforced masonry (URM) buildings, expressed as a function of

peak ground acceleration (PGA). In Cooke’s method, implemented in the free software

EXCALIBUR (Cooke 2001), each expert’s estimates of the unknown quantities of interest

are weighted according to their performance in answering a set of seed questions

considered relevant to the topic of interest, which are unambiguously worded and have a

unique and known numerical answer value. The responses from all experts are adopted

and the weightings of each expert are not revealed to participants in the process.

Behavioural methodologies, in turn, aim at producing some type of group consensus

among experts, who are typically encouraged to interact with one another and share

their assessments. One of the most well known behavioural methodologies is the Delphi

technique, which started to be developed in the early 1950s by Dalkey (1969). In this

method, experts are asked to anonymously judge the assessments made by other

8

experts within a panel. Each of the experts is then given a chance to reassess their

initial judgment based on the others’ review (Ouchi 2004). The process is the repeated

until a degree of agreement or consensus is reached between the expert estimates.

Later on, this method incorporated a self-rating mechanism, allowing experts to rate

their own expertise (Cooke 1991; Parenté and Anderson-Parenté 1987; Sackman 1975).

One of the best examples where a behavioural method has been used in building fragility

analysis is the ATC-13 (1985), in which a modified-Delphi method is applied to construct

Damage Probability Matrices expressing the likelihood of particular damage factors

(ratios of repair and replacement costs) being achieved over a range of Modified-Mercalli

Intensity (MMI) values, for 78 different building types in California (Jaiswal et al. 2012).

The main difference is that experts were asked to rate their experience and level of

confidence in their estimates, which were then used to weight their answers in the

combination of estimates of the value of interest by different experts (Jaiswal et al.

2012). The Nominal Group method is another well-known behavioural method, in which

experts are allowed to discuss their estimates directly with one another in a controlled

environment (Delbecq et al. 1975). According to Gustafson et al. (1973), this method is

considered more favourably than other group methodologies, particularly the Delphi

method.

Even though a group consensus method may help to identify experts’ errors and

misunderstandings during the elicitation process, there are no formal rules to apply in

order to reconcile differences when the consensus is difficult to achieve among different

experts (Ouchi 2004). Despite the literature on group consensus (Zahedi 1986;

Goicoechea et al. 1982; Eliashberg and Winkler 1981), the conformity induced by the

group interaction is still addressed as a major concern and motive of debate amid

researchers on the reliability of behavioural methodologies.

Mosleh et al. (1988) stressed out that the group interactive process could suffer, for

example, from the tendency for less confident experts to limit their participation, the

influence of dominant personalities and the tendency to reach speedy conclusions.

Likewise, Genest and Zidek (1986) pointed out that if unrestricted dialogue is allowed,

there might be room for strategic manipulation, bluffing, intimidating tactics and threats.

Cooke (1991), for example, has observed that more extreme probability estimates seem

to result from using the Delphi method, while Scheibe et al. (1975) pointed out that the

fact experts can see the responses of others may have a significant influence in swaying

expert’s initial judgments towards conformity to the majority of answers. Moreover,

authors such as Plous (1993) and Sniezek (1992), discussed issues related to group

polarization within this type of approach. It is generally agreed that mathematical

approaches yield more accurate results than do behavioural approaches in aggregating

expert opinions (Clemen and Winkler 1999; Mosleh et al. 1988).

2.4. Hybrid approaches

In addition to the main three above-mentioned approaches used to define fragility

curves for existing buildings, there is a forth type of approach, commonly designated as

hybrid, that combines different sources of data either analytical, empirical, or expert

judgment-based data. Hybrid damage probability matrices and fragility curves combine

usually post-earthquake damage statistics (empirical data) with simulated, analytical

damage statistics from a mathematical model of the building typology under

consideration (analytical data) (Calvi et al. 2006). Although they are actually rather

sparse, hybrid approaches can be particularly interesting either when there is a lack of

damage data at certain intensity levels for the geographical area under consideration or

when the calibration of analytical models needs to be carried out. Moreover, the use of

observational data reduces the computational effort that would be required to produce a

complete set of analytical fragility curves or DPMs (Calvi et al. 2006). One of the first

hybrid methodologies was proposed by Kappos et al. (1998), in which the damage data

9

used for the generation of the fragility curves was derived from a combination of

analytical simulations and post-earthquake surveys. In this work, nonlinear dynamic and

static analyses for all of the existing RC building typologies in Greece have been carried

out in order to extrapolate statistical data to PGA and/or spectral displacement values for

the cases in which no datasets were available, evidencing the potential of such type of

approaches (Kappos et al. 1998).

A hybrid method combining analytical, empirical and expert judgment-based data, was

used by the EERI-WHE study group in support of the PAGER project (Jaiswal and Wald

2010). This method aimed at defining the proportion of collapses for a given building

type given a shaking intensity expressed in the EMS-98 Intensity scale (Grünthal 1998)

for several nations worldwide where voluntary experts could be contacted. This exercise

highlighted the difficulty not only in correlating the expected percentage of damaged

buildings to a specific intensity scale, with which not all experts were familiar with, but

also in the definition of collapse. Given the large standard deviation of some of the

results obtained, Bayesian updating by means of empirical single event reported data

was used to improve experts’ forecast, as reported in D’Ayala et al. (2010) and Jaiswal

et al. (2011). Several improvements to this method were proposed by these authors,

such as the incorporation of uncertainty in the shaking intensity at which collapse

probability estimates are assigned, the improvement of the elicitation process, the

quantification of uncertainties associated with experts, the careful consideration of

variability in construction practices and building codes adopted worldwide when

comparing expert judgments for the same building types (Rossetto et al. 2014).

10

11

3. Review of analytical fragility assessment methodologies

This Chapter deals with the most relevant features concerning the construction of

fragility curves exclusively derived from analytical methodologies. Moreover, a

comprehensive review of some of the most well-known analytical fragility assessment

methodologies suitable to the European building stock is carried out aiming to contribute

to a better understanding of such methodologies, highlighting and commenting on their

main aspects, as for indicating the advantages and drawbacks of different methodologies

to support further decision making processes. Naturally, the following review has not

included all the existing procedures in literature since some of them are not applicable or

suitable to the European context, as for example (Erberik and Elnashai 2004; Jiang et al.

2012; Liel et al. 2009). However, the most important and widely used methodologies are

herein addressed.

Recent developments and technological improvements noted in the field of seismic

hazard assessment, such as the derivation of seismic hazard maps in terms of spectral

ordinates as opposed to macroseismic intensity or PGA, are seen as one of the main

reasons for which analytical methodologies have only been recently proposed for use in

risk and loss assessment (Calvi et al. 2006). Moreover, the use of such detailed and

transparent loss models allows detailed sensitivity studies to be undertaken, to which a

valuable insight on how much the loss results depend on the models, data, uncertainties

and assumptions employed can be given. Nevertheless, there is a general agreement

among the research community on the need to ensure an adequate balance between the

benefits of using analytical methodologies and the increased amount resources required

to construct an earthquake loss model based on such analyses. The capability of

numerical models to accurately predict the response of real structures, the accuracy in

transforming numerical indices of damage into actual damage of real structures, the

capability of accounting for human errors in the design and construction of buildings,

which are often the main causes of catastrophic collapses and the need to extend the

results obtained for few reference models to a large class of structures are some of the

issues stressed out by Calvi et al. (2006) that still need to be overcome.

Figure 2 illustrates the distribution of all the existing analytical methodologies considered

in this report, from where it is clear that these methodologies are distributed across the

Mediterranean Sea, the most seismic prone region in Europe. The number of

methodologies carried out in Italy and Turkey clearly stand out with respect to the

remaining countries, representing slightly more than 60% of the total number of

methodologies reviewed in this report. This fact can be explained by the significant

losses suffered by these two countries in the last decades from seismic events such as

the April 6, 2009 L’Aquila and the May 20, 2012 Emilia-Romagna earthquake in Italy, or

the August 17, 1999 Izmit and the October 23, 2011 Van earthquakes in Turkey. These

events with magnitudes, Mw, ranging from 5.8 up to 7.6, caused extended damage to

the building stock, triggering the opportunity for using empirical data for validating and

calibrating analytical methodologies.

According to D’Ayala and Meslem (2013), analytical fragility assessment methodologies

are commonly based on two main components, namely the structural response-to-

damage state functions, which are the product of two independent procedures, structural

and damage analysis, and to which a certain level and type of uncertainty should be

expected and accounted for by users when performing seismic risk assessments, and the

ground motion intensity-to-structural response functions. Consequently, the level of

uncertainty depends upon the simplifications and assumptions considered to lower

resource consumption to convenient levels, particularly in what regards data collection

and computational efforts. It is common in risk analysis and engineering safety problems

to distinguish between uncertainty that reflects the inherent natural variability of the

outcome of a repeatable experiment (aleatory uncertainty) and modelling and statistical

uncertainty due to limited or imperfect knowledge (epistemic uncertainty).

12

Figure 2. Distribution of the examined analytical fragility assessment methodologies by country:

Italy (12); Turkey (11); Greece (8); Portugal (3); Romania (2); Switzerland (2); Former Yugoslav Republic of Macedonia (1); Slovenia (1) and Spain (1).

It is likely that epistemic uncertainties will be reduced as the understanding of the

variables increases, as for example, through the collection and analysis of additional

data and the development of improved predictive models (Faber and Stewart 2003).

Modelling uncertainty arises from the fact that every model, conceptual or mathematical,

is unavoidably a simplified representation of the reality and thus derives from the lack of

knowledge on the geometrical and mechanical characteristics of the structure and/or by

the limitations of the model to correlate these characteristics and to perform structural

analyses. Statistical uncertainty is related to the statistical evaluation of results of tests

or observations. It may result from a limited number of observations or data, neglecting

systematic variations of the observed variables or possible correlations between these

variables.

Generally, most of the available methodologies to develop analytical fragility curves

include the following steps concerning uncertainty assessment: identification of sources

of uncertainty on capacity, demand and damage thresholds definition; quantification of

those uncertainties and their modelling when constructing fragility curves. With respect

to the structural analysis phase, uncertainties related to capacity and demand modelling

are typically accounted for in the estimation of the building performance, as shown in

Figure 3.

Uncertainty in capacity is directly affected by the parameters related not only to the

building’s structural characteristics, which include the mechanical properties, structural

details, geometric configuration and dimensions, but also to the mathematical model

used to compute the building’s structural capacity, which in turn depends on the

detailing level and completeness of the numerical model, and on the performance criteria

considered. Uncertainty in demand is introduced by the quality of the ground motion

(seismic demand) representation through real ground motion records or code-based

spectra that need to capture the record-to-record variability, i.e. the variability of the

seismic source mechanism, attenuation and site effects on the seismic event (FEMA

2003b; NIBS-FEMA 2003; ATC 2011).

The damage thresholds modelling, included in the damage analysis phase, is affected by

the definition of the different global limit states, the choice of the damage model and its

consistency with the type of analysis, the damage indicator used to represent the

damage states of a structure and the correlation with the chosen intensity measure

13

(FEMA 2003a; NIBS-FEMA 2003). It is perhaps one of the most challenging sources of

uncertainty to be overcome, as there is a lack of clear guidance in literature concerning

this topic, beyond some qualitative description of observed damage (D’Ayala and Meslem

2013).

For the time being, the existing expressions for the calculation of demands and

capacities are mostly defined at the element rather than at the global level. Several

definitions have been implemented in guidelines and codes for the estimation of the

global damage states through the observation of the progression of local damage at

elements. According to Eurocode 8 (CEN 2004), two limit states are defined in relation to

the fundamental performance requirements and compliance criteria for structures within

seismic regions:

Ultimate limit states (ULS), associated with collapse or with other forms of

structural failure which might endanger the safety of people;

Damage limitation states (DLS), associated with damage beyond which specified

service requirements are no longer met.

The fragility analysis phase includes the choice of the fitting and sampling methods, the

selection of models to express the fragility curves and the construction process itself,

taking into account the uncertainties considered and measured in the previous structural

and damage analysis phases (FEMA 2003a; Wen et al. 2004; Pagnini et al. 2011; ATC

2011).

Figure 3. Main components and phases considered in analytical fragility assessment methodologies and associated uncertainties.

14

3.1. Structural system

Structural walls, which can be taken as vertical planar elements that resist not only to

gravity loads but also to horizontal forces, provide stability to a building during an

earthquake. They may be monolithic as in the case of reinforced concrete walls, or be

diversified as in the case of masonry walls. The majority of the studies found in literature

that considered this structural system are related to the assessment of masonry structures,

as the example illustrated in Figure 4 (left) of a masonry structural wall system and (right)

the corresponding three-dimensional assemblage of all the structural walls, modelled

through a macro-element approach using the 3Muri® software (STADATA 2011), widely

used for performing nonlinear static (pushover) analysis of masonry structures. Relevant

studies were carried out by Barbat et al. (2006), Erberik (2008), Borzi et al. (2008c), who

adapted the SP-BELA (Simplified Pushover-Based Earthquake Loss Assessment) method to

masonry buildings, once it was originally developed for the determination of the seismic

vulnerability of RC buildings, and Ceran (2010), for example.

Figure 4. Example of a masonry structural wall system (left) and the corresponding three-dimensional assemblage of all the structural walls (right), modelled through a macro-element approach using the

3Muri® software (Ferreira et al. 2015).

