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UNIVERSITÀ DEGLI STUDI DI FERRARA Dipartimento di Ingegneria Corso di Laurea Magistrale in Ingegneria Civile

SEISMIC RISK ASSESSMENT AND RESILIENCE ENHANCEMENT AT URBAN SCALE. THE HYSTORICAL CITY CENTRE OF CONCORDIA SULLA SECCHIA (MO) - ITALY.

Laureando: ALBERTO BASAGLIA Relatori: Prof.ssa ALESSANDRA APRILE Prof. RICCARDO DALLA NEGRA Correlatori: Prof. FRANCESCO PILLA Prof. MARCO ZUPPIROLI

Anno Accademico 2014 – 2015


The current research was mostly developed during a study period at the Trinity College Dublin, made possible thanks to the “Erasmus+� program joined by the University of Ferrara.

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Acknowledgments First and foremost I offer my sincere gratitude to Prof. Alessandra Aprile who has supported me throughout my thesis with her patience and knowledge, and also gave me the opportunity to do this memorable experience abroad. I would like to thank also Prof. Francesco Pilla for all the valuable advice and help he gave me during my stay at the Trinity College Dublin. I gratefully acknowledge Prof. Riccardo Dalla Negra and staff members of the LABO.R.A Unife Prof. Marco Zuppiroli and Ph.D. Francesco Guidi for collecting and making available all data necessary for the development of the work, along with their support and suggestions. Last but not least, I thank my parents Rita and Renzo, and above all my grandfather Alfredo for their constant love and unrelenting encouragement, at all times and in all possible ways. I couldn’t have done it without you. I hope I will make you proud.

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Abstract Italy has always been a country at-risk to seismic activities, even though a complete seismic mapping of the entire territory has been achieved only with the approval of the "Nuove Norme Tecniche delle Costruzioni", included in the D.M. 14/01/2008,. Only recently then the assessment of seismic risk in built- up areas is being investigated, especially in nations like Italy, Spain and Portugal, where historical city centres are mainly made of masonry buildings that often present several structural fragilities and are built as aggregates. This kind of study so becomes crucial in the aim of seismic prevention, because it allows to evaluate the buildings' response, identifying in this way the most vulnerable areas of a settlement. Basing on this study, it is possible to plan retrofitting strategies, including strengthening works. This topic however presents many difficulties and requires a complex and interdisciplinary view. Seismic risk is defined indeed as the relationship between hazard, exposure and vulnerability, but it is truly the last one the most relevant, due to the effect it leads in occurrence of an earthquake, and being that can be managed. Then, finding a way to assess the vulnerability in an accurate and rapid way becomes essential, as we are not considering a single building anymore but a whole city. The aims of the current research are: doing a summary of all previous works in this field and proposing a unique method to assess the seismic vulnerability of an urban system that is detailed and effective. Then this methodology will be applied to the Italian city-centre of Concordia sulla Secchia (MO), affected by the Emilia-Romagna earthquake in 2012. The predicted damage scenarios will be compared to the effective post-seismic damages, judging the accuracy of the evaluation. Finally, critical reviews of the proposed method will be performed, highlighting its limits and issues, analysing with particular attention masonry buildings and giving suggestions for future revisions and developments.

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Riassunto L'Italia è da sempre un paese a rischio sismico, anche se una completa classificazione sismica dell’intero Paese è stata realizzata solamente con l'approvazione delle "Nuove Norme Tecniche per le Costruzioni" contenute nel D.M. del 14/01/2008. Solo recentemente quindi la valutazione del rischio sismico in aree costruite è oggetto di studio, specie in nazioni quali l’Italia, la Spagna e il Portogallo, dove i centri storici sono formati principalmente da edifici in muratura che presentano spesso diverse fragilità strutturali e sono costruiti in aggregato. Questo tipo di studio è diventato così cruciale nell’ottica della prevenzione sismica, poiché consente di stimare la risposta degli edifici, identificando in questo modo le aree più vulnerabili di un insediamento. Basandoci su questo studio, è possibile pianificare strategie di “retrofitting”, inclusi interventi locali. Questo argomento tuttavia presenta molteplici difficoltà e richiede una visione complessa ed interdisciplinare. Il rischio sismico infatti è definito come relazione tra pericolosità, esposizione e vulnerabilità, ma è proprio l’ultima ed essere la più importante, per gli effetti cui porta in occasione di un terremoto, ed essendo l’unico elemento che può essere modificato. Trovare un modo quindi d i valutare la vulnerabilità in maniera rapida e accurata diventa essenziale, poiché non si sta più considerando un singolo edificio ma una intera città. Gli obiettivo di questa tesi sono: effettuare una sintesi di tutti le ricerche precedenti in quest’ambito e proporre un unico metodo per valutare la vulnerabilità sismica di un sistema urbano che sia dettagliato ed efficace. Questa metodologia verrà quindi applicata al centro della città italiana di Concordia sulla Secchia (MO), colpita dal terremoto dell’Emilia-Romagna nel 2012. Gli scenari di danno ottenuti saranno confrontati con gli effettivi danni post-sismici, giudicando l’accuratezza della previsione. Infine, si farà una revisione critica del metodo proposto, evidenziandone i limiti e le problematiche, analizzando con particolare attenzione gli edifici in muratura e fornendo suggerimenti per futuri miglioramenti e sviluppi.

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Table of Contents

Table of Contents

LIST OF FIGURES.................................................................................................................V LIST OF TABLES..................................................................................................................IX CHAPTER 1

INTRODUCTION.........................................................................................1

1.1

Aim and objectives........................................................................................................1

1.2

Outline of the thesis.......................................................................................................2

CHAPTER 2

STATE OF ART............................................................................................3

2.1

Aim and objectives........................................................................................................3

2.2

Vulnerability assessment methods...............................................................................8

2.3

2.2.1

Direct or analytical techniques............................................................................9

2.2.2

Indirect or empirical techniques........................................................................11

2.2.3

Hybrid techniques.............................................................................................23

Seismic microzonation................................................................................................26

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Table of Contents

2.4

2.5

Advance-planning tools: politics of vulnerability reduction on urban scale .........28 2.4.1

Minimum urban structure: definition, contents and objectives.........................29

2.4.2

Limit conditions for settlements.......................................................................30

Development and usage of GIS software..................................................................34

CHAPTER 3

PROPOSED METHODOLOGY...............................................................37

3.1

Applied method: GNDT-II and Macroseismic combined approach......................41

3.2

Developments to the applied method........................................................................42 3.2.1

Vulnerability ellipses: a 2D study of the city....................................................42

3.2.2

Correlation between Iv (GNDT-II) and V (EMS-98) for R.C. buildings.........45

3.2.3

Implementation of seismic microzonation results............................................49

3.2.4

Reliability of an urban system: concept and definition.....................................53

CHAPTER 4

CASE STUDY: THE CITY OF CONCORDIA SULLA SECCHIA (MO), ITALY..............................................................................................59

4.1

Short history and geography of the city....................................................................59

4.2

Seismic microzonation of Concordia sulla Secchia (MO), Italy.............................61

4.3

Limit condition of Eme rgency (CLE) for Concordia sulla Secchia (MO), Italy...64

4.4

Detail level of post-seismic survey.............................................................................68

4.5

Vulnerability indexes..................................................................................................73

4.6

II

4.5.1

Masonry buildings.............................................................................................73

4.5.2

R.C. buildings...................................................................................................73

4.5.3

Other structural types........................................................................................75

Matlab program..........................................................................................................76


Table of Contents

CHAPTER 5

DISCUSSION OF RESULTS....................................................................79

5.1

Analysis of results........................................................................................................79

5.2

Visual maps obtained with GIS software..................................................................96

5.3

Comparison between pre dicted and observed damage.........................................110

5.4

Masonry buildings: in-depth analysis.....................................................................113 5.4.1

Effects of aggregates on the vulnerability assessment....................................113

5.4.2

Proposed correction and validation.................................................................115

5.4.3

Cost-benefit analysis of local strengthening...................................................118

CHAPTER 6

CONCLUSIONS.......................................................................................127

6.1

Summary and conclusions..........................................................................................127

6.2

Future developments...................................................................................................129

REFERENCES......................................................................................................................131 ANNEX A

GNDT-II ORIGINAL FORMS................................................................137

ANNEX B

GNDT-II FILLED FORMS FOR CLE BUILDINGS OF CONCORDIA SULLA SECCHIA (MO), ITALY...........................................................143

ANNEX C

GNDT-II FILLED FORMS FOR CLE MASONRY BUILDINGS OF CONCORDIA

SULLA

SECCHIA

(MO),

ITALY

AS

AGGREGATES177 ANNEX D

GNDT-II FILLED FORMS FOR CLE MASONRY BUILDINGS OF CONCORDIA SULLA SECCHIA (MO), ITALY WITH LOCAL STRENGTHENING.................................................................................183

ANNEX E

SEISMIC MICROZONATION MAP OF CONCORDIA SULLA SECCHIA (MO), ITALY.........................................................................197

ANNEX F

MATLAB SCRIPT....................................................................................201 III


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IV


List of Figures

List of Figures Figure 2.1.1 - Seismic classification of Italy progression, from 1909 to 1984 (Conference proceedings, Udine 04/07/2012) ...... ............................................................................ .............5 Figure 2.1.2 - Seismic classification of Italy (March 2015, source: Protezione Civile website) ...... ................................................................................................................................... ...........6 Figure 2.2.1 - Vulnerability methods used at different scales (Vicente et. Al, 2010)...... ..........8 Figure 2.2.2 - Capacity Spectrum Method (Fajfar, 1999) ................................................ ..........9 Figure 2.2.3 - FaMIVE method flowchart (Moghaddam, 2013).................................... ..........10 Figure 2.2.4 - Differentiation of structures into vulnerability classes (EMS-98) ......... ...........11 Figure 2.2.5 - Damage grade classification for masonry buildings (EMS-98) ........ ................12 Figure 2.2.6 - Damage grade classification for R.C. buildings (EMS-98)................ ...............13 Figure 2.2.7 - “Fuzzy pseudo partition” of numerical range 0-100 using 3 “fuzzy sets” (Klir and Yuan, 1995) .............................................................................................. ........................18 Figure 2.2.8 - “Fuzzy pseudo partition” of numerical range 0-100 using 5 “fuzzy sets” (Bernardini et al., 2007) ....................................................................................... ...................18 Figure 2.2.9 - I- µD curves “white” for the 6 vulnerability classes and analogous vulnerability parametric curves ................................................................................................... ..................21 Figure 2.2.10 - Example of building capacity curve and demand spectrum (HAZUS) ............................................................................................................................... ...................25 Figure 2.3.1 - Seismic microzonation map of Emilia Romagna region (updated 2011, source: http://www.geologi.emilia-romagna.it/).......................................... .........................................27 Figure 2.4.1 - Functional view of a settlement.......................................................... ...............28 Figure 2.4.2 - Effects of advance-planning on post-seismic functionality loss ........ ...............29 Figure 2.5.1 - Database and GIS framework......................................................... ...................34 Figure 2.5.2 - ArcGIS Desktop 10.0 workspace ................................................... ...................35 Figure 3.1.1 - Examples of fragility curves for two different vulnerability indexes (Vicente et al., 2011) ........................................................................................................... .......................40 Figure 3.2.1 - Definition of vulnerability ellipse .............................................. .......................42 Figure 3.2.2 - Vulnerability ellipse determination, Step 1 ................................ .......................43 Figure 3.2.3 - GNDT-II form, insight on Parameter 3 ...................................... .......................43 Figure 3.2.4 - Vulnerability ellipse determination, Step 3 ................................ .......................44 Figure 3.2.5 - Vulnerability ellipse determination, Step 4 ................................ .......................45

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List of Figures

Figure 3.2.6 - Vulnerability curves proposed for R.C. buildings..............................................47 Figure 3.2.7 - Proposed correlation for R.C. buildings.............................................................48 Figure 3.2.8 - I-ag curves of three correlations (Guagenti - Petrini, Margottini et al., Murphy O’Brien)....................................................................................................................................51 Figure 3.2.9 - Representation of a series system.......................................................................53 Figure 3.2.10 - Representation of a parallel system..................................................................54 Figure 3.2.11 - Reliability of a urban system for the emergency limit condition (CLE)..........54 Figure 3.2.12 - Reliability of a urban system for the life-saving limit condition (CLV)..........56 Figure 4.1.1 - Map of Concordia sulla Secchia (MO), Italy (source: http://comune.concordia. mo.it/)........................................................................................................................................60 Figure 4.2.1 - Example of soil boring in Concordia sulla Secchia (MO), Italy........................62 Figure 4.2.2 - Example of CPTm in Concordia sulla Secchia (MO), Italy...............................62 Figure 4.3.1 - Limit condition of emergency (CLE) of Concordia sulla Secchia (MO), Italy...........................................................................................................................................65 Figure 4.4.1 - ES (strategic building) form for CLE analysis...................................................69 Figure 4.4.2 - US (structural unit) form for CLE analysis........................................................70 Figure 4.6.1 - Visual representation of CLE buildings of Concordia sulla Secchia (MO), Italy under vulnerability assessment.................................................................................................78 Figure

5.1.1

-

Epicentres

map

of

2012

Emilia

earthquake,

Italy

(source:

http://www.protezionecivile.tn.it/territorio/primop_territorio/pagina49.html).........................80 Figure 5.1.2 - Fragility curves for minimum vulnerability index of a) masonry buildings; b) R.C. buildings of Concordia sulla Secchia (MO) CLE sub-system..........................................89 Figure 5.1.3 - Fragility curves for mean vulnerability index of c) masonry buildings; d) R.C. buildings of Concordia sulla Secchia (MO) CLE sub-system..................................................89 Figure 5.1.4 - Fragility curves for maximum vulnerability index of e) masonry buildings; f) R.C. buildings of Concordia sulla Secchia (MO) CLE sub-system..........................................89 Figure 5.1.5 - Collapse probability and number of collapsed buildings of Concordia sulla Secchia (MO) CLE sub-system.................................................................................................90 Figure 5.1.6 - Unusable probability and number of unusable buildings of Concordia sulla Secchia (MO) CLE sub-system.................................................................................................91 Figure 5.1.7 - Probability and number of dead and severely injured of Concordia s ulla Secchia (MO) CLE sub-system..............................................................................................................93 Figure 5.1.8 - Probability and number of homeless of Concordia sulla Secchia (MO) CLE sub-system.................................................................................................................................93 VI


List of Figures

Figure 5.1.9 - Comparison between collapse probability and the reliability of Concordia sulla Secchia (MO) CLE sub-system.................................................................................................94 Figure 5.2.1 - Intensity map of 20/05/2012 Emilia earthquake................................................98 Figure. 5.2.2 - Building stock vulnerability map of Concordia sulla Secchia (MO), Italy CLE sub-system) ..............................................................................................................................99 Figure. 5.2.3 - Mean damage grade distribution for I (EMS-98) = VII of Concordia sulla Secchia (MO), Italy, CLE sub-system....................................................................................100 Figure. 5.2.4 - Mean damage grade distribution for I (EMS-98) = VIII of Concordia sulla Secchia (MO), Italy, CLE sub-system....................................................................................101 Figure. 5.2.5 - Mapping results of collapse probability evaluation for I (EMS-98) = VII of Concordia sulla Secchia (MO), Italy, CLE sub-system..........................................................102 Figure. 5.2.6 - Mapping results of collapse probability evaluation for I (EMS-98) = VIII of Concordia sulla Secchia (MO), Italy, CLE sub-system..........................................................103 Figure. 5.2.7 - Mapping results of unusable building probability evaluation for I (EMS-98) = VII of Concordia sulla Secchia (MO), Italy, CLE sub-system...............................................104 Figure. 5.2.8 - Mapping results of unusable building probability evaluation for I (EMS-98) = VIII of Concordia sulla Secchia (MO), Italy, CLE sub-system..............................................105 Figure. 5.2.9 - Mapping results of dead and severely injured probability evaluation for I (EMS-98) = VII of Concordia sulla Secchia (MO), Italy, CLE sub-system...........................106 Figure. 5.2.10 - Mapping results of dead and severely injured probability evalua tion for I (EMS-98) = VIII of Concordia sulla Secchia (MO), Italy, CLE sub-system.........................107 Figure. 5.2.11 - Mapping results of homeless probability evaluation for I (EMS-98) = VII of Concordia sulla Secchia (MO), Italy, CLE sub-system..........................................................108 Figure. 5.2.12 - Mapping results of homeless probability evaluation for I (EMS-98) = VIII of Concordia sulla Secchia (MO), Italy, CLE sub-system..........................................................109 Figure 5.4.1 - Aggregate object of study: a) floor plan; b) building no. 1; c) building no. 2; d) building no. 3; e) building no. 4; f) building no. 5..................................................................114 Figure 5.4.2 - FEM model of the masonry aggregate object if study.....................................114 Figure 5.4.3 - “Curb - tie rod” technique: external isometric view........................................120 Figure 5.4.4 - “Curb - tie rod” technique: internal isometric view.........................................121 Figure 5.4.5 - “Curb - tie rod” technique: assembly section...................................................121 Figure 5.4.6 - “Curb - tie rod” technique: holding stake isometric view and details..............122

VII


List of Figures

VIII


List of Tables

List of Tables Table 2.2.1 - Linguistic frequencies of damage for vulnerability classes and macroseismic intensities, according to the EMS-98 scale (Grünthal, 1998)...................................................17 Table 2.2.2 - α-cuts (α=0, α=1) of fuzzy sets correlated to linguistic frequencies, individually or combined...............................................................................................................................19 Table 2.2.3 - Language completion of EMS-98 scale...............................................................20 Table 2.2.4 - Vulnerability (parameter) values for each EMS-98 class....................................21 Table 2.2.5 - GNDT-II form for masonry buildings.................................................................22 Table 2.2.6 - GNDT-II form for R.C. buildings.......................................................................22 Table 2.2.7 - Building structures (model building) according to HAZUS...............................24 Table 2.4.1 - Comparison between limit states/conditions for buildings/settlements..............31 Table 2.4.2 - Performance levels of urban functions in different limit conditions...................32 Table 2.4.3 - Main functions and urban systems considered for the seismic response assessment of the urban system................................................................................................33 Table 3.1.1 - Correlation between the vulnerability indexes and the vulnerability classes defined in terms of the EMS-98 scale for masonry buildings...................................................38 Table 3.2.1 - Parameters for damage/vulnerability index relation (Grimaz et al., 1996).........46 Table 3.2.2 - Analytical steps of the equivalence determination - 1.........................................47 Table 3.2.3 - Analytical steps of the equivalence determination - 2.........................................48 Table 3.2.4 - Proposed correlation between the vulnerability indexes and the vulnerability classes defined in terms of the EMS-98 scale for R.C. buildings.............................................48 Table 3.2.5 - Summary of correlations I - PGA found in literature (in chronological order, ascending).................................................................................................................................50 Table 3.2.6 - Values of parameters

and

for three correlations between

and ............51

Table 3.2.7 - General data of seismic events considered for Margottini correlations (from: ISC Bulletins; NEIS/PDE Bulletins; ING Bulletins; ENEA data)...................................................52 Table 4.2.1 - Seismic zones classification (D.L. 112/1998 – D.P.R. 380/2001)......................61 Table 4.2.2 - Acceleration intervals associated to each seismic zone (O.P.C.M. 3519/06).....61 Table 4.3.1 - Interfering buildings (CLE) belonging to the aggregate between Via Don Minzoni and Via della Pace, in Concordia sulla Secchia (MO), Italy......................................66 Table 4.3.2 - Other interfering buildings (CLE) in Concordia sulla Secchia (MO), Italy........66 Table 4.3.3 - Strategic buildings (CLE) in Concordia sulla Secchia (MO), Italy.....................67

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List of Tables

Table 4.4.1 - Correction factor for vulnerability index of other interfering buildings.............72 Table 4.5.1 - Vulnerability indexes and the vulnerability parameters for CLE sub-system masonry buildings of Concordia sulla Secchia (MO), Italy......................................................73 Table 4.5.2 - Vulnerability indexes and the vulnerability parameters for CLE sub-system R.C. buildings of Concordia sulla Secchia (MO), Italy....................................................................74 Table 4.5.3 - Vulnerability indexes and the vulnerability parameters for CLE sub-system steel or mixed structure buildings of Concordia sulla Secchia (MO), Italy......................................75 Table 5.1.1 - Directions considered for displaying results and angles associated)...................80 Table 5.1.2 - Mean damage grades for intensity level IEMS-98 = 5............................................81 Table 5.1.3 - Mean damage grades for intensity level IEMS-98 = 6............................................82 Table 5.1.4 - Mean damage grades for intensity level IEMS-98 = 7............................................83 Table 5.1.5 - Mean damage grades for intensity level IEMS-98 = 8............................................84 Table 5.1.6 - Mean damage grades for intensity level IEMS-98 = 9............................................85 Table 5.1.7 - Mean damage grades for intensity level IEMS-98 = 10..........................................86 Table 5.1.8 - Mean damage grades for intensity level IEMS-98 = 11..........................................87 Table 5.1.9 - Mean damage grades for intensity level IEMS-98 = 12..........................................88 Table 5.1.10 - Probabilities and numbers of collapsed buildings for increasing intensity levels.........................................................................................................................................90 Table 5.1.11 - Probabilities and numbers of unusable buildings for increasing intensity levels.........................................................................................................................................91 Table 5.1.12 - Probabilities and numbers of dead and severely injured for increasing intensity levels.........................................................................................................................................92 Table 5.1.13 - Probabilities and numbers of homeless for increasing intensity levels.............92 Table 5.1.14 - Reliability of the urban system for CLE, for increasing intensity levels..........94 Table 5.2.1 - List of FID revised for the GIS mapping.............................................................97 Table 5.3.1 - Qualitative to quantitative damage description of CLE forms..........................110 Table 5.3.2 - Comparison between predicted and observed damage grade for CLE sub-system of Concordia sulla Secchia (MO), Italy..................................................................................111 Table 5.4.1 - Additional parameters to the GNDT-II forms by Formisano et al. (2009) for masonry buildings in aggregate..............................................................................................113 Table 5.4.2 - Proposed revision of additional parameters to the GNDT-II forms for masonry buildings in aggregate.............................................................................................................115 Table 5.4.3 - Comparison between original and proposed scores and weights of the additional parameters to the GNDT-II form for masonry buildings in aggregate...................................116 X


List of Tables

Table 5.4.4 - Vulnerability indexes of CLE masonry buildings in Concordia sulla Secchia (MO), with and without the aggregate effect..........................................................................116 Table 5.4.5 - Effects of the additional aggregate parameters to the GNDT-II form or/and variation of the ductility factor in matching the observed damage of masonry buildings......117 Table 5.4.6 - Typical strengthening works in masonry buildings...........................................119 Table 5.4.7 - Cost estimate of tie rods positioning for CLE masonry buildings of Concordia sulla Secchia (MO), Italy........................................................................................................122 Table 5.4.8 - Cost estimate of steel curbs supply for CLE masonry buildings of Concordia sulla Secchia (MO), Italy........................................................................................................123 Table 5.4.9 - Cost estimate of cracks repairing for CLE masonry buildings of Concordia sulla Secchia (MO), Italy.................................................................................................................123 Table 5.4.10 - Effects of strengthening works on the vulnerability indexes of CLE masonry buildings of Concordia sulla Secchia (MO), Italy..................................................................124 Table 5.4.11 - Effects of strengthening works on the mean damage grade of CLE masonry buildings of Concordia sulla Secchia (MO), Italy..................................................................119

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List of Tables

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List of Tables

Chapter 1

INTRODUCTION

1.1

Aim and objectives

The aim of the current research is to define the concept of systems reliability at urban scale, proposing a unique and mostly complete method to assess it. In order to do that, a summary of previous works in this field has been made, introducing then further developments, such as the possibility of taking into account R.C. buildings and a 2D study of the city that considers the directional effect of seismic waves due to the different buildings’ orientation and shape. Furthermore, the Italian region Emilia-Romagna has experienced this kind of event in 2012, and a vast post-earthquake survey was commissioned. For the first time then, it has been possible to compare the predicted damages to the observed ones, testing the accuracy of the method and eventually proposing some corrections. The city of Concordia sulla Secchia (MO) has been chosen as a case study, for its city centre made by an heterogeneous mix of masonry and R.C. buildings, mostly built as aggregates during the years. Finally, the research wants to stimulate the preventive planning of strengthening works evaluating their impact on the vulnerability reduction with a cost/benefit analysis.

1


Chapter 1 - INTRODUCTION

1.2

Outline of the thesis

This dissertation is divided in six chapters. The first one provides an overall introduction to the project, presenting aims and objectives to achieve. The second chapter deals with the “state of art� of vulnerability assessment methods, giving an overview and summarizing current and past literature, but focusing in particular on their level of accuracy and complexity. Indeed it is important to assert that, when dealing with a large number of constructions, to reduce the time of a vulnerability assessment a certain margin of error has to be accepted. Finally, the method used in this research will be described in detail. In chapter three, all proposed developments to the applied method are presented, explaining how they have been formulated and how they can improve the evaluation making it more detailed and complete. The fourth chapter includes the description of the case study, the Italian city of Concordia sulla Secchia (MO), along with the different aspects of buildings in its city centre, the seismology of the area and the Limit Condition of Emergency (CLE) made by the "Protezione Civile", the national body that deals with prediction, prevention and management of exceptional events. Then an automated procedure of reliability assessment on urban scale made with the MATLABŽ software is presented. Chapter five shows the evaluation results obtained, first in a numerical way and then through visual maps produced with the GIS software. It is possible then to make a comparison between the predicted and observed damage, judging the accuracy of the method. A deeper analysis of masonry building is then carried out, proposing a correction and assessing the effects of local strengthening works. Finally, chapter six concludes the thesis with the summary and outcome of the current research and suggestions for future works.

2


List of Tables

Chapter 2

STATE OF ART

2.1

Seimic risk and urban seismic vulnerability: definitions

Seismic risk can be expressed as the result of the mathematical relationship between hazard, vulnerability and exposure: (1) where R is the probability of exceedance of a certain level of loss of an exposed element e, as a consequence of the occurrence of a seismic event of certain intensity i; H is the probability of exceedance of a certain level of seismic activity of intensity i, during a specified recurrence period T; V is the vulnerability, that is the intrinsic predisposition of a certain element e to suffer damage resulting from a seismic event of intensity i, E is the exposure of the elements at risk, reflecting the value of the one exposed. Mostly importantly in the risk definition above is the term probability, which tells that a level of uncertainty is always implied in the nature of all factors involved. 3


Chapter 2 - STATE OF ART

In Italy the first recognition of seismic areas occurred at the beginning of the 20 th century, following the earthquakes of Reggio Calabria and Messina, through a Royal Charter (Regio Decreto), issued on Decembre 28th , 1908. From this year, the seismic mapping of the Italian territory has been updated after every earthquake especially when it struck areas not considered at-risk yet. This has influenced buildings’ features, which present often several structural fragilities as they were built in areas before they were considered at seismic risk, thus without following the earthquake resistance design. Below is presented a summary of all relevant earthquakes happened in Italy after 1908 and the mapping updates they lead:  1927 Classification Major events: - Fucino (AQ), 1915 - Mugello (FI) e Amiata (SI), 1919 - Garfagnana (LU), 1920  1935 Classification Major event: Irpinia (AV) ed Ancona (AN), 1930  1962 Classification Major events: - Cansiglio (BL-TV-PN), 1936 - Puglia settentrionale, 1948 - Carnia (UD), 1959  1975 Classification Major event: Belice (AG-TP-PA), 1968  1984 Classification Major events: - Friuli, 1976 - Irpinia (AV), 1980 Figure 2.1.1 shows the seismic classification progression during the years, with a constant increase of areas listed and a better accuracy (“Seismic risk in Italy: technical aspects and legal implications“, Conference proceedings, Udine 04/07/2012). After the earthquake of Molise in 2003, the whole country has been recognized as at-seismic risk, and the classification itself started using a non-deterministic approach, estimating the probability that a specific area is subjected to a PGA (Peak Ground Acceleration) associated to an earthquake, with a 10% chance of being exceed in 50 years. 4


Chapter 2 – STATE OF ART

Figure 2.1.1 – Seismic classification of Italy progression, from 1909 to 1984

Finally, from July 1st 2012, with the approval of the “Nuove Norme Tecniche delle Costruzioni 2008” (D.M. 14/01/2008) the territory is ideally divided in squares with a 5 km side, and for each building in every of these areas a specified acceleration is appointed, derived from geotechnical analysis and then modified according to the “nominal design life”. Figure 2.1.2 shows the actual seismic classification of Italy (updated at March 2015, picture taken from the “Protezione Civile” website, http://www.protezionecivile.gov.it/resources/cms/ documents/A3_class20150416_r.pdf). Another factor in seismic risk is Exposure (E): it is essentially an insurance parameter, that summarize the nature, quantity and value of goods or activities located on the area that could be directly or indirectly affected by the earthquake. The first purpose of earthquake protection program though remains the safeguard of human lives, so it is fundamental to assess the number of casualties, dead or injured, basing on the number of collapsed or damaged buildings. 5


Chapter 2 - STATE OF ART

Figure 2.1.2 – Seismic classification of Italy (March 2015)

6


Chapter 2 – STATE OF ART

With the definition of the “urban system”, both the building’s function and the effects its collapse would have on the city become important while defining the exposure. Vulnerability (V) then is described as the “buildings’ potential for a certain level of damage, from a temporary interruption in usage to complete destruction, due to a seismic event of a given intensity”. It is used to indirectly measure: on one hand, the reduction in buildings’ structural efficiency, and on the other the buildings’ residual ability to guarantee its expected use and function under normal conditions. Obviously an increase of vulnerability leads to a higher damage level, but their relationship is not linear, and this is due to the inaccuracy and complexity of all factors involved in the seismic response of buildings. That is why finding the best method to evaluate the vulnerability becomes essential, because a likely prediction of damage levels and human losses can lead to an accurate preventive planning of strengthening works. Finally, when moving on an urban scale, the study of vulnerability doesn’t consider the single building anymore, but the overall response of the city, that is not simply the sum of all the buildings’ vulnerabilities.

