encrypted d3.1 syner-g rc final - vcei abstract in the syner-g project, work package 3 is concerned...

D 3.1

DELIVERABLE

PROJECT INFORMATION

Project Title: Systemic Seismic Vulnerability and Risk Analysis for

Buildings, Lifeline Networks and Infrastructures Safety Gain

Acronym: SYNER-G

Project N°: 244061

Call N°: FP7-ENV-2009-1

Project start: 01 November 2009

Duration: 36 months

DELIVERABLE INFORMATION

Deliverable Title: D3.1 - Fragility functions for common RC building types in

Europe

Date of issue: March 2011

Work Package: WP3 – Fragility Functions of Elements at Risk

Deliverable/Task Leader: UPAV

REVISION: Draft

Project Coordinator:

Institution:

e-mail:

fax:

telephone:

Prof.KyriazisPitilakis

Aristotle University of Thessaloniki

[email protected]

+ 30 2310 995619

+ 30 2310 995693

i

Abstract

In the Syner-G project, Work Package 3 is concerned with the identification of fragility

functions for elements and systems. Specifically, Task 3.1 aims to identify the main

typologies of buildings in Europe and review existing fragility functions, to compare these

functions amongst themselves and eventually compare them with new functions developed

under the auspices of Syner-G. Hence, this task is mainly comprised of a literature review

which has led to a collection of existing fragility functions and the identification of categories

for grouping buildings (a taxonomy) and for harmonising different intensity measures and

limit states. The main output of this deliverable that will be used in Syner-G is a set of

fragility functions (with associated uncertainty) for the main reinforced concrete typologies

present in the case study regions and a tool able to store, harmonize and compare the

different curves.

Keywords: fragility, European buildings, taxonomy, reinforced concrete, harmonisation

iii

Acknowledgments

The research leading to these results has received funding from the European Community's

Seventh Framework Programme [FP7/2007-2013] under grant agreement n° 244061.

v

Deliverable Contributors

University of Pavia Helen Crowley

Miriam Colombi

Vitor Silva

Naveed Ahmad

University of Patras Michael Fardis

Georgios Tsionis

Alexandra Papailia

Joint Research Centre Fabio Taucer

Ufuk Hancilar

Middle East Technical University Ahmet Yakut

M. Altug Erberik

vii

Table of Contents

Abstract ........................................................................................................................................ i

Acknowledgments ..................................................................................................................... iii

Deliverable Contributors ............................................................................................................ v

Table of Contents...................................................................................................................... vii

List of Figures ............................................................................................................................ ix

List of Tables .............................................................................................................................. xi

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

2 Existing Fragility Functions for European RC Buildings................................................ 3

2.1 DEFINITION OF FRAGILITY ....................................................................................... 3

2.2 REVIEW FORMS FOR FRAGILITY............................................................................. 3

2.3 METHODOLOGIES ..................................................................................................... 5

2.4 INTENSITY MEASURE TYPES (IMT) ......................................................................... 7

2.5 LIMIT STATES............................................................................................................. 9

3 Development of Fragility Functions for European RC Buildings................................. 11

3.1 UPAV METHOD......................................................................................................... 11

3.1.1 Mechanical models for RC buildings ............................................................. 11

3.1.2 Derivation of analytical fragility functions....................................................... 13

3.1.3 Application to the Case Study Buildings ........................................................ 16

3.1.4 Derivation of analytical fragility functions....................................................... 24

3.2 UPAT METHOD......................................................................................................... 25

3.2.1 Introduction .................................................................................................... 25

3.2.2 Building typologies – the base case .............................................................. 25

3.2.3 Damage scale, damage measure and intensity measures............................ 32

3.2.4 Design and vulnerability assessment ............................................................ 32

3.2.5 Fragility Functions.......................................................................................... 35

3.2.6 Parametric studies beyond the base case..................................................... 37

3.2.7 Concluding remarks....................................................................................... 40

4 Taxonomy of European Building Typologies ................................................................ 43

4.1 EXISTING TAXONOMIES ......................................................................................... 43

4.1.1 PAGER-STR.................................................................................................. 43

4.1.2 RISK-UE ........................................................................................................ 46

viii

4.2 PROPOSED TAXONOMY ......................................................................................... 49

5 Harmonisation of European Fragility Functions ........................................................... 53

5.1 INTENSITY MEASURE TYPE ................................................................................... 54

5.1.1 Macroseismic Intensity to PGA...................................................................... 54

5.1.2 Spectral acceleration to PGA......................................................................... 57

5.1.3 Spectral displacement to PGA....................................................................... 60

5.1.4 PGV to PGA................................................................................................... 61

5.2 LIMIT STATES........................................................................................................... 61

5.3 BUILDING TYPOLOGY ............................................................................................. 62

6 Comparison of Fragility Functions for European RC Buildings .................................. 67

6.1 COMPARISON OF FRAGILITY FUNCTIONS........................................................... 67

6.1.1 Calculation of mean and variability in fragility functions: first approach......... 68

6.1.2 Calculation of mean and variability in fragility functions: second approach... 69

6.2 EXAMPLES OF PROPOSED FRAGILITIES ............................................................. 71

6.2.1 Reinforced concrete with moment resisting frame buildings, mid rise ........... 71

6.2.2 Reinforced concrete with moment resisting frame buildings, mid rise,

seismically designed...................................................................................... 73


seismically designed, bare............................................................................. 75


seismically designed, bare, non ductile ......................................................... 77

7 Conclusions ...................................................................................................................... 81

References................................................................................................................................. 83

Appendix A ................................................................................................................................ 87

A Review forms .................................................................................................................... 87

Appendix B .............................................................................................................................. 199

B Tutorial............................................................................................................................. 199

ix

List of Figures

Fig. 1.1 Syner-G Fragility Function Manager tool: main window. ........................................... 1

Fig. 2.1 Examples of (a) vulnerability function and (b) fragility function .................................. 3

Fig. 2.2 Empty fragility function review form ........................................................................... 4

Fig. 2.3 Limit States and Damage States ............................................................................... 9

Fig. 3.1 Nonlinear static SDOF idealization, mechanical model, for RC building class ........ 12

Fig. 3.2 Flow chart for the derivation of displacement-based fragility functions. Global

Mechanism. ....................................................................................................... 15

Fig. 3.3 Mean of the acceleration spectra considered for NLTHA and comparison with EC8

Type I-C soil spectrum....................................................................................... 19

Fig. 3.4 (a) Period coefficient for low rise bare frame using the analytical drift limits, nd (b)

experimental drift limit (for light damage limit state exceedance) proposed by

Rossetto and Elnashai (2003) for European bare frames ................................. 23

Fig. 3.5 Geometry of 8-storey (a), 5-storey (b) and 2-storey (c) frames of the base case ... 28

Fig. 3.6 Plan of dual building................................................................................................. 29

Fig. 5.1 Harmonization of Fragility Curves – Syner-G tool.................................................... 53

Fig. 5.2 Settings (IMT conversions) – Syner-G Fragility Function Manager ......................... 54

Fig. 5.3 IBC 2006 standardized spectral shape .................................................................... 58

Fig. 5.4 (a) Original Kappos et al. (2006), RC1-HR-HC (b) harmonized Kappos et al. (2006),

RC1-HR-HC....................................................................................................... 61

Fig. 5.5 Settings (Damage scale conversions) – Syner-G Fragility Function Manager......... 62

Fig. 5.6 (a) Original Kappos et al. (2006) (b) harmonized Kappos et al. (2006) ................... 62

Fig. 5.7 Flow chart for a Reinforced Concrete with Moment Resisting Frame building class.

In the blue brackets the number of fragility functions sets concerning the project

is reported.......................................................................................................... 64

Fig. 5.8 Flow chart for a Reinforced Concrete with Dual System building class. In the blue

brackets the number of fragility functions sets concerning the project is reported.

........................................................................................................................... 65

Fig. 6.1(a) Yield limit state and (b) collapse limit state harmonised fragility functions for a

reinforced concrete with moment resisting frame buildings, mid rise model

building type ...................................................................................................... 67

Fig. 6.2 Dispersion of probability of exceedance for a given IML ......................................... 68

Fig. 6.3 Comparison of several probabilistic distributions with the observed data................ 68

Fig. 6.4 Mean, median, 10% and 90% confidence intervals for (a) limit state yielding curve

and (b) limit state collapse curve ....................................................................... 69

x

Fig. 6.5(a) Histogram of median values (b) histogram of dispersion values (c) correlation

between median and dispersion and (d) individual and mean ± one standard

deviation fragilities [from Bradley (2010)] .......................................................... 70

Fig. 6.6 Correlation between the individual fragility functions parameters ............................ 71

Fig. 6.7 (a) Yield limit state and (b) collapse limit state harmonised fragility functions for a


building type ...................................................................................................... 72

Fig. 6.8 Mean curve for (a) limit state yielding curve and (b) limit state collapse curve for


building type ...................................................................................................... 72


reinforced concrete with moment resisting frame buildings, mid rise, seismically

designed model building type............................................................................ 74



designed model building type............................................................................ 74



designed, bare model building type................................................................... 76



designed, bare model building type................................................................... 76



designed, bare, non ductile model building type ............................................... 78



designed, bare, non ductile model building type ............................................... 78

xi

List of Tables

Table 2.1 List of references considered and corresponding methods for RC buildings.......... 6

Table 2.2 List of references considered and corresponding IMT for RC buildings ................. 8

Table 2.3 Comparison of existing damage scales with the HRC damage scale [adapted from

Rossetto and Elnashai, 2003]............................................................................ 10

Table 3.1 Building typology matrix considered in the methodology ...................................... 16

Table 3.2 Structural properties defined to generate case study structural models for RC

buildings ............................................................................................................ 18

Table 3.3 Details of the accelerograms used in the present study for NLTHA ..................... 19

Table 3.4Period coefficient for RC building stock of Euro-Mediterranean region ................. 22

Table 3.5 Values of design acceleration for different ductility levels..................................... 26

Table 3.6 Beam height, hb, and column height, hc, in 2-storey ductile frames of the base case

........................................................................................................................... 29


........................................................................................................................... 29


........................................................................................................................... 30

Table 3.9 Column height, hc, beam height, hb, and beam width, bb, in nonductile buildings of

the base case .................................................................................................... 30

Table 3.10 Geometry of 5-storey ductile dual buildings of the base case ............................ 31

Table 3.11 Geometry of 8-storey ductile dual buildings of the base case ............................ 31

Table 3.12 Geometry of nonductile dual buildings of the base case .................................... 32

Table 3.13 Coefficients of variation....................................................................................... 37

Table 3.14 Properties of 2-storey frame buildings with lb = 4.0m.......................................... 38




Table 4.1 PAGER-STR Taxonomy (Jaiswal and Wald, 2008 – Version 1.4 )....................... 44

Table 4.2 RISK-UE Taxonomy (RISK-UE, 2001-2004) ........................................................ 47

Table 4.3 Syner-G Taxonomy............................................................................................... 49

Table 5.1 Datasets collected (adapted from Cua et al., 2010).............................................. 57

Table 5.2 NEHRP site classification (FEMA, 1997a) as applied by IBC-2006 (ICC 2006) ... 59

Table 5.3 Site amplification factors as given in IBC-2006 (ICC 2006) .................................. 60

Table 6.1 Log likelihood parameter per probabilistic distribution .......................................... 69

xii

Table 6.2 Correlation coefficient matrix ................................................................................ 70

Table 6.3 Mean and CoV of the lognormal fragility parameters for reinforced concrete with

moment resisting frame buildings, mid rise model building type ....................... 73

Table 6.4 Correlation coefficient matrix for reinforced concrete with moment resisting frame

buildings, mid rise model building type.............................................................. 73


moment resisting frame buildings, mid rise, seismically designed model building

type.................................................................................................................... 75


buildings, mid rise, seismically designed model building type........................... 75


moment resisting frame buildings, mid rise, seismically designed, bare model

building type ...................................................................................................... 77


buildings, mid rise, seismically designed, bare model building type.................. 77


moment resisting frame buildings, mid rise, seismically designed, bare non

ductile model building type ................................................................................ 79


buildings, mid rise, seismically designed, bare non ductile model building type 79

Introduction

1

1 Introduction

In the Syner-G project, Work Package 3 is concerned with the identification of fragility

functions for elements and systems. Specifically, Task 3.1 aims to identify the main

typologies of buildings in Europe and review existing fragility functions (focusing on

reinforced concrete and masonry buildings), to compare these functions amongst

themselves and eventually compare them with new functions developed under the auspices

of Syner-G. Hence, this task is mainly comprised of a literature review which has led to a

collection of existing fragility functions (as reported in Appendix A for European reinforced

concrete buildings) and the identification of categories for grouping buildings (a taxonomy)

and for harmonising different intensity measures and limit states. The main output of this

deliverable that will be used in Syner-G is a set of fragility functions (with associated

uncertainty) for the main reinforced concrete typologies present in the case study regions.

The first step involves the identification and the storage of the existing fragility function sets

throughout Europe. An effort in collecting the existing studies concerning fragility functions

has been carried out, together with an effort in constructing a tool able to store and process

the fragility function sets that were collected. The Syner-G Fragility Function Manager tool

has thus been created and it is able to store, visualize and manage a large number of

fragility functions sets. In Appendix B the tutorial of the Syner-G Fragility Function Manager

is reported to facilitate the use of this tool.

Fig. 1.1 Syner-G Fragility Function Manager tool: main window.

Introduction

2

Within this project, a different approach for categorizing and classifying buildings and thus a

new taxonomy, called the Syner-G taxonomy, has been proposed in order to homogenize

the existing model building types. Subsequently, it has been possible to develop the next

step of this task which is the comparison amongst existing fragility functions. Two different

modules have thus been developed in the tool: the Harmonize module and the Compare

module. The former function allows one to harmonize the curves using a target intensity

measure type (which has been selected as PGA herein) and a number of limit states of

reference (which have been selected as yielding and collapse herein). After the

harmonization, the Compare function can be used to plot together and to compare different

curves, and to calculate the mean and dispersion of the parameters of the curves. It should

be noted that the Filter button allows the user to first select the building types that are

feasibly comparable, in terms of fragility. Finally, new approaches proposed by UPAV and

UPAT (University of Pavia and University of Patras, respectively) have been implemented

within this task for the creation of analytical fragility functions for reinforced concrete

buildings in Europe. This deliverable includes a description of these methodologies and the

derived fragility functions.

Chapter 2 of this deliverable describes briefly the methodologies, the intensity measure

types and the limit states that have been found in the reviewed fragility studies. Chapter 3

explains the methodologies developed within this project by UPAV and UPAT for deriving

fragility functions for reinforced concrete buildings. Chapter 4 presents an overview of some

existing taxonomies used to describe different building classes, and the taxonomy proposed

within this project to identify European reinforced concrete and masonry structures. Chapter

5 and Chapter 6 relate specifically to the Syner-G Fragility Function Manager. In particular,

the procedures to harmonize and to compare fragility curves for a given building typology are

shown.

Existing Fragility Functions for European RC Buildings

3

2 Existing Fragility Functions for European RC

Buildings

2.1 DEFINITION OF FRAGILITY

The vulnerable conditions of a building can be described using vulnerability functions or

fragility functions.

Vulnerability functions describe the probability of losses (such as social losses or economic

losses) given a level of ground shaking, whereas fragility functions describe the probability of

exceeding different limit states (such as damage or injury levels) given a level of ground

shaking. In the following figure, a vulnerability function that relates the level of ground

shaking with the mean damage ratio (i.e. ratio of cost of repair to cost of replacement) and a

fragility function that relates the level of ground motion with the probability of exceeding three

limit states are both shown.

(a) (b)

Fig. 2.1 Examples of (a) vulnerability function and (b) fragility function

Vulnerability functions can be derived from fragility functions using consequence functions;

these functions describe the probability of loss given a level or performance (e.g. collapse).

This deliverable deals exclusively with fragility functions, as the consideration of

consequence functions is dealt with in WP4 of Syner-G.

2.2 REVIEW FORMS FOR FRAGILITY

In Task 3.1, a large number of fragility functions have been collected and stored into a

dynamic tool (the Syner-G Fragility Function Manager) for which a detailed tutorial is

provided in Appendix B. For each fragility study that has been considered, a review form has

been filled in with a brief summary of the functions.

The form is comprised of different fields:

o Reference: reference papers, documents, deliverables;


4

o Region of applicability: this region represents the reference place for which structures

and buildings have been analysed and fragility functions have been developed;

o Element at risk: list of the elements at risk considered by the fragility functions (i.e.,

buildings, bridges, lifelines, infrastructures, etc.);

o Typology of the element at risk considered: based on the original description provided

in the references (i.e. RC – low rise – high code, masonry – simple stone, steel, etc.);

o Syner-G Taxonomy: the description of the element at risk using the taxonomy

proposed within this project;

o Sample Data: description of the data (i.e., structures, accelerograms, etc.) that are

considered in the analyses to estimate the fragility functions;

o Intensity Measure Type: the reference ground motion parameter against which the

probability of exceedance of a given limit state is plotted (i.e. Macroseismic Intensity,

PGV, PGA, Spectral displacement, etc.);

o Fragility Function Parameters: description of the parameters used to define the

fragility functions (e.g., mean and standard deviation of a particular distribution);

o Figures: plot(s) of the fragility functions created by the Syner-G Fragility Function

Manager;

o Uncertainty: description of the sources of uncertainty that have been taken into

account for the estimation of the fragility curves(i.e., the variability in the properties of

the materials, the variability of the geometry of the structures, record-to-record

variability etc.);

o Comments: notes and comments on the analysed paper.

In Appendix A, all the compiled review forms are presented, whilst an empty form is shown

in the following figure.

Fig. 2.2 Empty fragility function review form


5

2.3 METHODOLOGIES

Different methods can be used to estimate a fragility function. It is possible to classify them

into four generic groups: empirical, expert opinion-based, analytical and hybrid. An

“unknown” class has been added due to the fact that it could be unclear from the reference

material the way in which the fragility functions have been estimated.

Empirical method. Empirical fragility curves are constructed based on statistics of observed

damage from past earthquakes, such as from data collected by post-earthquake surveys.

The use of observational data is the most realistic way to model fragility as all the variability

in the structural capacity of the exposed buildings and in the soil-structure interaction is

taken into account. Notwithstanding that, the incompleteness and deficiencies in the survey

forms and the errors produced in the computerisation of the data might lead to a notable

reduction of the size of the database during post-processing. Furthermore, it is often the

case that the undamaged buildings are not recorded after the earthquake and thus there is a

large uncertainty in the total number of buildings to be used in the derivation of the functions.

Moreover, these curves have the shortcoming of being derived for a specific region, they can

only be derived for buildings that have experienced damage from earthquakes and often

there is a large uncertainty in the level of ground shaking to which the buildings have been

subjected.

Expert opinion-based method. Expert opinion-based fragility curves depend on judgment

and information of experts. These experts are asked to provide an estimate of the mean loss

or probability of damage for different types of structures and several levels of ground

shaking. This method is not affected by the limitations regarding the quantity and quality of

structural damage data and statistics. However, the results are strictly correlated to the

individual experience of the experts consulted.

Analytical method. Analytical fragility curves are constructed starting from the statistical

elaboration of damage distributions that are simulated from analyses of structural models

under increasing earthquake intensity. It is worth noting that the application of the analytical

methods might be limited by the computational effort of the analyses. To reduce the

computational effort, simplified analytical models are often used, to allow for a large number

of analyses to be undertaken, such that the uncertainties can be adequately modelled.

Nevertheless, the variability in the definition of the structural and non-structural elements of

the model may significantly affect the analysis results. In fact the similarity between the

model and the real structure, which strongly influences the reliability of the results, is

dependent on the modelling capabilities. Usually, it is possible to divide analytical models

into two sub-classes: nonlinear static analysis and nonlinear dynamic analysis (and further

sub-classes could be created by separating plastic-hinge from fibre element-based models).

The first approach applies forces to a structural model that includes non-linear properties of

the materials and the total force is plotted against the displacement of the structure to define

a capacity curve. The structural capacity is often defined using an equivalent single degree

of freedom (SDOF) system. For what concerns the seismic demand, it is usually represented

as a demand curve in the form of acceleration and/or displacement response spectrum. The

second approach uses a detailed structural model that is subjected to ground motion

recordings (accelerograms). This kind of analysis is time consuming but it is closer to reality

and allows the influence of the record-to-record variability on the structural response to be

accounted for. However, this method can be sensitive to the number and characteristics of

the selected accelerograms.


6

Hybrid method. Hybrid fragility curves are based on the combination of different methods for

damage prediction. Often, the aim is to compensate for the lack of observational data, the

deficiencies of the structural models and the subjectivity in expert opinion data.

In the following table, the methods associated to each reference study that has been

considered in this deliverable are shown.

Table 2.1 List of references considered and corresponding methods for RC buildings

Method Reference

‚ LESSLOSS (2005) (Istanbul Case Study)

‚ Liel and Lynch (2009)

‚ Nuti et al. (1998)

‚ Rota et al. (2008)

Empirical

‚ Sarabandi et al. (2004)

Expert opinion-based ‚ Kostov et al. (2004)

‚ Borzi et al. (2007)

‚ Borzi et al. (2008a)

‚ Borzi et al. (2008)

‚ LESSLOSS (2005) (Istanbul Case Study and Lisbon Case Study)

‚ Polese et al. (2008)

‚ RISK-UE (2003) (CIMNE and UTCB approach)

‚ Vacareanu et al. (2004)

Analytical – Nonlinear Static

‚ Varga et al. (2010)

‚ Tsionis et al. (2011)

‚ Ahmad et al. (2011)

‚ Akkar et al. (2005)

‚ Dumova-Jovanoska(2000)

‚ Erberik and Elnashai(2004)

‚ Erberik(2008)

‚ Hancilar et al. (2006)


‚ Jeong and Elnashai(2007)

‚ Kircil and Polat(2006)

‚ Kwon and Elnashai(2007)

‚ Ozmen et al. (2010)

‚ RISK-UE (2003) (IZIIS approach)

Analytical – Nonlinear Dynamic

‚ Rossetto and Elnashai(2005)

‚ Kappos et al (2006) Hybrid

‚ RISK-UE (2003) (AUTH, IZIIS and UTCB approach)

Unknown ‚ Tahiri and Milutinovic(2010)


7

2.4 INTENSITY MEASURE TYPES (IMT)

As described in Section 2.1, the vulnerable conditions of a structure are defined for a certain

level of ground shaking. An intensity measure describes the severity of earthquake shaking.

In the reviewed papers, different Intensity Measure Types (IMTs) have been used to define

the level of ground shaking. It is possible to group these IMTs into two main classes:

empirical intensity measure types and instrumental intensity measure types.

With regards to the empirical IMTs, different macroseismic intensity scales could be used to

identify the observed effects of ground shaking over a limited area. A macroseismic intensity

scale is a qualitative scale given in terms of a description of the earthquake effects on the

earth’s surface, people and structures, where each step of the scale is usually expressed in

Roman numerals. There are several intensity levels in a scale that usually go from ‘not felt’

to ‘destruction’. The description of the different levels varies according to the macroseismic

intensity scale used. One of the advantages of this type of measure is that it does not need

any specific instrument to be measured and this is the reason why it is one of the oldest

tools to describe earthquake shaking. Data is gathered from people that have felt the

earthquake and subsequently an intensity value is assigned to the location. The nearer the

location is to the epicentre the higher is the value of the level assigned. In the reviewed

papers, fragility functions for RC buildings are estimated using the following different types of

macroseismic intensity:

o MCS: Mercalli-Cancani-SiebergIntensity Scale. This scale was proposed in 1902 as a

development of the Mercalli Scale provided between the end of the nineteenth

century and the beginning of the twentieth century. It was expanded to twelve

degrees instead of ten. This scale goes from I to XII where I means ‘Instrumental’,

and XII means ‘Cataclysmic’;

o MMI: Modified Mercalli Intensity Scale. The MCS scale was later improved (mid

twentieth century) and slightly modified by Richter and the scale is known today as

the Modified Mercalli Intensity Scale. It is composed of twelve degrees;

o MSK81: Medvedev-Sponheuer-Karnik Intensity Scale. This scale was originally

proposed in 1964 based on the experience derived from the application of MMI scale.

Then, minor modifications were made in the mid-1970s and early 1980s. This scale

goes from I to XII where I means ‘No perceptible’, and XII means ‘Very catastrophic’.

For what concerns the instrumental IMTs, the severity of ground shaking can be expressed

as an analytical value measured by an instrument or computed by analytical analysis of

recorded accelerograms. The estimation of the severity of the earthquake is no longer

subjective. In the reviewed papers, several instrumental IMTs are used to link the probability

of exceeding different limit states to the ground shaking:

o PGA: peak ground acceleration during an earthquake;

o PGV: peak ground velocity during an earthquake;

o Sa(Ty): spectral acceleration at the elastic period Ty of the considered structure;

o Sd(Ty) and Sd(TLS): spectral displacement at the elastic period (Ty) of the considered

structure or at the inelastic period (TLS) corresponding to a specific limit state,

respectively;

o RMS: root mean square of the acceleration;


8

o Roof Drift Ratio: represents the ratio of the maximum displacement response at the

roof and the height of the building.

In the following table, the IMTs used in each reference study that has been considered in

this deliverable are shown:

Table 2.2 List of references considered and corresponding IMT for RC buildings

Intensity Measure Type Reference

‚ Dumova-Jovanoska(2000) MMI


MCS ‚ Nuti et al. (1998)

MSK81 ‚ LESSLOSS (2005) – Istanbul Case Study

‚ Borzi et al (2007)

‚ Borzi et al (2008a)

‚ Borzi et al (2008)


‚ Jeong and Elnashai(2007)

‚ Kappos et al. (2006)


‚ Kostov et al. (2004)

‚ Kwon and Elnashai(2006)

‚ Liel and Lynch (2009)

‚ Ozmen et al. (2010)

‚ RISK-UE (2003) (AUTH approach)

PGA

‚ Rota et al. (2008)

‚ Ahmad et al (2011)

‚ Tsionis et al. (2011)

‚ Akkar et al. (2005) PGV

‚ Erberik (2008)

Sa(Ty) ‚ Kircil and Polat(2006)

‚ Erberik and Elnashai(2004)


‚ Kappos et al. (2006)


‚ LESSLOSS (2005) – Istanbul Case

Sd(Ty)

‚ Rossetto and Elnashai(2005)

‚ LESSLOSS (2005) – Lisbon Case Study

‚ Polese et al. (2008)

‚ RISK-UE (2003) (CIMNE and IZIIS and UTCB approach)


‚ Tahiri and Milutinovic(2010)

‚ Vacareanu et al. (2004)

Sd(TLS)

‚ Vargas et al. (2010)


9

Intensity Measure Type Reference

RMS ‚ Sarabandi et al. (2004)

Roof Drift Ratio ‚ Sarabandi et al. (2004)

2.5 LIMIT STATES

In seismic risk assessment, the performance levels of a building can be defined through

damage thresholds called limit states. A limit state defines the threshold between different

damage conditions, whereas the damage state defines the damage conditions themselves.

For instance, if the performance of a building is described by two limit states (Limit State 1

and Limit State 2), there will be three damage states (Damage State 1, Damage State 2 and

Damage State 3).

Methods for deriving fragility curves generally model the damage on a discrete damage

scale. In empirical procedures, the scale is used in reconnaissance efforts to produce post-

earthquake damage statistics, whereas in analytical procedures the scale is related to limit

state mechanical properties of the buildings, such as displacement capacity. For example,

the displacement capacity can be related to damage conditions that are identifiable through

limit states. In the following figure the difference between Damage States and Limit States is

represented.

Fig. 2.3 Limit States and Damage States

The number of Damage States (and consequently the number of Limit States) depends on

the damage state scale used. Some of the most frequently damage scales used are: HCR

(Rossetto and Elnashai, 2003), HAZUS99 (FEMA, 1999), Vision2000 (SEAOC,1995),

EMS98 (Grunthal, 1998), ATC-13 (ATC,1985). A summary and qualitative comparison of

some of the damage scales used in the selected fragility functions with the Homogenised

Reinforced Concrete (HRC) damage scale (Rossetto and Elnashai, 2003) is presented in

Table 2.3.

Lateral

Load Damage

State 1

Limit State 1

Displacement

Damage

State 2

Damage

State 3

Limit State 2


10

Depending on the methodology used to compute the fragility functions and depending on the

choices of the authors, different scales with different limit states/damage states can be

adopted. It should be noted that there are some studies that do not refer to any of the

damage scales reported in Table 2.3 but they follow specific damage state scales developed

by the authors.

Table 2.3 Comparison of existing damage scales with the HRC damage scale [adapted

from Rossetto and Elnashai, 2003]

HRC HAZUS99 Vision 2000 EMS98 ATC-13

None No damage

Slight Slight Fully operational

Grade 1

Light Light

Slight damage

Grade 2 Operational

Moderate

Moderate Moderate damage Life Safe

Grade 3

Heavy

Extensive Near Collapse

Partial Collapse

Extensive damage

Collapse

Grade 4 Major

Collapse Collapse

Development of Fragility Functions for European RC Buildings

11

3 Development of Fragility Functions for

European RC Buildings

3.1 UPAV METHOD

The UPAV team have focused on the development of analytical fragility functions for classes

of reinforced concrete buildings (Ahmad et al., 2011). The Displacement-Based method for

Earthquake Loss Assessment (DBELA) has been used. The DBELA methodology is a

nonlinear static analytical displacement-based methodology for seismic risk assessment and

loss estimation of buildings and building aggregates on a regional scale. The methodology

makes use of the existing displacement based approaches, developed mainly for the design

and assessment of structures. The displacement-based method is originally proposed and

developed elsewhere for both RC and masonry buildings (Calvi, 1999; Glaister and Pinho,

2003; Restrepo-Velez and Magenes, 2004; Crowley et al., 2004; Borziet al., 2008a-b).

However, it is further developed to derive fragility functions for Euro-Mediterranean 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), in a probabilistic way; considering the variability in the geometrical

and material properties of the buildings as well as the variability in the seismic demand.

3.1.1 Mechanical models for RC buildings

The mechanical model simulates the response of the structural system in terms of its

displacement capacity, energy dissipation and secant vibration period for seismic

assessment.

For what concerns RC buildings, they are assessed using a global response mechanism

(beam-sway or column-sway) of structural system. The SDOF system derivation for each

class of seismic response mechanism are discussed as follow.

The seismic response of bare/infilled RC frame and wall buildings can be assessed

considering a global response mechanism and an in-plane mechanical model. However,

local out-of-plane bulging and failure of infill walls may occur which, nevertheless, can be

associated with the damage scale used to define the global seismic response of structural

system (Rossetto and Elnashai, 2003).

An equivalent SDOF system (Fig. 3.1) is used to simulate the global response of buildings in

terms of displacement capacity, viscous damping and secant vibration period at different

damage states for performance evaluation given an earthquake event, represented using a

5% damped displacement response spectrum.


12

Fig. 3.1 Nonlinear static SDOF idealization, mechanical model, for RC building class

where:

o HT: total structure’s height;

o hi: ith floor height;

o Di: lateral displacement;

o mi: ith floor mass for a given deformed shape of building;

o Me and He: mass and height of the SDOF system;

o Fy and FLS: equivalent yield and ultimate limit state displacement that represents the

displacement capacity of the actual structures at the centre of seismic force for a

specified deformed shape;

o Ki and Ksec: initial pre-yield stiffness and the secant stiffness;

o Fy: yielding force;

o c: post-yield stiffness ratio that can be positive or negative to represent hardening or

softening structures, respectively.

It is worth mentioning that the force-displacement response of structural systems is

represented in terms of equivalent lateral strength and equivalent displacement capacity.

The lateral strength of structures is normalized by the seismic mass participation (i.e.

equivalent mass, where equivalent mass is obtained by normalizing the floor masses over

the deformed shape of the buildings). The deformed shape of the structural system is

obtained through nonlinear time history analysis of structural models with the consideration

of record-to-record variability.

For seismic assessment, the mechanical model is completely defined by the secant vibration

period, limit state displacement capacity and energy dissipation characteristics of structures

represented as viscous damping. These components can be calculated by the following

expressions:

""TLS ?Ty

o1-co /c

(1.1)

HT

hi

mi Fi

He

Me F

Fy

Ki Ksec

Fy FLS

c

F


13

Ty ? a © e( ‒gu ) ©HT

b (1.2)

""FLS ?sy k1 HT - (sLS /sy )k2 hs (1.3)

zeq ?zel -zhyst (1.4)

""zhyst ?C

o / 1or

Ã"

Å"Ä"

Ô

Ö (1.5)

where:

o TLS and Ty: limit state secant vibration period and the yield vibration period;

o a and b: coefficients that have different values according to the structural system;

o j: logarithmic standard deviation, which is the measure of period variability for a

given class due to the uncertainties in material and geometric properties and record-

to-record variability;

o i: number of standard deviations above/below mean value;

o µ = ÄLS/Äy: limit state ductility;

o ÄyandÄLS: yield displacement capacity and specified limit state displacement capacity;

o しy and しLS: interstorey yield drift and limit state interstorey drift, which can be defined

for different structural systems using analytical (based on concrete and steel strain

limits which are used to obtain section curvature, structural member’s chord rotation

and interstorey drifts) and/or experimental (obtained from laboratory investigation on

model structures) models (Calvi, 1999; Rossetto and Elnashai, 2003; Priestley et al.,

2007; Bal, 2008);

o HT: the height of the system;

o k1 and k2: displacement coefficients to convert multi degree of freedom (MDOF)

structural system to an equivalent SDOF system and simulate the displacement

capacity of MDOF system at the centre of seismic force (Priestley, 1997; Calvi, 1999;

Restrepo-Velez and Magenes, 2004);

o つeq: equivalent viscous damping of structural system;

o つel: elastic damping of the system (pre-yield);

o つhyst: hysteretic contribution of system damping due to nonlinear response of the

structural components, different values can be assigned to coefficient C depending

on the structural capability to dissipate seismic energy (Priestley et al., 2007). The

limit state parameter’s values are selected, considering a given damage scale e.g.

Rossetto and Elnashai (2003), Priestley et al., (2007) and Bal (2008), to predict the

corresponding damage states of structures for the derivation of fragility functions.

3.1.2 Derivation of analytical fragility functions

Considering different possible damage states of buildings (Rossetto and Elnashai, 2003),

there could be a number of fragility functions for a given typology which can be used to

estimate the number of buildings in different damage levels for a given earthquake event.