With respect to reinforced concrete structures, moment-resisting frames, infilled frames and

dual frame-wall systems are the most recurrent structural systems considered in fragility

assessment studies. Moment-resisting frame systems, as shown in Figure 5 (left), are

widely used to resist lateral loads through axial forces, shears, and moments in their beams,

columns and rigid beam-to-column connections. Their strength and ductility arise from the

combination of concrete and reinforcing steel that resist compressive and tensile forces

respectively. However, as pointed out by Barbat et al. (2006), in some particular cases as in

the city of Barcelona, Spain, most of the reinforced concrete buildings are not moment-

resisting frames but typically column and slab buildings in their waffled slab floor version,

which typology is highly not recommended for seismic prone areas due to their low ductility.

The majority of the methodologies herein analysed were developed for moment-resisting

frame buildings not only because they cover a large fraction of the European reinforced

concrete building stock, but also because the numerical representation of this particular

typology results in general more reliable due to its inherent simplicity when compared to

both infilled and dual frame-wall systems.

Reinforced concrete infilled frame systems can be defined as a framework of beams and

columns in which some bays of frames are infilled with masonry walls that may or may not

be mechanically connected to the frame. Due to the great in-plane stiffness and strength,

infill walls do not allow beams and columns to bend under horizontal loading, changing the

structural performance of the frame. Thus, due to horizontal earthquake-induced actions,

diagonal compression struts are formed in infills so that the structure behaves as a braced

15

frame rather than a moment frame. Moreover, infill walls can fill partially or completely the

height and or length of a bay. Soft-storey collapse mechanisms are introduced when infill

walls are discontinued at a determined storey. It has been experimentally documented that

the presence of infill walls significantly increases the strength, stiffness and seismic energy

dissipation capacity of buildings (Kappos et al. 2003; Tsionis et al. 2014). Relevant

methodologies concerning this particular issue were included in this review, namely those

developed by Kappos et al. (2003), Akkar et al. (2005), Kappos et al. (2006) and Del

Gaudio et al. (2015). Further comments concerning its influence and its consideration in

structural modelling will be addressed in the following section.

In reinforced concrete dual frame-wall systems, the lateral load-resisting structure

comprises both moment-frames and shear walls that act together in the same direction.

These walls are usually not perforated by openings and can be found around the staircases,

as demonstrated in Figure 5 (right), elevator shafts and at the perimeter of the building.

When wisely designed, the presence of such walls may have a positive effect not only on the

seismic performance of the frame structure but also on preventing soft-storey collapse

mechanisms. However, the slenderness of walls in dual frame-wall systems should be

carefully considered. Depending on the share of shear resistance at the base of the walls

and frames, Eurocode 8 (CEN 2004) defines three systems – frame-equivalent dual, wall-

equivalent dual and wall – and particular design rules for each of them. It is worth referring

that the studies by Dumova-Jovanoska (2000), Kappos et al. (2006), Kappos and

Panagopoulos (2009) and Bilgin (2013) were carried out to understand the differences in

terms of seismic fragility between moment-resisting frames, infilled frames and dual frame-

wall systems.

Figure 5. Examples of reinforced concrete moment-resisting frame (left) and dual frame-wall structural systems (right) (Dumova-Jovanoska 2000).

3.2. Components for response analysis

As becomes clear from the previous section, two groups of components can be considered in

analytical fragility and vulnerability assessment methodologies: structural and non-

structural components. Structural components are the main elements that directly

16

contribute to the seismic response of the structure and therefore are considered in both

mathematical and loss estimation models. Moreover, the linear and nonlinear behaviour of

structural components must be defined and explicitly simulated in the analysis to be

undertaken. Even though horizontal components such as roofs and floors systems have a

structural role, they are hardly explicitly modelled for the sake of modelling simplification,

being their effect usually simulated by introducing specific constraint conditions or

assumptions. Non-structural components may contribute to the response behaviour of the

structure, as in the case of masonry infill walls in RC buildings, or be considered only in loss

estimation modelling, in case they represent a significant weight over the building

construction cost (D’Ayala et al. 2014; Dolšek and Fajfar 2008).

Masonry infill walls are made of masonry bricks or blocks, varying in specific weight,

strength and brittleness, depending on age and quality of construction, and are numerically

represented by means of an equivalent diagonal strut model, as demonstrated in the

following Figure 6.

Figure 6. Numerical representation of infill masonry walls through equivalent diagonal strut model (Amato et al. 2008).

Non-structural components are only taken into account for the case of fragility assessment

of RC buildings, as clearly demonstrated in the above-mentioned studies of Kappos et al.

(2003), Akkar et al. (2005), Kappos et al. (2006) and Del Gaudio et al. (2015). Although

the consideration of the contribution of masonry infill walls in the analysis model has been

highly recommended due to its significant influence on the lateral resistance of a reinforced

concrete frame, as experimentally pointed out for example in Fiorato et al. (1970), Klingner

and Bertero (1976), Bertero and Broken (1983) and Mehrabi et al. (1994), still few studies

actually account for their effect on the seismic response of RC buildings.

A major reason for this tendency is related to the difficulty on determining the type of

interaction between the infill and the frame. D’Ayala and Meslem (2013) have pointed out

that the exclusion of infills’ contribution may lead to significant bias in resulting fragility

curves. Moreover, as stressed out in Figure 7, when masonry infilled RC buildings are

modelled as moment-resisting (or bare) frame structures, fragility curves tend to achieve

greater lateral displacement capacity for all damage levels, whereas, for the case when the

infilled frame model is considered, the building is found to be more vulnerable.

17

Figure 7. Comparison between fragility curves for 4-storey RC buildings, with and without considering the modelling of masonry infill walls (D’Ayala and Meslem 2012).

3.3. The selection of the analysis type

There are different options available for the choice of mathematical modelling and type of

analysis for structural assessment. As mentioned previously, uncertainties related to these

models are directly reliant on the level of complexity desired to conduct the fragility

assessment. In view of the above, analysis can be grouped, in decreasing order of

complexity, as follows:

Nonlinear Dynamic (NLD) analysis, which requires a set of ground motion records to

perform dynamic response history analysis of a mathematical model;

Nonlinear Static (NLS) analysis based on the use of a (first-mode or other) load

pattern to perform a pushover analysis of a structure, and then fit the resulting

capacity curve with an appropriate back-bone curve response model, e.g. elastic-

plastic, elastic-plastic with residual strength, quadrilinear, etc;

Nonlinear Static analysis based on Simplified Mechanical Models (SMM-NLS), in which

the capacity curve is obtained through simplified analytical methodologies that do

not require finite element modelling;

Linear Static (LS) analysis, which can be a modal response spectrum analysis or one

using the lateral force method.

The level of detailed modelling of each structural component will depend on the choice of

analysis type selected. For all types of analysis, D’Ayala et al. (2014) suggest that the user

should use median values of structural characteristics-related parameters when defining the

component behaviour. When median values are not available, mean values should be used.

The user should make sure to simulate all possible modes of component damage and failure

(axial, flexural, flexure-axial interaction, shear, and flexure-shear interaction), or P-Delta

effects, for example. Relevance guidance may be found in design standards, such as the

Eurocode 8 (CEN 2004).

3.3.1. Nonlinear Dynamic Analysis

From the methodologies considered in this report it was possible to identify different

approaches to perform nonlinear dynamic analysis for the structural assessment of

buildings: conventional approaches; incremental dynamic analyses (IDA), and hybrid

18

approaches. Some authors, as for example Akansel et al. (2012), Hancilar and Çaktr (2015)

or Özer and Erberik (2008), carried out a conventional approach by performing nonlinear

time-history (dynamic) analyses of RC structures, using software such as ANSYS® (ANSYS

2005), IDARC-2D® (IDARC-2D 1996) or OpenSEES® (2015). In these studies, the seismic

demand was obtained for different sets of ground motion, the capacity was determined in

terms of limit states and the corresponding fragility curves were obtained by assessing the

probability of reaching or exceeding each limit state for different levels of ground shaking

intensity. However, in Dumova-Jovanoska (2000), damage curves were derived by means

of a damage index, which was then plotted versus the Modified Mercalli Intensity.

Incremental Dynamic Analysis (IDA) is often perceived as the dynamic equivalent to a

pushover analysis, and has been recommended in ATC-63 (FEMA 2008) and ATC-58 (FEMA

2012) technical reports. Even though the IDA approach can be implemented to any building

typology to estimate different median capacities, it entails the definition of a complete

hysteretic behaviour of the materials and the repetition of the analysis for a large number of

acceleration time histories, to which a significant time consuming computation process

might be associated, depending on the level of complexity and material type considered.

Moreover, it is fundamental to ensure that the model is consistent with the type of analysis

to be carried out and that sufficient model complexity is retained. To this end, it is

necessary to define hysteretic curves for structural and possibly also for non-structural

elements, to use median values for structural characteristics-related parameters, to

simulate all possible modes of component damage and failure, and to define permanent

gravity actions (D’Ayala et al. 2014). Regarding the minimum number of ground motions

that should be used to provide stable estimates of the median capacity, it has been reported

that the use of 11 pairs of motions (i.e. 22 motion set, including two orthogonal

components of motion), should be sufficient for the purpose of this procedure (D’Ayala et al.

2014). According to this method, nonlinear response history analysis is performed for

increasing intensity of the ground motion, until either global dynamic or numerical instability

occurs in the analysis. The main output of IDA analyses is a curve that plots maximum

storey drift at any level of building or other EPD, versus spectral acceleration, Sa(T), or

other intensity measure, as demonstrated in the example of Figure 8. The collapse capacity

point of IDA curves is defined by the point from which the curve starts to become constant

over the intensity measure values.

Figure 8. IDA curve with the identification of yielding and collapse points (Kirçil and Polat 2006).

From the reviewed literature there are only a few authors that have conducted IDA, namely

Kirçil and Polat (2006) and Pitilakis et al. (2014b). In the first, IDA analyses were performed

to determine the yielding and collapse capacity of the sample buildings in terms of elastic

pseudo-spectral acceleration, under the effect of twelve artificial ground motions. Fragility

curves were then derived to express the probability of structural damage due to

19

earthquakes as a function of ground motion intensity, expressed in terms of 5% damped

pseudo elastic spectral acceleration (Sa) and assuming that the fragility curves can be

expressed in the form of two-parameter lognormal distribution functions (Kirçil and Polat

2006). Based on this assumption, the cumulative probability of occurrence of the damage,

equal or higher than damage level Di, was defined as:

(Eq.1)

where Φ is the standard normal distribution, X is the lognormal distributed pseudo elastic

spectral acceleration, λ and ζ are the mean and standard deviation of ln X. Here lognormal

probability paper was used for obtaining mean and standard deviation of ground motion

indices for each damage level. Lognormal probability paper was used for obtaining mean

and standard deviation of ground motion indices for each damage level. This method is

based on plotting ln X versus the corresponding standard normal variable on a lognormal

scale and performing a linear regression analysis to determine the mean and standard

deviation of ln X for each damage level Di (Gündüz 1996).

In Pitilakis et al. (2014b) in turn, two-dimensional incremental dynamic analyses were

performed to assess the seismic performance of the uncorroded and corroded RC moment-

resisting frame structures, designed which different seismic codes. The time-dependent

fragility curves were then derived in terms of the spectral acceleration at the fundamental

mode of the structure and the outcropping peak ground acceleration for the immediate

occupancy and collapse prevention limit states.

Finally, hybrid approaches within NLD analysis are often used, in which different types of

analyses are combined. Rota et al. (2010) used nonlinear static (pushover) analyses to

define the probability distributions of each damage state and nonlinear dynamic analyses to

determine the probability density function of the displacement demand corresponding to

different levels of ground motion. Casotto et al. (2015) took advantage of pushover analysis

to establish a number of damage limit states and then performed nonlinear dynamic

analysis to compare the maximum demand with the limit state capacity to allocate the

structure in a damage state.

Silva et al. (2013) stressed out that the technique by which the actual dynamic

phenomenon is reproduced when employing nonlinear dynamic analysis, i.e., applying an

acceleration time history at the base of the structure, leads in theory to more accurate

results, being hence one of the main advantages of this type of approaches for deriving

fragility curves. However, the intrinsic modelling complexity (e.g. hysteretic response

models, equivalent viscous damping) combined with the heavy computational effort, is often

impractical, thus favouring the employment of simpler methodologies, comprising nonlinear

static analysis.

3.3.2. Nonlinear Static Analysis

Nonlinear Static Analysis (NLS), or simply pushover analysis, has become a very popular

analysis tool for the seismic performance evaluation of both existing and new structures

under permanent vertical loads and gradually increasing lateral loads, with the latter

representing approximately the earthquake-induced forces. The capacity curve is the output

from NLS analysis and it represents a plot of the total base shear versus top displacement,

which is then fitted to a bilinear (elastic-plastic), as illustrated in Figure 9 (left), or multi-

linear (e.g. elastic-plastic with residual strength) curve. Moreover, as this analysis is carried

out up to failure, it enables the determination of collapse load and ductility capacity. The

20

derivation of a capacity curve by use of nonlinear static (pushover) analysis, does not

directly account for the specific seismic motion causing the collapse, as the dynamic

characteristics are not taken into account in the analysis. Moreover, the consideration of

higher mode effects once a local mechanism is formed and issues related to cumulative

damage have been pointed out as some of the main drawbacks of NLS analysis. In this

sense, a new extension to the previously mentioned conventional pushover analysis has

been proposed in recent years, the so-called Static Adaptive Pushover Analysis (Antoniou

and Pinho 2004; Papanikolaou et al. 2005). The main difference is that when performing a

SAPA, the lateral load distribution is not kept constant but it is rather continuously updated

during the analysis, according to the modal shapes and participation factors derived by

eigenvalue analysis carried out at each analysis step. Figure 9 (right) illustrates a set of

capacity curves derived for the randomly generated RC frames by adopting a displacement-

based adaptive pushover (Silva et al. 2013).