7


Chapter 2 - STATE OF ART

2.2

Vulnerability assessment methods

When assessing the seismic vulnerability of buildings it is essential to establish the project ’s objectives first, for choosing the most appropriate method to fulfil them. As said before, it is extremely important to understand the difference between detailed approaches, suitable when dealing with single buildings, and the ones less accurate but simpler and quicker, thus more efficient for larger scale analysis. Concerning the former category, the use of an exhaustive method lead to a very reliable evaluation obtained, however, through an in-depth analysis of the structure. Increasing the number of buildings and enlarging the area under assessment though, the amount of time required for this study drastically increase, so the use of less sophisticated and onerous approaches becomes more practical (see Figure 2.2.1). For that reason, vulnerability assessment methods at urban scale should be based on few parameters of an empirical nature, but whose effects is calibrated basing on recorded effects of past earthquakes. According to the most widely-recognised classification system, vulnerability assessment methods can be divided into three main groups, presented briefly in the following section.

Figure 2.2.1 – Vulnerability methods used at different scales

8


Chapter 2 – STATE OF ART

2.2.1

Direct or analytical techniques

Seismic bearing capacity of buildings is determined quantitatively through structural analysis using an appropriate mechanical model, more or less complex, for the whole building or just a single structural element. Clearly a more accurate model on one hand can lead to better results but on the other increases the time needed, thus they’re not generally applied in large scale assessments. It is also noticeable that, while for R.C. or steel buildings numerical simulations can consider nonlinear and/or dynamic behaviors, as the failure involves the ultimate resistance, for masonry buildings instead, especially in historical city centres, failures are mostly due to the loss of elements’ stability, that start to behave individually under horizontal loads. Examples of former methods are ATC-40 (1996), Fema 273 (1996) and the Capacity Spectrum Method (Fajifar, 1999, see Figure 2.2.2), while in the second group we find Vulnus (Bernardini et al., 1989-1990), C-sisma (Valluzzi et al., 2004) and the FaMIVE – Failure Mechanism Identification and Vulnerability Evaluation (D’Ayala & Speranza, 2002-20032004, see Figure 2.2.3).

Figure 2.2.2 - Capacity S pectrum Method

9


Chapter 2 - STATE OF ART

Figure 2.2.3 - FaMIVE method flowchart

10


Chapter 2 – STATE OF ART

2.2.2

Indirect or empirical techniques

This type of approach is the most widely used on large scale assessments. While mechanical models determine the vulnerability of buildings with an in-depth analysis of the structural behavior, empirical models attribute the vulnerability by dividing constructions in classes, or through typological indicators. An example of the first category is the Damage Probability Matrix, DPM, method (Bernardini, Giovinazzi, Lagomarsino, & Pardi, 2007), while in the latter we find the method developed by the “Gruppo Nazionale di Difesa dei Terremoti”, GNDT, (Benedetti e Petrini, 1984) that is applied also nowadays. With the issue of the European Macroseismic Scale (EMS-98, Grünthal) as a review and update of the former Medvedev-Sponheur-Karnink Scale (MSK-64) the main structural typologies have been divided into 6 vulnerability classes, from A to F (most vulnerable least vulnerable, see Figure 2.2.4).

Figure 2.2.4 – Differentiation of structures into vulnerability classes (EMS -98)

11


Chapter 2 - STATE OF ART

As shown in the figure above, the association with a class is not uniquely determined but a range is presented, with the more/less likely probabilities described by different symbols. It has been defined then that under a seismic event a building can undergo up to six different damage grades, from 0 (no damage) to 5 (collapse). As the way a building deforms under earthquake loading depends on its structural type, all damage grades have been presented, both graphically and with a short description, for masonry and R.C. buildings (see Figure 2.2.5 and 2.2.6).

Figure 2.2.5 – Damage grade classification for masonry buildings (EMS -98)

12


Chapter 2 – STATE OF ART

Figure 2.2.6 – Damage grade classification for R.C. buildings (EMS -98)

The intensity of an earthquake is quantified through 12 degrees, arranged by describing: a) Effects on humans b) Effects on objects and on nature c) Damage to buildings

13


Chapter 2 - STATE OF ART

It is remarked that the single intensity degrees can include the effects of shaking of the respective lower intensity degree(s) also, when these effects are not mentioned explicitly. I. Not felt a) Not felt, even under the most favourable circumstances. b) No effect. c) No damage. II. Scarcely felt a) The tremor is felt only at isolated instances (<1%) of individuals at rest and in a specially receptive position indoors. b) No effect. c) No damage. III. Weak a) The earthquake is felt indoors by a few. People at rest feel a swaying or light trembling. b) Hanging objects swing slightly. c) No damage. IV. Largely observed a) The earthquake is felt indoors by many and felt outdoors only by very few. A few people are awakened. The level of vibration is not frightening. The vibration is moderate. Observers feel a slight trembling or swaying of the building, room or bed, chair etc. b) China, glasses, windows and doors rattle. Hanging objects swing. Light furniture shakes visibly in a few cases. Woodwork creaks in a few cases. c) No damage. V. Strong a) The earthquake is felt indoors by most, outdoors by few. A few people are frightened and run outdoors. Many sleeping people awake. Observers feel a strong shaking or rocking of the whole building, room or furniture. b) Hanging objects swing considerably. China and glasses clatter together. Small, top- heavy and/or precariously supported objects may be shifted or fall down. Doors and windows

14


Chapter 2 â&#x20AC;&#x201C; STATE OF ART

swing open or shut. In a few cases window panes break. Liquids oscillate and may spill from well- filled containers. Animals indoors may become uneasy. c) Damage of grade 1 to a few buildings of vulnerability class A and B. VI. Slightly damaging a) Felt by most indoors and by many outdoors. A few persons lose their balance. Many people are frightened and run outdoors. b) Small objects of ordinary stability may fall and furniture may be shifted. In few instances dishes and glassware may break. Farm animals (even outdoors) may be frightened. c) Damage of grade 1 is sustained by many buildings of vulnerability class A and B; a few of class A and B suffer damage of grade 2; a few of class C suffer damage of grade 1. VII. Damaging a) Most people are frightened and try to run outdoors. Many find it difficult to stand, especially on upper floors. b) Furniture is shifted and top- heavy furniture may be overturned. Objects fall from shelves in large numbers. Water splashes from containers, tanks and pools. c) Many buildings of vulnerability class A suffer damage of grade 3; a few of grade 4. Many buildings of vulnerability class B suffer damage of grade 2; a few of grade 3. A few buildings of vulnerability class C sustain damage of grade 2. A few buildings of vulnerability class D sustain damage of grade 1. VIII. Heavily damaging a) Many people find it difficult to stand, even outdoors. b) Furniture may be overturned. Objects like TV sets, typewriters etc. fall to the ground. Tombstones may occasionally be displaced, twisted or o verturned. Waves may be seen on very soft ground. c) Many buildings of vulnerability class A suffer damage of grade 4; a few of grade 5. Many buildings of vulnerability class B suffer damage of grade 3; a few of grade 4. Many buildings of vulnerability class C suffer damage of grade 2; a few of grade 3. A few buildings of vulnerability class D sustain damage of grade 2.

15


Chapter 2 - STATE OF ART

IX. Destructive a) General panic. People may be forcibly thrown to the ground. b) Many monuments and columns fall or are twisted. Waves are seen on soft ground. c) Many buildings of vulnerability class A sustain damage of grade 5. Many buildings of vulnerability class B suffer damage of grade 4; a few of grade 5. Many buildings of vulnerability class C suffer damage of grade 3; a few of grade 4. Many buildings of vulnerability class D suffer damage of grade 2; a few of grade 3. A few buildings of vulnerability class E sustain damage of grade 2. X. Very destructive c) Most buildings of vulnerability class A sustain damage of grade 5. Many buildings of vulnerability class B sustain damage of grade 5. Many buildings of vulnerability class C suffer damage of grade 4; a few of grade 5. Many buildings of vulnerability class D suffer damage of grade 3; a few of grade 4. Many buildings of vulnerability class E suffer damage of grade 2; a few of grade 3. A few buildings of vulnerability class F sustain damage of grade 2. XI. Devastating c) Most buildings of vulnerability class B sustain damage of grade 5. Most buildings of vulnerability class C suffer damage of grade 4; many of grade 5. Many buildings of vulnerability class D suffer damage of grade 4; a few of grade 5. Many buildings of vulnerability class E suffer damage of grade 3; a few of grade 4. Many buildings of vulnerability class F suffer damage of grade 2; a few of grade 3. XII. Completely devastating c) All buildings of vulnerability class A, B and practically a ll of vulnerability class C are destroyed. Most buildings of vulnerability class D, E and F are destroyed. The earthquake effects have reached the maximum conceivable effects. Reading the intensities description it is recognizable that the EMS-98 main limits are the vagueness of adjectives (Few, Many, Most) and the lack of information (for each class and intensity, the frequency of two damage grades at most is portrayed), as shown in Table 2.2.1 (Bernardini et al., 2007). That prevents the possibility to exactly correlate DPMs (Damage Probability Matrices) to the scale. 16


Chapter 2 – STATE OF ART

Table 2.2.1 – Linguistic frequencies of damage for vulnerability classes and macroseismic intensities according to the EMS -98 scale (Grünthal, 1998). Dk (k=0÷5) is the damage grade.

Researchers have fill these gaps in two steps: at first with a linguistic integration of the terms used by the EMS-98, supplying also the missing frequencies (see Table 2.2.1), and then associating them to the most appropriate value through a numerical interpretation. Each of the three key adjectives of the scale (Few, Many, Most) has been initially related to a “fuzzy set ” (varying in a range, for a detailed explanation of the fuzzy logic see Zadeh, 1965) using the “fuzzy pseudo-partition” method (Klir & Yuan, 1995), as shown in figure 2.2.7. Needless to say that for each percentage the sum of the “membership” values (vertical axis) has be 1 (in analogy with the sum of all possible events’ probabilities). Note: “membership” values mean “degrees of truth”, with 0 for absolute falsity and 1 for absolute truth. Later the sets “Nearly All” and “Nearly None” have been added : in this way extreme values 0 and 100 are no longer assigned to adjectives “Few” and “Most” (Bernardini et al. 2007, see Figure 2.2.8).

17


Chapter 2 - STATE OF ART

“None” and “All” are then included as “crisp” sets (constant value, opposite of fuzzy) respectively as 0 and 1 with “membership” 1 (they don’t present numerical variation, i.e. they are fixed).

Figure 2.2.7 – “Fuzzy pseudo partition” of numerical range 0-100 using 3 “fuzzy sets” (Klir and Yuan, 1995)

Figure 2.2.8 – “Fuzzy pseudo partition” of numerical range 0-100 using 5 “fuzzy sets” (Bernardini et al., 2007)

The linguistic frequencies of all sets are stated in Table 2.2.2, associated respectively to the limit values (upper bound, u, and lower bound, 1) of their “α-cuts” (α=0, α=1), while expected probability values are listed in the “white” column. Note: having fixed a degree of membership

, an “α-cut ” is a crisp set of

membership grade is greater or equal to ,

18

.

values whose


Chapter 2 – STATE OF ART

The term “white” refers to independent samples that have the same probability distribution, i.e. the most likely.

Table 2.2.2 – α-cuts (α=0, α=1) of fuzzy sets correlated to linguistic frequencies, individually or combined

Finally it was possible to complete every DPM for the EMS-98 scale, with damage frequencies for each intensity and vulnerability class (see Table 2.2.3). In particular, to easily spot them: - original frequencies proposed by the EMS-98 scale (see Table 2.2.1) are in bold type; - proposed frequencies are in italic type; - in bold type with a grey background are then highlighted the changes to the original frequency values.

19


Chapter 2 - STATE OF ART CLASS A

CLASS D

Dk / I

0

1

2

3

4

5

Dk / I

0

1

2

3

4

5

V

All-Few

Few

None

None

None

None

V

All

None

None

None

None

None

VI

Many + 7/3 Few

Many

Few

None

None

None

VI

All

None

None

None

None

None

VII

1/3 Few

2 Few

Many

Many

Few

None

VII

All-Few

Few

None

None

None

None

VIII

None

1/3 Few

2 Few

Many

Many

Few

VIII

Many + 7/3 Few

Many

Few

None

None

None

IX

None

None

1/3 Few

3 Few

Many

Many

IX

7/3 Few

Many

Many

Few

None

None

X

None

None

None

5/6 Few

2 Few

Most

X

1/3 Few

2 Few

Many

Many

Few

None

XI

None

None

None

None

5/6 Few Most + 2 Few

XI

None

1/3 Few

2 Few

Many

Many

Few

XII

None

None

None

None

XII

None

None

2 Few

Most

Dk / I

0

1

2

3

4

5

None

All

CLASS B

1/3 Few 1/2 Few

CLASS E

Dk / I

0

1

2

3

4

5

V

All-Few

Few

None

None

None

None

V

All

None

None

None

None

None

VI

Many + 7/3 Few

Many

Few

None

None

None

VI

All

None

None

None

None

None

VII

7/3 Few

Many

Many

Few

None

None

VII

All

None

None

None

None

None

VIII

1/3 Few

2 Few

Many

Many

Few

None

VIII

All-Few

Few

None

None

None

None

IX

None

1/3 Few

2 Few

Many

Many

Few

IX

Many + 7/3 Few

Many

Few

None

None

None

X

None

None

1/3 Few

2 Few

Many + Few

Many

X

1/3 Few

2 Few

Many

Few

None

None

XI

None

None

None

Nearly Few

8/3 Few

Most

XI

1/3 Few

2 Few

Many

Many

Few

None

XII

None

None

None

None

None

All

XII

None

Nearly Few

2/3 Few

Few

2 Few

Most Few

Dk / I

0

1

2

3

4

5

Dk / I

0

1

2

3

4

5

V

All

None

None

None

None

None

V

All

None

None

None

None

None

VI VII

All-Few Many + 7/3 Few

Few Many

None Few

None None

None None

None None

VI VII

All All

None None

None None

None None

None None

None None

VIII

7/3 Few

Many

Many

Few

None

None

VIII

All

None

None

None

None

None

Many 2 Few

Many Many

Few Many

None Few

IX X

All-Few Many + 7/3 Few

Few Many

None Few

None None

None None

None None

4/3 Few Many + 2 Few

Many

XI

7/3 Few

Many

Many

Few

None

None

1/3 Few

Nearly All

XII

None

1/3 Few

Few

Few

Many

Many + Few

CLASS C

IX X

CLASS F

1/3 Few 2 Few None 1/3 Few

XI

None

None

None

XII

None

None

None

None

Table 2.2.3 – Language completion of EMS -98 scale

Trying to make a step forward and pursuing a more analytical approach, DPMs have been described then using a unique parameter, called “Vulnerability”, V

, independent of

intensity and determined by a fuzzy set related to each vulnerability class (see Giovinazzi and 20


Chapter 2 – STATE OF ART

Lagomarsino 2001). In this way the six vulnerability classes proposed by the EMS-98 scale are now defined by a numerical value, as shown in Table 2.2.4, and with a function it is possible to assess the mean damage grade for a fixed intensity value, I. VA

VB

VC

VD

VE

VF

0.88

0.72

0.56

0.40

0.24

0.08

Table 2.2.4 – Vulnerability (parameter) values for each EMS -98 class

(2)

(3)

is a “ductility factor”, assumed equal to 3. Corrective function

has been introduced to better fit the mean damage grade trends

for lower intensity values (I=V and I=VI) that otherwise will perfectly match the curves obtained from the DPMs of the EMS-98 scale, as shown in Figure 2.2.9.

Figure 2.2.9 – I-µD curves “white” for the 6 vulnerability classes and analogous vulnerability parametric curves

21


Chapter 2 - STATE OF ART

Another indirect method is the one proposed by the “Gruppo Nazionale di Difesa dei Terremoti” in 1994, that can be considered as the upgrade of the one presented by Benedetti and Petrini in 1984. They both involve the determination of a “Vulnerability Index”,

through the

filling of a form (see Annex A). The form is made of 11 sections, corresponding to as many structural or non-structural elements that play a significant role in the seismic response of buildings. As they don’t have the same impact, a “weight ” is defined, varying from 0.25 to 1.5. Parameters are then sub-divided in 4 classes (3 for R.C. buildings) of increasing vulnerability (A-D or A-C for R.C. buildings) and to each of them a score is assigned (see Table 2.2.5 and 2.2.6). #

PARAMETERS

CLASSES Cv,i

WEIGHT

A

B

C

D

pi

1

Type and organization of resisting system

0

5

20

45

1.00

2

Quality of resisting system

0

5

25

45

0.25

3

Conventional strength

0

5

25

45

1.50

4

Building position and foundations

0

5

15

45

0.75

5

Horizontal diaphragms

0

5

25

45

variable

6

Plan configuration

0

5

25

45

0.50

7

In height configuration

0

5

25

45

variable

8

Maximum distance between walls

0

5

25

45

0.25

9

Roof

0

15

25

45

variable

10

Non structural elements

0

0

25

45

0.25

11

General maintenance conditions

0

5

25

45

1.00

Table 2.2.5 – GNDT-II form for masonry buildings

#

PARAMETERS

CLASSES Cv,i A

B

C

pi

1

Type and organization of resisting system

0

1

2

4

2

Quality of resisting system

0

1

2

1

3

Conventional strength

-1

0

1

1

4

Building position and foundations

0

1

2

1

5

Horizontal diaphragms

0

1

2

1

6

Plan configuration

0

1

2

1

7

In height configuration

0

1

3

2

8

Connections and critical elements

0

1

2

1

9

Low ductility elements

0

1

2

1

10

Non structural elements

0

1

2

1

11

General maintenance conditions

0

1

3

2

Table 2.2.6 – GNDT-II form for R.C. buildings

22

WEIGHT


Chapter 2 â&#x20AC;&#x201C; STATE OF ART

The index is obtained as a weighted sum:

(4)

(5)

It is extremely important to assert that the definition of all parameters, weights and scores rely on statistical analyses of post-earthquake surveys on damaged buildings, so their accuracy is directly related to the size of the database available. In particular, the development of the method rely on data gathered after the seismic events of Friuli (1976) and Abruzzo (1984). As they struck historical city centres that consist mainly of masonry buildings, there is a lack of information (and accuracy) regarding R.C. constructions. For a correct assessment is also essential the preventive planning of a detailed inspection of buildings, as GNDT-II (second review) forms require specific informations.

2.2.3

Hybrid techniques

Hybrid models are an intermediate method between the mechanical and the empirical one and they have been increasingly used in USA and Europe during the last years. The HAZUSHazard approach (HAZUS 1999) in particular, developed by the FEMA (Federal Emergency Management Agency), is now considered as the standard procedure in seismic risk analysis in the United States. The vulnerability assessment is made in two steps: at first buildings are associated to one of the 36 structural model types, as shown in Table 2.2.7, according to the classification made by FEMA 178 (1992) which distinguish them by: - building typology - design type - total height

23


Chapter 2 - STATE OF ART

Table 2.2.7 â&#x20AC;&#x201C; Building structures (model building) according to HAZUS

A force-displacement curve is then assigned for each class, determined with an incremental analysis to collapse, that simulates the non- linear behaviour of the specific building type. Capacity curve is finally related with the demand spectrum in the ADRS (Acceleration Displacement Response Spectrum, see Figure 2.2.10) spectral field.

24


Chapter 2 – STATE OF ART

Figure 2.2.10 – Example of building capacity curve and demand s pectrum (HAZUS )

25


Chapter 2 - STATE OF ART

2.3

Seismic microzonation

After an earthquake, while observing damages on constructions and infrastructures it often happens to notice substantial differences in various built- up areas, even if they are not distant one from the other. In other occasions also, remarkable collapses and severe damages occurred in areas very far from the epicentre. A recent example is the L'Aquila earthquake of 6 April 2009, when these events happened both in the municipal territory of L'Aquila and in some distant municipalities, such as S. Pio delle Camere, the fraction of Castelnuovo (about 30 km SE of the epicentre). The quality of buildings definitely has a major influence, but these events are especially linked to local geologic and ground conditions, that can affect the earthquake propagation, as well as the soil instability. A “large-scale” seismic zonation (1:1.000.000) therefore is no more adequate for a detailed hazard assessment, and a microzonation study is needed (1.5000 or even 1:1000). In this way, it is possible indeed to pick out and characterize: - stable areas, where the seismic motion isn’t modified, compared to the one expected on rocks in ideal conditions; - stable with amplification areas, where the seismic motion is modified (increased or sometimes reduced) due to the geological/geotechnical and morphological peculiarities o f the soil; - unstable areas, where events of permanent strain can occur during an earthquake, such as landslides, surface fractures, subsidence and soil liquefaction. The seismic microzonation (SM) wants to improve the knowledge of effects that can alter the seismic motion while reaching the surface, and their spatial distribution. Through this study, it gives back useful data not only for future urban developments but also for the current buildings’ design and post-earthquake emergency planning and repair works. Three “in-depth level” of analysis are defined, of increasing complexity: - Level 1, it is a preparatory level for the actual Seismic Microzonation studies, as it simply consists of a collection of pre-existing data, elaborated to divide the territory in “microzones”, i.e. areas similar on a quality level; - Level 2, it introduces the quantitative element associated to every homogenous area, using also further and targeted surveys whereas needed, and defines a proper SM map; - Level 3, it gives back an SM map with also insights on themes or particular areas.

26


Chapter 2 – STATE OF ART

An example of seismic microzonation map is shown in Figure 2.3.1.

Figure 2.3.1 – Sesmic microzonation map of Emilia Romagna region (source: http://www.geologi.emilia-romagna.it/)

Dynamic characteristics of terrain such as predominant period, amplification factor, shear wave velocity and standard penetration test values can be used for seismic microzonation purpose, even if the last two are generally expensive to measure and not feasible to be carried out at large number of sites. “Seismic noise” data (also called “microtremor”) have also become a popular method for analyzing soil strata and are extensively used nowadays in these studies, as they are easy to perform, competitive and can be applied as well to areas subject to low seismicity.

27


Chapter 2 - STATE OF ART

2.4

Advance-planning tools: politics of vulnerability reduction on urban scale

A definition of vulnerability on urban scale is the “tendency of a settlement considered as a whole to undergo physical damage and loss of organization and functionality during an earthquake” (Fazzio, Olivieri, Parotto & Pizzo, 2010). It means that it is not possible to simply consider the overall vulnerability as the sum of all buildings’ vulnerabilities, as we have also to take into account the mutual relations between all elements of the city (see Figure 2.4.1).

Figure 2.4.1 – Functional view of a settlement

While studying the behavior of a city a mechanical model can be applied where the structural parameters of ductility, resistance and stiffness are replaced by different levels of urban standards. In this view undergoing a damage in considered as a loss of performance level. The aim of advance-planning then becomes to limit as much as possible this kind of loss, so the system can return to its normal standard in the shortest period of time, as shown in Figure 2.4.2. If

is the exact moment a seismic event hits the city and

level, the performance loss

is its original standard

without advance-planning is significantly bigger than

the one undergone but having applied before these urban politics. It is also acknowledged also the existence of a threshold, or a minimum performance level below which it becomes impossible for the settlement to recover and, in analogy with the collapse of a structure, the city experiences abandonment. 28


Chapter 2 – STATE OF ART

Figure 2.4.2 – Effects of advance-planning on post-seismic functionality loss

2.4.1

Minimum urban structure: definition, contents and objectives

The ideal aim of advance-planning politics would be not to have any performance loss after an earthquake (

, see Figure 2.4.2). Especially in historical city centre, or in

areas only recently listed as at seismic risk (see §2.1) however, this would be extremely expensive and required also a very long period to accomplish all strengthening works needed. If on one side then a certain amount of damage has to be admitted, defined as acceptable risk level, on the other it becomes really important to assess which is the maximum performance loss a city can experience without being abandoned. In other words, considering the settlement as a mechanical system, the essential elements’ configuration has to be found. The minimum urban structure (Fabietti, 1999, 2002) is defined as the combination of: - routes (from and to the city, roads, waterways or railways) - open spaces (parks, parking spaces, squares) - urban functions (trade, education, workplaces, ecc.) - strategic buildings (hospitals, fire brigades, city hall, ecc.) that allows the city not only to deal with the first emergency phase immediately after the earthquake, but guarantees also the maintenance and recover of all ordinary urban activities, social-economic and connective that are necessary, in the second phase, to prevent the city from being abandoned. The adjective “minimum” highlights the importance of carefully choosing only the elements whose collapse or even interruption of use would compromise the behavior of the entire system. In this way buildings’ function and their mutual relationships become more important than the constructions’ value or the number of occupants. 29


Chapter 2 - STATE OF ART

It is important to remark that the minimum urban structure is defined using an urban planning approach to the city, so its elements are not only those included in Civil Protection Plans, as they just take into account the emergency phase, but are included also those essential for the settlement to fully recover after the seismic event. Finally, vulnerability assessment studies on large scale are closely linked to the concept of minimum urban structure: indeed, while the first one tries to determine “what will resist after an earthquake?” the latter answers the question “what has to resist in any case?”, i.e. determining where strengthening works have to focus.

2.4.2

Limit conditions for settlements

In Italy with the approval of the “Nuove Norme Tecniche per le Costruzioni 2008” a performance-based approach for buildings’ design has been introduced, with the definition of four “limit states”: - operativeness (SLO); - damage (SLD); - life-saving (SLV); - collapse (SLC). They can be described as thresholds or physical and functional damaging levels, expressed both qualitatively and quantitatively. Four performance levels of buildings are determined, of increasing vulnerability, that point out the severity of damaging undergone after an earthquake, and the eventual amount of time needed to restore the full functionality or allow the habitability. In particular, they are: - fully operative; - operative; - life-saving; - near collapse. Passing on a urban scale, four limit conditions can be described likewise for a settlement (see Table 2.4.1), where damaging levels of a building are replaced by performance loss levels of the urban system.

30


Chapter 2 – STATE OF ART

Limit states for buildings

Limit states for settlements

(NTC 2008, § 3.2.1)

(Olivieri et al., 2013)

SLO

CLO

Limit state of operativeness

Limit condition of settlement operativeness

After the earthquake, the construction as a whole, including structural and non structural elements, as well as all the facilities consistent for its function, does not have to undergo any damage or significant interruption of use.

After the earthquake, the urban settlement as a whole does not undergo any damage or significant interruption of use. In particular are guaranteed the pre-seismic persistence and efficiency of public and private functions, connection routes and technological networks, and the preservation of residential activity.

SLD

CLD

Limit state of damage

Limit condition of settlement damage

After the earthquake, the construction as a whole, including structural and non structural elements, as well as all the facilities consistent for its function, suffers damages not leading though to put occupants at-risk and not significantly compromising the building’s resistance and stiffness towards vertical and horizontal loads, keeping it immediately usable even if with a partial interruption of use in some parts of the facilities.

After the earthquake the urban settlement as a whole undergoes physical and functional damages that will not lead to a significant compromise the continued use of strategic urban functions, ordinary activities, included residential ones, connections to and from the urban centre and the territorial context, although with a partial interruption of use (temporally or spatially, on limited extensions), or rather a lowering of performance levels.

SLV

CLV

Limit state of life-saving

Limit condition of settlement life-saving

After the earthquake, the construction undergoes breakages or collapses of non structural and system elements or significant damages to structural parts to which is linked a serious loss of stiffness towards horizontal loads; the building keeps on the other hand some of its resistance and stiffness towards vertical loads and a safety factor against seismic collapse

After the earthquake the urban settlement as a whole undergoes physical and functional damages that lead to the interruption of use of some of existing urban functions in the all area or most of it. The urban settlement keeps its functionality of all strategic function for the emergency response and the post-seismic recover whether inside or outside of it, directly related and dependent, and their connection and accessibility within the territorial context. It is guaranteed the possibility of keeping and resuming the pre-existent residential function according to spatially and temporally extensions consistent with the preservation and recover of the settlement essential features (determined regarding the specific aspects of every city) even after a limited or consistent interruption of use.

SLC

CLC

Limit state of collapse

Limit condition of settlement collapse

After the earthquake, the construction undergoes severe breakages and collapses of non structural and system elements and very serious damages to structural parts; the building however keeps a safety factor towards vertical loads and a scarce one also against collapse due to horizontal loads.

