Seismic vulnerability of reinforced concrete buildings ... - IKEE

ARISTOTLE UNIVERSITY OF THESSALONIKI SCHOOL OF ENGINEERING – DEPARTMENT OF CIVIL ENGINEERING

DIVISION OF GEOTECHNICAL ENGINEERING

SOTIRIA T. KARAPETROU Civi l Engineer, MSc

SEISMIC VULNERABILITY OF REINFORCED CONCRETE

BUILDINGS CONSIDERING AGING AND SOIL-STRUCTURE

INTERACTION EFFECTS

DOCTORAL THESIS

THESSALONIKI 2015

SOTIRIA T. KARAPETROU

SEISMIC VULNERABILITY OF REINFORCED CONCRETE BUILDINGS

CONSIDERING AGING AND SOIL-STRUCTURE INTERACTION EFFECTS

DOCTORAL THESIS

Submitted to the Department of Civil Engineering, Division of Geotechnical Engineering,

Laboratory of Soil Mechanics, Foundations & Geotechnical Earthquake Engineering

Date of defense: 27 November 2015 Examining Committee: Prof. K. Pitilakis, Supervisor Prof. M. Dolce, Member of the Advisory Committee Assist. Prof. D. Pitilakis, Member of the Advisory Committee Prof. G. Manos, Examiner Prof. Dr. S. Parolai, Examiner Assoc. Prof. D. Raptakis, Examiner Assist. Prof. A. Anastasiadis, Examiner

© Sotiria T. Karapetrou © AUTh Seismic vulnerability of reinforced concrete buildings considering aging and soil-structure interaction effects ISBN

‘Acceptance of this Doctoral Thesis by the Department of Civil Engineering of Aristotle University Thessaloniki does not imply acceptance of the opinions of the author’ (Law 5343/1932, article 202, par. 2)

ACKNOWLEDGMENTS

This thesis owes its existence to the help, support and inspiration of several people. First and

foremost I would like to express my sincere gratitude to my supervisor Prof. Kyriazis Pitilakis,

for the continuous support and guidance of my Ph.D. study and related research. I would like

to thank him for providing me the opportunity to work with challenging topics with large

amounts of independence and initiative. I am also grateful he offered me the opportunity to

participate in large European research projects he was scientifically in charge of. This gave me

the privilege to meet and collaborate with important researchers in the field of earthquake

engineering and seismology.

I sincerely thank my advisory committee: Prof. Mauro Dolce for his interest in my work and his

insightful comments and suggestions raising important points which helped me to improve it;

Assist. Prof. Dimitris Pitilakis for the scientific guidance and for sharing his insights with me on

the different issues investigated in my thesis.

I would also like to thank my examiners: Prof. George Manos for taking the time to review this

thesis and for providing constructive and pointed comments; Prof. Stefano Parolai for very

thoroughly revising my work and for our instructive collaboration during these years in the

frame of significant European research projects; Assoc. Prof. Dimitris Raptakis for his interest

in my work and our many discussions over several scientific issues of engineering and

seismological interest; Assist. Prof. Anastasios Anastasiadis for carefully reading my

manuscript and for his support and encouragement.

The work described in this thesis was financially supported by the European research projects

REAKT (2011-2014) “Strategies and tools of Real Time Earthquake Risk Reduction” and NERA

(2012-2014) “Network of European Research Infrastructures for Earthquake Risk Assessment

and Mitigation”. This support is gratefully acknowledged. The additional one-year fund from

AUTh Research committee is also greatly appreciated.

Special thanks go to my friends and colleagues from AUTh: Dr. Stavroula Fotopoulou, Dr.

Maria Manakou, Dr. Grigorios Tsinidis, Dr. Zafeiria Roumelioti, Dr. Anna Karatzetzou, Dr. Evi

Riga, Dr. Sotiris Argyroudis, Dr. Achileas Pistolas, Stella Karafragka, Aggelos Tsinaris, Dr.

Kostas Trevlopoulos and Anastasia Argyroudi for their support and help during the last four

years. I also thank Argyro Fillipa, Despoina Lamprou, Sofia Kotsiri, Katerina Tsagdi, Kelly

Valaouri, Ioannis Thomaidis, Evaggelia Yfantidou, Dimitra Giannoula and Ioannis-Prodromos

Thomaidis for our cooperation during their Master Theses in the frame of the postgraduate

program in Earthquake Engineering and Seismic Design of Structures.

Last but not least I would like to express my heart-felt gratitude to my husband Yannis for his

endless support and encouragement during this journey. None of this would have been

possible without his love and patience. This thesis is dedicated to him.

Sotiria T. Karapetrou

SUMMARY

The reliable vulnerability assessment of existing structures and infrastructures is a

prerequisite for seismic loss estimation, risk mitigation and management. At present, the

seismic vulnerability assessment of reinforced concrete (RC) buildings is made

considering fixed base conditions; moreover, the mechanical properties of the building

remain intact in time. In this research it is investigated whether these two fundamental

hypotheses are sound as aging and soil-structure interaction (SSI) effects might play a

crucial role in the seismic fragility analysis of RC structures. Stemming from the general

lack of seismic vulnerability studies for RC buildings that take into consideration the

effects of progressive deterioration and soil-structure interaction, one of the most

significant challenges of the present research is the quantification of an analytical

methodology to estimate the seismic vulnerability of RC buildings considering aging and

SSI effects.

To demonstrate the methodology for the time-dependent vulnerability assessment,

seven RC moment resisting frames, designed according to different seismic code levels,

are selected as case studies. The consideration of aging is achieved by including

probabilistic models of chloride induced corrosion deterioration of the RC elements within

the vulnerability assessment framework. Different corrosion aspects are considered in the

analysis including the loss of reinforcement cross-sectional area, the degradation of

concrete cover and the reduction of steel ultimate deformation. Two-dimensional

incremental dynamic analysis (IDA) is performed to assess the seismic performance of

the initial uncorroded and corroded RC moment resisting frame structures. The time-

dependent fragility functions are derived in terms of the spectral acceleration at the

fundamental mode of the structure Sa(T1, 5%) for the immediate occupancy and collapse

prevention limit states. Results show an overall increase in seismic vulnerability over

time due to corrosion highlighting the important influence of deterioration due to aging

effects on the structural behavior.

A further challenge of the present thesis is to investigate whether SSI and site effects

may affect the seismic performance and vulnerability of RC moment resisting frame

buildings and consequently modify the fragility curves. SSI is modeled applying the direct

one-step approach considering either linear elastic or nonlinear soil behavior while site

effects are inherently accounted for. To further examine the contribution of site and SSI

effects, a two-step uncoupled approach is also applied, which takes into account site

effects on the response of the fixed base structure, but neglects SSI effects. Additional

analyses are performed investigating the influence of the soil depth and stratigraphy

under nonlinear soil behavior on the seismic response and fragility of RC buildings.

Fragility curves are derived as a function of rock outcropping peak ground acceleration

for the immediate occupancy and collapse prevention limit states for the fixed base and

SSI models based on the statistical exploitation of the results of incremental dynamic

analysis of the given structural systems. Results show the significant role of SSI and site

effects under linear or nonlinear soil behavior in altering the expected structural

performance and fragility of fixed base structures.

In the context of seismic vulnerability assessment of RC buildings, the use of field

monitoring data constitutes a significant tool for the representation of the actual

structural state, reducing uncertainties associated with the building configuration

properties as well as many non-physical parameters (age, maintenance, etc.), enhancing

thus the reliability in the risk assessment procedure. In the present thesis, the seismic

vulnerability of existing RC buildings is evaluated, combining through a comprehensive

methodology, the numerical analysis and field monitoring data. The proposed

methodology is highlighted through the derivation of “time-building specific” fragility

curves for an eight-storey RC structure (hospital building), built almost five decades ago,

that is composed by two adjacent units separated through a structural joint. The

assessment of the dynamic characteristics is performed using ambient noise

measurements. The modal identification results are used to update and better constrain

the initial finite element model of the building, which is based on the available design and

construction documentation plans. Three-dimensional incremental dynamic analysis is

performed to derive the fragility curves for the initial as built model (“building-specific”)

and for the real structures as they are nowadays (“time-building specific”). The initial

“building specific” curves are evaluated through their comparison with conventional

generic curves that are commonly used in risk assessment studies. Moreover, in order to

enhance the reliability of the obtained results, the “time-building specific” fragility curves,

are compared to time-dependent curves derived for the hospital units adopting an

appropriate for the specific case study corrosion scenario. Results derived from both

approaches indicate that the consideration of the actual state of structures may

significantly alter their expected seismic performance leading to higher vulnerability

values.

Sotiria Karapetrou – Doctoral Thesis

CONTENTS

Contents ................................................................................................... i List of Figures ....................................................................................... vii List of Tables ....................................................................................... xxv Chapter 1 ................................................................................................ 1

Introduction ............................................................................................. 1 1.1 Statement of the problem ................................................................. 1 1.2 Objectives and scope of the research .................................................. 3 1.3 Outline of the Thesis ........................................................................ 3 Chapter 2 ................................................................................................ 7

Literature review on the seismic vulnerability assessment of RC buildings ......... 7 2.1 Introduction .................................................................................... 7 2.2 Background ..................................................................................... 7 2.3 Prerequisites for the derivation of fragility functions ............................ 11

2.3.1 Taxonomy/typology/classification ............................................................... 11

2.3.2 Intensity measures ................................................................................... 16

2.3.3 Damage indicators and states .................................................................... 18

2.3.3.1. Local damage indices .................................................................... 21

2.3.3.2. Global damage indices .................................................................. 25

2.3.3.3. Damage measures ....................................................................... 28

2.3.3.4. Drift damage formulation .............................................................. 29

2.3.4 Treatment of uncertainties ......................................................................... 33

2.4 Methodologies for deriving seismic fragility functions ........................... 36

2.4.1 Derivation of fragility functions based on analytical methods ........................... 38

2.4.1.1. Capacity Spectrum Method (CSM) .................................................. 40

2.4.1.2. Nonlinear dynamic analysis ........................................................... 42

2.4.1.3. Factors affecting the reliability of analytical fragility functions ............. 44

2.5 Review of previous studies .............................................................. 45 2.6 SYNER-G: The fragility function manager .......................................... 48 2.7 Current challenges in seismic vulnerability assessment of RC buildings .. 51 2.8 Evolution of building vulnerability over time ....................................... 52

2.8.1 Mechanisms acting on structural performance during lifetime .......................... 52

CONTENTS ii


2.8.2 Aging effects: Corrosion of reinforcement .................................................... 53

2.8.2.1. Chloride induced corrosion mechanism ............................................ 53

2.8.2.2. Probabilistic modeling of chloride induced corrosion initiation .............. 56

2.8.2.3. Evaluation of corrosion rate ........................................................... 59

2.8.3 Effects of chloride induced corrosion on seismic performance and fragility of RC

buildings ................................................................................................. 61

2.9 Evaluation of soil-structure interaction and site effects on seismic vulnerability ........................................................................................... 66

2.9.1 Dynamic soil-structure interaction ............................................................... 66

2.9.2 Evaluation of soil-structure interaction and site effects on seismic structural

response and vulnerability ......................................................................... 67

2.10 Building-specific fragility curves using field monitoring data ............... 69 Chapter 3 .............................................................................................. 73

Reference buildings and vulnerability assessment methodology ..................... 73 3.1 Introduction .................................................................................. 73 3.2 Description of the methodological framework ..................................... 73 3.3 Selection of the reference fixed base - intact frame buildings ............... 75

3.3.1 MRF buildings designed with no seismic code provisions ................................. 75

3.3.2 MRF buildings designed with low seismic code provisions ................................ 77

3.3.3 MRF buildings designed with high seismic code provisions .............................. 79

3.4 Finite element modeling in OpenSees ................................................ 81

3.4.1 Infill modeling .......................................................................................... 84

3.5 Selection of the seismic input motion ................................................ 86 3.6 Incremental dynamic analysis IDA .................................................... 88

3.6.1 Performing IDA ........................................................................................ 88

3.6.2 Limit damage states ................................................................................. 93

3.7 Derivation of fragility functions ........................................................ 95

3.7.1 Fragility curves of the fixed base, bare frame structures ................................ 99

3.7.2 Comparison of infilled - bare frame structures ............................................ 102

3.8 Comparison of the derived fragility curves with literature curves .......... 104

3.8.1 Bare MRF buildings ................................................................................. 105

3.8.1.1. Bare MRFs with no seismic code provisions .................................... 105

3.8.1.2. Bare MRFs with low seismic code provisions ................................... 109

3.8.1.3. Bare MRFs with high seismic code provisions .................................. 113

3.8.2 Regularly and irregularly infilled MRF buildings ........................................... 119

3.8.2.1. Infilled MRFs with no seismic code provisions ................................. 119

CONTENTS iii


3.8.2.2. Infilled MRFs with low seismic code provisions ................................ 121

3.8.2.3. Infilled MRFs with high seismic code provisions ............................... 123

3.8.3 Discussion ............................................................................................. 125

Chapter 4 ............................................................................................ 127

Time-dependent fragility functions for RC buildings ..................................... 127 4.1 Introduction ................................................................................. 127 4.2 Aging effects: Chloride induced corrosion ......................................... 127

4.2.1 Corrosion initiation time .......................................................................... 128

4.2.2 Deterioration modeling due to corrosion .................................................... 130

4.3 Pushover analysis ......................................................................... 134 4.4 Comparative dynamic analysis ........................................................ 136 4.5 Incremental dynamic analysis ......................................................... 142 4.6 Definition of damage states ............................................................ 144 4.7 Time-dependent fragility curves ...................................................... 145

4.7.1 Fixed base bare frame structures .............................................................. 147

4.7.2 Fixed base infilled frame structures ........................................................... 152

4.8 Time-variant quadratic model for the fragility parameters ................... 154 4.9 Discussion and concluding remarks .................................................. 157 Chapter 5 ............................................................................................ 159

Seismic vulnerability assessment of RC buildings considering soil-structure interaction effects .................................................................................. 159 5.1 Introduction ................................................................................. 159 5.2 Description of the parametric investigation ....................................... 160

5.2.1 Selection of prototype buildings ................................................................ 160

5.2.2 Soil-structure interaction (SSI) modeling ................................................... 161

5.2.2.1. Soil constitutive model ................................................................ 166

5.2.3 Parametric study .................................................................................... 169

5.2.3.1. Effect of SSI and site effects under nonlinear soil behavior ............... 169

5.2.3.2. Effect of soil depth and stratigraphy under nonlinear soil behavior ..... 170

5.3 Comparative dynamic analysis ........................................................ 171 5.4 Derivation of fragility curves ........................................................... 183

5.4.1 Comparison of SSI - fixed based structures under linear soil behavior ............ 186

5.4.2 Effect of SSI and site effects under linear and nonlinear soil behavior ............ 187

5.4.3 Effect of soil depth and stratigraphy under nonlinear soil behavior ................. 189

CONTENTS iv


5.5 Time-dependent fragility curves under the consideration of both aging and SSI effects ............................................................................................ 190 5.6 Conclusions .................................................................................. 193 Chapter 6 ............................................................................................ 197

Time-building specific vulnerability assessment of RC buildings using field monitoring data ..................................................................................... 197 6.1 Introduction ................................................................................. 197 6.2 Application study: AHEPA hospital ................................................... 198

6.2.1 Structural description .............................................................................. 198

6.2.2 Instrumentation arrays ........................................................................... 205

6.2.2.1. Permanent array ........................................................................ 205

6.2.2.2. Temporary array ........................................................................ 207

6.3 Description of the methodological framework .................................... 209 6.4 Operational modal analysis (OMA) using field monitoring data ............. 210

6.4.1 Modal identification methods .................................................................... 210

6.4.2 Operational modal analysis using ambient noise measurements .................... 215

6.4.3 System identification and operational modal analysis using seismic recordings 223

6.5 Finite element model updating ........................................................ 228 6.6 Nonlinear finite element modeling ................................................... 233 6.7 Selection of the input motion .......................................................... 234 6.8 Incremental dynamic analysis (IDA) ................................................ 235 6.9 Derivation of fragility curves ........................................................... 238 6.10 Comparison with the time-dependent fragility curves of the hospital building units ........................................................................................ 241

6.10.1 Deterioration modeling due to corrosion ........................................ 241

6.10.2 Derivation of the time-dependent fragility curves and comparison with

“time-building specific” curves .................................................................. 243

6.11 Discussion and Conclusive remarks ............................................... 245 Chapter 7 ............................................................................................ 249

Conclusions – Limitations – Recommendations for future research ................ 249 7.1 Summary of findings and contributions ............................................ 249 7.2 Limitations and recommendations for future work .............................. 254 References .......................................................................................... 257

CONTENTS v


Annex A ............................................................................................... 285

Seismic input motion .............................................................................. 285

A.1 Seismic input motion .............................................................................. 285

Annex B ............................................................................................... 293

Modal identification results of AHEPA hospital using earthquake data ............. 293

B.1 Grid models in MACEC ............................................................................. 293

B.2 Seismic input motion .............................................................................. 296

B.3 Modal identification ................................................................................. 299

Annex C ............................................................................................... 305

Seismic input motion – AHEPA hospital ..................................................... 305

C.1 Seismic input motion .............................................................................. 305

Εκτενής Περίληψη ............................................................................... 317

I.1 Εισαγωγή ..................................................................................... 317 I.2 Μεθοδολογία αποτίμησης της τρωτότητας ......................................... 318

I.2.1 Περιγραφή των υπό μελέτη φορέων .......................................................... 319

I.2.2 Σεισμικές διεγέρσεις εισαγωγής ................................................................. 323

I.2.3 Μη γραμμικές ανελαστικές βήμα προς βήμα δυναμικές αναλύσεις ................... 325

I.2.4 Κατασκευή καμπυλών τρωτότητας ............................................................. 326

I.2.5 Αξιολόγηση των καμπυλών τρωτότητας ...................................................... 328

I.3 Χρονικά εξαρτώμενη σεισμική τρωτότητα κτηρίων Ο/Σ λαμβάνοντας υπόψη τη γήρανση των υλικών .......................................................................... 330 I.4 Επιρροή της δυναμικής αλληλεπίδρασης εδάφους – κατασκευής στην εκτίμηση της σεισμικής τρωτότητας κτηρίων Ο/Σ ......................................... 338 I.5 Αποτίμηση σεισμικής τρωτότητας κτηρίων Ο/Σ με βάση μετρήσεις πεδίου. Εφαρμογή στο κτήριο της νευρολογικής κλινικής και διοικητικών υπηρεσιών του νοσοκομείου ΑΧΕΠΑ στη Θεσσαλονίκη ....................................................... 347 I.6 Συμπεράσματα .............................................................................. 358 I.7 Βιβλιογραφικές αναφορές ............................................................... 359

CONTENTS vi


LIST OF FIGURES

Figure 2.1. Graphical presentation of an example fragility curve ................................ 9

Figure 2.2. Conditional probabilities of exceeding different damage states ................... 9

Figure 2.3. Conditional probabilities of exceeding different damage states ................. 10

Figure 2.4. Flow chart for a Reinforced Concrete, Moment Resisting Frame building class

according to SYNER-G ......................................................................................... 15

Figure 2.5. Pie chart presenting the percentages of different intensity measure types

used for the development of fragility functions for reinforced concrete buildings (Pitilakis

et al., 2014a) .................................................................................................... 17

Figure 2.6. Relationship between damage parameter (or damage variable) and damage

index (Kappos, 1997) ......................................................................................... 19

Figure 2.7. Limit states and damage states (Crowley et al., 2011) ........................... 20

Figure 2.8. Variation in fundamental period of a structure during an earthquake

(DiPasquale et al., 1990) ..................................................................................... 27

Figure 2.9. Typical structural performance and associated damage states (Ghobarah,

2004) ............................................................................................................... 30

Figure 2.10. Correlation between the interstorey drift factor and damage for a 3, 6, 9

and 12 storey MRFs (Ghobarah, 2004) .................................................................. 31

Figure 2.11. Pie chart presenting the percentages of different methodologies used for

the development of fragility functions for reinforced concrete buildings (Pitilakis et al.,

2014a) ............................................................................................................. 38

Figure 2.12. Flowchart to describe the components of the calculation of analytical

fragility curves (after Kwon and Elnashai, 2007) ..................................................... 39

Figure 2.13. HAZUS procedure for building damage estimation based on CSM (Pitilakis

et al., 2014a) .................................................................................................... 41

Figure 2.14. (a) IDA curves for the individual records and the estimation of the

associated limit-state capacities for CP limit state and (b) summarization of the 15 IDA

curves into their 16, 50 and 84 % fractiles ............................................................. 43

Figure 2.15. Sources of uncertainty associated with analytical fragility assessment

(adapted from D’Ayala and Meslem, 2013) ............................................................. 44

Figure 2.16. Fragility curves (in terms of PGA) for medium-rise infilled frames, low (left)

and high code design (Kappos et al., 2006) ............................................................ 47

viii Seismic vulnerability of reinforced concrete buildings considering aging and SSI effects

Figure 2.17. Sd-based fragility curves for medium-rise infilled R/C frames, low (left) and

high code design (Kappos et al., 2006) .................................................................. 47

Figure 2.18. Interface of the Fragility Function Manager (adapted from Silva et al., 2014

in Pitilakis et al., 2014a) ..................................................................................... 50

Figure 2.19. Mean curve for (a) limit state yielding curve and (b) limit state collapse

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

designed model building type ............................................................................... 50

Figure 2.20. General description of the system remaining lifetime (Beushausen and

Alexander, 2010) ............................................................................................... 53

Figure 2.21. The electrochemical corrosion process (Malioka, 2009) ......................... 54

Figure 2.22. Left: Corrosion phases (adapted from Tuuti, 1982) of concrete structures.

Right: Effects on structural capacity and limit states (adapted from Malioka, 2009) ..... 55

Figure 2.23. Information required to determine the variables Cs and Cs,∆x (FIB-CEB TASK

GROUP 5.6, 2006) .............................................................................................. 58

Figure 2.24. Structural deterioration due to reinforcement corrosion ........................ 63

Figure 2.25. Izmit earthquake: (a) corrosion of reinforcement in columns and (b)

corrosion-induced loss of steel-concrete bond (Çağatay, 2005) ................................ 63

Figure 2.26. Capacity curves for the sound and corroded structure: achievement of the

Near Collapse (NC) limit state (Berto et al., 2012) .................................................. 64

Figure 2.27. Fragility curves of the different limit states for the initial and corroded

SDOF system (Yalciner et al., 2012) ...................................................................... 65

Figure 2.28. Fragility surfaces as a function of time and PGA for slight, moderate,

extensive and complete limit states considering chloride induced corroded buildings on

flexible foundations (Fotopoulou, 2012) ................................................................. 65

Figure 2.29. Schematic representation of the dynamical comparative approach:

complete inelastic finite element computations (SSI-FE) versus a two-step approach (T-

S) (Saez et al., 2011) ......................................................................................... 67

Figure 2.30. Fragility curves following both SSI-FE and T-S approaches. Parameters α

and β control the position and the slope of the curves. (Saez, 2009).......................... 68

Figure 2.31. Comparative plots of fragility curves for the fixed base and SSI models

(Rajeev and Tesfamariam, 2012) .......................................................................... 68

Figure 2.32. Structural health monitoring system architecture: (a) Monitored

constructions, (b) local server, (c) data transmission, (d) satellite communication and

seismic network, (e) master server (Rainieri, 2009) ................................................ 70

List of Figures ix

Figure 2.33. Methodological scheme for the estimation of the fragility curve

corresponding to the slight damage using the modal model given by the ambient

vibration experiment (Michel et al., 2012) .............................................................. 71

Figure 3.1. Methodological framework for the fragility analysis of the RC MRF buildings

....................................................................................................................... 74

Figure 3.2. Reference MRF model used for seismic vulnerability assessment: plan and

elevation view with geometrical properties and reinforcing details (diameters in inches) of

the Low rise-No code model (Bracci et al., 1992) ................................................. 76


elevation view with geometrical properties and reinforcing details (diameters in mm) of

the Mid rise-No code model (Pinto et al., 2002) ................................................... 77

Figure 3.4. Reference MRF models used for seismic vulnerability assessment: plan and

elevation view with geometrical properties and reinforcing details (diameters in mm) of

the (a) Mid rise-Low code and (b) High rise–Low code models (Kappos et al., 2006,

personal communication Kappos A. and Panagopoulos G.) ........................................ 78


elevation view with geometrical properties and reinforcing details of the Low rise-High

code (Greek) model (Gelagoti, 2010) .................................................................. 80


elevation view with geometrical properties and reinforcing details of the Mid rise-High

code (Greek) model (Kappos et al., 2006) ........................................................... 80


elevation view with geometrical properties and reinforcing details of the Mid rise-High

code (Portuguese) model (Abo El Ezz, 2008) ....................................................... 81

Figure 3.8. Fiber approach for the representation of the cross-sectional behavior along

an RC element ................................................................................................... 82

Figure 3.9. Material objects adopted in OpenSees for the representation of the uniaxial

stress-strain relationships of the concrete cover and core (left) and for the reinforcement

steel (right) ....................................................................................................... 83

Figure 3.10. Implemented infill panel model under horizontal loading. In-plane double-

single strut model .............................................................................................. 85

Figure 3.11. Normalized average elastic response spectrum of the input motions in

comparison with the corresponding reference spectrum proposed by Ambraseys et al.

(1996) .............................................................................................................. 88

x Seismic vulnerability of reinforced concrete buildings considering aging and SSI effects

Figure 3.12. IDA curves for the initial intact fixed base bare frame structures with no,

low and high seismic code provisions .................................................................... 90

Figure 3.13. IDA curves for the initial intact (regularly and irregularly) infilled structures

with no, low and high seismic code provisions ........................................................ 92

Figure 3.14. Definition of IO and CP limit states on the median IDA curve of the high

rise – low code MRF model .................................................................................. 94

Figure 3.15. Regression analysis for the computation of the median intensity measure

values for the high rise – low code model: (a) Sa (T1, 5%) - maxISD relationships (in

log-log scale) and (b) computation of the median IM values corresponding to the

Immediate Occupancy (IO) and Collapse Prevention (CP) limit states ........................ 96

Figure 3.16. Regression analysis for the intact fixed base bare frame structures with no,

low and high seismic code provisions .................................................................... 97

Figure 3.17. Regression analysis for the (regularly and irregularly) infilled structures

with no, low and high seismic code provisions ........................................................ 98

Figure 3.18. Seismic fragility curves of the High rise – Low code MRF model in terms of

Sa(T1, ξ=5%) for the Immediate Occupancy (IO) and Collapse Prevention (CP) damage

states ............................................................................................................... 99

Figure 3.19. Seismic fragility curves in terms of Sa(T1, ξ=5%) of the analyzed fixed-

base, bare frame structures for the Immediate Occupancy (IO) and Collapse prevention

(CP) states ...................................................................................................... 101

Figure 3.20. Comparative plots of the fragility curves in terms of Sa(T1, ξ=5%) of the

analyzed regularly infilled, irregularly infilled (pilotis) and bare frame structures for the

Immediate Occupancy (IO) and Collapse (CP) prevention states ............................. 103

Figure 3.21. Comparison of the harmonized derived fragility curves as a function of Sa

for low rise, non-seismically designed, RC frame building subjected to seismic ground

shaking with the corresponding curves provided by Borzi et al. (2007) for the same

building typologies ........................................................................................... 105



shaking with the corresponding curves provided by Erberik (2008) for the same building

typologies ....................................................................................................... 106



shaking with the corresponding curves provided by Kwon and Elnashai (2006) for the

same building typologies ................................................................................... 106

List of Figures xi


for mid rise, non-seismically designed, RC frame building subjected to seismic ground

shaking with the corresponding curves provided by Ahmad et al. (2011) for the same




shaking with the corresponding curves provided by Kircil and Polat (2006) for the same




shaking with the corresponding curves provided by Borzi et al. (2007; 2008) for the



for mid-rise RC frame buildings with low seismic code provisions subjected to seismic

ground shaking with the corresponding curves provided by Borzi et al. (2007; 2008) for

the same building typologies .............................................................................. 109



ground shaking with the corresponding curves provided by Rota et al. (2008) for the




ground shaking with the corresponding curves provided by Kappos et al. (2003) for the



for high-rise RC frame buildings with low seismic code provisions subjected to seismic

ground shaking with the corresponding curves provided by Kappos et al. (2003; 2006)

for the same building typologies ......................................................................... 111



ground shaking with the corresponding curves provided by RISK-UE (2003) for the same




ground shaking with the corresponding curves provided by Tsionis et al. (2011) for the


xii Seismic vulnerability of reinforced concrete buildings considering aging and SSI effects


for low-rise RC frame buildings with high seismic code provisions subjected to seismic





ground shaking with the corresponding curves provided by Kircil and Polat (2006) for the




ground shaking with the corresponding curves provided by Tsionis et al. (2011) for the



for mid-rise RC frame buildings with high seismic code provisions subjected to seismic





ground shaking with the corresponding curves provided by RISKUE-IZIIS (2003) and

RISKUE-UTBC (2003) for the same building typologies .......................................... 116



ground shaking with the corresponding curves provided by Tsionis et al., (2011) for the








ground shaking with the corresponding curves provided by Kircil and Polat (2006) for the




ground shaking with the corresponding curves provided by Tsionis et al., (2011) for the


List of Figures xiii


for low-rise regularly infilled RC frame buildings with no seismic code provisions

subjected to seismic ground shaking with the corresponding curves provided by Borzi et

al. (2008) for the same building typologies .......................................................... 119


for low-rise regularly infilled RC frame buildings with no seismic code provisions

subjected to seismic ground shaking with the corresponding curves provided by Erberik

(2008) for the same building typologies ............................................................... 120


for low-rise irregularly infilled RC frame buildings (pilotis) with no seismic code provisions




for low-rise irregularly infilled RC frame buildings (pilotis) with no seismic code provisions

subjected to seismic ground shaking with the corresponding curves provided by Tsionis et



for high-rise regularly infilled RC frame buildings with low seismic code provisions

subjected to seismic ground shaking with the corresponding curves provided by Kappos

et al. (2003;2006) for the same building typologies .............................................. 122


for high-rise irregularly infilled RC frame buildings (pilotis) with low seismic code

provisions subjected to seismic ground shaking with the corresponding curves provided

by Kappos et al., (2003;2006) for the same building typologies .............................. 122


for mid-rise regularly infilled RC frame buildings with high seismic code provisions

subjected to seismic ground shaking with the corresponding curves provided by Kappos

et al. (2003;2006) for the same building typologies .............................................. 123


for mid-rise regularly infilled RC frame buildings with high seismic code provisions




for mid-rise irregularly infilled RC frame buildings (pilotis) with high seismic code


by Kappos et al. (2003) for the same building typologies ....................................... 124

xiv Seismic vulnerability of reinforced concrete buildings considering aging and SSI effects


for mid-rise irregularly infilled RC frame buildings (pilotis) with high seismic code


by Borzi et al. (2008) for the same building typologies .......................................... 125

Figure 4.1. Pushover curves for the initial (t=0 years) and corroded (t=25, 50 and 75

years) bare frame structures.............................................................................. 135

Figure 4.2. Pushover curves for the initial (t=0 years) and corroded (t=50 years) infilled

(regularly and infilled) high rise frame structure design with low seismic code provisions

..................................................................................................................... 136

Figure 4.3. Snapshots of floor displacements (left) and storey drifts (right) at the time

of maxISD occurrence for the different time scenarios (Friuli earthquake 0.3g) ......... 139

Figure 4.4. Snapshots of floor displacements (left) and storey drifts (right) at the time

of maxISD occurrence for the different time scenarios (Friuli earthquake 0.3g) for the

infilled (regularly and irregularly) high rise building with low seismic code provisions . 141

Figure 4.5. Indicative IDA curves for the initial (t=0 years) and 50-year corroded

structures with no, low and high seismic code provisions ....................................... 143

Figure 4.6. Indicative IDA curves for the initial (t=0 years) and 50-year corroded

(regularly and irregularly) infilled structures with low seismic code provisions ........... 144

Figure 4.7. Sa(T1, 5%) – maxISD relationships for the bare frame high rise structure

designed with low seismic code provisions for the initial (t=0 years) and corroded (t= 25,

50 and 75 years) scenario ................................................................................. 146

Figure 4.8. Sa(T1, 5%) – maxISD relationships for the regularly and irregularly infilled

high rise structure designed with low seismic code provisions for the initial (t=0 years)

and corroded (t= 50 years) scenario ................................................................... 147

Figure 4.9. Time-dependent fragility curves in terms of Sa(T1, 5%) for the analyzed

fixed base, bare frame structures ....................................................................... 149

Figure 4.10. Fragility surfaces as a function of time and Sa(T1, 5%) for the Immediate

Occupancy (left) and Collapse Prevention (right) damage states (fit: Linear Interpolant)

for the bare frame low- rise building designed with no seismic code provisions 150



for the bare frame mid- rise building designed with no seismic code provisions 150



List of Figures xv

for the bare frame mid- rise building designed with low seismic code provisions

..................................................................................................................... 150



for the bare frame high- rise building designed with low seismic code provisions

..................................................................................................................... 151



for the bare frame low- rise building designed with high seismic code provisions

..................................................................................................................... 151



for the bare frame mid- rise building designed with high seismic code provisions

(Greek) ......................................................................................................... 151



for the bare frame mid- rise building designed with high seismic code provisions

(Portuguese) ................................................................................................. 152

Figure 4.17. Time-dependent fragility curves in terms of Sa(T1, 5%) for the analyzed

regularly infilled, irregularly infilled (pilotis) and bare frame structures..................... 153

Figure 4.18. Time-dependent quadratic fit of median Sa(T1, 5%) values for the Collapse

Prevention (CP) state for the bare frame structures ............................................... 155

Figure 5.1. Reference MRF models used for the seismic vulnerability assessment

considering soil-structure interaction: (a) Low rise-no code, (b) High rise-low code, (c)

Mid rise-high code ............................................................................................ 161

Figure 5.2. Description of the fixed base and soil-structure models under study ....... 162

Figure 5.3. Rayleigh proportional damping curves for the linear soil profile .............. 164

Figure 5.4. Vertical displacement and stress distribution after the static analysis of the

soil-structure system for the linear soil profile case and the Low rise – No code MRF

model ............................................................................................................ 165


soil-structure system for the linear soil profile case and the High rise – Low code MRF

model ............................................................................................................ 165

xvi Seismic vulnerability of reinforced concrete buildings considering aging and SSI effects


soil-structure system for the linear soil profile case and the Mid rise – High code MRF

model ............................................................................................................ 166

Figure 5.7. Hyperbolic backbone curve for soil nonlinear shear stress-strain response

and piecewise-linear representation in multi-surface plasticity (after Prevost, 1985;

Stewart et al., 2008; Parra, 1996) ...................................................................... 167

Figure 5.8. Shear modulus reduction curve by Darendeli, 2001 for clay soil with

plasticity index PI=30 and atmospheric pressure p’0 = 1 atm, utilized for the calibration

of the soil constitutive model in OpenSees ........................................................... 168

Figure 5.9. Schematic view of the modeling approaches to assess the influence of SSI

and site effects under linear elastic or inelastic soil behavior for the high-rise, non ductile

MRF structure .................................................................................................. 170

Figure 5.10. Finite element model of the soil-structure systems in OpenSees in the case

of the high-rise, non ductile MRF structure ........................................................... 170

Figure 5.11. Schematic representation of the analyzed cases for the investigation of the

effect of (a) soil depth and (b) stratigraphy under nonlinear soil behavior ................. 171

Figure 5.12. Acceleration time histories at the base of the Low-rise, No code

structure for the fixed base and SSI configurations considering linear soil behavior

(outcrop input motion: Friuli, 6/5/1976, Mw=6.5, R=23km) .................................... 172

Figure 5.13. Snapshots of floor displacement (left) and storey drifts (right) of the Low-

rise, No code structure at the time corresponding to maxISD for linear soil behavior

(Friuli earthquake 0.3g) .................................................................................... 173

Figure 5.14. Acceleration time histories at the base of the Mid-rise, High code

structure for the fixed base and SSI configurations considering linear soil behavior

(outcrop input motion: Friuli, 6/5/1976, Mw=6.5, R=23km) .................................... 173

Figure 5.15. Snapshots of floor displacement (left) and storey drifts (right) of the Mid-

rise, High code structure at the time corresponding to maxISD for linear soil behavior

(Friuli earthquake 0.3g) .................................................................................... 173

Figure 5.16. Acceleration time histories at the base of the High-rise, Low code

structure for the different analyzed configurations considering or not SSI, site effects and

soil nonlinearity (outcrop input motion: Friuli, 6/5/1976, Mw=6.5, R=23km) ............. 175

Figure 5.17. Maximum interstorey drift ratio (%) for the different analyzed

configurations of the High-rise, Low code building considering or not SSI, site effects

and soil nonlinearity for Friuli earthquake ............................................................ 176

List of Figures xvii

Figure 5.18. Snapshots of floor displacement (left) and storey drifts (right) for the

different analyzed configurations of the High-rise, Low code building at the time

corresponding to maxISD for linear and nonlinear (NL) soil behavior (Friuli earthquake

0.3g) .............................................................................................................. 176

Figure 5.19. Acceleration time histories at the base of the structure for the different

analyzed nonlinear SSI cases with varying soil depth and stratigraphy ..................... 178

Figure 5.20. Stress-strain hysteretic loops at various depths for the 30m homogeneous

and layered soil profiles .................................................................................... 179

Figure 5.21. Stress-strain hysteretic loops at various depths for the 60m homogeneous

and layered soil profiles .................................................................................... 180

Figure 5.22. Maximum interstorey drift ratios (%) for the different analyzed

configurations with varying soil depth and stratigraphy .......................................... 182

Figure 5.23. Snapshots of floor displacement (left) and storey drifts (right) at the time

maxISD occurs for nonlinear soil behavior and varying soil depth and stratigraphy .... 182

Figure 5.24. IDA curves for the prototype fixed base models (Low-rise, No-code; High-

rise, Low-code; Mid-rise, High code) founded on rock ............................................ 184

Figure 5.25. PGA - maxISD relationships for the fixed base high-rise, low code model

founded on rock ............................................................................................... 185

Figure 5.26. Comparative PGA - maxISD relationships for the SSI and fixed base models

of the high-rise, low code structure under linear (left) and nonlinear (right) soil behavior

Figure 5.27. Fragility curves in terms of rock outcropping PGA for the fixed base

structure founded on rock in comparison with the SSI model under linear soil behavior for

the MRF structures under study .......................................................................... 186

Figure 5.28. Fragility curves for the fixed base structure founded on rock in comparison

with the SSI model under linear and nonlinear soil behavior (left) and with the

corresponding fixed base models, which consider site effects (right) ........................ 188

Figure 5.29. Fragility curves for the fixed base structure considering site effects and the

SSI configurations under linear (left) and nonlinear (right) soil behavior .................. 188

Figure 5.30. Fragility curves for different analyzed nonlinear SSI cases with varying soil

stratigraphy for the shallower (left) and the deeper (right) soil profile ...................... 189

Figure 5.31. Comparative PGA - maxISD relationships for the SSI configurations of the

high-rise, low-code MRF under linear (left) and nonlinear (right) soil behavior for the

initial (t=0 years) and the 50-year corrosion scenario (t=50 years) ......................... 190

Figure 5.32. Time-dependent fragility curves in terms of PGA for the analyzed fixed

base and SSI structural configurations ................................................................ 192

xviii Seismic vulnerability of reinforced concrete buildings considering aging and SSI effects

Figure 5.33. Time-dependent fragility curves in terms of PGA for the high rise, low code

building when considering fixed base and SSI structural configurations under linear and

nonlinear soil behavior ...................................................................................... 193

Figure 6.1. General view of the AHEPA hospital complex ....................................... 198

Figure 6.2. (a) Typical floor plan and middle floor with the structural joint and (b)

typical soil profile of AHEPA hospital building (dimension in m) ............................... 201

Figure 6.3. Geometrical properties of the element sections of UNIT 1 and UNIT 2

presented in section A-A’ along the longitudinal direction of the hospital building

(dimensions in m) ............................................................................................ 202

Figure 6.4. Reinforcement layout of UNIT 1 and UNIT 2: red and blue correspond to the

beam and column reinforcement respectively (diameters in mm) ............................ 202

Figure 6.5. Diameters and position of the column reinforced bars of the different floor

levels for both UNIT 1 and UNIT 2 (diameters and dimensions in mm) ..................... 203

Figure 6.6. Floor plans of the basement, 1st and 4th floors and the roof with the

permanent and temporary instrumentation. All SXXXX are accelerometers of the

permanent network, all RE-XX and T4D50 are seismometers of the temporary networks

operating for short period of time inside the hospital. Photos of the SOSEWIN stations at

the 4th floor near the structural joint (RE-39) and at roof (SB0F8) .......................... 206

Figure 6.7. Permanent network array of AHEPA hospital ....................................... 206

Figure 6.8. Earthquake data for the longitudinal (east-west, EW), transverse (north-

south, NS) and vertical (V) components recorded at SOSEWIN sensors at the 4th floor

and the roof from the 11.10.2013 Volvi Earthquake (Mw=4.7, R=10km) ................... 207

Figure 6.9. Sections A-A΄ and B-B΄ along the longitudinal and transverse direction of

the hospital building with the temporary instrumentation ....................................... 208

Figure 6.10. Synchronized ambient noise recordings for the longitudinal component. All

the records have the same amplitude scale (y-axis) .............................................. 209

Figure 6.11. Methodological framework adopted in the present study ..................... 210

Figure 6.12. Stochastic Output-Only Identification ............................................... 211

Figure 6.13. Frequency Domain Decomposition (FDD) method .............................. 212

Figure 6.14. Stochastic subspace identification (SSI) method ................................ 215

Figure 6.15. Visualization of the building’s geometry in MACEC 3.2 ........................ 216

Figure 6.16. Indicative auto-correlation PSDs+ for time series recorded at stations near

the joint, (a) station installed at the basement and (b) station installed at the top ..... 217

List of Figures xix

Figure 6.17. Indicative cross-correlation PSDs+ between time series recorded at

stations of the basement and roof (a) near the joint and (b) far from the joint .......... 217

Figure 6.18. Singular values of Covariance-driven SSI method in decreasing order of

magnitude ....................................................................................................... 218

Figure 6.19. Modal identification applying the Peak Picking (PP), Frequency Domain

Decomposition (FDD) and the reference-based covariance-driven Stochastic Subspace

Identification (SSI-cov) methods using ambient noise measurements ...................... 219

Figure 6.20. Mode shapes corresponding to the five first indentified frequencies for UNIT

1 ................................................................................................................... 221

Figure 6.21. Mode shapes corresponding to the five first identified frequencies for UNIT

2 ................................................................................................................... 221

Figure 6.22. Mode shapes corresponding to the five first indentified frequencies for

BUILDING ....................................................................................................... 222

Figure 6.23. Contribution of the lateral components in the first two modes in the

longitudinal and transverse direction for UNIT 1 .................................................... 222

Figure 6.24. Grid models of the different systems analyzed in MACEC for the earthquake

events: Limnos 2014 ........................................................................................ 224

Figure 6.25. Input acceleration in the longitudinal and transverse direction recorded at

the base of UNIT 1 and the corresponding elastic acceleration response spectra for

Limnos, 24.05.2014 event ................................................................................. 225

Figure 6.26. Modal identification applying the Frequency Domain Decomposition (FDD)

and the Stochastic Subspace Identification (SSI) methods using earthquake recordings of

Limnos, 24.05.2014 event ................................................................................. 225

Figure 6.27. Mode shapes of the identified modes of UNIT 1, UNIT 2 and BUILDING for

the earthquake event of Limnos, 24.05.2014 event. .............................................. 226

Figure 6.28. The different updating scenarios adopted within this study .................. 230

Figure 6.29. Normalized average elastic acceleration response spectrum of the input

motions compared with the corresponding reference spectrum adopted from SHARE for a

475 year return period (http://portal.share-eu.org:8080/jetspeed/portal/) ............... 235

Figure 6.30. Assignments of the immediate occupancy (IO) and collapse prevention

(CP) limit damage state points on the IDA curves for the updated units ................... 237

Figure 6.31. PGA-maxISD relationships for updated finite element models of UNIT 1 and

UNIT 2 ............................................................................................................ 240

xx Seismic vulnerability of reinforced concrete buildings considering aging and SSI effects

Figure 6.32. Comparative plots of the initial fragility curves derived for the two adjacent

building units with the corresponding fragility curves provided by Kappos et al.