Generally, for a given limit state, a fragility function is derived considering a standard normal


14

cumulative distribution function of the logarithmic difference of the seismic intensity and

threshold capacity of limit states with certain level of standard deviation:

""

P D ‡ dLS / SD ? sdLS] _?H1d

lnSD

sdLS

Ã"

Å"Ä"

Ô"

Ö"Õ"

Ç"

É"È"È"

×"

Ú"Ù"Ù" (1.6)

where:

o P[..]: probability of reaching or exceedance a given limit state;

o f: standard normal cumulative distribution function;

o SD seismic intensity/demand;

o LSsd : limit state capacity of the system;

o く: natural logarithmic standard deviation which define the level of uncertainties in the

fragility functions;

The limit state capacity LSsd , usually median value, is obtained experimentally or numerically

using sophisticated numerical tools. The standard deviation く is obtained from the square

root square sum or similar combination of individual uncertainties.

For loss estimation on a regional scale the uncertainties and variability in structural

characteristics, geometrical and material uncertainties, can be obtained an through an on-

site survey of the building stock and laboratory investigation of structural materials. The

survey can better provide information on the likelihood of different geometrical features of

regional building stock e.g. beam/column depth, width, length, reinforcement details, number

of structure’s storeys, geometry of load resisting walls, etc (Bal et al., 2008), which affect the

seismic response of structural systems. A transparent and conceptual approach is presented

to derive analytical fragility functions for regional building stock, taking into account different

sources of local uncertainties explicitly, without making use of any constraint, in order to

obtain the global uncertainty of fragility functions i.e. く. To better understand different steps

involved in the methodology flowcharts are provided for the derivation of fragility functions,

while each of the major steps involved are described as follows.

1. The first step of the method is the generation of random population of buildings which

represent a given class of building within a given urban/rural exposure. Controlled Monte

Carlo simulation is used to generate thousands of buildings, each with different

geometrical and mechanical properties that are defined using a complete probabilistic

distribution with prescribed mean and coefficient of variation;

2. The second step of the method is to define random seismic demand on the generated

buildings which is performed through the use of random linear 5% damped displacement

response spectra. Spatial variability of ground motions is not considered in the fragility

function derivation, in order not be specific to a given region, which can be consider later

in the application of fragility functions for developing damage scenarios for regional risk

assessment and loss estimation;

3. For each of the spectrum:

a) for each limit state, the secant vibration period, displacement capacity and

viscous damping of the buildings from the random populations is computed using

calibrated structure-specific mathematical models;


15

Compute median T y and Fy of the

considered building class

Obtain SD(T y) from the 5% damped

elastic displacement responsespectrum at T y

Is SD(T y) > Fy ?

SD = SD(T y)

SD(T k) = SD(T y), where k = 0

Compute ok","z k and T k at SD(T k)

k = k + 1

Obtain the SD(T k) from the

overdamped displacement response

spectrum at T k

Is

(SD(T k) - SD(T k-1))/SD(T k-1)>"tol ?

SD = SD(T k)

k = k + 1

Y

N

Y

N

Select a given class of buildings with

geometric and material properties

Generate random building properties

following the prescribed distributions

using controlled Monte Carlo

simulation

Generate random population of

considered building class (i=1,....,n)

Generate random 5% damped linear

displacement reponse spectra with

increasing slopes

For each random spectrum

For each limit state, j

i = 1

Obtain Fi","z i and T i from the

generated building population

Obtain SD(T i) from the overdamped

displacement response spectrum at T i

Is SD(T i) > Fi ?

Pfi = 1 Pfi = 0

Is i = n ?

NY

Pfj = U Pfi /ni = 1

n

i = i + 1N

Plot Pfj against SD

YSymbols:

n = number of generated buildings

i = random building from generation

j = limit state

y = yield limit state

k = iteration number

P"= the condition is not satisfied

Y "= the condition is satisfied

F"? "displacement capacity

z"? "viscous damping

T = vibration period

SD = spectral displacement demand

Pf = probability of exceedance

Fig. 3.2 Flow chart for the derivation of displacement-based fragility functions. Global

Mechanism.


16

b) the displacement demand on each of the building is obtained from the

overdamped displacement response spectrum at the limit state vibration period of

that building which is then compared with the displacement capacity of the

building to predict its performance;

c) the number of buildings having capacity less than the demand is summed and

divided by the total number of the generated buildings to obtain the probability of

exceedance of a given limit state;

4. For each spectrum:

a) the median yield vibration period and median yield displacement capacity is

obtained from the generated building stock;

b) the spectral displacement demand at the median yield vibration period is

obtained from the 5% damped elastic displacement spectrum;

c) this is compared with the median yield displacement capacity. If the demand is

less than the yield displacement, that defines the median spectral displacement

demand on the building stock;

d) for spectral displacement demand greater than the median yield displacement,

the performance point is obtained in an iterative fashion which defines the

median spectral displacement demand;

5. The probability of exceedance for each limit state is plotted versus the median

displacement demand for each of the random spectra. Available cumulative distribution

functions are fit to the data and the unknowns of the functions are obtained to

completely describe the fragility functions for future applications.

3.1.3 Application to the Case Study Buildings

The methodology is used to derive analytical fragility functions for predominant building

classes of most European countries. The present report considers only the following building

classes, whereas other building classes will be considered in the future if necessary and will

be reported in an updated deliverable at the end of the project. The Syner-G taxonomy has

been used, as described in Chapter 4.

Table 3.1 Building typology matrix considered in the methodology

S. No. Construction label Building type description

S1 MRF/C-RC/R/R/B/D/R-

RC/X/L/X Low-rise ductile regular reinforced

concrete frame without masonry infill walls


RC/X/M/X Mid-rise ductile regular reinforced concrete

frame without masonry infill walls


RC/X/H/X High-rise ductile regular reinforced


S4 MRF/C-RC/IR/R/B/D/R-

RC/X/L/X Low-rise ductile irregular reinforced



RC/X/M/X Mid-rise ductile irregular reinforced



17

S. No. Construction label Building type description


RC/X/H/X High-rise ductile irregular reinforced


S7 MRF/C-RC/R/R/B/ND/R-

RC/X/L/X Low-rise non-ductile regular reinforced



RC/X/M/X Mid-rise non-ductile regular reinforced



RC/X/H/X High-rise non-ductile regular reinforced


S10 MRF/C-RC/IR/R/B/ND/R-

RC/X/L/X Low-rise non-ductile irregular reinforced



RC/X/M/X Mid-rise non-ductile irregular reinforced



RC/X/H/X High-rise non-ductile irregular reinforced


The methodology uses SDOF systems for seismic performance assessment and derivation

of analytical fragility functions. The SDOF system for different structural schemes are

derived using nonlinear dynamic time history analysis (NLTHA) in order to obtain the

equivalent strength and equivalent displacement capacity of the considered building classes

and develop structure-specific models for secant vibration period and displacement capacity

(i.e. from Eq.1.1 to Eq.1.3). Viscous damping is taken from existing experimental and/or

analytical investigations.

Case Study Structural Models

Prototype structural models, 2D, are designed and analyzed using NLTHA to derived static

SDOF systems. The structural models are generated using Monte Carlo simulation, 50

structural models are used for a given class, with structural characteristics prevailing in the

considered region (defined in a probabilistic fashion i.e. for each structural parameter 50

random values are generated using site-specific likelihood functions).

For RC buildings the available structural characteristics typical for Turkish building stock are

used (Bal et al., 2008) to generate structural models. However, the structural detailing typical

for Italian and Greek building stock (Bal, 2008) are also considered to generalize the findings

herein for the Euro-Mediterranean regions. For simplicity, the structural models are

considered with symmetric bay length, for a given structural model, and storey height, except

the irregular buildings in which the bottom storey is kept higher with respect to the upper

stories (Bal, 2008). The structural properties defined for the case study models are given in

Table 3.2 which represent the typical characteristic values for the Euro-Mediterranean

(particularly Greek, Italian and Turkish) building stock.


18

Table 3.2 Structural properties defined to generate case study structural models for

RC buildings

Parameters Mean value

C.O.V.(%)Lower bound

Upper bound

Probabilistic distribution

type

hs (m) 2.84 8 2.5 3.3 Truncated Lognormal

(Hg/hs) 1.13 14 1 1.4 Truncated Lognormal

tslb (m) 0.125 10 0.1 0.15 Truncated Lognormal

Lb (m) 3.37 38 1 7.5 Truncated Lognormal

HC1 (m) 0.45 12 0.3 0.6 Truncated Lognormal



HB (m) 0.48 14 0.3 0.6 Truncated Lognormal

WB(m) 0.24 14 0.15 0.3 Truncated Lognormal

fmc(Mpa) 16.73 51 2 40 Truncated Lognormal

fy-S420(Mpa) 440 15 250 700 Truncated Lognormal

fy-S220(Mpa) 371 24 150 550 Truncated Lognormal

where:

o hs: interstorey height;

o Hg/hs: ratio of ground floor height of irregular to regular frame’s;

o tslb: RC slab thickness;

o Lb: bay length;

o HCi: column depth (considered square) for low-, medium- and high-rise buildings;

o HB: beam depth;

o WB: beam width;

o fmc: compressive strength of concrete;

o fy: yield strength of steel;

o S220: pre-1979 reinforcing steel (Turkish building stock);

o S420: post-1980 reinforcing steel (Turkish building stock).

For a given building class, say low-rise, a total of 200 (100 structural models for each

reinforcing steel type i.e. S220 and S420, having 50 regular and 50 irregular cases)

structural models are generated considering regional variability in the geometric and material

properties of structures.

Mathematical modelling

For RC structures the mathematical models are prepared in a fiber-based Finite Element

Analysis tool OpenSees (McKenna et al., 2010). The RC beams and columns of structures

are modelled using the regularized forced-based fiber elements, the “beamwithhinges” force-

based fiber element proposed and developed by Scott and Fenves (2006), which is

computationally efficient and can be used to analyze large building stock in a short


19

timeframe. The elastic part of the “beamwithhinges” is provided with cracked, 50 percent

gross stiffness section properties. The plastic hinge length assigned to the structural

elements is obtained analytically using the model proposed by Priestley et al. (2007).

""Lp ? max 0 . 0 8 Lm - 0 . 0 2 2 f y d bl , 0 . 0 4 4 f y d bl* + (1.7)

where:

o Lp: plastic hinge length;

o Lm: shear span of beam/column;

o fy: reinforcing steel yield strength in MPa;

o dbl: diameter of longitudinal reinforcing steel bars.

Accelerograms used in NLTHA

The case study structural models are analyzed dynamically using nonlinear time history

analysis (NLTHA) with 10 natural accelerograms extracted from the PEER NGA data base

for soft soil condition with the mean spectrum compatible to EC8 Type I-C-soil spectrum, see

Table 3.3 for the spectral shape and Fig. 3.3 for details of each time history. These

accelerograms are previously selected and used by Pampanin (2002) and Menon and

Magenes (2008), however in the present study all the accelerograms are anchored to a

common PGA level thus resulting in different scaling factors than previously used

(Pampanin, Menon and Magenes, 2008).

0 1 2 3 4 50

0.5

1

1.5

2

2.5

3

3.5

4

Period (sec)

Spectr

al

accele

rati

on (

m/s

ec2

)

EC8-TypeI-C, Soil

Mean Spectrum

‒ 1 Std. Dev.

Fig. 3.3 Mean of the acceleration spectra considered for NLTHA and comparison with

EC8 Type I-C soil spectrum

Table 3.3 Details of the accelerograms used in the present study for NLTHA

Rec. Date Event Station/

Component

Magnitude

(Mw)

Distance

(km)

Soil Type

(NEHRP)

Duration

(sec)

PGA

(g)

1 4/25/1992 Cape Mendocino Fortuna-Fortuna

Blvd 7.1 23.6 C 44 0.116


20

Rec. Date Event Station/

Component

Magnitude

(Mw)

Distance

(km)

Soil Type

(NEHRP)

Duration

(sec)

PGA

(g)

2 6/28/1992 Landers Desert Hot

Springs 7.3 23.2 C 50 0.154

3 6/28/1992 Landers Yermo Fire

Station 7.3 24.9 D 44 0.152

4 10/18/1989 Loma Prieta Hollister

Diff. Array 6.9 25.8 D 39.64 0.279

5 1/17/1994 Northridge Beverly Hills 6.7 19.6 C 29.99 0.416

6 1/17/1994 Northridge

Canoga Park-

Topanga Can

6.7 15.8 D 24.99 0.356

7 1/17/1994 Northridge LA-

Hollywood Stor FF

6.7 25.5 D 40 0.231

8 1/17/1994 Northridge Sunland-Mt

Gleason Ave

6.7 17.7 C 29.99 0.157

9 11/24/1987 SuperstitnHills(B) El Centro

Imp.Co.Cent6.7 13.9 D 40 0.258

10 11/24/1987 SuperstitnHills(B) Plaster City 6.7 21 D 22.23 0.186

Derivation of Mechanical Models

Each of the structural model is analyzed dynamically using 10 accelerograms. The

accelerograms are anchored to a common PGA and scaled to exceed the yielding limit state

of structures, considering the global capacity curve. For each of the accelerograms the

equivalent base shear and equivalent displacement demand on the structure are obtained

using the proposed SDOF derivation of Priestley et al., 2007. However, the deformed shape

of the structure used in the SDOF derivation is obtained from the dynamic analysis of the

structure. The dynamically derived SDOF system is used to obtain the yield period of the

structural system i.e. at the yielding of reinforcing steel in beam/column for RC structures

depending on the prevailing mechanism (beam-sway and/or column-sway), and cracking of

shear walls in masonry structures.

""

Ty ? 2 r Feq

VBeq

(1.8)

""Feq ? miFi

2i ?

1n

Â / mi

i ?1n

Â Fi (1.9)

VBeq ?VB / Meq (1.10)

""Meq ? miFi /Feq

i ?1n

Â (1.11)

where:


21

o Äeq: equivalent displacement of structural system at the centre of seismic force;

o VBeq: equivalent base shear for the corresponding SDOF system;

o mi: floor mass;

o ÄI: floor displacement demand (obtained from NLTHA);

o VB: base shear demand;

o Meq: equivalent mass of the structural system.

For RC structures the yield limit state, at the reinforcing steel’s yield strain, proposed by

Crowley et al., (2006) after Priestley (1997) is used to compute the beam/column section

curvature, member chord rotation and interstorey drift limit using the analytical model

proposed by Priestley et al., (2007), for beam-sway mechanism, and Glaister and Pinho

(2003), for column-sway mechanisms.

""syb ? 0 .

2 8 3 gy

l b

hb

(1.12)

""syc ? 0 .

3 5 7 gy

hs

hc

(1.13)

where:

o しy: interstorey drift for beam-sway and column-sway mechanism respectively;

o iy: yield strain of reinforcing steel;

o lb: bay length;

o hb: beam depth;

o hs: interstorey height;

o hc: column depth.

The models are further modified for beam-sway, i.e. multiplying Eq. 1.12 by 1.40 to include

the flexure deformation contribution of columns (Priestley et al., 2007), and column-sway, i.e.

multiplying Eq. 1.13 by 1.20 to include the added flexibility of beams (Glaister and Pinho,

2003). The analytically predicted drift limits show good correlation with the experimental

observations (Priestley, 1998). The yield drift limits obtained experimentally for existing

European bare frames proposed by Rossetto and Elnashai (2003) is also used to compute

the yield vibration period.

The yield interstorey drift are computed using Eq.1.12 and Eq. 1.13 for each randomly

generated model, the minimum is selected, which is used to compute the equivalent lateral

strength and displacement capacity of structural models for each of the 10 accelerograms.

For a given structural model the interstorey drift is monitored, for a given NLTHA, and the

system vibration period is obtained using Eq. 1.8 upon the exceedance of interstorey yield

drift at any storey, considering a small analysis time step of 0.005s. The vibration periods

obtained for the considered case study structures are used to develop the period model, i.e.

Eq. 1.2.

Constrained regression with “b” set to 0.75 and 1.0, typical in the building codes and

available literature, is performed to compute the coefficient “a” of the period model. Table 3.4


22

reports the values estimated for the coefficient “a” for different structural schemes using both

analytical and experimental proposals for yield drift limits. The period model with constrained

“b” set to 0.75 and 1.0 and the coefficient “a” obtained from the regression analysis is used

to predict the yield vibration period of the cases study structural models which is then

compared with the actual period values obtained from NLTHA in order to investigate which

form, either b=0.75 or b=1.0, is well correlated with the observed period values. The error in

each period model is obtained by estimating the logarithmic difference of the period values,

between the model and NLTHA. The model with less estimate of dispersion results in

relatively well correlated period values which indicates the appropriate period model for

structures. Alternatively, regression analysis can be performed to obtain best estimate value

of both coefficients “a” and “b” of the period model. The period coefficient with “b” set equal

to 1.0 obtained for all the case study structural models, using both analytical and

experimental proposal for drift limits, is depicted in Fig. 3.4. For all the structural models the

dispersion in error is estimated to be 0.32 for period model with b=1.0 while 0.40 for model

with b=0.75, considering the analytical drift limits which is 0.34 for period model with b=1.0

while 0.41 for model with b=0.75, considering the experimental drift limits. Both the analytical

and experimental drift limits result in very similar results. Also, all the structural schemes

resulted in fairly the same period coefficient i.e. “a” of period model. The developed period

model is in good agreement with the analysis and proposal of Crowley and Pinho (2004) and

Bal (2008).

Additionally, the structural models are analyzed to develop the limit states displacement

capacity model (Eq. 1.3) for different performance levels of the structures. This includes the

determination of displacement coefficients k1 and k2in Eq. 1.3 which converts the MDOF

system to SDOF system and computes the displacement capacity at the centre of seismic

force.

Table 3.4Period coefficient for RC building stock of Euro-Mediterranean region

Analytical drift limits Experimental drift limits Std. Dev.

of Error

b b b

Steel

type Elevation

0.75 1 0.75 1 0.75 1

Regular 0.1541(0.5544) 0.0996(0.5522) 0.1697(0.5206) 0.1096(0.5174) 0.41 0.34S220

Irregular 0.1522(0.5000) 0.0962(0.4953) 0.1716(0.4858) 0.1085(0.4829) 0.41 0.32

Regular 0.1516(0.5483) 0.0979(0.5458) 0.1646(0.5356) 0.1064(0.5323) 0.40 0.34S420

Irregular 0.1517(0.5024) 0.0958(0.4976) 0.1749(0.5130) 0.1106(0.5100) 0.41 0.35


23

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.40

100

200

300

400

500

600

Period Coefficient, a

Num

ber

of

Obse

rvations

Mean = 0.0974

u = 0.5233

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.40

100

200

300

400

500

600

Period Coefficient, a

Num

ber

of

Obse

rvat

ions

Mean = 0.1088

u = 0.5108

(a) (b)

Fig. 3.4 (a) Period coefficient for low rise bare frame using the analytical drift limits,

and (b) experimental drift limit (for light damage limit state exceedance) proposed by

Rossetto and Elnashai (2003) for European bare frames

For RC structures, for simplicity reasons and consistency in the analytical and experimental

drift limits, the target interstorey drift limits proposed by Rossetto and Elnashai (2003) are

used to compute the effective height of each of the random structural models using the

effective height model proposed by Priestley et al., (2007).

""

H e?miFi Hi

i ?1n

Â

miFi

i ?1n

Â (1.14)

where:

o He: effective height of the SDOF system, which corresponds to the centre of seismic

force;

o Hi: floor height;

o mi: floor mass;

o ÄI: floor displacement demand for a given NLTHA.

The displacement coefficient at yield limit state (k) is obtained then by dividing He over the

total height of the structural model, HT. The coefficient k2 is theoretical equal to unity

however its uncertainty is also considered. The displacement coefficients, k1 and k2, take

into account the record to record variability in the deformed shape of the buildings besides

the characteristics of structural models to derive their corresponding equivalent SDOF

systems

The above hypotheses cannot be directly used to obtain displacement coefficient at post-

yield limit states (k2), hence the following procedure is used. NLTHA of all the structural

models is performed, through linear scaling of accelerograms, to exceed the near collapse

limit state of structures. The data is analyzed to obtain the equivalent displacement demand

when the target ultimate ductility 3 is exceeded at any storey, which corresponds to the

collapse limit state of structural model. In the next step Eq. (2) is used, inverting and re-

arranging, to obtain k2


24

""k 2 ? FLS / Fy

sP hs

(1.15)

where:

ÄLS: equivalent displacement at the near collapse limit state of structural model;

Äy: equivalent displacement at the yielding limit state;

しp: plastic interstorey drift demand;

hS: interstorey height.

3.1.4 Derivation of analytical fragility functions

The proposed methodology, described earlier, is used herein to derive analytical fragility

functions for the case study buildings. The scope of this study is focused on the derivation of

building damage functions and the definition of parameters necessary to produce the fragility

functions for future applications.

Controlled Monte Carlo simulation is used to generate random building stock with different

geometric and mechanical properties considering lognormal probability density function (pdf)

for all the parameters involved in the capacity evaluation. The lognormal pdf is considered

for simplicity reasons and to be conservative in structural capacity estimation.

The damage scale proposed by Crowley et al., (2004, 2006) is used for RC buildings with

the experimental drift limits proposed by Rossetto and Elnashai (2003) for the cracking limit

states in order to separate the non damaged buildings from the slightly damaged in the pre-

yield limit state of buildings. The displacement capacity and secant vibration period are

obtained at each limit state, using the calibrated empirical models i.e. Eq.1.1 and Eq. 1.2.

Once the regional building stock are generated and the limit state capacities are evaluated in

a probabilistic fashion, random linear 5 percent damped displacement response spectra are

generated. The global in-plane assessment is performed through overdamping the linear

spectrum, using overdamping factor proposed by EC8 (CEN, 1994) and the system viscous

damping, for each limit state:

""

j ?72-zeq

(1.16)

where:

o さ represents the overdamping factor;

o つeq represents the structures viscous damping.

The procedure outlined in Fig. 3.2 is used to derive the fragility functions for all the case

study buildings.


25

3.2 UPAT METHOD

3.2.1 Introduction

Fragility curves were developed for planwise regular RC frame buildings with or without

masonry infills and for dual (wall-frame) buildings without masonry infills (Tsionis et al.,

2011). The case of frame systems with the ground storey open and infilled above (pilotis)

was also examined. The variable parameters were the number of storeys, the level of

seismic design (in terms of design Peak Ground Acceleration – PGA – and design ductility

level); an additional parameter for the infilled frames was the amount of infills, while for the

dual buildings it is the percentage of seismic base shear taken by the walls.

Within the Syner-G project it has been agreed to harmonise fragility functions to two limit

states, namely yielding and collapse. Collapse at the member level was considered

equivalent to ultimate deformation in flexure or shear, with its established conventional

definition as the deformation corresponding to a 20% drop in peak resistance. The peak

chord rotation demand at the member end and the peak shear force demand were taken as

damage measures for the RC members. The fragility functions refer to individual members

and locations thereof.

The analysis performed for the estimation of the peak response quantities is according to

Eurocode 8 – Parts 1 and 3 – with certain simplifying assumptions for the frames. The

analysis gives the median value of the fragility curve corresponding to the damage scale and

damage measure of interest. The dispersion (く value) of the fragility curve takes into

account explicitly the model uncertainty for the estimation of the damage measure and the

uncertainty of the capacity in terms of the damage measure. This latter uncertainty includes

both model uncertainty and dispersion of material and geometric properties about their best

estimates.

A computational module has been constructed for the design of the building according to

Eurocodes 2 and 8 (with the associated analyses and any required analyses-design

iterations) and the development of the fragility curves. The module is computationally very

efficient and works in an automated way, once the design parameters are specified. Once

incorporated into a broader computational environment for the vulnerability assessment of

systems, the module can provide the fragility curves for individual RC buildings of a wide

variety of types.

3.2.2 Building typologies – the base case

The work focuses on prototype regular buildings of the following types:

o ductile reinforced concrete moment frame without masonry infill walls;

o ductile or nonductile reinforced concrete shear walls;

o nonductile reinforced concrete frame with masonry infill walls;

o nonductile reinforced concrete frame without masonry infill walls;

o reinforced concrete moment frame with open ground storey (pilotis).

The objective is to construct fragility curves for each type of building as a function of a few

parameters, such as:


26

o number of storeys:

- 2,

- 5 and

- 8;

o amount of infills in the frame: infilling at

- 0% (bare frame),

- 20%,

- 40%,

- 60%,

- 80% and

- 100%

of fully infilled bays (the reduction possibly due to openings in the masonry panel);

o heightwise distribution of infills in the frame:

- infills at all storeys or

- open ground storey (pilotis);

o level of seismic design:

- no seismic design, design for gravity loads only (e.g., according to EC2 alone);

- seismic design for:

• various levels of ductility, e.g. per EC8: DC L, DC M and DC H and

• various levels of design peak ground acceleration (PGA).

The examined combinations of ductility level and design PGA are listed in Table 3.5. In all

cases, the spectrum was taken as of Type 1 and Ground Category C (firm soil) per

Eurocode 8 with the recommended period values therein. The PGA values in Table 3.5

incorporate Ground C’s Soil factor S of 1.15

Table 3.5 Values of design acceleration for different ductility levels

Ductility level Design PGA (g) at top of Ground C

Low 0.15

Medium 0.15 0.20 0.25 0.30

High 0.20 0.25 0.30 0.35

All storeys of the prototype buildings have the same height hst = 3.0 m. The buildings are

rectangular in plan with the same bay length (lb = 5.0 m in the base case), column and beam

size in both horizontal directions. The slab thickness was taken equal to 0.15 m.

Frames, be it in pure frame buildings (bare, infilled or pilotis), shown in Fig. 3.5, or in dual

(wall-frame) ones, have constant bay length and interior column size throughout the plan.

Beam depth is also constant in each storey but may change from storey-to-storey, while the


27

beam width and the column size are constant in all storeys. Exterior columns and beams are

assumed to have half the elastic rigidity (effective secant-to-yield-point or conventional

cracked rigidity) of interior ones, so that at a given storey seismic moments and chord

rotation demands have the same magnitude in all beams and at both ends (point of inflection

at mid-span) and are the same in all interior columns, while exterior columns develop half

the elastic seismic moments of interior ones but the same seismic chord rotation demands

as the interior ones. On the basis of these considerations, only interior columns and beams

were designed and had their fragility function constructed. A final simplifying assumption for

the frames was that the point of inflection of columns is at storey mid-height.

The dimensions of columns, beams or walls were defined according to the design procedure

described in the following.

The dimensions of columns and beams in ductile frames with 2, 5 and 8 storeys and in

nonductile frames are given respectively in Table 3.6 to Table 3.9. They were chosen in an

iterative procedure to be the minimum possible satisfying all requirements of Eurocodes 2

(CEN, 2004a) and 8 (CEN, 2004b) – if applicable – including the limitation of storey drift ratio

to 0.5% under Eurocode 8’s damage limitation seismic action (half of the design seismic

action). The size of the columns of nonductile frames was the minimum required to meet the

ULS of axial force under the combination of persistent-and-transient actions according to

Eqs. (6.10a), (6.10b) of EN1990 (CEN, 2002), as well as Eurocode 2’s slenderness condition

for negligible second order effects at the two lowest storeys for unbraced frames (Section

5.8.3.1 in CEN, 2004a).

Dual buildings are made up of columns on a 5m×5m grid and two parallel rectangular walls

in each horizontal direction per 5×5 bays of the building plan, as shown in Fig. 3.6. For

simplicity and generality, no beams were considered to frame into the walls; in other words,

the walls share common floor displacements with the frames (the diaphragms being

considered as rigid) but do not participate in framing action. The dimensions of the frame

columns and beams in the dual buildings were chosen close to the minimum satisfying all

requirements of Eurocodes 2 (CEN, 2004a) and 8 (CEN, 2004b) – if applicable. The size of

the columns of nonductile dual buildings was the minimum required to meet the ULS of axial

force under the combination of persistent-and-transient actions according to Eqs. (6.10a),

(6.10b) in (CEN, 2002), as well as Eurocode 2’s slenderness condition for negligible second

order effects at the two lowest storeys of braced frames (Section 5.8.3.1 in CEN, 2004a).

The length of the wall section, lw, of nonductile dual buildings was chosen equal to the

minimum necessary to fulfil Eurocode 2’s lateral bracing condition for negligible second

order effects in braced frames (Section 5.8.3.3(1) in CEN, 2004a). In ductile dual buildings

the length of the wall, lw, and the size of the columns, were chosen together, to meet

Eurocode 8’s storey drift ratio limit of 0.5% under the damage limitation seismic action while

at the same time covering a wide range of values of the fraction of the building’s total base

shear, Vtot,base taken by the two walls, Vwall,base. It is reminded that, according to Eurocode 8

(CEN, 2004b):

o frame-equivalent dual buildings have 0.35Vtot,baseøVwall,baseø 0.50Vtot,base,

o wall-equivalent dual ones have 0.50Vtot,baseøVwall,baseø 0.65Vtot,base and

o wall buildings have Vwall,baseд 0.65Vtot,base.

These three categories of buildings have different values of the behaviour factor, q, and

different design rules. The dimensions of columns, beams and walls of ductile dual buildings

are given in Table 3.10 and Table 3.11, while for nonductile dual ones in Table 3.12.


28

Concrete C25/30 and Tempcore steel S500 of Class C according to Annex C of Eurocode 2

(CEN, 2004a) was used as the base case. In infilled frames, the thickness of masonry

panels is tw = 0.10 m. The compressive strength of masonry units and mortar was taken as

fbw = 4 MPa and fbw = 15 MPa respectively. The strength of masonry was estimated

according to Eurocode 6 (CEN, 2005b) as fwc =1.25×0.45 fbw0.7fmw

0.3 = 3.3 MPa and its Young

modulus as Ew = 600fwc=2 GPa, to account for cracking.

All vertical elements were assumed to be fixed at the base of the ground storey. Other than

this and the simplifying assumptions for frames highlighted above, the analysis performed for

the estimation of the peak response quantities as well as for the estimation of mean values

of member properties – including their force and deformation capacities – was in accordance

with Eurocode 8 – Parts 1 and 3. For these mean values, the following expected values of

material strengths were used:

o nominal strength plus 8 MPa for the concrete,

o 1.15 times the nominal yield stress for the reinforcing steel.

Fig. 3.5 Geometry of 8-storey (a), 5-storey (b) and 2-storey (c) frames of the base case


29

Fig. 3.6 Plan of dual building

Table 3.6 Beam height, hb, and column height, hc, in 2-storey ductile frames of the

base case

Design PGA (g) Ductility Class hb (m) hc (m)

0.10 L 0.35 0.35

L 0.35 0.35 0.15

M 0.35 0.35

M 0.35 0.35 0.20

H 0.35 0.35

M 0.35 0.40 0.25

H 0.35 0.40

M 0.40 0.40 0.30

H 0.40 0.40

0.35 H 0.40 0.45


base case


0.10 L 0.35 0.40

3rd-5th storey: 0.35 L

1st-2nd storey: 0.40 0.40

0.15

M 0.35 0.40


30

M 0.40 0.40 0.20

H 0.40 0.40

3rd-5th storey: 0.40

2nd storey: 0.50 M

1st storey: 0.40

0.45


2nd storey: 0.50

0.25

H

1st storey: 0.40

0.45


2nd storey: 0.50 M

1st storey: 0.45

0.30


2nd storey: 0.50

0.30

H

1st storey: 0.45

0.60

0.35 H 0.50 0.70


base case


0.10 L 0.40 0.55

4th-8th storey: 0.40 L

1st-3rd storey: 0.45 0.55

0.15

M 0.40 0.55

M 0.40 0.30 0.20

H 0.40 0.60

M 0.45 0.60 0.25

H 0.45 0.60

3rd -8th storey: 0.45

2nd storey: 0.50 M

1st storey: 0.45

0.65

3rd –8th storey: 0.45

2nd storey: 0.50

0.30

H

1st storey: 0.45

0.65

0.35 H 0.50 0.80

Table 3.9 Column height, hc, beam height, hb, and beam width, bb, in nonductile

buildings of the base case


31

Storeys hc (m) hb (m) bb (m)

2 0.20 0.40 0.30

5 0.30 0.40 0.30

8 0.40 0.40 0.30

Table 3.10 Geometry of 5-storey ductile dual buildings of the base case

Design PGA (g) Ductility Class hc (m) hb (m) lw (m) Vwall,b(%)

1.5 45

2.0 60 0.10 L 0.35 0.40

2.5 70

1.5 45

2.0 60 0.15 L, M 0.35 0.40

2.5 70

1.5 45

2.0 60 0.20 M, H 0.35 0.40

2.5 70

2.0 45

2.5 55 0.25 M, H 0.45 0.45

3.5 75

2.0 35

3.0 60 0.30 M, H 0.50 0.50

4.0 75

2.5 45

3.0 55 0.35 H 0.50 0.55

4.0 70

Table 3.11 Geometry of 8-storey ductile dual buildings of the base case

Design PGA (g) Ductility Class hc (m) hb (m) lw (m) Vwall,b(%)

1.75 45

2.5 60 0.10 L 0.40 0.40

3.5 75

1.75 45

2.5 60 0.15 L, M 0.40 0.40

3.5 75

2.0 40 0.20 M, H 0.45 0.45

3.0 65


32

4.0 75

2.0 40

3.0 60 0.25 M, H 0.45 0.50

4.0 75

2.5 45

3.5 65 0.30 M, H 0.50 0.50

4.0 70

2.5 40

3.5 60 0.35 H 0.55 0.55

4.5 70

Table 3.12 Geometry of nonductile dual buildings of the base case

Storeys hc (m) hb (m) lw (m) Vwall,b(%)

5 0.30 0.40 1.9 55

8 0.45 0.40 2.5 55

3.2.3 Damage scale, damage measure and intensity measures

Within the Syner-G project it has been agreed to harmonise all fragility functions to two limit

states: yielding and collapse. For RC members, the following damage measures were

considered:

o the peak chord rotation demand at the member end and

o the member peak shear force demand – considering the simultaneous value of the

plastic rotation ductility factor, if we are concerned with shear failure in a plastic hinge.

For each member the probability of failure was taken as the largest of those corresponding

to these two failure modes.

Regarding intensity measures, spectral displacement, Sd(T1), seems efficient and informative

for ductile failure modes (flexure), while spectral acceleration, Sa(T1), is better for brittle ones

(shear). However, for consistency within the project, peak ground acceleration (PGA) is

taken as the intensity measure. Besides, this choice tunes better with the use of design PGA

as the main seismic design parameter of a building.