Figure 9. Example of (bilinear) capacity curves derived from conventional pushover analysis (left) and

those obtained from using a displacement-based adaptive pushover (right), developed by Ferreira et al. (2015) and Silva et al. (2013), respectively.

Due to its ability to update the lateral load patterns according to the constantly changing

modal properties of the system, SAPA overcomes the intrinsic weaknesses of fixed-pattern

pushover analysis and provides a more accurate performance-oriented tool for structural

assessment, providing better response estimates than existing conventional approaches,

especially in the presence of significant strength or stiffness irregularities (Papanikolaou et

al. 2005). It is worth to recall that SAPA approach has been used in nonlinear studies

carried out both in masonry buildings, as in Lourenço et al. (2011) and in RC buildings, as in

Chaulagain et al. (2013). Furthermore, Abbasnia et al. (2013) has pointed out that SAPA

analyses can capture the results of IDA analysis with a reasonable accuracy. However, the

excessive force concentration at the locations of the structure where the damage first

develops, the combination of the modal contributions, the updating procedure of the lateral

load vector and the computation time were identified as major drawbacks of this approach

(D’Ayala et al. 2014).

3.3.3. Simplified Mechanism Models

A number of simplified analysis methodologies to derive fragility curves exist in the

literature. These methodologies are based on assumptions that allow the derivation of

vulnerability or fragility curves without running a full non-linear analysis. Although these

methodologies might have the advantage of allowing analysis of large populations of

21

buildings with relatively little calculation burden, the reliability of the results is highly

dependent on the expertise of the operator in choosing the underlying simplifications and

assumptions. Such methodologies are more common in the assessment of masonry

structures and can be subdivided in methodologies that yield fragility curves based on

lateral capacity and those based on displacement.

Collapse mechanism-based methodologies such as the VULNUS (Bernardini et al. 1990), or

FaMIVE (D’Ayala and Speranza, 2003) are procedures based on collapse-load factors or

collapse multipliers associated to different modes of collapse, intentionally developed for

assessing the fragility of masonry structures. The method proposed by Cosenza et al.

(2005) uses a similar approach for the assessment of reinforced concrete buildings. In

VULNUS and FaMIVE the aleatory variation associated with geometry and materials is

accounted for by applying the procedure to a large number of buildings at a particular

geographical location. Epistemic uncertainty related to the various parameters that enter

the calculation is accounted for by applying to each parameter a confidence range variable

between 0.10 and 0.30, while in VULNUS fuzzy membership classes are defined.

Simplified displacement-based methodologies use an idealised single degree of freedom

nonlinear oscillator to derive a bilinear capacity curve that accounts for the post-peak

behaviour of the structure. An application for RC structures was proposed by Pinho et al.

(2002) and improved by Crowley et al. (2004), giving rise to the DBELA method. A similar

application was developed for URM, the so-called SPBELA method (Borzi et al. 2007; Borzi

et al. 2008c). Both methodologies define the damage state limit thresholds of structures at

the level of the equivalent single element. Subsequently, an idealised bilinear capacity curve

to intersect then with a response spectrum is defined in order to define representative

performance points and ultimately derive fragility curves. A different approach is used by

D’Ayala (2005) to extend the applicability of the mechanism approach in FaMIVE within a

displacement-based assessment framework. A different capacity curve is associated to each

failure mechanism, parameterised in terms of total drift and ductility to define fragility

curves. The quality and reliability of these procedures is dependent on the validation of the

idealised capacity curves and definition of the associated limit states by experimental or

empirical evidence.

3.3.3.1. FaMIVE method

The FaMIVE (Failure Mechanism Identification and Vulnerability Evaluation) method,

estimates the building performance both in terms of base shear and deformation capacity

and identifies the most suitable strengthening and repair intervention by considering the

possible collapse mechanisms which can occur given geometry, materials, loading conditions

and constraints such as ring beams or tie-rods (D’Ayala and Speranza 2003). Both in-plane

and out-of-plane failure mechanisms are considered, being the latter illustrated in Figure

10. Using the concepts of limit state analysis, this method correlates collapse mechanisms

to specific construction features of the external bearing walls forming a masonry building

(D’Ayala et al. 1997). The analysis quantifies the collapse load factor (as a percentage of

gravity acceleration) associated with each mechanism so as to determine a lower bound of

the level of shaking which will trigger the onset of a specific failure mechanism (D’Ayala et

al. 2005). This method uses a nonlinear pseudo-static structural analysis by means of a

variant of the N2 method (Fajfar and Gašperšič 1996), included in Eurocode part 3 (CEN

2004), in which a degrading pushover curve is used to estimate the performance points, as

it has been described by Dolšek and Fajfar (2004).

The fragility curves for different limit states are then obtained by computing the median and

standard deviation values of the performance point displacements for each index building of

22

a given sample and by deriving the corresponding lognormal distributions (D’Ayala et al.

2014).

Moreover, this method can be applied to medium-size samples of buildings without requiring

a detailed analysis of the geometric, typological and structural parameters that characterize

the analysed buildings. The data that need to be collected focus on the parameters that

directly influence the structural performance of buildings. In this way, the method minimizes

the surveying time and the need for pre-existing information while providing an analytically

based vulnerability assessment (D’Ayala et al. 2005).

Figure 10. Out-of-plane failure mechanisms of the FaMIVE method (D’Ayala and Speranza 2003).

The method has been applied to estimate the performance of buildings in several locations

worldwide such as the Alfama District of Lisbon (D’Ayala et al. 1997), the Marche region in

Italy (D’Ayala and Speranza 2002), the historical center of Vittorio Venetto (Bernardini et al.

2008) and San Giuliano di Puglia (Indirli et al. 2004), Nepal (D’Ayala, 2004), India (D’Ayala

and Kansal, 2004), the Fener–Balat sample in Istanbul (D’Ayala and Yeomans 2004),

L’Aquila following the 2009 earthquake (D’Ayala and Paganoni, 2011), and recently in the

historical centres of Bovec and Ljubliana in Slovenia (Bosiljkov et al. 2012) and in the

Casbah of Algiers (Novelli and D’Ayala, 2014). Thus, within the FaMIVE database built over

the past years, capacity and fragility curves are available for various unreinforced masonry

typologies, from adobe to concrete blocks, for a number of reference typologies and in a

number of regions of the world (D’Ayala and Kishali 2012, D’Ayala 2013).

3.3.3.2. DBELA method

The Displacement-Based method for Earthquake Loss Assessment (DBELA) method is a

simplified nonlinear static analysis method for the seismic risk assessment of buildings, built

upon the urban assessment methodology proposed by Calvi (1999), and employed to

estimate the nonlinear capacity of thousands of RC frames randomly generated and the

corresponding demand from a large set of ground motion records. The fact that several

synthetic buildings and ground motion records are used in the calculations allows the

consideration of the material and geometrical uncertainties, as well as (to some extent) the

record-to-record variability (Silva et al. 2013). The principles of structural mechanics and

seismic response of buildings are used to estimate the seismic vulnerability of different

classes of buildings (D’Ayala et al. 2014), namely RC and URM buildings (Glaister and Pinho

23

2003; Restrepo-Velez and Magenes 2004; Crowley et al. 2004; Borzi et al. 2008a; Borzi et

al. 2008b). The method is further developed to derive fragility curves for building classes

considering their global and local vulnerabilities and their corresponding mechanical models,

defined completely by secant vibration period, viscous damping and limit state displacement

capacities. Each limit state marks the threshold between the levels of damage that a

building might withstand, usually described by a reduction in strength or by the exceedance

of certain displacement or drift levels. Once these parameters are obtained, the

displacement capacity of the first limit state is compared with the respective demand. If the

demand exceeds the capacity, the next limit states need to be checked successively, until

the demand no longer exceeds the capacity and the building damage state can be defined.

If the demand also exceeds the capacity of the last limit state, the building is assumed to

have collapsed. According to Silva et al. (2013), this procedure, which flowchart is

presented in Figure 11, provides a good balance between computational efficiency and

reliability, allowing a quick and simple assessment of the physical vulnerability of many

different building typologies.

Figure 11. Flowchart of the DBELA method (Silva et al. 2013).

3.3.3.3. SP-BELA method

The SP-BELA (Simplified Pushover-Based Earthquake Loss Assessment) method combines

the definition of a pushover curve using a simplified mechanic-based procedure, similar to

that proposed by Cosenza et al. (2005), to define the base shear capacity of the building

stock, with a displacement-based framework similar to that in DBELA, such that the

vulnerability of building classes at different limit states can be obtained. The main

component of the methodology involves the definition of the capacity of a population of

buildings based on a prototype structure, which is carried out using simplified pushover

analysis to obtain the collapse multiplier Borzi et al. (2008b). In Figure 12, the flowchart

behind the SP-BELA method is illustrated.

24

Figure 12. Flowchart of the SP-BELA method (Borzi et al. 2008b).

According to Borzi et al. (2008b), which have conducted a comparison between DBELA and

SP-BELA methodologies, pointed out that given its more simplified nature, DBELA requires

an assumption on the likely failure mode of structures, beam-sway or column-sway, to be

made a priori. Instead, in SP-BELA method such assumption is not required, since the

failure mechanism is computed by the algorithm itself, as discussed in Borzi et al. (2008b).

Moreover, the DBELA methodology requires a combination of the beam-sway and column-

sway curves depending on the proportions of the building stock that are assumed to fall into

either of these two groups. However, such assumptions are not necessary with the SP-BELA

procedure and the proportion of each mechanism is implicitly accounted for in the

generation of the vulnerability curves. It is reassuring to note from observing Figure 13,

that the SP-BELA curve is closer to the DBELA column-sway curve than the beam-sway

curve as the buildings considered herein have not been designed considering capacity

25

design principles and thus the formation of plastic hinges in the columns, as opposed to the

beams, is expected Borzi et al. (2008b).

Figure 13. Vulnerability curves for 4-storey buildings using the SP-BELA and DBELA methodologies for Limit State 2 (left) and Limit State 3 (right) conditions (Borzi et al. 2008b).

3.3.3.4. VULNUS method

The VULNUS method allows estimating the seismic vulnerability of a single building using

the fuzzy-set theory and the definition of collapse multipliers (Bernardini et al. 1989;

Bernardini et al. 1990). Developed by researchers of University of Padua in the second half

of the ‘80s, this method was recently modified according to the Italian Seismic Code and

written in Visual Basic programming language (Munari et al. 2009). The approach is based

on building survey, in order to collect geometrical and structural information, handled

through qualitative judgment (Florio 2010). VULNUS estimates the global vulnerability of

regular (both in plan and in height) masonry structures with a limited number of storeys. It

applies either to single buildings or building aggregates. The major limitation of this method

is the static treatment of the dynamic seismic action.

3.4. The selection of the model type

According to international scientific literature, three types of models are used for fragility

analysis, offering distinct choices of structural detailing. In decreasing order of complexity,

they are:

Multi-Degree-of-Freedom (MDoF) model (two/three-dimensional elements); Reduced MDoF model (two-dimensional elements);

Single-Degree-of-Freedom (SDoF) model.

Even though SDoF models are not the most accurate, the simplification to an equivalent

single-degree-of-freedom system is widely used when computing the performance point and

damage state of a structure in a number of methodologies for the determination of fragility

curves.

The employment of two-dimensional (planar) models for the derivation of fragility curves or

capacity curves has been quite widely employed in literature, for instance, in Erberik and

Elnashai (2004) for a 5-storey RC building, in UTCB (2006) for a 13-storey RC building in

Bucharest, or in Barbat et al. (2006) for a range of RC and URM in Barcelona with two to

26

eight storeys. The aim of using two-dimensional models is to reduce the computational

effort, especially when using nonlinear dynamic analysis. However it should be kept in mind

that the epistemic uncertainty associated with this modelling strategy can be significant,

especially for buildings with irregular geometries or with buildings with non-uniform

distribution of infills. Figure 14 shows the results from a study carried out by D’Ayala and

Meslem (2013) that compared the capacity curves of an RC frame structure with infills

obtained from a three-dimensional model with those obtained by the superposition of two-

dimensional models. It can be observed that there was a quite significant difference

between both procedures. By using two-dimensional models, the displacement

corresponding to first yielding of steel and first crushing of concrete member seems to be

overestimated. In addition, the peak loading capacity is underestimated by using two-

dimensional models. Moreover, despite the discrepancies in the estimated seismic response

of structures when employing different methodologies, as already shown by many authors

(Chopra and Goel 2000, Casarotti et al. 2009, Lin et al. 2004), it was concluded by Silva et

al. (2013) that these relevant differences are not necessarily reflected into the resulting

fragility curves, particularly for lower damage states. This occurs because often the focus is

not on the member level performance (in terms of bending moments or shear forces) of an

individual structure, but rather on the global damage state of the building.

Figure 14. Comparison of capacity curves obtained by the three-dimensional model with those

obtained by superposition of two-dimensional models (D’Ayala and Meslem 2013).