(2003;2006).................................................................................................... 241

Figure 6.33. Comparative plot of the “building-specific” fragility curves derived for the

initial and updated models of UNIT 1 and UNIT 2 .................................................. 241

Figure 6.34. Assignments of the IO and CP limit damage state points on the IDA curves

for the corroded units ....................................................................................... 244

Figure 6.35. PGA-maxISD relationships for the corroded (t=45years) hospital buildings

UNIT 1 and UNIT 2 ........................................................................................... 244

Figure 6.36. Comparative plots of the fragility curves corresponding to the initial,

updated and corroded models of UNIT 1 and UNIT 2 ............................................. 245

Figure A.1. Accelerograms of the real seismic records used as input motion for the IDA.

Figure A.2. Normalized elastic response spectra of the seismic records in comparison to

the corresponding median predicted spectrum of Ambraseys et al., (1996). .............. 289

Figure B.1. Grid models of the different systems analyzed in MACEC for the earthquake

events: NW from Lake Langada 2013, West from Kassandra peninsula in Halkidiki 2014

..................................................................................................................... 294


events: Thessaloniki 2012 ................................................................................. 294


events: Thessaloniki 2013 ................................................................................. 294


events: Kalamaria 2014, Limnos 2014 ................................................................. 295


events: West from Kassandra peninsula in Halkidiki 2013 ...................................... 295

Figure B.6. Input acceleration in the longitudinal and transverse direction recorded at

the base of UNIT 1 and the corresponding elastic acceleration response spectra for the

NW from Lake Langada, 6.12.2013 event. ........................................................... 297


the base of UNIT 1 and the corresponding elastic acceleration response spectra for

Limnos, 24.05.2014 event. ................................................................................ 297

List of Figures xxi



Kalamaria, 16.7.2014 event. .............................................................................. 298



West from Kassandra peninsula in Halkidiki, 22.8.2014 event. ................................ 298

Figure B.10. Modal identification applying the Frequency Domain Decomposition (FDD)


the Thessaloniki, 2012 event. ............................................................................ 300



the Thessaloniki, 2013 event. ............................................................................ 300



N West from Kassandra peninsula in Halkidiki, 26.10.2013 event. ........................... 301



NW from Lake Langada, 6.12.2013 event. ........................................................... 301



Limnos, 24.05.2014 event. ................................................................................ 302



Kalamaria, 16.07.2014 event. ............................................................................ 302



the West from Kassandra peninsula in Halkidiki, 22.08.2014 event. ......................... 303

Figure C.1. Accelerograms of the real seismic records used as input motion for the IDA

(continued). .................................................................................................... 306

Figure C.2. Normalized elastic response spectra of the seismic records in comparison to

the corresponding reference normalized spectrum adopted from SHARE for a 475 year

return period. .................................................................................................. 311

xxii Seismic vulnerability of reinforced concrete buildings considering aging and SSI effects

Σχήμα I.1. ∆ιάγραμμα ροής της μεθοδολογίας για την αποτίμηση της σεισμικής

τρωτότητας κτηρίων οπλισμένου σκυροδέματος .................................................... 319

Σχήμα I.2. Σχηματική αναπαράσταση των γεωμετρικών (διατομές) και των

κατασκευαστικών (λεπτομέρειες όπλισης) χαρακτηριστικών των πακτωμένων φορέων . 320

Σχήμα I.3. Σύγκριση μέσου κανονικοποιημένου ελαστικού φάσματος καταγραφών με το

στοχευόμενο μέσο κανονικοποιημένο φάσμα των Ambraseys et al. (1996) ................ 324

Σχήμα I.4. Ορισμός των επιπέδων βλάβης «Άμεση Χρήση μετά το σεισμό ΑΧ» και

«Αποφυγή Κατάρρευσης ΑΚ» επάνω στη διάμεσο καμπύλη απόκρισης των βήμα προς βήμα

δυναμικών αναλύσεων για την περίπτωση του υψηλού κτηρίου σχεδιασμένου με βάση

χαμηλό επίπεδο αντισεισμικού κανονισμού ........................................................... 326

Σχήμα I.5. Ανάλυση παλινδρόμησης για τον υπολογισμό των διαμέσων τιμών του μέτρου

έντασης που αντιστοιχούν στις θεωρούμενες στάθμες βλάβης για την περίπτωση του

υψηλού κτηρίου σχεδιασμένου με βάση χαμηλό επίπεδο αντισεισμικό κανονισμό: (α)

Σχέσεις Sa (T1, 5%) – maxISD σε λογαριθμική κλίμακα και (β) υπολογισμός των διαμέσων

τιμών του μέτρου έντασης για τις ΑΧ και ΑΚ στάθμες βλάβης ................................... 327

Σχήμα I.6. Καμπύλες τρωτότητας του υψηλού κτηρίου σχεδιασμένου με βάση χαμηλού

επιπέδου κανονισμό σε όρους Sa(T1, ξ=5%) για τις στάθμες βλάβης που αντιστοιχούν

στην Άμεση Χρήση «ΑΧ» μετά το σεισμό και την Αποφυγή Κατάρρευσης «ΑΚ» ........... 328

Σχήμα I.7. Σύγκριση των εναρμονισμένων καμπυλών τρωτότητας σε όρους Sa για την

περίπτωση του υψηλού μη τοιχοπληρωμένου κτηρίου σχεδιασμένου βάσει χαμηλού

επιπέδου αντισεισμικό κανονισμό με τις αντίστοιχες καμπύλες των Kappos et al. (2003;

2006) που αντιστοιχούν στην ίδια τυπολογία φορέα ............................................... 329

Σχήμα I.8. Καμπύλες αντίστασης του «γυμνού» και τοιχοπληρωμένου (ομοιόμορφη καθ’

ύψος κατανομή, pilotis) υψηλού κτηρίου σχεδιασμένο με βάση χαμηλό επίπεδο

Κανονισμού για τα θεωρούμενα χρονικά σενάρια ................................................... 332

Σχήμα I.9.Χρονικά εξαρτώμενες καμπύλες τρωτότητας συναρτήσει του Sa(T1, 5%) για τα

πακτωμένα, μη τοιχοπληρωμένα πλαισιακά κτήρια ................................................. 334

Σχήμα I.10.Επιφάνειες τρωτότητας συναρτήσει του χρόνου και Sa(T1, 5%) για τις

στάθμες βλάβης που αντιστοιχούν στην «Άμεση Χρήση μετά το σεισμό» (αριστερά) και της

«Αποφυγή Κατάρρευσης» (δεξιά) για την περίπτωση του μη τοιχοπληρωμένου υψηλού

κτηρίου σχεδιασμένο με βάση χαμηλό επίπεδο αντισεισμικό κανονισμό ...................... 335

Σχήμα I.11.Χρονικά εξαρτώμενες καμπύλες τρωτότητας συναρτήσει του Sa(T1, 5%) για

τα πακτωμένα, τοιχοπληρωμένα πλαισιακά κτήρια (ομοιόμορφη καθ’ ύψος κατανομή και

pilotis) ............................................................................................................ 336

Σχήμα I.12. Αναπαράσταση της χρονικά εξαρτώμενης διαμέσου (σε όρους Sa(T1, 5%))

των καμπυλών με πολυώνυμο δευτέρου βαθμού για την περίπτωση βλαβών που

List of Figures xxiii

αντιστοιχούν στη στάθμη επιτελεστικότητας ΑΚ, για το μη τοιχοπληρωμένο υψηλό κτήριο

σχεδιασμένο βάσει χαμηλού επιπέδου κανονισμό ................................................... 337

Σχήμα I.13. Σχηματική απεικόνιση των εφαρμοσμένων προσομοιωμάτων για τη μελέτη

της επιμέρους επιρροής της ∆ΑΕΚ και των τοπικών εδαφικών συνθηκών για την

περίπτωση του υψηλού κτηρίου σχεδιασμένο βάσει χαμηλού επιπέδου κανονισμό ....... 339

Σχήμα I.14. Σχηματική απεικόνιση των υπό μελέτη περιπτώσεων που εξετάζουν την

επιρροή (α) του βάθους και (β) της διαστρωμάτωσης του εδαφικού προφίλ για ανελαστική

συμπεριφορά εδάφους για την περίπτωση του υψηλού κτηρίου σχεδιασμένο βάσει

χαμηλού επιπέδου κανονισμό ............................................................................. 339

Σχήμα I.15. Καμπύλες τρωτότητας των πακτωμένων προσομοιωμάτων θεμελιωμένων σε

βράχο σε σύγκριση με τα προσομοιώματα ∆ΑΕΚ για ελαστική συμπεριφορά εδάφους. Οι

καμπύλες τρωτότητας αναφέρονται και στα τρία υπό μελέτη πλαισιακά κτήρια και

εκφράζονται σε όρους μέγιστης εδαφικής επιτάχυνσης PGA σε συνθήκες «οιονεί» βράχου

..................................................................................................................... 342

Σχήμα I.16. Καμπύλες τρωτότητας του πακτωμένου υψηλού κτηρίου θεμελιωμένο σε

βράχο και των προσομοιωμάτων ∆ΑΕΚ (αριστερά) καθώς και των πακτωμένων

προσομοιωμάτων που λαμβάνουν υπόψη την ΕΤΕΣ (δεξιά) για ελαστικό και ανελαστικό

έδαφος ........................................................................................................... 343

Σχήμα I.17. Καμπύλες τρωτότητας του πακτωμένου μοντέλου λαμβάνοντας υπόψη την

ΕΤΕΣ και των μοντέλων ∆ΑΕΚ για ελαστικό (αριστερά) και ανελαστικό (δεξιά) έδαφος . 343

Σχήμα I.18. Καμπύλες τρωτότητας των υπό μελέτη συστημάτων ∆ΑΕΚ για ανελαστικό

έδαφος με διαστρωμάτωση μικρότερου (αριστερά) και μεγαλύτερου (δεξιά) βάθους .... 344

Σχήμα I.19. Χρονικά εξαρτώμενες καμπύλες τρωτότητας σε όρους PGA των υπό μελέτη

πακτωμένων φορέων και των αντίστοιχων συστημάτων εδάφους – κατασκευής που

λαμβάνουν υπόψη τη ∆ΑΕΚ για ελαστική συμπεριφορά του εδάφους ........................ 345

Σχήμα I.20. Χρονικά εξαρτώμενες καμπύλες τρωτότητας σε όρους PGA για το υψηλό

κτήριο σχεδιασμένο με βάση χαμηλού επιπέδου κανονισμό θεωρώντας συνθήκες

πάκτωσης στο βράχο καθώς και τη ∆ΑΕΚ για ελαστικό και μη γραμμικό έδαφος .......... 346

Σχήμα I.21. ∆ιάγραμμα ροής της μεθοδολογίας για την αποτίμηση της σεισμικής

τρωτότητας κτηρίων οπλισμένου σκυροδέματος με βάση μετρήσεις πεδίου ................ 348

Σχήμα I.22. Νευρολογική κλινική του νοσοκομείου ΑΧΕΠΑ: τυπικός όροφος και όροφος

μεσοπατώματος των δυο επιμέρους κτηρίων και η ένωσή τους μέσω του κατασκευαστικού

αρμού ............................................................................................................. 349

Σχήμα I.23. Τομές Α-Α’ και Β-Β’ κατά τη διαμήκη και εγκάρσια διεύθυνση του

νοσοκομειακού κτηρίου με τη διάταξη του προσωρινού δικτύου ............................... 350

xxiv Seismic vulnerability of reinforced concrete buildings considering aging and SSI effects

Σχήμα I.24. Αποτελέσματα ταυτοποίησης των υπό μελέτη συστημάτων με βάση τις

μεθόδους FDD και SSI χρησιμοποιώντας μετρήσεις θορύβου ................................... 351

Σχήμα I.25. Σύγκριση μέσου κανονικοποιημένου ελαστικού φάσματος απόκρισης

επιταχύνσεων των κινήσεων εισαγωγής με το αντίστοιχο κανονικοποιημένο φάσμα του

SHARE για περίοδο επαναφοράς τα 475 έτη (http://portal.share-

eu.org:8080/jetspeed/portal/) ........................................................................... 354

Σχήμα I.26. Ορισμός των οριακών τιμών ΑΧ και ΑΚ των αναπροσαρμοσμένων

προσομοιωμάτων βάσει των καμπυλών απόκρισης των δυναμικών βήμα προς βήμα

επαυξητικών αναλύσεων .................................................................................... 355

Σχήμα I.27. Συγκριτικά γραφήματα των καμπυλών τρωτότητας για τα αρχικά αριθμητικά

προσομοιώματα των δυο επιμέρους κτηρίων Γ και ∆ και των καμπυλών των Kappos et al.

(2003;2006) για την ίδια τυπολογία .................................................................... 356

Σχήμα I.28. Συγκριτικά γραφήματα των καμπυλών τρωτότητας των αρχικών και

αναπροσαρμοσμένων κτηρίων Γ και ∆ .................................................................. 357

Σχήμα I.29. Συγκριτικά γραφήματα των καμπυλών τρωτότητας των αρχικών,

αναπροσαρμοσμένων και διαβρωμένων προσομοιωμάτων των κτηρίων Γ και ∆ ........... 357

LIST OF TABLES

Table 2.1. SYNER-G taxonomy for buildings .......................................................... 12

Table 2.2.Comparison of existing damage scales with the HRC damage scale (adapted

from Rossetto and Elnashai, 2003) ....................................................................... 21

Table 2.3. Damage states (adapted from Rossetto and Elnashai, 2003) ................... 22

Table 2.4. Damage states (Park et al., 1984; Williams and Sexsmith, 1995) ............. 25

Table 2.5. Range of the proposed damage index for different damage states (Ghobarah

et al., 1999) ...................................................................................................... 27

Table 2.6. Compliance criteria for assessment of RC flexural member in Eurocode 8 –

Part 3 (Fardis 2014) ........................................................................................... 28

Table 2.7. Description of the discrete damage scales adopted in Crowley et al. (2004)

for RC frame structures ....................................................................................... 29

Table 2.8. Damage states for damage index based on interstorey drift (Algan, 1982) . 31

Table 2.9. Damage states for damage index based on interstorey drift for ductile MRFs

(Ghobarah, 2004) .............................................................................................. 32

Table 2.10. Drift ratio (%) limits associated with various damage levels (Ghobarah,

2004) ............................................................................................................... 32

Table 2.11. Limit state criteria adopted for the reference building structure in Ji et al.

(2007) .............................................................................................................. 32

Table 2.12. Sources of uncertainty in fragility functions as identified in FEMA461 (2007)

....................................................................................................................... 34

Table 2.13. Statistical quantification of parameters affecting chloride induced corrosion

according to FIB-CEB Task Group (2006) ............................................................... 59

Table 2.14.Classification of icorr based on laboratory test or measurements on real size

structures ......................................................................................................... 60

Table 2.15. Chloride-induced corrosion rates (icorr-20) for the different exposure

classes according to DuraCrete (1998) .................................................................. 60

Table 2.16. Suggested ranges of icorr for EN 206 exposure classes (Rodriguez et al.,

1994) ............................................................................................................... 61

Table 3.1. Characteristics of the reference studied buildings .................................... 75

xxvi Seismic vulnerability of reinforced concrete buildings considering aging and SSI effects

Table 3.2. Parameter values for the definition of the material object ‘Concrete01’ in

OpenSees (unconfined concrete) .......................................................................... 83

Table 3.3. Characteristics of the infilled studied buildings ........................................ 86

Table 3.4. Lists of records used for the IDA .......................................................... 88

Table 3.5. Description of Immediate Occupancy and Collapse Prevention performance

levels according to FEMA356 for concrete frames .................................................... 93

Table 3.6. CP limit state maxISD values defined on the IDA curve for the bare frame

fixed base intact structures .................................................................................. 94

Table 3.7. CP limit state maxISD values defined on the IDA curve for the infilled fixed

base, intact structures ........................................................................................ 94

Table 3.8. Seismic fragility parameters in terms of Sa(T1, ξ=5%) for fixed base, bare

frame structures .............................................................................................. 100

Table 3.9. Seismic fragility parameters in terms of Sa(T1, ξ=5%) for fixed base, bare

frame structures .............................................................................................. 102

Table 3.10. Main parameters of the fragility curves from the literature used for the

comparison with the Low rise – No code model ..................................................... 105


comparison with the Mid rise – No code model ..................................................... 107


comparison with the Mid rise – Low code model .................................................... 109


comparison with the High rise – Low code model .................................................. 111


comparison with the Low rise – High code model .................................................. 113


comparison with the Mid rise – High code (Greek) model ....................................... 115


comparison with the Mid rise – High code (Portuguese) model. ............................... 117


comparison with the Low rise – No code (regularly and irregularly) infilled model ...... 119


comparison with the High rise – Low code (regularly and irregularly) infilled model .... 121


comparison with the Mid rise – High code (regularly and irregularly) infilled model .... 123

List of Tables xxvii

Table 4.1. Statistical characteristics of parameters affecting the chloride induced

corrosion of RC elements adopted in the present study .......................................... 130

Table 4.2. Loss in reinforcement (%) for the considered corrosion scenarios ............ 132

Table 4.3. Concrete cover strength reduction (%) for the considered corrosion scenarios

..................................................................................................................... 133

Table 4.4. Steel ultimate deformation reduction (%) for the considered corrosion

scenarios ........................................................................................................ 133

Table 4.5. Fundamental periods of the reference uncorroded (t=0 years) and corroded

(t=25, 50, 75 years) bare frame MRF structures ................................................... 133

Table 4.6. Fundamental periods of the uncorroded (t=0 years) and corroded (t=50

years) regularly and irregularly infilled MRF structures ........................................... 133

Table 4.7. CP limit state maxISD values defined on the IDA curve for the bare frame

structures over time ......................................................................................... 145

Table 4.8. CP limit state maxISD values defined on the IDA curve for the infilled

buildings for the initial and 50-year corrosion scenario ........................................... 145

Table 4.9. Time-dependent fragility parameters in terms of Sa(T1, 5%) for the fixed

base, bare frame structures ............................................................................... 148

Table 4.10. Time-dependent fragility parameters in terms of Sa(T1, 5%) for the bare,

regularly infilled and irregularly infilled (pilotis) frame buildings .............................. 154

Table 4.11. Coefficients of quadratic interpolation for the median IO and CP limit values

and the corresponding dispersion (in terms of log-standard deviation) ..................... 156

Table 5.1. Summary of parameters adopted for the linear soil profile case .............. 165

Table 5.2. Summary of parameters adopted for the pressure independent multi-yield

plasticity model ................................................................................................ 169

Table 5.3. Parameters of the fragility functions in terms of PGA for the fixed base

founded on rock models and for the SSI configurations under linear soil behavior ...... 187

Table 5.4. Parameters of the fragility functions in terms of PGA for the analyzed

structural configurations when considering or not SSI and site effects under linear or

nonlinear behavior for the case of the High rise – Low code building ........................ 188

Table 5.5. Parameters of the fragility functions in terms of PGA for the analyzed

structural configurations when considering the soil depth and stratigraphy under

nonlinear soil behavior ...................................................................................... 190

Table 5.6. Parameters of the fragility functions in terms of PGA for the considered

structural configurations and corrosion scenarios .................................................. 191

xxviii Seismic vulnerability of reinforced concrete buildings considering aging and SSI effects

Table 5.7. Time-dependent fragility parameters in terms of PGA for the high rise, low

code building considering fixed base and SSI (for linear or nonlinear soil behavior)

structural configurations .................................................................................... 193

Table 6.1. Main characteristics of the hospital building units (fc and fy represent the

strength of concrete and reinforcement steel respectively) ..................................... 200

Table 6.2. Serial number and position of all the stations used in the two-day ambient

noise experiment ............................................................................................. 208

Table 6.3. Modal identification results for UNIT 1, UNIT 2 and BUILDING estimated

using parametric and non-parametric identification techniques ............................... 219

Table 6.4. Earthquake events used for OMA of the hospital building ...................... 224

Table 6.5. Modal identification results for the recorded earthquake events compared to

the corresponding results for the noise measurements (FDD) ................................. 227

Table 6.6. Comparison of the updated finite element model of UNIT 1 with the initial

model and the experimental results (T: period, f: frequency) .................................. 232

Table 6.7. Comparison of the updated finite element model of UNIT 2 with the initial

model and the experimental results (T: period, f: frequency) .................................. 232

Table 6.8. List of records used for the IDA .......................................................... 235

Table 6.9. Statistical characteristics of parameters affecting the chloride induced

corrosion of RC elements adopted in the present study (according to the methodology of

Chapter 4) ...................................................................................................... 242

Table 6.10. Loss of reinforcement (%) and concrete cover strength reduction (%) for

the considered corrosion scenario (t=45 years) .................................................... 242

Table 6.11. Parameters of the derived fragility curves for the initial and updated finite

element models for UNIT 1 and UNIT 2 ............................................................... 245

Πίνακας I.1. Κύρια χαρακτηριστικά των πλαισιακών κτηριακών προσομοιωμάτων ...... 320

Πίνακας I.2. Κύρια χαρακτηριστικά των τοιχοπληρωμένων πλαισιακών κτηριακών

προσομοιωμάτων .............................................................................................. 323

Πίνακας I.3. Σεισμικές διεγέρσεις για τη διεξαγωγή των ανελαστικών δυναμικών

Πίνακας I.4. Οριακές τιμές της στάθμης βλάβης «Αποφυγή Κατάρρευσης» όπως έχουν

υπολογισθεί για τα «γυμνά» πλαίσια και τα θεωρούμενα χρονικά σενάρια .................. 332

Πίνακας I.5. Οριακές τιμές της στάθμης βλάβης «Αποφυγή Κατάρρευσης» όπως έχουν

υπολογισθεί για τα τοιχοπληρωμένα πλαίσια και τα θεωρούμενα χρονικά σενάρια ....... 333

List of Tables xxix

Πίνακας I.6. Κύρια χαρακτηριστικά των υπό μελέτη κτηρίων της νευρολογικής κλινικής

..................................................................................................................... 349

Πίνακας I.7. Αποτελέσματα ιδιομορφικών αναλύσεων με βάση την FDD και SSI

μεθοδολογία για το ΚΤΗΡΙΟ Γ, ΚΤΗΡΙΟ ∆ και ΕΝΙΑΙΟ ΚΤΗΡΙΟ .................................. 351

Πίνακας I.8. Σύγκριση του αναπροσαρμοσμένου προσομοιώματος του κτηρίου Γ με το

αντίστοιχο αρχικό και πειραματικό προσομοίωμα (T: ιδιοπερίοδος, f: ιδιοσυχνότητα) .. 353

Πίνακας I.9. Σύγκριση του αναπροσαρμοσμένου προσομοιώματος του κτηρίου ∆ με το

αντίστοιχο αρχικό και πειραματικό προσομοίωμα (T: ιδιοπερίοδος, f: ιδιοσυχνότητα) .. 353

xxx Seismic vulnerability of reinforced concrete buildings considering aging and SSI effects


CHAPTER 1

Introduction

1.1 Statement of the problem

In the last few decades, the significant increase in the social and economic losses caused

by earthquakes worldwide, has stimulated many studies on seismic risk of structures.

The disastrous effects of strong seismic events on social and economical scale, such as

the recent earthquakes of Japan (Tohoku, 2011) and New Zealand (Christchurch, 2011),

have emerged the need of developing operational tools in order to increase preparedness

and establish efficient mitigation and emergency management strategies. Thus scientific

research has been focused not only in the seismic design and analysis of new structures

but also on the assessment of the seismic performance of the existing ones. In order to

design efficient assessment tools that could be utilized by civil protection authorities,

decision makers in emergency management organizations, insurance companies,

engineers, seismologists etc., a reliable risk model for the region or for a specific

structure under consideration needs to be compiled in order to predict future losses due

to seismic events with a high accuracy level.

In this context, the reliable vulnerability assessment of existing structures and

infrastructures is a prerequisite for seismic loss estimation, risk mitigation and

management. Vulnerability is commonly expressed through fragility functions

representing the probability of exceeding a prescribed level of damage for a wide range

of ground motion intensities. There are numerous studies regarding the derivation of

fragility curves for reinforced concrete (RC) buildings (e.g. Rossetto and Elnashai, 2003;

Mosalam et al., 1997; Chryssanthopoulos et al., 2000; Kappos et al., 2006 etc.).

Traditionally, it is implicitly assumed that the structures are optimally maintained during

their lifetime and the impact of the progressive deterioration due to various time-

dependent mechanisms on structural performance is commonly neglected. Although

widely applied seismic vulnerability assessment methods (e.g. HAZUS methodology)

allow the integration of coefficients that depend on the maintenance condition or are

related to in-situ properties of building materials, such integration does not necessarily

CHAPTER 1: Introduction 2


increase the reliability of the results as the actual structural state may still not be

captured properly. Moreover the development of degradation phenomena in time is

generally neglected. On this basis deterioration of the material properties caused by

aggressive environmental attack is not accounted for. One of the primary sources of

structural degradation is the corrosion of RC members, generally associated to

carbonation process and chloride penetration, leading to the variation of the mechanical

properties of steel and concrete over time. Consequently, both safety and serviceability

of RC structures may be affected under the action of seismic (or even static) loading,

compromising the capability of the structures to withstand the loads for which they are

designed. Although there are a few studies devoted to the modeling and vulnerability

assessment of RC bridges that have undergone corrosion effects (Choe et al., 2008;

2009; 2010; Ghosh and Padgett, 2010; Simon et al., 2010), research on the fragility

analysis of RC buildings due to aging is still limited.

Besides aging effects the influence of soil conditions and SSI might also contribute to

the building’s seismic fragility. The general assumption that the structure is fixed to its

base ignoring the presence of the soil beneath its foundation may be realistic (or at least

conservative) when the structure is founded on rock or very stiff soil. However, in the

case of softer soil formations, SSI and local site effects may play an important role

modifying considerably the free field input motion as well as the dynamic characteristics

of the building and finally its response (Stewart et al., 1999). Although there are some

studies that take into account the local site effects by providing fragility curves for

buildings for different soil conditions (e.g. NIBS, 2004), the effect of SSI to the expected

structure’s performance has not received much attention. This may be due to the fact

that the incorporation of SSI phenomena in the analysis is generally considered beneficial

reducing the seismic demand and consequently the corresponding structural damage of

non-linear systems (Ciampoli and Pinto, 1995). Nevertheless, it has been shown that soil

deformability and SSI may modify the structural response and fragility leading to either

beneficial or unfavorable effects depending on the dynamic properties of the soil and the

structure as well as the characteristics (frequency content, amplitude, significant

duration) of the input motion (e.g. Dutta et al., 2004; Saez et al., 2011; Rajeev and

Tesfamariam, 2012).

In the context of building-specific vulnerability assessment, the use of conventional

generic fragility curves, although appropriate for assessing fragility and losses in a

regional/urban scale, may lead to inaccurate fragility and loss estimates in the case of

individual building assessment, which constitute crucial components in the framework of

decision making and risk mitigation strategies (e.g. seismic safety and rehabilitation

costs). This issue is crucial especially in the case of structures with strategic interest (e.g.



hospital buildings, harbor facilities, nuclear power plants etc.). The use of field

monitoring data for identifying the actual state of existing structures has recently drawn

attention in the civil engineering community for developing real time assessment tools

and reducing uncertainties involved within the risk assessment procedure (Gueguen et

al., 2007; Michel et al., 2008; 2012). Real-time monitoring of civil structures and

infrastructures provide valuable information to assess the structural health and identify

the actual state and vulnerability of the associated systems. Furthermore, it allows

monitoring the evolution of the structure’s safety during the earthquake crisis while it

constitutes the key component for rapid damage assessment or the preparation of

reliable damage scenarios. The integration of a comprehensive methodology for the

seismic vulnerability assessment of critical structures and infrastructures using

monitoring data, constitutes an efficient tool for reducing the uncertainties associated

with the risk assessment procedure improving seismic safety and allowing the

development of robust real time assessment tools and appropriate risk mitigation

strategies.

1.2 Objectives and scope of the research

The present thesis aims to propose and quantify an analytical methodology to assess the

seismic vulnerability of reinforced concrete buildings taking into account aging as well as

soil-structure interaction and site effects. Probabilistic fragility curves are proposed for

different structural typologies that might be used by scientists and practitioners for

efficient implementation within a probabilistic risk assessment framework on a regional

scale.

Moreover on a building-specific scale, an integrated methodology is proposed for the

derivation of seismic fragility functions using field monitoring data. The use of field

monitoring data constitutes a significant tool for the representation of the actual



thus the reliability in the risk assessment procedure. The methodology is highlighted

through its application on a hospital building located in Thessaloniki, Greece.

1.3 Outline of the Thesis

The thesis is organized into seven chapters with the following contents:

In the present chapter (Chapter 1), the motivation and the main objectives of the

research are presented.



In Chapter 2 the main issues involved in the seismic vulnerability assessment of RC

buildings are discussed. More specifically the chapter is divided into two parts. The first

part outlines the main components, parameters and methods to derive fragility functions,

which are used in the seismic risk assessment of reinforced concrete buildings at urban

and regional scale. Its aim is to provide a mean of understanding the main factors

governing the current practice in seismic vulnerability assessment. The second part of

the chapter discusses the needs and challenges that have not been thoroughly studied up

to now and are investigated in the present thesis aiming at enhancing the reliability and

robustness of seismic vulnerability assessment procedures.

Chapter 3 focuses on the quantification of an analytical procedure to assess the

vulnerability of reinforced concrete (RC) structures subjected to seismic motion.

Vulnerability is expressed in terms of probabilistic fragility curves, which describe the

probability of exceeding a predefined level of damage under a seismic excitation of a

given intensity. Furthermore the reference RC buildings are presented, that have been

selected in the context of the present thesis for the seismic vulnerability assessment

considering aging and soil-structure interaction effects. Seven two-dimensional RC

moment resisting frame structures (MRF) have been adopted from the literature to

represent varying typologies designed with different seismic code levels. The structural

detailing, material properties as well as modeling issues and associated assumptions are

addressed in full detail. To illustrate the methodological framework of the seismic

vulnerability assessment, fragility curves are derived for the fixed base, intact frame

buildings. The effects of aging and soil-structure interaction are investigated in the

ensuing chapters. In terms of numerical computations, incremental dynamic analysis

(IDA) of the structural models is performed for the estimation of the fragility function

parameters. Finally the derived fragility curves for the fixed base, intact frame buildings

are compared with proposed curves from the literature to verify the validity of the

proposed methodology.

In Chapter 4 time-dependent fragility functions of the reference MRF buildings are

developed taking into account deterioration due to aging effects. The consideration of

aging is achieved including probabilistic models of chloride induced corrosion

deterioration of the RC elements within the vulnerability assessment framework

presented in detail in Chapter 3. The structural models are analyzed assuming fixed base

conditions for their uncorroded (t=0 years) and corroded (t=25, 50, 75 years) states. In

particular chloride induced corrosion is considered based on probabilistic modeling of

corrosion initiation time and corrosion rate. Different corrosion aspects are considered in

the analysis including the loss of reinforcement cross-sectional area, the degradation of

concrete cover and the reduction of steel ultimate deformation. Furthermore the relative



contribution of infill walls on the expected structural performance over time is also

assessed, analyzing both regularly and irregularly infilled (i.e. pilotis) moment resisting

frames and comparing their seismic behavior with the corresponding bare frames.

The aim of the research presented in Chapter 5 is to investigate whether soil-

structure interaction (SSI) and site effects may affect the seismic performance and

vulnerability of reinforced concrete moment resisting frame buildings and consequently

modify the fragility curves. The direct one-step approach is applied for the SSI modeling

under linear or nonlinear soil behavior while site effects are inherently accounted for. To

further examine the contribution of site and SSI effects, a two-step uncoupled approach

is also applied, which takes into account site effects on the response of the fixed base

structures, but neglects SSI effects. Additional analyses are performed investigating the

influence of the soil depth and stratigraphy under nonlinear soil behavior on the seismic

response and fragility of RC buildings. Finally time-dependent fragility functions of the RC

buildings are derived considering both SSI and aging effects. The chloride induced

corrosion model presented in Chapter 4 is adopted considering two time-scenarios (t=0

and 50 years).

In Chapter 6 the seismic vulnerability of existing RC buildings is evaluated combining

through a comprehensive methodology, the numerical analysis and field monitoring data.

Monitoring data of the building are exploited for the representation of the actual


properties as well as many non-physical parameters (age, maintenance, etc.) increasing

thus the reliability of the derived fragility curves. The proposed methodology is

highlighted through the derivation of “time-building specific” fragility curves for an eight-

storey RC structure (hospital building), built almost five decades ago, that is composed

by two adjacent units connected with a structural joint. The assessment of the dynamic

characteristics is performed using ambient noise measurements recorded by a temporary

seismic network which was deployed inside the hospital. The modal identification results

are used to update and better constrain the initial finite element model of the building,

which is based on the available design and construction documentation plans. Three-

dimensional incremental dynamic analysis is performed to derive the fragility curves for

the initial as built model (“building-specific”) and for the real structures as they are

nowadays (“time-building specific”). The initial “building specific” curves are evaluated

through their comparison with conventional generic curves that are commonly used in

risk assessment studies. Moreover, in order to validate and enhance the reliability of the

obtained results, the “time-building specific” fragility curves, are compared to time-

dependent curves derived for the hospital units applying the analytical methodology



proposed in Chapter 4 adopting an appropriate for the specific case study corrosion

scenario.

Chapter 7 summarizes the main findings and contributions of the work providing also

recommendations and suggestions for future research.


CHAPTER 2

Literature review on the seismic vulnerability assessment of RC buildings

2.1 Introduction

The present chapter aims at providing a critical review of the main issues involved in the

seismic vulnerability assessment of reinforced concrete (RC) buildings. The first part

outlines the main components, parameters and methods to derive fragility functions,

which are used in the seismic risk assessment of RC buildings at urban and regional

scale. Its aim is to provide a mean of understanding the main factors governing the

current practice in seismic vulnerability assessment. The second part of the chapter

discusses the needs and challenges that have not been thoroughly investigated up to

now and are investigated in the present thesis aiming at enhancing the reliability and

robustness of seismic vulnerability assessment procedures.

2.2 Background

Seismic risk assessment can be defined as the estimation of the probability of expected

damages and losses due to seismic hazard. In the past decades the field of seismic risk

assessment has received significant attention (Calvi et al., 2006) due to the dramatic

increase in the losses caused by earthquakes, that has been observed worldwide. The

formulation of an earthquake loss model for a given region is a critical component not

only for predicting the economic impact of future seismic events but also for establishing

emergency preparedness and risk mitigation strategies by the national authorities. A

significant component of a loss model is the methodology to assess the vulnerability of

the built environment. The vulnerability of a structure is described in all engineering-

relevant approaches as vulnerability and/or fragility functions, which can be regarded as

a graphical representation of seismic risk. More specifically vulnerability functions provide

the probability of losses (social or economic) given the level of ground shacking whereas

fragility functions describe the probability of exceeding different limit states (usually

Chapter 2: Literature review on the seismic vulnerability assessment of RC buildings 8


expressed as physical damage) given the level of ground shaking. The former relates the

level of ground shaking with the mean damage ratio (e.g. ratio of cost of repair to cost of

replacement) and the latter relates the level of ground motion with the probability of

exceeding the limit states (Pitilakis et al., 2014a).

In structural performance evaluation, it is convenient to describe the system

performance in terms of demand and capacity. The demand can be defined in terms of

different response parameters (e.g. shear, bending moment, displacement, velocity,

acceleration, drift, ductility, energy dissipation etc.) in the system caused by the ground

excitation. The capacity of the system is the maximum forces or response that the

system can withstand without member or system failure. The assessment of vulnerability

is made for a particular characterization of ground motion, which represents the seismic

demand of the earthquake on the building. The selected parameter should correlate the

ground motion with the damage to the building. Thus the definition of two intermediate

variables is required, one describing the ground motion intensity measure (IM) and the

other describing the structural demand, also known as engineering demand parameter

(EDP).

Simply stated fragility defines the conditional probability P[∙] of the seismic demand

(D) placed upon the structure exceeding its capacity (C) for a given level of ground

motion intensity (IM), as shown in the following equation:

Fragility P D C IM (2.1)

Different mathematical procedures for developing fragility curves have been proposed

in the literature (e.g. ATC-13, 1985; Shinozuka et al., 2000; Cornell et al., 2002; NIBS,

2004; Nielson and DesRoches, 2007; Porter et al., 2007 etc.). However two-parameter

lognormal distribution functions are traditionally used due to their simple parametric form

(Shinozuka et al., 2000). Thus Equation 2.1 can be further represented through Equation

2.2, which gives the cumulative probability of exceeding a particular damage state dsi

conditioned on a measure of the seismic intensity IM.

[ ]itot mi

1 IMP ds ds IM Φ lnβ IM

(2.2)

where P[∙] denotes the probability of being at or exceeding a particular damage state dsi

for a given seismic intensity level defined by the earthquake intensity measure IM, Φ is

the standard normal cumulative distribution function, IMmi is the median threshold value

of the earthquake intensity measure IM required to cause the ith damage state and βtot is

the total standard deviation. According to Equation 2.2, to develop fragility curves the

definition of two parameters is required, namely IMmi and βtot.



Figure 2.1 presents the graphical representation of a fragility curve. The conditional

probabilities P[ds=i/IM] for a structure experiencing a specific damage state dsi

illustrated in Figure 2.2, are estimated based on the probabilities of exceedance

P[ds≥i/IM]. For example if four damage states are adopted (i=0,1,2,3) then the

probabilities that a structure experiences the different damage states are calculated as:

P0(=no damage)=1.0-P(ds ≥ slight damage)

P1(=slight damage)= P(ds ≥ slight damage) – P(ds ≥ moderate damage)

P2(=moderate damage)= P(ds ≥ moderate damage) - P(ds ≥ extensive damage)

P3(=extensive damage)= P(ds ≥ extensive damage)

The total sum of these probabilities is equal to 1.