3.2.4 Design and vulnerability assessment

A simplified analysis was performed for the estimation of the peak response quantities. The

design of ductile frame and dual buildings is fully according to Part 1 of Eurocode 8 (CEN,

2004b), while the design of nonductile buildings is performed according to Eurocode 2 (CEN,

2004a). The assessment of all buildings is done in accordance to Part 3 of Eurocode 8

(CEN, 2005a).

The procedures described in the following sub-sections have been implemented in computer

modules that produce the fragility curves for specific buildings, based on the main


33

parameters of the building (e.g. number of storeys, dimensions of structural elements, level

of seismic design). These programs may be incorporated as executable files in software for

vulnerability analysis of systems which include RC buildings as individual components.

Design of the buildings

For ductile buildings the design procedure according to Eurocodes 2 (CEN, 2004a) and 8

(CEN, 2004b) comprises the following steps:

1. Iterations of analysis (with the lateral force procedure of Eurocode 8) and of sizing of

interior columns and beams in frame systems, or of the walls in dual, so that under

the damage limitation seismic action the interstorey drift under the damage limitation

seismic action is less than the limit of Eurocode 8 (0.5%) in every storey.

2. Dimensioning of longitudinal reinforcement of interior beams in all storeys for the

ULS in bending under the following combinations of actions: a) the factored gravity

loads (persistent-and-transient actions according to Eqs. (6.10a), (6.10b) of EN1990),

and b) the combination of the design seismic action with the quasi-permanent gravity

loads (g + ね2q) using for the design seismic action the lateral force procedure of

Eurocode 8 and the design response spectrum. Relevant detailing rules for each

level of seismic design are taken into account.

3. Dimensioning of interior column vertical reinforcement in all storeys for the ULS in

bending with axial load for the combination of the design seismic action with the

quasi-permanent gravity loads using for the design seismic action the lateral force

procedure of Eurocode 8 and the design response spectrum. For frame systems and

frame-equivalent dual ones of buildings with more than two storeys, column vertical

reinforcement is also such that column moment capacities meet the capacity design

rule, ぇMRd,cд1.3ぇMRd,b, in each one of the two horizontal directions at all interior joints

except those of the roof. Relevant detailing rules for each level of seismic design are

taken into account.

4. Dimensioning of the end regions of interior beams for capacity design shears

computed on the basis of the moment resistances of the beam itself and of the

columns to which it is connected, taking into account the detailing rules for minimum

transverse reinforcement of critical regions.

5. Dimensioning of the end and the intermediate regions of interior columns for capacity

design shears, computed on the basis of the moment resistances of the column itself

and of the beams to which it is connected, taking into account the detailing rules for

minimum transverse reinforcement of critical regions, including confining

reinforcement.

For nonductile structures, the design procedure according to Eurocode 2 comprises the

following steps:

1. Sizing of interior columns so that their slenderness meets the condition for negligible

second order effects at the two lowest storeys in par. 5.8.3.1(1) of Eurocode 2 for the

default values of A, B and C. The effective length of the columns is taken according

to par. 5.8.3.2 of Eurocode 2, depending on whether the building is a frame

(considered as unbraced) or dual. In that latter case, its walls are sized so that their

elastic rigidity meets the condition of par. 5.8.3.3(1) of Eurocode 2 for negligible

second order effects at the system level. In all these calculations, members are

considered as fully cracked according to Eurocode 2 and the design values of the


34

long-term elastic properties of concrete are used. These calculations need a certain

number of iterations.

2. Dimensioning of interior columns and beams for the ULS in bending and shear under

the combination of persistent-and-transient actions according to Eqs. (6.10a), (6.10b)

of EN1990, taking into account the shears and moments in columns and beams due

to the geometric imperfections of par.5.2 of Eurocode 2 (column inclination), if the

system is a frame. If it is dual, its walls are dimensioned for the ULS in bending and

shear under the combination of persistent-and-transient actions (Eqs.(6.10a), (6.10b)

of EN1990) for the full lateral load generated in the building by the geometric

imperfections of par.5.2 of Eurocode 2 (column inclination). The Eurocode 2 detailing

rules for minimum longitudinal and transverse reinforcement are taken into account.

Some simplifications are adopted for the analysis. In detail:

o All-encompassing permanent and imposed loads per unit floor area are taken to

produce a triangular distribution of loads on the beams.

o Walls and columns are considered fixed at ground level.

o Floor diaphragms are considered as rigid.

o In dual buildings, walls are treated as cantilevers with the same floor displacements

as the frames.

o The points of inflection of columns under lateral loading are assumed at storey mid-

height; then seismic bending moments at column ends are taken equal to the shear

force of the column, times one-half of the clear column height.

o Interior columns and beams have twice the moment of inertia of exterior ones. Then,

for the studied regular buildings:

- interior columns take twice the seismic shear compared to exterior ones but have

the same seismic chord rotation demands;

- all beam points of inflection under lateral loading are at mid-span, i.e., the seismic

bending moments and the chord rotation demands at the ends of all beams in the

storey are the same;

- the seismic overturning moment is resisted by axial forces in the exterior columns

alone; seismic axial forces in interior columns are zero.

o Columns support the gravity loads from within a tributary area of each floor extending

up to beam mid-span.

Bending moments in columns or walls due to gravity loads are neglected

Seismic fragility assessment

The assessment is based on actual (mean) values of material strengths. The assessment

procedure includes the following main steps:

1. Estimation of the effective stiffness of interior columns and beams according to

Eurocode 8 – Part 3, notably as the secant stiffness to the yield point: EIeff= MyLs / 3

しy, where My and Ls are the yield moment and the shear span at the end of the

member and しy is the chord rotation at yielding, based on the section, member and

reinforcement properties.


35

2. Linear elastic analysis according to Eurocode 8 – Part 3, using the elastic response

spectrum and application of the “equal displacement rule” to estimate the inelastic

seismic chord rotation demands at the ends of all interior columns and beams and at

the base of the walls, as a function of the acting peak ground acceleration. The

elastic seismic chord rotation at the end of an interior beam or column is calculated

as しE= MELs/3 EIeff, where ME is the elastic seismic moment at the end of the element

and Lsthe shear span (M/V ratio) there.

3. Following the sequence of plastic hinge formation at the ends of beams and columns

and at the base of the walls, determination of the shear force demands in the

members on the basis of the expected value of the moment resistances. After plastic

hinge formation at the base of a wall, the wall shears throughout the height are

determined on the basis of the wall moment resistance at the base and the

amplification of shears for inelastic higher mode effects according to the provisions of

Eurocode 8 for DC H walls.

4. Estimation of the expected (mean) value of the ultimate chord rotations at the ends of

columns and beams under cyclic loading from the empirical expressions in Eurocode

8 – Part 3.

5. Estimation of the peak ground acceleration for which the (inelastic) chord rotation

demand at the ends of beams and columns (from step 2) exceeds the expected

ultimate chord rotation capacity in cyclic loading (from step 3).

6. Estimation of the peak ground acceleration for which the shear force demand in the

plastic hinge at each end of the beam or column (step 5) exceeds the corresponding

shear resistance under cyclic loading.

3.2.5 Fragility Functions

Fragility curves for individual buildings were developed based on the design and assessment

procedure described previously and assuming a lognormal distribution for multiplicative

random variables and a normal for additive ones. Fragility functions for the yield damage

state are based on the probability of the chord rotation demand being higher than the yield

chord rotation of the element in question. For the collapse damage state, the maximum of

the two probabilities of failure for the two potential failure modes was considered, in flexure

by exceedance of the ultimate chord rotation at the end and in shear, by exceedance of the

shear capacity in the plastic hinge or outside (whichever is most critical). For example, for

flexural failure, the probability of the chord rotation demand, しs, exceeding the ultimate chord

rotation capacity, しu, is calculated as:

PF = P[Demand > Capacity] = P[isししs>iuしum] (1.17)

Where しs is mean demand from the analysis, しum is the expected value of the capacity, i is

the chord rotation uncertainty factor, index s denotes demand and index u ultimate

conditions. Similarly for yielding, where the capacity is iyしym.

For shear failure of beams, columns or walls prior to the formation of a plastic hinge at the

member end, the probability of failure is:

PF = P[Demand > Capacity] = P[isV,el(VS+ Vo) >iRV(VR0 + VN)] (1.18)


36

Where VS and VR0 are respectively the shear demand and the shear capacity before plastic

hinging (or in monotonic loading, if more critical) and isV and iR are the corresponding

uncertainty factors. VN is the contribution of the element axial load to its shear resistance

(only in columns or walls) and Vo is the shear force due to gravity loads (only in beams).

For shear failure of beams, columns or walls after the formation of plastic hinges at their

ends, the probability of failure is:

PF = P[Demand > Capacity] = P[isV,el(VS+ Vo)>iRV{VRo(1 – aµし,pl) + VN}] (1.19)

whereµし,pl = isしし/しy is the chord rotation ductility and isし its uncertainty.

After plastic hinges develop at the columns, the shear force at the beam is conditioned by

the sum of bending moments of columns, ぇMRc. Then, the probability of failure is:

PF = P[Demand > Capacity] = P[isVpl(Vo + ぇMRc / lb) >iRVVR0] (1.20)

Where lb is the length of the beam.

Similarly, after plastic hinges develop at the beams, the shear force at the column is

conditioned by the sum of bending moments of beams, ぇMRb, and the probability of failure

is:

PF = P[Demand > Capacity] = P[isVpl(Vo + ぇMRb / lc>iR(VR0 +VN)] (1.21)

Where lc is the column length.

For shear failure of walls prior to the formation of a plastic hinge at the base, the probability

of failure is:

PF = P[Demand > Capacity] = P[isV.elVS>iRVVRw0] (1.22)

where the wall shear strength VRw is taken as the minimum between the capacity in shear

tension and in shear compression. After the plastic hinge develops at the base of the wall,

the shear force is determined by the moment capacity, My, and the probability of failure is

calculated as:

PF= P[isV Á[1+0.1(Sa(TC)/Sa(T) Mel/My)2 ]My/ls>iRV{VRo(1 – aµし,pl) + VN }] (1.23)

Where ls = M /V is the wall shear span at the base. The square-root expression at the left-

hand-side is the shear magnification factor of Eurocode 8 for DC H walls; it accounts for the

increase of shears due to higher modes after plastic hinging at the base of the wall.

The analysis gives the median value of the fragility curve corresponding to the damage scale

and damage measure of interest. The dispersion, く, of the fragility curve depends on the

model uncertainty for the estimation of the damage measure, くS, and on the uncertainty of

the capacity in terms of the damage measure, くR. This latter uncertainty includes both model

uncertainty and dispersion of material and geometric properties. The dispersion of the

fragility curve is calculated by combining the dispersion of the demand, of the capacity and

of the spectral value for given PGA, くSp, with the SRSS rule. In symbolic terms:

222 ++= SpRS くくくく (1.24)

The coefficients of variation, cv, for the different demand and capacity quantities (Fardis,

2009) are given in Table 3.13.


37

Table 3.13 Coefficients of variation

Demand cv,S Capacity cv,R

Beam chord rotation demand, for

given spectral value at the

fundamental period

0.25 Beam/column yield chord rotation 0.33

Column chord rotation demand,

for given spectral value at the

fundamental period

0.20 Beam/column ultimate chord rotation 0.38

Wall chord rotation demand, for


fundamental period

0.25

Beam/column/wall shear resistance in

diagonal tension (in or outside plastic

hinge)

0.15

Beam shear force demand, for


fundamental period

0.10 Wall yield chord rotation 0.395

Column shear force demand, for


fundamental period

0.15 Wall ultimate chord rotation 0.32

Wall shear force demand, for


fundamental period

0.20Wall shear resistance due to diagonal

compression 0.175

Spectral value, for given PGA and

fundamental period 0.25

The fragility curves for individual buildings of the different classes are given in Appendices A

(ductile frame structures), B (nonductile frame structures) and C (dual structures) of Tsionis

et al. (2011).

3.2.6 Parametric studies beyond the base case

In the base case described above certain design parameters have been fixed, namely:

o the bay length to lb = 5.0 m;

o concrete grade at C25/30;

o steel grade as S500 (500 MPa nominal yield strength).

Parametric studies have been carried out to investigate the sensitivity of the results and the

conclusions to the values of parameters considered fixed in the base case and examine the

effect of material and geometrical properties on the fragility curves of ductile frame

structures. More specifically, ductile frames were analysed for:

o concrete compressive strength fc = 20 MPa and fc = 40 MPa,

o steel yield strength fy = 400 MPa and fy = 500 MPa and for

o bay length lb = 4m and 6m.

The beam and column dimensions of the analysed buildings are given in Table 3.14 and

Table 3.15 for 2-storey frames with lb = 4m and lb = 6m respectively and in


38

Table 3.16 and Table 3.17 for 8-storey frames with lb = 4m and lb = 6m respectively.

Table 3.14 Properties of 2-storey frame buildings with lb = 4.0m

fc (MPa) fy (MPa) PGA / DC hb (m) hc (m)

0.10 / L 0.35 0.35

0.25 / M 0.35 0.35

0.25 / H 0.35 0.35 400

0.35 / H 0.35 0.35

0.10 / L 0.35 0.35

0.25 / M 0.35 0.35

0.25 / H 0.35 0.35

20

500

0.35 / H 0.35 0.35

0.10 / L 0.35 0.35

0.25 / M 0.35 0.35

0.25 / H 0.35 0.35 400

0.35 / H 0.35 0.35

0.10 / L 0.35 0.35

0.25 / M 0.35 0.35

0.25 / H 0.35 0.35

40

500

0.35 / H 0.35 0.35



0.10 / L 0.50 0.40

0.25 / M 0.50 0.40

0.25 / H 0.50 0.40 400

0.35 / H 0.50 0.45

0.10 / L 0.50 0.40

0.25 / M 0.50 0.40

0.25 / H 0.50 0.40

20

500

0.35 / H 0.50 0.45

0.10 / L 0.50 0.40

0.25 / M 0.50 0.40

0.25 / H 0.50 0.40 400

0.35 / H 0.50 0.40

0.10 / L 0.50 0.40

0.25 / M 0.50 0.40

40

500

0.25 / H 0.50 0.40


39

0.35 / H 0.50 0.40



0.10 / L 0.35 0.60

0.25 / M 0.35 0.60

0.25 / H 0.35 0.60 400

0.35 / H 0.40 0.75

0.10 / L 0.35 0.60

0.25 / M 0.35 0.60

0.25 / H 0.35 0.60

20

500

0.35 / H 0.40 0.75

0.10 / L 0.35 0.60

0.25 / M 0.35 0.60

0.25 / H 0.35 0.60 400

0.35 / H 0.40 0.60

0.10 / L 0.35 0.60

0.25 / M 0.35 0.60

0.25 / H 0.35 0.60

40

500

0.35 / H 0.40 0.60



0.10 / L 0.50 0.60

4th-8th storey: 0.50

3rd storey: 0.55

2nd storey: 0.60 0.25 / M

1st storey: 0.50

0.65


3rd storey: 0.55

2nd storey: 0.60 0.25 / H

1st storey: 0.50

0.65

400

0.35 / H 0.60 0.80

0.10 / L 0.50 0.60


20

500

0.25 / M

3rd storey: 0.55

0.65


40

2nd storey: 0.60

1st storey: 0.50


3rd storey: 0.55

2nd storey: 0.60 0.25 / H

1st storey: 0.50

0.65

0.35 / H 0.60 0.85

0.10 / L 0.50 0.60

0.25 / M 0.50 0.60

0.25 / H 0.50 0.60 400

0.35 / H 0.60 0.70

0.10 / L 0.50 0.60

0.25 / M 0.50 0.60

0.25 / H 0.50 0.60

40

500

0.35 / H 0.60 0.70

3.2.7 Concluding remarks

Based on the results obtained for the base case and the parametric studies, remarks on the

effect of the examined parameters on the vulnerability of different types of buildings are

given in the following.

For ductile frames (see Appendices A and D in Tsionis et al., 2011):

o buildings designed for higher ductility class are less vulnerable, though the difference

is not marked;

o buildings designed for higher values of PGA are less vulnerable, mainly as regards

the columns;

o beams are critical for the yield damage state;

o with the exception of low-ductility and low-rise buildings, beams are also critical for the

collapse damage state; their failure is due to shear;

o it was not possible to identify a clear trend of the vulnerability with the number of

storeys;

o buildings with higher fc and fy are less vulnerable – fy affects mainly the collapse

damage state of columns;

o buildings with longer bay span are more vulnerable.

For infilled nonductile frames (see Appendix B in Tsionis et al., 2011):

o bare frames are much more vulnerable than infilled frames;

o buildings with more openings in the infills are more vulnerable;

o in low and medium-rise buildings, columns are critical for the yield and the collapse

damage state, while in taller buildings, beams are critical for both damage states;


41

o low-rise and taller buildings exhibit similar vulnerability and are less vulnerable than

mid-rise ones.

For nonductile frames with open ground storey (see Appendix B in Tsionis et al., 2011):

o damage is concentrated at the ground storey;

o pilotis buildings show similar or higher vulnerability as bare frames;

o the vulnerability does not change significantly with the percentage of openings in

infills;

o in low and medium-rise buildings, columns are critical for the yield and the collapse

damage state, while in taller buildings, beams are critical for both damage states;

o buildings with less storeys seem to be more vulnerable.

For ductile dual buildings (see Appendix C in Tsionis et al., 2011):

o walls are the critical elements for both damage states; collapse is in most cases due

to shear;

o wall-equivalent and wall buildings have similar vulnerability, which is higher than in

frame-equivalent ones;

o buildings designed for higher PGA or for higher ductility are less vulnerable;

o taller buildings are slightly more vulnerable.

For nonductile dual buildings (see Appendix C in Tsionis et al., 2011):

o walls are critical for both damage grades, but columns and beams in all storeys have

high probabilities of damage;

o medium-rise and taller buildings exhibit similar vulnerability.

Taxonomy of European Building Typologies

43

4 Taxonomy of European Building Typologies

It is common knowledge that most of the population still reside in poorly constructed

dwellings with a high vulnerability to earthquakes. The knowledge of the building inventory of

a region and the capability to create uniform classes of building types are one the main

challenges required to carry out a seismic risk assessment. The first step should be the

creation of a reasonable taxonomy that is able to classify all the different kinds of structures.

The taxonomy of the existing buildings represents the classification of things (structures in

this case) in an ordered system that reflects their relationship.

There are already some existing taxonomies which aim to group all the different building

types spread in different countries of the world, especially in Europe: PAGER-STR which is

tailored for worldwide structures and RISK-UE which is suited to Europe. In Section 4.1

these two existing taxonomies will be briefly described, whereas in Section 4.2 the taxonomy

proposed within the Syner-G project will be presented.

4.1 EXISTING TAXONOMIES

4.1.1 PAGER-STR

The US Geological Survey’s Prompt Assessment of Global Earthquake for Response

(PAGER) program aims to provide early post-earthquake estimates of losses to allow rapid

emergency decisions to be taken. In the framework of this program, one of two main

developed and tested features is the creation of a global building stock model. PAGER

developed a building stock model using housing census and other statistical data coming

from different sources such as UN Statistical Data based on Global Housing (1993), UN-

HABITAT Database (2007), Housing Census Database (country specific), World Housing

Encyclopedia (WHE) and data compiled from published literature. It is possible to divide the

PAGER methodology into three phases: 1) database identification, preparation and

confidence ratio to estimate the quality of the data; 2) data aggregation and quality ranking;

3) data assignment for missing entries. The final result consists of an estimation of the

fractions of building types observed in each country, their functional use and average day

and night occupancy. The developed inventory database is available in a public domain,

subject to peer review, scrutiny and open enhancement. As more data become available, the

existing online inventory database will get replaced and updated.

As mentioned before, the first step of the project is related with the database identification.

For this reason, a very important part of this step is the identification of a taxonomy that is

able to include in its classification all the different types of the existing structures worldwide.

The PAGER taxonomy (known as PAGER-STR and shown in Table 4.1) identifies a few

main classes underlined in bold in the table and some sub-classes.


44

Table 4.1 PAGER-STR Taxonomy (Jaiswal and Wald, 2008 – Version 1.4 )

Label Description Average No. of stories

Typical

W WOOD 1-3 2

W1 Wood Frame, Wood Stud, Wood, Stucco, or Brick Veneer

1-2 1

W2 Wood Frame, Heavy Members, Diagonals or Bamboo Lattice, Mud Infill

All 1

W3 Wood Frame, Prefabricated Steel Stud Panels, Wood or Stucco Exterior Walls

2-3 2

W4 Log building 1-2 1

S STEEL All 1

S1 Steel Moment Frame All 1

S1L Low-Rise 1-3 2

S1M Mid-Rise 4-7 5

S1H High-Rise 8+ 13

S2 Steel Braced Frame All 1

S2L Low-Rise 1-3 2

S2M Mid-Rise 4-7 5

S2H High-Rise 8+ 13

S3 Steel Light Frame All 1

S4 Steel Frame with Cast-in-Place Concrete Shear Walls

All 1

S4L Low-Rise 1-3 2

S4M Mid-Rise 4-7 5

S4H High-Rise 8+ 13

S5 Steel Frame with Un-reinforced Masonry Infill Walls

All 1

S5L Low-Rise 1-3 2

S5M Mid-Rise 4-7 5

S5H High-Rise 8+ 13

C REINFORCED CONCRETE All 1

C1 Ductile Reinforced Concrete Moment Frame All 1

C1L Low-Rise 1-3 2

C1M Mid-Rise 4-7 5

C1H High-Rise 8+ 13

C2 Reinforced Concrete Shear Walls All 1

C2L Low-Rise 1-3 2

C2M Mid-Rise 4-7 5

C2H High-Rise 8+ 13

C3 Non-ductile Reinforced Concrete Frame with Masonry Infill Walls

All 1

C3L Low-Rise 1-3 2

C3M Mid-Rise 4-7 5

C3H High-Rise 8+ 13


45


Typical

C4 Non-ductile Reinforced Concrete Frame without Masonry Infill Walls

All 1

C4L Low-Rise 1-3 2

C4M Mid-Rise 4-7 5

C4H High-Rise 8+ 13

C5 Steel Reinforced Concrete (Steel Members Encased in Reinforced Concrete)

All 1

C5L Low-Rise 1-3 2

C5M Mid-Rise 4-7 5

C5H High-Rise 8+ 13

PC1 Precast Concrete Tilt-Up Walls All 1

PC2 Precast Concrete Frames with Concrete Shear Walls

All 1

PC2L Low-Rise 1-3 2

PC2M Mid-Rise 4-7 5

PC2H High-Rise 8+ 13

RM REINFORCED MASONRY All 1

RM1 Reinforced Masonry Bearing Walls with Wood or Metal Deck Diaphragms

All 1

RM1L Low-Rise 1-3 2

RM1M Mid-Rise (4+ stories) 4-7 5

RM2 Reinforced Masonry Bearing Walls with Concrete Diaphragms

All 1

RM2L Low-Rise 1-3 2

RM2M Mid-Rise 4-7 5

RM2H High-Rise 8+ 13

MH MOBILE HOME All 1

M MUD WALLS 1 1

M1 Mud walls without horizontal wood elements 1-2 1

M2 Mud walls with horizontal wood elements 1-3 2

A ADOBE BLOCK (UNBAKED DRIED MUD BLOCK) WALLS

1-2 1

A1 Adobe block, mud mortar, wood roof and floors 1-2 1

A2 Same as A1, bamboo, straw, and thatch roof 1-2 1

A3 Same as A1, cement-sand mortar 1-3 2

A4 Same as A1, reinforced concrete bond beam, cane and mud roof

1-3 2

A5 Same as A1, with bamboo or rope reinforcement

1-2 1

RE RAMMED EARTH/PNEUMATICALLY IMPACTED STABILIZED EARTH

1-2 1

RS RUBBLE STONE (FIELD STONE) MASONRY All 1

RS1 Local field stones dry stacked (no mortar). Timber floors. Timber, earth, or metal roof.

1-2 1


46


Typical

RS2 Same as RS1 with mud mortar. 1-2 1

RS3 Same as RS1 with lime mortar. 1-3 2

RS4 Same as RS1 with cement mortar, vaulted brick roof and floors

1-3 2

RS5 Same as RS1 with cement mortar and reinforced concrete bond beam.

1-3 2

DS RECTANGULAR CUT STONE MASONRY BLOCK

All 1

DS1 Rectangular cut stone masonry block with mud mortar, timber roof and floors

1-2 1

DS2 Same as DS1 with lime mortar 1-3 2

DS3 Same as DS1 with cement mortar 1-3 2

DS4 Same as DS2 with reinforced concrete floors and roof

1-3 2

UFB UNREINFORCED FIRED BRICK MASONRY All 1

UFB1 Unreinforced brick masonry in mud mortar without timber posts

1-2 1

UFB2 Unreinforced brick masonry in mud mortar with timber posts

1-2 1

UFB3 Unreinforced fired brick masonry, cement mortar, timber flooring, timber or steel beams

and columns, tie courses (bricks aligned perpendicular to the plane of the wall)

1-3 2

UFB4 Same as UFB3, but with reinforced concrete floor and roof slabs

1-3 2

UCB UNREINFORCED CONCRETE BLOCK MASONRY, LIME/CEMENT MORTAR

All 1

MS MASSIVE STONE MASONRY IN LIME/CEMENT MORTAR

All 1

TU PRECAST CONCRETE TILT-UP WALLS (Precast Wall Panel Construction (Mid to high

rise, Former Soviet Union style))

All 1

INF

INFORMAL CONSTRUCTIONS (PARTS OF SLUMS/SQUATTERS)

Constructions made of wood/plastic sheets/GI Sheets/light metal or composite etc., not

confirming to engineering standards.

All 1

UNK Unknown Category (Not specified) All 1

Note: All refers to all possible ranges of number of stories of a particular structure type.

4.1.2 RISK-UE

The European RISK-UE project named “An advanced approach to earthquake risk scenarios

with applications to different European towns” began in 1999 at the end of the International

Decade for Natural Disaster Reduction (IDNDR) and ended in September 2004. The aim of

the project was the assessment of earthquake scenarios at a city scale within a European

context. The main goal was to be the implementation of Risk Management Plans and Plans


47

of Action to effectively reduce seismic risk and it was thus carried out in close collaboration

with the decision makers of the selected cities. In fact, this study had been applied to seven

European cities: Barcelona, Bitola, Bucharest, Catania, Nice, Sofia and Thessaloniki.

This project was constructed based on a modular methodology comprised of different work

packages (WP). The WP01 entitled ‘Distinctive features of European towns’ provided a

methodology for collecting and classifying buildings and earthquake data for urban seismic

risk assessment in Europe. For this reason, a matrix for building typology description at a

European scale has been proposed within the project. In Table 4.2 the RISK-UE taxonomy is

shown. The RISK-UE building classification matrix comprises 23 principal classes grouped

by the structural types and material of construction. Three different height classes (low-rise,

mid-rise and high-rise) represent further sub-groups. A building design code and a

performance level (pre-code, low-code, moderate-code and high-code) can also be assigned

to all the categories reported in Table 4.2.

Table 4.2 RISK-UE Taxonomy (RISK-UE, 2001-2004)

Label Description Rise Average No. of

stories

M11L Low-rise 1-2

M11M Rubble Stone, fieldstone

Mid-Rise 3-5

M12L Low-rise 1-2

M12M Mid-Rise 3-5

M12H

Simple Stone

High-rise 6+

M13L Low-rise 1-2

M13M Mid-Rise 3-5

M13H

Massive Stone

High-rise 6+

M2L Adobe Low-Rise 1-2

M31L Low-rise 1-2

M31M Mid-Rise 3-5

M31H

Wooden slabs URM

High-rise 6+

M32L Low-rise 1-2

M32M Mid-Rise 3-5

M32H

Masonry vaults URM

High-rise 6+

M33L Low-rise 1-2

M33M Mid-Rise 3-5

M33H

Composite slabs URM

High-rise 6+

M34L Low-rise 1-2

M34M Mid-Rise 3-5

M34H

RC slabs URM

High-rise 6+

M4L Reinforced or confined masonry Low-rise 1-2


48


stories

M4M Mid-Rise 3-5

M4H High-rise 6+

M5L Low-rise 1-2

M5M Mid-Rise 3-5

M5H

Overall strengthened masonry

High-rise 6+

RC1L Low-rise 1-2

RC1M Mid-Rise 3-5

RC1H

RC moment frames

High-rise 6+

RC2L Low-rise 1-2

RC2M Mid-Rise 3-5

RC2H

RC shear walls

High-rise 6+

RC31L Low-rise 1-2

RC31M Mid-Rise 3-5

RC31H

Regularly infilled RC frames

High-rise 6+

RC32L Low-rise 1-2

RC32M Mid-Rise 3-5

RC32H

Irregular RC frames

High-rise 6+

RC4L Low-rise 1-2

RC4M Mid-Rise 3-5

RC4H

RC dual systems

High-rise 6+

RC5L Low-rise 1-2

RC5M Mid-Rise 3-5

RC5H

Precast concrete tilt-up walls

High-rise 6+

RC6L Low-rise 1-2

RC6M Mid-Rise 3-5

RC6H

Precast concrete frames with concrete shear walls

High-rise 6+

S1L Low-rise 1-2

S1M Mid-Rise 3-5

S1H

Steel moment frames

High-rise 6+

S2L Low-rise 1-2

S2M Mid-Rise 3-5

S2H

Steel braced frames

High-rise 6+


49


stories

S3L Low-rise 1-2

S3M Mid-Rise 3-5

S3H

Steel frames with URM infill walls

High-rise 6+

S4L Low-rise 1-2

S4M Mid-Rise 3-5

S4H

Steel frames with cast-in-place concrete shear walls

High-rise 6+

S5L Low-rise 1-2

S5M Mid-Rise 3-5

S5H

Steel and RC composite systems

High-rise 6+

WL Low-rise 1-2

WM Wooden structures

Mid-Rise 3-5

4.2 PROPOSED TAXONOMY

The main requirements of a taxonomy is that it should be detailed, collapsible and

expandable. From the extensive study of fragility functions in this project it has become clear

that existing taxonomies could leave out a large number of characteristics that could be used

to identify the buildings (and distinguish between vulnerability), and in many cases it is not

clear how these taxonomies should be simply expanded to include such information.

PAGER-STR is one example, where the main typologies of buildings around the world are

present in the taxonomy but a new method for classifying them could be proposed to make

the classification more modular, and allow for expandability in the future. In order to address

this issue, a new taxonomy was developed in the Syner-G project, as described below.

Different main categories have been identified to describe a building and they are presented

in Table 4.3 such as the force resisting frame mechanism, material, elevation, cladding, etc.

It has to be noted that a hierarchy is used for some categories where additional information

might or might not be available. For example, the material is masonry but a user may or may

not know whether it is reinforced or unreinforced, fired brick or stone, and thus the definition

of these second parameters is optional

Table 4.3 Syner-G Taxonomy

CATEGORY SUB-CATEGORY

Force Resisting Mechanism (FRM1)

‚ Moment Resisting Frame (MRF)

‚ Structural Wall (W)

‚ Flat Slab (FS)

‚ Bearing Walls (BW)

Force Resisting Mechanism (FRM2)

‚ Embedded beams (EB)

‚ Emergent beams (EGB)


50


‚ Precast (P)

‚ Confined Masonry (CM)

FRM Material (FRMM1)

‚ Concrete (C)

‚ Masonry (M)

FRM Material (FRMM2)

‚ Reinforced Concrete (RC)

‚ Unreinforced Masonry (URM)

‚ Reinforced Masonry (RM)

‚ High strength concrete (>50MPa) (HSC)

‚ Average strength concrete (20-50 MPa) (ASC)

‚ Low strength concrete (<20 MPa) (LSC)

‚ Adobe (A)

‚ Fired brick (FB)

‚ Hollow clay tile (HC)

‚ Stone (S)

‚ High yield strength reinforcing bars (>300MPa) (HY)

‚ Low yield strength reinforcing bars (<300MPa) (LY)

‚ Classification of reinforcing bars based on EC2 (A,B,C)

‚ Lime mortar (LM)

‚ Cement mortar (CM)

‚ Mud mortar (MM)

‚ Smooth rebars (SB)

‚ Non-smooth rebars

‚ Concrete Masonry Unit (CMU)

‚ Autoclaved Aerated Concrete (AAC)

‚ High % of voids (H%)

‚ Low % of voids (L%)

‚ Regular Cut (Rc)

‚ Rubble (Ru)

Plan (P)

‚ Regular (R)

‚ Irregular (IR)

Elevation (E)

‚ Regular geometry (R)

‚ Irregular geometry (IR)

Cladding (C)

‚ Regular infill vertically (RI)

‚ Irregular infill vertically (IRI)

‚ Bare (B)

Cladding Characteristics (CM)

‚ Fired brick masonry (FB)

‚ High % voids (H%)

‚ Low % voids (L%)

‚ Autoclaved Aerated Concrete (AAC)

‚ Precast concrete (PC)

‚ Glazing (G)

‚ Single layer of cladding (SL)

‚ Double layer of cladding (DL)

‚ Open first floor (Pilotis) (P)


51


‚ Open upper floor (U)

Detailing (D)

‚ Ductile (D)

‚ Non-ductile (ND)

‚ With tie rods/beams (WTB)

‚ Without tie rods/beams (WoTB)

Floor System (FS)

‚ Rigid (R)

‚ Flexible (F)

Floor System Material (FSM)

‚ Reinforced concrete (RC)

‚ Steel (S)

‚ Timber (T)

Roof System (RS)

‚ Peaked (P)

‚ Flat (F)

‚ Gable End Walls (G)

Roof System Material (RSM)

‚ Timber (Ti)

‚ Thatch (Th)

‚ Corrugated Metal Sheet (CMS)

Height Level (HL)

‚ Low-rise (1-3) (L)

‚ Mid-rise (4-7) (M)

‚ High-rise (8-19) (H)

‚ Tall (20+)(Ta)

Number of stories (NS)

[Here the number of stories is explicitly given, if known]

Code Level (CL)

‚ None (NC)

‚ Low (<0.1g) (LC)

‚ Moderate (0.1-0.3g) (MC)

‚ High (>0.3g) (HC)

The building typology is defined using the label put in the brackets for each parameter within

a given category.

Example: FRM1-FRM2/FRMM1-FRMM2/P/E/C-CM/D/FS-FSM/RS-RSM/HL-NS/CL

More than one label can be used per category separated by a dash. For example, a building

with moment resisting frames and walls (dual system) would be MRF-W, a building with

mixed construction of reinforced concrete and masonry would be RC-M. Not all categories

need to be defined due to the fact that there might be lack of information about the structure.