After the earthquake the urban settlement as a whole undergoes physical and functional damages that lead to the interruption of use of many existing urban functions, including residential one. The urban centre however keeps functionality of most strategic function for the emergency response and the overall system of those needed for the recover, located internally or externally directly related and dependent, and their connection and accessibility within the territorial context

Table 2.4.1 – Comparison between limit states/conditions for buildings/settlements

31


Chapter 2 - STATE OF ART

In addition to those, the Emergency Limit Condition (CLE) is also defined: after the earthquake, the settlement considered as a whole undergoes physical and functional damages that lead to the interruption of use of nearly all urban functions, including residential one. The urban centre keeps ONLY functionality of those infrastructures (buildings and connection routes) needed during the emergency phase. It can be considered as the ultimate bearing capacity for a settlement, and for this reason it can’t be acknowledged in the city-planning category, as it doesn’t take into account the recovery of the city. Specifically, the idea of the minimum urban structure described before (see §2.4.1) and the CLE are linked but not equivalent. Limit condition for settlement

Strategic functions for emergency *

Limit condition of maintenance operativity for settlement (CLO)

Strategic urban functions for the recover ** maintenance

Main and ordinary urban function **

Residence

maintenance

maintenance

(accepted local losses not significant on urban level)

(accepted local losses not significant on urban level)

Limit condition of damage for settlement (CLD) Limit condition of lifesaving for settlement (CLV) Limit condition of collapse for settlement (CLC)

maintenance

maintenance

temporary or marginal limitation

temporary limitation

maintenance

maintenance

temporary or marginal limitation

partial limitation

maintenance

temporary or localized limitation

partial limitation

relevant interruption

Limit condition of emergency (CLE)

maintenance

relevant interruption

relevant and averageterm interruption

long-term interruption

(most part)

technology networks can be considered within different functions depending on type and role cultural heritage (except single elements that could belong to different systems) if considered as a whole, could be included among strategic urban functions or main urban functions, depending on the features of the settlement

* **

Table 2.4.2 – Performance levels of urban functions in different limit conditions

Examples of buildings belonging to categories listed in Table 2.4.2 are presented below. It is important to remark that, as every city has peculiar aspects, the final decision on urban systems and functions considered essential for the emergency phase and the estimated time necessary for the recovery of aforementioned aspects, for every limit state conditions, is different for every settlement.

32


Chapter 2 â&#x20AC;&#x201C; STATE OF ART Function Strategic functions for emergency phase

Strategic functions for the recover

Main and ordinary urban functions Residence

Elements and urban systems included Strategic buildings (civil protection operations centres, health facilities, law enforcement organisations,fire brigades) Emergency areas (gathering areas, assembly areas) Accessibility and connection to strategic elements infrastructures Essential productive activities (industrial, crafts, higher services, cultural, receptive) different according to the settlement's features Main services (schools, primary administrative services) Cultural heritage and main urban places Productive activities, commercial, of service widespread) Urban textures and other residential areas (as widespread urbanisation areas with residential function)

Table 2.4.3 â&#x20AC;&#x201C; Main functions and urban systems considered for the seismic response assessment of the urban system

33


Chapter 2 - STATE OF ART

2.5

Development and usage of the GIS software

Visual representation of vulnerability assessment results is an extremely useful method of presenting a global overview of potential effects of an earthquake. In this way, it is easier to identify most affected areas and help both development of rescue plans and advance-planning works to mitigate the risk. This leads to the need for a multi-purpose tool connected to a relational database and within a Geographic Information System (GIS) environment, which is capable to gather, store, elaborate, analyze, handle and represent geographical data (see Figure 2.5.1).

Figure 2.5.1 â&#x20AC;&#x201C; Database and GIS framework

The GIS application software adopted in this study is ArcGIS Desktop 10.0 - ESRI 2010 (see Figure 2.5.2). In this environment, graphical units (polygons) were mapped as buildings registered from post-seismic surveys and associated with several features and attributes allowing their visualisation, selection and multiple searches. Various modules were developed via numerical algorithms for different tasks including, among the others: visualisation of general information and results by zones, vulnerability assessment, damage and loss estimation for different earthquake intensities and gathering buildingsâ&#x20AC;&#x2122; parameters and features used to estimate vulnerability.

34


Chapter 2 â&#x20AC;&#x201C; STATE OF ART

Figure 2.5.2 â&#x20AC;&#x201C; ArcGIS Desktop 10.0 workspace

Another important aspect of the database information associated within the GIS is that it periodically updates. For this reason it can be an extremely valuable tool in the management of large built-up areas, allowing data storage and easy accessibility as well as spatial analysis enabling the visualisation of data and results for different earthquake scenarios.

35


Chapter 2 - STATE OF ART

36


Chapter 3 - PROPOS ED D37 EVELOPMENTS TO THE APPLIED METHOD

Chapter 3

PROPOSED METHODOLOGY

3.1

Applied method: GNDT-II and Macroseismic combined approach

In the current research the applied method is an empirical or indirect technique and can be considered as the combination of GNDT-II and Macroseismic approaches. It has already been used to assess the vulnerability of Portuguese cities Coimbra and Seixal, (see Vicente et al., 2011 and Ferreira, Vicente et al., 2013). As said in §2.2, after a buildingâ&#x20AC;&#x2122;s inspection, that should be carried out with the highest possible level of detail regarding both geometrical and structural aspects, Vulnerability Index, , is determined using the given forms (see Annex A). Then, as researchers have defined numerical values of Vulnerability ( ) for each EMS-98 class (see Table 2.2.4), it is possible to compare vulnerability curves ( with both methods. With respect to a central mean damage value (

) obtained ) then, the

equivalence presented in Table 2.2.8 is achieved, which can finally lead to the analytical correlation below.

37


Chapter 3 - PROPOS ED DEV ELOPMENTS TO THE APPLIED MET HOD

Macroseismic method

Class A (V = 0.88)

Class B (V = 0.72)

Class A (V = 0.56)

GNDT-II level

IV = 45

IV = 20

IV = -5

Table 3.1.1 – Correlation between the vulnerability indexes and the vulnerability classes defined in terms of the EMS -98 scale for masonry buildings

(6) Note: the correlation presented is valid ONLY for masonry buildings. In §3.2.2 this limit will be partially overcome proposing an analogous correlation for R.C. buildings. In Table 2.2.8, EMS-98 class C is related to

: even if in §2.2.2 it has been

stated that the Vulnerability Index is defined in the range

, and that is true, the

negative value however has not to be considered a mistake, because it is only used to find the best numerical correlation between the two methods. Once vulnerability has been defined, the mean damage grade

, can be computed for each

Macroseismic intensity, using eq. 2 and 3. From these values then, using a probabilistic approach it is possible to determine damage distribution histograms for different events of varying seismic intensity and their respective vulnerability index. Most frequently applied methods are based on the binomial probability mass function PMF (7) or the beta probability density function PDF (8):

(7) where:

is the probability of having a -level of damage ( is the maximum damage level (

);

in this case)

(8)

Note: the PDF is defined on the interval

.

In the current research the beta distribution function was adopted, as previous works showed that it is the most versatile, as it allows to “control” its shape via the geometric parameters and . In this way it enables the fitting even of very narrow and broad damage distributions (Giovinazzi, 2005). 38


Chapter 3 - PROPOS ED DEV ELOPMENTS TO THE APPLIED MET HOD

Assuming that

and

, eq. 8 can be simplified to: (9)

where, for a continuous variable , both the variance and

and mean value

are related to

as defined below:

(10)

(11) As parameter

presents a reduced variation in the numerical damage distributions, it is

reasonable to adopt a unique value,

, to represent the variance of all possible damage

distributions. Based on this assumption, eq. 11 becomes: (12)

Probability histograms of specific damage grade

are derived from the difference

of cumulative probabilities: (13) where

are determined as:

(14)

39


Chapter 3 - PROPOS ED DEV ELOPMENTS TO THE APPLIED MET HOD

Besides histogram, a continuous and better way of visualize damage is using fragility curves. Similarly to vulnerability curves, they describe the relationship between earthquake intensity and damage, but through conditional cumulative probability,

, see Figure 2.2.11.

Figure 3.1.1 â&#x20AC;&#x201C; Examples of fragility curves for two different vulnerability indexes (Vicente et al., 2011)

Probabilities obtained can be finally used for a seismic loss assessment. At first equations have been derived to evaluate collapsed and unusable buildings (see 18 and 19).

(18)

(19)

where:

is the total number of buildings and damage level

are weights indicating the percentage of buildings associated with the , that have suffered collapse or that are considered unusable. The most

frequently used values are

and

, referring to the work by

Bramerini et al. (1995). Nevertheless, the most serious consequence of an earthquake are always casualties and the main goal of all risk mitigation strategies is to ensure human safety. Therefore the number of dead and severely injured and homelessness can be estimated using eq. 20 and 21.

40


Chapter 3 - PROPOS ED DEV ELOPMENTS TO THE APPLIED MET HOD

(20)

(21)

where:

is the size of the population.

41


Chapter 3 - PROPOS ED DEV ELOPMENTS TO THE APPLIED MET HOD

3.2

Developments to the applied method

In §3.1 the best method to assess the seismic risk at urban scale is presented by the author. In the current paragraph, all knowledge summarized in chapter 2 will be used to elaborate developments to the method stated above. This methodology will consider masonry buildings as well as modern R.C. ones. Predicted damages are going to be calibrated by comparison with the actual observations gathered after the Emilia-Romagna earthquake in 2012. Everything that follows then is an original contribution by the author.

3.2.1

Vulnerability ellipses: a 2D study of the city

A seismic vulnerability study wants to evaluate the buildings’ probability of undergoing a certain level of damage during an earthquake. An important guidance is provided by data collected after previous seismic events that record the actual effects suffered by constructions. A building has usually a non regular shape and presents different structural aspects in every direction. In this view, the vulnerability of a generic structural entity can be considered as the sum of two factors: one isotropic and the other anisotropic (Grimaz, 1993, see Figure 3.1.1). The isotropic part consists of all characteristics not related to the input direction, such as the building’s material and age. The anisotropic one on the contrary includes all traits dependant on it, like for example the construction’s resistance and the influence of boundary conditions. For this reason, while the isotropic part can be represented as a circle, the global (actual) vulnerability is symbolized by an ellipse whose main axes come to be proportional to the building’s vulnerability along the two main directions. This makes possible to express the vulnerability as a completely different entity dependent also on the input’s characteristics.

Figure 3.2.1 – Definition of vulnerability ellipse

42


Chapter 3 - PROPOS ED DEV ELOPMENTS TO THE APPLIED MET HOD

The vulnerability index described by eq. 4 or 5 is now considered as separated by the structural context and referred only to the most vulnerable direction. A method to take into account that a building usually undergoes a different level of damage changing the input’s direction is proposed below. Step 1 Main directions

and

of every building are determined, evaluating also its inclination with

reference to cardinal axes,

, unique for the entire city (see Figure 3.1.2).

Figure 3.2.2 – Vulnerability ellipse determination, S tep 1

In this way, the different orientation of buildings is contemplated. Step 2 Vulnerability indexes

and

, respectively along directions

and

are then assessed filling

twice the original GNDT-II form (see Annex A) but “splitting” the Parameter 3 (Conventional Strength, see Figure 3.1.2) in the two directions.

Figure 3.2.3 – GNDT-II form, insight on Parameter 3

43


Chapter 3 - PROPOS ED DEV ELOPMENTS TO THE APPLIED MET HOD

Instead of using the minimum/maximum value two conditions are considered:

Step 3 The vulnerability ellipse then can be analytically determined: considering its semi-axes and by calling

,

as

the building’s inclination towards the EAST (see Step 1), the

implicit equation of the rotated ellipse is:

(22)

It will be ideally positioned in the building’s centre. By mapping all of them it is possible to have an immediate overview on the city’s response to a seismic event. There could be areas in fact where the ellipses’ size for example is significantly different than the others, i.e. zones of remarkable higher/lesser vulnerability, or where ellipses share (more or less) the same angle, so the directional effect will have a comparable impact on them.

Figure 3.2.4 – Vulnerability ellipse determination, S tep 3

44


Chapter 3 - PROPOS ED DEV ELOPMENTS TO THE APPLIED MET HOD

Step 4 Given a random input direction of the earthquake, for each building an angle-dependant vulnerability index is now obtained (see Figure 3.1.3).

Figure 3.2.5 â&#x20AC;&#x201C; Vulnerability ellipse determination, S tep 4

Note: in this research a numerical simulation of the assessment will be done for 360 degrees, resulting in a 2D view of the city vulnerability. It is remarked the while this effect is more important in masonry buildings, it can affect also R.C. constructions because can present more irregularities (horizontally or vertically).

3.2.2

Correlation between Iv (GNDT-II) and V (EMS-98) for R.C. buildings

As said in §2.2.4, the correlation (6) between the vulnerability index method and the vulnerability parameter

defined by the GNDT

of the Macroseismic one is valid ONLY for

masonry building. This is a definitely a really strict limitation, as almost every city has constructions of different structural typologies, such as R.C., steel, wooden or mixed. While the latter however are not so common, especially in historical city centres, reinforced concrete has been adopted in Italy since the end of 19th century, and is now the most widely used material. It becomes essential then to find a correlation also for this structural type, to include also R.C. buildings in the vulnerability assessment. Figure 2.2.4 shows that, according to the EMS-98 classification, R.C. buildings are generally included between vulnerability class C and E, and only sometimes in class F. In analogy with the determination of the correlation for masonry buildings then, the study will mainly focus in the interval C-D-E.

45


Chapter 3 - PROPOS ED DEV ELOPMENTS TO THE APPLIED MET HOD

With reference to the study made by Grimaz et al. (1996) a damage index, , is defined, that together with the vulnerability index, called

in this case, can be used to express the relation

between damage, vulnerability and seismic action entity. The approach followed assumes a piecewise linear relation among the acceleration and damage, as shown by eq. 23.

(23)

where:

For

is an estimate of ground acceleration empirically derived by intensity; is the value of

corresponding to the initial occurrence of damage;

is the value of

corresponding to the building’s collapse.

and

a mathematical relation with the vulnerability index has been theorized: (24)

Parameters

,

,

,

and

(25) have been determined always in the work by Grimaz et al.

using post-seismic data from:  the 1976 Friuli earthquake, regarding in particular the city centre of Venzone (UD, intensity IX M.C.S.), Tarcento and San Daniele (UD, intensity VIII M.C.S.);  the 1984 event that struck the Parco d’Abruzzo (AQ, FR, IS, intensity VII M.C.S.) and previous works (see Guarenti and Petrini, 1989). Numerical values of the factors listed above have then been determined with the least squares minimization procedure (see Table 3.2.1).

αi

βi

αc

βc

γ

0.08

0.013037

1.5371

0.00097401

1.8087

Table 3.2.1 – Parameters for damage/vulnerability index relation (Grimaz et al., 1996)

The damage index obtained in this way can now be converted, using the correlation proposed by FEMA-NIBS (HAZUS, 1999), into the mean damage grade used by the Macroseismic

46

(26)


Chapter 3 - PROPOS ED DEV ELOPMENTS TO THE APPLIED MET HOD

method. A damage probabilistic distribution is assumed, derived from the discretization of a beta distribution defined in the interval [0 – 5]. For easier implementation of this procedure, the following approximation has been used (see Vicente et al., 2011): (26) At first, the three

curves have been recreated for the EMS-98 classes using eq. (2) and (3). The n values that best- fit the corresponding vulnerability curves have been figured out

through eq. (23), (24), (25) and (26). Result are shown below in Figure 3.2.1 and Table 3.2.2 and 3.2.3.

Figure 3.2.6 – Vulnerability curves proposed for R.C. buildings

R.C. (PROPOSED) V (EMS-98)

IV (GNDT-II)

yi

yc

0.56

-30

0.12

0.93

0.40

-50

0.15

2.60

0.24

-55

0.16

5.94

Table 3.2.2 – Analytical steps of the equivalence determination - 1

47


Chapter 3 - PROPOS ED DEV ELOPMENTS TO THE APPLIED MET HOD

y (ag /g) 0.02 0.03 0.04 0.06

0.09 0.13 0.18 0.26

0.38 0.55 0.80 1.16

1.68 2.43 3.52

0.00

0.00

0.00

0.00

0.00

0.01

0.08

0.18

0.33

0.54

0.85

1.00

1.00

1.00

1.00

0.00

0.00

0.00

0.00

0.00

0.00

0.01

0.05

0.09

0.16

0.27

0.41

0.62

0.93

1.00

0.00

0.00

0.00

0.00

0.00

0.00

0.00

0.00

0.04

0.07

0.11

0.17

0.26

0.39

0.58

µD 0.00

0.00

0.00

0.00

0.00

0.50

1.28

1.85

2.42

3.03

3.71

4.00

4.00

4.00

4.00

0.00

0.00

0.00

0.00

0.00

0.00

0.55

1.00

1.38

1.77

2.20

2.68

3.24

3.88

4.00

0.00

0.00

0.00

0.00

0.00

0.00

0.30

0.65

0.92

1.19

1.48

1.81

2.19

2.63

3.13

Table 3.2.3 – Analytical steps of the equivalence determination - 2

Macroseismic method

Class C (V = 0.56)

Class D (V = 0.40)

Class E (V = 0.24)

GNDT-II level

IV = -30

IV = -50

IV = -55

Table 3.2.4 –Proposed correlation between the vulnerability indexes and the vulnerability classes defined in terms of the EMS -98 scale for R.C. buildings

As remarked in §2.2.4, also in this case negative values of vulnerability index is defined in the interval

have been used. Still, while the

, there are only used to find the best

numerical correlation between the two methods. The analytical correlation is finally expressed below: (27)

Figure 3.2.7 – Proposed correlation for R.C. buildings

48


Chapter 3 - PROPOS ED DEV ELOPMENTS TO THE APPLIED MET HOD

3.2.3

Implementation of seismic microzonation results

The method applied in the present work uses intensity values, according to the EMS-98 scale, to determine mean damage grades of buildings and the associated probabilities (see eq. 2 and following). To currently make seismic classifications and hazard maps however, peak ground acceleration (PGA) values are worldwide adopted as they are more accurate. It is essential then to find a mathematical relationship between these two measures to use all data regarding earthquakes gathered. PGA and Intensity show low correlation levels for their different nature, as largely observed in literature. The first one indeed is an objective instrumental measure (expressed with rational numbers) of the seismic shaking of the ground. The second one instead results from the need of quantifying, through an ordinal and discrete scale, the â&#x20AC;&#x153;greatnessâ&#x20AC;? of an earthquake in a pre- instrumental period, as it derives by post-event surveys on its effects on people (that can experience the tremor in different ways) and constructions (which could present severe fragilities and for this reason suffer higher damages than ordinary buildings). Researchers have proposed during the years several mathematical relations, and the most known are summarized in Table 3.3.1, from the more recent to the oldest ones. The majority of them, anyway, can be brought back to the same form (Lagormarsino and Giovinazzi, 2006) depending on only two coefficients

and

: (28)

where

is the ground acceleration

;

is the Macroseismic intensity measured with the EMS-98 conventional scale; and

two coefficients which define respectively the acceleration value associated to

a Macroseismic intensity 5 (intercept) and the slope of the correlation curve.

49


Chapter 3 - PROPOS ED DEV ELOPMENTS TO THE APPLIED MET HOD

Table 3.2.5 â&#x20AC;&#x201C; S ummary of correlations

found in literature (in chronological order, ascending)

Table 3.3.2 shows the coefficients considered for three different correlations, developed using intensity data collected with reference to various Macroseismic scale (Bernardini et al. ): - Guagenti and Petrini (1989), calibrated on italian data, that refers to the MCS (Mercalli, Cancani, Sieberg) scale; - Murphy and Oâ&#x20AC;&#x2122;Brien (1977), which adopts the MMI (Mercalli modified) scale; - Margottini et al. (1992), that proposed a correlation for both MCS and MSK (Medvedev, Sponheuer, Karnik) scale.

50


Chapter 3 - PROPOS ED DEV ELOPMENTS TO THE APPLIED MET HOD

Correlation

c1

c2

Guagenti - Petrini (1989)

0.03

2.05

Margottini et al. (1992)

0.04

1.65

Murphy and O'Brien (1977)

0.03

1.75

Table 3.2.6 – Values of parameters

Figure 3.2.8 –

and

for three correlations between

and

curves of three correlations (Gauagenti - Petrini, Margottini and Murphy - O’Brien)

All three of them have been converted to the EMS-98 scale under the hypothesis that, for intensity above grade V, MSK and MMI scale could be considered equivalent to the EMS-98 one and that values of the M.C.S. scale can be brought back to the MSK through eq. 29 (Spence, 1999). (29) The current research will apply Margottini correlation, as it is the most recent one and has been quantified using 9 Italian earthquakes, occurred between 1980 and 1987 (see Table 3.3.3), and the 56 corresponding records of accelerometric stations available. As said in §2.3, an important aspect in earthquakes’ measurement is played by local effects, such as amplification or liquefaction occurrence, that can considerably alter the seismic response of a city.

51


Chapter 3 - PROPOS ED DEV ELOPMENTS TO THE APPLIED MET HOD

If a microzonation study is available for the city under vulnerability assessment, the amplification factor,

, of the PGA will be determined. This can be applied to each intensity

values considered by the Macroseismic method (see Figure 2.2.9) once it has been converted into an acceleration using eq. 28. The “adjusted” results will then be re-converted into intensities through the inverse of eq. 28 to continue with the procedure.

Note: if more than one amplification factor is determined, due to soil heterogeneity even at small scale, they will be assigned to each building according to their position. Date

Time

Area

Epic. Coord.

(GMT) Macro

Instr.

I0

Depth

(MCS)

(km)

Ms

mb

Ml

1980 Nov 23

183452

Irpinia

40.86 - 15.25 /

40.81 - 15.38

IX - X

18

6.8

6.0

6.5

1983 Nov 29

162952

Parma

40.77 - 10.30 /

40.70 - 10.34

VII

38

4.9

4.9

4.9

1984 Apr 29

50257

Gubbio

43.26 - 12.56 /

43.25 - 12.46

VII - VIII

7

5.2

5.1

5.0

1984 May 07

174941

Val Com.

41.67 - 14.00 /

41.73 - 13.90

VII - VIII

16

5.8

5.4

5.1

1984 May 11

104150

Val Com.

41.67 - 14.03 /

41.77 - 13.93

VII

15

5.2

5.2

4.7

1985 Jan 23

101018

Garfag.

44.11 - 10.48 /

44.14 - 10.57

VI

10

-

4.8

4.4

1985 May 20

100030

L'Aquila

42.32 - 03.35 /

42.33 - 13.45

V - VI

3

4.5

4.7

4.5

1987 Apr 24

023028

Reggio E.

44.68 - 14.46 /

44.82 - 10.70

VI

10

-

4.1

4.6

1987 May 20

204353

Reggio E.

44.68 - 14.46 /

44.83 - 10.68

VII

5

-

4.8

5.0

Table 3.2.7 – General data of seismic events considered for Margottini correlations (from: ISC Bulletins; NEIS /PDE Bulletins; ING Bulletins; ENEA data)

52


Chapter 3 - PROPOS ED DEV ELOPMENTS TO THE APPLIED MET HOD

3.2.4

Reliability of an urban system: concept and definition

It has been widely remarked in §2.4 that, moving from a single building’s view to the urban scale, constructions’ function (as their role in the emergency and/or the recovery phase) and their mutual connection and interaction come into play. The city has to be regarded at in fact as a mechanical system, an engine, with all elements linked one to the other in different ways. Increasing the number of buildings and the associated probabilities then, it becomes useful to find a way of combining all these numerical values to determine the urban system reliability, that should possibly be a simple and immediate number. While there are several methods of combining probabilities, the easiest but nevertheless the most effective one is bringing black complex schemes to a set of series and/or parallel systems (Pinto, Giannini, Franchin, 2004). Series system It represents a configuration where, if any of the system’s component fails, the entire system will fail. It can be ideally described with the weakest link concept. A graphical description of a series system is shown in Figure 3.4.1.

Figure 3.2.9 – Representation of a series system

In a series system of

components then, the following “events” are considered equivalent:

Therefore, given the failure probability of a single component,

, if all elements’ failure and

survival is assumed independent, the reliability of the entire system can be expressed with the

equation:

(30)

Parallel system It represents a configuration where, as long as not all system’s components fail (i.e. at least one of them survives), the entire system will work. Obviously, in a parallel configuration the total system reliability is higher than any of the single component’s one. 53


Chapter 3 - PROPOS ED DEV ELOPMENTS TO THE APPLIED MET HOD

A graphical description of the parallel system is shown in Figure 3.4.2.

Figure 3.2.10 – Representation of a parallel system

Therefore, given the failure probability of the single component,

, if all elements’ failure and

survival is assumed independent, the reliability of the entire system can be expressed as:

(31) These theories can be applied on urban scale, relating them to the concept of limit conditions for a settlement described in §2.4.2. Three of them have been analyzed: a) Limit condition of emergency (CLE) Only those activities and interventions essential during the emergency phase to handle rescue operations immediately after the seismic event are taken into account,. Note: every component has to work properly (see Figure 3.4.3).

Figure 3.2.11 – Reliability of a urban system for the emergency limit condition (CLE)

54


Chapter 3 - PROPOS ED DEV ELOPMENTS TO THE APPLIED MET HOD

The vulnerability assessment focuses then only on a small part of the settlement, evaluating its reliability as a series system using eq. 30. In particular, a strategic sub-system can include: - strategic building for the emergency phase (see Table 2.4.3); - interfering buildings (ordinary buildings located along emergency connection routes from/to the city and whose collapse, even partial, can cause significant delays to the evacuation and rescue procedures). Failure probability of components

is defined according to the importance class

of

buildings (see NTC’08, §2.4.2):  Importance class I and II (only interfering buildings) Collapse has to be prevented, as well as the failure of walls or any other thing that could interrupt the practicability of connection routes. (32)  Importance class III and IV (strategic buildings) The activity does not have to undergo any interruption. (33) b) Limit condition of life-saving (CLV) The complete functionality of all strategic building for the emergency phase is guaranteed, along with their connection and accessibility with the territorial context. Modest-to- long interruption of some urban functions is accepted, but the settlement keeps the possibility to recover its pre-seismic standards, including residential one. The vulnerability assessment focuses now on the whole settlement, considering it as a seriesparallel system: given the failure probability

of the -th component of the -th sub-system,

the reliability is evaluated using eq. 34.

55


Chapter 3 - PROPOS ED DEV ELOPMENTS TO THE APPLIED MET HOD

(34)

A graphical description of a series-parallel system is shown in Figure 3.4.4.

Figure 3.2.12 – Reliability of a urban system for the life-saving limit condition (CLV)

In this case: - ordinary buildings (neither strategic nor interfering) are now included; - redundancy of strategic sub-systems can be considered, i.e. those buildings with public function but not essential during the emergency phase, along with their associated interfering building. Similarly to the CLE, failure probability

of components is defined as:

 Importance class I and II (interfering and ordinary buildings) See eq. 32.  Importance class III and IV (strategic buildings) See eq. 33. 56


Chapter 3 - PROPOS ED DEV ELOPMENTS TO THE APPLIED MET HOD

c) Limit condition of damage (CLD) The complete functionality of all strategic building for the emergency phase is guaranteed, along with their connection and accessibility with the territorial context. Only a short-tomodest or partial interruption of some ordinary urban functions is accepted. Similarly to the CLV the vulnerability assessment focuses on the whole settlement, and the reliability procedure is equivalent to the one used for the previous limit condition (see eq. 34 and Figure 3.4.4). The only difference relies in the definition of the failure probability

, as a lower threshold

damage limit for ordinary and interfering building is now demanded: ď&#x201A;§ Importance class I and II (interfering and ordinary buildings) Only moderate damages like cracks or fall of plaster are accepted. (35) ď&#x201A;§ Importance class III and IV (strategic buildings) See eq. 33.

57


Chapter 3 â&#x20AC;&#x201C; PROPOS ED DEV ELOPMENTS TO THE APPLIED MET HOD

58


Chapter 4 â&#x20AC;&#x201C; CAS E STUDY: THE CITY OF CONCORDIA S ULLA S ECCHIA (MO), ITALY

Chapter 4

CASE STUDY: THE CITY OF CONCORDIA SULLA SECCHIA (MO), ITALY

4.1

Short history and geography of the city

Concordia sulla Secchia is an Italian village of 8.769 habitants (data from ISTAT) in the province of Modena (MO), Emilia Romagna region, located North-West of the chief town. It extends almost for 41 square kilometres and itâ&#x20AC;&#x2122;s located in a totally flat territory with an average height of 22 m MSL (Mean Sea Level). The village is crossed on his left side by a river called Secchia (see Figure 4.1.1). Talking about its history, Concordia was a fief belonging to the family of Pico della Mirandola, an Italian Renaissance philosopher, since the 1311, when Francesco I Pico had a mill built near the Secchia river. In 1704 the town was besieged and set to fire by French soldiers during the the War of Spanish Succession (1701-1714). In 1711, the village passed under the domain of the duke of Modena (House of Este), who acquired the possessions of Pico della Mirandola.

59


Chapter 4 – CAS E STUDY: THE CITY OF CONCORDIA S ULLA S ECCHIA (MO), ITALY

Figure 4.1.1 – Map of Concordia sulla Secchia (MO), Italy (source: http://www.comune.concordia.mo.it/)

60


Chapter 4 – CAS E STUDY: THE CITY OF CONCORDIA S ULLA S ECCHIA (MO), ITALY

4.2

Seismic microzonation of Concordia sulla Secchia (MO), Italy

Concordia sulla Secchia has undergone severe damages by the recent earthquake of 29 May 2012. The event has partially destroyed the church, the town hall and all historical buildings in the town centre and caused two fatalities. Basing on the seismic classification of the italian territory ( D.L. n. 112 del 1998 D.P.R. n. 380/2001 - "Testo Unico delle Norme per l’Edilizia”), which defines four zones, of increasing hazard, the city is included in Zone 3 (see Table 4.2.1). Zone 1

The mos dangerous one. Really strong earthquakes can occur.

Zone 2

Strong earthquake can occur.

Zone 3

Strong earthquake can occur, but only in rare occasions.