Figure 2.1. Graphical presentation of an example fragility curve

Figure 2.2. Conditional probabilities of exceeding different damage states



The vulnerability curve can be generated based on the estimation of the mean

damage ratio MDR. In Figure 2.3 an example vulnerability curve is presented. The MDR is

a representative single statistics that can be calculated assuming a repair cost for each

damage level (Hancilar et al., 2014). It is mathematically expressed as:

[ ]i ids

MDR CDR P ds i IM (2.3)

where CDRi represents the central damage ratio which is the ratio of the average cost of

repair at each damage state to the cost for building replacement (Hwang et al., 1994).

Figure 2.3. Conditional probabilities of exceeding different damage states

HAZUS (NIBS, 2004) is the first comprehensive methodology that contains models for

estimating potential losses of buildings from earthquake hazards at an urban scale. Its

first edition was released in 1997 (HAZUS, 97); the current version is HAZUS-MH v2.0,

which estimates the risk due to earthquakes, floods and hurricanes. Fragility curves for

buildings, utility and transportation networks are provided in HAZUS methodology. In the

first editions, the majority of the fragility functions were relied on the methodology and

data that were presented in ATC-13 (ATC, 1985) and ATC-25 (ATC, 1991) reports

following an expert judgment approach. Analytical studies have been later considered for

bridges and buildings.

In Europe, the first initiative to establish a methodology for the seismic risk

assessment of buildings include the RISK-UE (2004) project followed by LESSLOSS

(2007) both funded by European Commission framework programs for Research and

Technological Development.

Several research efforts have been made at a national level in Europe, aiming to

propose adequate generic fragility curves for buildings. Representative examples include

the SRM-LIFE (2007) projects in Greece and the RELUIS projects in Italy. Finally,



numerous other research efforts have been performed worldwide, developing fragility

functions and methods for the vulnerability assessment of different physical assets.

Among the latest developments is SYNER-G (2013) project. In the framework of the

project, a comprehensive review of existing fragility curves for the most important

elements at risk has been carried out, while new fragility curves have been developed

where necessary, considering the distinctive features of European elements (Kaynia,

2013). Moreover an integrated methodology has been developed for the systemic seismic

vulnerability and risk analysis of buildings, lifelines, infrastructures, transportation, utility

systems and critical facilities. The main goals of SYNER-G are summarized in the

following bullets:

to elaborate appropriate, in the European context, fragility relationships for the

vulnerability analysis and loss estimation of all elements at risk

to develop social and economic vulnerability relationships for quantifying the

impact of earthquakes

to develop a unified methodology and tools for systemic vulnerability assessment

accounting for all components exposed to seismic hazard, considering

interdependencies within a system unit and between systems

to validate the methodology and the proposed fragility functions in selected sites

(urban scale) and systems and to implement in an appropriate open source and

unrestricted access software tool.

The results of the studies carried out within the project can be found in Pitilakis et al.

(2014a).

2.3 Prerequisites for the derivation of fragility functions

The main parameters that are involved in the derivation of fragility functions, namely

taxonomy/typology/classification, intensity measures and damage states, are presented

in the following subsection. It should be noted herein that the main epistemic

uncertainties involved in the vulnerability assessment procedure are related to the

definition of the aforementioned parameters.

2.3.1 Taxonomy/typology/classification

The knowledge of the inventory of the general building stock in a region exposed to

seismic hazard and the capability to create uniform classes of building types are one of

the main challenges required to carry out a seismic risk assessment at an urban scale,

where it is practically impossible to perform the assessment at a building level. The

development of an efficient taxonomy able to adequately group different types of existing



buildings from different countries in Europe and worldwide is the key component in the

vulnerability assessment procedure. The classification is made based on the assumption

that buildings with similar structural characteristics are expected to perform in the same

way under a seismic excitation. For buildings the geometry, material properties and

seismic design level are among the common typology parameters.

Several building typologies exist. Prominent among these are: ATC-13 (ATC, 1985);

EMS-98 (Grunthal, 1998); ATC-14 (ATC, 1987), which was used with modifications in

FEMA 154 (ATC, 2002), HAZUS-MH (FEMA, 2006), and other FEMA-funded efforts; the

World Housing Encylopedia (WHE, http://www.world-housing.net/); RISK-UE 2004

(Mouroux et al., 2004); PAGER (Jaiswal and Wald, 2008; Jaiswal et al., 2010,

http://pager.world-housing.net.) and the most recent developed SYNER-G (Pitilakis et

al., 2014a, http://www.syner-g.eu/) for typical European structures.

In SYNER-G a great effort was paid to create a comprehensive taxonomy from which

European typologies for the most important elements at risk are defined (Hancilar and

Taucer, 2013). A taxonomy of existing buildings should allow their classification in terms

of their seismic resistance and response. As shown in Table 2.1, different main categories

are identified to describe a building, such as the force resisting mechanism, material,

elevation, code design level, cladding, etc. A hierarchy is used for some categories where

additional information might or might not be available, largely depending on the scale of

the studied region. Figure 2.4 presents a representative flowchart to group reinforced

concrete (RC) with moment resisting frame (MRF) buildings, taking into account the

height level, the code level, the cladding and the detailing. It is noted that each column

represents a different level of detail.

Table 2.1. SYNER-G taxonomy for buildings

CATEGORY SUB-CATEGORY Force Resisting Mechanism (FRM1) Moment Resisting Frame (MRF) Structural Wall (W) Flat Slab (FS) Bearing Walls (BW) Precast (P) Confined Masonry (CM)

Force Resisting Mechanism (FRM2) Embedded beams (EB) Emergent beams (EGB)

FRM Material (FRMM1) Concrete (C) Masonry (M)

FRM Material (FRMM2) Reinforced Concrete (RC) Unreinforced Masonry (URM) Reinforced Masonry (RM) High strength concrete (>50MPa) (HSC) Average strength concrete (20-50 MPa)

(ASC) Low strength concrete (<20 MPa) (LSC) Adobe (A)



CATEGORY SUB-CATEGORY Fired brick (FB) Hollow clay tile (HC) Stone (S) High yield strength reinforcing bars

(>300MPa) (HY) Low yield strength reinforcing bars

(<300MPa) (LY) Classification of reinforcing bars based on

EC2 (A,B,C) Lime mortar (LM) Cement mortar (CM) Mud mortar (MM) Smooth rebars (SB) Non-smooth rebars Concrete Masonry Unit (CMU) Autoclaved Aerated Concrete (AAC) High % of voids (H%) Low % of voids (L%) Regular Cut (Rc) Rubble (Ru)

Plan (P) Regular (R) Irregular (IR)

Elevation (E) Regular geometry (R) Irregular geometry (IR)

Cladding (C) Regular infill vertically (RI) Irregular infill vertically (IRI) Bare (B)

Cladding Characteristics (CM) Fired brick masonry (FB) High % voids (H%) Low % voids (L%) Autoclaved Aerated Concrete (AAC) Precast concrete (PC) Glazing (G) Single layer of cladding (SL) Double layer of cladding (DL) Open first floor (Pilotis) (P) Open upper floor (U)

Detailing (D) Ductile (D) Non-ductile (ND) With tie rods/beams (WTB) Without tie rods/beams (WoTB)

Floor System (FS) Rigid (R) Flexible (F)

Floor System Material (FSM) Reinforced concrete (RC) Steel (S) Timber (T)

Roof System (RS) Peaked (P) Flat (F) Gable End Walls (G)

Roof System Material (RSM) Timber (Ti) Thatch (Th) Corrugated Metal Sheet (CMS)

Height Level (HL) Number of stories (NS) [Here the number of stories is explicitly given,



CATEGORY SUB-CATEGORY Low-rise (1-3) (L) Mid-rise (4-7) (M) High-rise (8-19) (H) Tall (20+)(Ta)

if known]

Code Level (CL) None (NC) Low (<0.1g) (LC) Moderate (0.1-0.3g) (MC) High (>0.3g) (HC)



Figure 2.4. Flow chart for a Reinforced Concrete, Moment Resisting Frame building class according

to SYNER-G



2.3.2 Intensity measures

The selection of an appropriate earthquake intensity measure (IM) that characterizes the

strong ground motion (e.g. amplitude, duration, frequency content, energy content) and

correlates well with the building response is of high importance for the derivation of

fragility curves. The optimal selection of IM can be supported by examining the following

qualities (Mackie and Stojadinovic, 2003;2005, Mehanny, 2009, Padgett et al., 2008):

practicality, sufficiency, effectiveness, efficiency, robustness and hazard computability.

Practicality refers to whether or not there is any direct correlation between an IM and the

demand placed on the structure. A further criterion for evaluating practicality is whether

the IM is readily described by available attenuation relationships or other sources of

hazard data. A sufficient IM is statistically independent of ground motion characteristics

(such as magnitude and epicentral distance), rendering a demand model that is

conditionally independent of the earthquake scenario. The effectiveness of an IM is

determined by its ability to evaluate, in a closed form, the mean annual frequency of a

decision variable exceeding a given limiting value. An efficient IM reduces the amount of

variation in the estimated demand for a given IM value. Robustness describes the

efficiency trends of an IM-EDP pair across different structures and therefore fundamental

period ranges. Hazard computability refers to the availability of estimates of the expected

IM from hazard studies.

In general, IMs are grouped into two general categories: the empirical intensity

measures (e.g. European macroseismic scale EMS) and the instrumental intensity

measures (e.g. peak ground acceleration PGA, peak ground velocity PGV, peak ground

displacement PGD etc.) (Pitilakis et al., 2014a). The instrumental intensity measures

have the advantage that the severity of the earthquake is no longer subjective as they

are expressed as an analytical value measured by an instrument or computed analyzing

the seismic recordings and therefore are considered more accurate and representative of

the seismic intensity characteristics.

For the assessment of buildings the strong motion parameters that are used almost

invariably to characterize earthquake shaking are the peak ground acceleration (PGA)

and response spectral ordinates for a linear-elastic lightly-damped (often 5%) single

degree of freedom (SDOF) system. Response spectral ordinate usually refers to spectral

acceleration Sa(Ty) (or pseudo-spectral acceleration) or spectral displacement Sd(Ty) at

the elastic natural period Ty of the structure and their advantage in comparison to PGA is

that they provide information also on the frequency content of earthquake shaking. In

the pie chart of Figure 2.5 the percentages regarding the different IMs used for the

vulnerability assessment of European buildings (Pitilakis et al., 2014a) are presented. In



the reviewed studies, fragility functions have been derived in terms of macroseismic IMs

(Mercalli-Cancani-Sieberg Intensity Scale: MCS, Modified Mercalli Intensity Scale: MMI,

Medvedev-Sponheuer-Karnik Intensity Scale: MSK81, European Macroseismic Scale:

EMS98) and instrumental IMs (PGA, PGV, root mean square of the acceleration RMS,

Sa(Ty), Sd(Ty), spectral displacement at the inelastic period TLS corresponding to a specific

damage state: Sd(TLS), roof drift ratio). Sa(Ty), Sd(Ty), Sd(TLS) and roof drift ratio are

structure-dependent IMs as they are based on response parameters and thus require

structural information regarding the building typology. Figure 2.5 shows that PGA has

been the most commonly used intensity measure in the studied literature.

MMI 5%

MCS 2% MSK81

3%

PGA 38%

PGV5%Sa(Ty)

3%

Sd(Ty)15%

Sd(TLS)23%

RMS 3%

Roof Drift Ratio3%

Figure 2.5. Pie chart presenting the percentages of different intensity measure types used for the

development of fragility functions for reinforced concrete buildings (Pitilakis et al., 2014a)

One IM that has recently been shown to be useful in explaining structural response is

epsilon of Sa at a certain structural period Ty, which is defined as the normalized residual,

in terms of natural logarithms, between the observed and the predicted by a given GMPE

for Sa (Baker and Cornell, 2005). The reason why epsilon is a potentially useful IM is that

it is an indicator of peaks and troughs in response spectra scaled to a common Sa at a

given period: negative epsilon generally indicates a trough (hence a higher structural

response because it is influenced by neighboring higher Sa) and positive epsilon means a

peak (hence a lower structural response due to lower Sa at adjacent periods). The use of

epsilon for risk evaluation is possible if its value is known from hazard disaggregation or

by using probabilistic site-specific demand analysis but it is not a suitable parameter for

the construction of fragility functions unless it is combined with a fragility function using

Sa (e.g. Tothong and Luco, 2007).



2.3.3 Damage indicators and states

In order to derive seismic fragility curves for different elements at risk, it is necessary to

define multiple damage states for the element exposed to seismic hazard. To accomplish

this, the first step is the establishment of a damage indicator or damage measure in

terms of engineering demand parameters that are able to adequately describe its

expected seismic performance.

Generally, damage indices or damage measures aim to quantify the damage level of

structures under earthquake loading. Damage indices are damage functions that are

commonly defined based on the results of a numerical analysis, on the measured

response of a structure during an earthquake or on a comparison of a structure’s

physical properties before and after an earthquake (Williams and Sexsmith, 1995).

Also empirical damage indices may be defined based on databases of damage data

collected following one or more earthquake events.

In general damage indices may consist of one or more damage measures and can be

classified based on deformation terms, stiffness degradation, hysteretic energy

dissipation, number of seismic cycles, engineering experience, observational data as well

as rehabilitation and reconstruction (or replacement) cost. The relationship between a

damage parameter (d) and a damage index (D) is illustrated in Figure 2.6 for the simple

case where D is expressed in terms of a single parameter d (Kappos, 1997). As shown in

Figure 2.6 for D=0 it is d=d0>0, which implies that below a threshold value of the

damage parameter no damage is detected and the structural behavior remains elastic.

On the other hand when d=du structural failure (or complete collapse) is considered and

therefore D=1. For d>dr repair of the structure is required to restore its initial

conditions. The description of the curve shape D=f(d) and the selection of appropriate

values for du and dr is not an easy task due to the lack of sufficient experimental data for

different structural types and the difficulty in the definition of common failure criteria

between the different research groups. A possible expression of the damage index

(Kappos, 1997) could be:

a

cal 0a

u 0

(d d )D

(d d )

(2.4)

where dcal is the value of the damage parameter value calculated from the analysis and a

is an exponent which may be considered equal to unity in the absence of experimental

data. The relationship damage index – damage parameter, as illustrated in Figure 2.6,

can be expressed not only in structural but also in economical terms. In this case the

economic damage index is expressed as the ratio of the required cost of repair to the

corresponding cost of replacement (or reconstruction).



Numerous damage indices/measures are proposed in the scientific literature. They

may express analytically the comparison of a demand with a capacity quantity, or the

consequence of a mitigation action, or the assembled consequences of all damages (the

“impact”). In the case of reinforced concrete buildings subjected to earthquake loading,

the damage measures that are commonly used, are related to deformation quantities,

such as strain (compressive, tensile) and curvature, rotations at member ends, horizontal

storey displacements, relative displacements between two adjacent storeys (interstorey

drift) and/or fatigue loading terms. For indicators based on displacement or stiffness

degradation, the maximum seismic response of the structures is taken into consideration.

On the other hand, indicators related to degenerative behavior and/or cumulative

damage sustained under repeated load reversals depend on the amount of dissipated

hysteretic energy and take into account the effect of plastic cycles in the structural

response.

The parameters most widely used to evaluate structural damage are ductility and

plastic dissipated energy. In the case of ductility, collapse depends on a predefined

displacement value whilst, in the case of plastic dissipated energy, collapse of the

structure under cyclic loads depends on the amount of energy that can be plastically

dissipated. Indicators based on dynamic properties are used to quantify damage through

modal testing. This approach often includes vibration measurements of the structure due

to a particular excitation. In case of structural deterioration, changes in the measured

dynamic responses are expected. These changes are reflected in the modal properties of

the structure (natural frequencies, damping ratios, mode shapes), which can be

determined either experimentally or analytically. Indices developed on this basis may

provide information both on the extent of damage and its location.

Figure 2.6. Relationship between damage parameter (or damage variable) and damage index

(Kappos, 1997)



Different schemes are proposed for the classification of damage indices (Kappos,

1997). For example some categorizations are defined based on whether they refer to a

single element or to the whole structure (local or global) or whether they are structural

or economic, on the mathematical approach for their determination (deterministic or

probabilistic) or the type of analysis for their estimation (no analysis, linear elastic,

inelastic). In the next subchapter the most commonly used global and local damage

indices based on structural properties are presented.

Based on performance indicators, damage thresholds may be defined, that are called

limit states. A limit state defines the threshold between different damage conditions,

whereas the damage states define the damage conditions themselves. For example, the

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

limit states. In Figure 2.7 the difference between damage states and limit states is

presented (Crowley et al., 2011).

Figure 2.7. Limit states and damage states (Crowley et al., 2011)

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

damage scale. In empirical procedures, the scale is used in reconnaissance efforts to

produce post-earthquake damage statistics, whereas in analytical procedures the scale is

related to mechanical properties of the buildings.

The number of damage states (and consequently the number of limit states) depends

on the damage scale used and is related with the functionality of the components and/or

the repair duration and cost. Some of the most frequently damage scales used are: HCR

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

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

some of the damage scales applicable for RC buildings is presented in Table 2.2. It

should be noted that there are some studies that do not refer to any of the damage



scales reported in Table 2.2 but they follow specific damage state scales developed by

the authors.

Depending on the methodology used to compute the fragility functions, different

scales with different limit states/damage states can be adopted. Limit states in reinforced

concrete structures should be correlated to the predominant damage mode. In this

respect, the corresponding damage index that best reflects a flexural limit state may not

correlate well with damage such as diagonal cracking due to shear, or bond splitting due

to lack of confinement (Williams and Sexsmith, 1995).

Table 2.2.Comparison of existing damage scales with the HRC damage scale (adapted from Rossetto and Elnashai, 2003)

HRC HAZUS99 Vision 2000 EMS98 ATC-13 None No damage

Slight

Slight damage

Fully operational Grade 1

Slight

Light Light

Operational Grade 2

Moderate

Moderate Moderate damage Grade 3

Life Safe Heavy

Extensive Extensive damage

Near Collapse Grade 4

Major Partial Collapse Collapse

Collapse Collapse

2.3.3.1. Local damage indices

Local indices may involve a single damage parameter, such as maximum deformation or

dissipated energy, or two or more parameters. Most local indices are cumulative in

nature, reflecting the dependence of damage on both the amplitude and the number of

cycles of loading. Local damage indices may be further categorized as cumulative and

non-cumulative damage indices. A non-cumulative damage index can only capture the

maximum damage value whereas a cumulative damage index takes into account the

damage accumulation reflecting the dependence of damage on both the amplitude and

the number of cycles of loading.

Non-cumulative damage indices

The non-cumulative damage indices are usually expressed in ductility, deformation or

stiffness terms. The earliest and simplest form of damage indices is ductility. The ductility

ratio can be defined in terms of rotation, curvature or displacement and by choosing it as

a damage measure it is assumed that structural collapse is expected for maximum plastic



deformation, independent of the number of plastic cycles and the amount of dissipated

energy.

Banon et al. (1981) used the rotational ductility (μθ) at the end of a structural

member as its damage index:

m ymθ

y y

θ θθμ 1

θ θ (2.5)

where θm is the maximum rotation (including both elastic and plastic rotations) under

seismic loading and θy is the yield rotation, considering the member’s antisymmetric

double-curvature bending with the point of contraflexure in its mid-span.

An indicator based on kinematic or cyclic ductility was developed by Cosenza et al.

(1993). The proposed damage index is defined as:

u

μ 1Dμ 1

(2.6)

where μ is the kinematic or cyclic ductility of the structural element and μu the maximum

allowable ductility corresponding to the maximum displacement.

In Erduran and Yakut (2004) damage functions were developed for reinforced

concrete columns based on the drift ratio. More specifically the damage criterion used in

this study depends mainly on the ductility index which is the ratio of the given drift

divided by the yield drift, hence the yield drift. Different parameters that affect the

seismic behavior of a RC column were taken into account, namely the axial load level,

the slenderness, the amount and the yield strength of longitudinal reinforcement and the

amount of the transverse reinforcement. Moreover three ductility levels for the RC

column were considered (low, medium and high). Damage scores were assigned to

different levels of crack widths. The calibration of the corresponding damage states was

achieved based on the criterion suggested by the Japanese government. In Table 2.3 the

proposed limit values of the damage index (DI) corresponding to the different damage

state are summarized.

Table 2.3. Damage states (adapted from Rossetto and Elnashai, 2003)

Damage states Limit values of DI No damage DI < 0.005

Negligible 0.005 < DI < 0.075

Light 0.075 < DI < 0.30

Moderate 0.30 ≤ DI ≤ 0.90

Collapse 0.90 ≤ DI ≤1.00

In Jeong and Elnashai (2005) a damage index in terms of interstorey drift was

preferred to curvature demand, due to the fact that the former is easier to monitor and

accurate enough to estimate damage inflicted on critical columns. The demand-to-



capacity ratio (DCR) of each column is expressed based on Equation 2.7 and accounts for

the bi-directional response of the structure:

22

x y

∆x ∆yDCR∆u ∆u

(2.7)

where ∆x and ∆y are the interstorey drift in the x direction and in the y direction

respectively while ∆ux and ∆uy the ultimate interstorey drift where the curvature of the

column reaches the ultimate value under average axial force.

Damage indicators based on stiffness and strength degradation have also been

proposed in the literature. Lybas and Sozen (1977) proposed an indicator based on the

stiffness degradation of the damaged component while Banon et al. (1981) defined the

flexural damage ratio (FDR) as an indicator based on stiffness and strength degradation

that occur under cyclic loading. Roufaiel and Meyer (1987a) on the other hand used a

modified version of the flexural damage ratio index, considering the increase in flexibility

at maximum deformation and at failure state.

Cumulative damage indices

Different damage indices are proposed in the literature to model cumulative damage

under cyclic loading. Cumulative indicators are usually defined based on a low-cycle

fatigue formulation, in which damage is considered as a function of either the

accumulated plastic deformation or the hysteretic energy absorbed during the loading.

Stephens and Yao (1987) developed a cumulative damage index based on

displacement ductility considering for its calculation the positive and negative

displacement increments during cyclic loading. Jeong and Iwan (1988) index quantified

damage under cyclic loading combining the effects of cyclic at different amplitudes. More

specifically the proposed index relates the number of cycles at a specific amplitude with

the number of cycles to failure at that same amplitude. It also measured the influence of

both duration and ductility of response.

Many cumulative damage indices are related to the hysteretic behavior of the

concrete member under study. Gosain et al. (1977) first adopted as damage measure a

simple cumulative energy ratio, which was defined based on the force corresponding to

the element displacement in relation to the force corresponding to the element yielding

displacement. Furthermore modification factors were proposed in order to account for the

effect of shear span ratio and axial load. The plastic dissipated energy was firstly

introduced as a damage measure considering cumulative energy absorption (Akiyama,

1985). Researchers have proposed different variations of this type of damage index



including modification factors to account for the specific geometrical and loading

conditions of reinforced concrete elements.

Kratzig et al. (1989) developed a more complex index formulation based on the

definition of primary and follower half-cycles. A primary half-cycle (PHC) is defined as the

first half-cycle of loading at a given amplitude, with subsequent half-cycles termed as

followers unless they exceed the previous maximum amplitude. Thus, cumulative

damage caused by cyclic loading is taken into account even when no increase in

maximum deformation is noticed. The energy absorbed is considered to be equal to the

area of the hysteresis loops. The energy of each half – cycle may be assumed to be the

half of the complete cycle under the condition that the loops in the load – deformation

diagram are symmetrical.

Combined indices

Park and Ang (1985) damage indicator is a linear combination of maximum deformation

and hysteretic energy dissipation. The form of the Park-Ang index is:

Μe

u y u

dEδDI β

δ F δ (2.8)

where D is the damage index, δm is the maximum response deformation under an

earthquake, dE is the incremental dissipated hysteretic energy, δu is the ultimate

deformation capacity under monotonic loading, Fy is the yield strength of the longitudinal

reinforcement and βe is a nonnegative constant and is a factor which considers the effect

of cyclic loadings on structural damage. It is a function of shear span ratio, normalized

axial stress, longitudinal steel ratio and confinement steel ratio. The first term is the ratio

of maximum recorded deformation to the capacity deformation of a member under

monotonic loading conditions (ductility-based damage index) and the integral term is the

energy dissipation normalized by the product of the yield force and deformation capacity,

scaled by an empirical factor determined on the basis of a large number of test results.

Park et al. (1984) presented five damage levels based on observation of post-earthquake

damage of RC buildings. The suggested classification of limit states is presented in Table

2.4 (Williams and Sexsmith, 1995).

The modified Park-Ang index (Kunnath et al., 1992) slightly modifies Equation 2.8 to

consider only the permanent deformation in the first term. Also moment and curvature

are used instead of force and displacement:

m ye

u y y u

dEφ φDI β

φ φ M φ (2.9)



where φm is the maximum curvature under seismic loading, φu is the ultimate curvature,

φy is the yielding curvature, βe is an empirical coefficient defined as a function of the

structural characteristics and My the yielding bending moment.

Table 2.4. Damage states (Park et al., 1984; Williams and Sexsmith, 1995)

Damage states Limit values of DI

No damage or localized minor cracking DI < 0.1

Minor damage (light cracking throughout)

0.1 ≤ DI < 0.25

Moderate damage (severe cracking, localized spalling)

0.25 < DI < 0.4

Severe damage (crushing of concrete, reinforcement exposed)

0.4 ≤ DI ≤ 1.0

Collapse (Total or partial collapse of building)

DI ≥1.0

2.3.3.2. Global damage indices

The global damage state of the overall structure depends on both the distribution and

severity of localized damages. The use of local damage indices identifies the weak or

vulnerable elements that should be rehabilitated. However using local damage indices it

is difficult to estimate the structural response to a given ground motion and to assess the

residual strength and safety of a damaged structure. Thus global damage indices are

required for post-earthquake evaluation of structures , reliability studies and applications

in the performance-based engineering approach (Ghobarah et al., 1999).

The approach widely used to obtain the global damage state is to take an average of

the local indices, weighted by the local energy absorption (Park et al., 1987; Chung et

al., 1990; Kunnath et al., 1992). Thus the damage index for a single storey of a

structure is defined as:

i istorey

i

D ED

E

(2.10)

where Di is the local damage index at location i and Ei is the energy absorbed at location

i.

Park and Ang's (1985) global damage index is used to represent the performance

of structural systems. It is defined as a weighted average of the local damage indices of

each element. The weighting function for each element is proportional to the energy

dissipated in the element. The global damage index is given by the following equation:

i iD λD (2.11)



ii

i

Eλ

E

(2.12)

where Ei is energy dissipated at location i.

Bracci et al. (1989) presented a more generalized definition of the storey damage

index:

(b 1)

i istorey b

i i

w DD

w D

(2.13)

where b is an exponent giving greater emphasis on the most damage elements and wi is

the weights defined as the ratio of the gravity load supported by member i to the total

gravity load on the structure.

Damage causes changes in dynamic structural properties (natural

periods/frequencies, damping, mode shapes). Due to stiffness degradation and energy

dissipation usually an increase in the natural period and damping is expected respectively

(Dowell, 1979). Damping has been found to be too variable as a parameter to be a useful

damage indicator. Thus research has been focused on changes in period and more

specifically in fundamental period (or the fundamental frequency).

Newmark and Rosenblueth (1974) developed an indicator based on the fundamental

period from laboratory experiments on reinforced concrete elements. Modal damage

index, as expected, requires the identification of the natural frequencies of the structure

under study, which can be estimated from analytical processing of responses of the

structure to external vibrations. Then when structural damage occurs the changes in the

natural frequencies serve as damage indicators.

Roufaiel and Meyer (1987b) proposed a correlation for a simple global damage index

expressed in terms of deflections at roof level:

undy

damm yglobal

f y f y

f14.2δ 1

fδ δD

δ δ δ δ

(2.14)

where fund and fdam are respectively the fundamental frequencies of the structure before

and after being damaged and δf, δy are the ultimate and yielding deformation capacity

under monotonic loading respectively.

Softening indices (DiPasquale and Cakmak, 1987; 1989, DiPasquale et al., 1990)

were developed based on the combination of characteristic fundamental periods (or

frequencies) obtained at different states of the damage process. The maximum softening

Dms, the plastic softening Dps, the final softening Dfs, presented in the following equation

can be formulated in terms of the three periods indicated in Figure 2.8.



2 2

und dam undms ps fs2 2

m m dam

T T TD 1 , D 1 , D 1

T T T (2.15)

where Tund and Tdam: the fundamental period of the structure before and after the

earthquake and Tm is the maximum period obtained during the earthquake.

Figure 2.8. Variation in fundamental period of a structure during an earthquake (DiPasquale et al.,

1990)

Ghobarah et al. (1999) recognizing the difficulties in the analytical calculation of the

change in period as a measure of damage, proposed an approach for determining the

change in stiffness of the structure. According to this approach, pushover analysis is

performed twice, once before the structure is subjected to the earthquake and once after

the structure has been subjected to the seismic loading. Relating the initial stiffness

before and after subjecting the structure to seismic ground motion, a global stiffness

damage index can be calculated for the ith as follows:

i

i finaliKinitial

KDI 1

K (2.16)

where Kiinitial and Ki

final are the initial slopes of the base shear-storey drift relationships of

the ith storey. One of the main advantage of this approach is that the proposed global

damage index can be obtained for each storey level separately as well as for the whole

frame, without the need for an averaging or weighting of local damage indices to

integrate the effect of the frame elements. The limit values corresponding to the different

damage states for the proposed damage index can be defined as listed in Table 2.5.

Table 2.5. Range of the proposed damage index for different damage states (Ghobarah et al., 1999)

Damage states Limit values of DI No or slight damage 0.0 < DI < 0.15

Moderate (reparable) 0.15 < DI < 0.30

Severe (irreparable) 0.30 < DI < 0.80

Collapse 0.80 < DI ≤1.00



2.3.3.3. Damage measures

In many vulnerability assessment methods the use of damage measures over damage

indices is preferred. The most common damage measure that is used for the derivation

of fragility function for reinforced concrete buildings is the interstorey drift ratio. Other

damage measures that have also been used are the chord rotation and the material

strain.

Chord rotation

In Fardis et al. (2012) fragility curves were derived for RC frame and wall-frame

buildings designed to the EN-Eurocodes, using as damage measure the chord rotation at

the member end for two damage states: member yielding and ultimate condition in

flexure. Chord rotation at a member end is the angle between the normal to the member

section there and the chord connecting the two member ends in the deformed

configuration. In Part 3 of Eurocode 8 three performance levels/limit states are defined:

“Damage Limitation” (DL), similar to “Immediate Occupancy” in SEAOC 1995; ATC

1997; ASCE 2007

“Significant Damage” (SD), which corresponds to “Life Safety” in SEAOC 1995;

ATC 1997; ASCE 2007

“Near Collapse” (NC), similar to “Collapse Prevention” in SEAOC 1995; ATC 1997;

ASCE 2007

The limit states for flexural systems are defined in terms of chord rotations at the

member ends. At the “Damage Limitation” (DL) limit state, ductile mechanisms are

required to remain elastic (below yielding) while at other extreme, the “Near Collapse”

(NC) limit state, ductile elements are allowed to reach their ultimate deformation

capacity. At the “Significant Damage” (SD) limit state, the chord rotations at the member

ends of “ductile” elements are limited to 78% of the deformation limit in the “Near

Collapse” (NC) level. The ultimate chord rotation, θu, or plastic hinge rotation, θplu, under

cyclic loading is conventionally identified with a 20%-drop in moment resistance. Annex

A of Eurocode 8 Part 3 (CEN 2005a, 2009) gives expressions and rules for the calculation

of the mean value of the chord rotation at yielding θy or at ultimate θu,m. The compliance

criteria for the assessment of RC members in Eurocode 8 Part 3 are summarized on Table

2.6.

Table 2.6. Compliance criteria for assessment of RC flexural member in Eurocode 8 – Part 3 (Fardis 2014)

Mechanism Damage limitations (DL)

Significant damage (SD)

Near collapse (NC)

Flexure (ductile) θ ≤ θy θ ≤ 0.75θu,m θ ≤ θu,m



Material strain

In Crowley et al. (2004) a probabilistic displacement-based vulnerability assessment

procedure was proposed for earthquake loss estimation. Structural damage was

described based on the mechanical material properties of RC members. Four discrete

scales of structural damage were defined: none to slight, moderate, extensive or

complete. A qualitative description of each damage level is given in Table 2.7 along with

quantitative suggestions for the mechanical material properties, namely steel strains (εs)

and concrete strains (εc) based on the work of Priestley (1997) and Calvi (1999). The

first structural limit state is defined as the yield point of the structure while the second

and third limit states are attained when the sectional steel and concrete strains reach the

suggested limits of Table 2.7. Two alternative ranges of strain limits are suggested for

the limit states “Extensive” and “Collapse” due to the fact that the ultimate strains that

can be reached depend on the level of structural members confinement.

Table 2.7. Description of the discrete damage scales adopted in Crowley et al. (2004) for RC frame structures

Damage states Description

None to slight

Linear elastic response, flexural or shear type hairline cracks (<1.0mm) in some members, no yielding in any critical section; hence

limit state to damage band is structural yield point Limit state 1: Steel bar yielding

Moderate Member flexural strengths achieved, limited ductility developed, crack

widths reach 1.0mm, initiation of concrete spalling Limit state 2: εs = 0.010-0.015 εc = 0.004-0.005

Extensive

Significant repair required to building, wide flexural or shear cracks, buckling of longitudinal reinforcement may occur

Limit state 3: Inadequately confined members: εs = 0.015-0.030 εc = 0.005-0.010 Adequately confined members: εs = 0.040-0.060 εc = 0.010-0.020

Complete Repair of building not feasible either physically or economically,

demolition after earthquake required, could be due to shear failure of vertical elements or excessive displacements

2.3.3.4. Drift damage formulation

Drift is widely used in seismic vulnerability assessment studies of RC buildings either as

damage measure or damage indicator. Ductility alone is not able to describe adequately

failure due to damage concentration on the floor levels. In these cases the use of

maximum inter-storey drift ratio (ISD) is more appropriate as it is found to correlate well

with structural damage and levels of inelastic behavior.

The drift of a structure is a function of different parameters like stiffness, strength,

ductility, the type of applied load. Experimental studies for example have shown that

increase of axial load increases the shear resistance of the structural member and

reduces lateral drift (Ghobarah, 2004). In Figure 2.9, the relationship between



performance objectives and damage is illustrated based on the typical capacity curve in

terms of drift.

Figure 2.9. Typical structural performance and associated damage states (Ghobarah, 2004)

Roof drift is often used for damage assessment despite the fact that it cannot always

reflect the damage distribution along the structure’s height, which is important for soft

storey identification. Inter-storey drift, on the other hand, can be correlated well to

damage at each floor level. For example, in case of a moment resisting frame structure

with a soft storey, inter-storey drift of the soft storey would be a more reliable damage

indicator in comparison to the roof drift as it would allow capturing also the damage

distribution alone the structure’s height. Thus maximum interstorey drift of the soft

storey may indicate collapse while roof drift would possibly correspond to a lower

damage level. Therefore two parameters should be considered for the identification of

structural damage in a MRF: (a) the interstorey drift and (b) its distribution along the

height of the structure (Ghobarah, 2004).

Two sources are contributing to the ISD, the lateral translations by shear and flexural

deformation and the translations from rigid body motion due to lower storey rotation.

The first one relates structural deformations to member stress and strain resultants,

while the latter one does not contribute to structural demand.

Algan (1982) attempted an initial approach of estimating reinforced concrete building

damage based on inter-storey drift. In case of shear walls he proposed a damage

indicator for each storey defined as the difference of the drift index angle for that storey

and the joint rotation at the bottom floor level whilst in case of moment resisting



frames, drift is used directly as the damage index. The scale of damage that was used to

estimate the damage condition of the buildings is presented in Table 2.8.

Table 2.8. Damage states for damage index based on interstorey drift (Algan, 1982) Damage states Limit values of DI None (no repair) 0.0 < DI < 0.05

Minor (minor or no repair) 0.05 ≤ DI < 0.35

Moderate (some repair) 0.35 ≤ DI < 0.55

Substantial (a lot of repair) 0.55 ≤ DI <0.75

Major (demolition and rebuilding) 0.75 ≤ DI ≤1.00

Ghobarah (2004) defined for reinforced concrete moment resisting frames the storey

drift factor (SDF), an indicator based on the inter-storey drift and its distribution along

the height of the structure, which correlates quite well with damage in moment resisting

frames with soft storey. A value of the SDF=0 indicates equal interstorey drift along the

height whereas a value close to 1 represents the case where the overall drift is caused by

few storeys (e.g. soft storey). The SDF for a number of ductile, well-designed MRFs is

correlated with damage as shown in Figure 2.10. The damage index that is used in this

study is the final softening damage index, which represents the effect of stiffness

degradation following the loading history and can be related to damage at the element

and storey levels (Table 2.9).

Although Algan (1982) and Ghobarah (2004) used interstorey drift for the formulation

of a damage indicator, most vulnerability assessment studies are using maximum

interstorey drift as a damage measure for the derivation of fragility curves. Ghobarah

(2004) associated the different damage levels for RC buildings also with maximum

interstorey drift limits as presented in Table 2.10.

Figure 2.10. Correlation between the interstorey drift factor and damage for a 3, 6, 9 and 12

storey MRFs (Ghobarah, 2004)



Table 2.9. Damage states for damage index based on interstorey drift for ductile MRFs (Ghobarah, 2004)

Damage states Element Storey Global

No damage <0.2 <0.15 <0.1

Repairable damage (a) Light <0.3 <0.2 <0.15

(b) Moderate <0.4 <0.3 <0.2

Irreparable damage (>yield) >0.4 >0.3 >0.2

Severe damage – Life safe – Partial collapse 0.6-0.8 0.5-0.7 0.4-0.6

Collapse >0.8 >0.7 >0.6

Table 2.10. Drift ratio (%) limits associated with various damage levels (Ghobarah, 2004)

Damage states Ductile MRF

Nonductile MRF

MRF with infills

Ductile walls

Squat walls

No damage <0.2 <0.1 <0.1 <0.2 <0.1

Repairable damage (a) Light 0.4 0.2 0.2 0.4 0.2

(b) Moderate <1.0 <0.5 <0.4 <0.8 <0.4

Irreparable damage (>yield) >1.0 >0.5 >0.4 >0.8 >0.4

Severe damage – Life safe – Partial collapse 1.8 0.8 0.7 1.5 0.7

Collapse >3.0 >1.0 >0.8 >2.5 >0.8

According to Ji et al. (2007) for high-rise buildings, it is insufficient to use traditional

definitions of inter-storey drift ratio for damage measure of the structural performance.

There are two significant sources that contribute to the ISD: (1) the lateral translations

by shear and flexural deformation on one hand, which relates the structural deformations

to member stress and strain resultants and (2) the translations from rigid body motion

due to lower storey rotation, which does not contribute to structural demand. To this

aim, a new measure was proposed called inter-storey pure translation ratio (ISPT), which

can be calculated from post-processed deformation data by removing the rigid body

component. In Table 2.11 the proposed limit states criteria that are adopted in this study

are summarized for both maximum ISD and maximum ISPT respectively.

Table 2.11. Limit state criteria adopted for the reference building structure in Ji et al. (2007)

Level Limit State ISDmax (%) ISPTmax (%)

Limit State 1 (LS1) Serviceability 0.20 0.035

Limit State 2 (LS2) Damage Control 0.52 0.147

Limit State 3 (LS3) Collapse Prevention 1.10 0.265

Many previous studies and design standards have adopted drift limits for damage

assessment of reinforced concrete buildings (FEMA-356; HAZUS; Rossetto and Elnashai,

2003; Ghobarah, 2004; Akkar et al., 2005 etc.). Damage states have been defined based



on the drift for ductile, non-ductile, infilled and bare-frame reinforced concrete moment

resisting frames as well as shear walls. In general the damage scales that are used in

the different studies can be quite heterogeneous. In Hill and Rossetto (2008)

correspondences between the different scales are well detailed.

2.3.4 Treatment of uncertainties

Several sources of uncertainties are introduced in the assessment process and

accordingly impact the ensuing technical, economic and social decision. Therefore the key

point is to incorporate the uncertainties in a way that the information and the knowledge

relevant to the problem are presented in the most faithful manner (Aven and Zio, 2011).

The uncertainties are usually categorized in aleatory and epistemic. Aleatory

uncertainties stem from the intrinsic randomness of a phenomenon (e.g. earthquake

occurrence on a known fault) while epistemic uncertainties arise from the lack of

knowledge, ignorance or modeling (e.g. two dimensional idealization of buildings for

structural analysis). Apparently random observations due to: unknown factors; known

factors which are not modeled and pragmatic simplifications of reality, are generally

considered to be a result of aleatory uncertainties (Strasser et al., 2009). It may appear

that the characterization of any given uncertainty as aleatory or epistemic is self-evident,

but in fact the aleatory/epistemic quality is not an absolute attribute of uncertainty.

Rather, it depends on the deterministic or stochastic representation of the phenomenon.