3.4.1. MDoF models

A multi-degree-of-freedom model of a structure is a detailed three-dimensional or two-

dimensional model that includes elements for each identified lateral-load resisting

component in the building, as columns, beams, infills, walls, etc. For the employment of

three-dimensional or two-dimensional element-by-element models, the identification of

building’s components, the definition of the non-structural elements, the determination of

the foundation flexibility, level of diaphragm action, and the definition of permanent gravity

actions (i.e. dead loads and live loads) is necessary. Preferably, the building should be

modelled as three-dimensional, as for instance in Akansel et al. (2012), Pitilakis et al.

(2014b) or Hancilar and Çaktr (2015). However, in some cases, the user may wish to use

two-dimensional (planar) models in order to reduce the calculation effort. This may be

acceptable for buildings with regular geometries where the response in each orthogonal

direction is independent and torsional response is not significant.

27

3.4.2. Reduced MDoF models

A reduced MDoF model, such as a stick model or a single-bay frame one, is a simplified two-

dimensional lumped stiffness-mass-damping representation of a building, in which each of

the N floors is represented by one node having three degrees of freedom, two translational

and one rotational to allow the representation of both flexural and shear types of behaviour

(D’Ayala et al. 2014). This representation is not suitable for irregular buildings or buildings

where torsional effects are anticipated. As appropriate component level modelling requires

advanced structural skills and it is a critical aspect of the vulnerability estimation, when data

is not very accurate or resources are modest, it might be worth to adopt a reduced MDoF

model employing storey-level, rather than component-level, characterization of mass,

stiffness and strength. It should be noted that substantial approximations are made in

adopting these models, in the determination of storey level mass stiffness and strength,

which assume either an average or homogenous behaviour of single components. This may

substantially affect the expected global failure modes. The advantage is that such models

can be analysed within a few seconds using either nonlinear dynamic or static methods. Of

course, such modelling techniques are only appropriate for structures having rigid

diaphragms without appreciable plan irregularities.

One example of reduced MDoF models is given by the study developed by Kappos and

Panagopoulos (2009), in which inelastic static and dynamic time-history analyses were

carried out for RC buildings using the SAP2000N (Computers and Structures Inc. 2002) and

the DRAIN-2000 (Kappos and Dymiotis 2000) codes, respectively. RC members were

modelled using lumped plasticity beam-column elements, while infill walls were modelled

using diagonal equivalent strut elements for the inelastic static analyses and shear panel

isoparametric elements for the inelastic dynamic analyses. Moreover, to make the analysis

process less time-consuming, two-dimensional models of these buildings were analysed, as

exemplified in Figure 15. The fact that two-dimensional models ignore effects such as

torsion due to in-plan irregularity is stressed out as its major drawback.

Figure 15. Configuration and dimensions of typical four-storey irregularly infilled RC frame building (Kappos and Panagopoulos 2009).

3.4.3. SDoF models

A single-degree-of-freedom model is a simple one-dimensional (linear or nonlinear) element

representing the stiffness, mass, damping and ductility of the structure. This representation

is in general simplistic and assumes that higher vibration modes are not relevant to the

seismic response of the structure. Although a poor approximation of the real behaviour of

28

the structure is obtained with this type of model, SDoF equivalent models might be

employed when there are modest resources or the knowledge of the structural

characteristics is so poor that does not warrant the effort of detailed modelling. This

becomes possible by adopting mechanical models that are able to represent the dominant

response characteristics of specific structural typologies, in which the analytical formulation

is derived from the failure mechanisms and behaviour of structures observed during

experiments or real earthquakes. Thus, according to D’Ayala et al. (2014), each such model

should use analytic expressions or simple calculations to accurately simulate at least:

• The capacity curve of the structure;

• The first mode period and associated mass;

• The equivalent stiffness of the system.

There are several methodologies that use equivalent SDoF models for the numerical

representation of low- up to high-rise structures, as for example the above-mentioned

DBELA method. Moreover, the seismic performance-based assessment of typical masonry

buildings carried out either by Maio et al. (2015) or Simões et al. (2015), for example, were

conducted using the 3Muri® software (STADATA 2011), which is based on the nonlinear

macro-element model proposed by Gambarotta and Lagomarsino (1996) and further

modified by Penna (2002). In these studies, the performance point or target displacement

of the structure was computed from the intersection of the capacity curve of the structure

and the response spectrum. The capacity curve was obtained by converting the pushover

curve from the original MDoF model to an equivalent SDoF model, using the N2 Method,

originally proposed by Fajfar (1999) and adopted by both Eurocode 8 (CEN 2004) and the

Italian Seismic Code (NTC 2008). Del Gaudio et al. (2015) have instead applied the

Incremental N2 Method (IN2), which provides the relationship between seismic demand and

seismic intensity. The basic difference between the N2 Method and the original capacity

spectrum method (CSM), proposed by Freeman (1998) and widely implemented in the USA

and Japan, is in the inelastic demand definition. While the inelastic demand in the N2

Method is defined by an inelastic spectrum, in the CSM the inelastic demand is defined by

means of an equivalent highly-damped elastic spectrum.

Nevertheless, as the seismic demand is determined for an equivalent SDoF system, these

procedures are naturally based on a single-mode response with time-invariant displacement

shape, and therefore are all subjected to some limitations A comparison of these methods

showed that the N2 Method gave more accurate results than those provided by the CSM,

when considering the results from nonlinear dynamic analysis as the baseline method (Silva

et al. 2013).

3.5. Shear failure

Reinforced concrete and masonry walls do not reach failure only in flexural modes but they

can also fail in shear modes. If the shear strength of a wall is reached before its flexural

strength, failure occurs very suddenly, with little warning, and the ductility of the wall is

limited. Shear failure in members can occur in RC buildings designed without considering

the effect of horizontal actions, or in buildings with low concrete strength or without

sufficient horizontal reinforcement. Even though this failure mode can induce important

effects on fragility curves, hastening the attainment of higher damage levels, only very few

methodologies treat this issue explicitly.

29

3.6. Out-of-plane response of masonry buildings

The majority of the existing methodologies and software currently available for seismic

assessment of masonry structures usually considers only in-plane failure modes. However,

according to past observations after major earthquakes, the out-of-plane failure of masonry

walls has been stressed out as one of the most dominant modes of failure for unreinforced

masonry buildings (Ceran 2010, Ferreira 2015). The structural deficiencies that lead to this

type of failure are quite a few, from the poor wall-to-floor and wall-to-wall connections due

to insufficient anchorage, the absence of horizontal rigid diaphragms resulting in high wall

slenderness ratio, to poor material quality (Ceran 2010). Hence it is misleading to evaluate

the seismic vulnerability of masonry structures without considering their out-of-plane

behaviour. In addition to this, out-of-plane wall failures impose a significant risk to the

people living in these buildings, since they may be trapped by (parts of) overturned walls

(Ceran 2010).

The reason for which out-of-plane response of unreinforced masonry walls is often

disregarded is that, as stated by Paulay and Priestley (1992), it is one of the most complex

and ill-conditioned problems in seismic analysis of building structures, being this behaviour

governed both by strength and stability (Ceran 2010). Hence, many different approaches

for the analysis of the out-of-plane seismic behaviour of unreinforced masonry structures

have been developed to solve this problem during the last decades. Some of these

approaches were addressed and reviewed by Ferreira (2015), which grouped them in

numerical, experimental and analytical, as demonstrated in Figure 16, in which

experimental works can also be used for the calibration and validation of both numerical and

analytical methodologies.

A different line of investigation resorting to multibody dynamics theory has been recently

proposed by Costa (2012), for the numerical analysis of the out-of-plane dynamic behaviour

of unreinforced masonry buildings, in which portions of masonry walls considered

representative of the out-of-plane local mechanisms activated by seismic loads, are

modelled as kinematic chains (normally assumed as infinitely rigid bodies) whose nonlinear

behaviour is concentrated at the contact regions. According to Ferreira (2015), the main

advantages on the use of multibody dynamics to simulate complex local mechanisms rely on

the time-efficiency and small number of input parameters required. Moreover, a further

disadvantage of this technique is that it requires the definition of a realistic overturning

mechanism in order to create the multibody model, based on expert judgement or some

other type of analysis (Ferreira 2015).

Figure 16. Existing techniques for assessing the out-of-plane behaviour of unreinforced masonry structures (Ferreira 2015).

30

In the previously referred SP-BELA method, for example, the out-of-plane failure

mechanism is defined only considering the boundary conditions of walls supported at the

base and free at the top, and walls supported at both sides with or without axial load (Borzi

et al. 2008c). However, complex out-of-plane failure mechanism such as those described in

Restrepo-Velez and Magenes (2004) were not included as a consequence of the limited

information that is generally available at an urban scale.

In literature most approaches refer to equivalent frame systems to definition of the in-plane

behaviour of walls (Erberick 2008, Lagomarsino et al. 2006, Barbat 2004). Hence, the

resulting fragility curves ignore the possibility of out-of-plane behaviour, which is

particularly important in the case of URM buildings. The studies carried out by Tomaževic et

al. (1991), D’Ayala et al. (1997), Borzi et al. (2008), Karantoni et al. (2014), outlined the

relevance of out-of-plane failure on the overall fragility of masonry structures, as for

instance in the case of buildings with flexible roofs. Recently an increasing number of

authors have started considering simple out-of-plane modelling with limit-state mechanical

approaches. However, the quality of the connections among walls is often overlooked and

the corresponding fragility overestimated (D’Ayala and Meslem 2012).

3.7. Horizontal diaphragms in masonry buildings

The experience gathered from past earthquakes has proved that, among other parameters

that influence the resistance of existing masonry buildings, the effectiveness of the

connections between the horizontal (floors) and vertical (walls) elements together with the

in-plane stiffness of floors greatly affects the seismic response of the structure (Rota et al.

2011). Although generally conceived to carry vertical loads, the horizontal elements play a

significant role not only in the distribution of horizontal inertia forces during an earthquake

onto the walls proportional to their stiffness, but also in the prevention of out-of-plane mechanisms enabling a box-type of behaviour of the structure (Tomaževic et al. 1991). In

case of poor wall-to-floor connection, separation of the elements and overturning of walls

orthogonal to the seismic motion may occur, even at low to moderate intensity of shaking

Senaldi et al. (2014). Therefore, it is important to understand how the variability of stiffness

of different diaphragm typologies influences the global seismic response of the structure and

to account for this variability when developing fragility curves for masonry buildings.

Ceran (2010) has generated fragility curves for assessing the out-of-plane behaviour of

masonry buildings, also considered different sets of curves to account for both the presence

of rigid RC slabs and wooden flexible diaphragms. The meaningful influence of the type of

wall-to floor connection, slenderness ratio of the wall and the strength of masonry wall, over

the damage state probabilities was one of the main conclusions from this work. Moreover,

results have proved that non-engineered masonry buildings with very poor wall-to-floor

connections, in which the walls imitate cantilever-like behaviour, are extremely vulnerable

to even low- to-moderate levels of seismic action. Thus, as the out-of-plane behaviour may

be more critical than the in-plane behaviour, it should be considered when deriving fragility

curves for URM buildings.

3.8. Geometrical irregularities

In-height and in-plan irregularities, both in terms of stiffness and mass are capable to

generate stress distributions significantly different from those expected in regular

structures, which might cause severe damage or even the collapse of the structure.

31

Empirical observations of structures damaged by recent earthquakes have demonstrated

that generally simple and regular structural systems present a better seismic behaviour,

while complex and irregular systems lead to a poor behaviour. In addition, the absence of

masonry infill walls at the ground floor level is a very common practice in RC buildings due

to architectural and commercial purposes. However, this is responsible for triggering soft-

storey collapse mechanisms (e.g. Verderame et al. 2011; De Luca et al. 2014). In the

studies carried out by Erberik (2008), Oropeza et al. (2010) and Polese et al. (2008) in plan

irregularities were taken into account when generating fragility curves for URM buildings.

Rota et al. (2014) in turn, considered both in plan and in height irregularities. These studies

have confirmed the higher fragility of irregular structures, both in plan and in height.

3.9. Seismic demand and site-specific records

The seismic demand for a specific site is usually determined by means of code-based

spectra or real ground motion records. The assessment of the structural response through

dynamic analysis requires seismic input that should reflect the hazard as well as the near-

surface geology at the site. Generally, the signals that can be used for the seismic structural

analysis are of three types: artificial waveforms (compatible with a code response

spectrum); simulated accelerograms (obtained via modelling of the seismological part and

possibly accounting for the path and site effects), and natural records.

Like many codes worldwide, Eurocode 8 (CEN 2004) allows the use of real ground motion

records for the seismic assessment of structures. The main condition to be satisfied by the

chosen set is that the average elastic spectrum does not underestimate the code spectrum,

with a 10% tolerance, in a broad range of periods depending on the structure's dynamic

properties. In particular, Eurocode 8 allows employment of all three types of accelerograms

listed above as an input for seismic structural analysis. If at least seven records are used,

the mean response is considered, while for three to six records, the maximum response

should be considered. Appropriately selected real accelerograms are becoming the most

attractive option to get unbiased estimations of the seismic demand (Iervolino et al. 2008).

When assessing sites where no recorded accelerograms are available, it is common to

consult ground motion databases, such as the European strong-motion database

(www.isesd.hi.is) and the PEER Ground-Motion Database, for accelerograms that best match

the conditions of the site, in terms of magnitude, Mw, rupture distance, rrup, and average

shear-wave velocity between 0 and 30 m, vs,30. These databases provide free access to

thousands of strong-motion records from shallow crustal earthquakes and also easy-to-use

online tools for the selection of records according to criteria related to earthquake scenario,

local site conditions and response spectra. Even though using site-specific ground motions is

always preferable in order to reduce the uncertainty in demand of the analysis, one might

take advantage of collected accelerograms from these databases only when they present

similar characteristics as the assessment site, which is not always observed. Moreover, the

selection of suitable accelerograms requires a certain level of experience on both geological

and seismic hazard context of the specific site under assessment.