Zone 4

Least dangerous one. Earthquakes are rare.

Table 4.2.1 – Seismic zones classification (D.L. 112/1998 – D.P.R. 380/2001)

With the hazard study attached to the O.P.C.M. 3519/06, each zone has then been associated to an acceleration (

) interval (see Table 4.2.2).

Seismic zone

Acceleration with probability of exceedance equal to 10% in 50 years (ag )

1

ag > 0.25 g

2

0.15 < ag ≤ 0.25 g

3

0.05 < ag ≤ 0.15 g

4

ag ≤ 0.05 g

Table 4.2.2 – Acceleration intervals associated to each seismic zone (O.P.C.M. 3519/06)

With the Decree n° 70 of the 13/11/2012, a seismic microzonation study of the EmiliaRomagna region has been commissioned with the purpose of assessing the liquefaction hazard and amplification effects. Several geotechnical investigations have been made, in particular CPTm (Mechanical Cone Penetration tests), CPTe (Electric Cone Penetration tests), soil borings and MASW (Multichannel Analysis of Surface Waves).

61


Chapter 4 – CAS E STUDY: THE CITY OF CONCORDIA S ULLA S ECCHIA (MO), ITALY

Fig. 4.2.1 – Example of soil boring in Concordia sulla Secchia (MO), Italy

Figure 4.2.2 – Example of CPTm in Concordia sulla Secchia (MO), Italy

62


Chapter 4 – CAS E STUDY: THE CITY OF CONCORDIA S ULLA S ECCHIA (MO), ITALY

From soil borings and CPTm it has been determined that Concordia sulla Secchia is characterized by a ground type C (see §3.2.2 NTC’08). An example of both test is shown respectively in Figure 4.2.1 and 4.2.2. Local seismic

microzonation analysis

then,

made by

Martelli

et

al.

(source:

http://ambiente.regione.emilia-romagna.it/geologia/temi/sismica/speciale-terremoto/sisma2012-ordinanza-70-13-11-2012-cartografia) have evaluated that the expected PGA for Concordia sulla Secchia is

= 0.127 g (value included in the acceleration interval of zone 3,

see Table 4.2.1), and the existence of two different amplification zones whose factor are: - Zone (a): FAPGA = 1.5 - Zone (b): FAPGA = 1.7 These values will be used during the vulnerability assessment of the city, as described in §3.3, choosing for each building which one to use according to its location. The seismic microzonation map of Concordia sulla Secchia can be found in Annex E.

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Chapter 4 â&#x20AC;&#x201C; CAS E STUDY: THE CITY OF CONCORDIA S ULLA S ECCHIA (MO), ITALY

4.3

Limit condition of Emergency (CLE) of Concordia sulla Secchia (MO), Italy

The Protezione Civile department is an Italian public authority that deals with prediction, prevention and management of exceptional events, and is in charge of urban planning and public safety. One of their tasks is to provide all guidelines needed to define the Limit Condition of Emergency (CLE) of a settlement, regarding in particular all buildings, assembly areas and connection routes included in this sub-system of the city (for further informations see: http://protezionecivile.gov.it/resources/cms/documents/Allegato_modulistic a_DPCM_27_4_2012_attuazione_art11dl39_2009.pdf). The CLE has been determined also for the city of Concordia sulla Secchia: a map is shown in Figure 4.3.1, while a description of its elements is presented below. Emergency connection routes: - Via Corriera - Via Don Giovanni Minzoni (also known as Via Lungo Secchia) - Strada Provinciale 8 - Via per S. Possidonio - Via Gozzi - Viale P. Togliatti - Via Lenin - Via per Mirandola - Via Martiri della LibertĂ - Via del Volontariato - Via F. Santi Emergency area: Soccer field, located at the end of Via Gozzi, near the Sabbioncello canal. Interfering buildings: - all those included in the aggregate between Via Don Minzoni and Via della Pace (see Table 4.3.1) - other interfering buildings (see Table 4.3.2) 64


Chapter 4 – CAS E STUDY: THE CITY OF CONCORDIA S ULLA S ECCHIA (MO), ITALY

Figure 4.3.1 – Limit condition of emergency (CLE) of Concordia sulla Secchia (MO), Italy

Strategic buildings (see Table 4.3.3, building’s function is determined according to the Protezione Civile guidelines, see link above): - ES 05, Infant and nursery school - ES 02, Teaching building (Comprehensive Institute, from infant to secondary school) - ES 01, City Hall - ES 03, Nonreligious collective activities (Sports centre)

65


Chapter 4 – CAS E STUDY: THE CITY OF CONCORDIA S ULLA S ECCHIA (MO), ITALY FID (GIS MAP)

ID US (AEDES FORM)

PARTICLE NO. (CADASTRAL MAP CATALOGUE)

ADDRESS

CONSTRUCTION PERIOD (WITH EVENTUAL RENOVATION)

STRUCTURE CATEGORY

79

1712000 - 29

249

Via Don Minzoni 40

82-91

R.C.

78

171200 - 28

250 -251

Via Don Minzoni 38

72-81

MASONRY

77

171200 - 27

252 SX

Via Don Minzoni 37

72-81

R.C.

76

171200 - 26

252 DX

Via Don Minzoni 36

72-81

R.C.

75

171200 - 25

253

Via Don Minzoni 35

92-01

R.C.

74

171200 - 24

254

Via Don Minzoni 34

82-91

R.C.

73

171200 - 23

255 - 256

Via Don Minzoni 33

62-71

R.C.

72

171200 - 22

258

Via Don Minzoni 32 - 32A

72-81

R.C.

71 - 70

171200 - 21 + 20

259

Via Don Minzoni 30 - 31

72-81

R.C.

69

171200 - 19

260

Via Don Minzoni 33 - 37

92-01

R.C.

68

171200 - 18

262

Via Don Minzoni 26 -27 - 28

62-71

R.C.

67 - 1

171200 - 17

263

Via Don Minzoni 25

92-01

R.C.

67 - 2

171200 - 17

264 - 265

Via Don Minzoni 25

92-01

R.C.

66 - 1

171200 - 16

267

Via Don Minzoni 23

< 1919 + 92-01

R.C.

66 - 2

171200 - 16

269

Via Don Minzoni 23

< 1919 + 92-01

R.C.

63

171200 - 14

270

Via Don Minzoni 22

72-81

MASONRY

64

171200 - 13

272

Via Don Minzoni 21

92-01

MASONRY

65

171200 - 12

277

Via Don Minzoni 20A

< 1919

R.C.

61

171200 - 11

280

Via Don Minzoni 20

19-45

R.C.

60

171200 - 10

281

Via Don Minzoni 18

72-81

R.C.

59

171200 - 9

283

Via Don Minzoni 17

72-81

R.C.

106

171900 - 3

285

Via Don Minzoni 15

72-81

MASONRY

105

171900 - 2

289

Via Don Minzoni 14

72-81

MASONRY

104

171900 - 1

291

Via Don Minzoni 13

19-45

MASONRY

58

171200 - 8

299

Via Don Minzoni 11A

< 1919

MASONRY

57

171200 - 7

300

Via Don Minzoni 10

< 1919

MASONRY

56

171200 - 6

303

Via Don Minzoni 8

92-01

R.C.

55

171200 - 5

305

Via Don Minzoni 7

82-91

R.C.

54

171200 - 4

307

Via Don Minzoni 5-7

92-01

R.C.

53 - 52

171200 - 3 + 2 + 53

308 - 309 -310

Via Don Minzoni 2-3

62-71

R.C.

51

171200 - 1

311

Via Don Minzoni 1

62-71

R.C.

29

25050 - 999

312

Strada Provinciale 24

46-61 + 72-81

R.C.

Table 4.3.1 – Interfering buildings (CLE) belonging to the aggregate between Via Don Minzoni and Via della Pace, in Concordia sulla Secchia (MO), Italy FID

ID US

PARTICLE NO.

(GIS MAP)

(AEDES FORM)

(CADASTRAL MAP CATALOGUE)

ADDRESS

CONSTRUCTION PERIOD

STRUCTURE CATEGORY

33

241900 - 999

-

Via Lenin 15 - 21

32

235200 - 999

-

Via Lenin 34

19-45

R.C.

31

235000 - 999

-

Via Lenin 40

> 2002

R.C.

30

236100 - 999

-

Via Gozzi

46-61 + 72-81

R.C.

34

158300 - 999

-

Via Carducci 24

62-71

R.C.

35

136900 - 999

-

Via Martiri della Libertà 24

92-01 + > 2002

R.C.

(WITH EVENTUAL RENOVATION) 62-71

Table 4.3.2 – Other interfering buildings (CLE) in Concordia sulla Secchia (MO), Italy

66

R.C.


Chapter 4 – CAS E STUDY: THE CITY OF CONCORDIA S ULLA S ECCHIA (MO), ITALY FID (GIS MAP)

ID US (AEDES FORM)

PARTICLE NO. (CADASTRAL MAP CATALOGUE)

ADDRESS

CONSTRUCTION PERIOD (WITH EVENTUAL RENOVATION)

STRUCTURE CATEGORY

-

144200 - 999

ES 05

Via Lenin 43

72-81

R.C.

-

303600 - 999

ES 02

Via del Volontariato

> 2002 (2012)

STEEL

-

303500 - 999

ES 01

Via del Volontariato

> 2002 (2012)

MIXED (STEEL - R.C.)

-

303700 - 999

ES 03

Via della Protezione Civile

> 2002 (2013)

STEEL

Table 4.3.3 – S trategic buildings (CLE) in Concordia sulla Secchia (MO), Italy

67


Chapter 4 – CAS E STUDY: THE CITY OF CONCORDIA S ULLA S ECCHIA (MO), ITALY

4.4

Detail level of post-seismic survey

The CLE analysis of the urban settlement was made using the set of forms provided by the Technical Commitee within the O.P.C.M. 3907/2010. In particular 5 different forms are available (source: http://www.protezionecivile.gov.it/resour ces/cms/documents/IstruzioniSchedeCLE_2_0_open.pdf): - ES (strategic building) - AE (emergency area) - AC (accessibility/connection infrastructure) - AS (structural aggregate) - US (structural unit) In the current work, only ES and US forms have been used, which are shown respectively in Figure 4.4.1 and 4.4.2. To each acronym listed above, the subscript “1” has been added, to remark the “level of knowledge”. Vulnerability assessment forms are indeed classified by their detail level, i.e. how much information about the building’s structure and architecture are needed to completely fill them. Clearly, increasing the fields‘ number of the form, the evaluation is more accurate. Three levels of knowledge are defined:  L0, this form only provides the approximate acquisition of building’s data and is used for all structural types with the purpose of gathering them in a comprehensive database with a geographical interface;  L1, this form includes all information regarding the building’s location, geometry and type. It can be used to evaluate exposition and/or vulnerability (see §2.1).  L2, this form includes all elements involved while assessing the structure’s behaviour under seismic load. It should be the one truly used in vulnerability assessment. As said in §2.2.4, the vulnerability assessment of Concordia sulla Secchia was made with GNDT-II forms (L2). They have been filled however with data collected using CLE forms (L1). This difference in the forms’ level of knowledge will definitely affect the accuracy of the method.

68


Chapter 4 – CAS E STUDY: THE CITY OF CONCORDIA S ULLA S ECCHIA (MO), ITALY

Figure 4.4.1 – ES (strategic building) form for CLE analysis

69


Chapter 4 – CAS E STUDY: THE CITY OF CONCORDIA S ULLA S ECCHIA (MO), ITALY

Figure 4.4.2 – US (structural unit) form for CLE analysis

70


Chapter 4 – CAS E STUDY: THE CITY OF CONCORDIA S ULLA S ECCHIA (MO), ITALY

In addition, information gathered were also not accurate enough in some cases. In particular:  Masonry buildings - Quality of resisting system: CLE form only makes a vague distinction between “good” and “poor” masonry quality. They have been respectively associated then to class B and C(6) of the GNDT-II parameter; - Horizontal diaphragms: CLE form doesn’t include any information about them. Their deformability/stiffness and the connection level have been assumed basing on the construction period and the damage level; - Roof: no details on its eventual spread were listed, but only the presence/absence of ties and curbs. A modest roof spreading has been assumed for all buildings.  R.C. buildings - Quality of resisting system : no information about the concrete’s strength were given. The quality level has been ascribed basing on the construction period. A (good quality)

built after 1991

B (average quality)

built between 1991 and 1961

C (poor quality)

built before 1961

- Conventional strength: floor plans were not very accurate for R.C. buildings included in the aggregate. For this reason there have been issues not only figuring out the extent of every unit but also identifying the area of load-bearing elements (concrete pillars and infill masonry walls, in the second case homogenized with the Transformed Section Method using The Young modules,

);

- Connection and critical elements: also in this case, for the lack of details in the floor plans provided, the same classification used for “Quality of resisting system” parameter has been adopted; - Low ductility elements: (same as “Connection and critical elements”). Finally, for the interfering buildings, floor plans or any information were not provided at all. Under the although unlikely assumption that their vulnerability does not change upon direction, it has been determined as a mean value of the buildings’ vulnerabilities basing on the construction’s period. A “correction factor”, associated to the observed damage, has been finally added to keep into account that two buildings of the same age can easily have different construction features (see Table 4.4.1).

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Chapter 4 – CAS E STUDY: THE CITY OF CONCORDIA S ULLA S ECCHIA (MO), ITALY

CONSTRUCTION PERIOD

ΔIV

≤ 1919

+ 12.5

1919 - 1945

+ 10

1945 - 1961

+ 7.5

1962 - 1971

+5

1972 - 1981

+ 2.5

1982 - 1991

0

1992 - 2001

- 2.5

≥ 2002

-5

Table 4.4.1 – Correction factor for vulnerability index of other interfering buildings

For all reasons stated above, it is extremely important whether essential to remark that planning a high-detailed survey (L2) of all buildings before making the assessment is needed to have likely results.

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Chapter 4 – CAS E STUDY: THE CITY OF CONCORDIA S ULLA S ECCHIA (MO), ITALY

4.5

Vulnerability indexes

All GNDT-II filled forms for the CLE sub-system of Concordia sulla Secchia (MO) are attached to Annex B. In the paragraphs below a recap of vulnerability indexes for different structural types is presented.

4.5.1

Masonry buildings

Vulnerability forms were filled following the GNDT-II handbook’s instructions provided by the Regione Toscana website (see: http://www.regione.toscana.it/documents/10180/12262198 /vsm_man.pdf/095d3648-191d-43aa-ae88-ad78cff79fb3). Vulnerability indexes and the corresponding parameters of the Macroseismic method are shown in Table 4.5.1. FID

IX

IY

VX *

VY *

78

44.44

53.64

0.85

0.90

63

48.03

65.23

0.87

0.96

64

35.93

47.04

0.80

0.86

106

30.82

48.03

0.77

0.87

105

41.38

59.77

0.83

0.93

104

45.14

53.47

0.85

0.90

58

36.02

56.70

0.80

0.92

57

44.44

62.84

0.85

0.95

* for the correlation IV - V see eq. (6) Table 4.5.1 - Vulnerability indexes and the vulnerability parameters for CLE sub-system masonry buildings of Concordia sulla Secchia (MO), Italy

Values vary in the range 30.82 to 65.23, with a mean of 48.31: masonry buildings were highly affected by the earthquake, and more than half of them has undergone collapse.

4.5.2

R.C. buildings

In this case vulnerability forms were filled following the GNDT-II handbook’s instructions provided by the Regione Marche website (see: rischiosismico.regione.marche.it/Portals/0/RIS CHIOSISMICO/MANUALI/05---manuale2ca.pdf).

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Chapter 4 â&#x20AC;&#x201C; CAS E STUDY: THE CITY OF CONCORDIA S ULLA S ECCHIA (MO), ITALY

Vulnerability indexes and the corresponding parameters of the Macroseismic method are shown in Table 4.5.1. FID

IX

IY

VX **

VY **

79

42.50

42.50

1.14

1.14

77

37.50

37.50

1.11

1.11

76

47.50

50.00

1.16

1.17

75

30.00

30.00

1.07

1.07

74

50.00

50.00

1.17

1.17

73

52.50

55.00

1.19

1.20

72

67.50

67.50

1.24

1.24

71 - 70

67.50

67.50

1.24

1.24

69

35.00

35.00

1.10

1.10

68

42.50

42.50

1.14

1.14

67 - 1

42.50

42.50

1.14

1.14

67 - 2

32.50

32.50

1.09

1.09

66 - 1

67.50

67.50

1.24

1.24

66 - 2

50.00

50.00

1.17

1.17

65

57.50

57.50

1.21

1.21

61

75.00

77.50

1.26

1.27

60

32.50

35.00

1.09

1.10

59

57.50

60.00

1.21

1.22

56

45.00

45.00

1.15

1.15

55

52.50

52.50

1.19

1.19

54

60.00

60.00

1.22

1.22

53 - 52

55.00

57.50

1.20

1.21

51

52.50

55.00

1.19

1.20

29

60.00

60.00

1.22

1.22

33

38.75

38.75

1.12

1.12

32

43.75

43.75

1.15

1.15

31

47.50

47.50

1.16

1.16

30

52.71

52.71

1.19

1.19

34

66.41

66.41

1.24

1.24

35

31.25

31.25

1.08

1.08

* (ES 05)

36.25

36.25

1.11

1.11

* Strategic building with originally no FID ** for the correlation IV - V see eq. (27) Table 4.5.2 - Vulnerability indexes and the vulnerability parameters for CLE sub-system R.C. buildings of Concordia sulla Secchia (MO), Italy

74


Chapter 4 – CAS E STUDY: THE CITY OF CONCORDIA S ULLA S ECCHIA (MO), ITALY

Values vary in the range 30 to 77.50, with a mean of 49.61: while the average vulnerability of R.C. buildings is almost the same as masonry one, the range has a higher upper bound. Another peculiarity is that vulnerabilities are really similar in the two main directions, and sometimes they don’t even change. This is due to issues analyzed in §4.4.

4.5.3

Other structural types

All strategic constructions but one are made of steel or have mixed structure. Finding a correlation between

also for them could have been possible, but it would prove

pointless as there aren’t GNDT-II forms to assess their vulnerability. In the specific case of Concordia sulla Secchia (MO) however, this problem can be overcome because they have all been built after the earthquake. Thus it is reasonable to think that they were made following all ERD (Earthquake-Resistance Design) concepts included in the N.T.C. 2008 (see §2.1) that are particularly strict for strategic buildings, i.e. they require to keep a high performance level after the seismic event. Therefore their vulnerability index ( ) can be assumed equal to zero. Then, as these structural types are mainly included in EMS-98 class E (see Fig. 2.4.2), the equivalent Vulnerability ( ) value will be assigned (see Table 2.4.2). FID

IX

IY

VX

VY

* (ES 02)

0.1

0.1

0.24

0.24

* (ES 01)

0.1

0.1

0.24

0.24

* (ES 03)

0.1

0.1

0.24

0.24

* Strategic building with originally no FID Table 4.5.3 - Vulnerability indexes and the vulnerability parameters for CLE sub-system steel or mixed structure buildings of Concordia sulla Secchia (MO), Italy

Note:

and

are not exactly equal to zero only for computational issues (see Matlab

program, §4.6).

75


Chapter 4 â&#x20AC;&#x201C; CAS E STUDY: THE CITY OF CONCORDIA S ULLA S ECCHIA (MO), ITALY

4.6

Matlab program

The vulnerability assessment method is made of repetitive analytical steps, for each building and every direction, so it is highly convenient to develop an automated procedure. In the current work, the high-performance language for technical computing Matlab, developed by MathWorksÂŽ, has been used (see: https://it.mathworks.com/products/matlab/). At first it is necessary to make a .txt file with all data needed by the program. % Ix 42.5 41 37.5 47.5 30 50 52.5 67.5 67.5 35 42.5 42.5 32.5 67.5 50 44.8 25.93 57.5 75 32.5 57.5 26.16 37.93 42.01 32.57 41 45 52.5 60 55 52.5 60.00 38.75 43.75 47.5 52.71 66.41 31.25 36.25 0.1 0.1 0.1

76

Iy 42.5 50.19 37.5 50 30 50 55 67.5 67.5 35 42.5 42.5 32.5 67.5 50 62.01 37.04 57.5 77.5 35 60 43.37 56.32 50.35 53.26 59.39 45 52.5 60 57.5 55 60 38.75 43.75 47.5 52.71 66.41 31.25 36.25 0.1 0.1 0.1

alfa 157 178 175 176 176 183 191 191 197 206 197 195 205 210 208 206 205 203 203 199 204 210 210 210 210 210 213 218 215 220 218 199 132 137 137 157 139 144 137 120 120 120

IDstructure 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 1 1 1 1 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 2 2 2

Fa 1.7 1.7 1.7 1.7 1.7 1.7 1.7 1.7 1.7 1.7 1.7 1.7 1.7 1.7 1.7 1.7 1.7 1.7 1.7 1.7 1.7 1.7 1.7 1.7 1.7 1.7 1.7 1.7 1.7 1.7 1.7 1.7 1.7 1.7 1.7 1.7 1.7 1.7 1.7 1.7 1.7 1.7

Cu 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 2 2 1.5

Noccupants 0 0 0 0 5 3 14 0 0 3 0 4 4 0 0 0 0 4 0 0 2 1 0 0 0 0 3 3 0 3 1 9 30 7 15 25 7 27 90 700 45 26


Chapter 4 – CAS E STUDY: THE CITY OF CONCORDIA S ULLA S ECCHIA (MO), ITALY

All vulnerability ellipses are then determined using eq. 22 and, as all buildings have a different orientation, they will need to be “re-arranged” to share the same coordinate system. Note:

is measured with respect to the East direction, as shown by Figure 4.6.1, and the assessment is made for every angle ( –

Vulnerability indexes for every angle

) moving clockwise.

are converted into vulnerability parameters using eq.

6 and 27 respectively for masonry and R.C. buildings. Mean damage grades and probabilities have to be evaluated for every building for each intensity level ( –

, EMS-98) and for each angle ( –

). Therefore the simplest wa y

to do it is using different matrixes for increasing level of , where buildings are listed in rows and columns always represent the assessment directions. While the Beta Probability Function (see eq. 8) is already included in the Matlab library, the trapz function has been used to determine integers shown in eq. 14: it is defined as a trapezoidal numerical integration without unit spacing. Note: to avoid useless steps, the following assumption has been accepted. (the building has no damage)

(collapse is certain) Finally, all probabilities related to damages and casualties caused by the earthquake are settled, as well as the reliability of the urban system. The full Matlab script is attached to Annex F.

77


Chapter 4 – CAS E STUDY: THE CITY OF CONCORDIA S ULLA S ECCHIA (MO), ITALY

Figure 4.6.1 – Visual representation of CLE buildings of Concordia sulla Secchia (MO), Italy under vulnerability assessment

78


Chapter 5 – DIS CUSSION OF RES ULTS

Chapter 5

DISCUSSION OF RESULTS

5.1

Analysis of results

As said in §4.6, the vulnerability assessment was made for a complete rotation ( –

).

Presenting the results for every angle however would prove excessive, so meaningful directions were looked for. Epicentres map of the 2012 Emilia earthquake shows a spatial distribution with predominant direction WNW - ESE (see Figure 5.1.1, source: http://www.protezionecivile.tn.it/territorio/pr imop_territorio/pagina49.html). This direction then will be considered, along with the perpendicular one (NNE - SSW) and the two in between (ENE - WSW and NWN - SSE). They are summarized, with the respective numerical values of angles, in Table 5.1.1. Note: the automatic procedure in Matlab gives back results as matrixes, where columns always refer to various earthquake directions. The first one is associated to 0° (East – direction), so vales have to be picked in the

column for every angle listed in

Table 5.1.1. Effective earthquake direction (see above) are highlighted in red. 79


Chapter 5 – DIS CUSSION OF RES ULTS

Figure 5.1.1 – Epicentres map of 2012 Emilia earthquake, Italy (source: http://www.protezionecivile.tn.it/territorio/ primop_territorio/pagina49.html)

EARTHQUAKE DIRECTION

ANGLE (WITH RESPECT TO EAST)

ESE

22

SSE

67

SSW

112

WSW

157

WNW

202

NWN

247

NNE

292

ENE

337

Table 5.1.1 – Directions considered for displaying results and angles associated

At first the mean damage grades obtained through eq. 2 and 3 are presented, for increasing intensity level ( 80

). Rows’ order follows the one of Tables 4.3.1, 4.3.2 and 4.3.3.


Chapter 5 – DIS CUSSION OF RES ULTS MEAN DAMAGE GRADE, I (EMS-98) = 5 ESE

SSE

SSW

WSW

WNW

NWN

NNE

ENE

ANGLE (W.R. TO EAST)

22°

67°

113°

157°

202°

247°

292°

337°

1

0.83

0.83

0.83

0.83

0.83

0.83

0.83

0.83

2

0.38

0.44

0.43

0.38

0.38

0.44

0.43

0.38

3

0.79

0.79

0.79

0.79

0.79

0.79

0.79

0.79

4

0.86

0.86

0.86

0.85

0.86

0.86

0.86

0.85

5

0.74

0.74

0.74

0.74

0.74

0.74

0.74

0.74

6

0.87

0.87

0.87

0.87

0.87

0.87

0.87

0.87

7

0.88

0.88

0.89

0.88

0.88

0.88

0.89

0.88

8

0.93

0.93

0.93

0.93

0.93

0.93

0.93

0.93

9

0.93

0.93

0.93

0.93

0.93

0.93

0.93

0.93

10

0.78

0.78

0.78

0.78

0.78

0.78

0.78

0.78

11

0.83

0.83

0.83

0.83

0.83

0.83

0.83

0.83

12

0.83

0.83

0.83

0.83

0.83

0.83

0.83

0.83

13

0.76

0.76

0.76

0.76

0.76

0.76

0.76

0.76

14

0.93

0.93

0.93

0.93

0.93

0.93

0.93

0.93

15

0.87

0.87

0.87

0.87

0.87

0.87

0.87

0.87

16

0.40

0.49

0.55

0.47

0.40

0.49

0.55

0.47

17

0.24

0.29

0.33

0.28

0.24

0.29

0.33

0.28

18

0.90

0.90

0.90

0.90

0.90

0.90

0.90

0.90

19

0.94

0.94

0.94

0.94

0.94

0.94

0.94

0.94

20

0.76

0.77

0.78

0.77

0.76

0.77

0.78

0.77

21

0.90

0.90

0.90

0.90

0.90

0.90

0.90

0.90

22

0.24

0.32

0.39

0.32

0.24

0.32

0.39

0.32

23

0.34

0.43

0.50

0.42

0.34

0.43

0.50

0.43

24

0.37

0.41

0.45

0.42

0.37

0.41

0.45

0.42

25

0.29

0.40

0.47

0.39

0.29

0.40

0.47

0.39

26

0.36

0.45

0.53

0.45

0.36

0.45

0.53

0.46

27

0.84

0.84

0.84

0.84

0.84

0.84

0.84

0.84

28

0.88

0.88

0.88

0.88

0.88

0.88

0.88

0.88

29

0.90

0.90

0.90

0.90

0.90

0.90

0.90

0.90

30

0.89

0.89

0.90

0.89

0.89

0.89

0.90

0.89

31

0.88

0.88

0.89

0.88

0.88

0.88

0.89

0.88

32

0.90

0.90

0.90

0.90

0.90

0.90

0.90

0.90

33

0.80

0.80

0.80

0.80

0.80

0.80

0.80

0.80

34

0.83

0.83

0.83

0.83

0.83

0.83

0.83

0.83

35

0.85

0.85

0.85

0.85

0.85

0.85

0.85

0.85

36

0.88

0.88

0.88

0.88

0.88

0.88

0.88

0.88

37

0.92

0.92

0.92

0.92

0.92

0.92

0.92

0.92

38

0.75

0.75

0.75

0.75

0.75

0.75

0.75

0.75

39

0.79

0.79

0.79

0.79

0.79

0.79

0.79

0.79

40

0.00

0.00

0.00

0,00

0.00

0.00

0.00

0,00

41

0.00

0.00

0.00

0,00

0.00

0.00

0.00

0,00

42

0.00

0.00

0.00

0,00

0.00

0.00

0.00

0,00

BUILDING NO.