Uncertainty that is explicitly recognized by a stochastic model is aleatory. Uncertainty on

the model itself and its parameters is epistemic. Hence the aleatory/epistemic split of the

total uncertainty is model-dependent (Wen et al., 2003). In contrast to aleatory

uncertainties, the knowledge based (or epistemic) uncertainties depend on the quality of

the analysis and supporting databases, and generally can be reduced, at the expense of

more comprehensive (and costly) analysis (Ellingwood and Wen, 2005). Thus although

the distinction between aleatory and epistemic uncertainties depends on the problem that

is investigated, uncertainties should be treated as aleatory or epistemic depending on

whether they are reducible or not (DerKiureghian and Ditlevsen, 2009).

Sources of epistemic uncertainties in a fragility assessment study are associated with

small databases of poor quality, biased sampling techniques, inability to account for the

complete characteristics of ground shaking in the selection of IMs, the nonlinear models

for the variety of structural materials and components, imposed loading distribution to

identify critical response, effects of using monotonic response to represent capacity when

actual earthquake demand is cyclic in nature, differences in analytical programs etc.

Limitations in knowledge and ability to model the hazard and its demand on the system,

the response of the system to specific demands, the ensuing state of the system and



damage and the relation of costs to limit or damage states give further rise to epistemic

uncertainties. On the other hand sources of aleatory uncertainty include the natural

variation in earthquakes and their resulting ground shaking, the variability in material

properties for both structural strength and stiffness, construction errors etc.

Table 2.12 provides seven sources of uncertainty present in the development of

fragility functions from experimental data as defined in FEMA 461 (2007). As noted in

FEMA 461, the first four uncertainties (epistemic) can be reduced by careful planning of

the experimental program while the last two are simply denoted as randomness

(aleatory) uncertainty which can be directly considered using the experimental data.

In general the uncertainty in fragility is estimated through the standard deviation βtot

that describes the total variability associated with each fragility curve. Although many

researchers investigate the propagation of the uncertainties based on the aforementioned

categorization (e.g. Baker and Cornell, 2008; Bradley, 2010), aleatory and epistemic

uncertainties are often not separated.

In the simplest case, where only the uncertainties in seismic demand (βD) and

structural capacity (βC) are considered, the total variability βtot is determined assuming

that they are stochastically independent and lognormally distributed random variables

based on the following equation:

2 2tot D Cβ β β (2.17)

Table 2.12. Sources of uncertainty in fragility functions as identified in FEMA461 (2007)

N Description Classification

1 Testing a component isolated from its in-situ conditions such as electrical conduits, piping, or supported floor slabs Epistemic

2 Imperfect simulation of boundary conditions Epistemic

3 Extrapolation to in-situ conditions not fully simulated in the test Epistemic

4 Variability in configuration Epistemic

5 Employment of a loading history that cannot precisely replicate the loading experienced by components in a real building responding to

earthquake shaking Epistemic

6 Uncertainty in the definition of the several damage states, and the input loading at which they initiate Aleatory

7 Variability in material properties and fabrication/construction methods and details Aleatory

Based however on the categorization of the uncertainties into aleatory and epistemic,

the previous equation can be expressed as:

2 2 2 2tot DU DR CU CRβ β β β β (2.18)



where βDU and βDR are the aleatory and epistemic uncertainty in seismic demand

respectively while βCU and βCR are respectively the aleatory and epistemic uncertainty in

structural capacity.

It should be noted herein that capacity uncertainty reflects the variability of structural

properties as well as the fact that the modeling procedures are not perfect. Demand

uncertainty reflects the fact that IM is not exactly sufficient, so different records of

ground motion with equal IM may have different effects on the same structure (Selva et

al., 2013). Kwon and Elnashai (2006) investigated the effects of the uncertainties

associated with ground motion input and material variability on the fragility of a three-

storey reinforced concrete structure. Results produced based on Monte Carlo analysis,

showed that material properties contribute to the variability in structural response, but

the resulting variability is much smaller than that due to ground motion variability. In

Celik and Ellingwood (2010) the sensitivity of the response statistics of gravity load

designed reinforced concrete frames to the uncertainties in material and structural

properties and modeling parameters was investigated at various levels of earthquake

hazard. Damping, concrete strength, and joint cracking strain were found to have the

greatest impact on the response statistics. However, the uncertainty in ground motion

dominated the overall uncertainty in structural response, which is in line also with the

results of Kwon and Elnashai (2006).

In a general framework of seismic vulnerability assessment however three primary

sources of uncertainty are usually considered. Besides the uncertainties in capacity and

demand, which were previously described, also the definition of damage states, βDS, is

taken into account. In particular, damage state definition uncertainties are due to the

fact that the thresholds of the damage indices or parameters used to define damage

states are not known (Selva et al., 2013). In this case, the total variability is modeled by

the combination of the three contributors, assuming that they are stochastically

independent and lognormally distributed random variables and the equivalent expression

of Equation 2.17 can be expressed according to HAZUS prescriptions (FEMA, 2008) as:

( [ ])2 2tot C D DSβ CONV β β β (2.19)

The convolution procedure between βC and βD is extensively described in Gencturk

(2007). The HAZUS manual advocates βDS for all damage states. Recommendations are

also provided for the variability in the capacity: βC=0.25 for code compliant element and

βC=0.30 for pre-code constructions.



2.4 Methodologies for deriving seismic fragility functions

Several methods are available in the literature to derive fragility functions for RC

buildings. Conventionally, they are classified into four generic groups: empirical, expert

judgment, analytical and hybrid based on whether the damage data used for their

generation are derived from post earthquake surveys, expert opinion, analytical

simulations or combinations of these respectively (Rossetto and Elnashai, 2003; Pitilakis

et al, 2014a).

Empirical fragility curves for buildings (Spence et al., 1992; Sabetta et al., 1998;

Rossetto and Elnashai, 2003) are derived based on post-earthquake surveys and

observations of actual damage of the exposed stock. The main advantage of the

empirical method is the use of real observed data considering alongside the variability in

the structural capacity, site effects, soil-structure interaction, the path and source

characteristics. However this may be also a drawback as the severe limitations in their

application potential arise from the fact that empirical fragility curves are derived for a

given area and remain thus highly specific to the particular seismo-tectonic, geotechnical

and built-environment. Furthermore the observational data used for the curve generation

are scarce and usually based on low-magnitude events and therefore tend to be clustered

in the low-damage range. This leads to significant uncertainties associated with their

reliable use in the case of large magnitude events.

Judgment-based fragility curves are developed based on expert opinion. Probability

distribution functions are fit to the experts predictions to represent the range of damage

estimates at each intensity level. These methods have the advantage of not being

affected by the lack of extensive damage data (empirical curves) and since the experts

can provide damage estimates for any structural type, the curves include all factors

affecting the response of different structures. Their main weakness however remains the

difficulty to extrapolate their results in other countries with different construction

practices. The reliability of judgment-based curves is questionable as the results rely on

the individual experience of the expert consulted. To properly elicit expert opinion on

uncertain quantities, it is required to clear definitions, biases, assumption and expert

qualifications (Porter et al., 2007). Expert opinion is used by most rehabilitation codes in

the United States of America (ATC 1985; ATC 1996) while a recent effort to revive the

judgment-based methods has been carried out within the Global Earthquake Model

(www.globalquakemodel.org).

Analytical fragility curves (e.g. Mosalam et al., 1997; Chryssanthopoulos, 2000;

Reinhorn, 2001 etc) are based on the estimation of damage distributions through the

numerical analysis of structural models subjected to seismic loading. Analytical methods



may reduce the bias of the derived curves and increase the reliability of the vulnerability

estimates for different structures in comparison to expert opinion. In the past their use

might not be the common practice due to the significant computational effort involved

and the limitations in the modeling capabilities. Architectural assets are not taken into

account, the infill modeling remains a challenge, effects of soil-structure interaction such

as rocking and uplifting are not considered while many computational environments

present difficulties in converging when structural models are subjected to large demands

resulting to numerical failures which may precede the actual structural collapse. However

due to recent developments in the analysis techniques and solution algorithms, the

numerical approaches have become a very attractive technique for the estimation of

structures’ fragilities in terms of ease and efficiency. A detailed description of the

analytical methods will be presented in next section of this chapter.

Hybrid fragility curves (Singhal and Kiremidjian, 1998; Kappos et al., 2006) are

derived based on the combination of methods to compensate for the lack of observational

data, subjectivity of expert judgment and deficiencies of analytical procedures. For

buildings, hybrid fragility functions usually focus on the combination of empirical and

analytical data. In this case analytical fragility curves are combined with available

damage data from previous earthquakes to enhance their robustness. One rare example

of hybridization between analytical, empirical and expert opinion has been attempted

within the PAGER project (Jaiswal and Wald, 2010).

The pie chart of Figure 2.11 shows the percentages of the different methodologies

used among 50 studies/publications for reinforced concrete buildings in Europe, that

have been reviewed in the framework of SYNER-G (Pitilakis et al., 2014a). Figure 2.11

shows the popularity of analytical methods for the derivation of fragility functions for

European buildings. The “unknown” class in the chart refers to the cases where it was not

clear which method has been used.



Empirical 14%

Expert-opinion based

3%

Analytical 69%

Hybrid 11%

Unknown 3%

Figure 2.11. Pie chart presenting the percentages of different methodologies used for the development of fragility functions for reinforced concrete buildings (Pitilakis et al., 2014a)

2.4.1 Derivation of fragility functions based on analytical methods

The main issues that are involved in the analytical derivation of fragility functions are the

following:

definition of seismic hazard

numerical modeling of the reference structure

selection of intensity measure

analysis method that is performed for the calculation of the response parameters

selection of appropriate damage measure/indicator and the definition of the

corresponding damage states

quantification of the uncertainties considering the variability in seismic demand,

structural capacity, definition of damage states etc.

The different components of the analytical vulnerability analysis are illustrated in

Figure 2.12. The seismic hazard that is used as an input to a structure should be defined

taking into account the seismic nature of the region where the derived fragility curves will

be applied. Depending on the analysis method, the seismic input can be represented by a

response spectrum (static methods) or an acceleration time-history (dynamic methods).

The generation of the numerical models of the reference structures has to be made

taking into account not only the accuracy of the representation of the nonlinear behavior

but also the robustness and cost-efficiency of the model. The finite element modeling of a

structure can be coarse or detailed depending on the objective of the study. For the

assessment of seismic vulnerability at regional/urban scale, usually simplified models of

the common building typologies are employed. On the other hand in case of building-



specific fragility assessment probably a detailed three-dimensional model may be

required depending on the structural configuration. The nonlinear behavior of reinforced

concrete buildings may be represented using the concentrated or distributed plasticity

concept. In the first case plastic hinges are employed to represent the nonlinear behavior

of the critical reinforced concrete member sections based on moment-curvature

relationships. In the second case on the other hand, the fiber based approach using

constitutive material laws to represent the nonlinear behavior of concrete (confined or

unconfined) and reinforcement steel.

Figure 2.12. Flowchart to describe the components of the calculation of analytical fragility curves (after Kwon and Elnashai, 2007)

The analysis methods can be divided into two main categories: the nonlinear static and

dynamic approach respectively. In the pie chart of Figure 2.11, the total percentage

corresponding to the analytical method for deriving fragility functions (69%) is

presented, which can be further analyzed to the percentages showing the popularity of

each approach. More specifically, from the studies that use analytical methods for the

vulnerability assessment, 40% used the nonlinear dynamic approach and 29% the

nonlinear static approach. Continuously the most popular analysis methods are shortly

described, namely the Capacity Spectrum method and the general Dynamic Analysis.

Inelastic analyses, either static (pushover) or dynamic (time-history) are the most

appropriate approach to investigate the deformation capacity of the structure and to

provide estimate of their seismic vulnerability. The use of time-history analyses,

however, requires several assumptions regarding the selection of the suite of earthquake

ground motions and is also generally time-consuming because of the high number of

calculations involved. On the other hand pushover analysis is based on static loading and



cannot represent dynamic phenomena with a high degree of accuracy. Therefore it is

approximate in nature as inelastic dynamic response may differ significantly from

pushover analysis predictions particularly if higher mode effects become important. As a

general remark, the method that is followed for the derivation of analytical fragility

curves is related to the nature of each element at risk, the availability of resources (such

as expertise, advanced computational tools etc.) and the reliability of the analytical tools.

Continuously the most popular analysis methods are shortly described, namely the

Capacity Spectrum method and the general Dynamic Analysis.

2.4.1.1. Capacity Spectrum Method (CSM)

In recent years, there has been an increasing attention to simplified Nonlinear Static

Procedures. For instance, the ATC-40 (ATC, 1996) and FEMA 273 (FEMA, 1997)

guidelines presented performance-based engineering methods that rely on nonlinear

static analysis procedures, a move that was then followed by other similar documents

and codes (e.g. CEN, 2005). In all these procedures, pushover analysis is employed to

predict the inelastic force-deformation behavior of the structure, the different methods

then differing in the technique used to calculate the inelastic displacement demand for a

given ground motion.

The Capacity Spectrum method was first introduced in the 1970s as a rapid

evaluation procedure in a pilot project for assessing seismic vulnerability of buildings

(Freeman et al., 1975). In the 1980s, it was used as a procedure to find a correlation

between earthquake ground motion and building performance (ATC, 1982). The method

compares the capacity of a structure with the demands of the earthquake ground motion

on the structure. The capacity of the structure is represented by a force-displacement

curve which is obtained based on non-linear static (pushover) analysis. The base shear

forces and roof displacements are converted to the spectral accelerations and spectral

displacements of an equivalent Single-Degree-Of-Freedom (SDOF) system, respectively.

These spectral values define the capacity spectrum. The demands of the earthquake

ground motion are represented in the form of response spectra with different levels of

viscous damping (e.g. 5%, 10%, 15%, 20% and sometimes 30% to approximate the

reduction in structural response due to the increasing levels of damage). The

Acceleration-Displacement Response Spectrum (ADRS) format (Mahaney et al., 1993) is

used, in which spectral accelerations are plotted against spectral displacements, with the

periods represented by radial lines. The intersection of the capacity spectrum and the

demand spectrum provides an estimate of the inelastic acceleration (strength) and

displacement demand.



The capacity spectrum method has been also adapted as analysis procedure for the

fragility curve generation for RC buildings by HAZUS. For different levels of seismic code

(pre-code, low-, moderate- and high-level code) and for each building typology, the

HAZUS methodology defines bilinear capacity curves based on two control points: the

yield (Dy, Ay), and the ultimate capacity (Du, Au). Yield capacity represents the true

lateral strength of the building, whereas ultimate capacity represents the maximum

strength of the building when the global structural system has reached a fully plastic

state. The capacity curves, expressed in the spectral acceleration – spectral displacement

(Sa-Sd) format, are used to obtain the performance point of the structural element

(depending on the seismic response spectrum) and to deduce the spectral displacement,

which corresponds to a given damage level. The HAZUS methodology for the building

damage estimation based on the CSM is represented schematically in Figure 2.13.

Figure 2.13. HAZUS procedure for building damage estimation based on CSM (Pitilakis et al., 2014a)



2.4.1.2. Nonlinear dynamic analysis

Despite the relatively large computational efforts involved, the fragility functions

developed by means of nonlinear dynamic analyses are able to reproduce most

accurately in most cases the seismic response of typical civil engineering structures. This

analytical approach aims at the estimation of seismic demand on structural models based

on numerous nonlinear dynamic analyses with a series of acceleration time-histories. The

demand model can be formulated using two analysis methods: Probabilistic Seismic

Demand Analysis (PSDA) and Incremental Dynamic Analysis (IDA). The first method

(e.g. cloud analysis) attempts to represent seismicity through a wide selection of many

ground motions, grouped into bins. The latter method achieves the same by stepwise

increment of a few ground motion records.

The selection of the ground motion records that are used as input for the dynamic

analyses is of paramount importance for the reliable evaluation of the seismic response.

The quantity and the distribution of intensity measures in the sample of records have

indeed a great influence on the fragility parameters (both the standard deviation and the

median). The studied typology is usually restricted to a given geographical area, which

allows adequate time-histories based on specified intervals of magnitude, source-to-site

distance and possibly other scenario characteristics, such as focal depth and mechanism

to be selected (e.g. Bommer and Acevedo, 2004). Special software and strong ground

motion recordings from European and international databases can be used for this

purpose, as for example REXEL (Iervolino et al., 2010) and REXEL-DISP (Smerzini et al.,

2012). In the record selection and analysis processes it is important to consider records

with possible special features, such as near-source directivity pulses. Such records must

be appropriately accounted for, since the results can be significantly different than those

for records further from the source. When soil foundation- structure interaction (SSI) is

taken into consideration, modeling both soil and structure in a coupled system, the input

motion is normally introduced at the seismic bedrock and therefore it should refer to rock

conditions, as the SSI model directly captures site effects.

Incremental Dynamic Analysis (IDA)

Incremental dynamic analysis (IDA) is a promising computer-intensive method, which is

used for the evaluation of the seismic performance of structures. IDA procedure involves

the performing of a series of nonlinear dynamic analyses under a suite of multiple scaled

ground motion records whose intensities should be ideally selected to cover the whole

range from elasticity to global dynamic instability (Vamvatsikos and Cornell, 2002). IDA

curves of the structural response, which provide a relationship between a damage

measure quantity (i.e. engineering demand parameter EDP) and an intensity measure



(IM) of the applied scaled accelerograms, are then constructed by interpolating the

resulting EDP-IM discrete points. The reliability of the procedure generally relies primarily

on the proper formation of the nonlinear structural model, the compilation of a suite of

records, as well as on the selection of efficient EDPs and IMs. A representative set of

input ground motions should consist of approximately 15–30 ordinary records assuming

that a relatively efficient IM, like Sa(T1,5 %), is used and that peculiar features in the

records (e.g. ground motions containing pulses due to effects such as forward-directivity,

fling step, basin effects and site effects) that could potentially bias structural response

are eliminated. In addition, care should be taken in the selection of the scaling levels for

each record and in the post processing of the IDA analysis results. The scaling of the

records may provide good estimates of the distribution of EDP given IM provided that

their statistical relationship is effectively independent of magnitude M and source-to-site

distance R in the range of interest. An advanced tracing algorithm, such as the hunt & fill

(Vamvatsikos and Cornell, 2002; 2004), which ensures that the records are properly

scaled with the minimum required computational effort, is recommended to perform the

IDA. The engineering demand parameter EDP is an observable response parameter that

can be extracted from IDA. A typically adopted EDP is the maximum interstorey drift

ratio, θmax, which is known to relate well to dynamic instability and structural damage.

Limit-states (e.g. collapse prevention CP) can be defined on the IDA curve and the

corresponding capacities can be calculated. Figure 2.14(a) presents indicative plots of 15

continuous IDA curves derived by interpolation of the Sa(T1,5 %) θmax pairs for each

individual record and the associated CP limit-state capacities for a nine-story reinforced

concrete moment resisting frame building whereas Figure 2.14(b) illustrates the

corresponding summarized across all records IDA curves at 16, 50 and 84 % fractiles.

Figure 2.14. (a) IDA curves for the individual records and the estimation of the associated limit-state

capacities for CP limit state and (b) summarization of the 15 IDA curves into their 16, 50 and 84 % fractiles



2.4.1.3. Factors affecting the reliability of analytical fragility functions

Analytical fragility curves can be derived using a variety of approaches that employ

diverse structural modeling and analysis techniques, damage models and damage scales.

Thus the identification of the uncertainty sources in the capacity, demand and damage

thresholds and their quantification in the fragility function are fundamental for the

derivation of reliable fragility curves. Figure 2.15 presents the different sources of

uncertainties associated with analytical fragility assessment (D’Ayala and Meslem, 2013).

Uncertainties in the demand are associated with the record-to-record variability

reflecting the variability in the mechanism of the seismic source, path attenuation and

site effects of the seismic event as well as with the selection of intensity measure for the

efficient characterization of the strong ground motion. Uncertainties in the capacity are

introduced through geometrical, mechanical, structural and modeling parameters and

may be accounted for by randomizing the different involved parameters (such as

material parameters, mass, damping etc) adopting usually a normal or lognormal

probabilistic distribution or by analyzing a large number of real buildings defining thus a

median and standard deviation of the sample (e.g. D’Ayala, 2005; Vacareanu et al.,

2007). Uncertainties in the definition of damage thresholds are often neglected in

vulnerability assessment studies found in the literature. However in several studies

damage state thresholds are treated as aleatory uncertainty adopting a probability

(usually lognormal) distribution (e.g. Kappos et al., 2006; Shahzada et al., 2011; Uma et

al., 2011) while Aslani and Miranda (2004) consider also the epistemic uncertainty in the

mean value of this distribution.

Figure 2.15. Sources of uncertainty associated with analytical fragility assessment (adapted from

D’Ayala and Meslem, 2013)



2.5 Review of previous studies

The last twenty years many studies have been carried out regarding the derivation of

seismic fragility functions for reinforced concrete buildings based on different assessment

methods. Some of these studies based on analytical or hybrid methods are presented in

the following paragraphs.

Singhal and Kiremidjian (1995) derived fragility curves and damage probability

matrices for three sample building classes (low-, mid- and high rise RC frames) designed

according to SEAOC (1990) recommendations. Park and Ang’s (1985) index was used to

represent structural damage while as intensity measures the Spectral acceleration at the

structural period range of interest was selected. Nonlinear dynamic analysis was

performed using artificial records and the Monte Carlo simulation approach was used to

estimate the probabilities of damage conditional on different ground motion levels.

In Mosalam et al. (1997) fragility analyses for bare and infilled low-rise lightly

reinforced concrete frames were performed. Nonlinear static (pushover) analysis was

conducted considering the variability in reinforced concrete and masonry material based

on experimental data, in order to obtain trilinear capacity curves. Nonlinear analysis of

the trilinear SDOF systems was performed using synthetic accelerograms and the Monte

Carlo technique was employed to sample 200 capacity curves for each accelerogram. The

maximum interstorey drift was used as damage measure while the fragility curves were

derived in terms of PGA. Comparison of the obtained fragility curves showed good

agreement with those based on ATC-13 data and indicate that adding masonry infill walls

to low-rise frames produces substantial reduction in the likelihood of seismic damage.

Dumova-Jovanoska (2000) performed nonlinear dynamic analyses using synthetic

accelerograms to develop fragility functions and damage probability matrices for sample

reinforced concrete frame structures lower (6-storey building) and higher (16-storey

building) than 10 storeys. A modified Park and Ang damage model was chosen as a

measure of the structures’ response to earthquake excitation. Fragility curves were

derived in terms of Modified Mercalli Intensity to represent through this measure the

available data of occurred seismic events.

Erberik and Elnashai (2004) focused on the derivation of fragility curves for a mid-rise

flat slab building with masonry infills designed according to current US seismic codes to

resist both gravity and earthquake loadings. Nonlinear dynamic analysis was performed

employing real earthquake records that were selected to be compatible with the code

design spectrum. The variability in concrete compressive strength and steel yield

strength was taken into account through the Latin Hypercube Sampling (LHS) method.

Damage limit states were defined considering as damage measure the interstorey drift



ratio and fragility functions were developed in terms of spectral displacement. The

comparison between the derived curves for the flat-slab structure with the corresponding

curves for a moment resisting building indicated that using the fragility curves of the

latter to assess the seismic damage of the former may lead to non-conservative results.

In Akkar et al. (2005) fragility functions were determined for low- and mid-rise

concrete buildings with low level of seismic design, representing the most vulnerable

construction type in Turkey. A hybrid approach was employed where building capacities

were obtained from field data while their dynamic responses were calculated based on

time history analyses. The stiffness, strength and deformation capacities of the 32

sample buildings used, were determined by pushover analyses while their inelastic

dynamic structural characteristics were represented by equivalent single-degree-of-

freedom systems for which nonlinear dynamic analyses were performed to estimate their

seismic deformation demands. Drift ratio limits were defined for three performance

levels, namely the Immediate Occupancy, the Life Safety and the Collapse Prevention.

Fragility functions in terms of peak ground velocity (PGV) were derived separately for

buildings with different number of storeys (2,3,4 and 5-storey buildings).

In Rossetto and Elnashai (2005) fragility curves are derived for low-rise infilled

reinforced concrete frames of inadequate seismic design. Adaptive pushover analysis was

employed within a capacity spectrum framework to determine the structural performance

under increasing ground motion intensity. The Homogeneous Reinforced Concrete (HRC)

damage scale was used to determine the damage state of the building at the

performance point in terms of maximum interstorey drift. The derived fragility curves in

terms of spectral displacement, which are appropriate for use within a displacement-

based assessment framework, were compared with observational data and empirical

curves showing that the proposed methodology is capable of yielding analytical

vulnerability curves that provide reasonable predictions of observed post-earthquake

damage.

Kircil and Polat (2006) developed fragility functions for mid-rise reinforced concrete

frame buildings designed according to the 1975 Turkish seismic code. Incremental

dynamic analyses were performed for the sample 3, 5 and 7- storey buildings employing

artificial ground motions. Maximum interstorey drift was used as damage measure to

represent the structural response and define the damage limit states. Fragility curves

were derived in terms of elastic pseudo spectral acceleration, peak ground acceleration

and elastic spectral displacement for yielding and collapse damage levels with lognormal

distribution. Furthermore simple equations between the number of storeys and mean and

standard deviation of the curves were established that may be used for the preliminary

evaluation of mid-rise RC frame structures designed according to the 1975 Turkish code.



Kappos et al. (2006) developed fragility functions for RC frame and wall-frame

buildings, representative of structures in South European countries, according to a hybrid

method developed at Aristotle University of Thessaloniki (AUTh). This method combines

statistical data with appropriately processed results from non-linear dynamic or static

analyses, that permit extrapolation of statistical data to PGAs and/or spectral

displacements for which no data are available. Low-rise, mid-rise and high-rise buildings

were analyzed; each one was assumed to have three different configurations (bare,

regularly infilled and soft ground storey building). Four classes of seismic design were

considered: no code, low code, moderate code and high code. The damage was

expressed in economical terms and was defined as the ratio of repair cost to replacement

cost (i.e. direct loss index). Fragility curves were derived in terms of PGA (e.g. Figure

2.16), as well as spectral displacement Sd (e.g. Figure 2.17).

Figure 2.16. Fragility curves (in terms of PGA) for medium-rise infilled frames, low (left) and high

code design (Kappos et al., 2006)

Figure 2.17. Sd-based fragility curves for medium-rise infilled R/C frames, low (left) and high code

design (Kappos et al., 2006)

Polese et al. (2008) studied RC frame buildings constructed in Naples designed only

for gravity loading. The bilinear capacity curves of 400 RC frame buildings, with 1, 4 and

7 storeys and varying plan dimensions were obtained based on pushover analyses.

Sample buildings were generated by Monte Carlo simulation and the properties of their

capacity curves were obtained from the database of the 400 buildings. The capacity



spectrum method was applied for the EC8 spectrum with increasing values of peak

ground acceleration. Following the criteria suggested in HAZUS to relate component

deformation to average inter-storey drift ratio, the four significant damage thresholds of

slight, moderate, extensive and complete damage were detected along each push-over

curve in terms of roof displacement. Fragility curves were derived in terms of elastic

spectral displacement and it was shown that dispersions of geometrical configuration and

material properties have comparatively less influence on the vulnerability for all classes

investigated.

In Fardis et al. (2012) fragility curves were derived for regular RC frame and wall-

frame buildings designed according to EC2 and EC8. The aim of this study was to use the

seismic performance assessment methods and criteria of EC8 for existing buildings to

evaluate if the performance goals were also achieved for new European buildings.

Different building typologies were analyzed considering the following parameters: the

number of storeys, the level of seismic design, for the in-wall frame system the fraction

of the seismic base shear that is taken by the walls and for the frame systems with a

mixture of flexible and stiffer frames the ratio of the number of flexible frames to stiffer

ones. Two damage states were considered, namely the yielding and ultimate condition of

a member in flexure, and are defined in terms of chord rotation at the member end. For

the member ultimate condition in shear, the shear force outside or inside the plastic

hinge was considered. Fragility curves were derived in terms of PGA and it was shown

that the EC8 seismic performance goals for new RC buildings were met for all building

types considered except for the walls of medium ductility class, which appeared to fail

earlier in shear despite their design to EC8.

2.6 SYNER-G: The fragility function manager

The Fragility Function Manager (FFM) has been developed in the framework of SYNER-G

project, to store, visualize and manage a large number of fragility function sets not only

for buildings but also for bridges and other elements at risk. The FFM has been created

such that users can easily obtain standardized sets of available fragility functions from

the literature, that contain all the parameters required for their use in seismic risk

calculations. Each fragility function is accompanied by metadata to allow the user to

compare and select the functions of interest. Within the SYNER-G project, a large effort

was made to compile and upload European fragility functions for buildings to the FFM

(e.g. Ahmad et al., 2011; Akkar et al., 2005; Borzi et al., 2008a; Dumova-Jovanoska

2000; Erberik and Elnashai, 2004; Hancilar et al., 2006; Jeong and Elnashai, 2007;

Kappos et al., 2006; Kircil and Polat, 2006; Kostov et al., 2004; Kwon and Elnashai,

2006; Liel and Lynch, 2009; Ozmen et al., 2010; Polese et al., 2008; Rossetto and



Elnashai, 2003;2005; Tsionis et al, 2011 etc.). The general metadata provided for each

study includes the reference papers, the region of applicability, the building typology, the

SYNERG-taxonomy, the methodology used to develop the fragility functions, the intensity

measure types and the damage scales. The interface of the Fragility Function Manager

for buildings is illustrated in Figure 2.18.

The main features of the FFM tool are the following:

Uploading and viewing fragility functions: in order to add a set of fragility curves

to the FFM, the taxonomy, metadata and the input of the fragility parameter need

to be provided.

Harmonizing Intensity Measures types (IMTs): in order to directly compare

fragility functions from different studies, the various intensity measure types are

converted to a common target IMTs, namely PGA, PGV and Sa(T), using

appropriate conversion equation (Silva et al., 2014).

Harmonizing limit states: to directly compare fragility functions from different

authors, the limit states are harmonized into two thresholds, damage limitation or

yielding and collapse.

Comparison of fragility functions: once the user has harmonized the fragility

functions in terms of IMTs and limit states a number of features are available to

allow the functions to be compared. It is also possible to compare the damage

distributions from different sets using the “bar chart” feature.

A detailed description of the FFM tool and its features can be found in Silva et al. (2014).

Figure 2.19 shows the variability that can be observed in the harmonized fragility

functions for a user-selected class of buildings at the yield and collapse limit states.

Provided the same sources of uncertainty have been modeled in the derivation of each

fragility function, the variability between the functions can be considered epistemic

uncertainty. If we consider, however, that these fragility functions originally had the

same IMT and limit state and are all lognormal distributions, then we can estimate the

epistemic uncertainty and model it using the mean and standard deviation of the

parameters of the fragility functions (which each have a median and dispersion), as well

as the correlation between these parameters (Silva et al., 2014).



Figure 2.18. Interface of the Fragility Function Manager (adapted from Silva et al., 2014 in Pitilakis et al., 2014a)

Figure 2.19. Mean curve for (a) limit state yielding curve and (b) limit state collapse curve for reinforced concrete with moment resisting frame buildings, mid rise, seismically designed model

building type



2.7 Current challenges in seismic vulnerability assessment of RC buildings

As discussed in the previous chapters, significant efforts have been made in the context

of the most recent research projects (e.g. SYNER-G, GEM) to synthesize the available

vulnerability studies and to provide standard guidelines for the future development of

fragility functions. However many important issues have remained unsolved and need

further investigation. Among them the following are investigated in the present thesis:

Traditionally, in seismic vulnerability assessment, it is implicitly assumed that

structures are optimally maintained during their lifetime, thus neglecting any

deterioration mechanism that may adversely affect their structural performance.

On this basis, the impact of progressive deterioration of the material properties

caused by aggressive environmental conditions, as for example the corrosion due

to chloride penetration leading to the variation of the mechanical properties of

steel and concrete over time, is not accounted for. The safety and serviceability of

RC structures may then be affected under the action of seismic loading,

compromising the ability of the structures to withstand the loads they are

designed for. Consequently, fragility functions are not constant in time and should

account for aging effects introducing the time-dependent vulnerability

assessment.

The effects of soil-structure interaction (SSI) in the derivation of fragility functions

for RC buildings are not explicitly taken into account so far in any of the currently

available sets of fragility functions. In several cases however, these SSI effects

may modify considerably and sometimes in a detrimental way the analytical

fragility functions.

Uncertainties associated with the construction systems, material, mass and

geometry properties that are pronounced particularly in the case of existing

buildings may not be properly captured using generic fragility curves. Moreover

the structure may have suffered previous earthquakes without proper retrofitting

and strengthening and the structural system has several “weak” points

depredating its initial strength. This is practically impossible to be identified

without rigorous field monitoring.

Field monitoring is an excellent tool to improve the quality and credibility of the

vulnerability assessment; it can be used for traditional structural health

monitoring, to identify the actual structural state and hence to derive building-

specific fragility functions allowing the development of robust real time

assessment tools and appropriate risk mitigation strategies, which is of primary



importance in the case of structures, critical facilities, important public buildings

(e.g. schools, hospitals) and infrastructures of strategic interest.

Although their consideration in the assessment procedure enhances the reliability and

robustness of the results, up to date there are only few research studies dealing with

these issues. In the following sections the aforementioned topics are further discussed.

2.8 Evolution of building vulnerability over time

2.8.1 Mechanisms acting on structural performance during lifetime

Two different sources of deterioration, which cause damage to accumulate with time are

generally recognized: one has substantially slow, progressive effects and is usually linked

to environmental and operating conditions (e.g. aging, Pitilakis et al., 2014b); the other

has effects that are superposed occasionally to the first effects, and are usually related to

external sudden changes in the structural capacity (e.g. due to cumulative earthquake

damage, Réveillère et al., 2012; Iervolino et al., 2013).

Aging of structures can be defined as partial or total loss of their capacity via a slow,

progressive and irreversible process that occurs over a period of time. The aging process

affects directly structures by changing the characteristics of the materials of which they

are made leading to a loss in their resistance capacity. Common problems to concrete

material may include alkali-aggregate reaction, freezing and thawing, leaching, sulphate

attack, cracking due volume changes led by temperature variation, corrosion of concrete,

debonding of steel. Cracking, splitting, spalling and disintegration, loss of mortar and

stones are common defects occurring in masonry structures due to aging (Valliappan and

Chee, 2008). Aging effects as a consequence of chemical, physical and environmental

attacks (e.g. corrosion, erosion, fatigue) may lead to continuous stiffness and strength

degradation of materials, affecting the expected seismic performance and the

predominant damage mechanisms of structural systems. For building and strategic

infrastructures (such as bridges, tunnels and nuclear power plants) subjected to

aggressive environmental conditions, aging effects are associated to a significant

reduction of their safety and serviceability, potentially leading to unexpected failures

(e.g. Saydam and Frangopol, 2011). Thus, the ability of the structural system to

withstand various challenges from operation, environment and natural events may be

reduced. Once the structural capacity falls below a given performance threshold, the

structure may be intervened, leading to a new initial capacity, diminishing progressively

over time the ability to withstand future operating conditions (Figure 2.20).



Figure 2.20. General description of the system remaining lifetime (Beushausen and Alexander,

2010)

In all this, the economic aspects play a decisive role. The costs of adequate

prevention carried out at the design and execution phases are minimal compared to the

costs of rehabilitation/repairing interventions performed during the service life. Thus,

maximization of the utility combined with minimization of the costs is the target of the

engineering decision-making process. In order to support decision makers with a better

comprehension of the matter of safety assessment and its impacts, the concept of risk

management has recently become of great concern also in civil engineering (e.g.

Almusallam et al., 1996), being already popular in other disciplines (Mohammed et al.,

2004).

2.8.2 Aging effects: Corrosion of reinforcement

2.8.2.1. Chloride induced corrosion mechanism

For reinforced concrete buildings corrosion of the reinforcement is considered the most

serious deterioration mechanism. The high alkalinity of the concrete cover (pH

approximately equal to 13) theoretically protects reinforcement, forming an oxide layer

on the steel surface, the so called passive layer, that prevents the corrosion of

reinforcement. However there are two processes that may break down this passive layer,

namely the ingress of chlorides, producing the so called pitting corrosion, and carbon

dioxides, usually causing a more uniform corrosion pattern. The alkalinity of the concrete

mass is due to the Ca(OH)2 which is produced during the cement hydration, that is the

reaction of the cement with water. Depassivation of the protective layer occurs either

when chloride ions diffuse in the pore water and reach the reinforced bars or when the

pH value of the concrete surrounding the bars falls below 9 due to diffusion of

atmospheric CO2 and its reaction with Ca(OH)2 of the concrete mass (Apostolopoulos and

Papadakis, 2008). Environmental pollution, especially in urban and industrial

environments, results to a significant concentration of carbon dioxides and therefore

carbonation initiated corrosion prevails. On the other hand chloride induced corrosion,



which is reportedly considered as the most serious corrosion mechanism (fib, 1999),

predominates in marine environments, in coastal areas and when deicing salts come in

contact with concrete surface (Apostolopoulos and Papadakis, 2008; Berto et al., 2009).

Figure 2.21 illustrates the general corrosion process of steel in concrete, in which

steel loses its ions at the anode by the oxidation reaction (Fe Fe++ +2e-). The electrons

are released and transported to the cathode for the reduction of oxygen (O2 + 2H2O +

4e- 4OH-). The flow of ions through the concrete pore solution and electrons forms an

electrical current for the reactions to proceed. As a result, the electrical resistivity of

concrete, availability of oxygen and chemistry of the pore solution are the determining

factors for the corrosion kinetics of the carbon steel in a concrete medium (Tuutti, 1982).

The result of this procedure is the formation of hydrated ferric oxide (2Fe(OH)3

Fe2O3∙H2O + 2H2O) which is known as rust.

Figure 2.21. The electrochemical corrosion process (Malioka, 2009)

The identification of the corrosion phases is important as each phase is associated

with individual characteristics which not only affect the structural performance but also

the decision process in terms of time and maintenance actions (Malioka, 2009). There

are two main phases as illustrated in Figure 2.22: the initiation and the propagation

phase. During the initiation phase there is no weakening of the structural materials but

the passive layer protecting the reinforcement is destabilized under the effect

mainly of chlorides and carbon dioxides. At the end of the initiation phase the passive

layer of the outer reinforcement layer is de-passivated signifying that corrosion has

initiated. Corrosion initiates at the first layer of reinforcement when the

concentration of chlorides or carbon dioxides exceeds a critical value. In the

propagation phase due to the corrosion’s chemical reactions, pits form at the

anode areas i.e. the cross section of the steel decreases. Corrosion products

(rust) built up on the surface of the reinforcement and as the volume of rust

increases, expansive stresses are set up in the concrete surrounding the steel. Cracks are



then appearing at the concrete cover and after some time the corrosion products may

disperse through the cracks and become visible on the surface of the structure. That is

then a strong indication not only of corrosion initiation but of progressed corrosion.

Spalling will eventually occur if corrosion products continue to build up and these effects

will result to significant damage to the structure leading eventually to the reduction of

the structure’s serviceability and load carrying capacity beyond acceptable levels and

finally to failure. The duration of both corrosion phases will vary based on the

concrete characteristics e.g. strength, on the concrete cover depth as well as the

exposure conditions.

Figure 2.22. Left: Corrosion phases (adapted from Tuuti, 1982) of concrete structures. Right: Effects on structural capacity and limit states (adapted from Malioka, 2009)

The parameters that affect the evolution of chloride induced corrosion are related on

one hand to the structural design and construction (design and execution phase

parameters), and on the other hand to the environmental conditions (environmental

parameters). The design and execution phase parameters are the following:

Concrete cover depth: provides physical protection of the reinforcement and

affects significantly the corrosion initiation time.

Water to cement (w/c) ratio: controls the workability, strength and permeability of

concrete. High values of w/c ratio increase the concrete permeability and in

relation to the volume of the pores may accelerate the corrosion process. Typical

values of w/c ratio range between 0.35-0.40.

Cement content and type: high percent of cement content generally makes

concrete less permeable in the penetration of harmful substances. However the

influence of this parameter should be examined in combination with other factors,

such as w/c ratio.



Curing and compaction: two other parameters affecting the concrete permeability.

Poor compaction results to a reduction of concrete strength and a more porous

concrete increasing the permeability. The curing process provides the concrete

with the necessary strength and impermeability and poor curing affects mostly the

surface zone that protects the reinforcement in the concrete. Curing time is

affected by the w/c ratio, the cement type and content.

Regarding the environmental factors there are two parameters that are affecting in

principle the corrosion mechanism, namely oxygen and water (moisture). A structure

that is exposed to steady environmental (dry) conditions will face low risk of corrosion

damage. On the contrary under constantly changing conditions the risk of corrosion

increases as the concrete absorbs more water than it actually looses. The influence of the

environmental conditions however should be investigated also in combination with the

mechanism that will initiate corrosion. For chloride induced corrosion it is critical to

identify the source of chlorides as its occurrence is related to the level of chlorides at the

depth of the reinforcement. The period of exposure and the interaction with other

environmental parameters will define the time of corrosion initiation, depending also on

the design and execution parameters.