3.10. Definition of EDP values at damage thresholds

When detailed numerical models of the building are used, the damage in each structural

element is obtained through static or dynamic nonlinear analysis, in which damage state

attribution could be made as a function, for instance, of the its displacement capacity when

subjected to horizontal excitation (Lagomarsino and Cattari 2014). However, it is worth

noting that the identification of discrete damage states is not an easy task.

32

Engineering Demand Parameters are measures of the structural response that can be

obtained from the results of structural analyses. On one hand, typical choices from the

examined methodologies that have performed Nonlinear Dynamic Analysis are the Inter-

storey Drift (ISD), Global Drift (GD) or the Park and Ang (1985) damage index, among

others. On the other hand, top displacement is the most commonly utilized EDP from

Nonlinear Static (Pushover) Analysis. Threshold values of EPDs can be estimated either for

each individual building, or for building typologies.

The nonlinear analysis usually provides specific values of EDPs, normally at the level of

elements, which describe changes in structural behaviour. It is hence common practice to

use these EDP values or a combination of them to also define the threshold for each

damage state at local or global level. The definition of capacities for each building provides

the flexibility of tailoring the damage threshold values to a given building or sub-class of

building typologies and introduces capacity-demand correlations that may have a major

influence in the fragility analysis results.

Alternatively, one might employ the proposed simplified formula and relations from

literature, to directly estimate global damage state thresholds and the corresponding

median capacity values. Relations commonly used are expressed as functions of yield and

ultimate roof displacement.

EDP limit values may also be estimated from a (simplified bilinear) capacity curve of a

building. For example, Lagomarsino and Giovinazzi (2006) identified four damage states on

the global capacity curve and associated to each a median value of spectral displacement.

Moreover, Cattari and Lagomarsino (2012) have proposed a multi-scale approach for

masonry buildings that defines limit states thresholds also based on the capacity curve, by

checking the spread of damage in masonry elements (piers and spandrels), the inter-storey

drift in masonry walls, and the global behaviour of the building (described by its capacity

curve).

Likewise, D’Ayala (2013) has suggested four damage state thresholds for the generation of

fragility curves for masonry buildings, this time obtained through laboratory or in-situ

experimental tests reported in literature on whole buildings or full-size walls with different

failure modes. These values were used when developing the fragility curves with the FaMIVE

procedure.

Regarding the evaluation of different limit states at the level of the structure there is still a

lack of clear guidance in the literature.

3.11. Form of relation

In the vast majority of the existing fragility models and related methodologies, a lognormal

function defined by a mean and standard deviation is employed to represent the conditional

probability of exceeding a damage state, as in the case of the fragility curves built by Barbat

et al. (2006), presented in Figure 17 (left). Also in the FAMIVE method, fragility curves for

different limit states are obtained by computing the median and standard deviation values

of the performance point displacements for each building and by deriving lognormal

distributions (D’Ayala et al. 2014). However, as demonstrated by Ceran (2010), this

probability can also be obtained through a standard normal cumulative distribution function

for the construction of fragility curves, which in the case of Figure 17 (centre), are referring

to the ultimate limit state of the critical walls of three different Turkish case study masonry

buildings. Additionally, this probability can be obtained through a set of discrete values, as

observed in D’Ayala et al. (1997), which have generated fragility curves for the Alfama

District of Lisbon, illustrated in Figure 17 (right).

33

Figure 17. Continuous fragility curves for lognormal (left) and normal (centre) functions, and discrete fragility curves (right), developed by Barbat et al. (2006), Ceran (2010) and D’Ayala et al. (1997), respectively.

3.12. Intensity Measure

In order to understand the role that intensity measure (IM) plays on the seismic risk

assessment process, it is important to recall the definition of fragility curve, which

represents the conditional probability of reaching a given damage state for a given hazard

level characterized by a determined IM. Therefore, IMs are a key point on the derivation

process of fragility curves.

Although IMs can be chosen in different ways, for the analysis to be robust, they are

required to accurately represent the relevant seismological properties of ground motion

related to site and source (Luco and Cornell 2007). Given the spatial distribution of the

building stock, it is practical and advisable to use IMs for which ground motion prediction

equations (GMPEs, also known as attenuation relationships) are available. The selection of

IMs should aim at a reduced record-to-record variability of the selected EPD, enabling thus

its evaluation with a small number of time-history analyses (D’Ayala et al. 2014). Thus, the

identification of proper IM is subject to different constraints, which are related to the

adopted hazard model, to the typology of the exposed asset but also to the availability of

data for all different exposed assets (Lagomarsino and Cattari 2014).

As one can observe from the reviewed methodologies in Table 1, at the end of this chapter,

the most recurrently used IMs are the peak ground acceleration, peak ground velocity, peak

ground displacement, and (pseudo) spectral acceleration values. However, according to

Gehl et al. (2012), the standard method to develop fragility curves neglects the uncertainty

in the estimated damage caused by the use of a single IM, which cannot represent all

characteristics of the ground motion. In this sense, some efforts have been made recently

to consider the effect of several IMs on structural damage (Baker and Cornell 2005; Kafali

and Grigoriu 2007; Seyedi et al. 2010; Koutsourelakis 2010).

3.13. Sample size

The sample size accounts for the number of buildings (population) under analysis. It is

extremely difficult to generalise results or establish comparisons based on methodologies in

which only an individual building (or case study) is analysed. Although this generalisation

and comparison of results is always questionable, it is clear that the larger the population of

buildings analysed the higher the chances for generalising the respective results.

For the selection of the sample, it is important to identify the main parameters that

influence the seismic response of a building class, such as the lateral load resisting system,

34

mechanical properties of materials, geometric configuration, dimensions and detailing of

elements (D’Ayala et al. 2014). These parameters may show considerable scatter. Thus, a

comprehensive knowledge of the probabilistic distribution of the most important structural

parameters defining the population of buildings in the class of interest is needed. Based on

the fragility curves reviewed in this report, the most important characteristics that typically

are accounted for include:

• Building height, in discrete values or range of storeys;

• Design base shear and deformation capacity of the building;

• In plan irregularity;

• In height irregularity, defined for example by the presence of a soft/weak storey and

the ratio of its strength or stiffness to that of the adjacent storey;

• Material properties.

Monte Carlo simulations typically involve the generation of a large sample, which can

accurately represent the underlying population. This type of simulation it is not yet practical,

mainly because of the effort involved in the criterion, modelling and analysis of the sample,

unless automated software and generous computing resources are available. Thus, Monte

Carlo simulations are more practical for the simplest SDoF models. Its application together

with improved sampling strategies for example Latin Hypercube Sampling (LHS), rather

than classic random sampling, drastically reduces the computational cost and offers insights

into the actual population statistics. Lastly, it is noted that appropriate skills and expertise

are necessary to perform Monte Carlo simulations.

At this stage, the main features associated with the methodologies considered in this report

were approached and described. Thus, in the next Chapter 4, the criteria defined for the

qualitative evaluation of those fragility curves will be presented.

3.14. Summary table of the reviewed fragility curves

The following Table 1 displays an informative summary of some of the most important

features of each fragility curve methodology analysed in this report. Briefly, these are

grouped in four main categories, each containing subcategories: general features; capacity;

demand, and fragility curves’ inherent characteristics. In the following paragraphs the

authors will describe the taxonomy herein utilised in Table 1, even though most of these

features were previously addressed throughout the current Chapter 3.

The first category, termed general features, includes the respective reference of each

methodology, its geographical applicability, class of structures analysed and structural

system typology. In what regards the class of structures, EB stands for existing buildings

whose dimensions, materials and properties are known and used in the analyses, and PR

stands for prototype buildings. The structural system typologies analysed in this work

included unreinforced masonry (URM) and reinforced concrete (RC) structures. As already

mentioned, RC buildings include the following subcategories: moment-resisting frames; dual

frame-wall systems; infilled frames, and precast systems.

The second category comprises the following features related to capacity: components for

response analysis; number of floors; analysis type; model type; shear failure; out-of-plane

mechanism; horizontal diaphragm; geometrical irregularities, and engineering demand

parameter (EDP). In what concerns the components considered for response analysis, S and

NS stand for structural and non-structural elements, respectively. In relation to the different

type of analyses found in the reviewed methodologies, the following nomenclature was

used: NLD for nonlinear dynamic analysis; NLS for nonlinear static analysis, SMM-NLS for

simplified mechanic methods, and LS for linear static analysis. In what regards the model

35

type chosen for the analysis, three different designations were considered: MDoF (multi-

degree of freedom system); reduced MDoF, and SDoF (single-degree of freedom system)

models. For the shear failure, out-of-plane mechanism, horizontal diaphragms and geometrical irregularities subcategories, checkmarks and were used to identify if these

features were taken into consideration in the reviewed methodologies. Moreover, the

symbol (-) was used when a particular subcategory is not applicable to a certain

methodology. Finally, in what concerns the engineering demand parameters (EDP), the

following nomenclature was used: RD (roof displacement); TD (top displacement); ISD

(inter-storey drift); GD (global drift); VLS,i (median base shear capacity at the i th limit

state); VD (median base shear demand given the PGA); MPR (maximum plastic end rotation

of beams), and MFA (maximum floor acceleration).

The third category is related to the seismic demand-related features and includes both

seismic demand and site-specific subcategories. As the reviewed methodologies use either

ground motion records, including both real and synthetic records, or code-compliant

spectra, these two broad designations were herein considered. As previously explained, the

site-specific subcategory assesses if the seismic input considered for analysis in a given

methodology is related or not with the specific site in which the buildings under assessment are located. Thus, checkmarks and were used also here to identify if seismic input is

related or nor to the specific site.

The last category includes some of the most important features for deriving fragility curves,

including the damage state thresholds definition, number of damage states, form of

relationship, intensity measure and sample size. As described before in this Chapter 3,

damage state thresholds can be defined by means of either pre-set or custom definitions.

With respect to the form of relationship for the construction of fragility curves, three

different options are usually considered: CL (continuous lognormal); CN (continuous

normal), and DD (discrete distribution). In what regards the intensity measure (IM), the

following taxonomy was used: Sd(T) (spectral displacement); PGA (peak ground

acceleration); PGV (peak ground velocity); PGD (peak ground displacement); CAV

(cumulative absolute velocity); Sa(T) (spectral acceleration); MMI (modified Mercalli

intensity); Sv(T) (spectral velocity), and AI (Arias intensity). Finally, for the size of the

sample considered in each reviewed methodology, the authors attributed the following

classification: several buildings; few buildings, and one single building.

36

Table 1. Main features of the considered methodologies for deriving analytical fragility curves.

General Capacity Demand Fragility curve

Refe

ren

ce

Geog

rap

hic

al

ap

pli

cab

ilit

y

Cla

ss

Str

uctu

ral

syste

m

Com

pon

en

ts

for r

esp

on

se

an

aly

sis

Nu

mb

er o

f

sto

reys

An

aly

sis

typ

e

Mod

el ty

pe

Sh

ear f

ailu

re

Ou

t-of-

pla

ne

mech

an

ism

Horiz

on

tal

dia

ph

rag

m

Geom

etr

ical

irreg

ula

rit

ies

ED

P

Seis

mic

dem

an

d

Sit

e s

pecif

ic

Dam

ag

e

sta

tes

thresh

old

s

Nu

mb

er o

f

dam

ag

e

sta

tes

Form

of

rela

tion

sh

ip

In

ten

sit

y

measu

re

(IM

)

Sam

ple

siz

e

Ahmad et al. (2010)

TR, IT,

GR and

SI

PR RC moment-

resisting frame S 2,5,8 NLS SDoF (-) (-) TD

Ground motion records

Pre-set 5 CL Sd(T) and

PGA Several

Akansel et al.

(2012) TR PR

RC dual frame-wall

system S 3 NLD MDoF (-) (-) ISD

Ground motion

records Custom 3 CL

PGA, PGV,

PGD and CAV One

Akkar et al.

(2005) TR EB RC infilled frames S+NS 2,3,4,5

NLD +

NLS SDoF (-) (-) GD

Ground motion

records Custom 4 CL PGV Several

Barbat et al.

(2006) ES EB RC+URM S

2,5,8 +

2,4,6 NLS SDoF (-)+ (-)+ TD

Ground motion

records Pre-set 5 CL Sd(T) Several

Bilgin (2013) TR PR RC moment-

resisting + dual

frame-wall systems

S 3,4,5 NLS SDoF (-) (-) ISD Ground motion

records Custom 4 CL PGV Several

Borzi et al.

(2007) IT PR

RC moment-

resisting frame S 2,4,8

SMM-

NLS SDoF (-) (-)

Chord

rotations

Code-based

spectra Custom 4 CL PGA Several

Borzi et al.

(2008a) IT PR

RC moment-

resisting + dual frame-wall systems

S+NS 4 SMM-

NLS SDoF (-) (-)

Chord

rotations

Code-based

spectra Custom 4 CL PGA Several

Borzi et al. (2008b)

IT PR RC moment-

resisting frame S 2,3,4,5,6,8

SMM-NLS

SDoF (-) (-) Chord

rotations Code-based

spectra Custom 5 CL PGA Several

Borzi et al. (2008c)

IT PR URM S 2,3,4,5 SMM-NLS

SDoF Chord

rotations Code-based

spectra Custom 5 CL PGA Several

Casotto et al.