In this case, where information is unknown, it can be left by an X. In the following, two

examples are shown:

o MRF/C-RC/X/X/RI-FB-H%/ND/R-RC/X/L-2/NC: moment resisting frame, in reinforced

concrete with regular external infill panels in brick with a high percentages of voids,

with non-ductile design details, with rigid reinforced concrete floor, low-rise, 2 storeys,

not designed to a seismic code;

o BW/M/X/X/X/X/X/X/L/X: low-rise masonry bearing wall structure.

The proposed taxonomy is constructed with a modular structure. In this way, other

categories and sub-categories can easily be added and all the different kind of European

buildings can be taken into account. Subsequently, additional categories for describing the

non-structural elements might be added.

This modular structure represents a new and a different approach in categorizing and

classifying buildings. It has a flexible structure and it can be used to describe a considerable


52

amount of different buildings. It can be updated at any time with new categories being added

and different features can be added to existing categories. In Chapter 6 it will be shown how

the modularity of this new taxonomy approach is very useful in the comparison of different

fragility functions estimated throughout Europe.

Harmonisation of European Fragility Functions

53

5 Harmonisation of European Fragility

Functions

One of the main challenges of this project is the harmonisation of European Fragility

Functions. As mentioned before, in the reviewed papers, different Intensity Measure Types

have been used to describe the level of ground shaking and a different number of limit states

has been adopted according to the damage scale used. For the purpose of comparing all the

different existing studies and fragility functions, harmonisation is an essential step. To

compare different curves, the same intensity measure types, the same number of limit states

and the same building typology is needed. Once the harmonisation is done and the functions

are comparable, other studies can be carried out to understand the variability between

functions.

There are three main steps that have to be followed in the harmonisation process:

1. Harmonisation of the intensity measure types;

2. Harmonisation of limit states;

3. Harmonisation of the building typology.

In the following sections these phases are described in detail. The ‘Harmonize function’ is

one of the functions developed in the proposed tool to store and manage fragility functions. It

can harmonize functions selected by the user. In Fig. 5.1 a screenshot of the harmonize

window is shown. For what concerns the instructions useful to use the tool, refer to Appendix

B.

Fig. 5.1 Harmonization of Fragility Curves – Syner-G tool


54

5.1 INTENSITY MEASURE TYPE

As a first phase of the project, it has been decided to convert all the intensity measure types

into PGA due to the ease with which it can be used in seismic risk assessment, and the fact

that it was already being used in the majority of the studies considered. There are different

conversion equations that allow IMTs to be converted to peak ground acceleration and some

recommendations have been made in the selection of some of these considering the fact

that the region of interest is Europe and considering the recent GEM1 and GEM research

which includes validation efforts (Cua et al., 2010). In Fig. 5.2 the Settings window of the tool

that presents the IMT conversion equations is shown. It can be seen that the Target Intensity

Measure Type is set to PGA.

It has not been possible, or straightforward, to convert all the different intensity measure

types found in the reviewed papers due to some shortcomings or lack of conversion

equations. For example, the conversion of Sd(TLS) to PGA would require knowledge of the

mean inelastic period at the limit state that was considered in the non-linear analyses.

Nevertheless, the majority of the fragility functions have been harmonized and the following

IMTs have been converted to PGA: Macroseismic Intensity, Sa(Ty), Sd(Ty) and PGV.

Fig. 5.2 Settings (IMT conversions) – Syner-G Fragility Function Manager

5.1.1 Macroseismic Intensity to PGA

There are a number of studies that have dealt with the problem of estimating intensity from

peak ground motion. The conversion equations in this direction named GMICEs (Ground

Motion to Intensity Conversion Equations) are used for example in the ShakeMap process of

estimating intensity from the available peak ground motion observations (Wald et al., 1999a).

On the contrary, conversion equations in the other direction called IGMCEs (Intensity to

Ground Motion Conversion Equations) are less common. They are usually necessary with

historical earthquake studies, where intensity data are available, and it is of interest to

estimate peak ground motion. It has to be noted that though it is common practice to simply

invert a GMICE to get an IGMCE, it is not necessarily correct; they are usually not invertible.

The Faenza and Michelini (2010) relationship represents an exception, since it is based on

an orthogonal distance regression, and it is designed to be both a GMICE and an IGMCE.


55

However, this relationship is not universally applicable because it is based on few high

intensity data and most of the events are in a limited moderate magnitude range.

Within this project both GMICE and IGMCE have been used, even if the GMICEs

relationships are not exactly invertible. However, in practise, these latter relationships are

often used to estimate peak ground motion. Functional forms of GMICE from both active

crustal and subduction zone have been selected.

Wald et al. (1999b) is tailored for California and USA. Notwithstanding that, in the framework

of GEM1 some validation efforts have been carried out which demonstrate that it is possible

to adopt this relationships worldwide with good results. For this reason, this relationship is

recommended as the default in the European context, as long as the fragility function sets

are given in MMI. Other relationships are provided and recommended which also have been

tested during GEM1 project. These relations are strongly related with some specific

European countries.

The following conversion equations have been proposed in the tool. For each equation, the

region of applicability is shown:

o Faenza and Michelini (2010). It is tailored for Italy:

)log(58.268.1]/[ 2scmMCS PGAI -? (1.25)

)log(35.211.5 ]/[ scmMCS PGVI -? (1.26)

o Margottini et al. (1992). It is tailored for Italy. Two different intensity scales (MSK-64

and MCS) and two different types of intensity can be considered in this relationship:

the local one that estimates intensity in the nearest town and the global one that

estimates intensity in the accelerometric site:

64]/[258.0358.0)( 2 /-? MSKscm

IPGALog Local Intensity (1.27)

64]/[158.0850.0)( 2 /-? MSKscm

IPGALog General Intensity (1.28)

MCSscmIPGALog 220.0525.0)(

]/[ 2 -? Local Intensity (1.29)

MCSscmIPGALog 179.0687.0)(

]/[ 2 -? General Intensity (1.30)

o Wald et al. (1999b):

)log(66.366.1]/[ 2scmMMI PGAI -/? (1.31)

)log(47.335.2 ]/[ scmMMI PGVI -? (1.32)

o Tselentis and Danciu (2008).It is tailored for Greece:

)log(56.395.0]/[ 2scmMMI PGAI -/? (1.33)

o Murphy and O’Brien (1977). It is tailored to Southern Europe:

MMIscmIPGALog 240.0570.0)(

]/[ 2 -? (1.34)


56

o Sorensen et al., (2008a). There are four different weighting schemes and it is tailored

for the Marmara Region (Turkey):

)log(20.333.6]/[ 2smEMS PGAI -? for raw data (1.35)

)log(62.351.6]/[ 2smEMS PGAI -? for weighted data (1.36)

)log(52.438.6]/[ 2smEMS PGAI -? for average data (1.37)

)log(29.451.6]/[ 2smEMS PGAI -? for low average data (1.38)

o Sorensen et al., (2008b). There are four different weighting schemes and it is tailored

for the Vrancea Region (Romania):





o Sorensen et al., (2008c). There are four different weighting schemes and it is tailored

for the Campania Region (Italy):





All the aforementioned studies differ from each other in some details such as the definition of

peak ground motion, assignment of ground motion-intensity pairs, distance measures or the

type of metadata supplied. All these differences, along with the different intensity scales,

different magnitude and distance ranges, contribute to the scatter in the data as well as to

the differences in derived functional forms.

In the following table the datasets collected are shown to give a quick overview of the

characteristics of the GMICEs and IGMCEs datasets used. The distance metric are defined

as follows:

o Rrup: closest distance to rupture (Km);

o Repi: epicentral distance (Km);

o RJB: Joyner-Boore distance (Km).


57

Table 5.1 Datasets collected (adapted from Cua et al., 2010)

Reference Magnitude

Range

Distance

Range

[km]

PGM Definition

Intensity

Range

used

Distance

metric

Intensity

type

N° of pairs

Region

Faenza and

Michelini (2010)

3.0~M~6.9 <200 Larger of 2 horizontal

comps

2-8 Repi MCS 266 Italy

Margottini et al.

(1992)

4.5~M~6.8 Larger of 2 horizontal

comps

4-8.5

4-8

MSK-64 MCS

Italy

Wald et al. (1999c)

5.6~M~7.3 <276 Larger of 2 horizontal

comps

4-9 Rrup and RJB

MMI 342 California,

USA

Tselentis and

Danciu, (2008)

4.0~M~6.9 <141 Independent

horizontal comps

4-8 Repi MMI 310 Greece

Murphy and

O’Brien, (1977)

3.0~M~8.0 Largest of available (2

or 3) components

1-10 Repi MMI Southern Europe

Sorensen et al.,

(2008a)

5.9~M~7.4 <335 5-10 RJB EMS98 32 Marmara Sea

Region (Turkey)

Sorensen et al.,

(2008b)

6.4~M~7.7 <500 5-8 RJB EMS98 46 Vrancea Region

(Romania)

Sorensen et al.,

(2008c)

6.3~M~7 <660 3-11 RJB EMS98 21 Campania Region (Italy)

5.1.2 Spectral acceleration to PGA

In order to convert the Spectral acceleration (Sa) at the elastic period of vibration to the

value of PGA, a standardized response spectrum shape is needed. Currently, the procedure

of IBC-2006 is incorporated in the tool. It has been decided to use IBC-2006 instead of

Eurocode 8 for the sake of simplicity. EC8 is identified by two different spectra (Type I and

Type II) in accordance with the magnitude of the considered earthquake. This would lead to

more complex system to estimate the conversion and would add uncertainty to the result.

The IBC-2006 spectrum can be divided into four parts (see Fig. 5.3): a region with a linear

function for periods from zero (period corresponding to PGA) to TA, a region with constant

spectral acceleration for periods between TAand TAV, a region with constant spectral velocity

between periods from TAV to TVD and a region with constant spectral displacement for

periods of TVD and beyond.


58

Fig. 5.3 IBC 2006 standardized spectral shape

The elastic response spectrum is defined by the following equations:

)6.04.0()3.0()(AT

TSaTSa ©-©? if 0<T<TA (1.47)

)3.0()( SaTSa ? if TA<T<TAV (1.48)

TSaTSa )1()( ? if TAV<T<TVD (1.49)

2)1()( TTSaTSa VD©? if TVD<T<10 (1.50)

Where the transition periods are defined as follows:

AVA TT 2.0? (1.51)

)3.0()1( SaSaTAV ? (1.52)

]2/)5[(10 /? MVDT (1.53)

When the moment magnitude M is not known, the TVD period is assumed to be 10 seconds

(i.e. M=7). It should be noted, that in the case of rock site conditions (class B), the following

expressions have to be considered:

PGASSa AS ©?? 5.2)3.0( (1.54)

PGASSa Al ??)1( (1.55)

Using this aforementioned formula, one can go from spectral acceleration Sa(T) to the value

of PGA by simply inverting Eq.1.47 to 1.50. If different types of soil (see Table 5.2) are

considered, some more steps are needed. In this latter case, the amplification of ground

shaking to account for local site conditions has to be considered and soil amplification


59

factors that have to be used are given by IBC-2006 provisions. The methodology amplifies

rock PGA according to the factors given in Table 5.3, as expressed by the following formula:

Aii FPGAPGA ©? (1.56)

in which PGAi is the peak ground acceleration (in g) for site class i, PGA is the peak ground

acceleration for rock soil and FAi is the short period amplification factor for site class i for

spectral acceleration SAS. For what concerns Sa(0.3)i and Sa(1)I of different soil classes, the

following equations have to be used:

AiASASii FSSSa ©??)3.0( (1.57)

ViAlAlii FSSSa ©??)1( (1.58)

SASi and SAli represent short-period spectral acceleration for site class i (in g) and 1 second-

period spectral acceleration for site class i (in g), respectively. The values of the factors FAi

and FVi are reported in Table 5.3. Moreover also the period TAV that defines the transition

period from constant spectral acceleration and constant spectral velocity is a function of the

site class:

TAVi ?SAl

SAS

Ã"

Å"Ä"

Ô"

Ö"Õ"©

FVi

FAi

Ã"

Å"Ä"

Ô"

Ö"Õ" (1.59)

Where:

o SAl is 1 second-period spectral acceleration for site class B;

o SAS is short-period spectral acceleration for site class B;

o FVi is 1 second-period amplification factor for site class i and spectral acceleration SAl;

o FAi is short-period amplification factor for site class i and spectral acceleration SAS.

Using these formulae, the PGA for each class of soil and for each value of spectral

acceleration has been developed by the tool. The conversion starts from Sa(Ty) and for this

reason, the user is asked to provide the value of the elastic period Ty of the considered

structure that can be known or can be found using some empirical relationships that relate

the height of a building to its elastic period. There are a number of empirical existing

relationships that can be used [e.g. Crowley et al. (2004), Crowley et al. (2008), Bal (2008),

Shah (2009), Abo Al Ezz (2008) and RISK-UE project-WP4 (2001-2004)].

Table 5.2 NEHRP site classification (FEMA, 1997a) as applied by IBC-2006 (ICC 2006)

Site Class Site Class Description Shear Wave Velocity

VS,30 [m/s]

A Hard Rock, Eastern U.S. sites only >1500

B Rock 760-1500

C Very dense soil and soft rock 360-760

D Stiff soil 180-360

E Soft soil, profile with >3m of soft clay defined as soil with plasticity index PI>20, moisture content w >40%

<180

F Soils requiring site specific evaluations -


60

Table 5.3 Site amplification factors as given in IBC-2006 (ICC 2006)

Site Class Site Class B

Spectral Acceleration A B C D E

Short Period, SAS [g] Short-Period Amplification Factor, FA

~ 0.25 0.8 1.0 1.2 1.6 2.5

(0.25, 0.50] 0.8 1.0 1.2 1.4 1.7

(0.50, 0.75] 0.8 1.0 1.1 1.2 1.2

(0.75,1.0] 0.8 1.0 1.0 1.1 0.9

<1.0 0.8 1.0 1.0 1.0 0.9

1-Second Period, SAl [g] 1-Second Period Amplification Factor, FV

~ 0.10 0.8 1.0 1.7 2.4 3.5

(0.1, 0.2] 0.8 1.0 1.6 2.0 3.2

(0.2, 0.3] 0.8 1.0 1.5 1.8 2.8

(0.3, 0.4] 0.8 1.0 1.4 1.6 2.4

>0.4 0.8 1.0 1.3 1.5 2.4

5.1.3 Spectral displacement to PGA

As mentioned in Section 2.4 two different intensity measure types concerning spectral

displacement have been used in the fragility functions stored in the tool: Sd(Ty) and Sd(TLS).

The first value of Sd refers to the elastic period Ty of the considered structure whereas the

second value of Sd refers to the inelastic period corresponding to a specific limit state TLS. It

is not been possible to convert Sd(TLS) to PGA in this study due to the difficulty in identifying

TLS for each study. With regards Sd(Ty), it is possible to convert it into Sa(Ty) and then,

following the procedure described in Section 5.1.2 it is possible to estimate PGA. The

conversion equation from Sd(Ty) to Sa(Ty) is given by the following expression:

)(2

)(

2

yy

y TSaT

TSd ÕÕÖ

ÔÄÄÅ

Ã?

r (1.60)

In the following Figure an example of converted IMT from spectral displacement Sd(Ty) to

PGA is shown. A fragility function set of a moment resisting frame, high rise, high code

developed by Kappos et al. (2006) is considered.


61

DS1 DS2 DS3 DS4 DS5

Sd(Ty) [cm]50454035302520151050

Pro

babili

ty o

f exceedance

1

0.9

0.8

0.7

0.6

0.5

0.4

0.3

0.2

0.1

0

DS1 DS2 DS3 DS4 DS5

PGA [g]21.81.61.41.210.80.60.40.20

Pro

babili

ty o

f exceedance

1

0.9

0.8

0.7

0.6

0.5

0.4

0.3

0.2

0.1

0

(a) (b)

Fig. 5.4 (a) Original Kappos et al. (2006), RC1-HR-HC (b) harmonized Kappos et al.

(2006), RC1-HR-HC

5.1.4 PGV to PGA

The peak ground velocity is widely used for a considerable variety of engineering

applications and some of the reviewed fragility functions are based on the PGV. Bommer

and Alarcon (2006) found that there is a good correlation between PGV and Sa(0.5). Based

on this finding they proposed the following equation that has been implemented in the tool:

20

]/)[5.0(]/[

2smSascmPGV ? (1.61)

It is possible to convert PGV into Sa(0.5) and then, following the procedure described in

Section 5.1.2, it is possible to estimate PGA.

5.2 LIMIT STATES

As explained in Section 2.5, in the reviewed papers a different number of limit states can be

found in accordance with the damage scale used or in accordance with the decisions of the

authors. For the comparison of fragility functions, the same number of limit states is needed.

It is believed that using two limit states is the simplest way of harmonising the limit states for

large number of fragility functions as nearly all sets of fragility functions already have these

two thresholds (yielding and collapse). Moreover, some curves have only these two limit

states. The selection and the identification of the limit states can be based on the results of

experiments, engineering judgment or experience from previous earthquake. When the limit

state is defined quantitatively with terms such as “moderate damage” or “extensive damage”

it becomes difficult to compare the functions from different studies; such comparison is

slightly more straightforward for the threshold to yielding and collapse. It is possible to say

that the yielding limit state will almost always be either the first or the second curve whilst the

collapse limit state is usually the last curve in the set.

The proposed tool allows functions to be harmonised also with regards to the number of limit

states. In the ‘Harmonize function’ window (see Fig. 5.1) it is possible to assign the original

limit states of the fragility function set to the yielding and collapse limit states. For instance, if


62

three limit states are considered (LS1, LS2 and LS3), the user can decide to assign LS1 to

yielding and LS3 to collapse. Otherwise, he/she can also decide to assign a mean between

LS1 and LS2 to yielding limit states. In Fig. 5.5, the Settings window of the tool that presents

the Damage scale is shown. In this window the user can change the number and the name

of the limit states.

Fig. 5.5 Settings (Damage scale conversions) – Syner-G Fragility Function Manager

In the following figure, an example of a fragility function set with five limit states and its

harmonized set is shown. In this case, the tool converts Sd(Ty) into PGA and then it

harmonizes the number of limit states. The yielding is assigned to ‘DS1’ and collapse is

assigned to ‘DS5’. The fragility function set shown in the figure refers to a reinforced

concrete building, high rise and constructed with a high code design.

DS1 DS2 DS3 DS4 DS5

Sd(Ty) [cm]50454035302520151050

Pro

babili

ty o

f exceedance

1

0.9

0.8

0.7

0.6

0.5

0.4

0.3

0.2

0.1

0

Yielding Collapse

PGA [g]2.4152.1461.8781.611.3411.0730.8050.5370.2680

Pro

bab

ility

of

exc

ee

dan

ce

1

0.9

0.8

0.7

0.6

0.5

0.4

0.3

0.2

0.1

0

(a) (b)

Fig. 5.6 (a) Original Kappos et al. (2006) (b) harmonized Kappos et al. (2006)

5.3 BUILDING TYPOLOGY

As described in Section 4.2, a taxonomy for European buildings has been derived in this

project. This taxonomy has been assigned to all of the fragility functions presented in


63

Appendix A. The fragility functions for a given taxonomical description can then be filtered

using the Syner-G Fragility Function Tool, which has been carried out for the comparison of

the functions, as described in the following chapter.

One main class of reinforced concrete structures has been selected to compare curves and

subsequently to calculate the fragility function that represents the mean of the fragilities as a

demonstration: reinforced concrete with moment resisting frame buildings. A project has

been created to consider this main class and sub-projects have been developed to group the

structures taking into account the height level, the code level, the cladding and the detailing.

In Fig. 5.7, the developed projects are shown. Each column represents a different level of

detail. This way, the user can choose to compare fragility functions taking into account

different levels of information. For instance, it should be possible to compare all the available

fragility functions sets concerning reinforced concrete with moment resisting frame building

with low rise or all the available fragility functions sets concerning reinforced concrete with

moment resisting frame building with low rise, seismically designed, bare and ductile. In Fig.

5.8, the chart concerning the reinforced concrete buildings with dual system is also shown as

example.

It has to be noted that to implement the tree reported in Fig. 5.7 some studied fragility

functions have been removed due to the non-comparability with the other curves. First at all,

all the fragility functions based on the Sd(TLS) cannot be included in the analyses due to the

fact that it was not possible to convert them into PGA which is the reference intensity

measure type. Then, for what concerns reinforced concrete with moment resisting frame

buildings, the 3 fragility functions of Rossetto and Elnashai (2003) and the 1 fragility curve of

Dumova-Jovanoska (2000) have been removed. The former has been deleted because the

curves refer to a very generic reinforced concrete buildings, while the latter is based on MMI

and it has been noted that converting fragility functions based on macroseismic intensity to

PGA with the conversion equations described in Section 5.1.1 leads to results that are very

distant from the mean of the others curves. This is due to different factors such as the

uncertainty in the relationships between PGA and macroseismic intensity and the limitation

about the use of the conversion equations (e.g. range of the intensity measure).

Observing Fig. 5.7 it is of immediate comprehension to understand which are the model

building types that have to be analysed in the future research developments. In fact, there

are some classes that are represented by very few fragility curves (sometimes just one

fragility function) and for this reason it is not possible to conduct a critical review and an

exhaustive study of the uncertainties.

In Section 6.2 the comparison of some of these curves is reported and two different methods

to calculate the dispersion of the curves are presented. It has to be mentioned that the

created sub-projects contain the building classes that can be developed with the available

fragility functions set that are currently provided with the Syner-G Fragility Function Manager

tool as an output of this deliverable and they do not represent all the possible combinations

of building classes.


64

Fig. 5.7 Flow chart for a Reinforced Concrete with Moment Resisting Frame building

class. In the blue brackets the number of fragility functions sets concerning the

project is reported.

FRM and

material Height Level Code Level Detailing Cladding

MRF/C/RC

[78]

Non ductile [2]

Bare [4]

Non

seismically

designed [8]

Ductile [6]

Non ductile[8] Seismically

designed [17]

Bare [14]

Regular infill

vertically [3] Non ductile[3]

Low rise [25]

Non ductile[6]

Non ductile[3]

Non ductile[3]

Bare [6]

Regular infill

vertically [3]

Irregular infill

vertically [3]

Non

seismically

designed [12]

Ductile [6]

Non ductile [9]

Non ductile [4]

Bare [15]

Regular infill

vertically [4]

Irregular infill

vertically [1]

Seismically

designed [20]

Mid rise [32]

Non ductile[3] Bare [3]

Non

seismically

designed [7]

Ductile [7]

Non ductile[7] Bare [14]

Seismically

designed [14]

High rise[21]

Non ductile [4]

Regular infill

vertically [2]

Irregular infill

vertically [2] Non ductile [2]

Non ductile [1]

Regular infill

vertically [2] Non ductile[2]

Non ductile[2] Irregular infill

vertically [2]


65

Fig. 5.8 Flow chart for a Reinforced Concrete with Dual System building class. In the

blue brackets the number of fragility functions sets concerning the project is

reported.

MRF/W/C/RC

Low Rise

Mid Rise

High Rise

Seismically

Designed

Seismically

Designed

Bare

Bare

Bare

Regular

infill

vertically

Regular

infill

vertically

Irregular

infill

vertically

Ductile

Ductile

Ductile

Non ductile

Non ductile

Non ductile

Non ductile

Non ductile

FRM and

material Height Level Code Level Detailing Cladding

[39]

[7]

[15]

[19]

[12]

[4]

[5]

[9]

[8]

[10]

[3]

[3]

[3]

[5]

[7]

[6]

[6]

[7]

Seismically

Designed

[7]

Ductile

[3]

Ductile

[5]

[16]

Regular

infill

vertically

[9]

[7]

Ductile

Ductile

Non ductile

[6]

[6]

[5]

[5] Non ductile

Non Seismically

Designed [3]

Non Seismically

Designed [3]

Comparison of Fragility Functions for European RC Buildings

67

6 Comparison of Fragility Functions for

European RC Buildings

6.1 COMPARISON OF FRAGILITY FUNCTIONS

The aim of this Chapter is to look at how fragility functions from the numerous existing

studies presented in Appendix A compare. The Syner-G Fragility Function Manager has

been used to filter the fragility functions for a given taxonomy of buildings, and then they

have been harmonised using the procedures described in Chapter 5.

The following figures show the variation in the fragility functions for this class of buildings at

the yield and collapse limit states.

(a) (b)

Fig. 6.1(a) Yield limit state and (b) collapse limit state harmonised fragility functions

for a reinforced concrete with moment resisting frame buildings, mid rise model

building type

Two methods are presented herein to calculate the mean and uncertainty of the various

curves presented. The second approach has been selected to define a mean curve (and the

dispersion) for each model building type because it assumes lognormal functions to describe

the fragility of a class of buildings, which will simplify the simulation analyses in the Syner-G

software. Some examples of the mean curves are reported.


68

6.1.1 Calculation of mean and variability in fragility functions: first approach

As can be seen from Fig. 6.1a and Fig. 6.1b, the scatter of the results is quite large and

therefore, computing a mean or median curve would not be enough to represent the possible

variation of fragility for a given typology of buildings (especially when the taxonomical

description is broad). Hence, 10% and 90% confidence intervals have been calculated.

Since the uncertainty varies greatly along the x axis, the above continuous functions were

discretised for a large number of intensity measure levels and for each level, a probabilistic

distribution was adjusted based on the dispersion of the probabilities of exceedance of each

curve. The following figure shows the distribution of probability of exceedance for a given

IML:

Fig. 6.2 Dispersion of probability of exceedance for a given IML

The following figure shows some of the distributions that were used to represent the

cumulative probability function of the set of values presented in the previous figure. Although

only the results for a given IML are being presented here, this procedure was repeated

systematically for each level of intensity.

Fig. 6.3 Comparison of several probabilistic distributions with the observed data


69

In order to better understand which type of distribution provides a best fit to the data, a

parameter was computed (“log likelihood1”) that represents a quantitative measure of this

aspect. The following table contains the results for this specific example:

Table 6.1 Log likelihood parameter per probabilistic distribution

Distribution Normal Lognormal Weibull Exponential Beta Gamma

Log likelihood

14,31 13,20 16,81 -13,83 45,52 13,61

"

The Beta distribution proved to give better results for all intensity measure levels. Hence, the

parameters A and B of this distribution were computed for each intensity measure level and

using an inverse cumulative beta function, the 10% and 90% confidence intervals were

computed. The following figures presents these results:

"( a )""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""

( b )"

Fig. 6.4 Mean, median, 10% and 90% confidence intervals for (a) limit state yielding

curve and (b) limit state collapse curve

6.1.2 Calculation of mean and variability in fragility functions: second approach

As it is shown in Fig. 6.5 (Bradley 2010), it has been possible to quantify a mean ±one or

more standard deviation fragilities to describe a class of buildings. The epistemic uncertainty

in the fragility function can also be computed. Fig. 6.5a and Fig. 6.5b report histograms of

the median and dispersion values obtained for each of the individual fragility functions. This

way, it is possible to define also the uncertainty in the median and dispersion values using

the coefficient of variation. In addition of these information, Fig. 6.5c shows that there is a

correlation between the uncertainty in the median and dispersion. Finally, Fig. 6.5d shows

1For further information on this parameter, seewww.mathworks.com/help/toolbox/stats/mle.html


70

the individual fragility functions and the mean±one standard deviation fragilities. For each of

the model building types identified within this project, the mean fragility functions and the

median and standard deviation values together with their coefficients of variation have been

computed and they are shown in the following section.

Fig. 6.5(a) Histogram of median values (b) histogram of dispersion values (c)

correlation between median and dispersion and (d) individual and mean ± one

standard deviation fragilities [from Bradley (2010)]

Plotting different combinations of the computed parameters (mean of logarithmic mean,

standard deviation of the logarithmic mean, mean of the logarithmic standard deviation,

standard deviation of the logarithmic standard deviation), it is possible to observe a

correlation between them (Fig. 6.6). Based on the distribution of the parameters, a

correlation coefficient matrix can be computed as the one shown in Table 6.2.

Table 6.2 Correlation coefficient matrix

o1 u1 o2 u2

o1 1 -0.302 0.642 -0.098

u1 1 0.053 0.710

o2 1 0.209

u2 symmetric

1


71

Fig. 6.6 Correlation between the individual fragility functions parameters

6.2 EXAMPLES OF PROPOSED FRAGILITIES

As described in Section 5.3, some projects have been created to divide the available fragility

functions sets in classes where the same model building type can be analysed, harmonized

and compared. In the following, four examples are described to show in detail the capability

of the tool and the comparison between different literature studies. The selected examples

going from a lower level of detail (reinforced concrete building with mid rise) to a higher level

of detail (reinforced concrete building with mid rise, seismically designed, bare and non

ductile).

6.2.1 Reinforced concrete with moment resisting frame buildings, mid rise

Starting from the considerable amount of fragility functions sets stored in the Syner-G

Fragility Function Manager tool and filtering the sets using the Syner-G taxonomy boxes, the

MRF/C/RC/X/X/X/X/X/X/MR/X class has been chosen and 32 sets have been selected.

Once the project has been saved (MRF-C-RC-MidRise.sgp’), the Harmonize module has

been used to harmonize all the sets. This way, 32 sets with two limit states (yielding and

collapse) and the same intensity measure type of reference (PGA) have been created. Fig.

6.7a and Fig. 6.7b show the comparison of the yield limit state and the comparison of the

collapse limit states, respectively.


72

(a) (b)

Fig. 6.7 (a) Yield limit state and (b) collapse limit state harmonised fragility functions

for a reinforced concrete with moment resisting frame buildings, mid rise model

building type

Currently a separate tool has then be used to calculate the mean and the coefficient of

variation of the logarithmic mean and logarithmic standard deviation values of the curves,

but this will eventually be integrated into the Syner-G Fragility Function Manager. In Fig. 6.8

the mean curve and the individual fragility functions are shown and in Table 6.3 the mean

and coefficient of variation (CoV) of the lognormal parameters of the fragility functions (i.e.

logarithmic mean and logarithmic standard deviation) are reported. The correspondent

correlation coefficient matrix is reported in Table 6.4.

(a) (b)

Fig. 6.8 Mean curve for (a) limit state yielding curve and (b) limit state collapse curve

for reinforced concrete with moment resisting frame buildings, mid rise model

building type


73

Table 6.3 Mean and CoV of the lognormal fragility parameters for reinforced concrete

with moment resisting frame buildings, mid rise model building type

Reinforced Concrete – Mid Rise

Yielding Collapse

Logarithmic Mean

Logarithmic Standard Deviation

Logarithmic Mean


Mean -1.853 0.481 -0.879 0.452

CoV (%) 26 19 48 23

Table 6.4 Correlation coefficient matrix for reinforced concrete with moment resisting

frame buildings, mid rise model building type

o1 u1 o2 u2

o1 1 0.116 0.537 0.272

u1 0.116 1 0.278 0.008

o2 0.537 0.278 1 -0.109

u2 0.272 0.008 -0.109 1


seismically designed



MRF/C/RC/X/X/X/X/X/X/MR/C class has been chosen and 20 sets have been selected.

Once the project has been saved (MRF-C-RC-MiRise-DesignedCode’), the followed

procedure is the same of the one described in Section 6.2.1. Fig. 6.9a and Fig. 6.9b show

the comparison of the yield limit state and the comparison of the collapse limit states,

respectively.


74

(a) (b)


for a reinforced concrete with moment resisting frame buildings, mid rise, seismically

designed model building type

In the following figure the mean curve and the individual fragility functions are shown and in

Table 6.5 the mean and coefficient of variation (CoV) of the lognormal parameters of the

fragility functions (i.e. logarithmic mean and logarithmic standard deviation) are shown. The

correspondent correlation coefficient matrix is reported in Table 6.6.

(a) (b)


for reinforced concrete with moment resisting frame buildings, mid rise, seismically

designed model building type


75


with moment resisting frame buildings, mid rise, seismically designed model building

type

Reinforced Concrete – Mid Rise, Seismically Designed

Yielding Collapse

Logarithmic Mean


Logarithmic Mean


Mean -1.876 0.476 -0.738 0.430

CoV (%) 28 21 67 28


frame buildings, mid rise, seismically designed model building type

o1 u1 o2 u2

o1 1 0.152 0.386 0.094

u1 0.152 1 0.371 0.354

o2 0.386 0.371 1 -0.279

u2 0.094 0.354 -0.279 1


seismically designed, bare



MRF/C/RC/X/X/B/X/X/X/MR/C class has been chosen and 15 sets have been selected.

Once the project has been saved (MRF-C-RC-MiRise-DesignedCode-Bare’), the followed

procedure is the same of the one described in Section 6.2.1. Fig. 6.11a and Fig. 6.11b show

the comparison of the yield limit state and the comparison of the collapse limit states,

respectively.


76

(a) (b)



designed, bare model building type





(a) (b)



designed, bare model building type


77


with moment resisting frame buildings, mid rise, seismically designed, bare model

building type

Reinforced Concrete – Mid Rise, Seismically Designed, Bare

Yielding Collapse

Logarithmic Mean


Logarithmic Mean


Mean -1.939 0.458 -0.821 0.452

CoV (%) 28 23 64 25


frame buildings, mid rise, seismically designed, bare model building type

o1 u1 o2 u2

o1 1 0.189 0.504 -0.041

u1 0.189 1 0.276 0.723

o2 0.504 0.276 1 -0.089

u2 -0.041 0.723 -0.089 1


seismically designed, bare, non ductile



MRF/C/RC/X/X/B/ND/X/X/MR/C class has been chosen and 9 sets have been selected.

Once the project has been saved (MRF-C-RC-MiRise-DesignedCode-

Bare_Nonductile.sgp’), the followed procedure is the same of the one described in Section

6.2.1. Fig. 6.13a and Fig. 6.13b show the comparison of the yield limit state and the

comparison of the collapse limit states, respectively.


78

(a) (b)



designed, bare, non ductile model building type





(a) (b)



designed, bare, non ductile model building type


79


with moment resisting frame buildings, mid rise, seismically designed, bare non

ductile model building type

Reinforced Concrete – Mid Rise, Seismically Designed, Bare and Non Ductile

Yielding Collapse

Logarithmic Mean


Logarithmic Mean


Mean -1.832 0.474 -1.091 0.485

CoV (%) 33 21 48 24

Table 6.10 Correlation coefficient matrix for reinforced concrete with moment

resisting frame buildings, mid rise, seismically designed, bare non ductile model

building type

o1 u1 o2 u2

o1 1 0.158 0.783 0.033

u1 0.158 1 0.118 0.614

o2 0.783 0.118 1 -0.453

u2 0.033 0.614 -0.453 1

Conclusion

81

7 Conclusions

A number of studies related to the fragility of buildings have been reviewed in this task of the

project and the fragility functions have been stored in a tool able to collect, harmonize and

compare them. Thanks to this literature review the identification of the main reinforced

concrete building classes in Europe has been obtained and the key parameters that affect

their fragility have been identified and used to propose a new taxonomy. The application of

the Syner-G taxonomy proposed in the project to all existing functions has allowed the

fragility functions to be grouped together and directly compared. Furthermore, based on the

aforementioned grouping, a set of mean fragility functions, with associated uncertainty and

correlation coefficient matrix, for a number of reinforced concrete typologies have been

proposed.