2.8.2.2. Probabilistic modeling of chloride induced corrosion initiation

The need to identify and take into account the different uncertainties in corrosion

modeling requires the investigation of the corrosion mechanism and its effects on

structural response within a probabilistic framework. Recognizing the importance of this

issue, several probabilistic models have been proposed for the quantification of corrosion

in the design, construction, fragility analysis and maintenance of RC structures. A

summary of these models can be found in DuraCrete (2000). The DuraCrete project,

started in 1996 and was funded by the European Union with main aim to develop a

methodology for a durability based design approach for reinforced concrete structures

using probabilistic models that could take sufficiently into account the factors affecting

the structural performance. According to DuraCrete two exposure conditions are

considered of main concern particularly for chloride induced corrosion, namely the marine

and road environment (use of de-icing salts). Four different zones are further indentified

for the marine environment based on the water level: the atmospheric, the splash, the

tidal and the submerged zone.

A full probabilistic design approach has been adopted by FIB-CEB Task Group 5.6

(2006) for the modeling of chloride induced corrosion in uncracked concrete, which has

been developed in DuraCrete and has been slightly revised in the research project DARTS

(revised DuraCrete model), also funded by the European Union. The model is based on



Fick’s second law of diffusion (Collepardi et al., 1972) as according to most observations,

the transport of chlorides in concrete is diffusion controlled. This is however not valid for

the convection zone (i.e. the zone on the surface exposed to a frequent change of

wetting and subsequent evaporation), where the approach of Fick’s second law of

diffusion yields no satisfactory approximation for the chloride penetration. In this case

the data of the convection zone is neglected and Fick’s second law of diffusion is applied

starting at depth ∆x (which marks the depth of the convection zone) with a substitute

surface concentration Cs,∆x. With this simplifications Fick’s second law of diffusion yields a

good approximation of chloride distribution at a depth x≥ ∆x (FIB-CEB Task Group 5.6

2006). According to the proposed model, the prediction of time- and depth- dependent

critical chloride content is expressed through the following equation:

0 , 0

,

( , ) 12

crit s x

app C

a xC C x t C C C erf

D t

(2.20)

where Ccrit is the critical chloride content [wt.-%/c], C(x,t) is the chloride content in the

concrete at a depth x (structure surface: x=0 m) and at time t [wt.-%/c], C0 is the initial

chloride content of the concrete [wt.-%/c], Cs,∆x is the chloride content at a depth ∆x and

a certain point in time t [wt.-%/c], x is the depth with a corresponding content of

chlorides C(x,t) [mm], α is the concrete cover [mm], ∆x is the depth of the convection

zone (concrete layer, up to which the process of chloride penetration differs from Fick’s

second law of diffusion [mm], Dapp,C is the apparent chloride diffusion coefficient in

concrete [mm2/years], t is the time [years] and erf is an error function.

According to FIB-CEP Task Group 5.6 (2006), the critical chloride content is defined

as the total chloride content which leads to the depassivation of the reinforcement

surface and initiation of iron dissolution, irrespective of whether it leads to visible

corrosion damage on the concrete surface. The chloride content in the concrete is not

only caused by chloride ingress from the surface, but can also be due to chloride

contaminated aggregates, cements or water used for the concrete production. Especially

when building in marine environment, the chloride content of fine and coarse aggregates

and water can be considerable. The initial chloride content C0 is taken into account in

Equation 2.20. In contrast to the chloride profiles resulting from chloride ingress from the

surface, the distribution of the initial chloride content can be assumed to be uniform over

the whole cross section. The chloride content Cs at the concrete surface (x=0) as well as

the substitute surface content Cs,∆x at a depth ∆x are variables that depend on material

properties and on geometrical and environmental conditions. The information that are

required to determine Cs and Cs,∆x are presented in the flowchart of Figure 2.23.



Figure 2.23. Information required to determine the variables Cs and Cs,∆x (FIB-CEB TASK GROUP

5.6, 2006)

The apparent chloride diffusion coefficient in concrete Dapp,C is subjected to

considerable scatter and tends to reduce with increasing exposure time. Dapp,C can be

determined by means of the following Equation:

, ,0( ) ( )app C e RCM tD t k D k A t (2.21)

where DRCM,0 is the chloride migration coefficient [mm2/a], ke is the environmental

transfer variable, kt is the transfer parameter (constant, value: 1) and A(t) is the aging

function with:

0( )n

tA t

t

(2.22)

where t0 is the reference point in time [years] and n is the age component which varies

significantly according to the cement type and the type of exposure. The reference point

of time has been chosen to correspond to 28 days thus t0=0.0767. It should be noted

herein that the chloride migration coefficient DRCM,0 is one of the governing parameters

for the description of the material properties in the model and varies significantly in

dependence on the water/cement ratio and the type of binder. Suitable data for the

estimation of DRCM,0 may be obtained from literature to be used as starting variables in a

service life design calculation or in a vulnerability assessment study. The environmental

transfer variable ke has been introduced in order to take into account the influence of the

temperature of the structural element and can be estimated as:

1 1expe e

ref real

k bT T

(2.23)



where be is a regression variable [K], Tref is the standard test temperature [K] and Treal is

the temperature of the structural element or the ambient air [K]. The standard test

temperature is defined as 293 K (=20°C) and can be considered constant.

The statistical quantification of the different parameters according to FIB-CEB Task

Group 5.6 (2006) that are not considered constant, are summarized in Table 2.13.

Regarding the concrete cover α, it is chosen during the design phase. Depending on the

construction practices the actual concrete cover varies and therefore it is recommended

to considered it as a stochastic variable rather than a constant value. Different

distribution may be applied, such as normal, beta, Weibull, lognormal and Neville

distribution. For a statistic description of low concrete covers however (e.g. αnom=20 mm)

the lognormal, Neville and beta-distribution are considered to be appropriate (FIB-CEB

Task Group 5.6 2006).

Table 2.13. Statistical quantification of parameters affecting chloride induced corrosion according to FIB-CEB Task Group (2006)

Parameter Distribution Mean Standard deviation

Chloride migration coefficient DRCM,0 Normal m → Table B2-1 (cement type; w/c) s=0.2m

Aging exponent α Beta m → Table B2-2

(cement type; w/c) s, a, b → Table B2-2 (cement type; w/c)

Environmental transfer

variable ke

Regression variable be Normal m=4800 s=700

Temperature Treal Normal Evaluated weather station data

Evaluated weather station data

Critical chloride content CCrit Beta m=0.6 s=0.15; a=0.2; b=2.0

Based on Equation 2.20 and assuming that the chloride concentration near the

surface is constant, the corrosion initiation time can be estimated as:

12 12

1

,0 0

14

n

critini n

se t RCM

CaT erf

Ck k D t

(2.24)

2.8.2.3. Evaluation of corrosion rate

A fundamental parameter of the corrosion propagation phase is the corrosion rate icorr,

which is also required for the quantification of the corrosion effects on structural

performance. Corrosion rates are highly variable and dependent on concrete grade, cover

and environment (Stewart et al., 2011) and are generally measured as corrosion current

density (μA/cm2) which gives the quantity of metal that transforms into oxides by unit of

reinforcement surface and time (in mm/year). In recent years a number of formulations

have been proposed in the literature to calculate the corrosion rate, varying from

deterministic to fully probabilistic approaches (e.g. Val and Melchers, 1997; Stewart,

2004; Marsh and Frangopol, 2008; Sudret et al., 2008). Table 2.14 summarizes typical



values of icorr obtained in laboratory or measured on real size structures as suggested by

different authors. Based on the British Standard BS 6349-1 the mean corrosion rate for

the atmospheric zone is 0.04mm/year (3.45μΑ/cm2), 0.08mm/year (6.9 μΑ/cm2) for the

splash zone and 0.04mm/year (3.45μΑ/cm2) for the tidal zone. The corrosion rates

recommended by DuraCrete (1998), which take into account the concrete grades

suggested for the different exposure classes, are shown in Table 2.15. It is seen that the

recommended values do not differ significantly from those suggested in BS 6349-1.

Table 2.14.Classification of icorr based on laboratory test or measurements on real size structures

Corrosion risk Dhir et al.,

1994 (μA/cm2)

BRITE/EURAM (μA/cm2)

Middleton and Hogg, 1998 (μA/cm2)

Rodriguez and Andrade, 2001

(μA/cm2)

Negligible - <0.1 - < 0.1 – 0.2

Low 0.1 0.1 – 0.5 0.1-0.2 0.2 – 0.5

Moderate 1.0 0.5 – 1.0 0.2-1.0 0.5 – 1.0

High > 10.0 > 1.0 > 1.0 > 1.0

Table 2.15. Chloride-induced corrosion rates (icorr-20) for the different exposure classes

according to DuraCrete (1998)

Exposure class Mean (μA/cm2)

Standard deviation (μA/cm2) Distribution

Cl1 – Wet-rarely dry 0.345 0.259 Lognormal

Cl2 – Cyclic wet-dry 2.586 1.724 Lognormal

Cl3 – Airborne sea water 2.586 1.724 Lognormal

Cl4 - Submerged - - Lognormal

Cl5 – Tidal zone 6.035 3.448 Lognormal

Vu and Stewart (2000) proposed a mathematical expression for the calculation of the

corrosion rate at the beginning of corrosion propagation in terms of w/c ratio and the

thickness of the concrete cover α:

1.64

,0

37.8 1 /corr

w ci

a

(2.25)

Moreover they developed also an expression for the computation of the time-varying

corrosion rate as a function of propagation time:

0.29,0 0.85corr p corr pi t i t (2.26)

According to the above equation, the corrosion rate diminishes with time as corrosion

products formed around the reinforced bars impede the diffusion of iron ions. In most

research studies however a constant corrosion rate is usually considered during the

propagation period.



Rodriguez et al. (1994) have associated a range of representative corrosion rates to

the different exposure classes according to EN 206. Table 2.16 summarizes the proposed

chloride induced corrosion rates, which have been obtained by averaging the

instantaneous recorded values of icorr.

In Simioni (2009) the corrosion rate that was considered for the case studies under

investigation, has been evaluated on the basis of the climatic characteristics of the site

and the average concrete strength.

Table 2.16. Suggested ranges of icorr for EN 206 exposure classes (Rodriguez et al., 1994)

Exposure class icorr (μA/cm2)

D1 – Moderate humidity 0.1 – 0.2

D2 – Wet-rarely dry 0.1 – 0.5

D3 – Cyclic wet-dry 0.5 - 5

S1 – Airborne sea water 0.5 - 5

S2 - Submerged 0.1 - 1

S3 – Tidal zone 1 - 10

2.8.3 Effects of chloride induced corrosion on seismic performance and

fragility of RC buildings

The corrosion of rebars may cause significant effects on the behavior of RC structures

affecting not only the reinforcing steel and the surrounding concrete separately, but also

the interaction between the two materials resulting to a degradation of the bond

strength. These effects can be summarized as follows (Berto et al., 2009):

Reduction of steel cross-section which may lead to the degradation of the

structural resistance and bearing capacity (e.g. Ghosh and Padgett, 2010).

Modification of the mechanical characteristics of reinforced bars, such as reduction

of steel ultimate elongation which may result to loss of steel ductility (e.g.

Almusallam, 2001; Rodriguez and Andrade, 2001; Kobayashi, 2006).

Development of tensile stresses in the concrete surrounding the rebars which may

exceed the tensile strength of the material. This may be induced due to the

internal pressure generated by the increasing volume of corrosion products that

are formed along the steel bar surface. This may lead to cover cracking,

delamination of the outer concrete layers which together with the loss of bond

between steel and concrete may result to rebar slippage and finally to total loss of

anchorage (e.g. Coronelli and Gambarova, 2004; Simioni, 2009).



Loss of steel-concrete bond which is caused either by the reduction of the

confinement level of the rebars due to the longitudinal cracks that are developed

in the surrounding concrete or by the deterioration of the interface between the

two materials (e.g. formation of a rust layer around the steel bars) (e.g. Al-

Sulaimani et al., 1990; El Maaddawy et al., 2005; Berto et al., 2008)

All these effects may result to the reduction of the resistance and load bearing

capacity of the structure and to the variation of the failure mechanism from ductile to a

more fragility type (e.g. Saetta et al., 2008; Mohammed et al., 2011; Yalciner et al.,

2012; Rodriquez et al., 1997; Berto et al., 2009). Figures 2.24 and 2.25 present typical

structural failures as a result of reinforcement corrosion.

Under the aforementioned considerations, a reliable evaluation of the structural

performance usually requires to take into account degradation mechanisms such as rebar

corrosion as they may affect both the safety and serviceability of RC structures,

compromising their ability to withstand the loads they are designed for. When combined

with the earthquake loading, the effects may be even more detrimental. Recognizing the

importance of this issue, several probabilistic models have recently been introduced into

the time-variant vulnerability assessment of corroded RC structures (e.g. Ghosh and

Padgett, 2010; Choe et al. 2010). Although there are few studies devoted to the

modeling and vulnerability assessment of RC bridges that have undergone corrosion of

reinforcement (Choe et al., 2008; 2009; 2010; Ghosh and Padgett, 2010; Simon et al.,

2010), research on the fragility analysis of RC buildings due to aging effects is still

limited. There are few studies that have investigated the effects of reinforcement

corrosion on the seismic response of typical low and/or mid rise RC buildings in terms of

capacity curves estimating the residual load bearing capacity for the adopted degradation

scenarios by means of inelastic static analysis (Berto et al., 2009; Celarec et al., 2011).



(a) Uniform corrosion (b) Localized corrosion

(c) Corrosion of RC columns

Figure 2.24. Structural deterioration due to reinforcement corrosion

(a)

(b) Figure 2.25. Izmit earthquake: (a) corrosion of reinforcement in columns and (b) corrosion-

induced loss of steel-concrete bond (Çağatay, 2005)



Figure 2.26 presents the seismic capacity curves of the initial (intact) and the

corresponding corroded building provided by Berto et al. (2012). The curves reveal a

reduction of the load bearing capacity and particularly a significant reduction of the

ductility of the corroded building with respect to the undamaged one.

Figure 2.26. Capacity curves for the sound and corroded structure: achievement of the Near Collapse (NC) limit state (Berto et al., 2012)

On the other hand, the time-dependent fragility curves proposed by Yalciner et al.

(2012) taking into account the effect of reinforcement corrosion refer to a simple SDOF

system that may not be considered representative of the existing building typology. The

derived fragility curves of Figure 2.27 corresponding to different limit states, present a

shift to the left indicating an increase in the structure’s vulnerability with time.

Fotopoulou (2012) developed fragility curves for low-rise RC buildings exposed to

earthquake-induced landslide damage at different points in time considering chloride

induced corrosion. A 3D illustration of the fragility estimates over time (fragility surface)

was also shown (Figure 2.28) in order to obtain a better view of the evolution of

vulnerability with time. An increase of the structure’s fragility was observed with time

due to corrosion which was much more pronounced for higher damage levels.



(a) Immediate Occupancy (IO) (b) Life Safety (LS)

(c) Collapse Prevention (CP)

Figure 2.27. Fragility curves of the different limit states for the initial and corroded SDOF system (Yalciner et al., 2012)

Figure 2.28. Fragility surfaces as a function of time and PGA for slight, moderate, extensive and complete limit states considering chloride induced corroded buildings on flexible foundations

(Fotopoulou, 2012)



2.9 Evaluation of soil-structure interaction and site effects on seismic vulnerability

2.9.1 Dynamic soil-structure interaction

The common practice in seismic performance assessment assumes that structures are

fixed to their base, which may be a realistic hypothesis only when these are founded on

relatively solid rock or very stiff soil. The seismic response of a structure resting on

deformable soil however may differ significantly compared to the fixed base assumption

(Clough, 1955; Mylonakis and Gazetas, 2000). Soil-structure interaction (SSI) and local

site effects are generally shown to be more pronounced in the case of soft soil formations

and high rise structures modifying considerably the free field input motion as well as the

dynamic characteristics of the building and finally its response (Stewart et al., 1999).

The consideration of SSI is usually achieved by taking into account inertial and

kinematic interaction schemes resulting to an elongation of the natural period of the soil-

structure system and an increase of system damping due to the energy dissipation at the

soil-foundation level compared to the fixed base case (Veletsos and Meek, 1974).

Kinematic interaction affects the real Foundation Input Motion (FIM) due to the actual

stiffness of the foundation elements and the soil. In general, it deviates from free-field

motions as a result of ground-motion incoherence, wave inclination or foundation

embedment (Stewart et al., 1999). On the other hand, the inertial interaction causes

further deformation in the soil due to the inertial forces transmitted to the soil from the

oscillating mass of the super-structure. There are two main approaches that are

commonly used for the analysis of the SSI phenomenon: the direct approach and the

substructure approach. In the direct method, soil, foundation and structure are modeled

and analyzed as one single system while in the substructure approach (e.g. Wolf, 1985)

SSI is analyzed as two separate systems where the coupling of the interacting

subdomains is achieved through the concept of impedance functions (e.g. Gazetas,

1991).

Numerous studies have highlighted the effects of elastic dynamic soil-structure

interaction on elastic and inelastic structural response (for example: Ciampoli and Pinto,

1995; Rodriguez and Montes, 2000; Gazetas and Mylonakis, 2001; Aviles and Pirez-

Rocha, 2003); however there are only few studies investigating SSI and site effects on

structures under nonlinear soil behavior (Iida, 1998; Saez, 2009; Saez et al., 2013;

Pitilakis D. et al., 2013). The incorporation of SSI phenomena in the analysis of elastic

systems is generally believed to be beneficial. Nevertheless, research up to date has

resulted in rather contradictory findings especially when nonlinear structural behavior is

considered (Moghaddasi et al., 2011). SSI effects tend to reduce force demands on the



structure. However, in nonlinear soil-structure systems additional translation and rotation

effects may be introduced increasing the displacement demands of the structure

(Krammer, 1996).

2.9.2 Evaluation of soil-structure interaction and site effects on seismic

structural response and vulnerability

Soil conditions and soil-structure interaction, which affect the foundation compliance,

have not been thoroughly investigated within the framework of structural vulnerability

assessment. Although there are some studies that take into account the local site effects

by providing fragility curves for buildings for different soil conditions (e.g. NIBS, 2004),

the effect of SSI to the expected structure’s performance has not received much

attention. A summary of the few reported studies incorporating SSI in fragility analysis of

buildings is briefly discussed herein. Saez et al. (2011) investigated the effects of the

inelastic dynamic SSI on the seismic vulnerability assessment of buildings performing a

comparative dynamic analysis between a complete inelastic soil-structure system that

takes into account all nonlinearities of soil, superstructure and interface associated to the

SSI phenomenon and a two-step modeling approach that neglects radiation damping but

includes the nonlinear soil behavior modifying the imposed input motion to the fixed base

superstructure (Figure 2.29). Fragility curves were derived in terms of Arias Intensity

(AI) for the slight and moderate damage states (Figure 2.30). The authors showed that

soil deformability and SSI may modify the response and fragility of non-linear structures

leading to either beneficial or unfavorable effects depending on the dynamic properties of

the soil and the structure as well as the characteristics (frequency content, amplitude,

significant duration) of the input motion.

Figure 2.29. Schematic representation of the dynamical comparative approach: complete inelastic finite element computations (SSI-FE) versus a two-step approach (T-S) (Saez et al., 2011)



(a) Slight damage (b) Moderate damage

Figure 2.30. Fragility curves following both SSI-FE and T-S approaches. Parameters α and β control the position and the slope of the curves. (Saez, 2009)

Rajeev and Tesfamariam (2012) studied the effects of SSI on seismic fragilities of

non-ductile concrete frames highlighting the influence of the uncertainties in soil

properties, foundation geometrical parameters and ground motion characteristics. To

model the interaction between the adopted shallow foundation and soil interface, the

Beam on Nonlinear Winkler Foundation (BNWF) model was used, which is capable of

capturing the rocking and sliding effects as well as the permanent settlement of the

footing for both linear and nonlinear soil behavior. Fragility curves were developed in

terms of spectral acceleration at the fundamental period of the structures for the

Immediate Occupancy (IO), Life Safety (LS) and Collapse Prevention (CP) damage states

(Figure 2.31). It was shown that fragilities of the fixed base models may differ from the

SSI models depending on the type of the structure while the uncertainty in ground

motion was found to be the dominating parameter influencing the structural response of

the SSI models.

Figure 2.31. Comparative plots of fragility curves for the fixed base and SSI models (Rajeev and

Tesfamariam, 2012)



2.10 Building-specific fragility curves using field monitoring data

The devastating impacts from past seismic events have shown that prevention and

preparedness are key tools for improving the seismic safety and resilience to earthquake

disasters. Risk and vulnerability of urban sites to earthquake hazard lead to an emerging

need for developing operational frameworks that can be used by the authorities (e.g. civil

protection authorities, end users) in pre-crises situation to establish decision making

procedures and risk mitigation strategies (Dolce and Di Bucci, 2015). In this context, the

reliable vulnerability assessment of existing structures and infrastructures is a

prerequisite for seismic loss estimation, risk mitigation and management. Recent studies

investigated the effects of degradation phenomena on the structural response and

fragility under dynamic loading namely aging (progressive deterioration of material

properties) and cumulative earthquake damage (structural modifications or existing

damages from previous events) proving that conventional generic fragility curves

(Pitilakis et al., 2014a) may not accurately represent the actual state of existing

structural systems but need to be updated in order to reflect their real condition.

Moreover uncertainties associated with the construction systems, material, mass and

geometry properties that are pronounced particularly in the case of existing buildings

may not be properly captured using generic fragility curves. Although widely applied

seismic vulnerability assessment methods (e.g. HAZUS methodology) allow the

integration of coefficients that depend on the maintenance condition or are related to in-

situ properties of building materials (by means of destructive and non-destructive tests),

such integration does not necessarily increase the reliability of the results as the actual

structural state may still not be captured properly. Moreover the development of

degradation phenomena in time is generally neglected.

The use of field monitoring data for identifying the actual state of existing structures

has recently drawn attention in civil engineering community for developing real time

assessment tools and reducing uncertainties involved within the risk assessment

procedure (Gueguen et al., 2007; Michel et al., 2008; 2012). Real-time monitoring of

civil structures and infrastructures provide valuable information to assess the structural

health and identify the actual state and vulnerability of the associated systems.

Furthermore, it allows monitoring the evolution of the structure’s safety during the

earthquake crisis while it constitutes the key component for rapid damage assessment or

the preparation of reliable damage scenarios. In Rainieri et al. (2009; 2012) an approach

for robust evaluation and monitoring of instrumented buildings is proposed in the context

of rapid post-earthquake emergency management and structural health monitoring

(Figure 2.32).



Figure 2.32. Structural health monitoring system architecture: (a) Monitored constructions, (b) local server, (c) data transmission, (d) satellite communication and seismic network, (e) master

server (Rainieri, 2009)

In Michel et al. (2012), the main aim is to show how the experimental model

extracted from ambient vibration measurements may contribute in the framework of

seismic vulnerability assessment of existing buildings in moderate seismic-prone regions.

The proposed method (Figure 2.33) aimed at improving seismic vulnerability assessment

by reducing the epistemic uncertainties due to the lack of knowledge in building models.

Ambient vibration-based methods were used to adjust the building model to realities in

the field. The experimental modal model was adapted to the recent definition of seismic

hazard and full waveform or response spectra were employed to estimate whether or not

the building may suffer from damage by the end of shaking. However the method is

based on ambient vibrations, thus the model is relevant only for slight damage which

was considered as the end of the linear building response.



Figure 2.33. Methodological scheme for the estimation of the fragility curve corresponding to the slight damage using the modal model given by the ambient vibration experiment (Michel et al.,

2012)

The interest of scientific research as well as civil protection in the development of

integrated suites of tools and methodologies to rapidly extract, collect and integrate

information on the exposure of the urban environment seismic risk is growing constantly

not only in Europe but also worldwide. Currently research is concentrating on issues such

as rapid damage detection of single important structures, rapid and reliable damage

scenario preparation and early earthquake warning. On a building specific scale a

permanent instrumentation array installed inside the building (especially in the case of

structures/infrastructures with strategic interest) allows the development of a building-

specific alert procedure suitable for performing an automated building tagging and the

establishment of decision making strategies which will allow the Civil protection

authorities to act efficiently in real (or near real-time) and after the event. The main goal

is the fast assessment of structural health conditions in the early post- earthquake

phase. The key issue for the implementation of an advanced seismic protection system

requires reduction of the computational effort and the reaction time (Rainieri et al.,

2011). Automated identification procedures (Rainieri and Fabbrocino, 2010; Rainieri et

al., 2011; Magalhaes et al., 2008; 2009) may contribute significantly in this direction

allowing a fast evaluation of health conditions of a structure after an earthquake or

during a seismic sequence. One of the advantages of the wireless units with embedded

computing power is that they can be rapidly installed inside a building during a seismic

sequence and, later, collect the data from outside through the wifi connection. An

example is given in Picozzi et al. (2011), where the Navelli city hall was damaged by the

l’Aquila earthquake and later monitored with SOSEWIN instruments during the

aftershocks sequence. Since the units have computing power, that is they can process

the data and communicate the outcomes, software for damage detection or for

evaluating the residual capacity/vulnerability after a given number of shocks can be

installed in the firmware.



In this context, dynamic characterization of civil engineering structures (natural

frequencies, damping ratios, mode shapes) using monitoring data becomes increasingly

important in a wide range of research and application fields, such as dynamic response

prediction (e.g. Manos et al., 1996; Asmussen et al., 1996; Brownjohn, 2003; Fabbrocino

et al., 2010; Manos et al., 2014; Di Cesare et al., 2014), finite element model updating

(e.g. Teughels, 2003; Jaishi and Ren, 2005; Zarate and Caicedo, 2008; Savoia et al.,

2013; Ventura et al., 2002; Aras at al., 2011; Antonacci et al., 2012), structural health

monitoring (De Stefano, 2007; Spina et al., 2011) and damage detection (Peeters,

2000; Farrar et al., 2001; Ramos et al., 2010; Goulet et al., 2014). In order to predict or

modify the response of a structure, an accurate well-known mathematical model is

required that represents the dynamics of the structure, the so-called modal model

(Parloo, 2003). Rapid development of data acquisition and processing capabilities has

given rise to major advances in the experimental operational studies and more

specifically in the estimation of modal parameters of vibrating systems. A modal model of

an artificially excited structure can be obtained based on Experimental Modal Analysis

(EMA) by measuring the forces and vibrational structural responses (Ewins 1984;

Allemang 1994; Heylen et al., 1995). For large-scale applications however (e.g. civil

engineering structures) Operational Modal Analysis (OMA) is generally preferred to forced

vibration measurements due to the fact that the same modal parameters can be obtained

from vibration data in operational rather than laboratory conditions (Reynders, 2012).

Ambient vibration measurements are usually used to perform OMA and indentify the

modal parameters of a structure.

In order to derive ” building specific” fragility curves based on field monitoring data,

that represents the actual state and vulnerability of a structure, the measured modal

parameters can be used to improve the finite element models to better reflect the

measured data than the initial ones. The lack of correlation between the numerical

structural models and experimental observations may be attributed to poorly known

boundary conditions and material properties or modeling simplifications. Due to these

uncertainties the predicted analytical dynamics of an “as built” structure based on the

initial design plans, may differ from the measured dynamics of the real structure.


CHAPTER 3

Reference buildings and vulnerability assessment methodology

3.1 Introduction

In the present chapter the reference reinforced concrete (RC) buildings are presented,

that have been selected in the context of this thesis for the seismic vulnerability

assessment considering aging and soil-structure interaction effects. Vulnerability is

described in terms of probabilistic fragility functions representing the probability of

exceeding a predefined level of damage under a seismic excitation of a given intensity.

The analytical methodology that is applied for the derivation of the fragility curves is also

described.

The reference buildings are two-dimensional RC moment resisting frame structures

that have been adopted from the literature to represent varying typologies designed with

different seismic code levels. To illustrate the methodological framework of the

vulnerability assessment in this chapter, fragility curves are derived for the fixed base –

intact frame buildings. The effects of aging and soil-structure interaction are investigated

in the ensuing chapters. The derived fragility curves are compared with proposed curves

from the literature to verify the validity of the proposed methodology.

3.2 Description of the methodological framework

Figure 3.1 presents a schematic flowchart of the proposed framework adopted to assess

the seismic vulnerability of RC frame buildings. In order to derive generic fragility curves

and increase the reliability of the results, different building configurations are considered

through the selection of RC moment resisting frame (MRF) buildings of varying typologies

designed according to different seismic code levels. The analytical simulation of the

structural capacity is based on the structural detailing, the material properties and the

plasticity modeling. Aging and soil-structure interaction effects are incorporated in the

assessment methodology performed and are discussed in the ensuing Chapters 4 and 5.

Chapter 3: Reference buildings and vulnerability assessment methodology 74


The earthquake demand is defined based on the selection of real earthquake records so

as the seismic input motion is characterized by different characteristics in terms of

frequency content and duration. Two-dimensional Incremental Dynamic Analyses (IDA)

are conducted to assess the seismic performance of the structural systems. The damage

states are defined in terms of maximum interstorey drift (maxISD) for the Immediate

Occupancy (IO) and Collapse Prevention (CP) damage states. The fragility curves are

derived in terms of either the spectral acceleration at the fundamental elastic period of

the structure Sa(T1, ξ%) or the peak ground acceleration (PGA) based on the statistical

exploitation of the results of the IDA. In the probabilistic approach proposed herein,

several uncertainties are involved with respect to the capacity of the buildings, the

seismic demand and the definition of the damage states. The capacity uncertainty

reflects the variability of the structural properties and the fact that the modeling

procedures are not perfect. Demand uncertainty is associated with the randomness in the

ground motions and the record-to-record variability. Finally the uncertainties in the

definition of the damage states are due to the fact that the thresholds of the damage

indices or parameters used to define the damage states are generally not known.

Building configurations - selection of RC moment resisting frame buildings designed according to dif ferent code levels

Capacity of buildings- structural detailing - material properties - plasticity modeling

Earthquake demand- selection of seismic input motion

Incremental dynamic analysis- response parameter: maximum interstorey drift- failure mechanisms

Definition of limit damage states- def ined in terms of maximum interstorey drift Methodology for fragility

curve generation- statistical analysis- incorporation of uncertainties in seismic demand, structural capacity, def inition of damage states

Derivation of fragility functions -in terms of spectral acceleration corresponding to the fundamental period of the structures-in terms of peak ground acceleration

Figure 3.1. Methodological framework for the fragility analysis of the RC MRF buildings



3.3 Selection of the reference fixed base - intact frame buildings

Seven different reinforced concrete (RC) moment resisting frames (MRFs) have been

selected as reference structures. They have been designed according to different seismic

code levels in order to capture the different periods of construction. The SYNER-G

(www.syner-g.eu) taxonomy for RC structures is used to describe the different building

typologies (e.g. Crowley et al., 2011). Among the seven reference structures addressed,

two have been designed for gravity loads only with no seismic provisions (No code), two

have been designed with low level of seismic design according to the 1959 Greek seismic

code (‘Royal Decree’ of 1959) (Low code) whereas the remaining three have been

designed following the provisions of the Greek (EAK, 2000) and Portuguese modern

seismic codes (High code). Table 3.1 summarizes the main characteristics of the

reference models, namely the total mass, the fundamental elastic period, the concrete

and steel strength (characteristic values). Also the base shear coefficients for all

structural models are presented normalized to the gravitational acceleration

(g=9.81m/sec2). In the following paragraphs a more detailed description of the selected

typologies is presented. The assumptions associated with the design criteria of each

structural model adopted may be found in the corresponding references.

Table 3.1. Characteristics of the reference studied buildings

RC building Total mass [t]

Initial fundamental period T1 [sec]

fc [MPa]

fy [MPa]

Base shear

coefficient Low rise – No code 207 0.98 24 276 -

Mid rise – No code 198 0.66 16 343 -

Mid rise – Low code 135 0.58 14 400 0.06

High rise – Low code 334 0.89 14 400 0.06

Low rise – High code 35 0.40 20 500 0.26

Mid rise – High code (Greek) 130 0.66 20 400 0.08

Mid rise – High code (Portuguese) 266 0.48 28 460 0.14

3.3.1 MRF buildings designed with no seismic code provisions

The frame models with no seismic provisions have both been originally designed for the

purpose of experimental studies. The first one is a three storey – three bay frame model

(Bracci et al., 1992) representative of low rise buildings (Low rise – No code) with storey

height and bay width equal to approximately 3.7m and 5.5m respectively. The total

building height is 11m. It is designed for gravity loads and is non-seismically detailed.

The provisions of ACI 318-89 (ACI, 1989) code, with Grade 40 steel (fy=276MPa) and

ordinary Portland cement (fc=24MPa) is employed. More details regarding the design

information may be found in Bracci et al., (1992). The plan and elevation layouts of the



building are illustrated in Figure 3.2 including the section geometries and reinforcing

details. As shown in Table 3.1, the fundamental period of the structure presents higher

values for the particular building (Low rise – No code) than for the other structural

models. Even the total mass and the compressive concrete strength are relatively high.

This may be attributed to the fact that these properties have been specified in

accordance with the design and construction common practice more than 50 years ago,

making the building more flexible in comparison to the other ones. Moreover in Figure

3.2 it is seen that also the geometrical characteristics contribute to the high flexibility of

the structure as the floor height and the bay width of the model are relatively large

compared to the rest of the adopted buildings. As stated in Bracci et al. (1992), the

relative dimensions adapted for the frame members of the idealized prototype structure

were based on a survey of typical construction practices in the eastern United States

conducted by El-Attar et al. (1991a; 1991b) at Cornell University and Lao (1990) at State

University of New York (SUNY) at Buffalo.

Figure 3.2. Reference MRF model used for seismic vulnerability assessment: plan and elevation

view with geometrical properties and reinforcing details (diameters in inches) of the Low rise-No code model (Bracci et al., 1992)

The second model has been designed also for vertical loads only and is representative

of old construction practice of Southern Europe in the 1950s. The particular RC building

model is referred to as ICONS Project frame which was tested at European Laboratory for

Structural Assessment (ELSA) of the Joint Research Center (JRC) in Ispra, Italy (Pinho

and Elnashai 2001; Pinto et al., 2002). It is a four storey – three bay frame model with

storey height equal to 2.7m and is considered representative of mid-rise MRF structures



with no seismic code provisions. The first two bays have a width equal to 5m while the

third one is 2.5m wide. The material properties considered in the design phase are a low

strength concrete (fc=16MPa) and smooth longitudinal reinforcing steel of class Fe B22k

with nominal yield strength equal to fy=215MPa. However the mechanical properties of

steel obtained from non-destructive experimental tests (Pinto et al., 2002) differed

considerably from the nominal values, estimating the average yielding strength much

higher, approximately equal to fy=343MPa. The plan and elevation views of the model

with the geometric characteristics and the reinforcement are shown in Figure 3.3. More

information regarding the reinforcement detailing and material properties is provided in

Pinto et al. (2002).

Figure 3.3. Reference MRF model used for seismic vulnerability assessment: plan and elevation view with geometrical properties and reinforcing details (diameters in mm) of the Mid rise-No code model

(Pinto et al., 2002)

3.3.2 MRF buildings designed with low seismic code provisions

The buildings with low level of seismic design are a four storey and a nine storey – three

bay frame structures (Kappos et al., 2006) that are considered typical of mid (Mid rise –

Low code) and high rise (High rise-Low code) buildings respectively designed according

to the 1959 Greek seismic code (‘Royal Decree’ of 1959). In the latter regulations, the

ductility and the dynamic features of the constructions are completely ignored. According

to the code’s prescription the base shear coefficient, which is required for the

computation of the seismic base shear forces, is considered equal to the seismic

coefficient which varies for the different seismic zones defined for Greece and the type of



(a)

(b)

Figure 3.4. Reference MRF models used for seismic vulnerability assessment: plan and elevation view with geometrical properties and reinforcing details (diameters in mm) of the (a) Mid rise-Low code and (b) High rise–Low code models (Kappos et al., 2006, personal communication Kappos A. and

Panagopoulos G.)



the soil. For the buildings under study seismic zone II (seismic coefficient α=0.06) and

soil type A corresponding to rock soil conditions are considered.

Figure 3.4 shows the plan and elevation views for both models with their geometrical

and reinforcement layouts. The storey height for both models is 3m except for the 1st

storey which has a height equal to 4.5m. The total height for the mid- and high-rise

structures is 13.5m and 28.5m respectively. The length of both buildings is equal to 16m

with the length of the end bays being equal both to 6m and the mid-bay to 4m. The

material properties considered for the low-code designed structures are concrete and

steel strength equal to fc=14MPa and fy=400MPa respectively.

3.3.3 MRF buildings designed with high seismic code provisions

The frame structures designed based on modern seismic code provisions are considered

representative of low- and mid-rise buildings. In particular a two storey – one bay (Low

rise – High code) (Gelagoti, 2010) and a four storey – three bay frame model (Mid rise –

High code) (Kappos et al., 2006) have been selected, both designed according to the

provisions of Greek modern seismic code (EAK 2000). This code is characterized by

enhanced level of seismic design and ductile seismic detailing of RC members according

to the new generation of seismic codes (similar to Eurocode 8). The base shear

coefficient according to the Greek modern code is calculated for the low rise building

considering seismic zone III (seismic coefficient α=0.36) and rock soil conditions while

for the mid-rise building zone II was considered (α=0.16). Furthermore, a mid-rise frame

structure with three bays (Abo El Ezz, 2008) designed according to the Portuguese

modern seismic code (Romao, 2002) (Mid rise-High code) is studied. The frame is

designed following the capacity design rules that insure beam hinging side-sway pattern.

The base shear coefficient according to the latter regulations is calculated considering a

seismic zone A and rock soil conditions. The reference seismic coefficient depends on the

nature of the soil and the dynamic characteristics of the structure and is calculated equal

to 0.25.

The total height and length of the low-rise building is 7m and 5m respectively. The

height of the first storey is equal to 4m while in the second floor it decreases to 3m. The

concrete and steel strength are considered 20MPa and 500MPa respectively. The mid-rise

frame model designed with the modern Greek seismic code has a total height equal to

13.5m while its length is 16m, similarly to the mid rise – low code model of Figure 3.4.

The height of the first storey is 4.5m whereas the other storeys have a regular storey

height equal to 3m. The compressive concrete strength is considered equal to 20MPa and

the steel tensile strength equal to 400MPa. The frame model designed with the modern

Portuguese seismic code is a four-storey structure with regular storey height (3m). The



total height and length of the building are equal to 12m and 9m respectively. The

material properties for the particular frame model are concrete strength equal to 28MPa

and steel yielding strength equal to 460MPa.

The plan and elevation layouts as well as the geometrical properties and reinforcing

details of the three moment resisting frame models designed with high seismic code

provisions presented above are shown in Figures 3.5, 3.6 and 3.7 respectively.

Figure 3.5. Reference MRF model used for seismic vulnerability assessment: plan and elevation view with geometrical properties and reinforcing details of the Low rise-High code (Greek) model

(Gelagoti, 2010)

Figure 3.6. Reference MRF model used for seismic vulnerability assessment: plan and elevation view with geometrical properties and reinforcing details of the Mid rise-High code (Greek)

model (Kappos et al., 2006)



Figure 3.7. Reference MRF model used for seismic vulnerability assessment: plan and elevation view with geometrical properties and reinforcing details of the Mid rise-High code (Portuguese)

model (Abo El Ezz, 2008)

3.4 Finite element modeling in OpenSees

The numerical analyses are conducted using OpenSees (Mazzoni et al., 2009), a platform

designed around an object-oriented architecture facilitating the use of existing features

and the development of new components and modulus, making it particularly attractive

to model complex structural or geotechnical systems subjected to static or dynamic

loads. An extensive library of material models is provided, supporting also a wide range

of solution procedures and computation models.

Inelastic force-based formulations are employed for the simulation of the nonlinear

two-dimensional with three degrees of freedom beam-column frame elements, that are

subjected to both axial compression and bending, considering four Gauss-Lobatto

(Neuenhofer and Filippou, 1997) integration points along each member’s length. The

applied formulations allow both geometric (P-delta and large displacements/rotation

effects) and material nonlinearities to be captured.

Distributed material plasticity along the element length is considered for the beam-

column elements based on the fiber approach to represent the cross-sectional behavior

(Spacone et al., 1996). Each fiber is associated with a uniaxial stress-strain relationship;



the sectional stress-strain state of the beam-column elements is obtained through the

integration of the nonlinear uniaxial stress-strain response of the individual fibers in

which the section is subdivided (Figure 3.8).

RC Section UnconfinedConcrete Fibers(cover patch)

ConfinedConcrete Fibers

(core patch)

Steel Fibers(steel layer)

Beam – Column element

Fiber section

σ

ε

σ

ε

σ

ε

Figure 3.8. Fiber approach for the representation of the cross-sectional behavior along an RC

element

The modified Kent and Park model (Scott et al., 1982) is used to define the behavior

of the concrete fibers, yet different material parameters are adopted for the confined

(core) and the unconfined (cover) concrete. The uniaxial ‘Concrete01’ material is used to

construct a uniaxial Kent-Scott-Park concrete material object with degraded linear

unloading/reloading stiffness according to the work of Karsan-Jirsa (Karsan and Jirsa,

1969) with zero tensile strength. The steel reinforcement is modeled using the uniaxial

‘Steel01’ material to represent a uniaxial bilinear steel material with kinematic hardening

described by a nonlinear evolution equation. The material objects used for the

representation of the stress-strain relationships for concrete (cover and core) and

reinforcement steel are shown in Figure 3.9.