DIRECTION

Table 5.1.2 – Mean damage grades for intensity level IEMS-98 = 5

81


Chapter 5 – DIS CUSSION OF RES ULTS MEAN DAMAGE GRADE, I (EMS-98) = 6 ESE

SSE

SSW

WSW

WNW

NWN

NNE

ENE

ANGLE (W.R. TO EAST)

22°

67°

113°

157°

202°

247°

292°

337°

1

2.00

2.00

2.00

2.00

2.00

2.00

2.00

2.00

2

1.12

1.24

1.23

1.11

1.12

1.24

1.23

1.11

3

1.94

1.94

1.94

1.94

1.94

1.94

1.94

1.94

4

2.05

2.07

2.07

2.05

2.05

2.07

2.07

2.05

5

1.84

1.84

1.84

1.84

1.84

1.84

1.84

1.84

6

2.07

2.07

2.07

2.07

2.07

2.07

2.07

2.07

7

2.09

2.10

2.11

2.10

2.09

2.10

2.11

2.10

8

2.18

2.18

2.18

2.18

2.18

2.18

2.18

2.18

9

2.18

2.18

2.18

2.18

2.18

2.18

2.18

2.18

10

1.91

1.91

1.91

1.91

1.91

1.91

1.91

1.91

11

2.00

2.00

2.00

2.00

2.00

2.00

2.00

2.00

12

2.00

2.00

2.00

2.00

2.00

2.00

2.00

2.00

13

1.88

1.88

1.88

1.88

1.88

1.88

1.88

1.88

14

2.18

2.18

2.18

2.18

2.18

2.18

2.18

2.18

15

2.07

2.07

2.07

2.07

2.07

2.07

2.07

2.07

16

1.16

1.35

1.48

1.32

1.16

1.34

1.48

1.32

17

0.82

0.93

1.01

0.92

0.82

0.93

1.01

0.91

18

2.13

2.13

2.13

2.13

2.13

2.13

2.13

2.13

19

2.20

2.21

2.21

2.21

2.20

2.21

2.21

2.21

20

1.88

1.90

1.91

1.89

1.88

1.90

1.91

1.89

21

2.13

2.13

2.14

2.13

2.13

2.13

2.14

2.13

22

0.82

1.00

1.13

0.99

0.82

1.00

1.13

0.99

23

1.03

1.22

1.37

1.22

1.03

1.22

1.37

1.22

24

1.11

1.18

1.26

1.20

1.11

1.18

1.26

1.20

25

0.93

1.16

1.32

1.14

0.93

1.15

1,32

1.14

26

1.09

1.27

1.43

1.28

1.09

1.27

1.43

1.28

27

2.03

2.03

2.03

2.03

2.03

2.03

2.03

2.03

28

2.09

2.09

2.09

2.09

2.09

2.09

2.09

2.09

29

2.14

2.14

2.14

2.14

2.14

2.14

2.14

2.14

30

2.11

2.11

2.12

2.12

2.11

2.11

2.12

2.12

31

2.09

2.10

2.11

2.10

2.09

2.10

2.11

2.10

32

2.14

2.14

2.14

2.14

2.14

2.14

2.14

2.14

33

1.96

1.96

1.96

1.96

1.96

1.96

1.96

1.96

34

2.01

2.01

2.01

2.01

2.01

2.01

2.01

2.01

35

2.05

2.05

2.05

2.05

2.05

2.05

2.05

2.05

36

2.09

2.09

2.09

2.09

2.09

2.09

2.09

2.09

37

2.17

2.17

2.17

2.17

2.17

2.17

2.17

2.17

38

1.86

1.86

1.86

1.86

1.86

1.86

1.86

1.86

39

1.93

1.93

1.93

1.93

1.93

1.93

1.93

1.93

40

0.00

0.00

0.00

0.00

0.00

0.00

0.00

0.00

41

0.00

0.00

0.00

0.00

0.00

0.00

0.00

0.00

42

0.00

0.00

0.00

0.00

0.00

0.00

0.00

0.00

BUILDING NO.

DIRECTION

Table 5.1.3 – Mean damage grades for intensity level IEMS-98 = 6

82


Chapter 5 – DIS CUSSION OF RES ULTS MEAN DAMAGE GRADE, I (EMS-98) = 7 ESE

SSE

SSW

WSW

WNW

NWN

NNE

ENE

ANGLE (W.R. TO EAST)

22°

67°

113°

157°

202°

247°

292°

337°

1

4.30

4.30

4.30

4.30

4.30

4.30

4.30

4.30

2

2.68

2.91

2.89

2.66

2.66

2.91

2.89

2.66

3

4.19

4.19

4.19

4.19

4.19

4.19

4.19

4.19

4

4.40

4.43

4.43

4.40

4.40

4.43

4.43

4.40

5

4.00

4.00

4.00

4.00

4.00

4.00

4.00

4.00

6

4.44

4.44

4.44

4.44

4.44

4.44

4.44

4.44

7

4.48

4.50

4.51

4.49

4.49

4.50

4.51

4.49

8

4.66

4.66

4.66

4.66

4.66

4.66

4.66

4.66

9

4.66

4.66

4.66

4.66

4.66

4.66

4.66

4.66

10

4.13

4.13

4.13

4.13

4.13

4.13

4.13

4.13

11

4.30

4.30

4.30

4.30

4.30

4.30

4.30

4.30

12

4.30

4.30

4.30

4.30

4.30

4.30

4.30

4.30

13

4.07

4.07

4.07

4.07

4.07

4.07

4.07

4.07

14

4.66

4.66

4.66

4.66

4.66

4.66

4.66

4.66

15

4.44

4.44

4.44

4.44

4.44

4.44

4.44

4.44

16

2.76

3.11

3.34

3.05

3.05

3.10

3.34

3.05

17

2.09

2.32

2.48

2.28

2.28

2.31

2.48

2.28

18

4.55

4.55

4.55

4.55

4.55

4.55

4.55

4.55

19

4.72

4.72

4.73

4.72

4.72

4.72

4.73

4.73

20

4.07

4.11

4.13

4.10

4.10

4.11

4.13

4.10

21

4.55

4.56

4.58

4.56

4.56

4.56

4.58

4.56

22

2.09

2.45

2.70

2.42

2.42

2.45

2.70

2.42

23

2.51

2.88

3.15

2.86

2.86

2.87

3.16

2.86

24

2.66

2.79

2.95

2.83

2.83

2.79

2.95

2.83

25

2.32

2.75

3.05

2.71

2.71

2.75

3.05

2.71

26

2.62

2.97

3.26

2.97

2.97

2.96

3.26

2.98

27

4.35

4.35

4.35

4.35

4.35

4.35

4.35

4.35

28

4.48

4.48

4.48

4.48

4.48

4.48

4.48

4.48

29

4.58

4.58

4.58

4.58

4.58

4.58

4.58

4.58

30

4.51

4.52

4.54

4.54

4.54

4.52

4.54

4.54

31

4.48

4.48

4.51

4.50

4.50

4.48

4.51

4.50

32

4.58

4.58

4.58

4.58

4.58

4.58

4.58

4.58

33

4.22

4.22

4.22

4.22

4.22

4.22

4.22

4.22

34

4.33

4.33

4.33

4.33

4.33

4.33

4.33

4.33

35

4.39

4.39

4.39

4.39

4.39

4.39

4.39

4.39

36

4.48

4.48

4.48

4.48

4.48

4.48

4.48

4.48

37

4.64

4.64

4.64

4.64

4.64

4.64

4.64

4.64

38

4.04

4.04

4.04

4.04

4.04

4.04

4.04

4.04

39

4.17

4.17

4.17

4.17

4.17

4.17

4.17

4.17

40

0.02

0.02

0.02

0.02

0.02

0.02

0.02

0.02

41

0.02

0.02

0.02

0.02

0.02

0.02

0.02

0.02

42

0.02

0.02

0.02

0.02

0.02

0.02

0.02

0.02

BUILDING NO.

DIRECTION

Table 5.1.4 – Mean damage grades for intensity level IEMS-98 = 7

83


Chapter 5 – DIS CUSSION OF RES ULTS MEAN DAMAGE GRADE, I (EMS-98) = 8 ESE

SSE

SSW

WSW

WNW

NWN

NNE

ENE

ANGLE (W.R. TO EAST)

22°

67°

113°

157°

202°

247°

292°

337°

1

4.82

4.82

4.82

4.82

4.82

4.82

4.82

4.82

2

3.62

3.82

3.80

3.61

3.62

3.81

3.80

3.61

3

4.75

4.75

4.75

4.75

4.75

4.75

4.75

4.75

4

4.88

4.90

4.90

4.88

4.88

4.90

4.90

4.88

5

4.63

4.63

4.63

4.63

4.63

4.63

4.63

4.63

6

4.90

4.90

4.90

4.90

4.90

4.90

4.90

4.90

7

4.93

4.94

4.95

4.93

4.93

4.94

4.95

4.93

8

5.00

5.00

5.00

5.00

5.00

5.00

5.00

5.00

BUILDING NO.

DIRECTION

9

5.00

5.00

5.00

5.00

5.00

5.00

5.00

5.00

10

4.71

4.71

4.71

4.71

4.71

4.71

4.71

4.71

11

4.82

4.82

4.82

4.82

4.82

4.82

4.82

4.82

12

4.82

4.82

4.82

4.82

4.82

4.82

4.82

4.82

13

4.67

4.67

4.67

4.67

4.67

4.67

4.67

4.67

14

5.00

5.00

5.00

5.00

5.00

5.00

5.00

5.00

15

4.90

4.90

4.90

4.90

4.90

4.90

4.90

4.90

16

3.69

3.97

4.16

3.93

3.69

3.97

4.16

3.93

17

3.08

3.30

3.44

3.26

3.08

3.29

3.45

3.27

18

4.97

4.97

4.97

4.97

4.97

4.97

4.97

4.97

19

5.00

5.00

5.00

5.00

5.00

5.00

5.00

5.00

20

4.67

4.69

4.71

4.69

4.67

4.69

4.71

4.69

21

4.97

4.98

4.99

4.98

4.97

4.98

4.99

4.98

22

3.08

3.42

3.64

3.39

3.08

3.42

3.64

3.39

23

3.47

3.79

4.01

3.77

3.47

3.78

4.01

3.78

24

3.60

3.72

3.85

3.75

3.60

3.71

3.85

3.75

25

3.30

3.68

3.93

3.65

3.30

3.68

3.93

3.65

26

3.57

3.87

4.09

3.87

3.57

3.86

4.09

3.87

27

4.85

4.85

4.85

4.85

4.85

4.85

4.85

4.85

28

4.93

4.93

4.93

4.93

4.93

4.93

4.93

4.93

29

4.99

4.99

4.99

4.99

4.99

4.99

4.99

4.99

30

4.95

4.95

4.97

4.96

4.95

4.95

4.97

4.96

31

4.93

4.93

4.95

4.94

4.93

4.93

4.95

4.94

32

4.99

4.99

4.99

4.99

4.99

4.99

4.99

4.99

33

4.77

4.77

4.77

4.77

4.77

4.77

4.77

4.77

34

4.83

4.83

4.83

4.83

4.83

4.83

4.83

4.83

35

4.88

4.88

4.88

4.88

4.88

4.88

4.88

4.88

36

4.93

4.93

4.93

4.93

4.93

4.93

4.93

4.93

37

5.00

5.00

5.00

5.00

5.00

5.00

5.00

5.00

38

4.65

4.65

4.65

4.65

4.65

4.65

4.65

4.65

39

4.73

4.73

4.73

4.73

4.73

4.73

4.73

4.73

40

0.43

0.43

0.43

0.43

0.43

0.43

0.43

0.43

41

0.43

0.43

0.43

0.43

0.43

0.43

0.43

0.43

42

0.43

0.43

0.43

0.43

0.43

0.43

0.43

0.43

Table 5.1.5 – Mean damage grades for intensity level IEMS-98 = 8

84


Chapter 5 – DIS CUSSION OF RES ULTS MEAN DAMAGE GRADE, I (EMS-98) = 9 ESE

SSE

SSW

WSW

WNW

NWN

NNE

ENE

ANGLE (W.R. TO EAST)

22°

67°

113°

157°

202°

247°

292°

337°

1

5.00

5.00

5.00

5.00

5.00

5.00

5.00

5.00

2

4.36

4.50

4.49

4.35

4.36

4.50

4.49

4.35

3

5.00

5.00

5.00

5.00

5.00

5.00

5.00

5.00

4

5.00

5.00

5.00

5.00

5.00

5.00

5.00

5.00

5

5.00

5.00

5.00

5.00

5.00

5.00

5.00

5.00

6

5.00

5.00

5.00

5.00

5.00

5.00

5.00

5.00

7

5.00

5.00

5.00

5.00

5.00

5.00

5.00

5.00

8

5.00

5.00

5.00

5.00

5.00

5.00

5.00

5.00

BUILDING NO.

DIRECTION

9

5.00

5.00

5.00

5.00

5.00

5.00

5.00

5.00

10

5.00

5.00

5.00

5.00

5.00

5.00

5.00

5.00

11

5.00

5.00

5.00

5.00

5.00

5.00

5.00

5.00

12

5.00

5.00

5.00

5.00

5.00

5.00

5.00

5.00

13

5.00

5.00

5.00

5.00

5.00

5.00

5.00

5.00

14

5.00

5.00

5.00

5.00

5.00

5.00

5.00

5.00

15

5.00

5.00

5.00

5.00

5.00

5.00

5.00

5.00

16

4.41

4.61

4.73

4.58

4.41

4.60

4.73

4.58

17

3.95

4.12

4.23

4.10

3.95

4.12

4.23

4.10

18

5.00

5.00

5.00

5.00

5.00

5.00

5.00

5.00

19

5.00

5.00

5.00

5.00

5.00

5.00

5.00

5.00

20

5.00

5.00

5.00

5.00

5.00

5.00

5.00

5.00

21

5.00

5.00

5.00

5.00

5.00

5.00

5.00

5.00

22

3.96

4.22

4.38

4.19

3.96

4.21

4.38

4.20

23

4.26

4.48

4.63

4.47

4.26

4.48

4.63

4.47

24

4.35

4.43

4.52

4.45

4.35

4.43

4.52

4.46

25

4.13

4.41

4.58

4.38

4.13

4.40

4.58

4.38

26

4.33

4.53

4.68

4.54

4.33

4.53

4.68

4.54

27

5.00

5.00

5.00

5.00

5.00

5.00

5.00

5.00

28

5.00

5.00

5.00

5.00

5.00

5.00

5.00

5.00

29

5.00

5.00

5.00

5.00

5.00

5.00

5.00

5.00

30

5.00

5.00

5.00

5.00

5.00

5.00

5.00

5.00

31

5.00

5.00

5.00

5.00

5.00

5.00

5.00

5.00

32

5.00

5.00

5.00

5.00

5.00

5.00

5.00

5.00

33

5.00

5.00

5.00

5.00

5.00

5.00

5.00

5.00

34

5.00

5.00

5.00

5.00

5.00

5.00

5.00

5.00

35

5.00

5.00

5.00

5.00

5.00

5.00

5.00

5.00

36

5.00

5.00

5.00

5.00

5.00

5.00

5.00

5.00

37

5.00

5.00

5.00

5.00

5.00

5.00

5.00

5.00

38

5.00

5.00

5.00

5.00

5.00

5.00

5.00

5.00

39

5.00

5.00

5.00

5.00

5.00

5.00

5.00

5.00

40

1.08

1.08

1.08

1.08

1.08

1.08

1.08

1.08

41

1.08

1.08

1.08

1.08

1.08

1.08

1.08

1.08

42

1.08

1.08

1.08

1.08

1.08

1.08

1.08

1.08

Table 5.1.6 – Mean damage grades for intensity level IEMS-98 = 9

85


Chapter 5 – DIS CUSSION OF RES ULTS MEAN DAMAGE GRADE, I (EMS-98) = 10 ESE

SSE

SSW

WSW

WNW

NWN

NNE

ENE

ANGLE (W.R. TO EAST)

22°

67°

113°

157°

202°

247°

292°

337°

1

5.00

5.00

5.00

5.00

5.00

5.00

5.00

5.00

2

4.86

4.94

4.93

4.85

4.86

4.94

4.94

4.85

3

5.00

5.00

5.00

5.00

5.00

5.00

5.00

5.00

4

5.00

5.00

5.00

5.00

5.00

5.00

5.00

5.00

5

5.00

5.00

5.00

5.00

5.00

5.00

5.00

5.00

6

5.00

5.00

5.00

5.00

5.00

5.00

5.00

5.00

7

5.00

5.00

5.00

5.00

5.00

5.00

5.00

5.00

8

5.00

5.00

5.00

5.00

5.00

5.00

5.00

5.00

BUILDING NO.

DIRECTION

9

5.00

5.00

5.00

5.00

5.00

5.00

5.00

5.00

10

5.00

5.00

5.00

5.00

5.00

5.00

5.00

5.00

11

5.00

5.00

5.00

5.00

5.00

5.00

5.00

5.00

12

5.00

5.00

5.00

5.00

5.00

5.00

5.00

5.00

13

5.00

5.00

5.00

5.00

5.00

5.00

5.00

5.00

14

5.00

5.00

5.00

5.00

5.00

5.00

5.00

5.00

15

5.00

5.00

5.00

5.00

5.00

5.00

5.00

5.00

16

5.00

5.00

5.00

5.00

5.00

5.00

5.00

5.00

17

4.59

4.70

4.78

4.69

4.59

4.70

4.78

4.69

18

5.00

5.00

5.00

5.00

5.00

5.00

5.00

5.00

19

5.00

5.00

5.00

5.00

5.00

5.00

5.00

5.00

20

5.00

5.00

5.00

5.00

5.00

5.00

5.00

5.00

21

5.00

5.00

5.00

5.00

5.00

5.00

5.00

5.00

22

4.60

4.76

4.87

4.75

4.59

4.76

4.87

4.75

23

4.79

4.93

5.00

4.92

4.79

4.92

5.00

4.92

24

4.85

4.90

4.95

4.91

4.85

4.89

4.95

4.91

25

4.71

4.88

4.99

4.87

4.71

4.88

4.99

4.87

26

4.83

4.96

5.00

4.96

4.83

4.96

5.00

4.96

27

5.00

5.00

5.00

5.00

5.00

5.00

5.00

5.00

28

5.00

5.00

5.00

5.00

5.00

5.00

5.00

5.00

29

5.00

5.00

5.00

5.00

5.00

5.00

5.00

5.00

30

5.00

5.00

5.00

5.00

5.00

5.00

5.00

5.00

31

5.00

5.00

5.00

5.00

5.00

5.00

5.00

5.00

32

5.00

5.00

5.00

5.00

5.00

5.00

5.00

5.00

33

5.00

5.00

5.00

5.00

5.00

5.00

5.00

5.00

34

5.00

5.00

5.00

5.00

5.00

5.00

5.00

5.00

35

5.00

5.00

5.00

5.00

5.00

5.00

5.00

5.00

36

5.00

5.00

5.00

5.00

5.00

5.00

5.00

5.00

37

5.00

5.00

5.00

5.00

5.00

5.00

5.00

5.00

38

5.00

5.00

5.00

5.00

5.00

5.00

5.00

5.00

39

5.00

5.00

5.00

5.00

5.00

5.00

5.00

5.00

40

1.97

1.97

1.97

1.97

1.97

1.97

1.97

1.97

41

1.97

1.97

1.97

1.97

1.97

1.97

1.97

1.97

42

1.97

1.97

1.97

1.97

1.97

1.97

1.97

1.97

Table 5.1.7 – Mean damage grades for intensity level IEMS-98 = 10

86


Chapter 5 – DIS CUSSION OF RES ULTS MEAN DAMAGE GRADE, I (EMS-98) = 11 ESE

SSE

SSW

WSW

WNW

NWN

NNE

ENE

ANGLE (W.R. TO EAST)

22°

67°

113°

157°

202°

247°

292°

337°

1

5.00

5.00

5.00

5.00

5.00

5.00

5.00

5.00

2

5.00

5.00

5.00

5.00

5.00

5.00

5.00

5.00

3

5.00

5.00

5.00

5.00

5.00

5.00

5.00

5.00

4

5.00

5.00

5.00

5.00

5.00

5.00

5.00

5.00

5

5.00

5.00

5.00

5.00

5.00

5.00

5.00

5.00

6

5.00

5.00

5.00

5.00

5.00

5.00

5.00

5.00

7

5.00

5.00

5.00

5.00

5.00

5.00

5.00

5.00

8

5.00

5.00

5.00

5.00

5.00

5.00

5.00

5.00

BUILDING NO.

DIRECTION

9

5.00

5.00

5.00

5.00

5.00

5.00

5.00

5.00

10

5.00

5.00

5.00

5.00

5.00

5.00

5.00

5.00

11

5.00

5.00

5.00

5.00

5.00

5.00

5.00

5.00

12

5.00

5.00

5.00

5.00

5.00

5.00

5.00

5.00

13

5.00

5.00

5.00

5.00

5.00

5.00

5.00

5.00

14

5.00

5.00

5.00

5.00

5.00

5.00

5.00

5.00

15

5.00

5.00

5.00

5.00

5.00

5.00

5.00

5.00

16

5.00

5.00

5.00

5.00

5.00

5.00

5.00

5.00

17

5.00

5.00

5.00

5.00

5.00

5.00

5.00

5.00

18

5.00

5.00

5.00

5.00

5.00

5.00

5.00

5.00

19

5.00

5.00

5.00

5.00

5.00

5.00

5.00

5.00

20

5.00

5.00

5.00

5.00

5.00

5.00

5.00

5.00

21

5.00

5.00

5.00

5.00

5.00

5.00

5.00

5.00

22

5.00

5.00

5.00

5.00

5.00

5.00

5.00

5.00

23

5.00

5.00

5.00

5.00

5.00

5.00

5.00

5.00

24

5.00

5.00

5.00

5.00

5.00

5.00

5.00

5.00

25

5.00

5.00

5.00

5.00

5.00

5.00

5.00

5.00

26

5.00

5.00

5.00

5.00

5.00

5.00

5.00

5.00

27

5.00

5.00

5.00

5.00

5.00

5.00

5.00

5.00

28

5.00

5.00

5.00

5.00

5.00

5.00

5.00

5.00

29

5.00

5.00

5.00

5.00

5.00

5.00

5.00

5.00

30

5.00

5.00

5.00

5.00

5.00

5.00

5.00

5.00

31

5.00

5.00

5.00

5.00

5.00

5.00

5.00

5.00

32

5.00

5.00

5.00

5.00

5.00

5.00

5.00

5.00

33

5.00

5.00

5.00

5.00

5.00

5.00

5.00

5.00

34

5.00

5.00

5.00

5.00

5.00

5.00

5.00

5.00

35

5.00

5.00

5.00

5.00

5.00

5.00

5.00

5.00

36

5.00

5.00

5.00

5.00

5.00

5.00

5.00

5.00

37

5.00

5.00

5.00

5.00

5.00

5.00

5.00

5.00

38

5.00

5.00

5.00

5.00

5.00

5.00

5.00

5.00

39

5.00

5.00

5.00

5.00

5.00

5.00

5.00

5.00

40

2.96

2.96

2.96

2.96

2.96

2.96

2.96

2.96

41

2.96

2.96

2.96

2.96

2.96

2.96

2.96

2.96

42

2.96

2.96

2.96

2.96

2.96

2.96

2.96

2.96

Table 5.1.8 – Mean damage grades for intensity level IEMS-98 = 11

87


Chapter 5 – DIS CUSSION OF RES ULTS MEAN DAMAGE GRADE, I (EMS-98) = 12 ESE

SSE

SSW

WSW

WNW

NWN

NNE

ENE

ANGLE (W.R. TO EAST)

22°

67°

113°

157°

202°

247°

292°

337°

1

5.00

5.00

5.00

5.00

5.00

5.00

5.00

5.00

2

5.00

5.00

5.00

5.00

5.00

5.00

5.00

5.00

3

5.00

5.00

5.00

5.00

5.00

5.00

5.00

5.00

4

5.00

5.00

5.00

5.00

5.00

5.00

5.00

5.00

5

5.00

5.00

5.00

5.00

5.00

5.00

5.00

5.00

6

5.00

5.00

5.00

5.00

5.00

5.00

5.00

5.00

7

5.00

5.00

5.00

5.00

5.00

5.00

5.00

5.00

8

5.00

5.00

5.00

5.00

5.00

5.00

5.00

5.00

BUILDING NO.

DIRECTION

9

5.00

5.00

5.00

5.00

5.00

5.00

5.00

5.00

10

5.00

5.00

5.00

5.00

5.00

5.00

5.00

5.00

11

5.00

5.00

5.00

5.00

5.00

5.00

5.00

5.00

12

5.00

5.00

5.00

5.00

5.00

5.00

5.00

5.00

13

5.00

5.00

5.00

5.00

5.00

5.00

5.00

5.00

14

5.00

5.00

5.00

5.00

5.00

5.00

5.00

5.00

15

5.00

5.00

5.00

5.00

5.00

5.00

5.00

5.00

16

5.00

5.00

5.00

5.00

5.00

5.00

5.00

5.00

17

5.00

5.00

5.00

5.00

5.00

5.00

5.00

5.00

18

5.00

5.00

5.00

5.00

5.00

5.00

5.00

5.00

19

5.00

5.00

5.00

5.00

5.00

5.00

5.00

5.00

20

5.00

5.00

5.00

5.00

5.00

5.00

5.00

5.00

21

5.00

5.00

5.00

5.00

5.00

5.00

5.00

5.00

22

5.00

5.00

5.00

5.00

5.00

5.00

5.00

5.00

23

5.00

5.00

5.00

5.00

5.00

5.00

5.00

5.00

24

5.00

5.00

5.00

5.00

5.00

5.00

5.00

5.00

25

5.00

5.00

5.00

5.00

5.00

5.00

5.00

5.00

26

5.00

5.00

5.00

5.00

5.00

5.00

5.00

5.00

27

5.00

5.00

5.00

5.00

5.00

5.00

5.00

5.00

28

5.00

5.00

5.00

5.00

5.00

5.00

5.00

5.00

29

5.00

5.00

5.00

5.00

5.00

5.00

5.00

5.00

30

5.00

5.00

5.00

5.00

5.00

5.00

5.00

5.00

31

5.00

5.00

5.00

5.00

5.00

5.00

5.00

5.00

32

5.00

5.00

5.00

5.00

5.00

5.00

5.00

5.00

33

5.00

5.00

5.00

5.00

5.00

5.00

5.00

5.00

34

5.00

5.00

5.00

5.00

5.00

5.00

5.00

5.00

35

5.00

5.00

5.00

5.00

5.00

5.00

5.00

5.00

36

5.00

5.00

5.00

5.00

5.00

5.00

5.00

5.00

37

5.00

5.00

5.00

5.00

5.00

5.00

5.00

5.00

38

5.00

5.00

5.00

5.00

5.00

5.00

5.00

5.00

39

5.00

5.00

5.00

5.00

5.00

5.00

5.00

5.00

40

3.85

3.85

3.85

3.85

3.85

3.85

3.85

3.85

41

3.85

3.85

3.85

3.85

3.85

3.85

3.85

3.85

42

3.85

3.85

3.85

3.85

3.85

3.85

3.85

3.85

Table 5.1.9 – Mean damage grades for intensity level IEMS-98 = 12

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Chapter 5 – DIS CUSSION OF RES ULTS

Due to the number of buildings examined it would be redundant to show fragility curves (see Figure 3.1.1) for every structural unit. In §4.5.1 and §4.5.2 were stated minimum, maximum and mean values of the vulnerability indexes respectively for masonry and R.C. constructions. So, to have a concise but comprehensive view, it is displayed the trend of fragility curves for these values. a)

b)

Figure 5.1.2 – Fragility curves for minimum vulnerability index of a) masonry buildings; b) R.C. buildings of Concordia sulla Secchia (MO) CLE sub-system

c)

d)

Figure 5.1.3 – Fragility curves for mean vulnerability index of c) masonry buildings; d) R.C. buildings of Concordia sulla Secchia (MO) CLE sub-system

e)

f)

Figure 5.1.4 – Fragility curves for maximum vulnerability index of e) masonry buildings; f) R.C. buildings of Concordia sulla Secchia (MO) CLE su b-system

89


Chapter 5 – DIS CUSSION OF RES ULTS

After that, combined probabilities and counts of collapsed or unusable buildings after the seismic event are displayed, as well as the likelihood of having casualties or severely wounded and homeless (see eq. 18-21). COLLAPSE PROBABILITY (%)

DIRECTION

ESE

SSE

SSW

WSW

WNW

NWN

NNE

ENE

ANGLE (W.R. TO EAST)

22°

67°

113°

157°

202°

247°

292°

337°

5

0.00

0.00

0.00

0.00

0.00

0.00

0.00

0.00

6

0.03

0.03

0.03

0.03

0.03

0.03

0.03

0.03

7

40.18

40.53

40.94

40.48

40.17

40.53

40.95

40.49

8

68.82

70.26

71.68

69.99

68.81

70.24

71.69

70.01

9

81.63

84.41

86.24

83.96

81.62

84.37

86.25

84.00

10

89.82

91.48

92.16

91.26

89.82

91.46

92.16

91.28

11

92.96

92.96

92.96

92.96

92.96

92.96

92.96

92.96

INTENSITY (EMS-98)

NUMBER OF COLLAPSE

12

94.22

94.22

94.22

94.22

94.22

94.22

94.22

94.22

DIRECTION

ESE

SSE

SSW

WSW

WNW

NWN

NNE

ENE

ANGLE (W.R. TO EAST)

22°

67°

113°

157°

202°

247°

292°

337°

5

0

0

0

0

0

0

0

0

INTENSITY (EMS-98)

6

0

0

0

0

0

0

0

0

7

17

17

17

17

17

17

17

17

8

29

30

30

29

29

29

30

29

9

34

35

36

35

34

35

36

35

10

38

38

39

38

38

38

39

38

11

39

39

39

39

39

39

39

39

12

40

40

40

40

40

40

40

40

Table 5.1.10 – Probabilities and numbers of collapsed buildings for increasing intensity levels of Concordia sulla Secchia (MO) CLE sub-system

COLLAPSE 100

PROB (%) 90 NO. [-] 80 70 COLLAPSE PROBABILITY

60

50

NUMBER OF COLLAPSE

40 30

20 10 0

5

6

7

8

9

10

11

12

I (EMS-98)

Figure 5.1.5 – Collapse probability and number of collapsed buildings of Concordia sulla Secchia (MO) CLE sub-system

90


Chapter 5 – DIS CUSSION OF RES ULTS UNUSABLE BUILDINGS PROBABILITY (%)

DIRECTION

ESE

SSE

SSW

WSW

WNW

NWN

NNE

ENE

ANGLE (W.R. TO EAST)