Though there are different typologies of reinforced concrete structures, the majority of

fragility studies have been made through studying bare moment resisting frame buildings.

For this reason, it has been possible to propose a set of fragility functions for this main class

of buildings and some of its sub-classes. It has to be noted that a number of fragility

functions have been removed from the comparison for a number of reasons, which can be

assigned to “expert opinion”. For example, it has been noted that converting fragility

functions based on macroseismic intensity to PGA with the conversion equations described

in Section 5.1.1 leads to results that are very distant from the mean of the others curves.

This is due to different factors such as the uncertainty in the relationships between PGA and

macroseismic intensity and the limitation about the use of the conversion equations (e.g.

range of the intensity measure for which they are applicable). Moreover, all the fragility

curves based on the spectral displacement corresponding to a specific limit state (Sd(TLS))

could not be used in the comparison due to the fact that it was not possible to harmonize

these functions converting Sd(TLS) to PGA. Notwithstanding that, all the sets of fragility

functions have been stored in the tool and they can be further investigated by users of the

Fragility Function Manager.

To conclude, the efforts undertaken herein to analyze a consistent number of fragility

functions have been useful to understand the gaps that exist in research and that need to be

filled with future research. In particular, fragility functions for high rise MRF with seismic

design and infills were not identified in the review, and frame-wall structures without seismic

design were much less common than their seismically designed counterparts. The reason

for the reduced number of studies is likely to be related to the lower frequency of these

building typologies in Europe, but it is nevertheless suggested that Figure 5.7 and Figure 5.8

could provide some guidance on where to focus fragility function efforts in the future.

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83

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Review Forms

87

Appendix A

A Review forms

AhmadEtAl2010-RC

Reference Ahmad N., H. Crowley, R. Pinho. 2011. Analytical Fragility Functions for Reinforced

Concrete and Masonry Buildings and Buildings Aggregates of Euro-Mediterranean

Regions – UPAV methodology. Internal Report, Syner-G Project 2009/2012.

Region of

applicability

Euro-Mediterranean Regions (Greek, Italy, Turkey)

Element at risk Buildings

Typology of

element at risk

considered

RC frame structures (Regular and Irregular) – Low Rise – 2 Storey

RC frame structures (Regular and Irregular) – Mid Rise– 5 Storey

RC frame structures (Regular and Irregular) – High Rise– 8 Storey

Syner-G

Taxonomy

MRF/C/RC/R/R/B-X/ND/R-RC/X-X/LR-2/X

MRF/C/RC/IR/R/B-X/ND/R-RC/X-X/LR-2/X

MRF/C/RC/R/R/B-X/D/R-RC/X-X/LR-2/X

MRF/C/RC/IR/R/B-X/D/R-RC/X-X/LR-2/X

MRF/C/RC/R/R/B-X/ND/R-RC/X-X/MR-5/X

MRF/C/RC/IR/R/B-X/ND/R-RC/X-X/MR-5/X

MRF/C/RC/R/R/B-X/D/R-RC/X-X/MR-5/X

MRF/C/RC/IR/R/B-X/D/R-RC/X-X/MR-5/X

MRF/C/RC/R/R/B-X/ND/R-RC/X-X/HR-8/X

MRF/C/RC/IR/R/B-X/ND/R-RC/X-X/HR-8/X

MRF/C/RC/R/R/B-X/D/R-RC/X-X/HR-8/X

MRF/C/RC/IR/R/B-X/D/R-RC/X-X/HR-8/X

Sample data Buildings: 400 sample reinforced concrete buildings from a given class (say Low Rise). Prototype buildings

designed to simulate the existing Euro-Mediterranean buildings (Greece, Italy, Turkey in particular) analyzed

dynamically to derive equivalent static SDOF system using NLTHA. Mainly the limit state secant period and

displacement capacity models are developed.

Seismic Hazard: 10natural accelerograms from USA and IBC-2006 rock spectra (for fragility derivation)

Methodology Analytical – Nonlinear Static

Damage States Five damage states are considered:

‚ No damage

‚ Slight

‚ Moderate

‚ Extensive

Review Forms

88

‚ Complete

Intensity

Measure Type

Sd(TLS) [m] and PGA [g]

Fragility Function

Parameters

Lognormal distribution

IMT = Sd(TLS) [m]

Slight Moderate Extensive Complete Nonductile

Regular Mean

Standard

Deviation Mean

Standard

Deviation Mean

Standard

Deviation Mean

Standard

Deviation

Low-Rise 0.016 0.004 0.021 0.006 0.039 0.017 0.059 0.028

Mid-Rise 0.030 0.008 0.039 0.013 0.057 0.022 0.076 0.034

High-Rise 0.044 0.011 0.060 0.020 0.076 0.028 0.096 0.040

IMT = Sd(TLS) [m]


Irregular Mean

Standard

Deviation Mean

Standard

Deviation Mean

Standard

Deviation Mean

Standard

Deviation

Low-Rise 0.016 0.004 0.022 0.008 0.045 0.020 0.068 0.034

Mid-Rise 0.030 0.008 0.041 0.015 0.063 0.026 0.086 0.042

High-Rise 0.045 0.012 0.062 0.022 0.083 0.032 0.106 0.046

IMT = Sd(TLS) [m]

Slight Moderate Extensive Complete Ductile

Regular Mean

Standard

Deviation Mean

Standard

Deviation Mean

Standard

Deviation Mean

Standard

Deviation

Low-Rise 0.016 0.004 0.021 0.006 0.039 0.017 0.111 0.063

Mid-Rise 0.030 0.008 0.039 0.013 0.057 0.023 0.130 0.069

High-Rise 0.044 0.011 0.059 0.019 0.075 0.028 0.148 0.072

IMT = Sd(TLS) [m]


Irregular Mean

Standard

Deviation Mean

Standard

Deviation Mean

Standard

Deviation Mean

Standard

Deviation

Low-Rise 0.016 0.004 0.022 0.008 0.045 0.020 0.130 0.077

Mid-Rise 0.030 0.008 0.041 0.015 0.063 0.027 0.150 0.085

High-Rise 0.044 0.012 0.062 0.022 0.083 0.032 0.168 0.089

Review Forms

89

IMT = PGA [g]


Regular Mean

Standard

Deviation Mean

Standard

Deviation Mean

Standard

Deviation Mean

Standard

Deviation

Low-Rise 0.090 0.031 0.130 0.060 0.263 0.101 0.350 0.132

Mid-Rise 0.085 0.028 0.122 0.055 0.187 0.077 0.235 0.093

High-Rise 0.080 0.027 0.112 0.050 0.153 0.066 0.187 0.077

IMT = PGA [g]


Irregular Mean

Standard

Deviation Mean

Standard

Deviation Mean

Standard

Deviation Mean

Standard

Deviation

Low-Rise 0.090 0.031 0.132 0.063 0.277 0.110 0.368 0.143

Mid-Rise 0.085 0.029 0.124 0.058 0.196 0.083 0.250 0.101

High-Rise 0.080 0.027 0.116 0.053 0.165 0.072 0.203 0.084

IMT = PGA [g]


Regular Mean

Standard

Deviation Mean

Standard

Deviation Mean

Standard

Deviation Mean

Standard

Deviation

Low-Rise 0.090 0.031 0.130 0.060 0.262 0.100 0.517 0.192

Mid-Rise 0.085 0.028 0.121 0.052 0.185 0.075 0.328 0.123

High-Rise 0.080 0.027 0.113 0.051 0.154 0.067 0.260 0.102

IMT = PGA [g]


Irregular Mean

Standard

Deviation Mean

Standard

Deviation Mean

Standard

Deviation Mean

Standard

Deviation

Low-Rise 0.090 0.031 0.132 0.063 0.275 0.110 0.542 0.210

Mid-Rise 0.085 0.028 0.125 0.058 0.196 0.084 0.355 0.139

High-Rise 0.080 0.027 0.116 0.054 0.163 0.072 0.280 0.113

Figures

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Sd [cm]20181614121086420

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Sd [cm]20181614121086420

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Sd [cm]20181614121086420

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Mid Rise – Nonductile Reg Mid Rise – Nonductile

IrregularSlight Moderate Extensive Complete

Sd [cm]20181614121086420

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Sd [cm]20181614121086420

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Review Forms

91


Sd [cm]20181614121086420

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PGA [g]10.90.80.70.60.50.40.30.20.10

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PGA [g]10.90.80.70.60.50.40.30.20.10

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PGA [g]10.90.80.70.60.50.40.30.20.10

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PGA [g]10.90.80.70.60.50.40.30.20.10

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Review Forms

92


PGA [g]10.90.80.70.60.50.40.30.20.10

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PGA [g]10.90.80.70.60.50.40.30.20.10

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PGA [g]10.90.80.70.60.50.40.30.20.10

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PGA [g]10.90.80.70.60.50.40.30.20.10

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PGA [g]10.90.80.70.60.50.40.30.20.10

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Uncertainty Uncertainties in lateral stiffness, strength, and damage limit states are expressed by using controlled Monte

Carlo simulations. The possibility of beam-sway and column-sway structures are considered within each

building class which are identified for assessment using the flexibility-based sway index. On the other hand,

large number of randomly generated linear displacement response spectra are used for the derivation of

fragility functions.

Comments The considered building stock represents the Euro-Mediterranean buildings in general and Greek, Italian and

Turkish building stock in particular.

Review Forms

93

AkkarEtAl2005

Reference S. Akkar, H. Sucuoglu, & A. Yakut, “Displacement-based fragility functions for low- and mid-rise

ordinary concrete buildings”, Earthquake Spectra 21(4), 901-927, 2005

Region of applicability Turkey


Typology of element at

risk considered

RC frame structures – Low Rise – low level seismic design (1975 Turkish Seismic Code)

RC frame structures – Mid Rise – low level seismic design (1975 Turkish Seismic Code)

Syner-G Taxonomy MRF/C/RC/X/X/RI-FB/ND/X-X/X-X/LR-2/MC

MRF/C/RC/X/X/RI-FB/ND/X-X/X-X/LR-3/MC

MRF/C/RC/X/X/RI-FB/ND/X-X/X-X/MR-4/MC

MRF/C/RC/X/X/RI-FB/ND/X-X/X-X/MR-5/LC

Sample data Buildings: 32 sample reinforced concrete buildings from two to five-story. Real buildings in Duzce

Seismic Hazard: 82 recorded accelerograms from Turkey and USA

Methodology Analytical – Nonlinear Dynamic

Damage States Four damage states are considered:

‚ No damage

‚ Light

‚ Moderate

‚ Severe

Intensity Measure Type PGV [cm/s]

Fragility Function

Parameters


IMT = PGV [cm/s]

Light Moderate Severe

Mean Standard

Deviation Mean

Standard

Deviation Mean

Standard

Deviation

RC – 2 storeys 17.036 10.123 78.069 21.401 118.000 52.000

RC – 3 storeys 15.986 9.492 75.083 25.399 99.000 36.100

RC – 4 storeys 14.212 8.027 59.589 23.642 75.670 19.151

RC – 5 storeys 13.042 8.692 49.035 19.327 65.712 19.932

Figures


PGV

1009080706050403020100

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PGV

1009080706050403020100

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Review Forms

94


PGV

1009080706050403020100

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RC frame structures – 4 storeys RC frame structures – 5 storeys

Uncertainty Uncertainties in lateral stiffness, strength and damage limit states are expressed by using statistical

distribution. On the other hand, using a set of 82 strong ground motions spanning a broad range of

intensity incorporates randomness of seismic excitations.

Comments Almost 75% of approximately one million buildings in Istanbul are in this category.

Review Forms

95

BorziEtAl2007

Reference B Borzi, R. Pinho, H. Crowley, “SP-BELA: un metodo meccanico per la definizione della vulnerabilità

basato su analisi pushover semplificate”, ANIDIS, Pisa, 2007 (in italian)

Region of

applicability

Italy


Typology of element

at risk considered

Reinforced Concrete Buildings: non-seismically designed and seismically designed (c=5%, c=7.5%,

c=10%, c=12.5%)

Syner-G Taxonomy MRF/C/RC-ASC-HY/IR/R/B-X/ND/X-X/X-X/LR-2/NC

MRF/C/RC-ASC-HY/IR/R/B-X/ND/X-X/X-X/MR-4/NC

MRF/C/RC-ASC-HY/IR/R/B-X/ND/X-X/X-X/HR-8/NC

MRF/C/RC-ASC-HY/R/R/B-X/ND/X-X/X-X/LR-2/LC

MRF/C/RC-ASC-HY/R/R/B-X/ND/X-X/X-X/MR-4/LC

MRF/C/RC-ASC-HR/R/R/B-X/ND/X-X/X-X/HR-8/LC

Sample data Buildings: Random population of buildings is generated using Monte Carlo simulation where random

variables are used to describe the geometry and the material properties of the structures.



‚ No damage

‚ LS1

‚ LS2

‚ LS3

Intensity Measure

Type

PGA [g]

Fragility Function

Parameters

Lognormal Distribution

IMT = PGA [g]

Non-Seismically Designed

LS1 LS2 LS3

Mean StDev Mean StDev Mean StDev

2 storeys 0.15 0.08 0.27 0.15 0.33 0.17

4 storeys 0.17 0.08 0.32 0.17 0.38 0.20

8 storeys 0.23 0.12 0.48 0.27 0.57 0.33

Seismically Designed (Lateral force = 5%)

LS1 LS2 LS3

Mean StDev Mean Mean StDev Mean

2 storeys 0.17 0.08 0.28 0.14 0.35 0.18

4 storeys 0.23 0.11 0.35 0.20 0.42 0.24

8 storeys 0.33 0.17 0.62 0.34 0.80 0.44

Review Forms

96

Seismically Designed (Lateral force = 7.5%)

LS1 LS2 LS3


2 storeys 0.18 0.09 0.30 0.15 0.37 0.19

4 storeys 0.27 0.15 0.41 0.22 0.49 0.27

8 storeys 0.38 0.21 0.62 0.34 0.77 0.45

Seismically Designed (Lateral force = 10%)

LS1 LS2 LS3


2 storeys 0.20 0.10 0.34 0.19 0.41 0.22

4 storeys 0.31 0.17 0.46 0.25 0.54 0.29

8 storeys 0.40 0.19 0.57 0.30 0.67 0.35

Seismically Designed (Lateral force = 12.5%)

LS1 LS2 LS3


2 storeys 0.23 0.12 0.38 0.20 0.46 0.23

4 storeys 0.33 0.16 0.49 0.27 0.55 0.28

8 storeys 0.42 0.22 0.53 0.28 0.60 0.32

Figures

LS1 LS2 LS3

PGA

0.50.450.40.350.30.250.20.150.10.050

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2 storeys – Non-Seismically Designed 4 storeys – Non-Seismically Designed

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PGA

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PGA

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8 storeys – Non-Seismically Designed 2 storeys – Seismically Designed (c=5%)

Review Forms

97

LS1 LS2 LS3

PGA

0.50.450.40.350.30.250.20.150.10.050

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PGA

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LS1 LS2 LS3

PGA

0.50.450.40.350.30.250.20.150.10.050

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PGA

0.50.450.40.350.30.250.20.150.10.050

Pro

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of exceedance

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2 storeys – Seismically Designed (c=7.5%) 4 storeys – Seismically Designed (c=7.5%)

LS1 LS2 LS3

PGA

0.50.450.40.350.30.250.20.150.10.050

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LS1 LS2 LS3

PGA

0.50.450.40.350.30.250.20.150.10.050

Pro

bability

of exceedance

1

0.9

0.8

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8 storeys – Seismically Designed (c=7.5%) 2 storeys – Seismically Designed (c=10%)

LS1 LS2 LS3

PGA

0.50.450.40.350.30.250.20.150.10.050

Pro

bability

of exceedance

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LS1 LS2 LS3

PGA

0.50.450.40.350.30.250.20.150.10.050

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4 storeys – Seismically Designed (c=10%) 8 storeys – Seismically Designed (c=10%)

LS1 LS2 LS3

PGA

0.50.450.40.350.30.250.20.150.10.050

Pro

bability

of exceedance

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0.8

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PGA

0.50.450.40.350.30.250.20.150.10.050

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of exceedance

1

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0.8

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Review Forms

98

LS1 LS2 LS3

PGA

0.50.450.40.350.30.250.20.150.10.050

Pro

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8 storeys – Seismically Designed (c=12.5%)

Uncertainty The uncertainty in the geometric and material properties are accounted for in the methodology.

Review Forms

99

BorziEtAl2008

Reference B. Borzi, H. Crowley, R. Pinho, “The influence of infill panels on vulnerability curves for RC buildings”,

Proceedings of the 14th World Conference on Earthquake Engineering, Beijing, China, 2008.

Region of

applicability

Italy


Typology of element

at risk considered

Reinforced Concrete Buildings: non-seismically designed and seismically designed (c=10%). Bare frame

buildings, regularly infilled buildings and irregularly infilled buildings (pilotis).

Syner-G Taxonomy MRF/C/RC-ASC-HY/R/R/RI-FB/ND/X-X/X-X/MR-4/NC

MRF/C/RC-ASC-HY/R/R/IRI-FB-P/ND/X-X/X-X/MR-4/NC


MRF/C/RC-ASC-HY/R/R/RI-FB/ND/X-X/X-X/MR-4/LC

MRF/C/RC-ASC-HY/R/R/IRI-FB-P/X/X-X/X-X/MR-4/LC

MRF/C/RC-ASC-HY/R/R/B-X/ND/X-X/X-X/MR-4/LC

Sample data Random population of buildings is generated using Monte Carlo simulation where random variables are

used to describe the geometry and the material properties of the structures.



‚ No damage

‚ LS1

‚ LS2

‚ LS3

Intensity Measure

Type

PGA [g]

Fragility Function

Parameters


IMT = PGA [g]

Non-Seismically Designed

LS1 LS2 LS3


RC4storeys

Infilled 0.21 0.16 0.39 0.23 0.49 0.27

RC4storeys

Pilotis 0.21 0.10 0.34 0.16 0.41 0.19

RC4storeys

Bare 0.18 0.09 0.28 0.14 0.32 0.17

Review Forms

100

Seismically Designed, lateral force c=10%

LS1 LS2 LS3


RC4storeys

Infilled 0.39 0.22 0.49 0.28 0.57 0.32

RC4storeys

Pilotis 0.31 0.15 0.42 0.22 0.48 0.24

RC4storeys

Bare 0.30 0.16 0.43 0.21 0.51 0.25

Figures

LS1 LS2 LS3

PGA

0.50.450.40.350.30.250.20.150.10.050

Pro

bability

of exceedance

1

0.9

0.8

0.7

0.6

0.5

0.4

0.3

0.2

0.1

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LS1 LS2 LS3

PGA

0.50.450.40.350.30.250.20.150.10.050P

robability

of exceedance

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0.9

0.8

0.7

0.6

0.5

0.4

0.3

0.2

0.1

0

RCInfilled-4-NonSeismically Designed RCPilotis-4-NonSeismically Designed

LS1 LS2 LS3

PGA

0.50.450.40.350.30.250.20.150.10.050

Pro

bability

of exceedance

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0.9

0.8

0.7

0.6

0.5

0.4

0.3

0.2

0.1

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LS1 LS2 LS3

PGA

0.50.450.40.350.30.250.20.150.10.050

Pro

bability

of exceedance

1

0.9

0.8

0.7

0.6

0.5

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RCBare-4-NonSeismically Designed RCInfilled-4-Seismically Designed (10%)

LS1 LS2 LS3

PGA

0.50.450.40.350.30.250.20.150.10.050

Pro

bability

of exceedance

1

0.9

0.8

0.7

0.6

0.5

0.4

0.3

0.2

0.1

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LS1 LS2 LS3

PGA

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Pro

bability

of exceedance

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0.9

0.8

0.7

0.6

0.5

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0.3

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0.1

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RCPilotis-4-Seismically Designed(10%) RCBare-4-Seismically Designed (10%)


Review Forms

101

BorziEtAl2008a

Reference Borzi B., Pinho R., Crowley H., “Simplified pushover-based analysis for large-scale assessment of RC

buildings”, Engineering Structures, 30, 804-820, 2008a.

Region of

applicability

Italy


Typology of element

at risk considered

Reinforced Concrete Buildings – Non-seismically designed

Syner-G Taxonomy MRF/C/RC-ASC-HY/IR/R/B-X/ND/X-X/X-X/LR-2/NC

MRF/C/RC-ASC-HY/IR/R/B-X/ND/X-X/X-X/LR-3/NC




MRF/C/RC-ASC-HY/IR/R/B-X/ND/X-X/X-X/HR-8/NC

Sample data Random population of buildings is generated using Monte Carlo simulation where random variables are

used to describe the geometry and the material properties of the structures.



‚ No damage

‚ LS1

‚ LS2

‚ LS3

Intensity Measure

Type

PGA

Fragility Function

Parameters


IMT = PGA [g]

LS1 LS2 LS3


2storeys 0.15 0.08 0.27 0.15 0.33 0.17

3storeys 0.16 0.08 0.29 0.15 0.36 0.19

4storeys 0.17 0.08 0.32 0.17 0.38 0.20

5storeys 0.18 0.09 0.35 0.19 0.43 0.23

6storeys 0.21 0.12 0.40 0.22 0.47 0.26

8storeys 0.23 0.12 0.48 0.27 0.57 0.33

Review Forms

102

Figures

LS1 LS2 LS3

PGA

0.50.450.40.350.30.250.20.150.10.050

Pro

bability

of exceedance

1

0.9

0.8

0.7

0.6

0.5

0.4

0.3

0.2

0.1

0

LS1 LS2 LS3

PGA

0.50.450.40.350.30.250.20.150.10.050

Pro

bability

of exceedance

1

0.9

0.8

0.7

0.6

0.5

0.4

0.3

0.2

0.1

0

RC – 2 storeys RC – 3 storeys

LS1 LS2 LS3

PGA

0.50.450.40.350.30.250.20.150.10.050

Pro

bability

of exceedance

1

0.9

0.8

0.7

0.6

0.5

0.4

0.3

0.2

0.1

0

LS1 LS2 LS3

PGA

0.50.450.40.350.30.250.20.150.10.050

Pro

bability

of exceedance

1

0.9

0.8

0.7

0.6

0.5

0.4

0.3

0.2

0.1

0


LS1 LS2 LS3

PGA

0.50.450.40.350.30.250.20.150.10.050

Pro

bability

of exceedance

1

0.9

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DumovaJovanoska2000

Reference E. Dumova-Jovanoska, “Fragility curves for reinforced concrete structures in Skopje

(Macedonia) region”, Soil Dynamics and Earthquake Engineering 19(6), 455-466, 2000

Region of applicability Skopje – Former Yugoslav Republic of Macedonia


Typology of element at risk

considered

RC frame structures – Mid Rise – Macedonian design code

RC frame structures – High Rise – Macedonian design code

Syner-G Taxonomy MRF/C/RC/R/R/B-X/ND/X-X/X-X/MR-6/LC

MRF-W/C/RC/R/R/B-X/ND/X-X/X-X/HR-16/LC

Sample data Buildings: Schematic 6-storey and 16-storey frame structures

Seismic Hazard: 240 synthetic time histories were generated



‚ No damage

‚ Minor

‚ Moderate

‚ Severe

‚ Collapse

Intensity Measure Type MMI

Fragility Function Parameters Discrete Fragility Function. Both fragility curves and damage probability matrix are provided

Damage probability of exceedance matrix for RC frame structures lower than 10 stories

Damage probability of exceedance matrix

Damage States VII VIII IX X XI

Minor 0 0.91 55.62 91.43 98.44

Moderate 0 0 3.97 77.66 96.41

Severe 0 0 0 29.13 87.85

Collapse 0 0 0 0.34 62.53

Damage probability of exceedance matrix for RC frame structures higher than 10 stories

Damage probability of exceedance matrix

Damage States VII VIII IX X XI

Minor 0 0.11 51.09 88.22 99.56

Moderate 0 0 5.5 69.93 98.88

Severe 0 0 0 10.26 88.87

Collapse 0 0 0 0 33.04

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Figures

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MMI

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Minor Moderate Severe Collapse

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Uncertainty Compared with the high uncertainty related to earthquake phenomenon, the random character

of structural parameters can be considered to be of a lower order. This can be justification for

excluding the variation of these parameters within the frames of this investigation.

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ErberikAndElnashai2004

Reference M. A. Erberik & A. S. Elnashai, “Vulnerability analysis of flat slab structures”, 13th World

Conference on Earthquake Engineering, 2004

Region of applicability Mediterranean basin and USA



considered

Flat-slab RC buildings with masonry infill walls – Mid Rise

Syner-G Taxonomy FS/C/RC-ASC-HY/R/R/RI-X/D/X-X/X-X/MR-5/HC

Sample data Buildings: schematic 5-story flat slab structure designed according to the regulations of ACI 318-

99

Seismic hazard: 10 spectrum-compatible recorded accelerograms



‚ No damage

‚ Slight

‚ Moderate

‚ Extensive

‚ Complete

Intensity Measure Type Sd (TY) [mm]

Fragility Function Parameters Lognormal distribution

IMT = Sd (Ty) [mm]

Mean Standard

Deviation

Slight 6.948 2.487

Moderate 34.783 9.988

Extensive 48.919 14.029

Complete 69.909 21.164

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Uncertainty The yield strength of steel and the compressive strength of concrete have been chosen as the

random variables. In particular, a lognormal distribution is assumed for the yield strength of steel

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(mean= 475 MPa and cov = 6%) and a normal distribution is employed for the variability of

concrete strength (mean= 28 MPa and cov = 15%). To treat uncertainty, Latin Hypercube

Sampling (LHS) Technique is employed.

Comments The developed curves were compared with those in the literature derived for moment-resisting

RC frames. The study concluded that earthquake losses for flat-slab structures are in the same

range as for moment-resisting frames for low limit states, and considerably different at high

damage levels. This is due to the different structural response characteristics of the two

structural forms.

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Erberik2008

Reference M. A. Erberik, “Fragility-based assessment of typical mid-rise and low-rise RC buildings in Turkey”,

Engineering Structures 30(5), 1360-1374, 2008




risk considered

RC structures – Low Rise – bare frame

RC structures – Low Rise – infilled frame

RC structures – Mid Rise – bare frame

RC structures – Mid Rise – infilled frame

Syner-G Taxonomy MRF/C/RC-LSC/R/R/B-X/ND/X-X/X-X/LR-X/LC

MRF/C/RC-LSC/R/R/RI-FB/ND/X-X/X-X/LR-X/LC

MRF/C/RC-LSC/R/R/B-X/ND/X-X/X-X/MR-X/LC

MRF/C/RC-LSC/R/R/RI-FB/ND/X-X/X-X/MR-X/LC

Sample data Buildings: 28 RC buildings (bare, infilled, low-rise and mid-rise) constructed between 1973 and 1999

extracted from a building database of approximately 500 buildings in Duzce. Number of stories of the

selected buildings ranges from 2 to 6.

Seismic hazard: 100 recorded accelerograms from different parts of the world


Damage States Four Damage States are defined:

‚ No damage

‚ Serviceability (LS1)

‚ Damage control (LS2)

‚ Collapse prevention (LS3)

Intensity Measure Type PGV [cm/s]

Fragility Function

Parameters


IMT = PGV [cm/s]

LR - BR LR - INF MR - BR MR - INF

Mean Standard

Deviation Mean

Standard

Deviation Mean

Standard

Deviation Mean

Standard

Deviation

LS1 25.757 23.778 28.642 25.643 17.122 9.376 18.582 11.100

LS2 60.849 34.964 70.686 41.655 54.095 20.987 60.243 26.278

LS3 85.740 35.065 98.350 35.625 79.831 22.877 87.087 24.462

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Figures

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Uncertainty Structural variability is taken into account by considering the structural input parameters (period T and

strength ratio j) as random variables, and ground motion uncertainty is taken into account by

selecting a set of records with different characteristics.

Comments Reference fragility curves are generated for different classes of reinforced concrete structures.

Furthermore, the sensitivity of the parameters and techniques involved in the generation process are

investigated: the effect of post-yield to initial stiffness ratio variability (negligible), sampling technique

(negligible), sample size (negligible), limit state variability (significant), degrading hysteretic behaviour

(significant).

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HancilarEtAl2006

Reference U. Hancilar, E. Durukal, G. Franco, G. Deodatis, M. Erdik & A. Smyth,“Probabilistic Vulnerability

Analysis: An Application to A Typical School Building in Istanbul”, 1st European Conference on

Earthquake Engineering and Seismology (1st ECEES), Geneva, Switzerland, 3-8 September

2006. Paper Number: 889.

Region of applicability Istanbul - Turkey



considered

RC frame with RC shear walls–mid-rise –moderate-code

Syner-G Taxonomy MRF-W/C/RC/X/X/B-X/ND/X-X/X-X/MR-4/LC

Sample data Buildings: 55 public school buildings in Istanbul: 4-storey, rectangular shaped RC moment-

resisting frames with RC shear walls.

Seismic Hazard: 107 horizontal components of real earthquake accelerograms from mostly

Turkey and USA. The distance and magnitude ranges are 0-50 km and 5.8-7.6 respectively.



‚ No damage

‚ Slight

‚ Moderate

‚ Extensive

‚ Complete

Intensity Measure Type PGA[g]

Fragility Function

Parameters


IMT = PGA [g]

Mean Standard Deviation

Slight 0.148 0.090

Moderate 0.456 0.377

Extensive 1.099 0.812

Collapse 2.216 1.251

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Figures


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Uncertainty Fragility curves account for variation in geometric dimensions, material properties and the angle

of earthquake incidence, and also for the uncertainty in the estimation of seismic mass of the

building.

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HancilarEtAl2007

Reference U., Hancilar, E. Durukal, G. Franco, M. Erdik, G. Deodatis & A. Smyth, “Spectral Displacement-

Based Probabilistic Structural Fragility Analysis of A Standardized Public School Building in

Istanbul”, 8th Pacific Conference on Earthquake Engineering (8th PCEE), Singapore, 5-7

December 2007. Paper Number: 189.




considered

RC frame with RC shear walls – mid-rise – moderate-code

Syner-G Taxonomy MRF-W/C/RC/X/X/B-X/ND/X-X/X-X/MR-4/LC

Sample data Buildings:55 public school buildings in Istanbul: 4-storey, rectangular shaped RC moment-

resisting frames with RC shear walls.

Seismic Hazard: 107 horizontal components of real earthquake accelerograms from mostly

Turkey and USA. The distance and magnitude ranges are 0-50 km and 5.8-7.6 respectively.



‚ No damage

‚ Slight

‚ Moderate

‚ Extensive

‚ Complete

Intensity Measure Type Sd(Ty) [cm]


IMT = Sd(Ty) [cm]

o" d"

Slight 1.462 0.770



Collapse 20.305 9.104

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Figures


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Uncertainty Fragility curves account for variation in geometric dimensions, material properties and the angle

of earthquake incidence, and also for the uncertainty in the estimation of seismic mass of the

building.

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JeongAndElnashai2007

Reference S.-H. Jeong & A. S. Elnashai, “Probabilistic fragility analysis parameterized by fundamental

response quantities”, Engineering Structures 29(6), 1238-1251, 2007

Region of applicability Worldwide



considered

RC buildings – High Rise

Syner-G Taxonomy MRF/C/RC-HSC-HY/R/R/B-X/D/X-X/X-X/HR-12/HC

Sample data Buildings: 12 storeys with high ductility


Damage States Three damage states are considered:

‚ No damage

‚ Minor (yield - LS1)

‚ Complete (collapse – LS2)

Intensity Measure Type PGA [g]


IMT = PGA [g]

Mean Standard

Deviation

LS1 0.163 0.092

LS2 2.190 1.510

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Uncertainty The uncertainty associated with modelling simplifications is quantified by conducting

comparisons between the proposed approach and detailed multi-degree of freedom systems.

Comments Fragility curves for bridges are also shown.

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KapposEtAl2006

Reference A. J. Kappos, G. Panagopoulos, C.Panagiotopoulos, G. Penelis, “A hybrid method for the vulnerability

assessment of R/C and URM buildings” Bulletin of Earthquake Engineering, 4, 391-413, 2006.

Region of

applicability

Greece


Typology of

element at risk

considered

Reinforced Concrete and Unreinforced Masonry structures.

Reinforced Concrete Legend:

Type Structural System Height (number

of storeys)

Seismic Design

Level

RC1 Concrete moment frame

RC3.1 RC regularly infilled frame

RC3.2 RC irregularly infilled frame (pilotis)

RC4.1 RC dual systems – bare frames

RC4.2 RC dual systems - regularly infilled dual system

RC4.3 RC dual systems - irregularly infilled dual

system (pilotis)

(L)ow-rise (1-3)

(M)id-rise (4-7)

(H)igh-rise (8+)

(N)o/pre code

(L)ow code

(M)edium code

(H)igh code

Syner-G

Taxonomy

MRF/C/RC/R/R/B-X/ND/X-X/X-X/HR-X/LC

MRF/C/RC/R/R/RI-FB/ND/X-X/X-X/HR-X/LC

MRF/C/RC/R/R/IRI-FB-P/ND/X-X/X-X/HR-X/LC

MRF-W/C/RC/R/R/B-X/ND/X-X/X-X/HR-X/LC

MRF-W/C/RC/R/R/RI-FB/ND/X-X/X-X/HR-X/LC

MRF-W/C/RC/R/R/IRI-FB-P/ND/X-X/X-X/HR-X/LC

MRF/C/RF/R/R/RI-FB/ND/X-X/X-X/MR-X/LC

MRF/C/RC/R/R/RI-FB/D/X-X/X-X/MR-X/HC

MRF/C/RC/R/R/RI-FB/ND/X-X/X-X/MR-X/LC

MRF-W/C/RC/R/R/RI-FB/D/X-X/X-X/MR-X/HC

MRF/C/RC/R/R/B-X/D/X-X/X-X/HR-X/HC

MRF/C/RC/R/R/RI-FB/D/X-X/X-X/HR-X/HC

MRF/C/RC/R/R/IRI-FB-P/D/X-X/X-X/HR-X/HC

MRF-W/C/RC/R/R/B-X/D/X-X/X-X/HR-X/HC

MRF-W/C/RC/R/R/RI-FB/D/X-X/X-X/HR-X/HC

MRF-W/C/RC/P/P/IRI-FB-P/D/X-X/X-X/HR-X/HC


MRF/C/RC/R/R/RI-FB/D/X-X/X-X/MR-X/HC

BW/M/URM-FB/X/X/X-X/X/X-X/X-X/LR-2/NC

BW/M/URM-S/X/X/X-X/X/X-X/X-X/LR-2/NC

Sample data Buildings: earthquake-damaged Greek buildings + a large number of building types are modelled and

analyzed

Seismic Hazard: real earthquakes (1978 Thessaloniki earthquake) and 16 accelerograms.