Figure 3.9. Material objects adopted in OpenSees for the representation of the uniaxial stress-strain

relationships of the concrete cover and core (left) and for the reinforcement steel (right)

The parameters involved in the definition of the concrete material objects are the

following: the maximum concrete compressive strength fpc, the concrete strain at

maximum stress epsc0, the concrete crushing strength fpcu and the strain at ultimate

stress epsU. The confinement factor (i.e. the ratio of confined to unconfined concrete

strength) is taken equal to 1 for the buildings designed with no or low seismic code

provisions (i.e. no confinement is considered) and 1.2 for the structures designed with

high seismic design code level. For the cases where the confinement of the section is

taken into account, the strain epsU corresponding to the ultimate stress, is considered

equal to the 20% of the confined concrete compressive strength. Table 3.2 summarizes

the parameter values of the unconfined concrete material object adopted for the different

building configurations. The table presents the characteristic values for the concrete

material, which are considered in the analyses.

Table 3.2. Parameter values for the definition of the material object ‘Concrete01’ in OpenSees (unconfined concrete)

RC building fpc [MPa] epsc0 fpcu [MPa] epscU unconfined

Low rise – No code 24 0.002 4.9 0.012

Mid rise – No code 16 0.002 3.2 0.008

Mid rise – Low code 14 0.002 2.8 0.0098

High rise – Low code 14 0.002 2.8 0.0098

Low rise – High code 20 0.002 4.0 0.007

Mid rise – High code (Greek) 20 0.002 4.0 0.007

Mid rise – High code (Portuguese) 28 0.002 5.6 0.005

For the steel material object the main parameters that are required are the steel yield

stress Fy, the initial elastic tangent modulus of steel E0 and the strain-hardening ratio b

(i.e. the ratio between post-yield tangent and initial elastic tangent). In this study the



steel modulus and the strain-hardening ratio are taken equal to 200GPa and 0.005

respectively. The yield stress values for the different structural typologies are

summarized in Table 3.1 (fy values).

Hysteretic damping, which is usually responsible for the dissipation of the majority of

energy introduced by the earthquake action, is implicitly taken into account within the

nonlinear fiber model formulation of the inelastic frame elements. Additionally, to

account for the non-hysteretic viscous type of damping that is mobilized during the

dynamic response of the analyzed systems (e.g. internal friction in the structural

materials, connections, non-structural components etc.) tangent stiffness – proportional

damping is assigned with a damping ratio of 3%. In this case the stiffness coefficient is

recomputed each time the stiffness changes and on this basis the damping matrix is

reformed, assuming that the damping ratios in the specified modes do not change

regardless of the modal frequency (Charney, 2008). It has been shown (Priestley and

Grant, 2005) that tangent-stiffness proportional damping is more appropriate for

modeling elastic viscous damping in inelastic time-history analyses resulting to a more

realistic computation of the elastic damping forces and more reliable estimates of the

displacement responses.

3.4.1 Infill modeling

Masonry infill walls are widely used as interior partitions and external walls in RC

buildings and are generally treated as non-structural elements and are therefore not

considered in the design process. Nevertheless, post-earthquake damage observation,

experimental and numerical research have shown that their presence may have a

significant impact on the seismic response of RC frame buildings providing a considerable

increase in terms of strength, stiffness and energy dissipation (Smyrou et al., 2011;

Ricci, 2010). However their post-peak response is characterized by brittle mechanisms

associated to wall failure and wall-frame interaction. Moreover the variability in their

mechanical properties of the materials and the construction details as well as the

different possible collapse modes in-plane and out-of plane introduce many uncertainties

affecting the evaluation and prediction of their behavior. Generally infills have a

beneficial effect on structural seismic response, provided that they are placed regularly

throughout the building and that they don’t cause shear failures of the columns (Dolšek

and Fajfar, 2001).

For the modeling of the masonry infills a double strut model has been adopted

(Holmes, 1963; Stafford-Smith, 1962; 1966; Thiruvengadam, 1985; Chrysostomou,

1991; Hashemi and Mosalam, 2007). The in-plane behavior of the infill panel is simulated

in OpenSees considering a pair of diagonal compression struts that carry the axial loads



across two opposite corners, as illustrated in Figure 3.10. It should be noted that the

adopted infill model does not take shear failure into account.

Figure 3.10. Implemented infill panel model under horizontal loading. In-plane double-single strut

model

Inelastic struts are used to represent infill walls because they have sufficient accuracy

to capture key characteristics of force-displacement response. Each strut is assigned an

elasto-plastic force displacement relationship representing initial stiffness, peak strength

and post-peak behavior of the masonry. The thickness of the struts is considered equal

to the actual infill thickness. The equivalent strut width dw, is computed according to

Holmes (1961) as:

ww

db

3 (3.1)

where dw the diagonal length of the infill panel computed based on the infill length (Linf)

and height (hinf) whereas bw is the width of strut under compression. The expected

modulus of elasticity Em of the infill is computed based on its compressive strength fm.

Based on the values of these parameters, the stiffness of the equivalent strut, Kinf, is

calculated as:

w w m

infw

b t EK

d (3.2)

The axial strength of the equivalent infill strut for pure in-plane loading is determined

by transforming the expected infill shear strength, Vine, that is computed as:

ine me nV ν A (3.3)



where An is the area of the net mortared/grouted horizontal section across the infill panel

and vme is the expected masonry shear strength. Then the axial strength of the diagonal

member is obtained as follows:

ineN0

VP

cosθ (3.4)

where θ is the angle whose tangent is the infill height to length aspect ratio i.e.

tanθ=hinf/Linf

Dividing this value by the axial stiffness Kinf, the axial deflection at yield can be

produced as:

N0Αy0

inf

P∆

K (3.5)

To gain insight of the impact of infill panels on the response of RC frames of different

height and code design classes subjected to seismic action, the following models are

addressed: the low rise – no code, the high rise – low code and the mid rise – high code

(Portuguese) buildings. All frame models are analyzed considering both regular and

irregular infill distribution in elevation (pilotis). Table 3.3 summarizes the main

characteristics of the infilled models, namely the fundamental periods for regularly and

irregularly infilled frames as well as the adopted values of compressive and shear

strengths and the modulus of Elasticity. The consideration of infill walls provides a

significant increase in terms of stiffness leading thus to a decrease of the initial

fundamental period of the corresponding bare-frame buildings.

Table 3.3. Characteristics of the infilled studied buildings

RC building

Fundamental period

irregularly infilled (pilotis)

Tpil [sec]

Fundamental period

regularly infilled Tinf [sec]

Compressive Strength fm [MPa]

Shear Strength

vme [MPa]

Modulus of

Elasticity Em

[MPa] Low rise – No code 0.69 0.25 1.2 0.62 660

High rise – Low code 0.48 0.33 3 1 3000

Mid rise – High code

(Portuguese) 0.23 0.15 3 1 3000

3.5 Selection of the seismic input motion

A representative set of accelerograms is selected that will subsequently be used for non-

linear incremental dynamic analysis and will provide the necessary response statistics for

the fragility analysis. The selected scenario earthquake consists of a set of 15 real ground

motion records obtained from the European Strong-Motion Database



(http://www.isesd.hi.is) (Table 3.4). They are all referring to outcrop conditions recorded

at sites classified as rock according to EC8 (soil type A) with moment magnitude (Mw)

and epicentral distance (R) that range between 5.8<Mw<7.2 and 0<R<45km

respectively. Outcropping records are selected to avoid uncertainties related to soil

effects. Additionally in order to eliminate potential source of bias in structural response,

the selection of pulse-like records has been avoided. The primary selection criterion is

the average acceleration spectra of the set to be of minimal “epsilon” (Baker and Cornell,

2005) at the period range of 0.00<T<2.00sec with respect to a reference spectra defined

based on the ground motion prediction equation (GMPE) proposed by Ambraseys et al.

(1996) corresponding to the median of the Mw and R selection bin. Epsilon is computed

by subtracking the mean predicted logarithmic spectral acceleration that corresponds to

the fundamental structural period lnSa(T1) from the record’s lnSa(T1) and dividing it by

the logarithmic standard deviation as estimated by the prediction equation (Baker and

Cornell, 2005). In order to achieve minimal “epsilon”, the set mean spectrum is

constrained to match the mean Sa prediction with a tolerance dependent on

corresponding variance of Sa. The optimization procedure is performed by making use of

the REXEL software. REXEL is a freely available software that can be downloaded from

the website of the Italian network of earthquake engineering University labs

(http://www.reluis.it/index.php?lang=en), which allows to search for suites of waveforms

from the European Strong-motion Database, compatible to reference spectra, either

user-defined or automatically generated to EC8 (CEN-European Committee for

Standardization, 2003) or the Italian seismic code (Iervolino et al., 2010). The selected

records cover a wide range of seismic motions in terms of amplitude, frequency content

and significant duration. Figure 3.11 depicts the mean normalized elastic response

spectrum of the records in comparison to the corresponding median predicted spectrum

of Ambraseys et al. (1996). As shown in the figure, a good match between the two

spectra is achieved.

Before applying the selected outcropping records, the real seismic records are first

subjected to baseline correction and filtering. In particular, a Butterworth bandpass 4th

order filter type in the frequency range from f1=0.25 Hz to f2=10 Hz and a linear type

baseline correction were applied to all records using Seismosignal software (Seismosoft,

Seismosignal 2011). ANNEX A summarizes the acceleration time histories as well as the

elastic acceleration response spectra of the seismic records used as input motion.



Table 3.4. Lists of records used for the IDA

Earthquake Name Station ID Date Mw R (km) PGA (m/s2)

Waveform code

Friuli ST20 6/5/1976 6.5 23 3.499 000055xa

Montenegro ST64 15/4/1979 6.9 21 1.774 000198xa

Montenegro (aftershock) ST68 24/5/1979 6.2 30 0.667 000234xa

Valnerina ST225 19/9/1979 5.8 5 1.51 000242xa

Valnerina ST61 19/9/1979 5.8 22 0.6 000246xa

Campano Lucano ST93 23/11/1980 6.9 23 1.363 000287xa

Lazio Abruzzo ST140 7/5/1984 5.9 5 0.985 000365xa


Golbasi ST161 5/5/1986 6 29 0.538 000410ya

Golbasi ST161 6/6/1986 5.8 34 0.167 000412xa

Izmit (aftershock) ST575 13/9/1999 5.8 15 0.714 001243xa

Mt. Vatnafjoll ST2483 25/5/1987 6 42 0.131 005271ya

Kozani ST1320 13/5/1995 6.5 17 1.396 006115ya

South Iceland ST2497 17/6/2000 6.5 34 0.386 006269xa

Firuzabad ST3293 20/6/1994 5.9 39 0.216 007158xa

Figure 3.11. Normalized average elastic response spectrum of the input motions in comparison

with the corresponding reference spectrum proposed by Ambraseys et al. (1996)

3.6 Incremental dynamic analysis IDA

3.6.1 Performing IDA

The IDA procedure is used to determine the seismic performance and finally to assess

the seismic vulnerability of the selected reference buildings. IDA is an emerging analysis

method which involves performing a series of nonlinear dynamic analyses under a suite

of multiply scaled ground motion records whose intensities should be ideally selected to

cover the whole range from elasticity to global dynamic instability (Vamvatsikos and

Cornell, 2002). IDA curves of the structural response, which provide a relationship



between a damage measure quantity (i.e. engineering demand parameter EDP) and a

scalable intensity measure (IM) of the applied scaled accelerograms, are then

constructed by interpolating the resulting EDP-IM discrete points.

Within the framework of this thesis, the damage measure is expressed in terms of

maximum interstorey drift ratio, maxISD, which is known to relate well to dynamic

instability and structural damage of frame buildings. For the fixed-base (bare and infilled)

structures the intensity measure is described by the 5%-damped spectral acceleration at

the fundamental period of the structure [Sa(T1,ξ=5%)]. The latter is generally found to

be both efficient and sufficient for first-mode dominated, moderate period structures

(Shome and Cornell, 1999). 5% is used as damping value despite of the models’

damping due to the fact that hazard curves are usually produced for Sa(T1,5%).

IDA for the structural models is conducted by applying the 15 progressively scaled

records to cover the entire range of structural response, from elasticity to yielding, and

finally global instability. An advanced tracing algorithm, namely the hunt & fill

(Vamvatsikos and Cornell, 2002; 2004), which ensures that the records are properly

scaled with the minimum required computational effort, is used to perform the IDA for

the fixed-base structures. Analyses are performed at rapidly increasing levels of the

selected IM until numerical non-convergence is achieved, indicating global dynamic

instability. Additional analyses are performed at intermediate IM levels to sufficiently

capture the global collapse and increase the accuracy at lower IMs (Vamvatsikos and

Cornell, 2004). In particular a maximum of 12 runs is allowed for each record with an

initial step of 0.1g, a step increment of 0.05g and a first elastic run at 0.005g and 0.01g

for the no/low and high code structures respectively.

By interpolating the derived pairs of Sa(T1,5%)) and maxISD for each individual

record we get 15 continuous IDA curves for each structural model. Figures 3.12 and 3.13

present the derived IDA curves for each record in terms of Sa(T1,ξ=5%) and the

corresponding summarized across all records IDA curves at 16%, 50% and 84% fractiles

for the fixed base-intact, bare and infilled buildings respectively. IDA is record and

structural model specific; when a model is subjected to different ground motions, it will

often produce quite dissimilar responses that are difficult to be predicted a priori

(Vamvatsikos and Cornell, 2002).



Figure 3.12. IDA curves for the initial intact fixed base bare frame structures with no, low and high seismic code provisions



Figure 3.12. (Continued) - IDA curves for the initial intact fixed base bare frame structures with no, low and high seismic code provisions

It is observed that the IDA curves of individual time-histories in many cases display a

twisting pattern that corresponds to sequential segments of “softening” and “hardening”

with the local slope or stiffness decreasing and increasing respectively with higher IM.

The excessive “hardening” leads a system that showed high response at a given intensity

level, to exhibit the same or even lower response when subjected to higher seismic

intensities. This could be attributed to the fact that as the accelerogram is scaled up, the

structure may yield in an early cycle thus altering its properties and becoming less

responsive in later stronger cycles. This means that the structures may experience

acceleration or deceleration of the EDP accumulation rate, thus locally pulling the IDA

curve to relatively lower EDPs resulting to a non-monotonic function of the IM

(Vamvatsikos and Cornell, 2002).

Despite the fact that Sa(T1,5%) is proven to be an efficient IM, it is observed that IDA

curves still display a considerable record-to-record variability with dispersion in the order

of 20%-50% close to the flatline depending on the structural characteristics. Thus, once

the structures deform into the nonlinear range and become progressively more damaged,

the optimal period may move away from the first-mode elastic period T1 as witnessed by

the increased variability of the IDA curves close to global collapse. However, the a priori

selection of the appropriate periods before the end of the dynamic analysis is not an easy

task (e.g. Vamvatsikos and Cornell, 2005) which lies beyond the scope of this thesis.



Figure 3.13. IDA curves for the initial intact (regularly and irregularly) infilled structures with no, low and high seismic code provisions



3.6.2 Limit damage states

The selection of well-defined and realistic damage (or performance) states is a key issue

in the development of seismic fragility curves. Two limit states are defined in terms of

maximum interstorey drift ratio, maxISD, representing the Immediate Occupancy (IO)

and Collapse, or near Collapse Prevention (CP) performance levels. In the Immediate

Occupancy state the structure is characterized essentially by elastic behavior by limiting

structural damage (e.g. yielding of steel, significant cracking of concrete, non-structural

damage) whereas in the Collapse Prevention state there is a small risk of partial or

complete building collapse by limiting structural deformations and forces to the onset of

significant strength and stiffness degradation. Table 3.5 presents the definition of the two

performance levels according to FEMA356.

Table 3.5. Description of Immediate Occupancy and Collapse Prevention performance levels according to FEMA356 for concrete frames

Element: Concrete Frames Immediate Occupancy Level Collapse Prevention Level

Primary

Minor hairline cracking. Limited yielding possible at a few

locations. No crushing (strains below 0.003)

Extensive cracking and hinge formation in ductile elements. Limited cracking and/or splice

failure in some non-ductile columns. Severe damage in

short columns.

Secondary

Minor spalling in a few places in ductile columns and beams.

Flexural cracking in beams and columns.

Extensive spalling in columns and beams. Severe joint

damage. Some reinforcing buckled.

The first limit state is defined at 0.5% and 0.1% according to HAZUS prescriptions

(NIBS, 2004) for RC bare and infilled moment resisting frame structures, whereas the

second is assigned on the median (50%-fractile) IDA curve derived in terms of Sa(T1,

ξ%). In Figure 3.14 an example of the limit state definition for the bare frame high rise –

low code building is shown. The main idea is to place the CP limit state at a point where

the IDA curve is softening towards the flat line but at low enough values of maxISD so

that we still trust the structural model (Vamvatsitkos and Cornell, 2004). Tables 3.6 and

3.7 summarize the CP limit state values adopted for the bare and infilled frame structural

models respectively. It is observed that rather low CP limit values are obtained for the

regularly infilled building cases. This can be attributed to the elasto-plastic model that

has been adopted for the simulation of the nonlinear behavior of the infill panels, which

does not capture the post-peak behavior of the masonry and thus building collapse is

considered when the first softening occurs although after the infill failure the residual

strength remains stable until the collapse of the structural elements.



IO CP

Figure 3.14. Definition of IO and CP limit states on the median IDA curve of the high rise – low code MRF model

Table 3.6. CP limit state maxISD values defined on the IDA curve for the bare frame fixed base

intact structures

Low rise MRF-no

code

Mid rise MRF-no

code

Mid rise MRF-low

code

High rise MRF-low

code

Low rise MRF-high

code

Mid rise MRF-high code(Portuguese)

Mid rise MRF-high code (Greek)

0.028 0.014 0.013 0.0225 0.049 0.025 0.039

Table 3.7. CP limit state maxISD values defined on the IDA curve for the infilled fixed base, intact structures

Low rise MRF-no code-

regularly infilled

Low rise MRF-no code- pilotis

High rise MRF-low

code- regularly infilled

High rise MRF-low

code- pilotis

Mid rise MRF-high code(Portuguese)- regularly infilled

Mid rise MRF-high code(Portuguese)-

pilotis

0.005 0.019 0.005 0.023 0.003 0.03



3.7 Derivation of fragility functions

A fragility curve represents a graphical relationship of the probability of exceeding a

predefined level of damage (e.g. IO, CP) under a seismic excitation of a given intensity.

The results of the IDA (Sa(T1,5%)- maxISD values) are used to derive the fragility curves

expressed as two-parameter lognormal distribution functions:

ln IM ln IM

P DS / IM Φβ

(3.6)

where, Φ is the standard normal cumulative distribution function, IM is the intensity

measure of the earthquake expressed both in terms of Sa(T1,5%) (in units of g), IM and

β are the median values (in units of g) and log-standard deviations respectively of the

building fragilities and DS is the damage state.

The median values of Sa(T1,5%) corresponding to the prescribed performance levels

are determined based on a regression analysis of the nonlinear IDA results (Sa(T1,5%) –

maxISD pairs) for each structural model. More specifically, in accordance to previous

studies (e.g. Cornell et al., 2002), a linear regression fit of the logarithms of the

Sa(T1,5%) - maxISD data which minimizes the regression residuals is adopted in all

analysis cases. In Figure 3.15 an example of the computation of the median values of the

selected IM is illustrated for the bare frame high rise – low code building and for the

considered damage states: Immediate Occupancy and Collapse prevention. In Figure

3.15(a), the Sa(T1,5%) – maxISD pairs derived from the incremental dynamic analyses,

are presented in the log-log scale as well as the IO and CP performance levels. The fitting

line corresponding to the simulated data and the computation of the median intensity

measure values corresponding to IO and CP limit states are shown in Figure 3.15(b).

Figures 3.16 and 3.17 present the Sa (T1, 5%) - maxISD relationships (in log-log scale),

which are used to extract the IM values for the bare and infilled structural models

respectively.

The various uncertainties are taken into account through the log-standard deviation

parameter β, which describes the total dispersion related to each fragility curve. Three

primary sources of uncertainty contribute to the total variability for any given damage

state (NIBS, 2004), namely the variability associated with the definition of the limit state

value, the capacity of each structural type and the seismic demand. The uncertainty in

the definition of limit states is assumed to be equal to 0.4 while the variability of the

capacity is assumed to be 0.25 and 0.3 for the high and no/low code structures

respectively (NIBS, 2004). The third source of uncertainty associated with the demand,

is taken into consideration by calculating the dispersion of the logarithms of Sa(T1,5%) -



maxISD simulated data with respect to the regression fit. Under the assumption that

these three variability components are statistically independent, the total variability is

estimated as the root of the sum of the squares of the component dispersions. The

herein computed log-standard deviation β values of the curves vary from 0.57 to 0.72

and from 0.54 to 0.77 for the bare and infilled (regularly and pilotis) frame models

respectively.

ΙΟΙΜ CPΙΜ

(a) (b)

Figure 3.15. Regression analysis for the computation of the median intensity measure values for the high rise – low code model: (a) Sa (T1, 5%) - maxISD relationships (in log-log scale) and (b)

computation of the median IM values corresponding to the Immediate Occupancy (IO) and Collapse Prevention (CP) limit states



Figure 3.16. Regression analysis for the intact fixed base bare frame structures with no, low and high seismic code provisions



Figure 3.17. Regression analysis for the (regularly and irregularly) infilled structures with no, low and

high seismic code provisions



3.7.1 Fragility curves of the fixed base, bare frame structures

Figure 3.18 presents the seismic fragility curves derived for the High rise – Low code

moment resisting frame model in terms of Sa(T1,5%) for the IO and CP damage states. It

is seen that for a specific intensity level, for example 0.4g, the probability of exceeding

the IO and CP states are 97% and 20% respectively. For the same intensity value, the

probability of the structure suffering no damage, being thus in the fully operational state

when subjected to a seismic event is computed equal to 3%. On the other hand the

corresponding probabilities of the building experiencing the IO and CP states are 77%

and 20% respectively.

PCP

PIO

Figure 3.18. Seismic fragility curves of the High rise – Low code MRF model in terms of Sa(T1, ξ=5%) for the Immediate Occupancy (IO) and Collapse Prevention (CP) damage states

Figure 3.19 illustrates the graphs of fragility curves also for the rest of the analyzed

structures whereas Table 3.8 summarizes the lognormal distributed fragility parameters

(median and log-standard deviation) in terms of Sa(T1,5%) for all intact, bare frame

buildings when considering fixed base conditions. As expected the highest fragility values

are observed for the buildings with no seismic code provisions. Even when compared with

the models designed with low seismic code level the median values of the latter are

considerably higher being thus less vulnerable. The probability of exceeding especially

the Collapse Prevention state decreases significantly when the buildings are designed

with high seismic code provisions. However based on the results presented in Figure 3.19

and Table 3.8, buildings (i.e. mid rise – high code models) with the same classification

may present differences regarding their seismic performance and vulnerability. For the

mid- rise models designed with high code provisions (Greek and Portuguese) it is

observed that the percentage differences in the median intensity values may be even up



to 35%. This is attributed mainly to the different applied seismic criteria applied for the

design of two models. For the IO limit state which basically defines the end of the

building linear behavior, the geometric characteristics and the material properties of the

models exert greater influence on the seismic response and vulnerability. Therefore the

mid-rise building designed based on the Portuguese code, which is more regular from a

geometrical point of view (equal heights and bay widths) and for which the concrete and

steel strength values are higher presents lower vulnerability values. On the other hand

for the CP damage state, the median IM of the mid-rise building designed in accordance

with the Greek code regulations is higher, which can be attributed to the fact that its

reinforcement layout consists of a larger number of rebars of larger diameters.

Table 3.8. Seismic fragility parameters in terms of Sa(T1, ξ=5%) for fixed base, bare frame structures

RC building Median Sa(T1, ξ=5%) (g)

Dispersion IO CP

Low rise MRF-no code 0.08 0.56 0.62

Mid rise MRF-no code 0.15 0.43 0.62

Mid rise MRF-low code 0.27 0.77 0.60

High rise MRF-low code 0.13 0.64 0.57

Low rise MRF-high code 0.26 3.92 0.61

Mid rise MRF-high code (Greek) 0.20 1.73 0.67

Mid rise MRF-high code (Portuguese) 0.27 1.31 0.72



Figure 3.19. Seismic fragility curves in terms of Sa(T1, ξ=5%) of the analyzed fixed-base, bare frame structures for the Immediate Occupancy (IO) and Collapse prevention (CP) states



3.7.2 Comparison of infilled - bare frame structures

Table 3.9 summarizes the estimated fragility parameters for the different damage states

(e.g. IO, CP) as a function of Sa(T1,5%) for all the considered structural typologies.

Figure 3.20 presents comparative plots of fragility curves derived in terms of Sa(T1,5%)

for three representative bare, regularly infilled and irregularly infilled (pilotis) frames. It

is seen that the seismically designed bare frames are more vulnerable for both damage

states compared to the infilled ones as the presence of the infill walls significantly

increases the strength and stiffness of the structures. In particular, the regularly infilled

buildings present lower vulnerability values with respect to the ones with a pilotis. Thus,

as expected, the presence of the soft ground storey has a less favorable effect on the

overall capacity of the structures due to the localization of inelastic displacement demand

at the bottom bare storey. This observation is generally consistent with previous studies

(e.g. Kappos et al., 2003; 2006; D'Ayala et al., 2012) enforcing the validity of the

results. On the other hand, as far as the low rise building designed only for gravity loads

is concerned, the irregularly infilled frame sustains the greatest damage (for the CP

damage state) following by the corresponding bare frame whereas the fully infilled frame

shows the lower vulnerability values.

Table 3.9. Seismic fragility parameters in terms of Sa(T1, ξ=5%) for fixed base, bare frame structures

RC building Structural typology Median Sa(T1, ξ=5%) (g)

Dispersion IO CP

Low rise -no code

Bare frame 0.08 0.56 0.62 Regularly infilled 0.16 1.42 0.61

Pilotis 0.06 0.51 0.63

High rise -low code

Bare frame 0.13 0.64 0.57

Regularly infilled 0.22 1.74 0.69

Pilotis 0.15 1.43 0.73

Mid rise -high code (Portuguese)

Bare frame 0.27 1.31 0.72

Regularly infilled 0.70 2.06 0.54

Pilotis 0.30 1.65 0.77



Figure 3.20. Comparative plots of the fragility curves in terms of Sa(T1, ξ=5%) of the analyzed regularly infilled, irregularly infilled (pilotis) and bare frame structures for the Immediate

Occupancy (IO) and Collapse (CP) prevention states



3.8 Comparison of the derived fragility curves with literature curves

The comparison of the derived fragility curves of the different RC frame typologies

subjected to seismic loading with the curves available in the literature is of particular

interest not only for the validation of the applied methodology but also for the

investigation of the potential variability between the curves referring to the same building

class. The fragility function manager tool, developed in the framework of SYNER-G

project (Silva et al., 2014), is used for the comparison of the curves through their

harmonization in terms of intensity measure and damage scale/states. A detailed

description of the tool can be found in Chapter 2 of the present thesis (Section 2.6

“SYNER-G: The fragility function manager”).

The fragility curves selected from the literature, are derived based on empirical,

analytical and hybrid methods in terms of different intensity measures and damage

scales. The harmonization of the selected curves in terms of intensity measure (i.e. PGA,

PGV, Sd(TLS)), is performed using the spectral acceleration at the fundamental elastic

period Sa(T1) of the models analyzed in this study as the target intensity measure using

appropriate conversion equations. More specifically for the conversion of PGA to Sa(T1)

the standardized response spectrum of IBC-2006 (ICC, 2006) is utilized while PGV is

converted to Sa(T1) using the correlations proposed by Bommer and Alacorn (2006) in

combination with the response spectrum of IBC-2006. The conversion of the spectral

displacement Sd(TLS) corresponding to the inelastic period and a specific limit state TLS,

is achieved considering the target natural frequency of interest. The harmonization in

terms of limit states is conducted considering two different limit states, namely yielding

and collapse. Using these particular two limit states is the simplest way of harmonizing

limit states for a large number of fragility curves, as nearly all sets have these two

thresholds available, allowing thus a straightforward comparison. Yielding almost always

corresponds to either the first or the second curve whilst the collapse limit state usually

reflects the last curve in the set. More details regarding the harmonization procedures

available in the fragility function manager tool can be found in Silva et al. (2014).

In the following paragraphs the fragility curves of the different analyzed bare and

infilled frame models are compared with curves corresponding to the same building

typologies from the literature. The ensuing tables summarize the selected references and

the main assumptions associated with the proposed curves while the figures illustrate

comparative plots between the proposed curves for the yielding and collapse limit states

and the harmonized literature seismic fragility curves.



3.8.1 Bare MRF buildings

3.8.1.1. Bare MRFs with no seismic code provisions

The fragility curves of the low- and mid- rise bare frame models with no seismic code

provisions are compared with curves selected from the literature that correspond to the

same typology designed with no or low seismic code provisions. Tables 3.10 and 3.11

summarize the corresponding references and Figures 3.21 to 3.23 and 3.24 to 3.26

present the comparative plots for the low- and mid- rise buildings respectively.

Low rise – No code

Table 3.10. Main parameters of the fragility curves from the literature used for the comparison

with the Low rise – No code model

Reference Region of applicability Methodology Intensity measure

Cumulative distribution

function

Borzi et al., 2007 RC buildings non-

seismically designed in Italy

Analytical – Nonlinear static PGA Lognormal

Erberik, 2008 RC structures with

low seismic code level in Turkey

Analytical – Nonlinear dynamic PGV Lognormal

Kwon and Elnashai, 2006

RC buildings with no seismic design provisions

in central northern Europe and USA

Analytical – Nonlinear dynamic PGA Lognormal

Figure 3.21. Comparison of the harmonized derived fragility curves as a function of Sa for low rise, non-seismically designed, RC frame building subjected to seismic ground shaking with the

corresponding curves provided by Borzi et al. (2007) for the same building typologies



Figure 3.22. Comparison of the harmonized derived fragility curves as a function of Sa for low rise, non-seismically designed, RC frame building subjected to seismic ground shaking with the

corresponding curves provided by Erberik (2008) for the same building typologies

Figure 3.23. Comparison of the harmonized derived fragility curves as a function of Sa for low rise, non-seismically designed, RC frame building subjected to seismic ground shaking with the corresponding curves provided by Kwon and Elnashai (2006) for the same building typologies



Mid rise – No code


with the Mid rise – No code model

Reference Region of applicability Methodology Intensity

measure


function

Ahmad et al., 2011 RC bare irregular non-ductile MRF in Euro-

Mediterranean regions








Kircil and Polat, 2006 RC buildings designed with the 1975 Turkish seismic design code

Analytical – Nonlinear dynamic Sa(T1) Lognormal

Figure 3.24. Comparison of the harmonized derived fragility curves as a function of Sa for mid rise, non-seismically designed, RC frame building subjected to seismic ground shaking with the

corresponding curves provided by Ahmad et al. (2011) for the same building typologies




corresponding curves provided by Kircil and Polat (2006) for the same building typologies


corresponding curves provided by Borzi et al. (2007; 2008) for the same building typologies



3.8.1.2. Bare MRFs with low seismic code provisions

The fragility curves of the mid- and high- rise bare frame models with low seismic code


same typology designed based on low seismic code level. Tables 3.12 and 3.13

summarize the corresponding references and Figures 3.27 to 3.29 and 3.30 to 3.32

present the comparative plots for the mid- and high- rise buildings respectively.

Mid rise – Low code


with the Mid rise – Low code model


measure


function







Rota et al., 2008 RC structures in Italy Empirical PGA Lognormal

Kappos et al., 2003 RC MRF with low

seismic code provisions in Greece

Hybrid (statistical data and analytical

methods)

PGA Lognormal

Figure 3.27. Comparison of the harmonized derived fragility curves as a function of Sa for mid-rise RC frame buildings with low seismic code provisions subjected to seismic ground shaking with the corresponding curves provided by Borzi et al. (2007; 2008) for the same building typologies



Figure 3.28. Comparison of the harmonized derived fragility curves as a function of Sa for mid-rise RC frame buildings with low seismic code provisions subjected to seismic ground shaking with

the corresponding curves provided by Rota et al. (2008) for the same building typologies

Figure 3.29. Comparison of the harmonized derived fragility curves as a function of Sa for mid-rise RC frame buildings with low seismic code provisions subjected to seismic ground shaking with

the corresponding curves provided by Kappos et al. (2003) for the same building typologies



High rise – Low code


with the High rise – Low code model


measure


function




methods)

PGA Lognormal




methods)

PGA Lognormal

RISK-UE, 2003 RC MRF with low

seismic code provisions in Europe

Analytical – Nonlinear static

(UTCB approach) Sd(TLS) Normal

Tsionis et al., 2011

RC MRF with low seismic code

provisions in Euro-Mediterranean

Regions


Figure 3.30. Comparison of the harmonized derived fragility curves as a function of Sa for high-rise RC frame buildings with low seismic code provisions subjected to seismic ground shaking with the corresponding curves provided by Kappos et al. (2003; 2006) for the same building typologies



Figure 3.31. Comparison of the harmonized derived fragility curves as a function of Sa for high-rise RC frame buildings with low seismic code provisions subjected to seismic ground shaking with

the corresponding curves provided by RISK-UE (2003) for the same building typologies

Figure 3.32. Comparison of the harmonized derived fragility curves as a function of Sa for high-rise RC frame buildings with low seismic code provisions subjected to seismic ground shaking with

the corresponding curves provided by Tsionis et al. (2011) for the same building typologies



3.8.1.3. Bare MRFs with high seismic code provisions

The fragility curves of the low- and mid- rise bare frame models with low seismic code


same typology designed based on high seismic code level. Table 3.14 and Figures 3.33 to

3.35 present the corresponding references and the comparative plots for the low-rise

building respectively. Tables 3.15 and 3.16 summarize the corresponding references and

Figures 3.36 to 3.38 and 3.39 to 3.41 depict the comparative plots for the mid-rise

buildings designed with the Greek and the Portuguese seismic codes respectively.

Low rise – High code


with the Low rise – High code model


measure


function

Kappos et al., 2003 RC MRF with high



methods)

PGA Lognormal




RC MRF with high seismic code


Regions


Figure 3.33. Comparison of the harmonized derived fragility curves as a function of Sa for low-rise RC frame buildings with high seismic code provisions subjected to seismic ground shaking

with the corresponding curves provided by Kappos et al. (2003) for the same building typologies




with the corresponding curves provided by Kircil and Polat (2006) for the same building typologies


with the corresponding curves provided by Tsionis et al. (2011) for the same building typologies



Mid rise – High code (Greek)


with the Mid rise – High code (Greek) model


measure


function




methods)

PGA Lognormal

RISK-UE, 2003


provisions in Fyrom

Analytical – Nonlinear dynamic (IZIIS approach)

Sd(TLS) Lognormal


provisions in Europe

Hybrid (IZIIS approach)

Sd(TLS) Lognormal


provisions in Europe

Hybrid (UTCB approach)

Sd(TLS) Lognormal




Regions


Figure 3.36. Comparison of the harmonized derived fragility curves as a function of Sa for mid-rise RC frame buildings with high seismic code provisions subjected to seismic ground shaking





with the corresponding curves provided by RISKUE-IZIIS (2003) and RISKUE-UTBC (2003) for the same building typologies


with the corresponding curves provided by Tsionis et al., (2011) for the same building typologies



Mid rise – High code (Portuguese)


with the Mid rise – High code (Portuguese) model.


measure


function



Hybrid (statistical data and analytical methods)

PGA Lognormal






Regions







with the corresponding curves provided by Kircil and Polat (2006) for the same building typologies


with the corresponding curves provided by Tsionis et al., (2011) for the same building typologies



3.8.2 Regularly and irregularly infilled MRF buildings

3.8.2.1. Infilled MRFs with no seismic code provisions

The fragility curves of the low-rise (regularly and irregularly) infilled frame models with

no seismic code provisions are compared with curves selected from the literature that

correspond to the same typology designed with no or low seismic code provisions. Table

3.17 summarizes the corresponding references while Figures 3.42 to 3.43 and 3.44 to

3.45 present the comparative plots for the regularly and irregularly infilled models

respectively.

Low rise – No code


with the Low rise – No code (regularly and irregularly) infilled model


measure


function




Erberik, 2008 RC structures with

low seismic code level in Turkey

Analytical – Nonlinear dynamic PGV Lognormal


RC MRF with no seismic code


Regions


Figure 3.42. Comparison of the harmonized derived fragility curves as a function of Sa for low-rise regularly infilled RC frame buildings with no seismic code provisions subjected to seismic ground shaking with the corresponding curves provided by Borzi et al. (2008) for the same

building typologies



Figure 3.43. Comparison of the harmonized derived fragility curves as a function of Sa for low-rise regularly infilled RC frame buildings with no seismic code provisions subjected to seismic

ground shaking with the corresponding curves provided by Erberik (2008) for the same building typologies

Figure 3.44. Comparison of the harmonized derived fragility curves as a function of Sa for low-rise irregularly infilled RC frame buildings (pilotis) with no seismic code provisions subjected to seismic ground shaking with the corresponding curves provided by Borzi et al. (2008) for the

same building typologies



Figure 3.45. Comparison of the harmonized derived fragility curves as a function of Sa for low-rise irregularly infilled RC frame buildings (pilotis) with no seismic code provisions subjected to seismic ground shaking with the corresponding curves provided by Tsionis et al. (2008) for the


3.8.2.2. Infilled MRFs with low seismic code provisions

The fragility curves of the high-rise (regularly and irregularly) infilled frame models with

low seismic code provisions are compared with curves selected from the literature that

correspond to the same typology designed with low seismic code provisions. Table 3.18

summarizes the corresponding references while Figures 3.46 and 3.47 present the

comparative plots for the regularly and irregularly infilled models respectively.

High rise – Low code


with the High rise – Low code (regularly and irregularly) infilled model


measure


function




methods)

PGA Lognormal




methods)

PGA Lognormal



Figure 3.46. Comparison of the harmonized derived fragility curves as a function of Sa for high-rise regularly infilled RC frame buildings with low seismic code provisions subjected to seismic ground shaking with the corresponding curves provided by Kappos et al. (2003;2006) for the


Figure 3.47. Comparison of the harmonized derived fragility curves as a function of Sa for high-rise irregularly infilled RC frame buildings (pilotis) with low seismic code provisions subjected to

seismic ground shaking with the corresponding curves provided by Kappos et al., (2003;2006) for the same building typologies



3.8.2.3. Infilled MRFs with high seismic code provisions

The fragility curves of the mid- rise (regularly and irregularly) infilled frame models with

high seismic code provisions (Portuguese code) are compared with curves selected from

the literature that correspond to the same typology designed with high seismic code

provisions. Table 3.19 summarizes the corresponding references while Figures 3.48 to

3.49 and 3.50 to 3.51 present the comparative plots for the regularly and irregularly

infilled models respectively.

Mid rise – High code (Portuguese)


with the Mid rise – High code (regularly and irregularly) infilled model


measure


function

Borzi et al., 2008 RC buildings






methods)

PGA Lognormal




methods)

PGA Lognormal

Figure 3.48. Comparison of the harmonized derived fragility curves as a function of Sa for mid-rise regularly infilled RC frame buildings with high seismic code provisions subjected to seismic ground shaking with the corresponding curves provided by Kappos et al. (2003;2006) for the




Figure 3.49. Comparison of the harmonized derived fragility curves as a function of Sa for mid-rise regularly infilled RC frame buildings with high seismic code provisions subjected to seismic

ground shaking with the corresponding curves provided by Borzi et al. (2008) for the same building typologies

Figure 3.50. Comparison of the harmonized derived fragility curves as a function of Sa for mid-rise irregularly infilled RC frame buildings (pilotis) with high seismic code provisions subjected to seismic ground shaking with the corresponding curves provided by Kappos et al. (2003) for the




Figure 3.51. Comparison of the harmonized derived fragility curves as a function of Sa for mid-rise irregularly infilled RC frame buildings (pilotis) with high seismic code provisions subjected to

seismic ground shaking with the corresponding curves provided by Borzi et al. (2008) for the same building typologies

3.8.3 Discussion

In general the comparison of the derived fragility curves for the different building

typologies subjected to seismic loading with the literature curves is judged satisfactory.

It should be noted herein that the bare frame buildings, for which seismic fragility

analyses have been already carried out in past studies, a very good agreement between

the literature and the current curves is observed (i.e. Low rise – No code and Kwon and

Elnashai, 2006; High rise – Low code and Kappos et al., 2006; Mid rise – High code and

Kappos et al., 2003 etc.) verifying the reliability of the proposed fragility curves.