(2015) IT PR RC (precast) S 1

NLD +

NLS

MDoF +

SDoF (-) (-)

Maximum top-

drift

Ground motion

records Custom 5 CL Sa(T) Several

Ceran (2010) TR PR URM S Multiple SMM-

NLS SDoF

Base + flexural

strength

Code-based

spectra Custom 3 CN PGA Several

D'Ayala

(2005) TR EB URM S Multiple

SMM-

NLS SDoF

Collapse load

factor

Code-based

spectra Custom 6 CL Sd(T) Several

Del Gaudio et

al. (2015) IT EB RC infilled frames S+NS Multiple

SMM-

NLS SDoF (-) (-) TD

Code-based

spectra Pre-set 6 CL PGA Several

37

General Capacity Demand Fragility curve

Refe

ren

ce

Geog

rap

hic

al

ap

pli

cab

ilit

y

Cla

ss

Str

uctu

ral

syste

m

Com

pon

en

ts

for r

esp

on

se

an

aly

sis

Nu

mb

er o

f

sto

reys

An

aly

sis

typ

e

Mod

el ty

pe

Sh

ear f

ailu

re

Ou

t-of-

pla

ne

mech

an

ism

Horiz

on

tal

dia

ph

rag

m

Geom

etr

ical

irreg

ula

rit

ies

ED

P

Seis

mic

dem

an

d

Sit

e s

pecif

ic

Dam

ag

e

sta

tes

thresh

old

s

Nu

mb

er o

f

dam

ag

e

sta

tes

Form

of

rela

tion

sh

ip

In

ten

sit

y

measu

re

(IM

)

Sam

ple

siz

e

Dumova-Jovanoska

(2000)

MK EB

RC moment-

resisting + dual

frame-wall

systems

S 6,16 NLD Reduced

MDoF (-) (-)

Park and Ang

damage index

Ground motion

records Custom 5 DD MMI Several

Erberik

(2008) TR EB URM S 1,2,3,4,5

NLD +

NLS SDoF VLS,i, VD

Ground motion

records Custom 3 CN PGA Several

Fardis et al.

(2012) Europe PR

RC moment-

resisting + dual frame-wall

systems with

infills

S+NS 2, 5, 8 NLS SDOF (-) (-) Chord rotation,

shear force

Code-based

spectra Custom 2 CL PGA One

Hancilar and Çaktr (2015)

TR EB RC moment-

resisting frame S 5,10,15,20 NLD MDoF (-) (-)

ISD, MPR and MFA

Ground motion records

Custom 13,11,15 CL

Sa(T), Sv(T),

Sd(T), PGA, PGV, PGD, AI

and CAV

Several

Kappos and

Panagopoulos

(2009)

GR EB

RC moment-

resisting + dual-

frame systems

S

Low, mid

and high

rise

NLS Reduced

MDoF (-) (-)

Ratio of roof

displacement

to total height

Ground motion records

Pre-set 6 CL PGA Several

Kappos et al.

(2003) GR EB

RC dual frame-

wall + infilled

frame systems

S+NS 1-3,4-7,8-

19 NLS

Reduced

MDoF (-) (-) ISD

Ground motion

records Pre-set 6 CL PGA Several

Kappos et al.

(2006) GR EB

RC dual frame-wall + infilled

frame systems

S+NS 4-7,>8 NLD +

NLS

Reduced MDoF +

SDoF

(-) (-) ISD Ground motion

records Pre-set 6 CL

Sd(T) and

Sa(T) Several

Kappos et al. (2007)

GR EB URM S Multiple NLD + NLS

Reduced

MDoF +

SDoF

RD, ISD, TD Ground motion

records Pre-set 5 CL Sd(T) Several

Karantoni et

al. (2014) GR PR URM S Multiple LS MDoF

Extent of

damage

Code-based

spectra Custom 5 CL Sa(T) Several

Kircil and

Polat (2006) TR EB

RC moment-

resisting frame S 3,4,5,6,7 NLD

Reduced

MDoF (-) (-) ISD

Ground motion

records Custom 2 CL Sa(T) Several

Lagomarsino

and Cattari (2014)

IT PR URM S

Low, mid

and high rise

SMM-

NLS SDoF ISD

Code-based

spectra Custom 4 CL PGA Few

Lang (2002) CH EB RC+ URM S 2-7 SMM-

NLS SDoF (-)+ (-)+ TD

Code-based

spectra Custom 5 CN Sd(T) Several

Oropeza et al. (2010)

CH EB URM S 15 NLS SDoF TD Code-based

spectra Pre-set 5,6 CL Sd(T) One

38

General Capacity Demand Fragility curve

Refe

ren

ce

Geog

rap

hic

al

ap

pli

cab

ilit

y

Cla

ss

Str

uctu

ral

syste

m

Com

pon

en

ts

for r

esp

on

se

an

aly

sis

Nu

mb

er o

f

sto

reys

An

aly

sis

typ

e

Mod

el ty

pe

Sh

ear f

ailu

re

Ou

t-of-

pla

ne

mech

an

ism

Horiz

on

tal

dia

ph

rag

m

Geom

etr

ical

irreg

ula

rit

ies

ED

P

Seis

mic

dem

an

d

Sit

e s

pecif

ic

Dam

ag

e

sta

tes

thresh

old

s

Nu

mb

er o

f

dam

ag

e

sta

tes

Form

of

rela

tion

sh

ip

In

ten

sit

y

measu

re

(IM

)

Sam

ple

siz

e

Özer and

Erberik

(2008)

TR PR RC moment-

resisting frame S 3,5,7,9 NLD

Reduced

MDoF (-) (-) ISD

Ground motion

records Custom 4 CL PGV Few

Pagnini et al.

(2011) PT EB URM S 4

SMM-

NLS SDoF Ultimate drift

Code-based

spectra Custom 5 CL Sd(T) One

Pasticier et

al. (2008) IT EB URM S 3

NLS +

NLD

Reduced

MDoF TD

Ground motion

records Custom 4 CL PGA One

Pitilakis et al.

(2014) GR EB

RC moment-

resisting frame S 3,4,9 NLD MDoF (-) (-) ISD

Ground motion

records Custom 3 CL PGA Few

Polese et al.

(2008) IT EB

RC moment-

resisting frame S 1-3,4-6,>7 NLS SDoF (-) (-) TD

Code-based

spectra Pre-set 5 CL Sd(T) Few

Rota et al.

(2010) IT PR URM S 3

NLD +

NLS SDoF GD

Ground motion

records Custom 5 CL PGA One

Rota et al.

(2014) IT PR URM S 2-4 NLS SDoF TD

Code-based

spectra Custom 4 CL PGA Few

Silva et al.

(2013) TR EB

RC moment-

resisting frame S 4

NLD +

NLS

Reduced

MDoF+

SDoF

(-) (-) TD Ground motion

records Custom 4 CL Sa(T) Few

Silva et al. (2014)

PT EB RC+URM S 1,2,3,4,5-

7,>8 NLD + NLS

Reduced

MDoF +

SDoF

(-)+ (-)+ GD and ISD Ground motion

records Pre-set 5 CL Sa(T) Few

Simões et al. (2015)

PT EB URM S 4,5 NLS SDoF TD Code-based

spectra Custom 5 CL Sa(T) Few

Tsionis and Fardis (2014)

GR PR

RC moment-

resisting + dual

frame-wall

systems with infills

S+NS 2, 5, 8 NLS SDOF (-) (-) Chord rotation,

shear force Code-based

spectra Custom 2 CL PGA One

Vacareanu et

al. (2004) RO EB

RC moment-

resisting frame +

dual frame-wall

systems

S+NS 8,11,12,13 NLS SDoF (-) (-) Park and Ang

damage index, ISD

Code-based

spectra Pre-set 5 CL Sd(T) Few

Vacareanu et

al. (2007) RO EB

RC moment-resisting frame +

dual frame-wall

systems

S+NS 11 NLS SDoF (-) (-) TD Code-based

spectra Pre-set 5 CL Sd(T) One

39

4. Criteria and evaluation of fragility curves

Having identified and discussed the most important features influencing the accuracy,

complexity and uncertainty associated with the methodologies used to derive fragility

curves, in this Chapter the criteria for the qualitative evaluation of these methodologies,

will be described and applied. The proposed criteria are based on the work carried out by

Rossetto et al. (2014), from which we adopt similar principles to cover four fundamental

categories related to capacity, demand, methodology for fragility analysis, and

uncertainty, as previously discussed in Chapter 3. However, the criteria in the present

report differ in some aspects. In contrast to Rossetto et al. (2014), which have

developed a quantitative (scoring) method for combining fragility curves, the aim of the

present report is to provide a set of qualitative criteria to support the selection process

of the most appropriate fragility curves for the European building stock, which was

intended to be exclusively qualitative, and not quantitative.

The following criteria were examined for each of the above-mentioned categories,

presented in Table 1 of the previous Chapter 3. To each set of fragility curves, low (L),

medium (M) or high (H) rating is assigned to each criterion, as shown in Table 2 and

further detailed in the following sections.

Table 2. Qualitative assessment criteria and respective rating.

Category Evaluation criteria Rating

Low (L) Medium (M) High (H)

Capacity

Non-structural elements No (-) Yes Classes of building height 1 2, 3 > 3

Analysis type NLS-SMM, LS NLS NLD

Model type SDoF

models Reduced

MDoF models MDoF

models Shear failure No (-) Yes

Out-of-plane mechanism (URM) No (-) Yes Horizontal diaphragms (URM) No (-) Yes

Geometric irregularities No (-) Yes

Demand Seismic demand

Code-based spectra

< 7 accelerograms

≥ 7 accelerograms

Site-specific No (-) Yes

Methodology

Damage state thresholds definition Pre-set (-) Custom

Intensity measure 1 2,3 > 3

Sample size One

building Few

buildings Several buildings

Sampling method One-index

building

Three-index

building

Multiple-index

building

Uncertainty Capacity No (-) Yes

Seismic demand No (-) Yes Damage state thresholds No (-) Yes

It is not the purpose of this report to rank and identify the ‘best’ set of fragility curves,

as the authors acknowledge the fact that all methodologies present advantages and

drawbacks. Moreover one cannot compare them globally, because each methodology

was developed for very particular conditions, such as, for instance, the assessment

scale, the analysis computational effort, human and time resources consumption.

Nevertheless, according to Calvi et al. (2006) an optimal or ideal fragility assessment

methodology should feature the following main characteristics:

40

• The most recent developments in the field of seismic hazard assessment should

be incorporated;

• All sources of uncertainty should be explicitly accounted for;

• The methodology should be easily adaptable to the different construction

practices around the world, as well as allow for the inclusion of new construction

types and the influence of retrofitting on the response of existing structures;

• A balance should be struck between the computational intensity and the amount

of detailed data that is required and the consequent degree of confidence in the

results.

It is unlikely that a single methodology can fulfil all of these requirements and therefore,

reliable fragility assessment of a given region is likely to request the employment of at

least two different approaches, which should complement and/or verify each other (Calvi

et al. 2006).

The criteria herein proposed aim to provide guidance on the selection of fragility curves

for the European building stock, based on a two-step selection procedure. Firstly, one

should short down the spectra of available fragility curves by considering those that

apply to the geographical region and building typology of interest. Secondly, one should

select the fragility curves that better fit the specific purpose, based on the four

fundamental categories that constitute the proposed evaluation criteria. In the following

sections, detailed information will be given concerning the assessment of each single

feature.

4.1. Capacity

As mentioned in the previous Chapter 3, the consideration or not of non-structural

components in fragility assessment of buildings is generally more relevant in the case of

RC buildings. Here, the consideration of the contribution of masonry infill walls in the

analysis model, taken as non-structural components, has been highly recommended due

to its significant influence on the lateral resistance of a reinforced concrete frame.

Therefore, according to this criterion, the reviewed fragility curves that have considered

the presence of non-structural components in their analyses when assessing RC

buildings were given a high rating (H), while those that have only considered the

structural components were assigned a low (L) rating.

The criterion defined for the number of storeys classifies the reviewed fragility curves

according to the variability of the number of storeys considered in the analysis. This is

relevant to understand the different behaviour of low-, mid- and high-rise buildings,

which naturally have distinct fragilities. Thus, fragility curves in which the variability in

terms of number of storeys was not considered in the analyses were given a low rating

(L). Accordingly, fragility curves that have considered up to three different numbers of

storeys in their analyses were given a medium rating (M). Finally, fragility curves that

have considered in their analyses more than three different numbers of storeys were

given a high rating (H).

Considering that the reliability associated to the type of analysis chosen for structural

assessment is strongly related to the level of detail of that analysis, in the present

criteria the authors assigned NLD analysis high (H), NLS analysis medium (M) and NLS-

SMM or LS analyses low rating (L).

Based on the same reasoning as for the analysis type, the model types selected for

structural assessment were evaluated as a function of their level of detail. Thus, MDoF

models were assigned high (H), reduced MDoF models medium (M), and SDoF models

low rating (L).

As mentioned in Chapter 3, shear failure in members can occur in buildings that are

designed for horizontal actions or in buildings with low shear resistance. This failure

mode can have important effect on fragility curves as it hastens the attainment of higher

41

damage levels. Therefore, the fragility curves in which shear failure mode was

considered in the analyses were assigned high rating (H). In contrary, those fragility

curves in which this failure mode was not considered in the analyses or no clear

explanation is provided about its consideration were assigned a low rating (L).