22°

67°

113°

157°

202°

247°

292°

337°

5

0.59

0.60

0.61

0.60

0.59

0.60

0.61

0.60

6

9.62

9.80

9.96

9.77

9.62

9.80

9.97

9.77

7

22.78

23.98

24.70

23.78

22.78

23.96

24.70

23.79

8

11.35

11.46

11.12

11.49

11.35

11.46

11.12

11.48

9

6.19

4.82

3.85

5.05

6.19

4.84

3.84

5.03

10

2.55

1.60

1.21

1.73

2.55

1.61

1.20

1.71

11

2.36

2.36

2.36

2.36

2.36

2.36

2.36

2.36

INTENSITY (EMS-98)

NUMBER OF UNUSABLE BUILDINGS

12

2.93

2.93

2.93

2.93

2.93

2.93

2.93

2.93

DIRECTION

ESE

SSE

SSW

WSW

WNW

NWN

NNE

ENE

ANGLE (W.R. TO EAST)

22°

67°

113°

157°

202°

247°

292°

337°

5

0

0

0

0

0

0

0

0

6

4

4

4

4

4

4

4

4

7

10

10

10

10

10

10

10

10

8

5

5

5

5

5

5

5

5

INTENSITY (EMS-98)

9

3

2

2

2

3

2

2

2

10

1

1

1

1

1

1

1

1

11

1

1

1

1

1

1

1

1

12

1

1

1

1

1

1

1

1

Table 5.1.11 – Probabilities and numbers of unusable buildings for increasing intensity levels of Concordia sulla Secchia (MO) CLE sub-system

UNUSABLE BUILDINGS 100

PROB (%) 90 NO. [-] 80

UNUSABLE BUILDINGS PROBABILITY

70 60

50

NUMBER OF UNUSABLE BUILDINGS

40 30

20 10 0

5

6

7

8

9

10

11

12

I (EMS-98)

Figure 5.1.6 – Unusable probability and number of unusable buildings of Concordia sulla Secchia (MO) CLE sub-system

91


Chapter 5 – DIS CUSSION OF RES ULTS DIRECTION DEAD AND SEVERELY INJURED PROBABILITY (%) ANGLE (W.R. TO EAST) 5

INTENSITY (EMS-98)

NUMBER OF DEAD AND SEVERELY INJURED

INTENSITY (EMS-98)

ESE

SSE

SSW

WSW

WNW

NWN

NNE

ENE

22°

67°

113°

157°

202°

247°

292°

337°

0.00

0.00

0.00

0.00

0.00

0.00

0.00

0.00

6

0.01

0.01

0.01

0.01

0.01

0.01

0.01

0.01

7

12.05

12.16

12.28

12.14

12.05

12.16

12.28

12.15

8

20.64

21.08

21.50

21.00

20.64

21.07

21.51

21.00

9

24.49

25.32

25.87

25.19

24.49

25.31

25.87

25.20

10

26.95

27.44

27.65

27.38

26.94

27.44

27.65

27.38

11

27.89

27.89

27.89

27.89

27.89

27.89

27.89

27.89

12

28.27

28.27

28.27

28.27

28.27

28.27

28.27

28.27

DIRECTION

ESE

SSE

SSW

WSW

WNW

NWN

NNE

ENE

ANGLE (W.R. TO EAST)

22°

67°

113°

157°

202°

247°

292°

337°

5

0

0

0

0

0

0

0

0

6

0

0

0

0

0

0

0

0

7

124

125

127

125

124

125

127

125

8

213

217

222

216

213

217

222

217

9

252

261

267

260

252

261

267

260

10

278

283

285

282

278

283

285

282

11

288

288

288

288

288

288

288

288

12

291

291

291

291

291

291

291

291

Table 5.1.12 – Probabilities and numbers of dead and severely injured for increasing intensity levels of Concordia sulla Secchia (MO) CLE sub-system DIRECTION HOMELESS PROBABILITY (%) ANGLE (W.R. TO EAST)

INTENSITY (EMS-98)

NUMBER OF HOMELESS

INTENSITY (EMS-98)

ESE

SSE

SSW

WSW

WNW

NWN

NNE

ENE

22°

67°

113°

157°

202°

247°

292°

337°

5

0.59

0.60

0.61

0.60

0.59

0.60

0.61

0.60

6

9.64

9.82

9.99

9.79

9.64

9.82

9.99

9.79

7

50.90

52.35

53.36

52.11

50.90

52.33

53.37

52.13

8

59.53

60.64

61.29

60.48

59.52

60.63

61.30

60.49

9

63.33

63.91

64.22

63.82

63.33

63.90

64.22

63.83

10

65.42

65.63

65.72

65.61

65.42

65.63

65.72

65.61

11

67.43

67.43

67.43

67.43

67.43

67.43

67.43

67.43

12

68.89

68.89

68.89

68.89

68.89

68.89

68.89

68.89

DIRECTION

ESE

SSE

SSW

WSW

WNW

NWN

NNE

ENE

ANGLE (W.R. TO EAST)

22°

67°

113°

157°

202°

247°

292°

337°

5

6

6

6

6

6

6

6

6

6

99

101

103

101

99

101

103

101

7

525

540

550

538

525

539

550

538

8

614

625

632

624

614

625

632

624

9

653

659

662

658

653

659

662

658

10

675

677

678

676

674

677

678

676

11

695

695

695

695

695

695

695

695

12

710

710

710

710

710

710

710

710

Table 5.1.13 – Probabilities and numbers of homeless for increasing intensity levels of Concordia sulla Secchia (MO) CLE sub-system

92


Chapter 5 – DIS CUSSION OF RES ULTS

Figure 5.1.7 – Probability and number of dead and severely injured of Concordia sulla Secchia (MO) CLE sub-system

Figure 5.1.8 – Probability and number of homeless of Concordia sulla Secchia (MO) CLE sub-system

Note: it is noticeable that unused building probability increases until

and then suddenly

decreases returning to zero. This is due to the mathematical relationship with and

, see eq. (19).

With higher intensity levels indeed, buildings consequently undergo more damages (

), until they are no more considered just unusable as they experience

collapse. The number of dead and severely injured or homeless then, is evaluated using the average daily occupancy of buildings. While building’s damage is not time dependant, casualties and wounded count on the contrary can drastically change depending on the time the earthquake strikes. Seismic event of May, 20th in Emilia for example has occurred during the night (04:03:52 Italian time, 02:03:52 UTC). If it had happen at noon the impact on the population would surely have been different.

93


Chapter 5 – DIS CUSSION OF RES ULTS

Finally, survival probability or rather reliability of the urban system for the limit condition of Emergency (CLE) is shown, for increasing intensity level ( RELIABILITY OF URBAN SYSTEM FOR CLE (%)

).

DIRECTION

ESE

SSE

SSW

WSW

WNW

NWN

NNE

ENE

ANGLE (W.R. TO EAST)

22°

67°

113°

157°

202°

247°

292°

337°

5

85.04

85.01

84.99

85.02

85.04

85.02

84.99

85.02

6

7.68

7.53

7.38

7.55

7.68

7.53

7.38

7.55

INTENSITY (EMS-98)

7

6.9E-37

1.8E-37

4.9E-38

1.9E-37

4.9E-38

2.2E-37

8

0.00

0.00

0.00

2.2E-37 7.0E-37 0.00

0.00

0.00

0.00

0.00

9

0.00

0.00

0.00

0.00

0.00

0.00

0.00

0.00

10

0.00

0.00

0.00

0.00

0.00

0.00

0.00

0.00

11

0.00

0.00

0.00

0.00

0.00

0.00

0.00

0.00

12

0.00

0.00

0.00

0.00

0.00

0.00

0.00

0.00

Table 5.1.14 – Reliability of the urban system for increasing intensity levels of Concordia sulla Secchia (MO) CLE sub-system

RELIABILITY OF THE URBAN SYSTEM PROB (%)

100 90 80 70

COLLAPSE PROBABILITY

60

50

RELIABILITY OF CLE URBAN SUB-SYSTEM

40 30 20 10 0

5

6

7

8

9

10

11

12

I (EMS-98)

Figure 5.1.9 – Comparison between collapse probability and the reliability of Concordia sulla Secchia (MO) CLE sub-system

From the figure above it is possible to notice that, as soon as the collapse probability is nonzero, the reliability of the system decreases sharply. It is clear also that emergency sub-system of Concordia sulla Secchia (MO) at the current state is not able to withstand a seismic event above intensity value

94

.


Chapter 5 – DIS CUSSION OF RES ULTS

Another possible remark is that numerical values don’t have a significant variability changing the earthquake direction. This can be partly due to the lack of information regarding in particular R.C. buildings, already explained in §4.4 and that forced the assumption of vulnerability indexes equal or very much alike in all directions (see §4.5.2). The direction’s influence however was taken into account only by one parameter on the eleven included in the GNDT-II form (see §3.1), so it is strongly advisable a revision of the form to increase the weight (i.e. the importance) of this parameter.

95


Chapter 5 – DIS CUSSION OF RES ULTS

5.2

Visual maps obtained with the GIS sofwtare

After returning the numerical results obtained with the Matlab procedure, it is possible to use the GIS software to represent also these data directly on the city map, having in this way a more immediate view of earthquake effects for different directions and/or increasing intensities. Values have been organized so in Excel files, using a different sheets for every seismic intensity. The association was made through the FID (building’s ID), see Table 4.5.1, 4.5.2 and 4.5.3. Note: there were some ambiguities while comparing the GIS classification and the cadastral map cataloguing. In particular: - if a building was identified by two distinct FIDs, the single analysis result will be duplicated and linked to both GIS IDs; - if, on the contrary, two different structural units shared the same FID, the GIS “Cut Polygons Tool” have been used (under the Editor menu) to distinguish the structural units; - finally, strategic buildings originally didn’t have the FID, so they have been provided with one following the existing numerical order. The revised list of FIDs corresponding to each building, used for the GIS maps is shown in Table 5.2.1, with highlighted in red the changes made.

96


Chapter 5 – DIS CUSSION OF RES ULTS FID

FID

(ORIGINAL)

(CORRECT)

79

79

78

78

77

77

76

76

75

75

74

74

73

73

72

72

71 - 70

71 70

69

69

68

68

67 - 1

108

67 - 2

67

66 - 1

109

66 - 2

66

63

63

64

64

65

65

61

61

60

60

59

59

106

106

105

105

104

104

58

58

57

57

56

56

55

55

54

54

53 - 52

53 52

51

51

29

29

33

33

32

32

31

31

30

30

34

34

35

35

* (ES 05)

113

* (ES 02)

111

* (ES 01)

110

* (ES 03)

112

* Strategic building with originally no FID

Table 5.2.1 – List of FID revised for the GIS mapping

97


Chapter 5 – DIS CUSSION OF RES ULTS

It can be seen in Tables 5.1.2 - 5.1.14 and was remarked at the end of the previous paragraph that analysis results don’t significantly change varying the earthquake direction, so only maps regarding the actual orientation of the 2012 seismic event (see §5.1) will be presented. In addition, as the INGV (Istituto Nazionale di Geofisica e Vulcanologia) determined that the earthquake

actual

intensity

was

in

the

interval

(source:

http://terremoti.ingv.it/pdf/QUEST_Emilia2012_RapportoFinale.pdf, see Figure 5.2.1), only analysis results related to this interval will be displayed, to be both concise and more adherent to actual damage undergone by the city

Figure 5.2.1 - Intensity map of 20/05/2012 Emilia earthquake

At first a viewing of the mean vulnerability index for CLE buildings is produced. Then mean damage grades and all probabilities then are shown, always displaying on facing pages the same aspect but for increasing intensities. In this way it is possible to have an immediate comparison of how effects will change with a stronger seismic event.

98


Chapter 5 – DIS CUSSION OF RES ULTS

Figure 5.2.2 – Building stock vulnerability map of Concordia sulla Secchia (MO), Italy CLE sub-system

99


Chapter 5 – DIS CUSSION OF RES ULTS

Figure 5.2.3 – Mean damage grade distribution for I (EMS -98) = VII of Concordia sulla Secchia (MO), Italy, CLE sub-system

100


Chapter 5 – DIS CUSSION OF RES ULTS

Figure 5.2.4 – Mean damage grade distribution for I (EMS -98) = VIII of Concordia sulla Secchia (MO), Italy, CLE sub-system

101


Chapter 5 – DIS CUSSION OF RES ULTS

Figure 5.2.5 – Mapping results of collapse probability evaluation for I (EMS -98) = VII of Concordia sulla Secchia (MO), Italy, CLE sub-system

102


Chapter 5 – DIS CUSSION OF RES ULTS

Figure 5.2.6 – Mapping results of collapse probability evaluation for I (EMS -98) = VIII of Concordia sulla Secchia (MO), Italy, CLE sub-system

103


Chapter 5 – DIS CUSSION OF RES ULTS

Figure 5.2.7 – Mapping results of unusable building probability evaluation for I (EMS -98) = VII of Concordia sulla Secchia (MO), Italy, CLE sub-system

104


Chapter 5 – DIS CUSSION OF RES ULTS

Figure 5.2.8 – Mapping results of unusable building probability evaluation for I (EMS -98) = VIII of Concordia sulla Secchia (MO), Italy, CLE sub-system

105


Chapter 5 – DIS CUSSION OF RES ULTS

Figure 5.2.9 – Mapping results of dead and severely injured probability evaluation for I (EMS -98) = VII of Concordia sulla Secchia (MO), Italy, CLE sub-system

106


Chapter 5 – DIS CUSSION OF RES ULTS

Figure 5.2.10 – Mapping results of dead and severely injured probability evaluation for I (EMS -98) = VIII of Concordia sulla Secchia (MO), Italy, CLE sub-system

107


Chapter 5 – DIS CUSSION OF RES ULTS

Figure 5.2.11 – Mapping results of homeless probability evaluation for I (EMS -98) = VII of Concordia sulla Secchia (MO), Italy, CLE sub-system

108


Chapter 5 – DIS CUSSION OF RES ULTS

Figure 5.2.12 – Mapping results of homeless probability evaluation for I (EMS -98) = VIII of Concordia sulla Secchia (MO), Italy, CLE sub-system

109


Chapter 5 – DIS CUSSION OF RES ULTS

5.3

Comparison between predicted and observed damage

The importance of this research resides also in the possibility of testing the accuracy of the method. Indeed, while similar assessments were realized for other cities, mainly in Italy and Portugal (see Vicente et al., 2011, Ferreira et al., 2013, Staniscia S., 2013), they were just predictions as they didn’t have damages data about previous earthquakes to make a comparison. As the Emilia region instead has undergone a seismic event in 2012 and a vast post-seismic survey was commissioned, it was possible for the first time to evaluate the correctness of the method. CLE forms (see Figure 4.4.1 and 4.4.2) report the actual damage description, so at first every qualitative term has been associated to a numerical interval of the mean damage grade

, as shown in Table 5.3.1. OBSERVED DAMAGE DESCRIPTION ABSENT LIGHT MODERATE SEVERE REALLY SEVERE

OBSERVED DAMAGE GRADE INTERVAL 0- 1 1- 2 2- 3 3- 4 4- 5

Table 5.3.1 – Qualitative to quantitative damage description of CLE forms

Respectively in §5.1 and §5.2 the direction and intensity of the seismic event that has struck the city of Concordia sulla Secchia (MO) were identified. Analysis results related to them have so been picked to compare the predicted mean damage grade with the one observed after the shock, as it is shown in Table 5.3.2.

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Chapter 5 – DIS CUSSION OF RES ULTS

FID

STRUCTURAL TYPE

CONSTRUCTIO N PERIO D

OBSERVED DAMAGE DESCRIPTIO N

OBSERVED DAMAGE GRADE INTERVAL

79

R.C.

82 - 91

VERY SEVERE

78

MASONRY

72 - 81

77

R.C.

72 - 81

76

R.C.

75

PREDICTED DAMAGE GRADE I (EMS-98) = 7

I (EMS-98) = 8

4 -5

4.30

4.82

VERY SEVERE

4 -5

2.34

3.32

ABSENT

0 -1

4.19

4.75

72 - 81

MODERATE - SEVERE

2 -4

4.42

4.89

R.C.

92 - 01

ABSENT

0 -1

4.00

4.63

74

R.C.

82 - 91

LIGHT

1 -2

4.44

4.90

73

R.C.

62 - 71

LIGHT

1 -2

4.49

4.94

72

R.C.

72 - 81

VERY SEVERE

4 -5

4.66

5.00

71 - 70

R.C.

72 - 81

VERY SEVERE

4 -5

4.66

5.00

69

R.C.

92 - 01

LIGHT

1 -2

4.13

4.71

68

R.C.

62 - 71

MODERATE - SEVERE

2 -4

4.30

4.82

67 - 1

R.C.

92 - 01

LIGHT

1 -2

4.30

4.82

67 - 2

R.C.

92 - 01

LIGHT

1 -2

4.07

4.67

66 - 1

R.C.

< 1919 + 92 - 01

VERY SEVERE

4 -5

4.66

5.00

66 - 2

R.C.

< 1919 + 92 - 01

VERY SEVERE

4 -5

4.44

4.90

63

MASONRY

72 - 81

VERY SEVERE

4 -5

2.49

3.46

64

MASONRY

92 - 01

VERY SEVERE

4 -5

2.08

3.07

65

R.C.

< 1919

LIGHT

1 -2

4.55

4.97

61

R.C.

19 - 45

VERY SEVERE

4 -5

4.72

5.00

60

R.C.

72 - 81

ABSENT

0 -1

4.10

4.69

59

R.C.

72 - 81

MODERATE - SEVERE

2 -4

4.56

4.98

106

MASONRY

72 - 81

LIGHT

1 -2

2.15

3.14

105

MASONRY

72 - 81

VERY SEVERE

4 -5

2.38

3.35

104

MASONRY

19 - 45

VERY SEVERE

4 -5

2.35

3.33

58

MASONRY

< 1919

MODERATE - SEVERE

2 -4

2.30

3.28

57

MASONRY

< 1919

MODERATE - SEVERE

2 -4

2.44

3.40

56

R.C.

92 - 01

MODERATE - SEVERE

2 -4

4.35

4.85

55

R.C.

82 - 91

MODERATE - SEVERE

2 -4

4.48

4.93

54

R.C.

92 - 01

VERY SEVERE

4 -5

4.58

4.99

53 - 52

R.C.

62 - 71

MODERATE - SEVERE

2 -4

4.53

4.96

51

R.C.

62 - 71

MODERATE - SEVERE

2 -4

4.49

4.94

29

R.C.

46 - 61 + 72 - 81

VERY SEVERE

4 -5

4.58

4.99

33

R.C.

62 - 71

ABSENT

0 -1

4.22

4.77

32

R.C.

19 - 45

ABSENT

0 -1

4.33

4.83

31

R.C.

> 2002

MODERATE - SEVERE

2 -4

4.39

4.88

30

R.C.

46 - 61 + 72 - 81

LIGHT

1 -2

4.48

4.93

34

R.C.

62 - 71

VERY SEVERE

4 -5

4.64

5.00

35

R.C.

92 - 01 + > 2002

ABSENT

0 -1

4.04

4.65

* (ES 05)

R.C.

72 - 81

ABSENT

0 -1

4.17

4.73

* (ES 02)

OT HER

> 2002 (2012)

ABSENT

0 -1

0.02

0.43

* (ES 01)

OT HER

> 2002 (2012)

ABSENT

0 -1

0.02

0.43

* (ES 03)

OT HER

> 2002 (2013)

ABSENT

0 -1

0.02

0.43

* Strategic building with originally no FID

Table 5.3.2 – Comparison between predicted and observed damage grade for CLE sub-system of Concordia sulla Secchia (MO), Italy

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Chapter 5 – DIS CUSSION OF RES ULTS

Table 5.3.1 shows that previsions matched the effective damage only in 14 buildings on 42, with therefore an overall error of 66.67%. Possible reasons for this lack of accuracy could be:  Masonry buildings This structural type is very often built in aggregates, especially in historical city centres like the one under assessment. Effects of a seismic event so could significantly change considering this feature. A possible solution will be explained in the next paragraph.  R.C. buildings As explained in §4.4, the post-seismic survey for this kind of constructions wasn’t detailed enough to completely fill the GNDT-II form. Missing informations were assumed mainly basing on the construction period. Table 5.3.1 reveals however that buildings of the same age can present completely different damage level. It is remarked then the importance of a proper survey to perform an accurate vulnerability assessment. In addition, form itself used for R.C. buildings can be considered “raw”, as it hasn’t been used as much as the masonry one, and has undergone just one revision since 1986 (a new form is stated to be released in 1999 but is still experimental and therefore not available, see: ftp://ftp.ingv.it/pro/gndt/Strumenti/Schede/Schede.htm). Finally, the correlation between the GNDT-II and Macroseismic method (see eq. 27) is only the first proposal: analogously to the one for masonry buildings indeed, following researches can suggest a better interpolation.

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Chapter 5 – DIS CUSSION OF RES ULTS

5.4

Masonry buildings: in-depth analysis

A typical feature of masonry buildings, especially in historical city centres like the one under assessment, is that they are built in “aggregates”. For this reason it can be difficult to understand if two contiguous residential units belong to the same structural system or have to be considered separately. Therefore, a seismic analysis of such structural complexes has to take into account the possible interaction between adjacent buildings.

5.4.1

Effects of aggregates on the vulnerability assessment

Contiguous buildings’ impact during a seismic event was studied by Formisano et al. (2009). They proposed an integration of the original GNDT-II form (that now is considered valid only for detached buildings) with other 5 parameters to describe the positive/negative effects of being in an aggregate. Vulnerability indexes indeed can increase but also decrease, as close by constructions can sometimes work as a “restraint”, mitigating in this way the earthquake effects. A 5 units aggregate of the historical city centre of Sessa Aurunca, in the Italian province of Caserta (CE), was considered as case study (see Figure 5.4.1). Scores and weights of these new parameters have been calibrated through a FEM analysis with the software 3MURI by S.T.A.DATA (see Figure 5.4.2) and are shown in Table 5.4.1. #

PARAMETERS

CLASSES Cv,i

WEIGHT

A

B

C

D

pi

1

Interactions in elevation

-20

0

15

45

1.00

2

Floor plans interactions

-45

-25

-15

0

1.50

3

Presence of offset ceilings

0

15

25

45

0.50

4

Structural of typological heterogeneity

-15

-10

0

45

1.20

5

Percentage difference within facade openings

-20

0

25

45

1.00

Table 5.4.1 – Additional parameters to the GNDT-II forms by Formisano et al. (2009) for masonry buildings in aggregate

In the paper anyway is stated that only a few number of constructions were studied, so while results were considered promising, they need to be validated through numerical and theoretical studies on a larger number of building aggregates.

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Chapter 5 – DIS CUSSION OF RES ULTS

Figure 5.4.1 – Aggregate object of study: a) floor plan; b) building no. 1; c) building no. 2; d) building no. 3; e) building no. 4; f) building no. 5

Figure 5.4.2 – FEM model of the masonry aggregate object if study

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Chapter 5 – DIS CUSSION OF RES ULTS

5.4.2

Proposed correction and validation

While examining the aggregates parameters of the Formisano method, two issues have come to attention:  4 out of 5 parameters have negative scores for one or more classes. In the unlikely but still possible event however that a building is always featured by the lowest vulnerable class (A), the vulnerability index will come out as a negative value too (as the score assigned to all A-classes in the GNDT-II form is equal to zero). This is inconsistent with the definition of

that has to be in the range

, see §2.2.2;

 it is said before that being in an aggregate can increase or lower the vulnerability, but the variation though has not to be excessive. As 5 parameters have been added to the 11 of the original form, a reasonable range should be the in the range

, and this is not

consistent with the actual scores of the Formisano parameters. In the current research then, it has been proposed a revision of both scores and weights, trying to avoid negative values while maintaining as much as possible a similarity with the original method. Suggested form is presented in Table 5.4.2. #

PARAMETERS

CLASSES Cv,i

WEIGHT

A

B

C

D

pi

1

Interactions in elevation

0

15

25

45

1.25

2

Floor plans interactions

0

5

15

45

1.75

3

Presence of offset ceilings

0

25

35

45

0.75

4

Structural of typological heterogeneity

0

10

20

45

1.50

5

Percentage difference within facade openings

0

15

35

45

1.25

Table 5.4.2 – Proposed revision of additional parameters to the GNDT-II forms for masonry buildings in aggregate

It is noticeable from the table above that all modified scores are now in the range like the original ones in the GNDT-II form, while weights have all been increased a little. A comparison between the original and the proposed forms is shown in Table 5.4.3, to display their equivalence.

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Chapter 5 – DIS CUSSION OF RES ULTS

ORIGINAL SCORES AND WEIGHTS

PROPOSED SCORES AND WEIGHTS

A

B

C

D

A

B

C

D

-125.5

-42

30

166.5

0

80

157.5

292.5

Numerical gap between classes * 0

83.5

155.5

Difference with the original gap (%)

292

0

4.38

1.27

0.17

* setting class A as zero value. Table 5.4.3 – Comparison between original and proposed scores and weights of the additional parameters to the GNDT-II form for masonry buildings in aggregate

Vulnerability indexes of the CLE masonry buildings of Concordia sulla Secchia (MO) are then evaluated with the modified parameters stated above. They are shown in Table 5.4.4, comparing them with the original ones to better observe the changes. Filled forms with the aggregate effect are also attached to Annex C. FID

ORIGINAL GNDT-II FORM

AGGREGATE FORM

IX

IY

IX

IY

78

44.44

53.64

48.48

53.33

63

48.03

65.23

53.61

62.96

64

35.93

47.04

43.25

49.21

106

30.82

48.03

22.81

27.49

105

41.38

59.77

53.74

63.43

104

45.14

53.47

45.79

50.38

58

36.02

56.70

32.93

43.84

57

44.44

62.84

37.78

47.47

Table 5.4.4 – Vulnerability indexes of CLE masonry buildings in Concordia sulla Secchia (MO), with and without the aggregate effect

Another possible correction of the applied method could be changing the ductility factor value,

(see eq. 3). In the vulnerability assessment of Concordia sulla Secchia (MO) the

value

was assumed, according to previous works (see Vicente et al., 2011, Ferreira et

al., 2013). The parameter though has been originally defined in the PhD thesis by Giovinazzi S. (2005), where the Author assumed instead the lesser value

116

.


Chapter 5 – DIS CUSSION OF RES ULTS

A new comparison between the predicted and observed damages then has been made. The single and combined effect of corrections proposed above was tested, trying to find in this way the best match. Results are shown in Table 5.4.5, always referring to the actual 2012 earthquake’s direction and intensity range described in §5.1 and §5.2. FID

OBSERVED DAMAGE GRADE INTERVAL

ORIGINAL GNDT-II FO RM

ORIGINAL GNDT-II FO RM

AGGREGATE FO RM

AGGREGATE FO RM

Q =3

Q = 2.3

Q =3

Q = 2.3

I(EMS-98)= 7

I(EMS-98)= 8

I(EMS-98)= 7

I(EMS-98)= 8

I(EMS-98)= 8

I(EMS-98)= 8

I(EMS-98)= 8

I(EMS-98)= 8

78

4-5

2.91

3.81

3.03

4.11

2.97

3.87

3.11

4.20

63

4-5

3.17

4.02

3.36

4.37

3.22

4.07

3.43

4.41

64

4-5

2.64

3.59

2.69

3.88

2.81

3.73

2.90

4.04

106

1-2

2.42

3.39

2.39

3.63

2.06

3.05

1.93

3.21

105

4-5

2.97

3.86

3.11

4.19

3.23

4.07

3.44

4.42

104

4-5

2.92

3.82

3.04

4.14

2.87

3.78

2.98

4.10

58

2–4

2.83

3.74

2.92

4.05

2.53

3.49

2.54

3.76

57

2-4

3.07

3.94

3.24

4.28

2.68

3.62

2.74

3.92

25%

38%

25%

50%

25%

50%

38%

87.5%

MATCHING PERCENTAGE

Table 5.4.5 – Effects of the additional aggregate parameters to the GNDT-II form or/an d variation of the ductility factor in matching the observed damage of masonry buildings

The joint effect of the modified aggregate parameters and the lower ductility factor gives the best results, with 7 building’s on 8 matching the observed damage level for the intensity . A not significant variation is observed though for the lower bound of the range, so it is reasonable to achieve that the actual magnitude of the seismic event that struck Concordia sulla Secchia (MO) was closer to the higher intensity value. It is important to state however, that also in this work masonry buildings haven’t been examined in a significant number. Additional studies on a larger scale are so needed to validate or revise the proposed corrections.

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Chapter 5 – DIS CUSSION OF RES ULTS

5.4.3

Cost-benefit analysis of local strengthening

After assessing the damage undergone by a city after the earthquake, the next significant and logical step would be to study how these effects change with the planning of various strengthening works. Strengthening works can be generally divided in “global” and “local”. This distinction in made basing on how “intrusive” they are, i.e. how big is the extent of the rehabilitation process and how much it changes the structural system. Historical city centres, like the one of Concordia sulla Secchia (MO), are generally formed by masonry buildings that, not only for their cultural and architectural heritage value but mostly for their modest load-bearing capacity, are not suitable for intensive renovations. Local strengthening works then are taken into account. To perform a cost/benefit analysis so, the price of every intervention has been referred to the official Bill of quantities (BOQ), released by the Emilia Romagna region (source: http://bur.regione.emilia-romagna.it/bur/areabollettini/n.120-del-02.08.2011-parte-seconda-1/approvazione-dellaggiornamento-dellelencoprezzi-regionale-per-opere-di-riparazione-e-consolidamento-sismico-di-edifici-esistenti/allega to-elenco-prezzi). Among all possible works the more used ones were picked, and are listed in Table 5.4.6. The choice of interventions however depends on the specific characteristics of buildings considered, so the case study of the current research has to be considered only as an example, and not as a general guideline.