It should be noticed that the scatter observed between the proposed and the

literature curves reveal the high aleatory and epistemic uncertainties associated with the

different fragility curves found in the literature. The scatter between the curves

corresponding to the yielding limit state is shown in most cases to be smaller in

comparison to the collapse limit state which can be attributed to the fact that the

structural behavior near collapse is highly nonlinear and depends significantly on the

modeling assumptions and analysis methods that have been adopted in each study. For

example the comparison of the fragility curves of the High rise – Low code bare frame

model with the curves proposed by Tsionis et al. (2011), show a very good match for the

yielding damage state. For the collapse state however significant differences are

observed in the shape of the curves. More specifically the curve of Tsionis et al. (2011)

corresponding to the collapse state results to higher fragility values in comparison to the



corresponding yielding state for intensity levels lower than 0.1g. This can be attributed to

the fact that the structure is characterized as non-ductile expecting potential shear

failures of the vertical structural elements to occur leading thus to brittle failure

mechanisms. In the analyses conducted in the present thesis, the potential of shear

failures is not taken into account in the modeling phase and this is the reason the two

studies present such different fragility curve shape for the collapse state. Furthermore

the variability between the curves corresponding to the two damage states is expected to

be higher for the infilled structures. The modeling techniques adopted for the simulation

of the infill panels and the definition of their material properties may vary significantly

between the different studies affecting thus the vulnerability results.

Finally it should be noted that the simplified typologies that are used for the fragility

analyses in the present thesis as well as the fragility curves proposed in the literature

which are derived analyzing single degrees of freedom systems or simplified two-

dimensional structures, are developed to be used as generalized curves for seismic risk

assessment at regional or urban scale. Thus although the conventional generic fragility

curves are considered appropriate for assessing fragility and losses in a regional/urban

scale, their use may lead to inaccurate fragility and loss estimates in the case of

individual building assessment. This becomes particularly evident through the significant

variability observed between the different sets of derived curves referring to the same

building typology. This issue constitutes a crucial component in the framework of decision

making and risk mitigation strategies (e.g. seismic safety and rehabilitation costs) on a

building-specific scale and will be discussed in more detail in Chapter 6 of the thesis

where field monitoring data are used for the seismic vulnerability assessment of existing

structures.


CHAPTER 4

Time-dependent fragility functions for RC buildings

4.1 Introduction

The aim of the present chapter is the development of time-dependent fragility functions

taking into account deterioration due to aging effects. To demonstrate the methodology

for the time-dependent vulnerability assessment, the seven RC moment resisting frames,

presented previously in Chapter 3, are used as case studies. All seven models are

analyzed assuming fixed base conditions for their un-corroded (t=0 years) and corroded

state (t=25, 50, 75 years). The consideration of aging is achieved by including

probabilistic models of chloride induced corrosion deterioration of the RC elements within

the vulnerability assessment framework presented in detail in previous Chapter 3. Among

the various aging processes, chloride-induced corrosion is considered based on

probabilistic modeling of corrosion initiation time and corrosion rate. Different corrosion

aspects are considered in the analysis including the loss of reinforcement cross-sectional

area, the degradation of concrete cover and the reduction of steel ultimate deformation.

The relative contribution of infill walls on the expected structural performance over time

is also assessed, analyzing both regularly and irregularly infilled (i.e. pilotis) moment

resisting frames and comparing their seismic behavior with the corresponding bare

frames. Part of this research has been published in Bulletin of Earthquake Engineering

scientific journal (Pitilakis et al., 2014b).

4.2 Aging effects: Chloride induced corrosion

The impact of deterioration of the material properties caused by aggressive

environmental attack (such as e.g. corrosion, temperature variations, sulphate attack,

fatigue) is investigated. Among the most common environmental deterioration factors,

reinforcement corrosion, generally associated to carbonation and chloride ingress, is

considered the most significant degradation mechanism, leading to the adverse variation

Chapter 4: Time-dependent fragility functions for RC buildings 128


of the mechanical properties of steel and concrete over time (Saetta et al., 2008). The

deterioration related to the corrosion of reinforcement steel bars in concrete structures is

basically a two-phase process consisting of the initiation and the propagation phase. As

soon as the concentration of chlorides or carbon dioxides exceeds a critical value, the so

called “passive layer” protecting the outer reinforcement is destroyed signifying the

initiation of corrosion. Then the corrosion is gradually propagating causing the formation

of corrosion products (rust), leading progressively to concrete cracking and spalling as

the volume of rust increases and finally resulting to significant structural damage. The

parameters that affect the corrosion initiation and its progress in time may be

categorized based on whether they are associated with the design and execution phase

(e.g. concrete cover depth, water/cement ratio) or with the environmental exposure

(humidity, temperature, carbon dioxide or chlorides concentration) (e.g. Malioka, 2009).

Thus, corrosion may affect a RC structure in a variety of ways, including, among other,

cover spalling, degradation of concrete cover, loss of steel-concrete bond strength and

loss of steel cross-sectional area. In this respect, in case of significant loss of ductility

due to high corrosion levels, a reduction in the load-carrying capacity of the structure, as

well as a shift to more brittle failure mechanisms is expected (e.g. Rodriquez et al.,

1997; Berto et al., 2009; Mohammed et al., 2011; Yalciner et al., 2012). Under these

considerations, a reliable evaluation of the structural performance usually requires to

take into account degradation mechanisms such as rebar corrosion as they may affect

both the safety and serviceability of RC structures, compromising their ability to

withstand the loads they are designed for. When combined with the earthquake loading,

the effects may be even more detrimental. In the present research the corrosion of

reinforcing bars due to the ingress of chlorides is considered, as it is reportedly one of

the most serious and widespread deterioration mechanisms of RC structures. In the

following Sections 4.2.1 and 4.2.2 the chloride induced corrosion model adopted herein is

presented in detail.

4.2.1 Corrosion initiation time

The severe uncertainties involved in corrosion phenomena point out the need for a

probabilistic approach to predict degradation phenomena (DuraCrete, 2000). Recognizing

the importance of this issue, several probabilistic models have recently been introduced

into the time-variant vulnerability assessment of corroded bridges and RC frame

buildings (e.g. Ghosh and Padgett, 2010; Choe et al., 2010; Fotopoulou et al., 2012;

Karapetrou et al., 2013a; Karapetrou et al., 2013b; Karapetrou et al., 2013c; Pitilakis et

al., 2014b). The models have been proposed to quantify and account for corrosion in the

design, construction, fragility analysis and maintenance of RC structures. A summary of



these models can be found e.g. in DuraCrete (1998). The probabilistic model proposed by

FIB-CEB Task Group 5.6 (2006) is adopted herein to model corrosion initiation time due

to chloride ingress that is expressed as:

12 12

1

0 0

14 ,

ncrit

ini nse t RCM

CT erf

Ck k D t

(4.1)

where Tini=corrosion initiation time (years), α=cover depth (mm), Ccrit.=critical chloride

content expressed as a percentage by weight of cement (wt % cement), Cs = the

equilibrium chloride concentration at the concrete surface expressed as a percentage by

weight of cement (wt % cement), t0= reference point of time (years), DRCM,0=Chloride

migration Coefficient (m2/s), ke=environmental function, kt=transfer variable defined

deterministically according to Choe et al. (2008) equal to 0.832, erf=Gaussian error

function and n=aging exponent.

The statistical quantification of the model parameters describing the chloride induced

corrosion adopted for the present study is given in Table 4.1 in accordance with FIB-CEB

Task Group 5.6 (2006) prescriptions and the available literature (e.g. Choe et al., 2009;

Ghosh and Padgett, 2010). An atmospheric exposure environment (e.g. ke=0.67, Choe et

al., 2009) with water-to cement ratio of the concrete material equal to 0.5 is assumed for

the considered chloride induced deterioration scenario. It is noted that the adopted

corrosion rate implies a relatively high corrosion level (Stewart, 2004). The rate of

corrosion is considered to be constant on average along the service life of the structures

(Ghosh and Padgett, 2010).

First Order Second Moment (FOSM) reliability analysis is conducted using Rt software

(Mahsuli and Haukaas, 2013) to assess Tini that varies for the different models under

study, depending on their structural characteristics and more specifically on the cover

depth considered for each case (see Table 4.1). The seven RC moment resisting frames

that are used as case studies are presented in detail in Chapter 3. Based on the applied

probabilistic model, mean values for Tini are estimated as 7.01 and 14.11 years

respectively for the structural models designed with no or low seismic provisions (cover

depth a=20mm, Table 4.1) in the first case and with modern seismic code in the second

one (cover depth a=25mm, Table 4.1).



Table 4.1. Statistical characteristics of parameters affecting the chloride induced corrosion of RC elements adopted in the present study

Parameter Mean Coefficient of variation (cov) Distribution

Cover Depth (mm) α 20/25 0.40/0.32 Lognormal

Environmental function ke 0.67 0.17 Normal

Chloride migration Coefficient (DRCM,0) (m2/s) 1.58E-11 0.20 Normal

Aging exponent n 0.362 cov=0.677 , a=0.0, b=0.98 Beta

Critical Chloride Concentration (Ccrit) wt % cement

0.6 cov=0.25, a= 0.2, b=2.0 Beta

Surface Chloride Concentration (Cs) wt % cement

1.283 0.20 Normal

Rate of Corrosion (icorr) mA/cm2 2 0.25 Normal

4.2.2 Deterioration modeling due to corrosion

The effects of corrosion are assumed to be distributed uniformly around the perimeter

and along the concrete members. Furthermore it should be noted that uniform

parameters are considered for all the structural elements without further distinction

between internal and external environment. Once the protective passive film around the

reinforcement dissolves due to continued chloride ingress, corrosion initiates and the

time-dependent loss of reinforcement cross-sectional area can be expressed as (e.g.

Ghosh and Padgett, 2010):

2

2

4

4

for t( )

for t

i ini

ini

n D TA t

n D t T

(4.2)

where n=number of reinforcement bars, Di=initial diameter of steel reinforcement,

t=elapsed time in years and D(t)=reinforcement diameter at the end of (t – Tini) years,

which can be defined as:

( ) ( )i corr iniD t D i t T (4.3)

where icorr=rate of corrosion (mA/cm2), κ=corrosion penetration (μm/year)

(κ=11.6μm/year uniform corrosion penetration for generalized corrosion, Stewart, 2004).

The effect of loss of reinforcement is more pronounced for smaller diameters, thus higher

steel area losses are expected with decreasing bar diameters (Stewart, 2004).

Due to the radial pressure developed along the steel bar surfaces, caused by the

increasing volume of the corrosion products, the tensile stresses in the concrete

surrounding the rebars may exceed the tensile strength leading thus to the cracking of

the concrete cover. The cracking and spalling of the cover concrete are taken into



account by reducing the concrete cover strength according to the model proposed by

Coronelli and Gambarova (2004) and applied latter in Simioni (2009):

11

* cc

co

ff

K

(4.4)

where K is a coefficient related to bar diameter and roughness (K=0.1 for medium-

diameter ribbed bars), εco is the strain at the peak compressive stress fc, ε1 is the

average tensile strain in the cracked concrete calculated as:

1f o

o

b bb

(4.5)

where bo is the section width in the virgin state before corrosion cracking while bf

corresponds to the increased section width due to corrosion cracking and rust expansion.

An approximation of the width increase is given by:

f o bars crb b n w (4.6)

where nbars is the number of the bars in the layer under compression, wcr is the total

crack width for a given corrosion level:

2 1, ( )cr i corr rsi

w u X (4.7)

where νrs is the ratio of volumetric expansion of the rust products with respect to the

virgin material, X is the depth of the corrosion attack equal to the reduction in bar radius

and ui,corr is the opening of each single corrosion cracks. In the present study νrs is

assumed equal to 2 as proposed in Simioni (2009). The most influential parameters for

the reduction of concrete cover strength are the depth of corrosion attack X, the number

of the reinforcement bars nbars and the section width in its virgin state bo. In particular

higher values of bar radius reduction due to corrosion cracks lead to higher concrete

cover strength reduction, which is also expected with increasing number of reinforced

bars and/or decreasing width of the section. However the latter two parameters have

significantly higher effect on the reduction of concrete cover strength in comparison to

the first one.

Regarding the effects of corrosion on steel mechanical properties the loss of steel

ductility is taken into account through the reduction of steel elongation at maximum load.

Thus, the reduction of the steel ultimate deformation εsu is calculated based on linear

interpolation of the experimental results by Rodriguez and Andrade (2001), where the

reduction reaches values of 30% and 50% for losses of reinforcement cross-sectional

area of 15% and 28% respectively.



The distribution of the loss of reinforcement area as well as the reduction in concrete

cover strength due to corrosion of the RC elements for the considered corrosion scenarios

(t=25, 50 and 75 years) are calculated as a function of the corrosion rate and the

corrosion initiation time variables. Tables 4.2, 4.3 and 4.4 summarize respectively the

mean percentages (%) of reinforcement area loss, cover concrete strength and steel

ultimate deformation reduction due to corrosion within the elapsed time (t-Tini). The

estimated covs vary from 0.05 to 0.10 and from 0.25 to 0.50 for the loss of

reinforcement and cover strength reduction variables respectively. For the purpose of the

present research, the mean values of the corrosion modeling parameters are adopted for

the analysis of the degraded structural models in OpenSees. Overall, for a given

corrosion scenario, beams are shown to be more affected compared to columns since

their reinforcement layout include steel bars of lower diameters. An increase of the initial

fundamental period of the fixed base bare and infilled frame structures (Tables 4.5 and

4.6 respectively) is expected since corrosion effects cause progressive stiffness

degradation as well. The bare frame structural models under study present a percentage

increase in the natural period that varies between 4-14% for the transition from 0 years

to 25 years, 3-8% from 25 to 50 years and 2-5% from 50 to 75 years, depending on the

characteristics of the initial and corroded structures. In the case of regularly distributed

infills the percentage decrease in natural period varies between 63-74% and 65-77% for

the uncorroded (t=0years) and corroded structures (t=50years) respectively depending

on the different structural characteristics. Similarly for the models with pilotis the

percentage decrease in relation to the initial bare frame ones varies between 30-52%

and 30-48% for their uncorroded and corroded state respectively. Finally the increase of

the fundamental period of the infilled models due to corrosion for the 50-year time

scenario is estimated equal to 3-7% and 4-35% for the regularly and irregularly infilled

systems respectively.

Table 4.2. Loss in reinforcement (%) for the considered corrosion scenarios

Steel area loss (%)

t (years)

Structural element

Low rise-No

code

Mid rise -No code

Mid rise -Low code

High rise-Low code

Low rise -High code

Mid rise -high code

(Portuguese)

Mid-rise/High

code (Greek)

25 Beam 5 6 6 6 3 4 4

Column 5 6 5 5 3 4 3

50 Beam 12 14 14 14 11 14 11

Column 11 15 12 11 8 12 9

75 Beam 18 21 22 21 18 23 19

Column 16 23 18 18 14 20 15



Table 4.3. Concrete cover strength reduction (%) for the considered corrosion scenarios

Cover strength reduction (%)

t (years)

Structural element

Low rise-No

code

Mid rise -No code

Mid rise -Low code

High rise-Low

code

Low rise -High code

Mid rise -High code

(Portuguese)

Mid rise-High code

(Greek)

25 Beam 54 58 50 53 33 40 41

Column 40 40 33 33 23 21 28

50 Beam 74 77 70 73 62 69 70

Column 61 61 53 54 50 47 56

75 Beam 82 84 79 81 73 79 80

Column 71 71 64 65 63 60 68 Table 4.4. Steel ultimate deformation reduction (%) for the considered corrosion scenarios

Steel ultimate deformation reduction (%)

t (years)

Low rise-No code

Mid rise-No code

Mid rise – Low code

High rise-Low code

Low rise -High code

Mid rise – High code

(Portuguese)

Mid rise-High code (Greek)

25 9 12 11 10 6 9 6

50 20 27 25 24 20 27 20

75 33 42 39 35 33 41 33

Table 4.5. Fundamental periods of the reference uncorroded (t=0 years) and corroded (t=25, 50,

75 years) bare frame MRF structures

Fundamental Period (sec)

t (years)

Low rise-No

code

Mid rise -No code

Mid rise -Low code

High rise-Low code

Low rise-high code

Mid rise - High code

(Portuguese)

Mid rise- High code (Greek)

0 0.98 0.66 0.58 0.89 0.40 0.48 0.67

25 1.06 0.77 0.62 0.94 0.42 0.50 0.70

50 1.12 0.84 0.64 0.97 0.44 0.53 0.75

75 1.15 0.88 0.66 0.99 0.46 0.55 0.78

Table 4.6. Fundamental periods of the uncorroded (t=0 years) and corroded (t=50 years)

regularly and irregularly infilled MRF structures

RC building Time scenario

Fundamental period

irregularly infilled (pilotis)

Tpil [sec]

Fundamental period

regularly infilled

Tinf [sec]

Low rise – No code 0 0.69 0.25 50 0.78 0.26

High rise – Low code 0 0.48 0.33 50 0.50 0.34

Mid rise – High code (Portuguese) 0 0.23 0.15 50 0.31 0.16



4.3 Pushover analysis

The seismic performance of the intact and the corroded structures is first assessed by

means of a nonlinear static procedure, commonly known as pushover analysis, using

OpenSees software platform. The pushover procedure allows tracing the sequence of

yielding and failure on the member and structure level, as well as the progress of the

overall capacity curve of the structure. The method has been widely used for the seismic

assessment of buildings mainly due to its conceptual simplicity and computational

efficiency with respect to the fully nonlinear dynamic analysis. Although pushover

analysis provides crucial information on response parameters that cannot be obtained

with conventional elastic methods (either static or dynamic), it is not exempt from some

limitations such as the inability to account for the characteristics of earthquake records

and the variation in applied seismic demand with increasing structural degradation as

well as the poor representation of the deformed shape of structures that do not respond

predominantly in the first mode (e.g. Krawinkler and Seneviratna, 1998; Fajfar, 2000).

In this research the derived nonlinear structural models are displaced to a predefined

roof displacement and the resulting internal deformations and forces are determined. As

already described previously, the nonlinear behavior of the beams and columns is

represented using the distributed plasticity concept whereas lumped plasticity approach

is considered for the infill walls. A triangular lateral load pattern with a displacement

control integration scheme is adopted and the intensity of the load is monotonically

increased until either the limit displacement at the control node (located at the highest

floor) is reached or structural collapse is detected. The limit displacement is selected to

represent a very large displacement which forces the structure to reach collapse. The

latter ensures that the full capacity of the structure is developed. Figure 4.1 shows the

derived pushover curves in terms of normalized base shear V/W (base shear V divided by

the total weight W in kN) against peak roof drift ratio θroof for the initial (t=0 years) and

corroded (t= 25, 50 and 75 years) bare frame structures under study whereas Figure 4.2

presents indicatively the capacity curves for the high-rise building with regularly and

irregularly (pilotis) distributed infills for its uncorroded (t=0 years) and corroded (t=50

years) states. Regarding the effects of the infill panels, the comparison of the bare frame

high-rise building with the corresponding (regularly and irregularly) infilled models shows

that the contribution of the infills increases significantly the stiffness of the structure

leading as expected to higher base shear values and smaller yield roof drifts.

Furthermore the maximum roof drift of the infill models is significantly smaller compared

to the bare frame building. This could be attributed to the fact that building collapse

occurs with the masonry infill failure since the applied model for the nonlinear response

of the masonry panels does not capture the post-peak behavior of the infills.



Figure 4.1. Pushover curves for the initial (t=0 years) and corroded (t=25, 50 and 75 years) bare

frame structures



Figure 4.2. Pushover curves for the initial (t=0 years) and corroded (t=50 years) infilled (regularly and infilled) high rise frame structure design with low seismic code provisions

Regarding the effects of aging it can be clearly seen from the figures that the

structures undergo a progressive strength and stiffness degradation as well as a loss of

ductility over time due to corrosion.

4.4 Comparative dynamic analysis

To illustrate the influence of corrosion effects on the seismic performance of the selected

building typologies, a preliminary comparative analysis of the structural models is carried

out at different points in time for a test ground motion. More specifically, dynamic

analyses are conducted using Friuli earthquake record (waveform code 000055xa, see

Table 3.4 of Chapter 3 and ANNEX A) as input motion scaled to a PGA level equal to

0.3g.

The results are presented in terms of displacement response and maximum

interstorey drift ratios maxISD(%). More specifically to investigate the structural

behavior of the considered building (bare frame) typologies under seismic loading for the

adopted time scenarios (t=0, 25, 50, 75 years), the distribution of floor displacements

and storey drifts with the structures’ height is illustrated in Figure 4.3, corresponding to

the time of maximum interstorey drift occurrence (maxISD). Similar graphs are

presented also for the high-rise MRF structure designed with low seismic code provisions

including regularly and irregularly distributed infills in Figure 4.4.

The low-rise building with no seismic code provisions is characterized by a global

sidesway mechanism. The expected performance of this type of no ductile frame

designed only for gravity loads is a soft storey mechanism due to the presents of strong-

stiff beams and weak-flexible columns in terms of both strength and stiffness. Maximum

interstorey drift (maxISD) and the resulting storey mechanisms occur in different floor



levels for the different time scenarios. In particular for the uncorroded structure, maxISD

occurs in the third floor whereas for the 25-, 50- and 75- year scenarios variation of the

sidesway mechanism is observed with the maxISD being detected systematically at the

second floor. Although the maximum interstorey drift is not increasing significantly with

time for the specific analyzed case, it is observed that the maximum roof displacement of

the building increases up to 35% for the transition from 0 years to 75 years.

Regarding the dynamic response of the mid-rise building with no seismic code

provisions, maxISD occurs for all time scenarios in the second floor of the building. The

building is characterized by a sidesway mechanism while soft storeys are identified at the

second and third floors. The roof displacement and masxISD are increasing with time up

to 20% and 28% respectively from the transition from t=0 years to t=75 years.

For the mid-rise MRF with low seismic code provisions, maxISD is located for the

initial and 25-year corrosion scenarios in the first floor of the building whereas for the 50-

and 75- year scenarios maxISD is located in the third floor. An increase of the maxISD

and the roof displacement at the time maxISD occurs is observed with time up to 13%

and 16% respectively for the 75-year corroded building compared to its initial intact

state.

The high-rise building designed with low seismic code provisions is of particular

interest as the effect of higher modes is expected to be pronounced on the seismic

response of the structure. Thus although maxISD occurs for all scenarios in the eighth

floor of the building, a decrease of both maxISD and roof displacement is observed with

time presenting however much more significant contribution of the higher modes. In

particular it is noticed that for the corroded structural states (mainly for t=50 and 75

years) the contribution of the second mode to the response is more pronounced in

relation to the initial uncorroded state of the building influencing the inelastic behavior of

the structure and resulting to the modification of the sidesway mechanism increasing the

displacement demands at the lower strorey levels.

The predicted mechanism for the structures designed according to high seismic code

provisions is a beam hinging pattern according to the design of the frame with capacity

design principle of strong columns and week beams. For the low-rise building designed

based on a high seismic code level, maxISD occurs for all cases in the second floor

presenting a percentage increase up to 41% with time. On the contrary roof

displacement is increasing with time only for the 50-year corroded building in relation to

the intact uncorroded one whereas a decrease of the roof displacement is observed for

the 25- and 75- time scenarios. This may be attributed to the variation of the sidesway

mechanisms that is observed for the latter scenarios, where although roof displacement

decreases, a significant increase in the interstorey drift of the second floor in relation to



the ground floor is observed. The percentage increase of the interstorey drift of the

second floor is estimated up to 69% and 80% in comparison to the first floor for t=25

and t=50 years respectively when this increase is limited to 32% and 26% for the initial

and 50- years corrosion scenario respectively.

As far as the mid-rise building is concerned that is designed with high code level

according to the Portuguese provisions, maxISD occurs for all non- and corroded systems

in the third floor. Although the roof displacement does not increase significantly with time

(2-7%), the increase in the maxISD value is much higher (12-30%) in relation to the

initial uncorroded scenario (t=0 years). On the other hand for the mid-rise building

designed according the Greek seismic code standards (high code level), maxISD is

located for all time scenarios at the first floor of the structure. Roof displacement at the

time maxISD occurs and maximum interstorey drift increase with time 5-8% and 5-20%

respectively for the considered corrosion scenarios in relation to the initial uncorroded

state of the building.

Regarding the contribution of the infills, the dynamic response of the regularly and

irregularly infilled high-rise building with low seismic code provisions is investigated. As it

clearly seen in Figure 4.4 the predicted behavior of both infilled models (fully infilled and

pilotis) constitutes by the formation of a first soft storey mechanism while in the case of

the bare frame model, storey mechanisms were detected at the eighth floor. Lower roof

displacements and maxISD values are developed for both fully infilled structure and the

model with pilotis compared to the bare frame building. Finally an increase of the roof

displacement at the time of maxISD and of the maximum interstorey drift is observed for

the transition from t=0 years and t=50 years due to corrosion.

Based on the above results it is seen that on a global scale, corrosion effects may

result to the reduction of the resistance and load bearing capacity of the structure and to

the variation of the failure mechanisms. It should be noted however that the results

presented herein refer to the specific test ground motion (Friuli 1976, Mw=6.5, R=23 km)

aiming to provide insight on the impact of aging on the variation of the global structural

response in terms of displacement demands. The ground motion characteristics

(frequency content, duration) in relation to the dynamic properties of the buildings may

lead to modifications of the structural response without however affecting the general

conclusions of this part.



Figure 4.3. Snapshots of floor displacements (left) and storey drifts (right) at the time of maxISD occurrence for the different time scenarios (Friuli earthquake 0.3g)



Figure 4.3. (Continued) - Snapshots of floor displacements (left) and storey drifts (right) at the time of maxISD occurrence for the different time scenarios (Friuli earthquake 0.3g)



Figure 4.3. (Continued) - Snapshots of floor displacements (left) and storey drifts (right) at the time of maxISD occurrence for the different time scenarios (Friuli earthquake 0.3g)

Figure 4.4. Snapshots of floor displacements (left) and storey drifts (right) at the time of maxISD occurrence for the different time scenarios (Friuli earthquake 0.3g) for the infilled (regularly and

irregularly) high rise building with low seismic code provisions



4.5 Incremental dynamic analysis

The IDA procedure is used to determine the seismic performance and to assess the time-

dependent seismic vulnerability of the given structures under the influence of aging. IDA

is performed for all structural systems and for all time scenarios according to the

procedure described in detail in Chapter 3. The 15 selected seismic records (Table 3.4 of

Chapter 3 and ANNEX A) are progressively scaled until global dynamic instability of the

structural models is achieved for the considered time periods t=0, 25, 50 and 75 years.

By interpolating the derived pairs of Sa(T1,5%) and maxISD for each individual record 15

continuous IDA curves are derived for each structural model and time scenario. Figures

4.5 and 4.6 present indicative graphs of the derived IDA curves for each record in terms

of Sa(T1,5%) and the corresponding summarized across all records IDA curves at 16%,

50% and 84% fractiles for three representative bare frame structures and for one

representative (regularly and irregularly) infilled building, for their initial state (t=0

years) and for the 50-year corrosion scenario.



Figure 4.5. Indicative IDA curves for the initial (t=0 years) and 50-year corroded structures with no, low and high seismic code provisions



Figure 4.6. Indicative IDA curves for the initial (t=0 years) and 50-year corroded (regularly and irregularly) infilled structures with low seismic code provisions

4.6 Definition of damage states

The definition of the two considered damage states, namely the Immediate Occupancy

(IO) and the Collapse Prevention (CP) states are described in Chapter 3. The first limit

state is defined at 0.5% and 0.1% according to HAZUS prescriptions (NIBS, 2004) for RC

bare and infilled moment resisting frame structures respectively, whereas the second is

assigned on the median (50%-fractile) IDA curve derived in terms of Sa(T1, 5%). Tables

4.7 and 4.8 summarize the time-variant CP limit state values adopted for the bare and

infilled frame structural models respectively. The bare frame structural models under

study present a percentage decrease as expected in the CP limit value that varies

between 0-12 % for the transition from 0 years to 25 years, 4-21% from 25 to 50 years

and 5-18% from 50 to 75 years, depending on the characteristics of the initial and

corroded structures. Similarly for the buildings with regularly and irregularly distributed

infills, the percentage decrease from 0 to 50 years is varying between 10-17% and 2-8%

respectively, depending on the structural typology and characteristics.



Table 4.7. CP limit state maxISD values defined on the IDA curve for the bare frame structures over time

Time scenario (years)

Low rise

MRF-no code

Mid rise MRF-no

code

Mid rise MRF-low

code

High rise MRF-low

code

Low rise

MRF-high code

Mid rise MRF-high code(Portuguese)

Mid rise MRF-high

code (Greek)

0 0.028 0.014 0.013 0.0225 0.049 0.025 0.039

25 0.025 0.014 0.012 0.021 0.046 0.022 0.037

50 0.024 0.011 0.011 0.02 0.043 0.02 0.033

75 0.021 0.009 0.0095 0.017 0.037 0.019 0.03

Table 4.8. CP limit state maxISD values defined on the IDA curve for the infilled buildings for the

initial and 50-year corrosion scenario


Low rise MRF-no code-

regularly infilled

Low rise MRF-no code- pilotis

High rise MRF-low

code- regularly infilled

High rise

MRF-low code- pilotis

Mid rise MRF-high code(Portuguese)- regularly infilled

Mid rise MRF-high code(Portuguese)-

pilotis

0 0.005 0.019 0.005 0.023 0.003 0.03

50 0.0045 0.0175 0.0045 0.0225 0.0025 0.028

4.7 Time-dependent fragility curves

The results of the IDA (Sa(T1,5%)- maxISD) are used to derive time-dependent (or

aging-dependent) fragility curves expressed as the two-parameter time-variant

lognormal distribution function based on the Equation 3.6 described in Chapter 3, Section

3.7:

ln ln/

IM IM tP DS IM

t

(4.8)

where the median values (in units of g) IM t and log-standard deviations β(t) of the

fragility functions are the time-varying parameters which are defined at different points

in time along the buildings’ lifetime.

The median values of Sa(T1,5%) corresponding to the prescribed performance levels

are determined based on a regression analysis of the nonlinear IDA results (Sa(T1,5%) –

maxISD) for each structural model and time scenario. A linear regression fit of the

logarithms of the Sa(T1,5%) - maxISD data which minimizes the regression residuals is

adopted in all analysis cases. Figure 4.7 presents representative Sa(T1, 5%) - maxISD

relationships (in log-log scale) for the bare frame high rise, low-code designed structure

for the initial (t=0 years) and corroded scenarios (t=25, 50 and 75 years). Similar plots



in terms of Sa(T1, 5%) - maxISD are also shown in Figure 4.8 for the same structural

typology including regularly and irregularly distributed infills, for the initial and 50-year

corrosion scenarios.


parameter β(t), which describes the total dispersion related to each fragility curve and is

defined according to Section 3.7 of Chapter 3.

Figure 4.7. Sa(T1, 5%) – maxISD relationships for the bare frame high rise structure designed with low seismic code provisions for the initial (t=0 years) and corroded (t= 25, 50 and 75 years)

scenario



Figure 4.8. Sa(T1, 5%) – maxISD relationships for the regularly and irregularly infilled high rise structure designed with low seismic code provisions for the initial (t=0 years) and corroded (t=

50 years) scenario

4.7.1 Fixed base bare frame structures

Table 4.9 presents the lognormal distributed fragility parameters (median and log-

standard deviation) in terms of Sa(T1,5%) for the initial (t=0 years) and corroded (t=25,

50 and 75 years) bare frame buildings whereas Figure 4.9 illustrates the corresponding

graphs of fragility curves. In Figures 4.10 to 4.16 a 3D illustration of the fragility

estimates over time (fragility surface) is also shown in order to obtain a better view of

the evolution of vulnerability with time.



As it can be seen, the vulnerability of the structures increases over time due to

corrosion. This increase is generally more noticeable for the CP limit state. In particular,

the change in the median Sa(T1,5%) value for the IO and CP limit states after 75 years is

in the order of 20% and 40% respectively for most of the analyzed structures. The

greater and lower increase in fragility is expected for the mid rise - no code structure and

for the mid rise - high code structure designed with the modern seismic code of Greece

respectively. The scatter in the time-dependent medians of the fragility functions could

be probably attributed to the different structural typologies and code design criteria

adopted as well as to the different corrosion initiation time calculated for the no/low and

high code structures.

Table 4.9. Time-dependent fragility parameters in terms of Sa(T1, 5%) for the fixed base, bare

frame structures

RC building Time scenario (years)

Median Sa(T1,5%) (g) Dispersion β(t)

IO CP

Low rise MRF-no code

0 0.08 0.56 0.62 25 0.07 0.41 0.59 50 0.07 0.39 0.59 75 0.06 0.33 0.6

Mid rise MRF-no code

0 0.15 0.43 0.62 25 0.12 0.33 0.63 50 0.10 0.23 0.60 75 0.10 0.19 0.59

Mid rise MRF-low code

0 0.27 0.77 0.6 25 0.25 0.67 0.62 50 0.24 0.57 0.62 75 0.22 0.45 0.61

High rise MRF-low code

0 0.13 0.64 0.57 25 0.12 0.53 0.58 50 0.11 0.48 0.58 75 0.11 0.39 0.59

Low rise MRF-high code

0 0.26 3.92 0.61 25 0.24 3.27 0.64 50 0.2 2.68 0.62 75 0.2 2.18 0.64

Mid rise MRF-high code (Portuguese)

0 0.27 1.31 0.72 25 0.25 1.13 0.69 50 0.24 0.96 0.64 75 0.24 0.90 0.66


0 0.2 1.73 0.67 25 0.18 1.56 0.66 50 0.15 1.24 0.69 75 0.14 1.14 0.67



Figure 4.9. Time-dependent fragility curves in terms of Sa(T1, 5%) for the analyzed fixed base, bare frame structures



Figure 4.10. Fragility surfaces as a function of time and Sa(T1, 5%) for the Immediate Occupancy

(left) and Collapse Prevention (right) damage states (fit: Linear Interpolant) for the bare frame low- rise building designed with no seismic code provisions


(left) and Collapse Prevention (right) damage states (fit: Linear Interpolant) for the bare frame mid- rise building designed with no seismic code provisions


(left) and Collapse Prevention (right) damage states (fit: Linear Interpolant) for the bare frame mid- rise building designed with low seismic code provisions




(left) and Collapse Prevention (right) damage states (fit: Linear Interpolant) for the bare frame high- rise building designed with low seismic code provisions


(left) and Collapse Prevention (right) damage states (fit: Linear Interpolant) for the bare frame low- rise building designed with high seismic code provisions


(left) and Collapse Prevention (right) damage states (fit: Linear Interpolant) for the bare frame mid- rise building designed with high seismic code provisions (Greek)




(left) and Collapse Prevention (right) damage states (fit: Linear Interpolant) for the bare frame mid- rise building designed with high seismic code provisions (Portuguese)

4.7.2 Fixed base infilled frame structures

Table 4.10 summarizes the estimated fragility parameters for the different damage states

(e.g. IO, CP) as a function of Sa(T1,5%) for all the considered structural typologies and

time scenarios. Figure 4.17 presents comparative plots of fragility curves derived in

terms of Sa(T1,5%) for three representative bare, regularly infilled and irregularly infilled

(pilotis) frames for the initial and 50-year corrosion scenario. It is seen that the

seismically designed bare frames are more vulnerable for both damage states compared

to the infilled ones as the presence of the infill walls significantly increases the strength

and stiffness of the structures. In particular, the regularly infilled buildings present lower

vulnerability values with respect to the ones with a pilotis. Thus, as expected, the

presence of the soft ground storey has a less favorable effect on the overall capacity of

the structures due to the localization of inelastic displacement demand at the bottom

bare storey. This observation is generally consistent with previous studies (e.g. Kappos

et al., 2003; 2006; D'Ayala et al., 2012) enforcing the validity of our results. On the

other hand, as far as the low-rise building designed only for gravity loads is concerned,

the irregularly infilled frame sustains the greatest damage following by the corresponding

bare frame whereas the fully infilled frame shows the lower vulnerability values. The

above observations are generally noticeable for the different analyzed time scenarios (0

and 50 years).



Figure 4.17. Time-dependent fragility curves in terms of Sa(T1, 5%) for the analyzed regularly infilled, irregularly infilled (pilotis) and bare frame structures



Table 4.10. Time-dependent fragility parameters in terms of Sa(T1, 5%) for the bare, regularly infilled and irregularly infilled (pilotis) frame buildings

RC building Structural typology


Median Sa(T1, 5%) (g) Dispersion β(t)

IO CP


Bare frame 0 0.08 0.56 0.62 50 0.07 0.39 0.59

Regularly infilled 0 0.16 1.42 0.61 50 0.13 1.39 0.72

Pilotis 0 0.06 0.51 0.63 50 0.04 0.37 0.63

High rise MRF-low

code

Bare frame 0 0.13 0.64 0.57 50 0.11 0.48 0.58


Pilotis 0 0.15 1.43 0.73 50 0.14 1.29 0.70

Mid rise MRF-high

code (Portuguese)

Bare frame 0 0.27 1.31 0.72 50 0.24 0.96 0.64


Pilotis 0 0.3 1.65 0.77 50 0.28 1.51 0.76

4.8 Time-variant quadratic model for the fragility parameters

To continuously evaluate and predict the seismic vulnerability of the structures with time,

fragility parameters at different points in time along their service life are required.

Analytical functions representing time-dependent fragility models constitute an efficient

tool for estimating the fragility parameters at any point in time for the given structural

typology and corrosion parameters without the need to conduct complete fragility

analysis. Based on Gosh and Padgett (2010) a quadratic model of the form

parameter(t)=p1t2+p2t+p3, is found to best fit the time-dependent variation in fragility

parameters, where parameter(t) is either the median m(t) or dispersion β(t) at t years

and p1, p2, p3 the quadratic coefficients from regression analysis. Figure 4.18 shows the

quadratic coefficients estimated for the time-dependent median of the bare frame

structures corresponding to the Collapse Prevention (CP) damage state. Table 4.11

summarizes the coefficients of the quadratic equations for the fragility parameters for the

two defined damage states and for the different structural typologies considered. These

coefficients can be then used in Equation 4.8 to evaluate the building fragilities at any

point in time as:

2

1 2 3

21 2 3

_ _ _

_ _ _

ln ln/ m m mIM p t p t p

P DS IM tp t p t p

(4.9)

where the subscripts on the coefficients indicate median m or dispersion β.



Figure 4.18. Time-dependent quadratic fit of median Sa(T1, 5%) values for the Collapse

Prevention (CP) state for the bare frame structures



Figure 4.18. (Continued) - Time-dependent quadratic fit of median Sa(T1, 5%) values for the

Collapse Prevention (CP) state for the bare frame structures

Table 4.11. Coefficients of quadratic interpolation for the median IO and CP limit values and the corresponding dispersion (in terms of log-standard deviation)

RC MRF Quadratic coefficients Median IO Median CP Dispersion

Low-rise No code p1mIO p2mIO p3mIO p1mCP p2mCP p3mCP p1β p2β p3β

Mid-rise No code 2e-06 0.00 0.08 3e-05 -0.005 0.547 2e-05 -0.001 0.619

Mid-rise Low code 1e-05 -0.001 0.148 2e-05 -0.004 0.429 -0.005 0.023 0.597

High-rise Low code -1e-06 0.0 0.271 -6e-06 -0.003 0.764 -0.008 0.061 0.512

Low-rise High code 5e-06 0.0 0.133 8e-06 -0.003 0.637 0.002 -0.010 0.585

Mid-rise High code (Greek)

2e-06 -0.001 0.199 3e-05 -0.010 1.749 -0.001 0.017 0.634

Mid-rise High code

(Portuguese) 8e-06 -0.001 0.262 7e-05 -0.028 3.931 -0.004 0.040 0.550



4.9 Discussion and concluding remarks

The seismic vulnerability of RC frame buildings has been assessed taking into

account the aging of RC buildings due to rebar corrosion. Three main aspects for

corrosion have been included in the analysis namely the loss of reinforcement cross-

sectional area, the degradation of concrete cover and the reduction of steel ultimate

deformation. Seven MRF structures corresponding to different code design levels and

described according to the SYNER-G taxonomy, have been analyzed for four time periods

(t=0, 25, 50 and 75 years) by employing 2D incremental dynamic analysis (IDA). The

relative contribution of infill walls on the seismic performance and fragility of selected

representative buildings is also assessed. Both regularly infilled and irregularly infilled

(pilotis) frames are analyzed for the initial and 50-year corrosion scenario.

Time-dependent probabilistic fragility functions have been derived for the IO and CP

limit states and different periods in time in terms of Sa(T1,5%). A significant increase in

the seismic fragility of the structures is observed over time due to corrosion, highlighting

the importance of considering the deterioration effects due to aging on the seismic

vulnerability of structures. It should be stressed however that the results have been

produced under the assumption of uniform corrosion effects for all structural elements

(external and internal) adopting external environmental conditions. The potential of

pitting corrosion or the consideration of a different corrosion scenario for the internal and

external structural elements was not investigated in the context of the present thesis.

The consideration of regularly infilled walls is shown to yield a substantial decrease in

fragility of the initial as-built and corroded bare frame structures. However, the

irregularly infilled frames may have either a favorable or detrimental effect in fragility of

the reference bare frames depending on the structural typology and code design level

(e.g. seismically or non-seismically designed frames).

By exploiting the available fragility data of the bare frame buildings at different points

in time, simple quadratic functions are introduced for the efficient assessment of the

time-dependent shift in the fragility parameters (median and dispersion) for each

damage state due to corrosion. The advantage of such time-dependent models is that the

fragility parameters can be estimated at any point in time without conducting complete

fragility analyses.