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Methodology Hybrid approach combines statistical data with appropriately processed results from nonlinear dynamic or

static analyses

Damage States Six damage states are considered:

DS0 – No damage

DS1 – Slight

DS2 – Moderate

DS3 – Substantial to Heavy

DS4 – Very Heavy

DS5 - Complete

Intensity

Measure Type

PGA [g] and Sd(Ty) [cm]

Fragility Function

Parameters


IMT = PGA [g]

DS1 DS2 DS3 DS4 DS5

Mean StDev Mean StDev Mean StDev Mean StDev Mean StDev

RC1HL 0.007 0.005 0.074 0.052 0.181 0.127 0.336 0.234 0.664 0.463

RC3.1HL 0.016 0.011 0.118 0.082 0.256 0.178 0.361 0.251 0.668 0.465

RC3.2HL 0.054 0.037 0.123 0.086 0.255 0.177 0.430 0.300 0.820 0.571

RC4.1HL 0.003 0.002 0.024 0.019 0.270 0.214 1.028 0.818 3.943 3.135

RC4.2HL 0.050 0.040 0.144 0.115 0.337 0.268 1.108 0.881 4.910 3.904

RC4.3HL 0.065 0.052 0.148 0.118 0.368 0.292 1.258 1.001 3.873 3.079

RC3.1ML 0.020 0.013 0.069 0.047 0.252 0.204 0.279 0.198 0.316 0.212

RC3.1MH 0.620 0.041 0.137 0.085 0.352 0.267 0.702 0.469 1.547 1.098

RC4.2ML 0.024 0.017 0.174 0.152 0.416 0.315 0.703 0.569 0.906 0.691

RC4.2MH 0.098 0.081 0.236 0.183 0.649 0.513 1.234 0.898 2.471 1.841

IMT = Sd(Ty) [cm]

DS1 DS2 DS3 DS4 DS5


RC1HH 0.481 0.321 3.847 2.568 20.198 13.481 56.387 37.636 91.855 61.308

RC3.1HH 0.601 0.401 3.246 2.167 12.023 8.025 36.670 24.475 72.979 48.710

RC3.2HH 2.284 1.525 5.651 3.772 15.028 10.031 24.166 16.130 42.801 28.568

RC4.1HH 1.260 0.966 5.544 4.251 36.669 28.116 76.363 58.550 131.18 100.578

RC4.2HH 1.260 0.966 4.788 3.671 32.511 24.927 64.644 49.564 129.54 99.322

RC4.3HH 1.512 1.159 5.292 4.058 22.430 17.198 65.652 50.337 122.10 93.622

RC3.1ML 0.213 0.157 0.743 0.578 2.473 1.765 2.785 1.925 3.285 2.377

RC3.1MH 0.460 0.270 1.200 0.693 2.310 1.500 5.090 3.790 10.740 7.500

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IMT = Sd(Ty) [mm]

DS1 DS2 DS3 DS4

Mean StDev Mean StDev Mean StDev Mean StDev

URM-Brick-

2storeys 17.190 9.450 20.720 10.750 25.370 13.320 41.180 28.800

URM-Stone-

2storeys 14.940 13.420 24.990 27.560 31.160 24.060 36.210 23.790

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URM brick – 2 storeys – Sd URM stone – 2 storeys - Sd

Uncertainty Three primary sources of uncertainty are taken into account: uncertainty in the definition of damage state,

variability in the capacity curve and uncertainty associated with the seismic demand.

Comments In the paper, just some of the fragility curves developed by the authors are reported.

For what concerns masonry buildings, the database does not include any specific information regarding the

type of masonry (stone or brick) therefore the assumption that all URM buildings constructed before 1940

were stone masonry and all the rest brick masonry was adopted, based on historical evidence on types of

masonry construction in Greece.

Review Forms

119

KircilAndPolat2006

Reference M. S. Kirçil & Z. Polat, “Fragility analysis of mid-rise R/C frame buildings”, Engineering

Structures, Vol 28(9),pp.1335-1345, 2006




considered

RC frame structures – Mid Rise – 1975 Turkish seismic design code

Syner-G Taxonomy MRF/C/RC-LSC/IR/IR/B-X/ND/X-X/X-X/LR-3/LC

MRF/C/RC-LSC/IR/IR/B-X/ND/X-X/X-X/MR-5/LC

MRF/C/RC-LSC/IR/IR/B-X/ND/X-X/X-X/MR-7/LC

Sample data Buildings: 3-5-7 storeys designed with the 1975 Turkish seismic design code

Seismic Hazard: 12 artificial accelerograms


Damage States Three Damage States are considered:

‚ No damage

‚ Yielding

‚ Collapse

Intensity Measure Type PGA [g], Sa(Ty) [g], Sd(Ty) [cm]

Fragility Function Parameters Lognormal distribution.

IMT = PGA [g]

Yielding Collapse

Mean StDev Mean StDev

3 storeys 0.093 0.029 0.799 0.165

5 storeys 0.073 0.016 0.701 0.166

7 storeys 0.058 0.013 0.662 0.159

IMT = Sa(Ty) [g]

Yielding Collapse


3 storeys 0.196 0.065 1.735 0.492

5 storeys 0.143 0.029 1.413 0.442

7 storeys 0.111 0.036 1.280 0.465

IMT = Sd(Ty) [cm]

Yielding Collapse


3 storeys 1.279 0.335 11.455 3.180

5 storeys 1.568 0.249 15.712 4.080

Review Forms

120

7 storeys 1.762 0.447 20.095 6.210

Figures

Yielding Collapse

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RC frame structures – 3 storeys– PGARC frame structures – 3 storeys–Sa(Ty)

Yielding Collapse

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Uncertainty A combination of 12 sample buildings is considered by varying the number of stories and the

type of reinforcement. The uncertainty due to the scatter of material properties was not

considered. Only mean values of material strength determined by experiment were taken into

account. Twelve artificial ground motions have been used to take the random nature of

earthquakes into consideration.

Review Forms

121

Comments Although the Turkish building was revised in 1998, most of the buildings in Istanbul were

constructed before 1998.

Since two different types of reinforcement steel were considered for each sample building, two

different reinforcement-type-dependent fragility curves were obtained for each sample building

in terms of each ground motion index. They are combined.

Review Forms

122

KostovEtAl2004

Reference M. Kostov, E. Vaseva, A. Kaneva, N. Koleva, G. Varbanov, D.Stefanov, E. Darvarova, D. Solakov, S.

Simeonova & L. Cristoskov,“Application to Sofia”, RISK-UE WP13, 2004.

Region of applicability Sofia - Bulgaria



risk considered

Reinforced Concrete buildings and Masonry buildings

Legend:

Type1_1: Masonry buildings with deformable floors (wooden, steel floor) - 1-4 storeys - Constructed

Before 1919;

Type1_2: Masonry buildings with deformable floors (wooden, steel floor) - 1-4 storeys - Constructed

After 1919;

Type2_1: Masonry Buildings with RC floors -1-5 storeys - Constructed From 1920 and 1945;

Type2_2:Masonry Buildings with RC floors -1-5 storeys - Constructed After 1945;

Type3_1:Mixed Buildings with brick shear walls - 1-6 storeys - Constructed Before 1945;

Type3_2: Mixed Buildings with brick shear walls - 1-6 storeys - Constructed After 1945;

Type5_1:Large Panel RC Buildings - 5-9 storeys - Constructed From 1964 to 1987;

Type5_2:Large Panel RC Buildings - 5-9 storeys - Constructed After 1987.

Syner-G Taxonomy BW/M/X/X/X/X-X/X/F-T/X-X/LR-X/NC

BW/M/X/X/X/X-X/X/F-T/X-X/LR-X/NC

BW/M/X/X/X/X-X/X/R-RC/X-X/LR-X/NC

BW/M/X/X/X/X-X/X/R-RC/X-X/LR-X/NC

MRF/C/RC/X/X/RI-FB/X/R-RC/X-X/MR-X/X

MRF/C/RC/X/X/RI-FB/X/R-RC/X-X/MR-X/X

PC/C/RC/X/X/X-X/X/R-RC/X-X/MR-X/X

PC/C/RC/X/X/X-X/X/R-RC/X-X/MR-X/X

Sample data Buildings: RC frame and wall, masonry buildings of different periods in Sofia

Seismic hazard: deterministic event (1858 earthquake)

Methodology Expert judgement


‚ No damage

‚ Light damage

‚ Medium damage

‚ Heavy damage

‚ Destruction

Review Forms

123


Fragility Function

Parameters


IMT = PGA [g]

Light Medium Heavy Destruction

Mean Standard

Deviation Mean

Standard

Deviation Mean

Standard

Deviation Mean

Standard

Deviation

Type1_1 0.14 0.13 0.20 0.19 0.23 0.22 0.33 0.31

Type1_2 0.16 0.15 0.23 0.22 0.26 0.24 0.45 0.42

Type2_1 0.15 0.14 0.22 0.20 0.36 0.33 0.48 0.45

Type2_2 0.16 0.15 0.26 0.24 0.41 0.38 0.56 0.52

Type3_1 0.24 0.21 0.36 0.31 0.45 0.39 0.57 0.49

Type3_2 0.30 0.26 0.46 0.40 0.57 0.49 0.81 0.70

Type5_1 0.33 0.27 0.46 0.38 0.51 0.43 0.78 0.66

Type5_2 0.36 0.30 0.53 0.45 0.64 0.55 0.91 0.77

Figures


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Review Forms

124


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Type5_1 Type5_2

Uncertainty The uncertainty is related to material strength, load combination, computational model, construction

quality and behaviour factor.

Comments Damage probability matrices were produced according to EMS98 methodology and then converted to

vulnerability curves.

Review Forms

125

KwonAndElnashai2006

Reference O.-S. Kwon & A. Elnashai, “The effect of material and ground motion uncertainty on the seismic

vulnerability curves of RC structures”, Engineering Structures 28(2), 289–303, 2006.

Region of applicability Central-Northern Europe and USA



considered

RC buildings – Mid Rise – no seismic design provisions

Syner-G Taxonomy MRF/C/RC-ASC-LY/R/R/B-X/ND/X-X/X-X/LR-3/NC

Sample data Buildings: 3 storeys ordinary moment resisting reinforced concrete frame

Seismic hazard: recorded (three sets of ground motions) and artificial accelerograms (six set of

ground motions).



‚ None

‚ Serviceability

‚ Damage control

‚ Collapse prevention


Fragility Function Parameters For the purpose of comparison amongst different ground motion sets, actual data with linear

interpolation are plotted in order to insure that differences are not masked by regression

smoothing. Anyway, lognormal distribution can be taken into account.

IMT = PGA [g]

Serviceability Damage control Collapse

Mean Standard

Deviation

Mean Standard

Deviation

Mean Standard

Deviation

Low Ratio a/v 0.05 0.02 0.10 0.05 0.17 0.10

Normal Ratio a/v 0.09 0.03 0.21 0.08 0.50 0.16

High Ratio a/v 0.13 0.04 0.30 0.05 0.74 0.10

Figures

Serviceability Damage Control Collapse

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RC buildings – Mid Rise – Low Ratio a/v RC buildings – Mid Rise – Normal Ratio a/v

Review Forms

126


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RC buildings – Mid Rise – High Ratio a/v

Uncertainty The effects of aleatory uncertainties from material (normal distribution of concrete and steel

strength) and ground motion on the vulnerability curves are investigated. The effect of

randomness in material response parameters is far less significant than the effect of strong-

motion characteristics.

Comments The verification of the analysis model and environmental is taking into account through

comparison with shaking table experiments.

One curve for each set of ground motions used is shown in order to demonstrate the difference

in fragility due to the strong motion characteristics.

Review Forms

127

LESSLOSS2005-IstanbulAnalytical

Reference LESSLOSS Deliverable Report D84 – Report on Building Stock Data and Vulnerability Data for each

Case Study, 2005




risk considered

Reinforced concrete buildings and Masonry Buildings

Legend:

Structure System Height (number of

storeys) Construction date

RC – Reinforced Concrete frame building

MA – Masonry Buildings

RCSW - Reinforced Concrete shear wall

building (including tunnel formwork systems)

LR – Low Rise (1-4)

MR – Mid Rise (5-8)

HR – High Rise (8+)

(including basement)

Pre 1979 (included)

Post 1979

Syner-G Taxonomy MRF/C/RC/X/X/X-X/ND/X-X/X-X/LR-X/LC

MRF/C/RC/X/X/X-X/ND/X-X/X-X/LR-X/LC

MRF/C/RC/X/X/X-X/ND/X-X/X-X/HR-X/LC

BW/M/URM/X/X/X-X/X/X-X/X-X/LR-X/X

BW/M/URM/X/X/X-X/X/X-X/X-X/MR-X/X

W/C/RC/X/X/X-X/ND/X-X/X-X/LR-X/LC

W/C/RC/X/X/X-X/ND/X-X/X-X/MR-X/LC

W/C/RC/X/X/X-X/ND/X-X/X-X/HR-X/LC

MRF/C/RC/X/X/X-X/ND/X-X/X-X/LR-X/MC

MRF/C/RC/X/X/X-X/ND/X-X/X-X/MR-X/MC

MRF/C/RC/X/X/X-X/ND/X-X/X-X/HR-X/MC



W/C/RC/X/X/X-X/ND/X-X/X-X/LR-X/MC

W/C/RC/X/X/X-X/ND/X-X/X-X/MR-X/MC

W/C/RC/X/X/X-X/ND/X-X/X-X/HR-X/MC

Sample data Buildings and Seismic Hazard from the past earthquakes (Erzincan 1992, Dinar 1995, Adana/Ceyhan

1998, Kocaeli 1999, Duzce, 1999)



‚ No damage

‚ Slight

‚ Moderate

‚ Extensive

‚ Complete

Intensity Measure

Type

Sd(Ty) [cm]

Review Forms

128

Fragility Function

Parameters


IMT = Sd(Ty) [cm]


Mean Standard

Deviation Mean

Standard

Deviation Mean

Standard

Deviation Mean

Standard

Deviation

RC-LR

Pre1979 2.83 3.42 5.45 6.18 12.92 13.30 28.81 36.01

RC-MR

Pre1979 5.03 4.00 11.83 10.11 26.05 27.26 54.55 69.28

RC-HR

Pre1979 8.62 6.86 24.99 24.06 40.12 44.10 90.92 115.47

MA-LR

Pre1979 2.20 2.84 5.47 7.75 13.19 20.23 25.80 38.36

MA-MR

Pre1979 3.36 2.67 7.89 6.74 17.37 18.18 36.37 49.19

RCSWLR

Pre1979 2.83 3.42 5.45 6.18 12.92 13.30 28.81 36.01

RCSWMR

Pre1979 4.32 3.43 8.88 7.58 19.54 20.45 48.56 61.66

RCSWHR

Pre1979 8.62 6.86 24.99 24.06 40.12 44.10 90.92 115.47

RC-LR

Post1979 3.34 3.67 6.75 7.54 16.87 18.84 33.43 36.75

RC-MR

Post1979 5.75 4.57 14.37 11.43 28.75 22.86 66.87 73.49

RC-HR

Post1979 11.19 8.27 27.98 20.67 48.05 42.49 108.93 123.67

MA-LR

Post1979 2.94 3.79 7.03 9.97 16.48 25.28 32.25 47.95

MA-MR

Post1979 3.83 3.05 9.58 7.62 19.16 15.24 44.58 49.00

RCSWLR

Post1979 3.34 3.67 6.75 7.54 16.87 18.84 33.43 36.75

RCSWMR

Post1979 5.75 4.57 10.07 8.01 23.00 18.29 55.66 61.18

RCSWHR

Post1979 11.19 8.27 27.98 20.67 48.05 42.49 108.93 123.67

Review Forms

129

Figures


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Review Forms

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RCSW-MR-Post1979 RCSW-HR-Post1979

Uncertainty The uncertainties associated with the definition of the damage level, with the building load capacity and

with the earthquake ground motion are taken into consideration.

Review Forms

131

LESSLOSS2005-InstanbulEmpirical

Reference LESSLOSS Deliverable Report D84 – Report on Building Stock Data and Vulnerability Data for

each Case Study, 2005




considered

Reinforced concrete buildings

Syner-G Taxonomy MRF/C/RC/X/X/X-X/X/X-X/X-X/LR-X/X

MRF/C/RC/X/X/X-X/X/X-X/X-X/MR-X/X

MRF/C/RC/X/X/X-X/X/X-X/X-X/HR-X/X

Sample data Buildings and Seismic Hazard from the past earthquakes (Erzincan 1992, Dinar 1995,

Adana/Ceyhan 1998, Kocaeli 1999, Duzce, 1999)

Methodology Empirical

Damage States Six damage states are considered (EMS98):

DS0 – No damage

DS1 – Negligible to Slight Damage

DS2 – Slight to Substantial Damage

DS3 – Substantial to Heavy Damage

DS4 – Very Heavy Damage

DS5 - Destruction

Intensity Measure Type MSK81

Fragility Function

Parameters

IMT = MSK81

Low Rise Mid Rise High Rise

Mean Standard

Deviation

Mean Standard

Deviation

Mean Standard

Deviation

DS1 7.52 1.41 8.18 1.51 8.10 1.54

DS2 8.66 1.42 9.30 1.46 9.29 1.37

DS3 9.43 1.73 10.03 1.73 9.94 1.71

DS4 10.48 1.81 11.07 1.85 11.03 1.79

DS5 11.10 1.77 11.69 1.77 11.68 1.75

Figures

DS1 DS2 DS3 DS4 DS5

MSK81

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MSK81

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Low Rise Mid Rise

Review Forms

132

DS1 DS2 DS3 DS4 DS5

MSK81

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High Rise

Comments The vulnerability curves for masonry structures are assumed to be similar to the vulnerability

curves of low-rise RC structures.

Review Forms

133

LESSLOSS2005-Lisbon

Reference LESSLOSS Deliverable Report D84 – Report on Building Stock Data and Vulnerability Data for

each Case Study, 2005

Region of applicability Lisbon-Portugal



risk considered


Legend:

ID Building Typology Number of Storeys

1 Adobe and Rubble Stone 1




5 Adobe and Rubble Stone From 5 to 7

6 Adobe and Rubble Stone From 8 to 15

7 Adobe and Rubble Stone More than 15

8 Masonry ø1960 1

9 Masonry ø1960 2

10 Masonry ø1960 3

11 Masonry ø1960 4

12 Masonry ø1960 From 5 to 7

13 Masonry ø1960 From 8 to 15

14 Masonry ø1960 More than 15

15 Masonry 1961-1985 1

16 Masonry 1961-1985 2

17 Masonry 1961-1985 3

18 Masonry 19611985 4

19 Masonry 1961-1985 From 5 to 7

20 Masonry 1961-1985 From 8 to 15

2 Masonry 1961-1985 More than 15

22 Masonry 1986-2001 1

23 Masonry 1986-2001 2

24 Masonry 1986-2001 3

25 Masonry 1986-2001 4

26 Masonry 1986-2001 From 5 to 7

27 Masonry 1986-2001 From 8 to 15

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134

28 Masonry 1986-2001 More than 15

ID Building Typology Number of Storeys

29 RC ø1960 1

30 RC ø1960 2

31 RC ø1960 3

32 RC ø1960 4

33 RC ø1960 From 5 to 7

34 RC ø1960 From 8 to 15

35 RC ø1960 More than 15

36 RC 1961-1985 1

37 RC 1961-1985 2

38 RC 1961-1985 3

39 RC 1961-1985 4

40 RC 1961-1985 From 5 to 7

41 RC 1961-1985 From 8 to 15

42 RC 1961-1985 More than 15

43 RC 1986-2001 1

44 RC 1986-2001 2

45 RC 1986-2001 3

46 RC 1986-2001 4

47 RC 1986-2001 From 5 to 7

48 RC 1986-2001 From 8 to 15

49 RC 1986-2001 More than 15

Syner-G Taxonomy BW/M/A/X/X/X-X/X/X-X/X-X/LR-1/X

BW/M/A/X/X/X-X/X/X-X/X-X/LR-2/X

BW/M/A/X/X/X-X/X/X-X/X-X/LR-3/X

BW/M/A/X/X/X-X/X/X-X/X-X/MR-4/X

BW/M/A/X/X/X-X/X/X-X/X-X/MR-X/X

BW/M/A/X/X/X-X/X/X-X/X-X/HR-X/X

BW/M/URM/X/X/X-X/X/X-X/X-X/LR-1/X



BW/M/URM/X/X/X-X/X/X-X/X-X/MR-4/X

BW/M/URM/X/X/X-X/X/X-X/X-X/MR-X/X

BW/M/URM/X/X/X-X/X/X-X/X-X/HR-X/X

MRF/C/RC/X/X/X-X/X/X-X/X-X/LR-1/X



MRF/C/RC/X/X/X-X/X/X-X/X-X/MR-4/X

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135

MRF/C/RC/X/X/X-X/X/X-X/X-X/MR-X/X

MRF/C/RC/X/X/X-X/X/X-X/X-X/HR-X/X

MRF/C/RC/X/X/X-X/ND/X-X/X-X/LR-1/LC



MRF/C/RC/X/X/X-X/ND/X-X/X-X/MR-4/LC

MRF/C/RC/X/X/X-X/ND/X-X/X-X/MR-X/LC

MRF/C/RC/X/X/X-X/ND/X-X/X-X/HR-X/LC

MRF/C/RC/X/X/X-X/X/X-X/X-X/LR-1/MC



MRF/C/RC/X/X/X-X/X/X-X/X-X/MR-4/MC

MRF/C/RC/X/X/X-X/X/X-X/X-X/MR-X/MC

MRF/C/RC/X/X/X-X/X/X-X/X-X/HR-X/MC

Sample data Buildings: residential building database surveyed in the Portuguese 2001 Censos



‚ No damage

‚ Slight

‚ Moderate

‚ Extensive

‚ Complete

Intensity Measure Type Sd(TLS) [cm]

Fragility Function

Parameters


IMT = Sd(TLS) [cm]



1 1.16 2.01 2.31 4.02 4.33 7.54 10.11 17.58

2 2.04 3.55 4.20 7.30 8.09 14.07 18.87 32.82

3 2.66 4.62 5.66 9.85 11.27 19.59 26.29 45.72

4 3.00 5.22 6.70 11.66 13.87 24.11 32.35 56.27

5 2.85 3.37 6.78 8.01 14.71 17.39 34.33 40.58

6 3.72 4.39 9.66 11.42 22.29 26.35 52.02 61.49

7 5.95 7.03 15.46 18.27 35.67 42.16 83.23 98.38

8 1.26 1.80 2.51 3.59 5.02 7.18 11.72 16.76

9 2.24 3.21 4.52 6.46 9.13 13.05 21.27 30.41

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IMT = Sd(TLS) [cm]



10 2.55 2.86 5.19 5.82 10.60 11.89 24.67 27.67

11 2.94 3.30 6.06 6.80 12.55 14.08 29.14 32.68

12 3.72 4.17 7.79 8.74 16.45 18.45 38.08 42.72

13 5.05 5.66 10.82 12.14 23.44 26.29 54.10 60.68

14 8.08 9.06 17.31 19.42 37.51 42.07 86.55 97.08

15 1.26 1.80 2.51 3.59 5.02 7.18 11.72 16.76

16 2.24 3.21 4.52 6.46 9.13 13.05 21.27 30.41

17 2.55 2.86 5.19 5.82 10.60 11.89 24.67 27.67

18 2.94 3.30 6.06 6.80 12.55 14.08 29.14 32.68

19 3.72 4.17 7.79 8.74 16.45 18.45 38.08 42.72

20 5.05 5.66 10.82 12.14 23.44 26.29 54.10 60.68

21 8.08 9.06 17.31 19.42 37.51 42.07 86.55 97.08

22 1.23 1.72 2.47 3.43 5.76 8.00 14.39 20.01

23 2.22 3.09 4.52 6.29 10.44 14.52 25.98 36.13

24 2.96 4.12 6.17 8.58 14.06 19.55 34.78 48.37

25 2.92 3.07 6.27 6.58 14.06 14.78 34.54 36.29

26 3.76 3.95 8.36 8.78 18.38 19.31 44.70 46.97

27 5.08 5.06 11.85 11.80 25.40 25.29 60.96 60.71

28 8.13 8.09 18.97 18.89 40.64 40.47 97.54 97.13

29 1.47 1.69 3.66 4.23 5.86 6.76 13.56 15.64

30 2.64 3.04 6.60 7.61 10.85 12.51 25.36 29.26

31 3.52 4.06 8.79 10.15 14.95 17.25 35.40 40.84

32 3.76 3.68 8.73 8.55 16.66 16.32 40.04 39.21

33 4.84 4.74 10.08 9.87 22.57 22.10 55.22 54.08

IMT = Sd(TLS) [cm]

Review Forms

137



34 5.37 5.26 12.09 11.84 26.87 26.32 67.18 65.79

35 8.60 8.42 19.35 18.95 43.00 42.10 107.49 105.26

36 1.43 1.59 3.58 3.97 5.73 6.35 13.25 14.69

37 2.58 2.86 6.45 7.14 10.60 11.75 24.79 27.47

38 3.44 3.81 8.60 9.53 14.62 16.19 34.60 38.34

39 3.55 3.08 8.25 7.14 15.74 13.62 37.83 32.73

40 4.57 3.95 9.52 8.24 21.33 18.45 52.17 45.14

41 5.08 4.39 11.42 9.88 25.39 21.96 63.47 54.91

42 8.12 7.03 18.28 15.81 40.62 35.14 101.55 87.86

43 1.43 1.59 3.58 3.97 5.73 6.35 14.33 15.88

44 2.61 2.89 6.81 7.54 10.89 12.07 27.22 30.17

45 3.52 3.91 9.13 10.12 15.48 17.15 38.69 42.87

46 3.71 3.21 8.89 7.69 17.26 14.94 43.16 37.34

47 4.87 4.22 11.42 9.88 24.37 21.09 60.93 52.72

48 5.59 4.83 13.96 12.08 30.47 26.36 76.16 65.89

49 8.94 7.73 22.34 19.33 48.75 42.17 121.86 105.43

Figures


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49

Comments They use an alternative approach to compute the performance point taking into account the

definition of the input motion in terms of a power spectral density function and an equivalent

stationary time duration T.

Review Forms

143

LielAndLynch2009

Reference A. B. Liel & K. P. Lynch, “Vulnerability of reinforced concrete frame buildings and their

occupants in the 2009 L’Aquila, Italy earthquake”, University of Colorado, Natural

Hazards Center, 2009

Region of applicability Italy



considered

RC – Mid Rise

Syner-G Taxonomy MRF/C/RC/X/X/RI-X/ND/X-X/X-X/MR-X/LC

Sample data Buildings: 483 RC frame buildings. These data include information about building

location, characteristics, damage and post-earthquake loss of functionality.

Seismic Action: L’Aquila Earthquake, 6th April 2009. Ground-shaking intensity is

estimated for each site based on Italy Shakemap.



‚ Negligible

‚ Insignificant

‚ Moderate

‚ Heavy

‚ Collapse


Fragility Function

Parameters


IMT = PGA [g]

Insignificant Moderate Heavy Collapse

Mean Standard

Deviation

Mean Standard

Deviation

Mean Standard

Deviation

Mean Standard

Deviation

0.33 0.17 0.39 0.12 0.45 0.17 3.6 1.1

Figures

Insignif icant Moderate Heavy

PGA

0.60.550.50.450.40.350.30.250.20.150.10.050

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Comments The collapse fragility curve is not shown because there are not sufficient data to

estimate it correctly.

Review Forms

144

NutiEtAl1998

Reference C. Nuti, I. Vanzi & S. Santini, “Seismic risk of Italian hospitals”, 11th European Conference on

Earthquake Engineering, 1998




considered

RC – Low Rise ( ~ 3 )

RC – Mid-High Rise ( > 3 )

Masonry – Low Rise ( ~ 3 )

Masonry – Mid-High Rise ( > 3 )

Mixed – Low Rise ( ~ 3 )

Mixed – Mid-High Rise ( > 3 )

Syner-G Taxonomy BW/M/URM/X/X/X-X/X/X-X/X-X/LR-X/NC

BW/M/URM/X/X/X-X/X/X-X/X-X/MR-X/NC

MRF/C/RC/X/X/RI-X/ND/X-X/X-X/LR-X/LC

MRF/C/RC/X/X/RI-X/ND/X-X/X-X/MR-X/LC

BW/C-M/X/X/X/X-X/X/X-X/X-X/LR-X/NC

BW/C-M/X/X/X/X-X/X/X-X/X-X/MR-X/NC

Sample data Buildings: observed damage after the Italian earthquake of Irpinia, Belice and Friuli. 6 different

classes of building: low-rise and high rise RC, masonry and mixed.


Damage States Three damage states are considered:

‚ No damage

‚ Immediate occupancy

‚ Structural Stability

Intensity Measure Type MCS Scale (Mercalli – Cancani – Sieberg)


IMT = MCS

Mean Standard

Deviation

Immediate Occupancy 6.046 0.782

RC – (n° storeys<=3)

Structural Stability 11.823 1.306


RC – (n° storeys >3)



MA – (n° storeys<=3)


Review Forms

145

IMT = MCS

Mean Standard

Deviation


MA – (n° storeys >3)



MX – (n° storeys<=3)



MX – (n° storeys >3)


Figures

Immediate Occupancy Structural Safety

MCS

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Mixed – Low Rise ( ~ 3 ) Mixed – Mid-High Rise ( > 3 )

Comments The paper examines also the fragility of hospital facilities and presents a risk assessment of

Italian hospital facilities.

Vulnerability curves for structural and non-structural components were combined to produce

vulnerability curves for the whole building. Non-structural elements and infills were not

considered for the structural stability damage state of the whole building.

Review Forms

146

OzmenEtAl2010

Reference H.B. Ozmen, M. Inel, E. Meral and M. Bucakli, “Vulnerability of Low and Mid-Rise Reinforced

Concrete Buildings in Turkey”, 14ECEE, Ohrid, 2010




considered

Reinforced Concrete Buildings – low and mid rise – Modern code (TEC-1998) or Pre-Modern

code (TEC-1975)

Legend:

‚ S2-75C16sCon = 2 storeys – TEC75 – 16MPa concrete strength – lateral reinforcement detailing conforms the corresponding code




Syner-G Taxonomy MRF/C/RC-LSC-LY/X/X/B-X/ND/X-X/X-X/LR-2/MC

MRF/C/RC-LSC-LY/X/X/B-X/ND/X-X/X-X/MR-4/MC

MRF/C/RC-LSC-LY/X/X/B-X/D/X-X/X-X/MR-7/MC

MRF/C/RC-ASC-HY/X/X/B-X/D/X-X/X-X/MR-4/HC

Sample data Buildings: 48 3-D building models to reflect existing building stock with different parameters.

Seismic Hazard: 292 earthquake records with different range of intensities



‚ No damage

‚ Immediate Occupancy (IO)

‚ Life Safety (LS)

‚ Collapse Prevention (CP)


Fragility Function Parameters Lognormal Distribution

IMT = PGA [g]

IO LS CP


S2-75C16sCon 0.501 0.226 0.824 0.177 0.935 0.139

S4-75C16sCon 0.392 0.241 0.572 0.257 0.619 0.239

S7-75C16sCon 0.398 0.254 0.648 0.272 0.789 0.325

S4-98C25sCon 0.435 0.205 0.756 0.175 0.970 0.172

Review Forms

147

Figures

CP LS IO

PGA

1.51.41.31.21.110.90.80.70.60.50.40.30.20.10

Pro

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of exceedance

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CP LS IO

PGA

1.51.41.31.21.110.90.80.70.60.50.40.30.20.10

Pro

bability

of exceedance

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S2-75C16sCon S4-75C16sCon

CP LS IO

PGA

1.51.41.31.21.110.90.80.70.60.50.40.30.20.10

Pro

bability

of exceedance

1

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PGA

1.51.41.31.21.110.90.80.70.60.50.40.30.20.10

Pro

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of exceedance

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S7-75C16sCon S4-98C25sCon

Comments Only the values of to the figures reported in the paper are stored.

Review Forms

148

PoleseEtAl2008

Reference M. Polese, G. M. Verderame, C. Mariniello, I. Iervolino & G. Manfredi, “Vulnerability analysis for

gravity load designed RC buildings in Naples – Italy”, Journal of Earthquake Engineering,

12(S2), 234-245, 2008


Element at risk Building


considered

RC frame buildings - Low Rise - non seismically designed (pre-code)

RC frame buildings - Mid Rise - non seismically designed (pre-code)

RC frame buildings - High Rise - non seismically designed (pre-code)

Syner-G Taxonomy MRF/C/RC/X/X/B-X/ND/X-X/X-X/LR-X/NC

MRF/C/RC/X/X/B-X/ND/X-X/X-X/MR-X/NC

MRF/C/RC/X/X/B-X/ND/X-X/X-X/HR-X/NC

Sample data Buildings: 1-4-7 storey rectangular shaped moment resisting frame non seismically designed.

More than 400 buildings

Seismic Hazard: Eurocode 8 spectral shape for soil type B



‚ No damage

‚ Slight

‚ Moderate

‚ Extensive

‚ Complete



IMT = Sd(TLS) [cm]

Slight Moderate Extensive Collapse


Low Rise 4.911 2.965 6.066 2.828 8.874 5.550 13.526 7.436

Mid Rise 6.589 3.926 11.599 6.194 18.228 9.606 38.044 21.087

High Rise 8.520 4.674 15.435 7.938 20.603 11.875 43.991 25.106

Figures


Sd(TLS)

1009080706050403020100

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Sd(TLS)

1009080706050403020100

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RC frame buildings - Low Rise RC frame buildings – Mid Rise

Review Forms

149


Sd(TLS)

1009080706050403020100

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RC frame buildings - High Rise

Uncertainty Fragility curves account for variation of geometric dimensions, material properties, limit state

threshold and demand uncertainty.