118


Chapter 5 – DIS CUSSION OF RES ULTS ITEM CODE

TYPE OF INTERVENTION

PARAMETER OF THE GNDT-II FORM INFLUENC ED

UNIT

RATE [€]

NOTES

GENERAL MAINTENANCE CONDITIONS (11)

m2

164.58

-

D.06

Repairing of widespread masonry cracks made with injections, net and shotcrete

E.06

Shaping of traces to place the tie rods

m

19.37

E.07

Supply and installation of steel tie rods

kg

9.24

E.08

Supply and installation of holding stakes for tie rods anchorage

kg

7.13

ROOF (9)

They have to be used together

761.83

Demolishing the roof

1019.74

Without demolishing the roof

F.06

Building of a reinforced concrete curb on the top floor

F.09

Building of a curb on the top floor through external wrap with a steel profile

m

Can be realized without removing the roof and, if combined with tie rods, even applied on single walls

F.22

Connecting the existing wooden ceiling to the load-bearing masonry walls

each

Stiff but badly connected wooden ceilings

F.24

Consolidation of the existing flat plank wood floor overlaying it with a new one

F.25

Consolidation of the flat plank wood floor or brick ceiling, both with timber framing, building a reinforced concrete slab

F.27

Consolidation of the existing mixed ceiling (concrete - bricks) building a reinforced concrete slab

m2

m2 HORIZONTAL DIAPHRAGM S (5)

m2

2

m

Deformable and badly connected wooden ceilings. Remarkable difference in weight (attention in particular with poor quality masonry) and stiffness between the two methods Deformable and badly connected R.C. ceilings. Attention to the weight increase in poor quality masonry

Table 5.4.6 – Typical strengthening works in masonry buildings

Main structural issues of masonry constructions in the city centre of Concordia sulla Secchia (MO) are specifically linked to:  lack of a curb or tie rods on the top floor;  widespread presence of cracks in walls. While the second one can be easily fixed, the first on the contrary present some difficulties, for the lack of working space due the contiguity of buildings. A curb in R.C. or with a steel profile has in fact to be made on the whole perimeter of the unit to work properly, but in an aggregate one or more sides of the construction could result inaccessible. A non definitive but possible alternative so could be using the “curb - tie rods” mixed technique that can be applied only on two facing walls and not the necessarily entire building (source: http://jargo.itim.mi.cnr.it/pubblicazioni/Volume3/PP-ALLEGATI/6-3B2-ANALISITECNICHE-INTERVENTO-I-PARTE.pdf). 119


Chapter 5 – DIS CUSSION OF RES ULTS

The “curb - tie rod” is a sort of tie beam that, matched with a metallic profile, is able to absorb the horizontal loads of a roof. It can be done without removing the roof so can be considered as a local or not intrusive strengthening work. For this reason, if on one hand it has a limited effect as the steel curb doesn’t redistribute the roof loads on masonry walls that therefore have to carry the same weight, on the other it does not alter in a negative way the resistance mechanism of the building. This type of intervention is also reversible, even if in not plastered buildings it can have an high visual impact thus requires a minimal maintenance (rustpreventive treatment). Figures 5.4.3, 5.4.4, 5.4.5 and 5.4.6 show technical details of the “curb - tie rod” technique, along with the assembling process (source: http://www.comune.bagnodiromagna.fc.it/upload/ RUE_Bagno/ALLEGATI/2A3%20Miglioramento%20del%20comportamento%20sismico%2 0dei%20Complessi%20Stori/NORME%20allegato%202a3%20miglioramento%20del%20co mportamento%20sismico.pdf).

Figure 5.4.3 – “Curb - tie rod” technique: external isometric view

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Chapter 5 – DIS CUSSION OF RES ULTS

Figure 5.4.4 – “Curb - tie rod” technique: internal isometric view

Figure 5.4.5 – “Curb - tie rod” technique: assembly section

121


Chapter 5 – DIS CUSSION OF RES ULTS

Figure 5.4.6 – “Curb - tie rod” technique: holding stake isometric view and details

This technique has been applied then to all masonry buildings under assessment, as well as consolidating injections for the widespread presence of masonry cracks. A cost estimate of the works is displayed in Tables 5.4.7, 5.4.8 and 5.4.9. TRACK LAYING S HAPES

FID

HOLDING S TAKES

TIE RODS

FOR ANCHORAGE

TOTAL

[€/m]

[m]

[€]

[€/kg]

[kg]

[€]

[€/kg]

[kg]

[€]

78

19.37

69

1336.53

9.24

170

1572.22

7.13

160

1140.80

€ 4049.55

63

19.37

50

968.50

9.24

123

1139.29

7.13

160

1140.80

€ 3248.59

64

19.37

22

426.14

9.24

54

501.29

7.13

40

285.20

€ 1212.63

106

19.37

134

2595.58

9.24

330

3053.30

7.13

300

2139.00

€ 7787.88

105

19.37

113

2188.81

9.24

279

2574.80

7.13

320

2281.60

€ 7045.21

104

19.37

33

639.21

9.24

81

751.93

7.13

80

570.40

€ 1961.54

58

19.37

117

2266.29

9.24

289

2665.94

7.13

280

1996.40

€ 6928.63

57

19.37

140

2711.80

9.24

345

3190.02

7.13

320

2281.60

€ 8183.42

TOTAL COS T OF WORK

€ 40417.46

Table 5.4.7 - Cost estimate of tie rods positioning for CLE masonry buildings of Concordia sulla Secchia (MO), Italy

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Chapter 5 – DIS CUSSION OF RES ULTS

FID

STEEL CURB [€/m]

[m]

[€]

78

64.9

54

3504.60

63

64.9

32

2076.80

64

64.9

15

973.50

106

64.9

71

4607.90

105

64.9

99

6425.10

104

64.9

20

1298.00

58

64.9

65

4218.50

57

64.9

61

3958.90

TOTAL COST OF WORK

€ 27063.30

Table 5.4.8 - Cost estimate of steel curbs supply for CLE masonry buildings of Concordia sulla Secchia (MO), Italy

FID

CRACKS REPAIRING [€/m2]

[m2]

[€]

78

164.58

170.71

28095.45

63

164.58

134.22

22089.93

64

164.58

51.19

8424.85

106

164.58

90.21

14846.76

105

164.58

238.63

39273.73

104

164.58

103.52

17037.32

58

164.58

144.68

23811.43

57

164.58

260.43

42861.57

TOTAL COST OF WORK

€ 196441.04

Table 5.4.9 - Cost estimate of cracks repairing for CLE masonry buildings of Concordia sulla Secchia (MO), Italy

Finally the cost-benefit analysis is carried out: at first vulnerability indexes are re-evaluated considering the effect of single interventions and then their association on the vulnerability indexes and the mean damage grade, always referring to the actual intensity of the 2012 earthquake (see §5.2). Note: filled GNDT-II forms taking into account the strengthening works are attached to Annex D.

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Chapter 5 – DIS CUSSION OF RES ULTS

EFFECTS OF S TRENGHTEN ING WORKS ON VULN ERABILITY INDEX FID

INITIAL

CURB - TIE RO D

CONSOLIDATING INJECTIO NS

CURB - TIE RO D + INJECTIO NS

IX

IY

IX

IY

ΔIX ( %)

ΔIY ( %)

IX

IY

ΔIX ( %)

ΔIY ( %)

IX

IY

ΔIX ( %)

ΔIY ( %)

78

44.44

53.64

42.15

51.34

5.17

4.29

30.65

39.85

31.03

25.71

28.35

37.55

36.21

30.00

63

48.03

65.23

45.88

63.08

4.48

3.30

35.14

52.33

26.87

19.78

32.97

50.18

31.34

23.08

64

35.93

47.04

32.96

44.07

8.25

6.30

22.59

33.70

37.11

28.35

19.63

19.63

45.36

34.65

106

30.82

48.03

28.67

37.28

6.98

5.45

29.39

37.99

4.65

3.64

27.24

27.24

11.36

9.09

105

41.38

59.77

39.08

57.47

5.56

3.85

27.59

45.98

33.33

23.08

25.29

25.29

38.89

26.92

104

45.14

53.47

42.36

50.69

6.15

5.19

32.64

40.97

27.69

23.38

29.86

29.86

33.85

28.57

58

36.02

56.70

33.72

54.41

6.38

4.05

22.22

42.91

38.30

24.32

19.92

19.92

44.68

28.38

57

44.44

62.84

42.15

60.54

5.17

3.66

30.65

49.04

31.03

21.95

28.35

28.35

36.21

25.61

6.02

4.51

ΔImean (%)

28.75

21.28

ΔImean (%)

34.77

25.79

ΔImean (%) W/O FID 106

32.20

23.80

ΔImean (%) W/O FID 106

38.08

28.17

ΔImean (%)

TO TAL COST O FWORK

€ 67.481

TO TAL COST O FWORK

€ 196.441

TO TAL COST O FWORK

€ 263.922

MEAN COST (PER UNIT)

€ 8.435

MEAN COST (PER UNIT)

€ 24.555

MEAN COST (PER UNIT)

€ 32.990

Table 5.4.10 – Effects of strengthening works on the vulnerability indexes of CLE masonry buildings of Concordia sulla Secchia (MO), Italy EFFECTS OF S TRENGHTEN ING WORKS ON MEAN DAMAGE GRAD E INITIAL

CURB - TIE RO D

µD

FID

µD

CONSOLIDATING INJECTIO NS

ΔµD (%)

µD

CURB - TIE RO D + INJECTIO NS

ΔµD (%)

µD

ΔµD (%)

I=7

I=8

I=7

I=8

I=7

I=8

I=7

I=8

I=7

I=8

I=7

I=8

EMS98

EMS98

EMS98

EMS98

EMS98

EMS98

EMS98

EMS98

EMS98

EMS98

EMS98

EMS98

I=7 EMS98

I=8 EMS98

78

2.91

3.81

2.83

3.75

2.76

1.75

2.42

3.39

16.74

11.06

2.34

3.32

19.53

13.02

63

3.17

4.02

3.10

3.97

2.28

1.42

2.73

3.66

13.95

9.00

2.65

3.60

16.32

10.61

64

2.64

3.59

2.54

3.50

3.97

2.57

2.17

3.16

17.77

11.98

2.07

3.06

21.64

14.76

106

2.42

3.39

2.34

3.32

3.15

2.07

2.36

3.34

2.10

1.38

2.29

3.27

5.25

3.46

105

2.97

3.86

2.89

3.80

2.66

1.68

2.49

3.45

16.13

10.63

2.41

3.38

18.83

12.51

104

2.92

3.82

2.82

3.74

3.34

2.11

2.47

3.44

15.13

9.94

2.38

3.35

18.50

12.29

58

2.83

3.74

2.75

3.68

2.81

1.79

2.35

3.32

16.89

11.26

2.27

3.25

19.68

13.23

57

3.07

3.94

3.00

3.88

2.54

1.59

2.60

3.55

15.51

10.13

2.52

3.47

18.12

11.93

2.94

1.87

ΔImean (%)

14.28

9.42

ΔImean (%)

17.23

11.48

ΔImean (%)

16.02

10.57

ΔImean (%) W/O FID 106

18.95

12.62

ΔImean (%)

W/O FID 106 TO TAL COST O FWORK

€ 67.481

TO TAL COST O FWORK

€ 196.441

TO TAL COST O FWORK

€ 263.922

MEAN COST (PER UNIT)

€ 8.435

MEAN COST (PER UNIT)

€ 24.555

MEAN COST (PER UNIT)

€ 32.990

Table 5.4.11 – Effects of strengthening works on the mean damage grade of CLE masonry buildings of Concordia sulla Secchia (MO), Italy

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The “curb - tie rod” technique cost is relatively modest but it has also a limited impact, with an average -5% on the vulnerability index, and approximately -2% on the mean damage grade. This is caused by the higher importance given by the GNDT-II form to the roof tendency to spread (full, partial, none) rather than the presence/absence of a curb on the top floor. This is not consistent with the actual effect a curb and/or tie rods have on the structural response. It is generally acknowledged indeed that these works can significantly improve the resistance of a building during a seismic event. For this reason the GNDT-II form needs to revise this element, as at the current state it only lowers the vulnerability to the “B” class. Repairing the masonry cracks instead has a cost more or less three times higher than the former work, but has also a far more significant impact. An average -25% on vulnerability indexes is noticed (-28% leaving out the FID 106 building, which is the only one with a good maintenance condition) and slightly less than -12% (-13.3% without FID 106) on the mean damage grade. Combination of the two interventions finally leads to an average -30% on the vulnerability index (-33% without FID 106) and approximately -14% (-16%) on the mean damage grade. Again, it is important to remark that the analysis above is highly dependent on the specific issues of buildings under assessment. Others constructions with different structural deficiencies cold definitely lead to dissimilar results. We can conclude however then local strengthening works can lead only to minor, but still quite significant, changes on the buildings’ vulnerability. In any case they remain the only possible option in listed buildings, status shared by a large number of masonry constructions in Italy, but are generally advisable also in all cases for their low complexity and relatively modest price. With the same fixed budget indeed they can be applied to a larger number of units than more complex works.

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CHAPTER 6 - CONCLUS IONS

Chapter 6

CONCLUSIONS

6.1

Summary and conclusions

The aim of the current research was to make a step forward in the seismic risk assessment at urban scale. A new way of viewing a settlement was proposed, that combines city-planning concepts with the system reliability theory. For the first time also, predicted damage scenarios could be compared to the real ones observed after a seismic event, and the impact of strengthening works in the resilience enhancement was studied. From the analysis of results, it is possible to draw the following conclusions:  GNDT-II method has the indeed ambitious purpose of defining the vulnerability of buildings in an accurate and rapid way. Even if a certain level of error is considered acceptable, it needs to undergo more revisions. In particular: Masonry buildings Forms have to redefine the weight of the “Conventional Strength” parameter, giving an higher influence on

to the change of earthquake direction. The lack of accuracy on

matching the observed damages then has been fixed considering the aggregate effect. Even 127


CHAPTER 6 - CONCLUS IONS

if the results are promising, only 8 buildings were examined, suggesting the need for a wider sample. R.C. buildings The prediction accuracy was definitely affected by the inadequate level of detail of the post-seismic survey. GNDT-II forms however don’t seem either as reliable as masonry one, and no previous research where they had been used was found. The correlation presented between

for this structural type also is just the first proposal. It will surely

be improved by future works, in analogy with the one for masonry buildings.  an innovative aspect is surely the theoretical and mathematical definition of the reliability for an urban system in various limit conditions. It is possible to display so the settlement response under a catastrophic event in a simple and immediate way through a unique value. Still in the case study of Concordia sulla Secchia (MO) only the CLE sub-system was studied, so future researches will have to investigate also other limit conditions;  microzonation data have then been applied for the first time in a vulnerability assessment. The purpose in fact was not only to increase the accuracy of the method, but also to remark how important it is to take into account local effects such as amplification or damping, that can have a significant impact during a seismic event also in small cities like Concordia sulla Secchia (MO). Summarizing, the current work can’t be considered of course as conclusive within the study of seismic risk assessments, but it has surely made important additional steps to get to a complete and accurate method.

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6.2

Future developments

In addition to all the improvements and revisions listed in the paragraph above, a further aim of future researches would be to include also all other elements that form a settlement. Some preliminary studies of this kind have already been done. In particular:  steel buildings, see the form released by the NDMA (National Disaster Management Authority, India, source: http://www.ndma.gov.in/images/disaster/earthquake/10b%20Steel _Survey_Form.pdf) or the work by Bermúdez et al. (2008);  timber structures, see Parisi et al. (2008), Park and von de Lindt (2009) and Murta et al. (2010);  dams, whose breakage would have dramatic effects in cities with an average elevation below or really close the sea level. The consequent flooding indeed would not only cause additional damages but also severely slow down all emergency procedures. See Tosun et al. (2006), Singh et al. (2011) and Pagano and Sica (2012);  pipelines, see Manshoori M. R. (2011), Fatma Zohra H., Mahmuod B. and Luc D. (2012), Lanzano G., Salzano E., Santucci de Magistris F. and Fabbrocino G. (2013) and Chen Y., Niu Z., Bai J. and Wang Y. (2014);  connection routes, see D’Andrea et al. (2005), Cirianni et al. (2008) and Khademi et al. (2015);  bridges, as their breakage or just temporary interruption of usage could prevent the access to the city of rescue vehicles (ambulances and fire trucks) as well as the inhabitants evacuation from it. See Lazzali and Farsi (2009), Galy et al. (2012) and Kibboua et al. (2013). The main and most important objective however is always to make as many comparisons as possible between predicted and observed damage. A damage scenario indeed is effective during the emergency phase or to help the planning of strengthening works solely and exclusively if it is consistent with the reality. The issue of this kind of research on the other hand relies in the impossibility of “testing” the seismic response of a city. The only way is to wait for earthquakes to occur, that unfortunately bring also with them severe damages and casualties.

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130


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Annex A

GNDT-II ORIGINAL FORMS

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142


ANNEX B

Annex B

GNDT-II FILLED FORMS FOR CLE BUILDINGS OF CONCORDIA SULLA SECCHIA (MO), ITALY

143


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144


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145


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146


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147


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ANNEX C

Annex C

GNDT-II FILLED FORMS FOR CLE MASONRY BUILDINGS OF CONCORDIA SULLA SECCHIA (MO), ITALY AS AGGREGATES

177


ANNEX C

178


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ANNEX D

Annex D

GNDT-II FILLED FORMS FOR CLE MASONRY BUILDINGS OF CONCORDIA SULLA SECCHIA (MO), ITALY WITH LOCAL STRENGTHENING

183


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Annex E

SEISMIC MICROZONATION MAP OF CONCORDIA SULLA SECCHIA (MO), ITALY

197


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198


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199


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200


ANNEX F

Annex F

MATLAB SCRIPT

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202


ANNEX F % SEISMIC VULNERABILITY ASSESSMENT OF AN URBAN SYSTEM clear all close all clc %-------------------------------------------------------------------------% % 1. LOAD DATA load data_CLE.txt % CLE = limit condition of EMERGENCY (series) % CLV = limit condition of LIFE SAFETY (series-parallel) % CLD = limit condition of DAMAGE (series-parallel) Ix=data_CLE(:,1); Iy=data_CLE(:,2); alfadeg=data_CLE(:,3); % conversion degrees in radians alfarad=alfadeg.*(pi/180); IDstructure=data_CLE(:,4); % 0 = masonry % 1 = r.c. % 2 = others (steel, mixed structures) Fa=data_CLE(:,5); % ag amplification factor (seismic micro-zonation) Cu=data_CLE(:,6); % importance factor (Tab. 2.4.II NTC'08) Noccupants=data_CLE(:,7); % number of occupants for each building %-------------------------------------------------------------------------% % 2. VULNERABILITY ELLIPSES % 2.1 Pre-allocation x=zeros(length(Ix),360); y=zeros(length(Ix),360); X=zeros(length(Ix),360); Y=zeros(length(Ix),360); Ialfa=zeros(length(Ix),360); % 2.2 Ellipses for j=1:length(Ix) for k=1:360 a=Ix(j); b=Iy(j); theta=linspace(0,2*pi,360); x(j,k)=a.*cos(theta(k)); y(j,k)=b.*sin(theta(k)); % x, y, NOT rotated ellipse's points X(j,k)=x(j,k)*cos(alfarad(j))-y(j,k)*sin(alfarad(j)); Y(j,k)=x(j,k)*sin(alfarad(j))+y(j,k)*cos(alfarad(j)); % X, Y, alfa-rotated ellipse's points Ialfa(j,k)=sqrt((X(j,k).^2)+(Y(j,k).^2)); end end

203


ANNEX F % 2.3 Definition of a general reference system % % % %

It is necessary to "rearrange" the ellipses after the rotation, so that in every row the first column (0째) represents the vulnerability value associated to that angle (as the angle of rotation is different for every ellipse, they all have different reference system)

% Pre-allocation I=zeros(length(Ix),1); for u=1:length(Ix) I(u)=find(X(u,:)==max(X(u,find(Y(u,:)>-1 & Y(u,:)<1)))); %#ok<FNDSB> X(u,:)=[X(u,I(u):end),X(u,1:I(u)-1)]; Y(u,:)=[Y(u,I(u):end),Y(u,1:I(u)-1)]; end % 2.4 Referring a vulnerability index for every alfa angle % IMPORTANT: the simulation considers every alfa angle (0째- 360째) starting % from the positive horizontal axis and moving CLOCKWISE for m=1:length(Ix) for h=1:360 Ialfa(m,h)=sqrt((X(m,h).^2)+(Y(m,h).^2)); end end % IMPORTANT: matrix Ialfa % rows = # building % columns = vulnerability index (GNDT-II) for angles 0-360째 % 2.5 Plotting ellipses (optional) % % % % % % % %

t=1; figure(1) for u=1:size(x,1) subplot(6,7,t) plot(x(u,:),y(u,:)), hold on plot(X1(u,:),Y1(u,:),'r'), axis equal t=t+1; end

%-------------------------------------------------------------------------% % 3. CORRELATION BETWEEN VULNERABILITY INDEX AND VULNERABILITY % (GNDT II) (EMS-98) % 3.1 Pre-allocation Valfa=zeros(length(Ix),360); % 3.2 Correlation for m=1:length(Ix) for h=1:360 if IDstructure(m)==0; Valfa(m,h)=0.592+0.0057.*Ialfa(m,h); elseif IDstructure(m)==1; Valfa(m,h)=0.8568+0.0083.*Ialfa(m,h)0.00003874608.*(Ialfa(m,h).^2); elseif IDstructure(m)==2;

204


ANNEX F Valfa(m,h)=0.24; end end end % IMPORTANT: matrix Valfa % rows = # building % columns = vulnerability (EMS-98) for angles 0-360° % % % % % % %

MASONRY buildings (IDstructure = 0) V=0.592+0.0057*Ialfa R.C. buildings (IDstructure = 1) V=0.8568-0.0083*Ialfa-0.00003874608*(Ialfa.^2) STEEL or MIXED STRUCTURE buildings (IDstructure = 2) V=0.24 IMPORTANT: vulnerability class F (EMS-98) hasn't been taken into account

%-------------------------------------------------------------------------% % 4. MEAN DAMAGE GRADE % 4.1 Pre-allocation f=zeros(length(Ix),360); muD_I5=zeros(length(Ix),360); muD_I6=zeros(length(Ix),360); muD_I7=zeros(length(Ix),360); muD_I8=zeros(length(Ix),360); muD_I9=zeros(length(Ix),360); muD_I10=zeros(length(Ix),360); muD_I11=zeros(length(Ix),360); muD_I12=zeros(length(Ix),360); % 4.2 Assessment of the mean damage grade for each intensity level % IMPORTANT: matrix muD_In % n = intensity value (5-12) % rows = # building % columns = muD for angles 0-360° % to plot a FRAGILITY curve for the "x" building in the "y"-angle take the % [x y] point in each muD_In matrix % IMPORTANT: the MARGOTTINI correlation between ag-I has been considered %-------------------------------------------------------------------------% % I=5 --> ag=0.04 for j=1:length(Ix) for h=1:360 I(j)=5+((log10((Fa(j)*0.04)/0.04)/log10(1.65))); % Change-of-base of the logarithm % % % % %

if I<=7 f(j,h)=exp((Valfa(j,h)/2)*(I-7)); elseif I>7 f(j,h)=1; end 205


ANNEX F % %

f is a function introduced to fit better the curves for lower intensity values (I<7)

muD_I5(j,h)=(2.5+3*tanh((I(j)+(6.25*Valfa(j,h))13.1)/3))*exp((Valfa(j,h)/2)*(5-7)); muD_I5(j,h)=max(min(muD_I5(j,h),5),0); % muD is defined between 0 and 5 end end %-------------------------------------------------------------------------% % I=6 --> ag=0.066 for j=1:length(Ix) for h=1:360 I(j)=5+((log10((Fa(j)*0.066)/0.04)/log10(1.65))); % Change-of-base of the logarithm % % % % % % %

if I<=7 f(j,h)=exp((Valfa(j,h)/2)*(I-7)); elseif I>7 f(j,h)=1; end f is a function introduced to fit better the curves for lower intensity values (I<7)

muD_I6(j,h)=(2.5+3*tanh((I(j)+(6.25*Valfa(j,h))13.1)/3))*exp((Valfa(j,h)/2)*(6-7)); muD_I6(j,h)=max(min(muD_I6(j,h),5),0); % muD is defined between 0 and 5 end end %-------------------------------------------------------------------------% %I=7 --> ag=0.1089 for j=1:length(Ix) for h=1:360 I(j)=5+((log10((Fa(j)*0.1089)/0.04)/log10(1.65))); % Change-of-base of the logarithm muD_I7(j,h)=(2.5+3*tanh((I(j)+(6.25*Valfa(j,h))-13.1)/3)); muD_I7(j,h)=max(min(muD_I7(j,h),5),0); % muD is defined between 0 and 5 end end %-------------------------------------------------------------------------% 206


ANNEX F % I=8 --> ag=0.1797 for j=1:length(Ix) for h=1:360 I(j)=5+((log10((Fa(j)*0.1797)/0.04)/log10(1.65))); % Change-of-base of the logarithm muD_I8(j,h)=(2.5+3*tanh((I(j)+(6.25*Valfa(j,h))-13.1)/3)); muD_I8(j,h)=max(min(muD_I8(j,h),5),0); % muD is defined between 0 and 5 end end %-------------------------------------------------------------------------% % I=9 --> ag=0.2965 for j=1:length(Ix) for h=1:360 I(j)=5+((log10((Fa(j)*0.2965)/0.04)/log10(1.65))); % Change-of-base of the logarithm muD_I9(j,h)=(2.5+3*tanh((I(j)+(6.25*Valfa(j,h))-13.1)/3)); muD_I9(j,h)=max(min(muD_I9(j,h),5),0); % muD is defined between 0 and 5 end end %-------------------------------------------------------------------------% % I=10 --> ag=0.4892 for j=1:length(Ix) for h=1:360 I(j)=5+((log10((Fa(j)*0.4892)/0.04)/log10(1.65))); % Change-of-base of the logarithm muD_I10(j,h)=(2.5+3*tanh((I(j)+(6.25*Valfa(j,h))-13.1)/3)); muD_I10(j,h)=max(min(muD_I10(j,h),5),0); % muD is defined between 0 and 5 end end %-------------------------------------------------------------------------% % I=11 --> ag=0.8072 for j=1:length(Ix)

207


ANNEX F

for h=1:360 I(j)=5+((log10((Fa(j)*0.8072)/0.04)/log10(1.65))); % Change-of-base of the logarithm muD_I11(j,h)=(2.5+3*tanh((I(j)+(6.25*Valfa(j,h))-13.1)/3)); muD_I11(j,h)=max(min(muD_I11(j,h),5),0); % muD is defined between 0 and 5 end end %-------------------------------------------------------------------------% % I=12 --> ag=1.3318 for j=1:length(Ix) for h=1:360 I(j)=5+((log10((Fa(j)*1.3318)/0.04)/log10(1.65))); % Change-of-base of the logarithm muD_I12(j,h)=(2.5+3*tanh((I(j)+(6.25*Valfa(j,h))-13.1)/3)); muD_I12(j,h)=max(min(muD_I12(j,h),5),0); % muD is defined between 0 and 5 end end %-------------------------------------------------------------------------% % 5. DAMAGE DISTRIBUTION PROBABILITIES ESTIMATION % A probabilistic approach is used based on the BETA DENSITY FUNCTION % IMPORTANT: for EACH muD in EACH direction, 6 probabilities are defined % P(D0), P(D1), P(D2), P(D3), P(D4), P(D5) % IMPORTANT: matrix Prob_In % n = intensity value (5-12) % rows = P(D0) for the 1st row of muD_In % P(D1) " " % P(D2) " " % P(D3) " " % P(D4) " " % P(D5) " " % zeros (to separate the values) % P(Di) , i=0:5, for the 2nd row of muD_In % zeros % ecc. % columns = P(Di) for angles 0-360° %-------------------------------------------------------------------------% % I=5 Prob_I5=zeros(length(Ix)*6+length(Ix)-1,360);

208


ANNEX F

j=0; for k=1:7:length(Ix)*6+length(Ix)-1 j=j+1; for h=1:360 if muD_I5(j,h)==5 Prob_I5(k,h)=0; Prob_I5(k+1,h)=0; Prob_I5(k+2,h)=0; Prob_I5(k+3,h)=0; Prob_I5(k+4,h)=0; Prob_I5(k+5,h)=1; elseif muD_I5(j,h)==0 % the building has no damage Prob_I5(k,h)=1; Prob_I5(k+1,h)=0; Prob_I5(k+2,h)=0; Prob_I5(k+3,h)=0; Prob_I5(k+4,h)=0; Prob_I5(k+5,h)=0; else % intermediate values of muD