Acknowledging that the out-of-plane response of URM buildings is often neglected in

numerical modelling, despite representing one of the dominant modes of failure, the

fragility curves that accounted or not for this particular failure mode in the analyses were

given high (H) and low rating (L), respectively.

Given that the stiffness of different diaphragm typologies influences the global seismic

response of URM buildings, the criterion defined to evaluate the reviewed fragility curves

was based on whether the variability of the horizontal diaphragms was considered or not

in the analysis, assigning high (H) and low rating (L), respectively.

Finally, as mentioned before in this report, irregularities are capable to generate stress

distributions significantly different from those expected in regular structures, which

might cause severe damage or even the collapse of the structure. However, the effect of

these irregularities is not always considered when performing seismic fragility

assessment of both RC and URM buildings. Hence, high (H) and low rating (L) was

assigned to the reviewed methodologies that have considered or not geometrical

irregularities, respectively.

4.2. Demand

The criterion established for the description of the seismic demand was based on the

Eurocode 8 recommendations (CEN 2004). Thus, a high rating (H) was assigned to

methodologies in which at least seven real ground motion records were used to estimate

the seismic demand. Then, methodologies which have determined the seismic demand

for a specific site by means of considering less than seven real ground motion records

were assigned as medium (M). Finally, methodologies where code-based spectra were

considered were evaluated as low (L).

In what concerns the criterion for the site-specific input, the reviewed methodologies are

given high rating (H) when the seismic demand is related to the specific site of the

assessed structures and low (L) in the contrary case, even when covering similar

magnitudes, rupture distances and average shear-wave velocities.

4.3. Fragility curve (methodology)

Bearing in mind the two approaches for the definition of EDPs threshold values

mentioned and described in the previous Chapter 3, the calculation of custom values for

each specific building was assigned as high (H), while the use of pre-set values for

building typologies was given low rating (L).

Regarding the IM used for the derivation of fragility curves, low (L), medium (M) and

high (H) rating was assigned those that use respectively one, two and three or more

IMs. This criterion does not address the issue of correlation of damage to the IM and the

effort needed to calculate the IM, which are difficult to assess even qualitatively and are

often conflicting (e.g. spectral values and composite IMs are better correlated to

structural damage than peak ground acceleration, but require additional calculations).

As it is found extremely difficult to generalise results or establish comparisons based on

methodologies in which only an individual building (or case study) was analysed, the

evaluation of this subcategory aims at distinguishing from the reviewed methodologies

those that are carried out for larger samples, increasing its applicability and

generalisation to particular building typologies of the European building stock. Hence,

samples sizes of several (hundreds) of buildings were assigned as high (H), while those

42

with few (dozens) of buildings were assigned as (M). Finally, those methodologies in

which only one single building was analysed were evaluated as low (L) in this

subcategory.

4.4. Treatment of uncertainty

Uncertainty in capacity is introduced either through geometrical, mechanical, structural

or modelling parameters. Usually, in order to create a number of building models for the

structural analysis, uncertainty in capacity is addressed by treating both geometric and

material properties, mass and damping, as random variables. The treatment of

uncertainty in capacity was evaluated as sufficient and marked high (H) if at least one of

the following sources were accounted for the derivation of fragility curves: mechanical

properties; geometric parameters; structural detailing, or numerical modelling. On the

contrary, if none of the previous sources of uncertainty in capacity were considered, the

rating was evaluated as low (L).

The uncertainty in the demand is associated with the natural variability of ground motion

characteristics, which comprises the variability of the seismic source, path attenuation

and site effects of the seismic event. This type of uncertainty is typically taken into

account either through the selection (and scaling) of natural ground motion records or

by generating artificial records. The treatment of uncertainty in demand was herein

evaluated as high (H) if record-to-record variability is considered.

Uncertainty in the definition of damage state thresholds is often neglected in fragility

assessment procedures found in the literature. However, in a few cases a probability

distribution is assigned to the damage state thresholds. In the present criterion,

methodologies in which uncertainty in damage state thresholds was considered were

assigned as high rating (H) and those that haven’t considered it in were given low rating

(L).

43

Table 3. Application of the qualitative assessment criteria on the reviewed fragility curves.

General Capacity Demand Fragility curve Uncertainty R

efe

ren

ce

Geog

rap

hic

al

ap

pli

cab

ilit

y

Cla

ss

Str

uctu

ral

syste

m

Com

pon

en

ts

for r

esp

on

se

an

aly

sis

Cla

sses o

f

bu

ild

ing

heig

ht

An

aly

sis

typ

e

Mod

el ty

pe

Sh

ear f

ailu

re

Ou

t-of-

pla

ne

mech

an

ism

Horiz

on

tal

dia

ph

rag

m

Geom

etr

ical

irreg

ula

rit

ies

Seis

mic

dem

an

d

Sit

e s

pecif

ic

Dam

ag

e

sta

tes

thresh

old

s

In

ten

sit

y

measu

re

(IM

)

Sam

ple

siz

e

Cap

acit

y

Seis

mic

dem

an

d

Dam

ag

e

thresh

old

s

Ahmad et al. (2010)

TR, IT,

GR and

SI

PR RC L M M L L (-) (-) H H L L M H H H H

Akansel et al.

(2012) TR PR RC L L H H L (-) (-) H H H H H L H L L

Akkar et al.

(2005) TR EB RC H H H L L (-) (-) L H H H L H H H H

Barbat et al.

(2006) ES EB RC+URM L + H M M L H (-)+L (-)+H H H L L L H L H H

Bilgin (2013) TR EB RC L M M L H (-) (-) L H H H L H H H H

Borzi et al. (2007) IT PR RC L M L L H (-) (-) L L H H L H H H H

Borzi et al.

(2008a) IT PR RC H L L L L (-) (-) L L H H L H H H H

Borzi et al. (2008b)

IT PR RC L H L L H (-) (-) L L H H L H H H H

Borzi et al. (2008c)

IT PR URM H H L L H H H L L H H L H H H H

Casotto et al.

(2015) IT PR RC L L H H L (-) (-) L H L H L H H H H

Ceran (2010) TR PR URM H H L L H H H H L H H L H H H H

D'Ayala (2005) TR EB URM H H L L L H L L L H H L H H H L

Del Gaudio et al.

(2015) IT EB RC H H L L L (-) (-) L L H H L H H H L

44

General Capacity Demand Fragility curve Uncertainty

Refe

ren

ce

Geog

rap

hic

al

ap

pli

cab

ilit

y

Cla

ss

Str

uctu

ral

syste

m

Com

pon

en

ts

for r

esp

on

se

an

aly

sis

Cla

sses o

f

bu

ild

ing

heig

ht

An

aly

sis

typ

e

Mod

el ty

pe

Sh

ear f

ailu

re

Ou

t-of-

pla

ne

mech

an

ism

Horiz

on

tal

dia

ph

rag

m

Geom

etr

ical

irreg

ula

rit

ies

Seis

mic

dem

an

d

Sit

e s

pecif

ic

Dam

ag

e

sta

tes

thresh

old

s

In

ten

sit

y

measu

re

(IM

)

Sam

ple

siz

e

Cap

acit

y

Seis

mic

dem

an

d

Dam

ag

e

thresh

old

s

Dumova-Jovanoska (2000)

MK EB RC L L H M L (-) (-) L H H H L H L H L

Erberik (2008) TR EB URM H H H L H L L H H H H L H H H H

Fardis et al.

(2012) Europe PR RC H M M L H (-) (-) H L L H L L H H L

Hancilar and Çaktr

(2015) TR EB RC L H H H L (-) (-) L H H H H H H H H

Kappos and

Panagopoulos (2009)

GR EB RC L M M M L (-) (-) L H H L L H H H H

Kappos et al.

(2003) GR EB RC H M M M L (-) (-) H H H L L H H H H

Kappos et al. (2006)

GR EB RC H M H M H (-) (-) L H H L M H H H H

Kappos et al.

(2007) GR EB URM H H H M L L L L H H L L H L H L

Karantoni et al.

(2014) GR PR URM H H L H H H H L L L H L H H H H

Kircil and Polat

(2006) TR EB RC L H H M L (-) (-) L H H H L H L H H

Lagomarsino and

Cattari (2014) IT PR URM H M L L H L L H L H H L M H H H

Lang (2002) CH EB RC+URM L+H H L L H (-)+H (-)+L L L H H L H L H H

Oropeza et al.

(2010) CH EB URM H L M L L L L H L H L L L H L L

Özer and Erberik (2008)

TR PR RC L H H M L (-) (-) L H H H L M H H H

45

General Capacity Demand Fragility curve Uncertainty

Refe

ren

ce

Geog

rap

hic

al

ap

pli

cab

ilit

y

Cla

ss

Str

uctu

ral

syste

m

Com

pon

en

ts

for r

esp

on

se

an

aly

sis

Cla

sses o

f

bu

ild

ing

heig

ht

An

aly

sis

typ

e

Mod

el ty

pe

Sh

ear f

ailu

re

Ou

t-of-

pla

ne

mech

an

ism

Horiz

on

tal

dia

ph

rag

m

Geom

etr

ical

irreg

ula

rit

ies

Seis

mic

dem

an

d

Sit

e s

pecif

ic

Dam

ag

e

sta

tes

thresh

old

s

In

ten

sit

y

measu

re

(IM

)

Sam

ple

siz

e

Cap

acit

y

Seis

mic

dem

an

d

Dam

ag

e

thresh

old

s

Pagnini et al.

(2011) PT EB URM H L L L L L L L L H H L L H L L

Pasticier et al.

(2008) IT EB URM H L H M H L L L H H H L L L L L

Pitilakis et al.

(2014) GR EB RC L M H H L (-) (-) L H H H L M H H H

Polese et al.

(2008) IT EB RC L M M L L (-) (-) H L H L L M H H H

Rota et al. (2010) IT PR URM H L H L H L H L H H H L L H L H

Rota et al. (2014) IT PR URM H M M L H L L H L H H L M H H H

Silva et al. (2013) TR EB RC L L H M L (-) (-) L H H H L M H H H

Silva et al. (2014) PT EB RC+URM L+H H H M L (-)+L (-)+L H H H L L M H H H

Simões et al. (2015)

PT EB URM H M M L H L H H L H H L M H H L

Tsionis and Fardis (2014)

GR PR RC H M M L H (-) (-) H L L H L L H H L

Vacareanu et al.

(2004) RO EB RC H H M L L (-) (-) L L H L L M H H H

Vacareanu et al. (2007)

RO EB RC H L M L L (-) (-) L L H L L L L L L

46

47

5. Current trends in seismic fragility curves

This Chapter aims to present the main trends possible to extract from the existing

methodologies for deriving analytical fragility curves for the European building stock,

based on the evaluation criteria described in Chapter 4. Even though the following

output is not exhaustive, this exercise is highly interesting for perceiving how the

scientific community in general is approaching this issue in each of the its main aspects.

It would be indeed of great interest to extend this exercise to all the remaining

approaches used to derive fragility curves, including also other methodologies developed

worldwide.

Figure 18 depicts the distribution of the examined fragility curves in terms of date (year)

of publication. Globally one can observe that the number of studies roughly doubled in

ten years, which somehow evidences that the study of fragility curves is a topic of

growing interest and investment by the scientific community and founding institutions.

Figure 18. Distribution of the examined studies over the years.

As already emphasized in Chapter 3, the distribution of studies per country is presented

in Figure 19 (left), from which stays clear the huge contribution of researchers from

Italy, Turkey and Greece to the development of analytical fragility curves. This is

naturally associated to the higher seismicity and to the high number of earthquakes that

harmed these countries in recent years, opening up the possibility of calibrating

analytical models from empirical data collected by means of post-earthquake damage

observation. From Figure 19 (centre) one can observe that 62% of the studies are

developed for existing buildings (EB) against the 38% developed for prototype buildings

(PR). Finally, even though unreinforced masonry (URM) buildings remain one of the most

common and vulnerable building typologies worldwide, approximately 62% of the

examined fragility curve studies were developed for reinforced-concrete (RC) buildings.

This might be explained due to severe damage and corresponding losses associated to

the behaviour of this particular typology in recent earthquakes, often triggered either by

lack of adequate seismic designing or building/construction detailing.

2000

2001

2002

2003

2004

2005

2006

2007

2008

2009

2010

2011

2012

2013

2014

2015

0

2

4

6

8

Num

ber

of stu

die

s

Year

X

48

Figure 19. Distribution of the examined studies by country (left), building type used in the analysis (centre), and structural material (right).

Figure 20 presents the results of the evaluation carried out considering the aspects of

the capacity. From the first pie chart, in Figure 20 (a), it is possible to observe that 31%

of the studies regarding fragility curves for RC buildings do not take into account the

influence of non-structural components such as infill masonry walls. Figure 20 (b)

depicts how the examined studies treat the variability of the building height (or number

of storeys), from which one can conclude that about 38% of these studies considered

more than three different classes, 36% considered two or three different classes, and

26% considered only one class on their analyses.

In Figure 20 (c), the distribution of the results from the evaluation carried out regarding

the analysis type is presented, from which one can observe that approximately 33% of

the studies have performed NLD analysis for the computation of the seismic response of

structures. Moreover, NLS and SMM-NLS analyses were conducted in 38% and 28% of

the reviewed studies, respectively. In turn, Figure 20 (d) presents the model type

considered within each reviewed fragility curve, from which it is possible to observe that

approximately 62% have considered SDoF systems, 26% have considered reduced MDoF

systems, and only about 13% have considered MDoF systems.