Comments The variability in yield and ultimate rotation and in the seismic demand was found to have a

significant effect on the fragility curves, mainly for mid-rise and high-rise buildings.

Review Forms

150

RISK-UE 2003 WP4 – AUTH approach

Reference A. J. Kappos, C.Panagiotopoulos, G. Panagopoulos, El. Papadopoulos. WP4 – Reinforce Concrete

Buildings (Level 1 and Level 2 analysis). RISK-UE, 2003.

Region of applicability Greece



risk considered

Reinforced Concrete

Reinforced Concrete Legend:

Type Structural System Height (number

of storeys)

Seismic Design

Level

RC1 Concrete moment frame

RC3.1 RC regularly infilled frame

RC3.2 RC irregularly infilled frame (pilotis)

RC4 RC dual systems (RC frames and walls)

RC4.1 RC dual systems – bare frames

RC4.2 RC dual systems - regularly infilled dual

system

(L)ow-rise (1-3)

(M)id-rise (4-7)

(H)igh-rise (8+)

(N)o/pre code

(L)ow code

(M)edium code

(H)igh code

Syner-G Taxonomy MRF/C/RC/R/R/B-X/ND/X-X/X-X/LR-X/LC

MRF/C/RC/X/X/B-X/ND/X-X/X-X/MR-X/LC

MRF/C/RC/R/R/B-X/ND/X-X/X-X/HR-X/LC

MRF/C/RC/R/R/RI-FB/ND/X-X/X-X/LR-X/LC


MRF/C/RC/R/R/RI-FB/ND/X-X/X-X/HR-X/LC

MRF/C/RC/R/R/IRI-FB-P/ND/X-X/X-X/LR-X/LC

MRF/C/RC/R/R/IRI-FB-P/ND/X-X/X-X/MR-X/LC

MRF/C/RC/R/R/IRI-FB-P/ND/X-X/X-X/HR-X/LC

MRF-W/C/RC/R/R/X-X/ND/X-X/X-X/LR-X/LC

MRF-W/C/RC/R/R/X-X/ND/X-X/X-X/MR-X/LC

MRF-W/C/RC/R/R/X-X/ND/X-X/X-X/HR-X/LC

MRF-W/C/RC/R/R/B-X/ND/X-X/X-X/LR-X/LC

MRF-W/C/RC/R/R/B-X/ND/X-X/X-X/MR-X/LC

MRF-W/C/RC/R/R/B-X/ND/X-X/X-X/HR-X/LC

MRF-W/C/RC/R/R/RI-FB/ND/X-X/X-X/LR-X/LC

MRF-W/C/RC/R/R/RI-FB/ND/X-X/X-X/MR-X/LC

MRF-W/C/RC/R/R/RI-FB/ND/X-X/X-X/HR-X/LC

MRF/C/RC/R/R/B-X/D/X-X/X-X/LR-X/HC

MRF/C/RC/X/X/B-X/ND/X-X/X-X/MR-X/HC

MRF/C/RC/R/R/B-X/ND/X-X/X-X/HR-X/HC

MRF/C/RC/R/R/RI-FB/ND/X-X/X-X/LR-X/HC

MRF/C/RC/R/R/RI-FB/ND/X-X/X-X/MR-X/HC

MRF/C/RC/R/R/RI-FB/ND/X-X/X-X/HR-X/HC

Review Forms

151

MRF/C/RC/R/R/IRI-FB-P/ND/X-X/X-X/LR-X/HC

MRF/C/RC/R/R/IRI-FB-P/ND/X-X/X-X/MR-X/HC

MRF/C/RC/R/R/IRI-FB-P/ND/X-X/X-X/HR-X/HC

MRF-W/C/RC/R/R/X-X/ND/X-X/X-X/LR-X/HC

MRF-W/C/RC/R/R/X-X/ND/X-X/X-X/MR-X/HC

MRF-W/C/RC/R/R/X-X/ND/X-X/X-X/HR-X/HC

MRF-W/C/RC/R/R/B-X/ND/X-X/X-X/LR-X/HC

MRF-W/C/RC/R/R/B-X/ND/X-X/X-X/MR-X/HC

MRF-W/C/RC/R/R/B-X/ND/X-X/X-X/HR-X/HC

MRF-W/C/RC/R/R/RI-FB/ND/X-X/X-X/LR-X/HC

MRF-W/C/RC/R/R/RI-FB/ND/X-X/X-X/MR-X/HC

MRF-W/C/RC/R/R/RI-FB/ND/X-X/X-X/HR-X/HC

Sample data Buildings: earthquake-damaged Greek buildings + a large number of building types are modelled and

analysed

Seismic Hazard: real earthquakes (1978 Thessaloniki earthquake) and 16 accelerograms

Methodology Hybrid approach combines statistical data with appropriately processed results from nonlinear

dynamic or static analyses

Damage States Six damage states are considered:

DS0 – No damage

DS1 – Slight

DS2 – Moderate

DS3 – Substantial to Heavy

DS4 – Very Heavy

DS5 - Complete

Intensity Measure Type PGA

Fragility Function

Parameters


IMT = PGA [g]

Low Code

DS1 DS2 DS3 DS4 DS5


RC1L 0.008 0.006 0.076 0.064 0.165 0.140 0.255 0.215 0.328 0.276

RC1M 0.008 0.006 0.081 0.059 0.143 0.104 0.205 0.149 0.267 0.194

RC1H 0.037 0.026 0.139 0.097 0.262 0.182 0.447 0.312 1.019 0.710

RC3.1L 0.119 0.100 0.241 0.203 0.300 0.253 0.393 0.331 0.540 0.455

RC3.1M 0.034 0.025 0.181 0.132 0.251 0.182 0.290 0.211 0.346 0.251

RC3.1H 0.078 0.055 0.230 0.161 0.309 0.215 0.439 0.306 1.505 1.049

RC3.2L 0.032 0.027 0.130 0.110 0.194 0.164 0.271 0.228 0.341 0.288

RC3.2M 0.003 0.002 0.026 0.019 0.103 0.075 0.145 0.106 0.198 0.144

RC3.2H 0.114 0.079 0.194 0.135 0.343 0.239 0.612 0.427 1.330 0.927

RC4L 0.035 0.032 0.212 0.189 0.371 0.331 0.607 0.541 0.977 0.871

IMT = PGA [g]

Review Forms

152

Low Code

DS1 DS2 DS3 DS4 DS5

Mean StDev Mean StDev Mean Mean StDev Mean StDev Mean

RC4M 0.021 0.016 0.152 0.121 0.389 0.309 0.741 0.590 1.504 1.197

RC4H 0.012 0.010 0.124 0.099 0.423 0.337 2.487 1.979 5.885 4.683

RC4.1L 0.128 0.114 0.327 0.291 0.613 0.546 0.841 0.749 1.181 1.053

RC4.1M 0.120 0.096 0.412 0.328 0.759 0.604 1.306 1.040 2.225 1.771

RC4.1H 0.125 0.099 0.263 0.209 0.487 0.388 3.010 2.395 7.447 5.926

RC4.2L 0.094 0.084 0.375 0.335 0.622 0.554 0.827 0.737 1.139 1.015

RC4.2M 0.116 0.092 0.303 0.241 0.565 0.450 0.860 0.684 1.700 1.353

RC4.2H 0.127 0.101 0.273 0.217 0.659 0.525 2.566 2.042 5.617 4.470

High Code

DS1 DS2 DS3 DS4 DS5


RC1L 0.013 0.011 0.126 0.102 0.420 0.343 0.721 0.588 1.092 0.891

RC1M 0.011 0.008 0.112 0.078 0.348 0.243 1.079 0.752 1.870 1.304

RC1H 0.063 0.042 0.304 0.203 1.222 0.816 2.246 1.499 3.358 2.241

RC3.1L 0.146 0.119 0.359 0.292 0.923 0.752 2.137 1.742 2.793 2.277

RC3.1M 0.120 0.084 0.248 0.173 0.484 0.337 1.041 0.726 2.066 1.441

RC3.1H 0.114 0.076 0.319 0.213 0.978 0.653 1.884 1.257 5.504 3.674

RC3.2L 0.164 0.134 0.413 0.337 0.707 0.577 1.083 0.883 1.441 1.175

RC3.2M 0.112 0.078 0.259 0.181 0.530 0.370 0.692 0.483 0.918 0.641

RC3.2H 0.160 0.107 0.513 0.342 0.789 0.527 1.421 0.948 2.527 1.687

RC4L 0.269 0.232 0.603 0.521 1.634 1.411 1.990 1.718 2.813 2.429

RC4M 0.119 0.091 0.340 0.261 0.841 0.646 1.522 1.168 3.011 2.311

RC4H 0.154 0.118 0.898 0.689 2.351 1.805 4.240 3.254 6.885 5.284

RC4.1L 0.353 0.305 0.691 0.597 1.600 1.382 2.488 2.148 3.169 2.737

RC4.1M 0.161 0.124 0.423 0.325 1.193 0.916 1.761 1.352 3.535 2.713

RC4.1H 0.158 0.122 0.841 0.646 2.097 1.609 4.737 3.635 8.433 6.472

RC4.2L 0.314 0.271 0.722 0.624 2.130 1.839 2.545 2.198 3.081 2.661

RC4.2M 0.158 0.122 0.452 0.347 0.944 0.725 1.711 1.313 3.507 2.692

Figures

DS1 DS2 DS3 DS4 DS5

PGA

2.42.221.81.61.41.210.80.60.40.20

Pro

bability

of exceedance

1

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DS1 DS2 DS3 DS4 DS5

PGA

2.42.221.81.61.41.210.80.60.40.20

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RC1-LR-LC RC1-MR-LC

Review Forms

153

DS1 DS2 DS3 DS4 DS5

PGA

2.42.221.81.61.41.210.80.60.40.20

Pro

bability

of exceedance

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DS1 DS2 DS3 DS4 DS5

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2.42.221.81.61.41.210.80.60.40.20

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RC1-HR-LC RC3.1-LR-LC

DS1 DS2 DS3 DS4 DS5

PGA

2.42.221.81.61.41.210.80.60.40.20

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of exceedance

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2.42.221.81.61.41.210.80.60.40.20

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RC3.1-MR-LC RC3.1-HR-LC

DS1 DS2 DS3 DS4 DS5

PGA

2.42.221.81.61.41.210.80.60.40.20

Pro

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of exceedance

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2.42.221.81.61.41.210.80.60.40.20

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RC3.2-LR-LC RC3.1-MR-LC

DS1 DS2 DS3 DS4 DS5

PGA

2.42.221.81.61.41.210.80.60.40.20

Pro

bability

of exceedance

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DS1 DS2 DS3 DS4 DS5

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2.42.221.81.61.41.210.80.60.40.20

Pro

bability

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RC3.2-HR-LC RC4-LR-LC

DS1 DS2 DS3 DS4 DS5

PGA

2.42.221.81.61.41.210.80.60.40.20

Pro

bability

of exceedance

1

0.9

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DS1 DS2 DS3 DS4 DS5

PGA

2.42.221.81.61.41.210.80.60.40.20

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RC4-MR-LC RC4-HR-LC

Review Forms

154

DS1 DS2 DS3 DS4 DS5

PGA

2.42.221.81.61.41.210.80.60.40.20

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bability

of exceedance

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DS1 DS2 DS3 DS4 DS5

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2.42.221.81.61.41.210.80.60.40.20

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RC4.1-LR-LC RC4.1-MR-LC

DS1 DS2 DS3 DS4 DS5

PGA

2.42.221.81.61.41.210.80.60.40.20

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of exceedance

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RC4.1-HR-LC RC4.2-LR-LC

DS1 DS2 DS3 DS4 DS5

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2.42.221.81.61.41.210.80.60.40.20

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of exceedance

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2.42.221.81.61.41.210.80.60.40.20

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RC4.2-MR-LC RC4.2-HR-LC

DS1 DS2 DS3 DS4 DS5

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2.42.221.81.61.41.210.80.60.40.20

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RC1-LR-HC RC1-MR-HC

DS1 DS2 DS3 DS4 DS5

PGA

2.42.221.81.61.41.210.80.60.40.20

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bability

of exceedance

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RC1-HR-HC RC3.1-LR-HC

Review Forms

155

DS1 DS2 DS3 DS4 DS5

PGA

2.42.221.81.61.41.210.80.60.40.20

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2.42.221.81.61.41.210.80.60.40.20

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RC3.1-MR-HC RC3.1-HR-HC

DS1 DS2 DS3 DS4 DS5

PGA

2.42.221.81.61.41.210.80.60.40.20

Pro

bability

of exceedance

1

0.9

0.8

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PGA

2.42.221.81.61.41.210.80.60.40.20

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RC3.2-LR-HC RC3.1-MR-HC

DS1 DS2 DS3 DS4 DS5

PGA

2.42.221.81.61.41.210.80.60.40.20

Pro

bability

of exceedance

1

0.9

0.8

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DS1 DS2 DS3 DS4 DS5

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2.42.221.81.61.41.210.80.60.40.20

Pro

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of exceedance

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RC3.2-HR-HC RC4-LR-HC

DS1 DS2 DS3 DS4 DS5

PGA

2.42.221.81.61.41.210.80.60.40.20

Pro

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of exceedance

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DS1 DS2 DS3 DS4 DS5

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2.42.221.81.61.41.210.80.60.40.20

Pro

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of exceedance

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RC4-MR-HC RC4-HR-HC

DS1 DS2 DS3 DS4 DS5

PGA

2.42.221.81.61.41.210.80.60.40.20

Pro

bability

of exceedance

1

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0.8

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PGA

2.42.221.81.61.41.210.80.60.40.20

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RC4.1-LR-HC RC4.1-MR-HC

Review Forms

156

DS1 DS2 DS3 DS4 DS5

PGA

2.42.221.81.61.41.210.80.60.40.20

Pro

bability

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PGA

2.42.221.81.61.41.210.80.60.40.20

Pro

bability

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RC4.1-HR-HC RC4.2-LR-HC

DS1 DS2 DS3 DS4 DS5

PGA

2.42.221.81.61.41.210.80.60.40.20

Pro

bability

of exceedance

1

0.9

0.8

0.7

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0.5

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DS1 DS2 DS3 DS4 DS5

PGA

2.42.221.81.61.41.210.80.60.40.20

Pro

bability

of exceedance

1

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0.8

0.7

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RC4.2-MR-HC RC4.2-HR-HC

Uncertainty Three primary sources of uncertainty are taken into account: uncertainty in the definition of damage

state, variability in the capacity curve and uncertainty associated with the seismic demand.

Review Forms

157

RISK-UE 2003 WP4 – CIMNEapproach

Reference RISK-UE An Advanced approach to earthquake risk scenarios with applications to different European

towns. WP4: Vulnerability of current buildings Risk-UE 2003. CIMNE Approach.

Region of

applicability

Barcelona - Spain


Typology of element

at risk considered

Reinforced Concrete and Masonry buildings – Moderate Code

Legend:

Type Structure System Height ( number of storeys)

M3.3 Composite Slabs URM

RC1 RC moment frame

(L)ow Rise (1-2)

(M)id Rise (3-5)

(H)igh Rise (6+)

Syner-G Taxonomy BW/M/URM/X/X/X-X/X/X-X/X-X/MR-X/MC

BW/M/URM/X/X/X-X/X/X-X/X-X/MR-X/MC



Sample data Typical residential buildings in Barcelona which are reasonably represented by the RISK-UE Building

Typology Matrix



‚ No damage

‚ Slight damage

‚ Moderate damage

‚ Extensive Damage

‚ Very heavy damage and Collapse

Intensity Measure

Type

Sd(TLS) [cm]

Fragility Function

Parameters


IMT = Sd(TLS) [cm]


Mean Standard

Deviation

Mean Standard

Deviation

Mean Standard

Deviation

Mean Standard

Deviation

M3.3M 0.477 0.199 0.714 0.380 1.590 1.381 3.718 2.956

M3.3H 0.481 0.148 0.840 0.609 2.075 1.505 3.224 2.338

RC1M 1.030 0.294 1.515 0.564 2.652 1.413 6.155 4.132

RC1H 1.383 0.395 1.971 0.584 2.744 0.961 5.179 2.454

Review Forms

158

Figures


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M3.3M M3.3H


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RC1M RC1H

Review Forms

159

RISK-UE 2003 WP4 – IZIIS approach


towns. WP4: Vulnerability of current buildings Risk-UE 2003. IZIIS Approach

Region of applicability FYROM – Federal Yugoslav Republic of Macedonia



risk considered

Reinforced Concrete Buildings – High Code

Legend:

Type Structure system Height (number of storeys)

RC1 RC moment frame

RC4 RC dual system

(L)ow Rise (1-2)

(M)id Rise (3-5)

(H)igh Rise (6+)

Syner-G Taxonomy MRF/C/RC/X/X/X-X/X/X-X/X-X/HR-X/HC

MRF-W/C/RC/X/X/X-X/X/X-X/X-X/MR-X/HC

MRF-W/C/RC/X/X/X-X/X/X-X/X-X/HR-X/HC

Sample data Buildings: RC structures in Macedonia constructed with modern practice. Actual seismic design code

(1981). Seismic Hazard: An extensive strong motion database from 1979 Montenegro earthquake is

used. Some world-wide earthquake records as well as local strong motion data from 1994 Bitola

earthquake are also included in the stated set.



‚ No damage

‚ Slight

‚ Moderate

‚ Extensive

‚ Complete

Intensity Measure Type Sd(TLS)

Fragility Function

Parameters


IMT = Sd(TLS) [cm]


Mean Standard

Deviation

Mean Standard

Deviation

Mean Standard

Deviation

Mean Standard

Deviation

RC1M 2.833 1.510 4.355 1.962 5.682 2.561 12.004 6.542

RC4M 0.793 0.423 1.381 0.591 1.820 0.758 3.326 1.385

RC4H 2.190 1.063 3.358 1.139 4.467 1.371 9.178 3.014

Review Forms

160

Figures


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RC1M RC4M


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RC4H

Review Forms

161

RISK-UE 2003 WP4 – IZIIS hybrid approach


towns. WP4: Vulnerability of current buildings Risk-UE 2003. IZIIS Hybrid Approach.

Region of applicability Europe



risk considered

Reinforced Concrete – Moderate Code and High Code

Legend:

Type Structure system Height (number of storeys)

RC1 RC moment frame (L)ow Rise (1-2)

(M)id Rise (3-5)

(H)igh Rise (6+)

Syner-G Taxonomy MRF/C/RC/X/X/X-X/X/X-X/X-X/LR-X/MC



MRF/C/RC/X/X/X-X/X/X-X/X-X/LR-X/HC

MRF/C/RC/X/X/X-X/X/X-X/X-X/MR-X/HC

MRF/C/RC/X/X/X-X/X/X-X/X-X/HR-X/HC

Sample data

Methodology Hybrid


‚ No damage

‚ Slight

‚ Moderate

‚ Extensive

‚ Complete


Fragility Function

Parameters


IMT = Sd(TLS) [cm]

Moderate Code


Mean Standard

Deviation

Mean Standard

Deviation

Mean Standard

Deviation

Mean Standard

Deviation

RC1L 0.119 0.050 0.147 0.079 0.180 0.118 0.268 0.213

RC1M 1.809 0.754 2.176 1.159 2.598 1.710 4.037 3.210

RC1H 4.236 1.764 5.088 2.712 6.070 3.996 9.454 7.518

Review Forms

162

High Code


Mean Standard

Deviation

Mean Standard

Deviation

Mean Standard

Deviation

Mean Standard

Deviation

RC1L 0.130 0.054 0.215 0.115 0.311 0.205 0.677 0.538

RC1M 2.286 0.952 3.751 1.999 5.411 3.562 11.946 9.499

RC1H 8.016 3.339 13.190 7.029 19.000 12.507 41.932 33.343

Figures


Sd(TLS)

109876543210

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109876543210

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RC1–LR–MC RC1-MR-MC


Sd(TLS)

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RC1–HR–MC RC1-LR-HC


Sd(TLS)

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RC1–MR–HC RC1-HR-HC

Review Forms

163

RISK-UE 2003 WP4 - UTCB approach

Reference RISK-UE An Advanced approach to earthquake risk scenarios with applications to different

European towns. WP4: Vulnerability of current buildings Risk-UE 2003. UTCB Approach




risk considered

Reinforced Concrete – Low Code and Moderate Code

Legend:


RC1 RC moment frame

RC2 RC shear walls

(L)ow Rise (1-2)

(M)id Rise (3-5)

(H)igh Rise (6+)

Syner-G Taxonomy MRF/C/RC/X/X/X-X/X/X-X/X-X/HR-X/LC


W/C/RC/X/X/X-X/X/X-X/X-X/HR-X/HC

W/C/RC/X/X/X-X/X/X-X/X-X/MR-X/MC

Sample data

Methodology Analytical - Nonlinear Static


‚ No damage

‚ Slight

‚ Moderate

‚ Extensive

‚ Complete


Fragility Function

Parameters


IMT = Sd(TLS) [cm]

Low Code


Mean Standard

Deviation

Mean Standard

Deviation

Mean Standard

Deviation

Mean Standard

Deviation

RC1H 9.659 7.004 23.687 20.583 40.097 41.274 107.030 129.580

RC2H 0.642 0.466 1.722 1.497 2.999 3.087 8.197 9.924

Moderate Code


Mean Standard

Deviation

Mean Standard

Deviation

Mean Standard

Deviation

Mean Standard

Deviation

RC1H 14.415 10.452 28.629 24.877 45.623 46.962 113.107 136.937

Review Forms

164

RC2M 0.568 0.412 1.351 1.174 2.267 2.334 6.030 7.300

Figures


Sd(TLS)

302826242220181614121086420

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RC1H – LC RC1H – MC


Sd(TLS)

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RC2H – LC RC2M – MC

Uncertainty Normal probability distribution for concrete strength and a lognormal probability distribution for steel

strength are used.

Review Forms

165

RISK-UE 2003 WP4 – UTCB hybrid approach

Reference RISK-UE An Advanced approach to earthquake risk scenarios with applications to different European towns.

WP4: Vulnerability of current buildings Risk-UE 2003. UTCB Hybrid Approach

Region of

applicability

Europe


Typology of

element at risk

considered

Reinforced Concrete

Legend:


RC1 RC moment frame

RC2 RC shear walls

(L)ow Rise (1-2)

(M)id Rise (3-5)

(H)igh Rise (6+)

Syner-G

Taxonomy

MRF/C/RC/X/X/X-X/X/X-X/X-X/LR-X/NC

MRF/C/MC/X/X/X-X/X/X-X/X-X/MR-X/NC

MRF/C/RC/X/X/X-X/X/X-X/X-X/HR-X/NC

W/C/RC/X/X/X-X/X/X-X/X-X/LR-X/NC

W/C/RC/X/X/X-X/X/X-X/X-X/MR-X/NC

W/C/RC/X/X/X-X/X/X-X/X-X/HR-X/NC

MRF/C/RC/X/X/X-X/X/X-X/X-X/LR-X/LC

MRF/C/RC/X/X/X-X/X/X-X/X-X/MR-X/LC

MRF/C/RC/X/X/X-X/X/X-X/X-X/HR-X/LC

W/C/RC/X/X/X-X/X/X-X/X-X/LR-X/LC

W/C/RC/X/X/X-X/X/X-X/X-X/MR-X/LC

W/C/RC/X/X/X-X/X/X-X/X-X/HR-X/LC

MRF/C/RC/X/X/X-X/X/X-X/X-X/LR-X/MC



W/C/RC/X/X/X-X/X/X-X/X-X/LR-X/MC

W/C/RC/X/X/X-X/X/X-X/X-X/MR-X/MC

W/C/RC/X/X/X-X/X/X-X/X-X/HR-X/MC

MRF/C/RC/X/X/X-X/X/X-X/X-X/LR-X/HC

MRF/C/RC/X/X/X-X/X/X-X/X-X/MR-X/HC

MRF/C/RC/X/X/X-X/X/X-X/X-X/HR-X/HC

W/C/RC/X/X/X-X/X/X-X/X-X/LR-X/HC

W/C/RC/X/X/X-X/X/X-X/X-X/MR-X/HC

W/C/RC/X/X/X-X/X/X-X/X-X/HR-X/HC

Sample data

Methodology Hybrid


‚ No damage

Review Forms

166

‚ Slight

‚ Moderate

‚ Extensive

‚ Complete

Intensity

Measure Type

Sd(TLS) [cm]

Fragility Function

Parameters


IMT = Sd(TLS) [cm]

Pre Code


Mean Standard

Deviation

Mean Standard

Deviation

Mean Standard

Deviation

Mean Standard

Deviation

RC1L 0.173 0.125 0.384 0.334 0.631 0.650 1.617 1.958

RC1M 0.469 0.340 1.033 0.898 1.693 1.743 4.381 5.304

RC1H 1.075 0.779 2.385 2.072 3.918 4.033 10.144 12.281

RC2L 0.012 0.009 0.040 0.035 0.072 0.074 0.173 0.209

RC2M 0.148 0.107 0.318 0.276 0.517 0.532 1.350 1.635

RC2H 0.494 0.358 1.100 0.955 1.808 1.861 4.664 5.646

Low Code


Mean Standard

Deviation

Mean Standard

Deviation

Mean Standard

Deviation

Mean Standard

Deviation

RC1L 0.247 0.179 0.543 0.472 0.890 0.916 2.308 2.795

RC1M 0.420 0.305 0.941 0.817 1.550 1.595 4.004 4.848

RC1H 0.692 0.502 1.524 1.324 2.511 2.585 6.501 7.871

RC2L 0.049 0.036 0.106 0.092 0.172 0.177 0.440 0.532

RC2M 0.309 0.224 0.702 0.610 1.148 1.182 2.968 3.593

RC2H 0.581 0.421 1.298 1.128 2.124 2.186 5.512 6.673

Moderate Code - 5A - UTCB 1970-77


Mean Standard

Deviation

Mean Standard

Deviation

Mean Standard

Deviation

Mean Standard

Deviation

RC1L 0.259 0.188 0.570 0.495 0.947 0.975 2.450 2.966

RC1M 0.445 0.322 0.994 0.863 1.636 1.684 4.240 5.133

RC1H 0.729 0.528 1.629 1.416 2.684 2.762 6.941 8.403

RC2L 0.037 0.027 0.079 0.069 0.129 0.133 0.345 0.418

RC2M 0.296 0.215 0.649 0.564 1.076 1.108 2.779 3.365

RC2H 0.618 0.448 1.378 1.197 2.253 2.319 5.841 7.072

Review Forms

167

Moderate Code – 5B - UTCB 1978-89


Standard

Deviation

Mean Standard

Deviation

Mean Standard

Deviation

Mean Standard

Deviation

Mean

RC1L 0.618 0.448 1.471 1.278 2.468 2.541 6.517 7.890

RC1M 1.556 1.129 3.696 3.212 6.200 6.382 16.378 19.829

RC1H 3.545 2.571 8.412 7.310 14.093 14.507 37.247 45.094

RC2L 0.037 0.027 0.093 0.081 0.144 0.148 0.393 0.475

RC2M 0.531 0.385 1.219 1.059 2.024 2.083 5.292 6.407

RC2H 1.742 1.263 4.014 3.488 6.673 6.869 17.509 21.197

High Code


Standard

Deviation

Mean Standard

Deviation

Mean Standard

Deviation

Mean Standard

Deviation

Mean

RC1L 0.778 0.564 1.749 1.520 2.885 2.969 7.506 9.087

RC1M 1.952 1.415 4.398 3.822 7.262 7.475 18.890 22.870

RC1H 4.434 3.215 10.002 8.691 16.518 17.003 42.947 51.995

RC2L 0.049 0.036 0.106 0.092 0.172 0.177 0.455 0.551

RC2M 0.667 0.484 1.457 1.266 2.382 2.452 6.124 7.414

RC2H 2.211 1.603 4.822 4.190 7.879 8.110 20.241 24.505

Figures


Sd(TLS)

109876543210

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Review Forms

168


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RC1-LR-LC RC1-MR-LC


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RC1-HR-LC RC2-LR-LC


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RC2-MR-LC RC2-HR-LC


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Review Forms

169


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109876543210

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RC1-LR-MC5B RC1-MR-MC5B


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RC2-MR-MC5B RC2-HR-MC5B

Review Forms

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RC2-MR-HC RC2-HR-HC

Review Forms

171

RossettoAndElnashai2005

Reference T. Rossetto & A. Elnashai,“A new analytical procedure for the derivation of displacement-based

vulnerability curves for populations of RC structures”, Engineering Structures 27(3), 397-409,

2005




considered

Infilled RC frames – low rise – inadequate seismic provisions

Syner-G Taxonomy MRF/C/RC/R/R/RI-FB/ND/X-X/X-X/LR-3/LC

Sample data Buildings: 3 storeys regular infilled frame without seismic design with variation of concrete, steel

and infill properties

Seismic Hazard: 3 sets of 10 recorded accelerograms


Damage States Seven damage states are considered:

‚ None

‚ Slight

‚ Light

‚ Moderate

‚ Extensive

‚ Partial Collapse

‚ Collapse

Intensity Measure Type Sd(Ty) [m]


IMT = Sd(Ty) [m]

Mean Standard

Deviation

Slight 0.0005 0.0003

Light 0.0009 0.0004

Moderate 0.0032 0.0007

Extensive 0.0121 0.0026

Partial Collapse 0.0312 0.0070

Collapse 0.0515 0.0115

Review Forms

172

Figures

Slight Light Moderate Extensive Partial Collapse

Collpase

Sd(Ty)

65.554.543.532.521.510.50

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Uncertainty Uncertainty both in the material properties and ground motion is considered.

Review Forms

173

RossettoAndElnashai2003

Reference Rossetto & A. Elnashai. Derivation of vulnerability functions for European-type RC structures based on

observational data. Engineering Structures 25(10), 1241-1263, 2003.