Prob_I5(k,h)=trapz(linspace(0,0.1),betapdf(linspace(0,0.1),8*(muD_I5(j,h)/5 ),8-(8*(muD_I5(j,h)/5)))); Prob_I5(k+1,h)=trapz(linspace(0.1,0.3),betapdf(linspace(0.1,0.3),8*(muD_I5( j,h)/5),8-(8*(muD_I5(j,h)/5)))); Prob_I5(k+2,h)=trapz(linspace(0.3,0.5),betapdf(linspace(0.3,0.5),8*(muD_I5( j,h)/5),8-(8*(muD_I5(j,h)/5)))); Prob_I5(k+3,h)=trapz(linspace(0.5,0.7),betapdf(linspace(0.5,0.7),8*(muD_I5( j,h)/5),8-(8*(muD_I5(j,h)/5)))); Prob_I5(k+4,h)=trapz(linspace(0.7,0.9),betapdf(linspace(0.7,0.9),8*(muD_I5( j,h)/5),8-(8*(muD_I5(j,h)/5)))); Prob_I5(k+5,h)=trapz(linspace(0.9,1),betapdf(linspace(0.9,1),8*(muD_I5(j,h) /5),8-(8*(muD_I5(j,h)/5)))); if Prob_I5(k,h)==Inf Prob_I5(k,h)=1-sum(Prob_I5(k+1:k+5,h)); elseif Prob_I5(k+5,h)==Inf Prob_I5(k+5,h)=1-sum(Prob_I5(k:k+4,h)); end % Correction for Inf values (sum(Prob_In)=1) end

209


ANNEX F end end %-------------------------------------------------------------------------% % I=6 Prob_I6=zeros(length(Ix)*6+length(Ix)-1,360); j=0; for k=1:7:length(Ix)*6+length(Ix)-1 j=j+1; for h=1:360 if muD_I6(j,h)==5 % the collapse is certain Prob_I6(k,h)=0; Prob_I6(k+1,h)=0; Prob_I6(k+2,h)=0; Prob_I6(k+3,h)=0; Prob_I6(k+4,h)=0; Prob_I6(k+5,h)=1; elseif muD_I6(j,h)==0 % the building has no damage Prob_I6(k,h)=1; Prob_I6(k+1,h)=0; Prob_I6(k+2,h)=0; Prob_I6(k+3,h)=0; Prob_I6(k+4,h)=0; Prob_I6(k+5,h)=0; else % intermediate values of muD

Prob_I6(k,h)=trapz(linspace(0,0.1),betapdf(linspace(0,0.1),8*(muD_I6(j,h)/5 ),8-(8*(muD_I6(j,h)/5)))); Prob_I6(k+1,h)=trapz(linspace(0.1,0.3),betapdf(linspace(0.1,0.3),8*(muD_I6( j,h)/5),8-(8*(muD_I6(j,h)/5)))); Prob_I6(k+2,h)=trapz(linspace(0.3,0.5),betapdf(linspace(0.3,0.5),8*(muD_I6( j,h)/5),8-(8*(muD_I6(j,h)/5)))); Prob_I6(k+3,h)=trapz(linspace(0.5,0.7),betapdf(linspace(0.5,0.7),8*(muD_I6( j,h)/5),8-(8*(muD_I6(j,h)/5)))); Prob_I6(k+4,h)=trapz(linspace(0.7,0.9),betapdf(linspace(0.7,0.9),8*(muD_I6( j,h)/5),8-(8*(muD_I6(j,h)/5)))); Prob_I6(k+5,h)=trapz(linspace(0.9,1),betapdf(linspace(0.9,1),8*(muD_I6(j,h) /5),8-(8*(muD_I6(j,h)/5))));

210


ANNEX F if Prob_I6(k,h)==Inf Prob_I6(k,h)=1-sum(Prob_I6(k+1:k+5,h)); elseif Prob_I6(k+5,h)==Inf Prob_I6(k+5,h)=1-sum(Prob_I6(k:k+4,h)); end % Correction for Inf values (sum(Prob_In)=1) end end end %-------------------------------------------------------------------------% % I=7 Prob_I7=zeros(length(Ix)*6+length(Ix)-1,360); j=0; for k=1:7:length(Ix)*6+length(Ix)-1 j=j+1; for h=1:360 if muD_I7(j,h)==5 % the collapse is certain Prob_I7(k,h)=0; Prob_I7(k+1,h)=0; Prob_I7(k+2,h)=0; Prob_I7(k+3,h)=0; Prob_I7(k+4,h)=0; Prob_I7(k+5,h)=1; elseif muD_I7(j,h)==0 % the building has no damage Prob_I7(k,h)=1; Prob_I7(k+1,h)=0; Prob_I7(k+2,h)=0; Prob_I7(k+3,h)=0; Prob_I7(k+4,h)=0; Prob_I7(k+5,h)=0; else % intermediate values of muD

Prob_I7(k,h)=trapz(linspace(0,0.1),betapdf(linspace(0,0.1),8*(muD_I7(j,h)/5 ),8-(8*(muD_I7(j,h)/5)))); Prob_I7(k+1,h)=trapz(linspace(0.1,0.3),betapdf(linspace(0.1,0.3),8*(muD_I7( j,h)/5),8-(8*(muD_I7(j,h)/5)))); Prob_I7(k+2,h)=trapz(linspace(0.3,0.5),betapdf(linspace(0.3,0.5),8*(muD_I7( j,h)/5),8-(8*(muD_I7(j,h)/5))));

211


ANNEX F

Prob_I7(k+3,h)=trapz(linspace(0.5,0.7),betapdf(linspace(0.5,0.7),8*(muD_I7( j,h)/5),8-(8*(muD_I7(j,h)/5)))); Prob_I7(k+4,h)=trapz(linspace(0.7,0.9),betapdf(linspace(0.7,0.9),8*(muD_I7( j,h)/5),8-(8*(muD_I7(j,h)/5)))); Prob_I7(k+5,h)=trapz(linspace(0.9,1),betapdf(linspace(0.9,1),8*(muD_I7(j,h) /5),8-(8*(muD_I7(j,h)/5)))); if Prob_I7(k,h)==Inf Prob_I7(k,h)=1-sum(Prob_I7(k+1:k+5,h)); elseif Prob_I7(k+5,h)==Inf Prob_I7(k+5,h)=1-sum(Prob_I7(k:k+4,h)); end % Correction for Inf values (sum(Prob_In)=1) end end end % %------------------------------------------------------------------------% % % I=8 Prob_I8=zeros(length(Ix)*6+length(Ix)-1,360); j=0; for k=1:7:length(Ix)*6+length(Ix)-1 j=j+1; for h=1:360 if muD_I8(j,h)==5 % the collapse is certain Prob_I8(k,h)=0; Prob_I8(k+1,h)=0; Prob_I8(k+2,h)=0; Prob_I8(k+3,h)=0; Prob_I8(k+4,h)=0; Prob_I8(k+5,h)=1; elseif muD_I8(j,h)==0 % the building has no damage Prob_I8(k,h)=1; Prob_I8(k+1,h)=0; Prob_I8(k+2,h)=0; Prob_I8(k+3,h)=0; Prob_I8(k+4,h)=0; Prob_I8(k+5,h)=0; else

212


ANNEX F % intermediate values of muD

Prob_I8(k,h)=trapz(linspace(0,0.1),betapdf(linspace(0,0.1),8*(muD_I8(j,h)/5 ),8-(8*(muD_I8(j,h)/5)))); Prob_I8(k+1,h)=trapz(linspace(0.1,0.3),betapdf(linspace(0.1,0.3),8*(muD_I8( j,h)/5),8-(8*(muD_I8(j,h)/5)))); Prob_I8(k+2,h)=trapz(linspace(0.3,0.5),betapdf(linspace(0.3,0.5),8*(muD_I8( j,h)/5),8-(8*(muD_I8(j,h)/5)))); Prob_I8(k+3,h)=trapz(linspace(0.5,0.7),betapdf(linspace(0.5,0.7),8*(muD_I8( j,h)/5),8-(8*(muD_I8(j,h)/5)))); Prob_I8(k+4,h)=trapz(linspace(0.7,0.9),betapdf(linspace(0.7,0.9),8*(muD_I8( j,h)/5),8-(8*(muD_I8(j,h)/5)))); Prob_I8(k+5,h)=trapz(linspace(0.9,1),betapdf(linspace(0.9,1),8*(muD_I8(j,h) /5),8-(8*(muD_I8(j,h)/5)))); if Prob_I8(k,h)==Inf Prob_I8(k,h)=1-sum(Prob_I8(k+1:k+5,h)); elseif Prob_I8(k+5,h)==Inf Prob_I8(k+5,h)=1-sum(Prob_I8(k:k+4,h)); end % Correction for Inf values (sum(Prob_In)=1) end end end % %------------------------------------------------------------------------% % % I=9 Prob_I9=zeros(length(Ix)*6+length(Ix)-1,360); j=0; for k=1:7:length(Ix)*6+length(Ix)-1 j=j+1; for h=1:360 if muD_I9(j,h)==5 % the collapse is certain Prob_I9(k,h)=0; Prob_I9(k+1,h)=0; Prob_I9(k+2,h)=0; Prob_I9(k+3,h)=0; Prob_I9(k+4,h)=0; Prob_I9(k+5,h)=1; elseif muD_I9(j,h)==0 213


ANNEX F % the building has no damage Prob_I9(k,h)=1; Prob_I9(k+1,h)=0; Prob_I9(k+2,h)=0; Prob_I9(k+3,h)=0; Prob_I9(k+4,h)=0; Prob_I9(k+5,h)=0; else % intermediate values of muD

Prob_I9(k,h)=trapz(linspace(0,0.1),betapdf(linspace(0,0.1),8*(muD_I9(j,h)/5 ),8-(8*(muD_I9(j,h)/5)))); Prob_I9(k+1,h)=trapz(linspace(0.1,0.3),betapdf(linspace(0.1,0.3),8*(muD_I9( j,h)/5),8-(8*(muD_I9(j,h)/5)))); Prob_I9(k+2,h)=trapz(linspace(0.3,0.5),betapdf(linspace(0.3,0.5),8*(muD_I9( j,h)/5),8-(8*(muD_I9(j,h)/5)))); Prob_I9(k+3,h)=trapz(linspace(0.5,0.7),betapdf(linspace(0.5,0.7),8*(muD_I9( j,h)/5),8-(8*(muD_I9(j,h)/5)))); Prob_I9(k+4,h)=trapz(linspace(0.7,0.9),betapdf(linspace(0.7,0.9),8*(muD_I9( j,h)/5),8-(8*(muD_I9(j,h)/5)))); Prob_I9(k+5,h)=trapz(linspace(0.9,1),betapdf(linspace(0.9,1),8*(muD_I9(j,h) /5),8-(8*(muD_I9(j,h)/5)))); if Prob_I9(k,h)==Inf Prob_I9(k,h)=1-sum(Prob_I9(k+1:k+5,h)); elseif Prob_I9(k+5,h)==Inf Prob_I9(k+5,h)=1-sum(Prob_I9(k:k+4,h)); end % Correction for Inf values (sum(Prob_In)=1) end end end % %------------------------------------------------------------------------% % % I=10 Prob_I10=zeros(length(Ix)*6+length(Ix)-1,360); j=0; for k=1:7:length(Ix)*6+length(Ix)-1 j=j+1; for h=1:360 if muD_I10(j,h)==5 214


ANNEX F % the collapse is certain Prob_I10(k,h)=0; Prob_I10(k+1,h)=0; Prob_I10(k+2,h)=0; Prob_I10(k+3,h)=0; Prob_I10(k+4,h)=0; Prob_I10(k+5,h)=1; elseif muD_I10(j,h)==0 % the building has no damage Prob_I10(k,h)=1; Prob_I10(k+1,h)=0; Prob_I10(k+2,h)=0; Prob_I10(k+3,h)=0; Prob_I10(k+4,h)=0; Prob_I10(k+5,h)=0; else % intermediate values of muD

Prob_I10(k,h)=trapz(linspace(0,0.1),betapdf(linspace(0,0.1),8*(muD_I10(j,h) /5),8-(8*(muD_I10(j,h)/5)))); Prob_I10(k+1,h)=trapz(linspace(0.1,0.3),betapdf(linspace(0.1,0.3),8*(muD_I1 0(j,h)/5),8-(8*(muD_I10(j,h)/5)))); Prob_I10(k+2,h)=trapz(linspace(0.3,0.5),betapdf(linspace(0.3,0.5),8*(muD_I1 0(j,h)/5),8-(8*(muD_I10(j,h)/5)))); Prob_I10(k+3,h)=trapz(linspace(0.5,0.7),betapdf(linspace(0.5,0.7),8*(muD_I1 0(j,h)/5),8-(8*(muD_I10(j,h)/5)))); Prob_I10(k+4,h)=trapz(linspace(0.7,0.9),betapdf(linspace(0.7,0.9),8*(muD_I1 0(j,h)/5),8-(8*(muD_I10(j,h)/5)))); Prob_I10(k+5,h)=trapz(linspace(0.9,1),betapdf(linspace(0.9,1),8*(muD_I10(j, h)/5),8-(8*(muD_I10(j,h)/5)))); if Prob_I10(k,h)==Inf Prob_I10(k,h)=1-sum(Prob_I10(k+1:k+5,h)); elseif Prob_I10(k+5,h)==Inf Prob_I10(k+5,h)=1-sum(Prob_I10(k:k+4,h)); end % Correction for Inf values (sum(Prob_In)=1) end end end % %------------------------------------------------------------------------% % % I=11 Prob_I11=zeros(length(Ix)*6+length(Ix)-1,360);

215


ANNEX F

j=0; for k=1:7:length(Ix)*6+length(Ix)-1 j=j+1; for h=1:360 if muD_I11(j,h)==5 % the collapse is certain Prob_I11(k,h)=0; Prob_I11(k+1,h)=0; Prob_I11(k+2,h)=0; Prob_I11(k+3,h)=0; Prob_I11(k+4,h)=0; Prob_I11(k+5,h)=1; elseif muD_I11(j,h)==0 % the building has no damage Prob_I11(k,h)=1; Prob_I11(k+1,h)=0; Prob_I11(k+2,h)=0; Prob_I11(k+3,h)=0; Prob_I11(k+4,h)=0; Prob_I11(k+5,h)=0; else % intermediate values of muD

Prob_I11(k,h)=trapz(linspace(0,0.1),betapdf(linspace(0,0.1),8*(muD_I11(j,h) /5),8-(8*(muD_I11(j,h)/5)))); Prob_I11(k+1,h)=trapz(linspace(0.1,0.3),betapdf(linspace(0.1,0.3),8*(muD_I1 1(j,h)/5),8-(8*(muD_I11(j,h)/5)))); Prob_I11(k+2,h)=trapz(linspace(0.3,0.5),betapdf(linspace(0.3,0.5),8*(muD_I1 1(j,h)/5),8-(8*(muD_I11(j,h)/5)))); Prob_I11(k+3,h)=trapz(linspace(0.5,0.7),betapdf(linspace(0.5,0.7),8*(muD_I1 1(j,h)/5),8-(8*(muD_I11(j,h)/5)))); Prob_I11(k+4,h)=trapz(linspace(0.7,0.9),betapdf(linspace(0.7,0.9),8*(muD_I1 1(j,h)/5),8-(8*(muD_I11(j,h)/5)))); Prob_I11(k+5,h)=trapz(linspace(0.9,1),betapdf(linspace(0.9,1),8*(muD_I11(j, h)/5),8-(8*(muD_I11(j,h)/5)))); if Prob_I11(k,h)==Inf Prob_I11(k,h)=1-sum(Prob_I11(k+1:k+5,h)); elseif Prob_I11(k+5,h)==Inf Prob_I11(k+5,h)=1-sum(Prob_I11(k:k+4,h)); end % Correction for Inf values (sum(Prob_In)=1) end

216


ANNEX F

end end %-------------------------------------------------------------------------% % % I=12 Prob_I12=zeros(length(Ix)*6+length(Ix)-1,360); j=0; for k=1:7:length(Ix)*6+length(Ix)-1 j=j+1; for h=1:360 if muD_I12(j,h)==5 % the collapse is certain Prob_I12(k,h)=0; Prob_I12(k+1,h)=0; Prob_I12(k+2,h)=0; Prob_I12(k+3,h)=0; Prob_I12(k+4,h)=0; Prob_I12(k+5,h)=1; elseif muD_I12(j,h)==0 % the building has no damage Prob_I12(k,h)=1; Prob_I12(k+1,h)=0; Prob_I12(k+2,h)=0; Prob_I12(k+3,h)=0; Prob_I12(k+4,h)=0; Prob_I12(k+5,h)=0; else % intermediate values of muD

Prob_I12(k,h)=trapz(linspace(0,0.1),betapdf(linspace(0,0.1),8*(muD_I12(j,h) /5),8-(8*(muD_I12(j,h)/5)))); Prob_I12(k+1,h)=trapz(linspace(0.1,0.3),betapdf(linspace(0.1,0.3),8*(muD_I1 2(j,h)/5),8-(8*(muD_I12(j,h)/5)))); Prob_I12(k+2,h)=trapz(linspace(0.3,0.5),betapdf(linspace(0.3,0.5),8*(muD_I1 2(j,h)/5),8-(8*(muD_I12(j,h)/5)))); Prob_I12(k+3,h)=trapz(linspace(0.5,0.7),betapdf(linspace(0.5,0.7),8*(muD_I1 2(j,h)/5),8-(8*(muD_I12(j,h)/5)))); Prob_I12(k+4,h)=trapz(linspace(0.7,0.9),betapdf(linspace(0.7,0.9),8*(muD_I1 2(j,h)/5),8-(8*(muD_I12(j,h)/5)))); Prob_I12(k+5,h)=trapz(linspace(0.9,1),betapdf(linspace(0.9,1),8*(muD_I12(j, h)/5),8-(8*(muD_I12(j,h)/5)))); 217


ANNEX F

if Prob_I12(k,h)==Inf Prob_I12(k,h)=1-sum(Prob_I12(k+1:k+5,h)); elseif Prob_I12(k+5,h)==Inf Prob_I12(k+5,h)=1-sum(Prob_I12(k:k+4,h)); end % Correction for Inf values (sum(Prob_In)=1) end end end %-------------------------------------------------------------------------% % 5.1 Counting of probabilities associated with each damage grade PD0=zeros(8,360); PD1=zeros(8,360); PD2=zeros(8,360); PD3=zeros(8,360); PD4=zeros(8,360); PD5=zeros(8,360); PD0(1,:)=((sum(Prob_I5(1:7:length(Ix)*6+length(Ix)1,:),1))./length(Ix)).*100; PD0(2,:)=((sum(Prob_I6(1:7:length(Ix)*6+length(Ix)1,:),1))./length(Ix)).*100; PD0(3,:)=((sum(Prob_I7(1:7:length(Ix)*6+length(Ix)1,:),1))./length(Ix)).*100; PD0(4,:)=((sum(Prob_I8(1:7:length(Ix)*6+length(Ix)1,:),1))./length(Ix)).*100; PD0(5,:)=((sum(Prob_I9(1:7:length(Ix)*6+length(Ix)1,:),1))./length(Ix)).*100; PD0(6,:)=((sum(Prob_I10(1:7:length(Ix)*6+length(Ix)1,:),1))./length(Ix)).*100; PD0(7,:)=((sum(Prob_I11(1:7:length(Ix)*6+length(Ix)1,:),1))./length(Ix)).*100; PD0(8,:)=((sum(Prob_I12(1:7:length(Ix)*6+length(Ix)1,:),1))./length(Ix)).*100; PD1(1,:)=((sum(Prob_I5(2:7:length(Ix)*6+length(Ix)1,:),1))./length(Ix)).*100; PD1(2,:)=((sum(Prob_I6(2:7:length(Ix)*6+length(Ix)1,:),1))./length(Ix)).*100; PD1(3,:)=((sum(Prob_I7(2:7:length(Ix)*6+length(Ix)1,:),1))./length(Ix)).*100; PD1(4,:)=((sum(Prob_I8(2:7:length(Ix)*6+length(Ix)1,:),1))./length(Ix)).*100; PD1(5,:)=((sum(Prob_I9(2:7:length(Ix)*6+length(Ix)1,:),1))./length(Ix)).*100; PD1(6,:)=((sum(Prob_I10(2:7:length(Ix)*6+length(Ix)1,:),1))./length(Ix)).*100; PD1(7,:)=((sum(Prob_I11(2:7:length(Ix)*6+length(Ix)1,:),1))./length(Ix)).*100; PD1(8,:)=((sum(Prob_I12(2:7:length(Ix)*6+length(Ix)1,:),1))./length(Ix)).*100;

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ANNEX F PD2(1,:)=((sum(Prob_I5(3:7:length(Ix)*6+length(Ix)1,:),1))./length(Ix)).*100; PD2(2,:)=((sum(Prob_I6(3:7:length(Ix)*6+length(Ix)1,:),1))./length(Ix)).*100; PD2(3,:)=((sum(Prob_I7(3:7:length(Ix)*6+length(Ix)1,:),1))./length(Ix)).*100; PD2(4,:)=((sum(Prob_I8(3:7:length(Ix)*6+length(Ix)1,:),1))./length(Ix)).*100; PD2(5,:)=((sum(Prob_I9(3:7:length(Ix)*6+length(Ix)1,:),1))./length(Ix)).*100; PD2(6,:)=((sum(Prob_I10(3:7:length(Ix)*6+length(Ix)1,:),1))./length(Ix)).*100; PD2(7,:)=((sum(Prob_I11(3:7:length(Ix)*6+length(Ix)1,:),1))./length(Ix)).*100; PD2(8,:)=((sum(Prob_I12(3:7:length(Ix)*6+length(Ix)1,:),1))./length(Ix)).*100; PD3(1,:)=((sum(Prob_I5(4:7:length(Ix)*6+length(Ix)1,:),1))./length(Ix)).*100; PD3(2,:)=((sum(Prob_I6(4:7:length(Ix)*6+length(Ix)1,:),1))./length(Ix)).*100; PD3(3,:)=((sum(Prob_I7(4:7:length(Ix)*6+length(Ix)1,:),1))./length(Ix)).*100; PD3(4,:)=((sum(Prob_I8(4:7:length(Ix)*6+length(Ix)1,:),1))./length(Ix)).*100; PD3(5,:)=((sum(Prob_I9(4:7:length(Ix)*6+length(Ix)1,:),1))./length(Ix)).*100; PD3(6,:)=((sum(Prob_I10(4:7:length(Ix)*6+length(Ix)1,:),1))./length(Ix)).*100; PD3(7,:)=((sum(Prob_I11(4:7:length(Ix)*6+length(Ix)1,:),1))./length(Ix)).*100; PD3(8,:)=((sum(Prob_I12(4:7:length(Ix)*6+length(Ix)1,:),1))./length(Ix)).*100; PD4(1,:)=((sum(Prob_I5(5:7:length(Ix)*6+length(Ix)1,:),1))./length(Ix)).*100; PD4(2,:)=((sum(Prob_I6(5:7:length(Ix)*6+length(Ix)1,:),1))./length(Ix)).*100; PD4(3,:)=((sum(Prob_I7(5:7:length(Ix)*6+length(Ix)1,:),1))./length(Ix)).*100; PD4(4,:)=((sum(Prob_I8(5:7:length(Ix)*6+length(Ix)1,:),1))./length(Ix)).*100; PD4(5,:)=((sum(Prob_I9(5:7:length(Ix)*6+length(Ix)1,:),1))./length(Ix)).*100; PD4(6,:)=((sum(Prob_I10(5:7:length(Ix)*6+length(Ix)1,:),1))./length(Ix)).*100; PD4(7,:)=((sum(Prob_I11(5:7:length(Ix)*6+length(Ix)1,:),1))./length(Ix)).*100; PD4(8,:)=((sum(Prob_I12(5:7:length(Ix)*6+length(Ix)1,:),1))./length(Ix)).*100; PD5(1,:)=((sum(Prob_I5(6:7:length(Ix)*6+length(Ix)1,:),1))./length(Ix)).*100; PD5(2,:)=((sum(Prob_I6(6:7:length(Ix)*6+length(Ix)1,:),1))./length(Ix)).*100; PD5(3,:)=((sum(Prob_I7(6:7:length(Ix)*6+length(Ix)1,:),1))./length(Ix)).*100; PD5(4,:)=((sum(Prob_I8(6:7:length(Ix)*6+length(Ix)1,:),1))./length(Ix)).*100; PD5(5,:)=((sum(Prob_I9(6:7:length(Ix)*6+length(Ix)1,:),1))./length(Ix)).*100;

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ANNEX F PD5(6,:)=((sum(Prob_I10(6:7:length(Ix)*6+length(Ix)1,:),1))./length(Ix)).*100; PD5(7,:)=((sum(Prob_I11(6:7:length(Ix)*6+length(Ix)1,:),1))./length(Ix)).*100; PD5(8,:)=((sum(Prob_I12(6:7:length(Ix)*6+length(Ix)1,:),1))./length(Ix)).*100; % 5.2 Estimation of collapsed and unusable buildings Wub3=0.4; Wub4=0.6; % see "Bramerini et al. 1995" Pcollapse=PD5; percentage Ncollpase=round((Pcollapse.*length(Ix))./100); (rounded) Punusable_buildings=PD3.*Wub3+PD4.*Wub4; percentage Nunusable_buildings=round((Punusable_buildings.*length(Ix))./100); (rounded)

% % number % % number

% 5.3 Estimation of casulaties, severly injured and homelessness Pdead_severely_injured=0.3.*PD5; % percentage Ndead_severely_injured=round((Pdead_severely_injured.*sum(Noccupants))./100 ); % number (rounded) Phomeless=PD3.*Wub3+PD4.*Wub4+PD5.*0.7; % percentage Nhomeless=round((Phomeless.*sum(Noccupants))./100); % number (rounded) %-------------------------------------------------------------------------% % 6. RELIABILITY ASSESSMENT OF THE URBAN SYSTEM % Limit condition of EMERGENCY --> SERIES system % - buildings with class of usage I or II (interfering) % Pfailure=P(D4)+P(D5) % - buildings with class of usage III or IV (strategic) % Pfailure=P(D2)+P(D3)+P(D4)+P(D5) % 6.1 Preallocation PCLE_I5=zeros(length(Ix),360); PCLE_I6=zeros(length(Ix),360); PCLE_I7=zeros(length(Ix),360); PCLE_I8=zeros(length(Ix),360); PCLE_I9=zeros(length(Ix),360); PCLE_I10=zeros(length(Ix),360); PCLE_I11=zeros(length(Ix),360); PCLE_I12=zeros(length(Ix),360); PCLE=zeros(8,360); % 6.2 Reliability of single buildings for each intensity value for j=1:length(Ix) if Cu(j)==0.7 || Cu(j)==1

220


ANNEX F PCLE_I5(j,:)=1-sum(Prob_I5(7*(j-1)+5:7*(j-1)+6,:),1); PCLE_I6(j,:)=1-sum(Prob_I6(7*(j-1)+5:7*(j-1)+6,:),1); PCLE_I7(j,:)=1-sum(Prob_I7(7*(j-1)+5:7*(j-1)+6,:),1); PCLE_I8(j,:)=1-sum(Prob_I8(7*(j-1)+5:7*(j-1)+6,:),1); PCLE_I9(j,:)=1-sum(Prob_I9(7*(j-1)+5:7*(j-1)+6,:),1); PCLE_I10(j,:)=1-sum(Prob_I10(7*(j-1)+5:7*(j-1)+6,:),1); PCLE_I11(j,:)=1-sum(Prob_I11(7*(j-1)+5:7*(j-1)+6,:),1); PCLE_I12(j,:)=1-sum(Prob_I12(7*(j-1)+5:7*(j-1)+6,:),1); elseif Cu(j)==1.5 || Cu(j)==2 PCLE_I5(j,:)=1-sum(Prob_I5(7*(j-1)+3:7*(j-1)+6,:),1); PCLE_I6(j,:)=1-sum(Prob_I6(7*(j-1)+3:7*(j-1)+6,:),1); PCLE_I7(j,:)=1-sum(Prob_I7(7*(j-1)+3:7*(j-1)+6,:),1); PCLE_I8(j,:)=1-sum(Prob_I8(7*(j-1)+3:7*(j-1)+6,:),1); PCLE_I9(j,:)=1-sum(Prob_I9(7*(j-1)+3:7*(j-1)+6,:),1); PCLE_I10(j,:)=1-sum(Prob_I10(7*(j-1)+3:7*(j-1)+6,:),1); PCLE_I11(j,:)=1-sum(Prob_I11(7*(j-1)+3:7*(j-1)+6,:),1); PCLE_I12(j,:)=1-sum(Prob_I12(7*(j-1)+3:7*(j-1)+6,:),1); end end % 6.3 Reliability of the system for each intensity value PCLE(1,:)=prod(PCLE_I5).*100; PCLE(2,:)=prod(PCLE_I6).*100; PCLE(3,:)=prod(PCLE_I7).*100; PCLE(4,:)=prod(PCLE_I8).*100; PCLE(5,:)=prod(PCLE_I9).*100; PCLE(6,:)=prod(PCLE_I10).*100; PCLE(7,:)=prod(PCLE_I11).*100; PCLE(8,:)=prod(PCLE_I12).*100; % IMPORTANT: PCLE is the reliability of the urban system for the limit % condition of EMERGENCY and it is assesed for % - each intensity value (5:8, rows) % - each direction of the earthquake (1:360, columns) %-------------------------------------------------------------------------%

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Profile for Tema Grafico

Alberto Basaglia - Ingegnere Civile - Tesi 2015  

Seismic risk assessment and resilience enhancement at urban scale. The hystorical city centre of Concordia sulla Secchia (MO) - Italy.

Alberto Basaglia - Ingegnere Civile - Tesi 2015  

Seismic risk assessment and resilience enhancement at urban scale. The hystorical city centre of Concordia sulla Secchia (MO) - Italy.

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