Even though most of these studies do not mention it in a clear and direct way, it was

found that about 65% of the examined studies for RC buildings have not considered the

shear failure mechanism in the seismic response of structures, as illustrated in Figure 20

(e). In turn, from Figure 20 (f) one can observe that about 69% of the studies

exclusively concerning the fragility assessment of URM buildings do not include the out-

of-plane collapse mechanisms, despite the fact that recent earthquakes and research

have demonstrated that out-of-plane mechanisms are one of the most damaging failure

mechanisms for masonry structures.

Finally, Figure 20 (g) and Figure 20 (h) depict how the consideration of horizontal

diaphragms and geometric irregularities is treated in the examined studies. It is possible

to observe that in 62% and 64% of the cases studies do not take into consideration the

variability of horizontal diaphragms or geometric irregularities, respectively.

EUR (2%)

SI (2%)

MK (2%)

CH (5%)

RO (5%)

GR (19%)

IT (29%)

TR (26%) SP (2%)

PT (7%)

PR

38%

EB

62%

URM

38%

RC

62%

49

(a) (b)

(c) (d)

(e) (f)

(g) (h)

Figure 20.Distribution of the examined studies regarding capacity: components for structural assessment (a); classes of building height (b); analysis type (c); model type (d); shear failure (e);

out-of-plane mechanism (f); horizontal diaphragms (g) and geometrical irregularities (h).

H (Yes)

69%

L (No)

31%

H (>3)

38%

M (2,3)

36%

L (1)

26%

H (NLD) 33%M (NLS) 38%

L (NLS-SMM/LS) 28%

H (MDoF) 26%

M (Reduced MDoF) 13%

L (SDoF) 62%

H (Yes)

35%

L (No)

65%

H (Yes)

31%

L (No)

69%

H (Yes) 38%

L (No) 62%

H (Yes)

36%

L (No)

64%

50

Figure 21 (left) shows how the seismic demand is treated amongst the examined

studies. As one can perceive, the reviewed studies have determined the seismic demand

by means of real ground motion records (51%) according to the Eurocode 8

recommendations (at least 7 accelerograms) or by using code-based spectra (49%) in

equal numbers. Moreover, from Figure 21 (right), it is possible to observe that in 85% of

the studies the seismic demand is related to the specific site of the assessed structures.

Nevertheless, one should keep in mind that the remaining 15% mainly adopted real

ground motion records (>7 accelerograms).

Figure 21. Distribution of the examined studies regarding demand: representation of seismic

demand (left), and consideration of site-specific seismic demand input data (right).

With respect to the general aspects of fragility curves, Figure 22 presents the

distribution of the results in what regards the damage states thresholds, IMs, sample

size and sampling method subcategories. Figure 22 (left) depicts how the damage state

thresholds were defined, from which it is possible to observe that approximately 72% of

the examined studies have considered a custom definition for the construction of the

respective fragility curves, against 28% that used pre-defined damage state thresholds.

Moreover, from Figure 22 (centre) it is possible to observe that about 90% of the

examined studies generate the fragility curves as a function of a single IM, which is in

contradiction the recommendations of several authors (Baker and Cornell 2005; Kafali

and Grigoriu 2007; Seyedi et al. 2010; Koutsourelakis 2010).

In Figure 22 (right) is presented the distribution of the size (or scale) of the building

sample considered in each of the examined studies. It can be observed that roughly

56% of these studies considered a sample of several (hundreds) of buildings, 23%

considered a sample composed by few (dozens) of buildings, and 21% have carried out

the analysis considering only one single structure.

Figure 22. Distribution of the examined studies regarding the damage states thresholds definition (left), IMs (centre), and sample size (right).

H (>7 accelerograms)

51%

L (Code-based spectra)

49%

H (Related)

85%

L (Unrelated)

15%

H (Custom)

72%

L (Pre-set)

28%

H (>3)

5%

M (2,3)

5%

L (1)

90%

H (Hundreds)

23%

M (Few)

56%

L (One)

21%

51

Finally, Figure 23 depicts whether uncertainties related to capacity, demand and damage

state thresholds were addressed or not in the examined studies. From Figure 23 (left) it

is possible to observe that 82% of the studies have considered uncertainties in capacity

on their analyses. These can be related to geometrical, mechanical, structural or

modelling parameters. From Figure 23 (centre), one can observe that about 15% of the

examined studies have not considered the uncertainty in the seismic demand. Lastly,

Figure 23 (right) shows that approximately 31% of studies have not considered the

uncertainty in the definition of damage state thresholds.

Figure 23. Distribution of the examined studies regarding the uncertainty in capacity (left), demand (centre), and damage state thresholds (right).

H (Yes)

82%

L (No)

18%

H (Yes)

85%

L (No)

15%

H (Yes)

69%

L (No)

31%

52

53

6. Concluding remarks

This final chapter presents a general overview of the work developed throughout this

report, which was focused on reviewing existing analytical fragility curves suitable for the

European building stock. To conclude, possible future research lines are proposed.

In Chapter 2, a brief overview of the existing approaches – namely analytical, empirical,

based on expert judgement and hybrid – for the derivation of fragility curves was

presented and the main advantages and drawbacks of the most common methodologies

for each type of approach were discussed.

In Chapter 3, particular attention was given to analytical methodologies for deriving

fragility curves. A comprehensive literature review was carried out focusing exclusively

on the methodologies for deriving fragility curves developed specifically for the European

building stock. Additionally, the most relevant factors that influence the reliability of the

reviewed analytical methodologies were carefully addressed and discussed, in order to

provide a clear insight about the existing literature.

Moreover, in Chapter 4, these factors were taken into account for the establishment of

evaluation criteria, aiming to provide valuable support on the selection of the most

appropriate set of fragility curves for a given geographical location and structural

typology.

Finally, in Chapter 5, the main trends of existing fragility curves for the European

building stock were identified, by carrying out a statistical analysis of the evaluation

criteria outputs of all the subcategories described in the previous chapters.

It is important to stress out that in this report only analytical methodologies for deriving

fragility curves were addressed. It would be interesting to extend this study to empirical,

expert judgment elicitation and hybrid approaches. Moreover, it would be equally

interesting to extend this work beyond the European context. The evaluation criteria

herein proposed, though aiming at a qualitative assessment, are a starting point for

further research on how fragility curves should be ideally derived, and a useful guide to

support the decisions regarding the selection of methodologies and approaches for the

generation of fragility curves.

Additionally, given the large number of methodologies that have been developed and

applied in the last decades for developing analytical fragility curves, guidelines for

the future development of these curves are needed. In this way, the selection of

curves by non-expert users will be much easier, promoting the use of seismic risk

assessment in risk mitigation policymaking. In order to improve existing fragility

curves, the following challenges should be further investigated:

The consideration of shear failure should be taken into account when deriving

fragility curves not only in URM buildings but also in RC structures (elements);

The uncertainty in the definition of damage states thresholds should be equally

considered when deriving fragility curves;

Fragility curves should be developed for other building types, such as prefabricated

structures of variable size and use, as tackled by Cassotto et al. (2015);

The impact of aging and progressive deterioration of the material properties caused

by aggressive environmental conditions, as for example the corrosion of RC

structural elements due to chloride penetration, which induce significant variation of

the mechanical properties, should be taken into consideration, as attempted by

Pitilakis et al. (2014);

The effect of soil-structure interaction should be considered in the derivation of

fragility functions for RC buildings, as tackled for instance in Pitilakis et al. (2014);

Existing fragility curves should be validated with empirical and experimental data.

54

55

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List of abbreviations and symbols

ATC, Applied Technology Council

AI, Arias Intensity

CL, Continuous Lognormal Distribution

CN, Continuous Normal Distribution

CSM, Capacity Spectrum Method

DCM, Displacement Coefficient Method

DD, Discrete Distribution

DLS, Damage Limitation States

DPM, Damage Probability Matrix

EB, Existing Building

EDP, Engineering Demand Parameter

EEFIT, Earthquake Engineering Field Investigation Team

EERI, Earthquake Engineering Research Institute

ELSA, European Laboratory for Structural Assessment

EU, European Union

GD, Global Drift

GEM, Global Earthquake Model

GMPE, Ground Motion Prediction Equation

GVC, Global Vulnerability Consortium

IDA, Incremental Dynamic Analysis

IM, Intensity Measure

IN2, Incremental N2 Method

ISD, Inter-storey Drift

JRC, Joint Research Centre

LHS, Latin Hypercube Sampling

LS, Linear Static

MDoF, Multi Degree of Freedom

MFA, Maximum Floor Acceleration

MMI, Modified-Mercalli Intensity

MPR, Maximum Plastic end Rotation of beams

Mw, Moment magnitude

NC, Near Collapse

NLD, Non-linear Dynamic Analysis

NLS, Non-linear Static Analysis

PR, Prototype (building)

RC, Reinforce Concrete

RD, Roof Displacement

rrup, rupture distance

SAPA, Static Adaptive Pushover Analysis

Sa(T), Spectral acceleration

SD, Significant Damage

Sd(T), Spectral displacement

SDoF, Single Degree of Freedom

SMM, Simplified Mechanical Methods

Sv(T), Spectral velocity

TD, Top Displacement

UD, Ultimate Displacement

URM, Unreinforced Masonry

ULS, Ultimate Limit States

VD, Median base shear demand given the PGA

VLS,i, Median base shear capacity at the i th limit state

vs,30, Average shear-wave velocity between 0 and 30 m

66

67

List of figures

Figure 1. Flow diagram for deriving analytical fragility curves. .................................... 6

Figure 2. Distribution of the examined analytical fragility assessment methodologies by

country: Italy (12); Turkey (11); Greece (8); Portugal (3); Romania (2); Switzerland

(2); former Yugoslav Republic of Macedonia (1); Slovenia (1) and Spain (1). ............. 12

Figure 3. Main components and phases considered in analytical fragility assessment

methodologies and associated uncertainties. .......................................................... 13

Figure 4. Example of a masonry structural wall system (left) and the corresponding

three-dimensional assemblage of all the structural walls (right), modelled through a

macro-element approach using the 3Muri® software (Ferreira et al. 2015). ................ 14

Figure 5. Examples of reinforced concrete moment-resisting frame (left) and dual frame-

wall structural systems (right) (Dumova-Jovanoska 2000). ...................................... 15

Figure 6. Numerical representation of infill masonry walls through equivalent diagonal

strut model (Amato et al. 2008). ........................................................................... 16

Figure 7. Comparison between fragility curves for 4-storey RC buildings with and without

considering masonry infill walls in structural modelling (D’Ayala and Meslem 2012). .... 17

Figure 8. IDA curve with the identification of yielding and collapse points (Kirçil and Polat

2006). ............................................................................................................... 18

Figure 9. Example of (bilinear) capacity curves derived from conventional pushover

analysis (left) and those obtained from using a displacement-based adaptive pushover

(right), developed by Ferreira et al. (2015) and Silva et al. (2013), respectively. ........ 20

Figure 10. Out-of-plane failure mechanisms of the FaMIVE method developed by D’Ayala

and Speranza (2003). .......................................................................................... 22

Figure 11. Flowchart of the DBELA method (Silva et al. 2013). ................................. 23

Figure 12. Flowchart of the SP-BELA method (Borzi et al. 2008b). ............................. 24

Figure 13. Vulnerability curves for 4-storey buildings using the SP-BELA and DBELA

methodologies for Limit State 2 (left) and Limit State 3 (right) conditions (Borzi et al.

2008b). ............................................................................................................. 25

Figure 14. Comparison of capacity curves obtained by the three-dimensional model with

those obtained by superposition of two-dimensional models (D’Ayala and Meslem 2013).

......................................................................................................................... 26

Figure 15. Configuration and dimensions of typical four-storey irregularly infilled RC

frame building (Kappos and Panagopoulos 2009). ................................................... 27

Figure 16. Existing techniques for assessing the out-of-plane behaviour of unreinforced

masonry structures (Ferreira 2015). ...................................................................... 29

Figure 17. Continuous fragility curves for lognormal (left) and normal (centre) functions,

and discrete fragility curves (right), developed by Barbat et al. (2006), Ceran (2010) and

D’Ayala et al. (1997), respectively. ........................................................................ 33

Figure 18. Distribution of the examined methodologies over the years. ...................... 49

Figure 19. Distribution of the examined methodologies by country (left), building type

used in the analysis (centre), and structural material (right). ................................... 50

Figure 20. Distribution of the examined methodologies regarding capacity: components

for structural assessment (a); classes of building height (b); analysis type (c); model

type (d); shear failure (e); out-of-plane mechanism (f); horizontal diaphragms (g) and

geometrical irregularities (h). ............................................................................... 51

68

Figure 21. Distribution of the examined methodologies regarding demand:

representation of seismic demand (left), and consideration of site-specific seismic

demand input data (right). ................................................................................... 52

Figure 22. Distribution of the examined methodologies regarding the damage states

thresholds definition (a), IMs (b), sample size (c), and sampling method (d) .............. 53

Figure 23. Distribution of the examined methodologies regarding the uncertainty in

capacity (left), demand (centre), and damage state thresholds (right) ....................... 53

69

List of tables

Table 1. Main features of the considered methodologies for deriving analytical fragility

curves. .............................................................................................................. 37

Table 2. Qualitative assessment criteria and respective rating. .................................. 41

Table 3. Application of the qualitative assessment criteria on the reviewed fragility

curves. .............................................................................................................. 45

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doi:10.2788/586263

ISBN 978-92-79-54136-0

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