Region of

applicability

Europe


Typology of

element at risk

considered

RC buildings

Syner-G Taxonomy

Sample data Buildings: 340000 existing RC structures from 99 post-earthquakes damage distribution

Seismic hazard: 19 earthquakes


Damage States Seven damage states:

‚ None

‚ Slight

‚ Light

‚ Moderate

‚ Extensive

‚ Partial Collapse

‚ Collapse

Intensity Measure

Type

PGA [g], Sa(Ty) [g], Sd(Ty) [m], Sd(TLS) [m]

Fragility Function

Parameters

Distribution: P=1-exp(-cGMd)

IMT = PGA [g]

c" d"

Slight 1.556 1.60

Light 1.055 1.80

Moderate 0.250 3.00


P.Collapse 0.009 5.80

Collapse 0.001 8.00

IMT = Sa(Ty) [g]

c" d"

Slight 0.633 1.80

Light 0.396 1.80

Moderate 0.153 1.80

Review Forms

174



Collapse 0.010 3.00

IMT = Sd(Ty) [m]

c" d"

Slight 25.82 1.10

Light 21.08 1.20

Moderate 6.500 1.15



Collapse 2.000 2.40

IMT = Sd(TLS) [m]

c" d"



Collapse 0.600 2.40

Figures

Slight Light Moderate Extensive P.Collapse Collapse

PGA [g]32.72.42.11.81.51.20.90.60.30

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Sa(Ty) 43.63.22.82.421.61.20.80.40

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RC – PGA RC-Sa(Ty)


Sd(Ty) [cm]3531.52824.52117.51410.573.50

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Extensive P.Collapse Collapse

Sd(TLS) [cm]0.3150.280.2450.210.1750.140.1050.070.0350

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RC – Sd(Ty) RC-Sd(TLS)

Uncertainty Large uncertainties are associated with the empirical relationships due to the nature and scarcity of

observational data

Review Forms

175

RotaEtAl2008

Reference M. Rota, A. Penna, C.L. Strobbia, “Processing Italian damage data to derive typological fragility curves”,

Soil Dynamics and Earthquake Engineering 28(10-11), 933-947, 2008

Region of

applicability

Italy


Typology of

element at risk

considered

Masonry Buildings, Reinforced Concrete Buildings and Mixed Structures

Legend:

Label Description Number of Storeys

MX1 Mixed 1-2

MX2 Mixed ‡3

RC1 Reinforced Concrete – seismic design 1-3

RC2 Reinforced Concrete – no seismic design 1-3

RC3 Reinforced Concrete – seismic design ‡4

RC4 Reinforced Concrete – no seismic design ‡4

IMA1 Masonry – irregular layout – flexible floors – with tie rods

or tie beams

1-2

IMA2 Masonry – irregular layout – flexible floors – w/o tie rods

or tie beams

1-2

IMA3 Masonry – irregular layout – rigid floors – with tie rods or

tie beams

1-2

IMA4 Masonry – irregular layout – rigid floors – w/o tie rods or

tie beams

1-2

IMA5 Masonry – irregular layout – flexible floors – with tie rods

or tie beams

‡3

IMA6 Masonry – irregular layout – flexible floors – w/o tie rods

or tie beams

‡3

IMA7 Masonry – irregular layout – rigid floors – with tie rods or

tie beams

‡3

IMA8 Masonry – irregular layout – rigid floors – w/o tie rods or

tie beams

‡3

RMA1 Masonry – regular layout – flexible floors – with tie rods

or tie beams

1-2

RMA2 Masonry – regular layout – flexible floors – w/o tie rods

or tie beams

1-2

RMA3 Masonry – regular layout – rigid floors – with tie rods or

tie beams

1-2

RMA4 Masonry – regular layout – rigid floors – w/o tie rods or

tie beams

1-2

Review Forms

176

Label Description Number of Storeys

RMA5 Masonry – regular layout – flexible floors – with tie rods

or tie beams

‡3

RMA6 Masonry – regular layout – flexible floors – w/o tie rods

or tie beams

‡3

RMA7 Masonry – regular layout – rigid floors – with tie rods or

tie beams

‡3

RMA8 Masonry – regular layout – rigid floors – w/o tie rods or

tie beams

‡3

Syner-G

Taxonomy

BW/M-C/X/X/X/X-X/X/X-X/X-X/LR-X/NC

BW/M-C/X/X/X/X-X/X/X-X/X-X/MR-X/NC

MRF/C/RC/X/X/X-X/X/X-X/X-X/LR-X/LC

MRF/C/RC/X/X/X-X/X/X-X/X-X/LR-X/NC

MRF/C/RC/X/X/X-X/X/X-X/X-X/MR-X/NC

BW/M/URM/IR/X/X-X/X/F-X/X-X/LR-X/NC

BW/M/URM/IR/X/X-X/X/F-X/X-X/LR-X/NC

BW/M/URM/IR/X/X-X/X/R-X/X-X/LR-X/NC

BW/M/URM/IR/X/X-X/X/R-X/X-X/LR-X/NC

BW/M/URM/IR/X/X-X/X/F-X/X-X/MR-X/NC

BW/M/URM/IR/X/X-X/X/F-X/X-X/MR-X/NC

BW/M/URM/IR/X/X-X/X/R-X/X-X/MR-X/NC

BW/M/URM/X/X/X-X/X/R-X/X-X/MR-X/NC

BW/M/URM/R/X/X-X/X/F-X/X-X/LR-X/NC

BW/M/URM/R/X/X-X/X/F-X/X-X/LR-X/NC

BW/M/URM/R/X/X-X/X/R-X/X-X/LR-X/NC

BW/M/URM/R/X/X-X/X/R-X/X-X/LR-X/NC

MRF/C/RC/R/X/X-X/X/F-X/X-X/MR-X/NC

BW/M/URM/R/X/X-X/X/F-X/X-X/MR-X/NC

BW/M/URM/R/X/X-X/X/R-X/X-X/MR-X/NC

BW/M/URM/R/X/X-X/X/R-X/X-X/MR-X/NC

Sample data Buildings: Damage on masonry and reinforced concrete buildings collected after 1980 Irpinia, 1984

Abruzzo, 1997 Marche, 1998 Pollino and 2002 Marche earthquakes

Seismic Hazard: real earthquakes and Sabetta and Pugliese (1987) GMPE


Damage States Six damage states are considered

‚ DS0 - No damage

‚ DS1 – Negligible to Slight

‚ DS2 – Moderate

‚ DS3 – Substantial to Heavy

‚ DS4 – Very Heavy

‚ DS5 - Destruction

Review Forms

177

Intensity Measure

Type

PGA [g]

Fragility Function

Parameters


IMT = PGA [g]

DS1 DS2 DS3 DS4 DS5


MX1 5.8E+02 4.2E+07 2.1E+04 2.0E+08 2.5E+07 2.3E+13 4.0E+03 1.0E+06 9.7E+01 1.2E+03

MX2 3.0E+03 1.4E+09 9.6E+00 1.4E+02 3.9E+00 1.7E+01 2.2E+01 1.8E+02 2.5E+01 1.3E+02

RC1 4.3E+01 2.1E+03 5.2E+00 1.3E+01 2.6E+00 3.9E+00 1.8E+00 1.9E+00

RC2 2.2E+00 1.8E+01 1.4E+00 1.7E+00 9.5E-01 6.7E-01 2.1E+00 2.3E+00 3.0E+00 3.5E+00

RC4 2.1E-01 2.2E-01 3.5E-01 1.6E-01 3.8E-01 1.6E-01 4.8E-01 2.2E-01 7.2E-01 4.0E-01

IMA1 2.4E+09 2.1E+23 2.5E+25 5.9E+50 2.1E+06 5.5E+11 3.0E+04 4.3E+07 3.4E+02 7.9E+03

IMA2 2.3E+03 1.1E+11 6.1E+04 7.7E+10 2.8E+04 2.5E+09 6.3E+01 4.9E+03 5.7E+00 3.0E+01

IMA3 1.1E+03 8.6E+07 2.1E+05 1.5E+10 5.4E+04 2.3E+08 2.0E+04 1.0E+07 4.1E+01 2.4E+02

IMA4 9.5E+03 1.3E+11 1.5E+02 9.7E+04 2.7E+02 9.0E+04 5.3E+02 9.1E+04 2.5E+02 8.5E+03

IMA5 2.8E+07 3.1E+19 3.3E+13 1.3E+28 5.1E+01 4.3E+03 4.3E+01 8.9E+02

IMA6 1.4E+02 2.3E+08 7.3E+02 9.8E+06 2.7E+01 2.8E+03 6.0E+00 5.4E+01 2.1E+00 4.7E+00

IMA7 1.7E+00 1.1E+02 6.5E+00 1.9E+02 2.7E+00 1.5E+01 2.0E+01 2.1E+02 5.4E+01 4.0E+02

IMA8 8.9E+00 7.7E+04 8.0E-01 6.9E+00 7.6E-01 3.0E+00 1.9E+00 7.1E+00 8.4E+00 4.1E+01

RMA1 7.4E+07 9.4E+17 1.6E+18 4.6E+33 8.3E+07 3.9E+13 2.7E+03 1.8E+05

RMA2 2.3E+16 2.4E+37 6.4E+21 1.1E+43 1.9E+21 1.5E+40 4.4E+10 8.7E+18 1.1E+04 3.8E+06

RMA3 3.1E+06 3.0E+13 1.2E+09 5.5E+15 8.2E+05 4.7E+09 3.7E+03 2.8E+05

RMA4 5.6E+31 2.4E+66 1.4E+13 2.0E+24 4.7E+04 1.2E+08 5.6E+03 9.9E+05 6.7E+01 4.4E+02

RMA5 4.5E+06 2.4E+15 1.4E+09 7.6E+17 3.6E+04 2.1E+08 4.5E+00 1.2E+01

RMA6 1.8E+19 2.1E+43 1.8E+17 6.4E+34 1.2E+06 6.0E+11 2.2E+03 9.6E+05 3.3E+04 1.7E+07

RMA7 3.1E+00 7.2E+01 4.1E+00 1.9E+01 3.0E+00 8.3E+00 2.1E+00 3.3E+00 1.3E+00 7.7E-01

RMA8 2.8E+15 3.2E+33 1.6E+02 5.7E+04 1.1E+01 1.6E+02 1.6E+00 3.3E+00 1.8E+03 9.9E+04

Review Forms

178

Figures

DS1 DS2 DS3 DS4 DS5

PGA

0.50.450.40.350.30.250.20.150.10.050

Pro

bability

of exceedance

1

0.9

0.8

0.7

0.6

0.5

0.4

0.3

0.2

0.1

0

DS1 DS2 DS3 DS4 DS5

PGA

0.50.450.40.350.30.250.20.150.10.050

Pro

bability

of exceedance

1

0.9

0.8

0.7

0.6

0.5

0.4

0.3

0.2

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MX1 MX2

DS1 DS2 DS3 DS4

PGA

0.50.450.40.350.30.250.20.150.10.050

Pro

bability

of exceedance

1

0.9

0.8

0.7

0.6

0.5

0.4

0.3

0.2

0.1

0

DS1 DS2 DS3 DS4 DS5

PGA

0.50.450.40.350.30.250.20.150.10.050

Pro

bability

of exceedance

1

0.9

0.8

0.7

0.6

0.5

0.4

0.3

0.2

0.1

0

RC1 RC2

DS1 DS2 DS3 DS4 DS5

PGA

0.50.450.40.350.30.250.20.150.10.050

Pro

bability

of exceedance

1

0.9

0.8

0.7

0.6

0.5

0.4

0.3

0.2

0.1

0

DS1 DS2 DS3 DS4 DS5

PGA

0.50.450.40.350.30.250.20.150.10.050

Pro

bability

of exceedance

1

0.9

0.8

0.7

0.6

0.5

0.4

0.3

0.2

0.1

0

RC4 IMA1

DS1 DS2 DS3 DS4 DS5

PGA

0.50.450.40.350.30.250.20.150.10.050

Pro

bability

of exceedance

1

0.9

0.8

0.7

0.6

0.5

0.4

0.3

0.2

0.1

0

DS1 DS2 DS3 DS4 DS5

PGA

0.50.450.40.350.30.250.20.150.10.050

Pro

bability

of exceedance

1

0.9

0.8

0.7

0.6

0.5

0.4

0.3

0.2

0.1

0

IMA2 IMA3

DS1 DS2 DS3 DS4 DS5

PGA

0.50.450.40.350.30.250.20.150.10.050

Pro

bability

of exceedance

1

0.9

0.8

0.7

0.6

0.5

0.4

0.3

0.2

0.1

0

DS1 DS2 DS3 DS4

PGA

0.50.450.40.350.30.250.20.150.10.050

Pro

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0.8

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0.4

0.3

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0

IMA4 IMA5

Review Forms

179

DS1 DS2 DS3 DS4 DS5

PGA

0.50.450.40.350.30.250.20.150.10.050

Pro

bability

of exceedance

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0.9

0.8

0.7

0.6

0.5

0.4

0.3

0.2

0.1

0

DS1 DS2 DS3 DS4 DS5

PGA

0.50.450.40.350.30.250.20.150.10.050

Pro

bability

of exceedance

1

0.9

0.8

0.7

0.6

0.5

0.4

0.3

0.2

0.1

0

IMA6 IMA7

DS1 DS2 DS3 DS4 DS5

PGA

0.50.450.40.350.30.250.20.150.10.050

Pro

ba

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0.9

0.8

0.7

0.6

0.5

0.4

0.3

0.2

0.1

0

DS1 DS2 DS3 DS4

PGA

0.50.450.40.350.30.250.20.150.10.050

Pro

bability

of exceedance

1

0.9

0.8

0.7

0.6

0.5

0.4

0.3

0.2

0.1

0

IMA8 RMA1

DS1 DS2 DS3 DS4 DS5

PGA

0.50.450.40.350.30.250.20.150.10.050

Pro

bability

of exceedance

1

0.9

0.8

0.7

0.6

0.5

0.4

0.3

0.2

0.1

0

DS1 DS2 DS3 DS4

PGA

0.50.450.40.350.30.250.20.150.10.050

Pro

bability

of exceedance

1

0.9

0.8

0.7

0.6

0.5

0.4

0.3

0.2

0.1

0

RMA2 RMA3

DS1 DS2 DS3 DS4 DS5

PGA

0.50.450.40.350.30.250.20.150.10.050

Pro

bability

of exceedance

1

0.9

0.8

0.7

0.6

0.5

0.4

0.3

0.2

0.1

0

DS1 DS2 DS3 DS4

PGA

0.50.450.40.350.30.250.20.150.10.050

Pro

bability

of exceedance

1

0.9

0.8

0.7

0.6

0.5

0.4

0.3

0.2

0.1

0

RMA4 RMA5

DS1 DS2 DS3 DS4 DS5

PGA

0.50.450.40.350.30.250.20.150.10.050

Pro

bability

of exceedance

1

0.9

0.8

0.7

0.6

0.5

0.4

0.3

0.2

0.1

0

DS1 DS2 DS3 DS4 DS5

PGA

0.50.450.40.350.30.250.20.150.10.050

Pro

ba

bili

ty o

f e

xc

ee

da

nc

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0.9

0.8

0.7

0.6

0.5

0.4

0.3

0.2

0.1

0

RMA6 RMA7

Review Forms

180

DS1 DS2 DS3 DS4 DS5

PGA

0.50.450.40.350.30.250.20.150.10.050

Pro

bability

of exceedance

1

0.9

0.8

0.7

0.6

0.5

0.4

0.3

0.2

0.1

0

RMA8

Uncertainty The use of real data allows taking into account all the characteristics of the building stock and the ground

motion.

Review Forms

181

SarabandiEtAl2004

Reference P. Sarabandi, D. Pachakis, S. King & A. Kiremidjian, “Empirical fragility functions from recent

earthquakes”, 13th World Conference on Earthquake Engineering, Vancouver, Canada, 2004

Region of applicability Worldwide and USA



considered

C1 – concrete moment resisting frame

C2 – concrete frame with concrete shear wall

Syner-G Taxonomy MRF/C/RC/X/X/B-X/X/X-X/X-X/X-X/X

MRF-W/C/RC/X/X/X-X/X/X-X/X-X/X-X/X

Proposed Taxonomy FEMA 310 (FEMA, 1998) very similar to that used in HAZUS (FEMA, 1999) and several recent

ATC projects

Sample data Buildings: only those buildings located near free-field strong motion recording stations (and on

similar site conditions) were extracted from available databases (SAC and LADiv88 building

datasets)

Seismic hazard: 1994 Northridge earthquake, 1999 Chi-Chi earthquake


Damage States Four different characterizations are used: ATC-13 (ATC,1985), HAZUS99 (FEMA,1999), FEMA

273/356 (FEMA, 2000) and Vision2000 (SEAOC,1995)

The performance characterization was developed in terms of percent of loss so that the

performance of each building could be characterized using all four schemes.

Intensity Measure Type MMI, Sd(TLS) [in], RMS, Drift Ratio [%]


C1

IMT = Sd(TLS) [in]


Slight 293.118 1240

Moderate 40.637 100.626

Review Forms

182

Extensive 34.216 55.730

Complete 30.745 40.943

IMT = MMI


Slight 7.857 1.070

Light 8.748 1.390


Heavy 9.907 1.750

Major 10.306 2.014

Destroyed 10.500 1.997

IMT = MMI


Operational 8.669 1.330

Life Safe 9.803 1.230

Near Collapse 10.268 1.144

Collapse 10.402 1.090

IMT = RMS


Operational 0.072 0.066

Life Safe 0.150 0.150

Near Collapse 0.305 0.365


C2

IMT = MMI


Slight 8.088 1.090

Light 8.850 1.130


Heavy 9.522 1.191

Review Forms

183

Major 9.694 1.217


IMT = fR [%]


Slight 0.176 0.108

Light 0.244 0.149


Heavy 0.316 0.177

Major 0.339 0.186


Figures


Sd(Ty)

302520151050

Pro

bability o

f exceedance

1

0.9

0.8

0.7

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Slight Light Moderate Heavy Major Destroyed

MMI

1211.51110.5109.598.587.576.56

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C1-Sd(Ty)-HAZUS99 C1 – MMI - ATC13

Operational Life Safe Near Collapse Collapse

MMI

1211.51110.5109.598.587.576.56

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Operational Life Safe Near Collapse Collapse

RMS

0.20.180.160.140.120.10.080.060.040.020

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C1 – MMI – Vision 2000 C1 – RMS – Vision 2000


MMI

1211.51110.5109.598.587.576.56

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Drift Ratio dR

10.90.80.70.60.50.40.30.20.10

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C2 – MMI - ATC13 C2 – Drift Ratio - ATC13

Comments The correlations of building performance with the ground motion measures, the correlations of

building performance in terms of damage states and performance levels and the correlation for

building performance in terms of percent of loss were developed. These correlations were also

developed for class C3 (concrete frame with masonry infill shear wall), but due to the size of the

dataset (13 buildings) buildings in this class were not further analyzed.

The comparison with the fragility curves in terms of spectral displacement developed within

HAZUS and within this study is also shown.

Review Forms

184

TahiriAndMilutinovic2010

Reference F. T.Tahiri, Z.M. Milutinovic, “Seismic Risk, vulnerability and retrofit requirements of educational

buildings in Kosovo”, 14ECEE, Ohrid, 2010

Region of applicability Kosovo



considered

School Buildings – Reinforced Concrete

Syner-G Taxonomy MRF/C/RC/X/X/X-X/X/X-X/X-X/LR-X/LC

Sample data Buildings: a typical RC structure is selected from several numbers of educational buildings in the

region of Gjilian. The building was designed on 1983. The design and construction of

educational buildings was done according to SDC.

Seismic Hazard: an earthquake tremor M5.2, h=10 km, I=VII which stroke the city of Gjilian on

24 April 2002 was used.

Methodology Unknown


‚ No damage

‚ Slight

‚ Moderate

‚ Extensive

‚ Complete

Intensity Measure Type Sd (TLS) [cm]

Fragility Function Parameters Lognormal Distribution

IMT = Sd(TLS) [cm]


Slight 1.020 0.379



Collapse 12.271 15.970

Figures


SD(TLS)

7.576.565.554.543.532.521.510.50

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Comments It is a school building and it is designed and constructed with safety factor of 1.5.

A set of unified fragility curves are obtained with integration of structural and nonstructural

components.

Review Forms

185

TsionisEtAl2011

Reference Tsionis G., A. Papailia, M.N. Fardis. 2011. Analytical Fragility Functions for Reinforced Concrete

Buildings and Buildings Aggregates of Euro-Mediterranean Regions – UPAT methodology. Internal

Report, Syner-G Project 2009/2012

Region of

applicability

Euro-Mediterranean Regions


Typology of element

at risk considered


Legend:

1 - moment resisting frame building, low rise, designed with low code, bare and ductile

2 - moment resisting frame building, low rise, designed with medium code, bare and ductile

3 - moment resisting frame building, low rise, designed with high code, bare and ductile

4 - moment resisting frame building, mid rise, designed with low code, bare and ductile

5 - moment resisting frame building, mid rise, designed with medium code, bare and ductile

6 - moment resisting frame building, mid rise, designed with high code, bare and ductile

7 - moment resisting frame building, high rise, designed with low code, bare and ductile

8 - moment resisting frame building, high rise, designed with medium code, bare and ductile

9 - moment resisting frame building, high rise, designed with high code, bare and ductile

10 –shear walls, mid rise, designed with low code

11 –shear walls, mid rise, designed with medium code

12 –shear walls, mid rise, designed with high code

13 –shear walls, high rise, designed with low code

14 –shear walls, high rise, designed with medium code

15 –shear walls, high rise, designed with high code

16 –dual system, mid rise, designed with low code

17 –dual system, mid rise, designed with medium code

18 –dual system, mid rise, designed with high code

19 – dual system, high rise, designed with low code

20 –dual system, high rise, designed with medium code

21 –dual system, high rise, designed with high code

22 –dual system, mid rise, designed with old code, non ductile

23 –dual system, high rise, designed with old code, non ductile

24 – dual system, mid rise, designed with low code, non ductile

25 - dual system, high rise, designed with low code, non ductile

26 - moment resisting frame building, low rise, designed with old code, infill and non ductile

27 - moment resisting frame building, mid rise, designed with old code, infill and non ductile

28 - moment resisting frame building, high rise, designed with old code, infill and non ductile

29 - moment resisting frame building, low rise, designed with low code, infill and non ductile

30 - moment resisting frame building, mid rise, designed with low code, infill and non ductile

31 - moment resisting frame building, high rise, designed with low code, infill and non ductile

32 - moment resisting frame building, low rise, designed with old code, bare and non ductile

33 - moment resisting frame building, mid rise, designed with old code, bare and non ductile

Review Forms

186

34 - moment resisting frame building, high rise, designed with old code, bare and non ductile

35 - moment resisting frame building, low rise, designed with low code, bare and non ductile

36 - moment resisting frame building, mid rise, designed with low code, bare and non ductile

37 - moment resisting frame building, high rise, designed with low code, bare and non ductile

38 - moment resisting frame building, low rise, designed with old code, pilotis and non ductile

39 - moment resisting frame building, mid rise, designed with old code, pilotis and non ductile

40 - moment resisting frame building, high rise, designed with old code, pilotis and non ductile

41 - moment resisting frame building, low rise, designed with low code, pilotis and non ductile

42 - moment resisting frame building, mid rise, designed with low code, pilotis and non ductile

43 - moment resisting frame building, high rise, designed with low code, pilotis and non ductile

Syner-G Taxonomy MRF/C/RC/R/R/B-X/D/X-X/X-X/L-X/LC

MRF/C/RC/R/R/B-X/D/X-X/X-X/L-X/MC

MRF/C/RC/R/R/B-X/D/X-X/X-X/L-X/HC

MRF/C/RC/R/R/B-X/D/X-X/X-X/M-X/LC

MRF/C/RC/R/R/B-X/D/X-X/X-X/M-X/MC

MRF/C/RC/R/R/B-X/D/X-X/X-X/M-X/HC

MRF/C/RC/R/R/B-X/D/X-X/X-X/H-X/LC

MRF/C/RC/R/R/B-X/D/X-X/X-X/H-X/MC

MRF/C/RC/R/R/B-X/D/X-X/X-X/H-X/HC

W/C/RC/R/R/X-X/X/X-X/X-X/M-X/LC

W/C/RC/R/R/X-X/X/X-X/X-X/M-X/MC

W/C/RC/R/R/X-X/X/X-X/X-X/M-X/HC

W/C/RC/R/R/X-X/X/X-X/X-X/H-X/LC

W/C/RC/R/R/X-X/X/X-X/X-X/H-X/MC

W/C/RC/R/R/X-X/X/X-X/X-X/H-X/HC

MRF-W/C/RC/R/R/X-X/X/X-X/X-X/M-X/LC

MRF-W/C/RC/R/R/X-X/X/X-X/X-X/M-X/MC

MRF-W/C/RC/R/R/X-X/X/X-X/X-X/M-X/HC

MRF-W/C/RC/R/R/X-X/X/X-X/X-X/H-X/LC

MRF-W/C/RC/R/R/X-X/X/X-X/X-X/H-X/MC

MRF-W/C/RC/R/R/X-X/X/X-X/X-X/H-X/HC

MRF-W/C/RC/R/R/X-X/ND/X-X/X-X/M-X/NC

MRF-W/C/RC/R/R/X-X/ND/X-X/X-X/H-X/NC

MRF-W/C/RC/R/R/X-X/ND/X-X/X-X/M-X/LC

MRF-W/C/RC/R/R/X-X/ND/X-X/X-X/H-X/LC

MRF/C/RC/R/R/RI-X/ND/X-X/X-X/L-X/NC

MRF/C/RC/R/R/RI-X/ND/X-X/X-X/M-X/NC

MRF/C/RC/R/R/RI-X/ND/X-X/X-X/H-X/NC

MRF/C/RC/R/R/RI-X/ND/X-X/X-X/L-X/LC

MRF/C/RC/R/R/RI-X/ND/X-X/X-X/M-X/LC

MRF/C/RC/R/R/RI-X/ND/X-X/X-X/H-X/LC

MRF/C/RC/R/R/B-X/ND/X-X/X-X/L-X/NC

Review Forms

187

MRF/C/RC/R/R/B-X/ND/X-X/X-X/M-X/NC

MRF/C/RC/R/R/B-X/ND/X-X/X-X/H-X/NC

MRF/C/RC/R/R/B-X/ND/X-X/X-X/L-X/LC

MRF/C/RC/R/R/B-X/ND/X-X/X-X/M-X/LC

MRF/C/RC/R/R/B-X/ND/X-X/X-X/H-X/LC

MRF/C/RC/R/R/IRI-P/ND/X-X/X-X/L-X/NC

MRF/C/RC/R/R/IRI-P/ND/X-X/X-X/M-X/NC

MRF/C/RC/R/R/IRI-P/ND/X-X/X-X/H-X/NC

MRF/C/RC/R/R/IRI-P/ND/X-X/X-X/L-X/LC

MRF/C/RC/R/R/IRI-P/ND/X-X/X-X/M-X/LC

MRF/C/RC/R/R/IRI-P/ND/X-X/X-X/H-X/LC

Sample data Some prototype regular buildings have been analyzed.


Damage States Two damage states are considered:

‚ Yielding

‚ Collapse

Intensity Measure

Type

PGA [g]

Fragility Function

Parameters


IMT = PGA [g]

Yielding Collapse


1 0.200 0.085 0.459 0.126

2 0.179 0.076 0.832 0.283

3 0.181 0.081 0.966 0.278

4 0.245 0.101 0.667 0.174

5 0.176 0.084 0.887 0.465

6 0.176 0.090 0.990 0.491

7 0.284 0.121 0.855 0.228

8 0.167 0.089 0.839 0.423

9 0.171 0.077 0.941 0.459

10 0.127 0.070 0.168 0.033

11 0.147 0.079 0.191 0.036

12 0.193 0.110 0.449 0.173

13 0.138 0.077 0.172 0.017

14 0.149 0.082 0.186 0.029

15 0.174 0.084 0.307 0.100

16 0.124 0.058 0.217 0.025

17 0.125 0.068 0.199 0.037

Review Forms

188

IMT = PGA [g]

Yielding Collapse


18 0.148 0.079 0.413 0.137

19 0.090 0.048 0.265 0.128

20 0.101 0.054 0.365 0.176

21 0.168 0.085 0.401 0.112

22 0.094 0.052 0.163 0.036

23 0.131 0.069 0.176 0.020

24 0.109 0.060 0.175 0.037

25 0.123 0.061 0.177 0.020

26 0.635 0.283 1.488 0.688

27 0.615 0.261 1.948 1.000

28 0.598 0.293 2.526 8.714

29 0.599 0.251 7.543 57.178

30 0.540 0.265 5.443 38.289

31 0.473 0.217 5.597 45.129

32 0.093 0.043 0.224 0.107

33 0.157 0.066 0.482 0.232

34 0.169 0.079 0.476 0.971

35 0.223 0.092 2.973 25.069

36 0.170 0.072 1.129 5.025

37 0.151 0.069 1.767 14.426

38 0.075 0.026 0.189 0.081

39 0.093 0.042 0.275 0.145

40 0.159 0.074 0.427 0.218

41 0.202 0.080 0.693 0.192

42 0.169 0.072 0.498 0.266

43 0.133 0.061 0.387 0.199

Review Forms

189

Figures

Yielding Collapse

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Uncertainty Uncertainty both in the demand and in the capacity have been considered in the analyses

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VacarenauEtAl2004

Reference R. Vacareanu, R. Radoi, C. Negulescu. & A. Aldea, ”Seismic vulnerability of RC buildings in

Bucharest, Romania”, 13th World Conference on Earthquake Engineering, Vancouver, Canada

2004

Region of applicability Bucharest - Romania



considered

RC buildings – 13 storeys – low code

Syner-G Taxonomy MRF/C/RC-ASC-HY/IR/IR/RI-AAC/X/X-X/X-X/HR-13/LC

Sample data Buildings: 1 RC frame structures. 12/13 storeys. Low code

Seismic hazard: 1 recorded accelerogram



‚ None

‚ Slight

‚ Moderate

‚ Extensive

‚ Complete

Intensity Measure Type Sd (TLS) [cm]


IMT = Sd (TLS) [cm]

Mean Standard

Deviation

Slight 4.940 3.395


Extensive 29.281 22.484

Complete 85.328 84.706

Figures


Sd(TLS)

80706050403020100

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Uncertainty The compressive strength of concrete and the yield strength of steel are, as a minimum, the

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parameters that are treated as the random variables. Following Galambos et al. (1982), a

normal probability distribution for concrete strength and a lognormal distribution for steel

strength is used.

Comments Based on HAZUS and ATC-40 methodologies with some alternative approach (Chopra and

Goel, 1999). HAZUS gives the fragility function parameters that are appropriate for each type of

building. In order to calibrate the fragility function parameters which are appropriate for

Bucharest building types, the Monte Carlo Simulation Technique can be used. It involves the

selection of the input capacity random variables required for the pushover analyses, the

pushover analyses and the simulation of the structural damage.

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VargasEtAl2010

Reference Y. F. Vargas, L.B. Pujades and A.H. Barbat, “ Probabilistic assessment of the global damage in

reinforced concrete structures”, 14ECEE, Ohrid, 2010.

Region of applicability Spain



considered

Reinforced Concrete Building

Syner-G Taxonomy WS/C/RC/X/R/X-X/X/X-X/X-X/HR-8/X

Sample data Buildings: family housing, regular in plant, with waffle slabs instead of beams. 8 storeys.

Seismic Hazard: Eurocode 8, Type 1 for soil type D is taken as target spectrum. A series of

accelerograms from Spanish database and European database with mean elastic response

spectrum compatible with the target spectrum are considered.



‚ No damage

‚ Slight

‚ Moderate

‚ Severe

‚ Collapse

Intensity Measure Type Sd(TLS) [m]


IMT = Sd(TLS) [m]


Slight 0.096 0.029


Severe 0.164 0.035


Figures

Slight Moderate Severe Collapse

Sd(TLS)

0.60.550.50.450.40.350.30.250.20.150.10.050

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Uncertainty The uncertainty of the mechanical properties of the materials and the uncertainty of the seismic

demand are taken into account.

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Appendix B

B Tutorial

Once the Syner-G tool is installed on the computer, the program is ready to run. The

following window will appear.

The user has three options to start working with the tool:

1. Open an Existing Project: the user can upload an existing project by clicking on the

button highlighted in the screenshot (button number 1). The Syner-G projects have

the *.sgp extension. They contain a group of Fragility Functions sets;

2. Insert Existing Fragility Function: the user can upload existing Fragility Functions sets

by clicking on button number 2. The Syner-G Fragility Functions set has the *.xml

extension;

3. Insert New Fragility Functions: the user can manually upload a new Fragility

Functions set by clicking on button number3 and by following the steps required by a

specific form described later in the document.

3. Insert new FragilityFunctions

2. Insert existing Fragility Functions

1. Open an existing Project Create a New Project:

the user is allowed to

open a new empty

project and then

choose to follow

Option1, Option 2 or

Option 3

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The toolbar is composed of different buttons which are briefly described in the following

table:

This button represents Create a New Project, Open an Existing

Project, Insert an Existing Fragility Function and Insert a New

Fragility Function. These different options that can be used to work

with the tool will be described later in the document

These buttons represent Save the Project, Print Chart and Preview

Chart

These buttons represent the Zoom in and the Zoom out tool

These buttons represent Copy Chart that allows the user to copy

the chart and secondly to paste it into another document, Chart

Option that allows the user to change the chart’s properties

(colours, legend, scale, etc.) and Settings that allows the user to

change the settings of the tool. The latter will be described later.

These buttons will open Notepad or the Calculator

These buttons represent the Help System and Syner-G Website

link that allows the user to go directly to the Syner-G website

(www.vce.at/SYNER-G/)

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The Settings button can be used to change some default settings such as the units, the

Ground Motion Intensity Conversion Equation or the Limit States that a user wants to use to

harmonize the set of Fragility Functions contained in his/her own project.

General Tab: the user can choose the

numerical accuracy represented by the

number of decimal places and the units for

the acceleration, velocity and

displacements. The units will be always

shown in the main window bottom_right.

IMT conversions Tab: the Target Intensity

Measure Type is the Peak Ground

Acceleration and it represents the

Intensity Measure Type of reference.

When a Fragility Function will be

harmonized, its IMT will be converted to

PGA. Then a list of conversion equations

is uploaded in the tool to convert IMTs of

the set of Fragility Functions into the

Target IMT.

Damage scale conversions Tab: the user

can choose the number of limit states to

be the limit states of reference when

he/she wants to harmonize the curves. It

is possible to give your own name to the

limit state.

The Syner-G default button allows the user to set all the choices to the default

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Once an Existing Project or a set of existing Fragility Functions are uploaded in the tool, the

users can visualize or modify data, compare results, harmonize different sets of Fragility

Functions and save their own project.

To visualize a set of Fragility Functions the user can double click on the name of the set of

functions or tick on the corresponding box. The different panels reported in the main window

of the tool are shown and described in the following screenshot.

To select and visualize the curves, the user can also use a drop down menu, select the set

of Fragility Functions and then click on Plot button (red rectangle in the screenshot above).

On the bottom left of the main window, six buttons allow the user to select all the curves, to

filter the curves following his/her criteria, to remove the filter or the selected curves, to enter

the compare module or the harmonize module.

List of the Fragility Functions

uploaded in the tool

Original Data: main characteristics of the

selected set of Fragility Functions

Syner-G

Taxonomy:

Proposed Syner-G

Taxonomy

Plot of the selected

set of Fragility

Functions

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The Filter button allows the user to select the curves of interest. There are different kind of

filters. It is possible to filter the curve by the main parameters or by the Syner-G Taxonomy.

Once the user has selected a set of Fragility Functions he/she can modify, save, export or

remove the data clicking on the following buttons:

1. Show Values: the user is able to visualize the mean and the standard deviation of the

fragility curves, the statistical distribution, the minimum and the maximum of the IMT,

the number and the name of the limit states used. He/she can also modify these data

and decide to apply the changes or to save them;

2. SaveChanges: the user is able to save the changes;

3. Export pdf: the user is able to export the data and all the information that are

visualized in the main window in a *.pdf document;

4. Remove: the user is able to Remove from the project the selected set of Fragility

Functions.

A drop down menu will

show all the categories that

can be filtered and selected

It has to be mentioned that

the possibility to filter by

Syner-G taxonomy is very

useful in the comparison

module. The user can

select the fragility functions

sets belonging to the same

building class and compare

the results The Remove Filter button will remove

all the selected filters

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Show Values

Export pdf

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Instead of using an existing set of Fragility Functions, the user can upload his/her own set of

curves using the ‘Insert new Fragility Functions’ button in the toolbar. A Fragility Function

Creation window, as the one shown in the following screenshots, will appear. The user has

to fill the fields reported in the Four Steps Tabs and click on the Finish button (Step 4 Tab) to

upload the set of curves in the tool.

Step 1 Step 2

Step 3 Step 4

Click on the Finish button to upload

the set of curves in the tool

The user can check his/her fragility function set

plotting the chart before uploading it

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Harmonize module

To harmonize a set of curves the user has to select the set by ticking the corresponding box

and then clicks on the Harmonize button. It is possible to harmonize more than one set of

curves at a time. The Harmonization of the Fragility Curves window will appear. The user

can choose the name of the new harmonized curves, decide the limit state conversion, and

the IMT conversion. Some default conversions are proposed. Then he/she has to click on

the Finish button and the harmonized set of curves will be uploaded at the end of the list of

the set of Fragility Functions shown in the white box. If the user is harmonizing two or more

sets of functions he/she has to click on the Next button until all the curves are harmonized.

Then he/she has to click on the Finish button to import the curves into the tool.

In the menu bar at the top of the window there is the ‘Tool’ drop down menu. The user can

select ‘IMT conversion’ to visualize all the conversion equations that are stored in the tool.

Different conversion equations from PGV, Sd(Ty), Sa(Ty) and macroseismic intensity to

PGA have been uploaded.

Original Function Harmonized Function

Name of the

Original Function

Name of the

Harmonized

Function

Tutorial

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Tutorial

208

Compare Module

To compare two or more different sets of curves, the user has to tick the boxes that

correspond to the chosen set of Fragility Functions and then click on the Compare Button.

By ticking the boxes in the legend of the chart it is possible to add or remove curves from the

plot itself.

List of the Fragility

Function sets that

are compared

A user can decide

to visualize a

different number

of limit states.

He/she can just

tick the boxes

corresponding to

the limit states of

interest.

Tutorial

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Two more possibilities to visualize the comparison beyond the cumulative density functions

are provided in the tool.

The first one can be selected by clicking on the “See Values” on the bottom_right of the

Compare window. In this case, the user can visualize point by point the values of the curves.

He/She can also decide to sort them by fragility functions or by limit states.

The second one can be selected by clicking on the “Bars Chart” on the bottom_right of the

Compare window. In this case, the user can visualize the discrete probability density

function. Moving the bar at the bottom of the figure the user can decide the intensity

measure level for which he/she wants to know the probability.

Intensity measure level for which the probability

is calculated

A user can decide to sort the values of the

curves by fragility function or by limit state

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