Overall, the present research provides a further insight on the seismic vulnerability of

typical RC frame buildings by proposing time (or aging)-dependent fragility functions

applicable to a variety of RC typologies exposed to aging. Validation of the suggested

time-dependent fragility curves with field post earthquake surveys and adequate field

experiments and large scale laboratory tests in prototype structures or building



components is certainly warranted to enhance their reliability and robustness and finally

to ensure their efficient implementation in seismic vulnerability assessment studies.


CHAPTER 5

Seismic vulnerability assessment of RC buildings considering soil-structure

interaction effects

5.1 Introduction

Besides aging the influence of soil conditions and soil-structure interaction (SSI) might

also contribute to the building’s seismic fragility. Although there are some studies that

take into account the local site effects by providing fragility curves for buildings for

different soil conditions, the effect of SSI to the expected structure’s performance has

not received much attention. This may be due to the fact that the incorporation of SSI

phenomena in the analysis is generally considered beneficial reducing the seismic

demand and consequently the corresponding structural damage of non-linear systems

(Ciampoli and Pinto, 1995). Nevertheless, it has been shown that soil deformability and

SSI may modify the structural response and fragility leading to either beneficial or

detrimental effects depending on the dynamic properties of the soil and the structure as

well as the characteristics (frequency content, amplitude, significant duration) of the

input motion (e.g. Dutta et al., 2004; Saez et al., 2011).

The objective of the research presented in Chapter 5 is to study whether soil structure

interaction and site effects may affect the seismic performance and vulnerability of

reinforced concrete moment resisting frame buildings and consequently modify the

fragility curves. SSI is modeled applying the direct one-step approach considering either

linear elastic or nonlinear soil behavior while site effects are inherently accounted for. To

further examine the contribution of site and SSI effects, a two-step uncoupled approach

is also applied, which takes into account site effects on the response of the fixed base

structures, but neglects SSI effects. Additional analyses are performed investigating the

influence of the soil depth and stratigraphy under nonlinear soil behavior on the seismic

response and fragility of RC buildings. Finally time-dependent fragility functions are

derived of the RC buildings considering both SSI and aging effects. The chloride induced

Chapter 5: Seismic vulnerability assessment of RC buildings considering SSI effects 160


corrosion model presented in Chapter 4 is adopted considering two time-scenarios (t=0

and 50 years). Fragility curves are derived as a function of rock outcropping peak ground

acceleration for the Immediate Occupancy and Collapse Prevention limit states for the

fixed base and SSI models based on the methodology described in detail in Chapter 3.

Results show the significant role of SSI and site effects under linear or nonlinear soil

behavior in altering the expected structural performance and fragility of fixed base

structures. Moreover an overall increase in seismic vulnerability over time due to

corrosion is observed highlighting the important influence of deterioration due to aging

effects on the structural behavior. The research presented in this chapter has been

published in Bulletin of Earthquake Engineering (Pitilakis et al., 2014b) and Soil

Dynamics and Earthquake Engineering (Karapetrou et al., 2015) scientific journals.

5.2 Description of the parametric investigation

5.2.1 Selection of prototype buildings

In this study SSI is considered for three representative bare frames designed according

to different seismic code levels and height classes. More specifically the low rise - no

code (Bracci et al., 1992), the high rise - low code (Kappos et al., 2006) and the mid rise

- high code (Greek) (Kappos et al., 2006) buildings, which are described in detail in

Chapter 3, are adopted as reference structures. The selected fixed base reference

structures are presented in Figure 5.1. The numerical modeling of the nonlinear

structural models is conducted in OpenSees (Mazzoni et al., 2009) as described in

Chapter 3.



Figure 5.1. Reference MRF models used for the seismic vulnerability assessment considering soil-

structure interaction: (a) Low rise-no code, (b) High rise-low code, (c) Mid rise-high code

5.2.2 Soil-structure interaction (SSI) modeling

The consideration of SSI is usually achieved by taking into account inertial and kinematic

interaction schemes resulting to an elongation of the natural period of the SSI system

and an increase of system damping due to the energy dissipation at the soil-foundation

level (Veletsos and Meek, 1974). The general assumption that the structure is fixed to its

base ignoring the presence of the soil beneath its foundation may be realistic (or at least

conservative) when the structure is founded on rock or very stiff soil. However, in the

case of softer soil formations, SSI and local site effects may play an important role

modifying considerably the free field input motion as well as the dynamic characteristics

of the building and finally its response (Stewart et al., 1999).

The dynamic analyses of the fixed base and SSI configurations are conducted using

OpenSees software. Figure 5.2 illustrates a general schematic view of the reference

structural models in the case of fixed base and SSI configurations. The soil is modeled in

two-dimensions with two degrees-of-freedom using the plane strain formulation of

the quad element. To account for the finite rigidity of the underlying half-space, a

Lysmer-Kuhlemeyer (Lysmer and Kuhlemeyer, 1969) dashpot is incorporated at the base

of the soil profile. The soil profile is excited at the base by a horizontal force time history,

which is proportional to the known velocity time history of the ground motion (Joyner



and Chen, 1975; Lysmer, 1978). It is noted that due to the consideration of an elastic

half-space it was possible to directly apply the outcropping rock motion at the base of the

soil model (Kwok et al., 2007). A sensitivity analysis is conducted to identify the

appropriate dimensions of the considered soil grid so as to assure free field and “quasi

transparent” conditions at the boundaries. Thus, the grid adopted for the low and mid-

rise structures has a total length of 120m with a depth of 30m that includes

approximately 3600 four-node quadrilateral elements, whereas for the high rise model

the total length and the number of quadrilateral elements increase to 220m and 6600

respectively. The geometry of the mesh is based upon the concept of resolving the

propagation of the shear waves at or below a particular frequency allowing an adequate

number of elements to fit within the wavelength of the chosen shear wave. This ensures

that the mesh is refined enough to capture satisfactorily the propagating waves.

Considering that the maximum frequency of interest is set to 10Hz a relatively dense

discretization is adopted with quadratic elements of 1.0m x 1.0m.

(a)

Outcrop

Elastic bedrock

Fixed base modelSSI-FE model

Free field

Soil profile Vs0,30

(b)

Input Motion

Rigid beam-column element

Free Field

Lysmer-Kuhlemeyer (1969)dashpot

120.0m

30

.0m

Elastic Bedrock

Vso,30

Figure 5.2. Description of the fixed base and soil-structure models under study



Even though soil material nonlinearity can be incorporated in the direct approach, first

an elastic soil profile is considered with an average shear wave velocity Vs,30 equal to

200m/sec corresponding to ground type C of the Eurocode 8 soil classification system. A

very soft soil has been specifically selected in order to amplify the effects of the SSI.

Moreover, to gain further insight into the influence of SSI and site effects on the seismic

fragility analysis, the SSI effect considering soil nonlinearity is investigated for the high-

rise building designed with low seismic code provisions, for which SSI effects are

expected to be much more pronounced in comparison to the rest of the adopted

structures. The soil constitutive model utilized in OpenSees is described in the following

subsection.

Viscous damping is employed in the frequency-dependent Rayleigh form (Rayleigh

and Lindsay, 1945). Although, the damping of the soil materials is normally of hysteretic

type and frequency independent, this damping form facilitates the dynamic analysis, as

the damping matrix is built as a linear combination of the mass and stiffness matrices

(Chopra, 2001):

C a M K (5.1)

where α is the mass proportional damping constant, and β is the stiffness proportional

damping constant. Figure 5.3 illustrates schematically the damping as a function of the

frequency corresponding to the adopted soil profile. The selection of the frequencies f1

and f2 (ω1 and ω2) is made, in order the resulting damping curve to simulate an almost

constant damping at the frequency range of interest. In particular the frequency range of

interest is defined based on the predominant frequencies of the soil deposit, f1 and f2=5f1

Hz (e.g. Kwok et al., 2007). This range includes the model’s natural frequencies and the

predominant frequencies of the input motions. Assuming constant frequency for both

modes ξ, the damping parameters are finally given by the following expressions:

1 2

1 2 1 2

12 , 2

(5.2)

where ω1 and ω2 are the natural (cyclic) frequencies of the modes. A small amount of

mass and stiffness proportional Rayleigh damping (ξ=5% for the soil material) is

assigned to account for energy dissipation during seismic loading for the linear soil profile

cases.

The elastic bedrock (Vs,bedrock=900m/sec) lies at 30m beneath the ground surface. The

Lysmer-Kuhlemeyer (Lysmer and Kuhlemeyer, 1969) dashpot is defined based on the

viscous uniaxial material model and the ‘zeroLength’ element formulation at the same

location, to connect the two previously defined dashpot nodes. This material model

requires a single input, the dashpot coefficient c that is defined according to Joyner and



Chen (1975) as the product of the mass density and shear wave velocity of the

underlying bedrock including also the base area of the soil profile in order to maintain

proportional results for any horizontal element size. The nodes at the lateral boundaries

corresponding to each depth level are tied together in order to achieve a simple shear

deformation pattern of the soil profile. Full contact between the soil and structures’ nodes

is assumed forbidding thus any relative movement between the structure and the soil

(i.e. no detachment or sliding are allowed). The connection of the soil with the structure

is achieved by applying common nodes and appropriate constrains (to ensure equal

displacement) for both the soil and the structure’s foundation. A continuous raft

foundation is considered modeled as an elastic beam-column element of infinite rigidity.

Rigid foundation was considered for sake of simplicity. In case of flexible or isolated

footings As expected, the consideration of SSI causes an elongation of the fundamental

period of the soil-structure models compared to the corresponding fixed based cases

leading to a much more flexible system. More specifically, the low-strain fundamental

period of the SSI systems increases for the low-rise, no code structure from 0.98s, which

corresponds to the fundamental period of the fixed base model presented in Chapter 3,

to 1.28s, for the high-rise, low code model from 0.89s to 1.46s and for the mid-rise, high

code building from 0.66s to 0.91s. Table 5.1 summarizes the parameters of the soil

material properties adopted. Figures 5.4, 5.5 and 5.6 illustrate contour plots of the

vertical displacements and stress distribution developed at the soil profile after the static

analysis of the soil-structure systems. The contour plots are derived using the GiD post-

processor tool (CIMNE, 2013)

Figure 5.3. Rayleigh proportional damping curves for the linear soil profile



Table 5.1. Summary of parameters adopted for the linear soil profile case

Parameter Description Value adopted

Vs,30 of the soil deposit (m/sec) Shear wave velocity 200 Vs,b of the bedrock (m/sec) Shear wave velocity 900

ρo,s (Mg/m3) Mass density of the soil 1.8 ρo,b (Mg/m3) Mass density of the bedrock 2.2

G (kPa) Shear Modulus 72000 nu Poisson’s ratio of soil 0.3

E (kPa) Soil Elasticity Modulus 187200

Figure 5.4. Vertical displacement and stress distribution after the static analysis of the soil-structure system for the linear soil profile case and the Low rise – No code MRF model

Figure 5.5. Vertical displacement and stress distribution after the static analysis of the soil-structure system for the linear soil profile case and the High rise – Low code MRF model



Figure 5.6. Vertical displacement and stress distribution after the static analysis of the soil-structure system for the linear soil profile case and the Mid rise – High code MRF model

5.2.2.1. Soil constitutive model

For the high-rise non-ductile frame structure, where SSI effects are expected to be much

more pronounced, soil-structure interaction is investigated for both linear elastic and

nonlinear soil behavior. For the simulation of the nonlinear soil behavior, the soil profile is

considered as a homogenous cohesive medium with an average shear wave velocity Vs,ave

and an undrained shear strength Cu. For the nonlinear soil profile Vs,ave is considered

equal to 300m/sec in order to reach approximately the same levels of the corresponding

shear wave velocity for the linear soil profile (Vs=200m/sec) at the end of the time-

history analysis and allow for direct comparison. To achieve this preliminary iterative

nonlinear dynamic analyses of the systems were performed considering the records

scaled at a PGA level equal to 0.3g. Soil nonlinearity is described based on an advanced

constitutive model, which follows the concept of multi-yield surface (nested-surface)

plasticity (Iwan, 1967; Prevost, 1985; Mroz, 1967; Yang, 2000) where each yield

surface is defined in the deviatoric stress space as (Elgamal, 1992; Gu et al., 2009):

1

230

2:f K

(5.3)

where τ= the deviatoric stress tensor; α= the back-stress tensor referring to the center

of the yield surface f=0 and K= the size of the yield surface defining the region of

constant plastic shear modulus. For non-pressure sensitive cohesive soil material the

yield surfaces are of the Von Mises type.

The nonlinear shear stress-strain response of the soil is described by the hyperbolic

backbone curve (Gu et al., 2009) as:



1

r

G

(5.4)

where τ= the octahedral shear stress; γ= the octahedral shear strain; G= the low-strain

shear modulus and γr= a reference shear strain defined as:

max max

max maxr G

(5.5)

where τmax is the shear strength corresponding to the shear strain γmax.

Within the multi-surface plasticity framework the yield surfaces define regions of

constant shear moduli in the stress space and are utilized to represent the hyperbolic

backbone curve through a piecewise linear representation. As depicted in Figure 5.7 each

linear segment represents the domain of a yield surface fm with shear modulus Hm for

m=1,2,...NYS with NYS denoting the total number of yield surfaces (Stewart et al.,

2008). The outermost yield surface fNYS, which corresponds to the peak shear strength

τmax, represents the failure surface and corresponds to zero shear modulus HNYS.

The yield surface, the hardening law and the flow rule constitute the key components

of the applied pressure-independent multi yield surface incremental plasticity model

(Kramer and Elgamal, 2001; Parra, 1996; Yang and Elgamal, 2008). During the static

analysis phase the material behavior is linear elastic. In the subsequent dynamic (fast

rate) loading phase, the stress-strain response is turned to elastic-plastic following the

multi-surface plasticity concept, with Von Mises yield surfaces, an associative flow rule

and a kinematic hardening law (Prevost, 1985) employed to capture the Masing

hysteretic cyclic response behavior (Masing, 1926).

τ

γ

τmax

1

fmfNYS f1 γm γmax

Deviatoric plane

Hyperbolic backbone curve

Hm/2τm

Figure 5.7. Hyperbolic backbone curve for soil nonlinear shear stress-strain response and

piecewise-linear representation in multi-surface plasticity (after Prevost, 1985; Stewart et al., 2008; Parra, 1996)



A user-defined backbone curve is defined where the parameters controlling the shear

behavior of the constitutive model are calibrated to yield the shear modulus reduction

curve provided by Darendeli (2001) for clay soil with plasticity index PI=30 and

atmospheric pressure p’0 = 1 atm, which is presented in Figure 5.8. The backbone curve

is appropriately adjusted to render the undrained shear strength Cu using the following

equation (Yang and Elgamal, 2008):

3

2m

uC

(5.6)

where σm is the product of the last modulus and strain pair in the defined modulus

reduction curve. Since the model considers elastoplastic soil behavior, a considerable

amount of hysteretic energy dissipation is represented by the multi-yield function

considering that extensive plastic deformation is expected to occur during ground

shaking. A small amount of mass and stiffness proportional Rayleigh damping ξ=1.2%

(α=0.314, β=0.000255) is assigned to account for the energy dissipation during the

elastic part of the cyclic response, which corresponds to the small-strain damping ratio

defined based on the damping ratio curve for clay soil proposed by Darendeli (2001) with

plasticity index PI=30 and atmospheric pressure p’0 = 1 atm. The parameters of the soil

material properties adopted are summarized in Table 5.2.

Figure 5.8. Shear modulus reduction curve by Darendeli, 2001 for clay soil with plasticity index PI=30 and atmospheric pressure p’0 = 1 atm, utilized for the calibration of the soil constitutive

model in OpenSees



Table 5.2. Summary of parameters adopted for the pressure independent multi-yield plasticity model

Parameter Description Value adopted/Data sources

Vs,ave (m/sec) Low-strain shear wave velocity 300 ρo (Mg/m3) Mass density 1.8

p'r (atm) Reference pressure 1.0

d Pressure dependent coefficient 0.0 Gr (kPa) Shear Modulus at p'

r 162000 nu Poisson’s ratio of soil 0.3

E (kPa) Soil Elasticity Modulus 421200 Br (kPa) Bulk Modulus at p'

r 351000 φ Friction angle 0.0

Cu (kPa) Undrained shear strength 110.0

G/Gmax or γmax Modulus reduction curve or shear strain at failure

Darendeli (2001) for clay soil with plasticity index PI=30 and atmospheric

pressure p’0 = 1 atm

5.2.3 Parametric study

The three representative MRF buildings which are selected for the investigation of the SSI

and site effects in their seismic vulnerability are analyzed considering at first linear soil

behavior. The applied modeling approaches in the case of fixed base and SSI

configurations are schematically described in Figure 5.2. The fixed base models are

assumed to be founded on rock and are analyzed by imposing outcropping bedrock input

motions. On the other hand SSI is modeled applying the direct method based on the

one-step approach where the entire soil-foundation-structure system is analyzed in a

single step. For the high-rise non-ductile RC frame structure, for which SSI effects are

expected to be much more pronounced, further sensitivity analyses are conducted to

investigate on an extensive basis the influence of SSI and site effects considering soil

nonlinearity, which are described in the following subsections.

5.2.3.1. Effect of SSI and site effects under nonlinear soil behavior

Figure 5.9 represents schematically for the high-rise, non-ductile structure the applied

modeling approaches. A first series of analyses is conducted for the fixed base structure

founded on rock by imposing outcropping bedrock input motions. The influence of SSI

and site effects on the seismic response and fragility of the building is investigated for

both linear elastic and nonlinear soil behavior considering a depth for the finite element

model of Figure 5.10 equal to H=30m. Additionally, a two-step uncoupled approach is

also applied using OpenSees in which a 1D seismic response analysis of the given (elastic

or inelastic) soil profile is first performed and then the obtained free field motion is

imposed as input ground motion to the fixed base structural model. It is noted that the

1D soil profile is composed of four-node quadrilateral elements using the same vertical

discretization as the one used for complete 2D SSI model. This approach takes into



account site effects including (or not) soil nonlinearity, but neglects SSI effects. Thus, it

allows gaining further insight into the relative contribution of site and SSI effects in

fragility analysis.

Fixed base model

Outcrop

Elastic bedrock

SSI-FE model

Free field

Elastic or inelastic soil profile

Two-step modelingapproach

Figure 5.9. Schematic view of the modeling approaches to assess the influence of SSI and site effects under linear elastic or inelastic soil behavior for the high-rise, non ductile MRF structure

Input Motion

Rigid beam‐column element

Free Field

Elastic Bedrock

Vs,ave

Lysmer‐Kuhlemeyer (1969) dashpot

Figure 5.10. Finite element model of the soil-structure systems in OpenSees in the case of the high-

rise, non ductile MRF structure

5.2.3.2. Effect of soil depth and stratigraphy under nonlinear soil behavior

To further examine the importance of site effects and inelastic SSI on the seismic

performance and vulnerability of RC buildings, additional analyses are performed

investigating the influence of the soil depth and stratigraphy under nonlinear soil

behavior. Figure 5.11 presents schematically the analyzed cases. To study the effect of

soil stratigraphy an additional layered soil medium is considered where the low-strain

shear wave velocity of the profile increases with depth H. More specifically, the adopted

soil profile consists of three layers with an average low-strain shear wave velocity Vs,ave

equal to 300m/sec to allow for direct comparison with the homogeneous nonlinear soil



medium considered previously. The average value Vs,ave is computed based on the shear

wave velocity and thickness of each layer as:

31 2

1 2 3

,s avei

si s s s

H HVH HH HV V V V

(5.7)

where Vs1, Vs2, Vs3 and H1, H2, H3 are the shear wave velocities and thicknesses of the

surface, intermediate and bottom layers respectively.

Furthermore to study the effect of the soil depth H in the fragility analysis, the

inelastic soil-structure systems for both homogeneous and layered soil profiles are

analyzed for varying soil depth. In particular, two soil profiles are considered, the H=30m

profile which corresponds to the shallow soil medium with fundamental elastic period

equal to TH=30=0.4sec and a deeper one where the depth and fundamental period

increase to H=60m and TH=60=0.8sec respectively.

Vs,ave=300m/sec H=30m,60m

Bedrock (a)

Vs1=250m/sec

Vs2=290m/sec

Vs3=350m/sec

H1=H/6

H2=H/2

H3=H/3

Bedrock (b)

Figure 5.11. Schematic representation of the analyzed cases for the investigation of the effect of (a) soil depth and (b) stratigraphy under nonlinear soil behavior

5.3 Comparative dynamic analysis

To illustrate the relative influence of SSI and site effects on the seismic response under

linear or nonlinear soil behavior of the structural typologies under study, a preliminary

comparative dynamic analysis is carried out for the different considered modeling

approaches (i.e. SSI coupled and fixed base-site effects analysis cases considering or not

soil nonlinearity) for a test ground motion. More specifically, dynamic analyses are

conducted using Friuli earthquake record (waveform code 000055xa, see Table 3.4 of

Chapter 3 and ANNEX A) as input motion scaled to a PGA level equal to 0.3g. At this level

of shaking the soil is normally expected to exhibit yielding and nonlinear cyclic

deformations. The analyzed nonlinear models can accommodate these effects, which

however cannot be captured by the corresponding linear elastic models. The results are



presented in terms of acceleration time histories at the base of the structure at first for

the soil-structure systems for which only linear soil behavior is considered in comparison

with the reference free field outcropping motion directly imposed to the fixed base

structure founded on rock. The arias intensity (Ia) values for each case are also shown.

Furthermore the distribution of floor displacements and storey drifts along the structures’

height are also presented which correspond to the time of maximum interstorey drift

occurrence maxISD. It should be noted herein that for the SSI configurations, only the

deformation component that causes structural distortion is considered. Thus, the

horizontal displacement and the rocking motion of the foundation are not included in the

presented results as the particular components may not contribute to the structural

distortion.

Figures 5.12 and 5.14 show that the amplitude, in acceleration terms, is amplified

with respect to the free field outcropping motion for the soil-structure systems, which

consider linear elastic soil behavior for both the low-rise, no code and the mid-rise, high-

code MRF structures. Figures 5.13 and 5.15 show that for both soil-structure systems

considering linear soil behavior, maxISD values are higher in comparison to the

corresponding fixed base models. The systems are characterized by a global plastic

sidesway mechanism and the maximum interstorey drift occurs in the same storey where

the corresponding fixed base models presented their maximum values. More specifically

for the low-rise, no-code building, maxISD is located in the third floor (top floor) whereas

for the mid-rise, high-code MRF, maxISD occurs in the ground floor.

Figure 5.12. Acceleration time histories at the base of the Low-rise, No code structure for the fixed base and SSI configurations considering linear soil behavior (outcrop input motion:

Friuli, 6/5/1976, Mw=6.5, R=23km)



Figure 5.13. Snapshots of floor displacement (left) and storey drifts (right) of the Low-rise, No code structure at the time corresponding to maxISD for linear soil behavior (Friuli earthquake

0.3g)

Figure 5.14. Acceleration time histories at the base of the Mid-rise, High code structure for the fixed base and SSI configurations considering linear soil behavior (outcrop input motion:

Friuli, 6/5/1976, Mw=6.5, R=23km)

Figure 5.15. Snapshots of floor displacement (left) and storey drifts (right) of the Mid-rise,

High code structure at the time corresponding to maxISD for linear soil behavior (Friuli earthquake 0.3g)



Similar results are presented continuously for the different analyzed models for the

high-rise non-ductile MRF structure. It can be noticed in Figure 5.16 that the amplitude,

in acceleration terms, is amplified with respect to the free field outcropping motion for

the soil-structure system, which considers linear elastic soil behavior. This amplification is

even more noticeable for the corresponding fixed base model where site effects are taken

into account. On the contrary, when considering soil nonlinearity, the derived seismic

response at the base of the structure is decreased compared to the free field outcropping

motion. This could be attributed to the effect of hysteretic damping in nonlinear systems,

which generally tends to reduce acceleration values at the ground surface as the level of

shear strain increases. A further deamplification of the response is expected for the

nonlinear SSI system compared to the corresponding fixed base model that considers

site effects. The latter could be justified considering that SSI introduces additional

damping to the system due to the energy dissipation at the soil-foundation interface.

Figure 5.17 displays the maximum calculated interstorey drift ratios maxISD (%) for

the different analyzed configurations of the high-rise, low code building for a selected

input motion i.e. Friuli 1976. The highest drift values are shown for the fixed base linear

model, which considers soil conditions (site effects), whereas the lowest ones are

presented for the fixed base structural configuration without considering any site effects,

i.e. the building receives directly the outcrop input motion. It is seen that for the

nonlinear cases the derived drift demands of the structure do not increase proportionally

to the acceleration values. In particular, while the amplitude of the acceleration time

histories is deamplified for the nonlinear systems with respect to the free field

outcropping motion, the corresponding drift values are higher for the models, which

consider soil nonlinearity. This trend is more pronounced for the nonlinear SSI coupled

system compared to the corresponding fixed base case, probably due to the increased

deformation demand introduced at the soil-foundation interface. A better correlation with

drift demand is shown when using Ia as a metric of the seismic intensity. This is

reasonable considering that Ia characterizes not only the seismic intensity (as PGA) but

also the total energy content of the seismic excitation. To further investigate the

structural behavior of the different systems under seismic loading, the distribution of

floor displacements and storey drifts with the structure’s height is illustrated in Figure

5.18, corresponding to the time of maximum interstorey drift occurrence maxISD. The

systems are characterized by a global plastic sidesway mechanism and the maximum

interstorey drift occurs for all cases in the 8th floor of the building. Based on the

deformed shapes of Figure 5.18, it becomes clear that for the fixed base model founded

on rock the contribution of higher modes is not significant. However for the soil-structure

systems as well as for the fixed base models accounting for site effects it is seen that the



second mode contributes to the response of the upper floors as well, thus leading to

higher drift values in comparison to the fixed base building founded on rock.

Figure 5.16. Acceleration time histories at the base of the High-rise, Low code structure for

the different analyzed configurations considering or not SSI, site effects and soil nonlinearity (outcrop input motion: Friuli, 6/5/1976, Mw=6.5, R=23km)



Figure 5.17. Maximum interstorey drift ratio (%) for the different analyzed configurations of

the High-rise, Low code building considering or not SSI, site effects and soil nonlinearity for Friuli earthquake

Figure 5.18. Snapshots of floor displacement (left) and storey drifts (right) for the different analyzed configurations of the High-rise, Low code building at the time corresponding to

maxISD for linear and nonlinear (NL) soil behavior (Friuli earthquake 0.3g)

Preliminary dynamic analyses are also conducted to demonstrate the effect of soil

depth and layering on the nonlinear seismic response of the SSI coupled models Two



different earthquake records are used in this case as input accelerations, scaled at PGA

equal to 0.3g, i.e. Campano Lucano (23/11/1980, Mw=6.9, R=23km) and Kozani

(13/5/1995, Mw=6.5, R=17km) records with waveform codes 000287xa and 006115ya

(Table 3.4 of Chapter 3 and ANNEX A) respectively. These records are characterized by

quite different characteristics in terms of both frequency content and duration. The

Campano Lucano record is associated with a longer significant duration and a rather low

frequency content whereas Kozani record represents a low-duration, high frequency

motion. Thus, for the SSI system increased nonlinearity is expected and consequently

increased drift demands on the structure for the former rather than for the latter motion.

Figure 5.19 depicts the derived acceleration time histories at the base of the structure

(the Ia values are also shown) for the different analyzed nonlinear SSI cases with varying

soil depth and stratigraphy for the two selected acceleration scenarios. It is readily seen

that the acceleration values are generally amplified for the 3-layer soil profile compared

to the corresponding values of the homogeneous soil profile. This could be attributed to

the increased trapping of seismic waves in the thinner upper layer of the layered soil

profile due to the impedance contrast between the sublayers and the underlying bedrock.

The soil depth may also affect the response at the base of the structure. In particular,

the 60m soil profile shows reduced acceleration values compared to the respective 30m

profile. This is evident for both considered representative records and is mainly

associated to the attenuation of the seismic motion with the distance from the bedrock

(i.e. radiation damping) that is increased for the deeper soil profile.

Figures 5.20 and 5.21 present stress-strain hysteretic loops at various depths

(corresponding to soil elements at the middle of each sublayer of the 3-layer profile) for

the homogeneous and the layered 30m and 60m soil profiles respectively. In general

larger loops are observed and thus increased energy dissipation and damping of the

system from the surface layer to the deeper ones as the shear wave velocity of the layer

decreases. Shear modulus degradation is also shown with increasing shear strain that is

more pronounced for the deeper layers. These trends are much more obvious for the

long-duration, low frequency Campano Lucano earthquake motion highlighting the

significant role of the ground motion characteristics in altering the nonlinear seismic

response. In the surface layer, where the shear wave velocity (Vs) of the layered soil

profile is lower compared to the corresponding homogeneous profile (Vs =250m/sec and

300m/sec respectively), the average secant shear modulus of the curve is decreased for

the layered profile that is indicative of the lower stiffness of the layer. This trend is

reversed for the deeper layer where the Vs of the layered soil profile shows greater shear

modulus values compared to the corresponding homogeneous profile (Vs= 350m/sec and

300m/sec respectively). Finally, in the intermediate layer, where the Vs values of the



homogeneous and layered soil profiles are quite close (Vs= 300m/sec and 290m/sec

respectively), the equivalent shear modulus (and thus the average slope) of the curves

are almost identical while the loop is relatively larger for the layered soil profile.

Figure 5.19. Acceleration time histories at the base of the structure for the different analyzed

nonlinear SSI cases with varying soil depth and stratigraphy



Figure 5.20. Stress-strain hysteretic loops at various depths for the 30m homogeneous and layered soil profiles



Figure 5.21. Stress-strain hysteretic loops at various depths for the 60m homogeneous and layered soil profiles



Figure 5.22 illustrates the maximum calculated interstorey drift ratios (%) for the

analyzed SSI coupled configurations with varying soil depth and stratigraphy for the two

representative ground motions. It is observed that the SSI models associated with the

homogeneous soil profiles show lower drift ratios compared to the corresponding models

with the layered soil profiles. In addition, as expected, higher drift values are presented

for the long-duration, low frequency Campano Lucano earthquake motion (000287xa)

than for the low-duration, high frequency Kozani earthquake (006115ya) for all analysis

cases. This is in line with the low-strain fundamental period of the SSI system (TSSI=1.46

sec), which is shown to be closer to the predominant periods of the Campano Lucano

earthquake motion allowing further amplifications in drift demands due to possible

resonance phenomena. These trends are consistent with the estimated Ia values (shown

in Figure 5.19) indicating good correlations with the drift demand. Figure 5.23 presents

snapshots of the floor displacement and storey drift distribution along the building’s

height at the time maxISD occurs, indicating that the depth of the considered soil

medium may affect significantly the seismic behavior of the structure. This becomes

particularly evident for the Kozani earthquake event. While for the 30m-soil profile the

higher mode effects influence the inelastic behavior of the structure, when the depth of

the soil medium increases to 60m, the contribution of these effects seems to be less

important. Furthermore the estimated maximum drift ratios (Figure 5.23) for the Kozani

earthquake are shown to be higher for the shallower (homogeneous and layered) profiles

(30m) in comparison to the deeper soil mediums (60m). This is to be expected as it has

been previously shown that the deeper soil profile reduces the response values at the

base of the structure due to higher attenuation. Moreover Kozani earthquake spectrum is

mostly amplified in periods around 0.3sec, which is closer to the predominant elastic

period of the 30m profile (0.4sec) than the 60m (0.8sec) one resulting to higher drift

ratios for the shallower than for the deeper soil medium. On the contrary for the

Campano Lucano earthquake there is not a clear trend for the homogeneous and layered

soil profiles. In particular, while the increase of the soil depth results to lower drift ratio

values of the structure for the homogeneous case, greater drift values are shown for the

stratified deeper profile compared to the corresponding shallower one. The lower drift

values observed for the homogeneous deeper soil profile in comparison to the

corresponding shallower one are mainly associated with the increased attenuation of the

deeper soil profile. On the other hand, the greater drift values shown for the stratified

deeper profile could be related to the nonlinear behavior of the SSI system which effects

seem to be more pronounced for the stratified deeper soil medium, thus resulting to

larger structural deformations yielding finally higher drift demands close to global

dynamic instability (Vamvatsikos and Cornell, 2004).



Figure 5.22. Maximum interstorey drift ratios (%) for the different analyzed configurations

with varying soil depth and stratigraphy

Figure 5.23. Snapshots of floor displacement (left) and storey drifts (right) at the time maxISD occurs for nonlinear soil behavior and varying soil depth and stratigraphy



5.4 Derivation of fragility curves

The IDA procedure is used to determine the seismic performance and finally assess the

seismic vulnerability of the given structure under the influence of SSI and site effects.

The damage measure is expressed in terms of maximum interstorey drift ratio (maxISD),

which is known to relate well to dynamic instability and structural damage of frame

buildings. The seismic intensity is described using the peak ground acceleration (PGA)

recorded on rock outcropping conditions or soil type A according to EC8. PGA recorded on

rock conditions, and not on the corresponding free field considering site effects, is

selected as an IM for the derivation of fragility curves. In that way, the uncertainties

associated with local soil conditions and surface geology are directly included in the

analysis. Moreover, the use of outcropping PGA allows comparison of all analyzed models

with the reference fixed based structure founded on rock. Although other IMs (e.g. the

5%-damped first-mode spectral acceleration, Sa(T1, 5%)) appear preferable to PGA

producing lower dispersion in the IDA results (e.g. Vamvatsikos and Cornell, 2005) or

being more stable and significant when dealing with different earthquakes (e.g. Housner

Intensity (HI) and Effective Peak Acceleration (EPA)), within the framework of this study

PGA is considered a more appropriate IM mainly due to its simplicity, taking also into

account the uncertainties in estimating the period lengthening of the non-linear SSI

systems. Besides, a structure-independent IM such as PGA is more practical allowing

generalization of the results and permitting direct comparison with currently available

seismic fragility curves (Pitilakis et al., 2014a).

IDA for the different analyzed models is conducted by applying the 15 progressively

scaled records as described in detail in Chapter 3. The hunt & fill tracing algorithm

(Vamvatsikos and Cornell 2002; 2004) which ensures that the records are properly

scaled with the minimum required computational effort, is used to perform the IDA for

the fixed base model founded on rock. A maximum of 12 runs for each record is allowed

while the tracing algorithm was configured to use in terms of PGA, an initial step of 0.1g,

a step increment of 0.01g and a first elastic run designated at 0.005g. Similarly a

stepping algorithm is used for the models including SSI and site effects to perform the

IDA comprising first an elastic run at 0.005g and an initial step of 0.1. It should be noted

that for certain records it was necessary to reduce the step size of the algorithm to

increase the accuracy close to the flatline of the IDA curve. To reach the standards of the

hunt and fill algorithm the minimum number of converging runs is allowed to vary from 8

to 12 per record depending on the characteristics of each record itself.

By interpolating the derived pairs of PGA and maxISD for each individual record, 15

continuous IDA curves are derived for each structural model. Figure 5.24 presents the



derived IDA curves for each record in terms of PGA and the corresponding summarized

across all records IDA curves at 16%, 50% and 84% fractiles for the reference fixed base

structures founded on rock adopted in the present research.

Figure 5.24. IDA curves for the prototype fixed base models (Low-rise, No-code; High-rise, Low-

code; Mid-rise, High code) founded on rock

The limit values of the damage states are defined for the fixed base structures founded

on rock and have already been presented in Chapter 3 of the present thesis. The

Immediate Occupancy damage state is defined according to HAZUS equal to 0.5%

whereas the limit values corresponding to the Collapse Prevention (CP) state are defined

on the IDA curves and are calculated equal to 2.8% for the low-rise MRF designed with

no seismic code provisions, 2.25% for the high-rise frame building designed with low

seismic code provisions and 3.9% for the mid-rise building with high seismic design code

level.

The median PGA values corresponding to the prescribed performance levels are

determined based on a regression analysis of the nonlinear IDA results (PGA- maxISD

pairs) for each structural model. More specifically, a linear regression fit of the logarithms

of the PGA - maxISD data respectively which minimizes the regression residuals is

adopted in all analysis cases. Figure 5.25 illustrates representative PGA - maxISD

relationships for the high-rise low-code fixed base structural model founded on rock when



outcrop ground motions are imposed while Figure 5.26 presents comparative PGA -

maxISD diagrams of the structure considering SSI and fixed base models under linear

and nonlinear soil conditions respectively. It is worth noting that while for the linear

elastic soil behavior the fixed base model tends to yield higher interstorey drift ratios

compared to the SSI model for PGA level lower than approximately 0.5g, when soil

nonlinearity is considered these results are reversed with the nonlinear SSI model

presenting higher drift values for the entire PGA level range.


parameter β as described in detail in Chapter 3. The herein computed log-standard

deviation β values of the curves vary from 0.64 to 0.78 for all structural models.

Figure 5.25. PGA - maxISD relationships for the fixed base high-rise, low code model founded on

rock

Figure 5.26. Comparative PGA - maxISD relationships for the SSI and fixed base models of

the high-rise, low code structure under linear (left) and nonlinear (right) soil behavior



5.4.1 Comparison of SSI - fixed based structures under linear soil behavior

Figure 5.27 depicts comparative plots of fragility curves for the three representative

buildings derived as a function of PGA for the fixed-base and SSI models. A great

increase in fragility is observed for the SSI models with respect to the fixed base

structures founded on rock outcropping conditions. This trend is more pronounced for the

high-rise structure designed with low seismic code provisions. In particular, the median

PGA values for the IO and CP limit states decrease by 50% and 59% respectively for the

high-rise, low-code structure due to the consideration of site and SSI effects. In general

it is observed that when investigating the effects of SSI and the soil conditions on the

vulnerability the number of stories prevail the seismic code design level.

The results show that the soil properties and SSI effects may play a crucial role in the

expected structural damage, as it is expressed in terms of the maximum interstorey drift

ratio, and therefore they should not be neglected for assessment purposes. Table 5.3

summarizes the estimated median and β values of the different damage states (e.g. IO,

CP) as a function of PGA for all the considered building configurations.

Figure 5.27. Fragility curves in terms of rock outcropping PGA for the fixed base structure founded on rock in comparison with the SSI model under linear soil behavior for the MRF structures

under study



Table 5.3. Parameters of the fragility functions in terms of PGA for the fixed base founded on rock models and for the SSI configurations under linear soil behavior

RC building Foundation conditions

Median PGA (g) Dispersion

IO CP

Low rise – No coed MRF

Fixed base – outcropping rock 0.10 0.73 0.74

SSI models- Vs=200 m/sec 0.06 0.44 0.65

High rise – Low code MRF

Fixed base - outcropping rock 0.14 0.68 0.65


Mid rise – High code (Greek) MRF

Fixed base - outcropping rock 0.10 1.31 0.78


5.4.2 Effect of SSI and site effects under linear and nonlinear soil behavior

For the high-rise MRF designed with low seismic code provisions, in which SSI is found to

dominate the structural response, the consideration of soil nonlinearity in SSI is also

investigated as well as the relative contribution of SSI and site effects under linear and

nonlinear soil behavior. Table 5.4 presents the lognormal distributed fragility parameters

(median and log-standard deviation) in terms of rock outcropping PGA for the building

considering or not SSI and site effects under linear or nonlinear soil behavior. Figure 5.28

depicts comparative plots of fragility curves for the different SSI or fixed base models

which consider site effects compared to the reference fixed base model without modifying

the ground motion due to site effects. It is shown that the SSI model, which considers

soil nonlinearity is less vulnerable compared to the SSI system where linear elastic soil

behavior is taken into account. This observation is more noticeable for the CP damage

limit state. These trends are even more pronounced for the corresponding fixed base

models, which consider site effects. Nevertheless, a significant overall increase of the

building’s fragility with respect to the fixed base model founded on rock is clearly shown

in all analysis cases. Thus, local soil properties and SSI effects may play a crucial role in

the expected structural damage, as it is expressed in terms of the maximum interstorey

drift ratio, and therefore they should not be neglected for assessment purposes.

In Figure 5.29 the fragility curves for the different coupled SSI cases and fixed base

models are compared considering linear elastic and inelastic soil behavior. An important

difference between the linear elastic and non-linear case is observed. When soil behavior

is assumed linear elastic, the coupled approach, where SSI and site effects are

considered inherently, has practically no difference with the uncoupled fixed base model

where site effects are taken into account. On the other hand, when soil non-linearity is

taken into consideration then the coupled case of SSI and site effects leads to a



significant increase of the vulnerability compared to the fixed base case where site

effects are simply taken into account through the 1D analysis modifying in that way the

bedrock input motion. Thus, while both nonlinear models (SSI and fixed base) are

associated with the presence of higher attenuation and larger shear strains, SSI also

introduces additional translation and rotation effects at the soil-structure interface

resulting to increased displacement demands to the structure.

Table 5.4. Parameters of the fragility functions in terms of PGA for the analyzed structural configurations when considering or not SSI and site effects under linear or nonlinear behavior for

the case of the High rise – Low code building

RC building/soil-structure system Median PGA (g)

Dispersion β IO CP

Fixed base, rock 0.14 0.68 0.65 SSI linear, coupled 0.07 0.28 0.68

Fixed base, linear site effects 0.06 0.28 0.65 SSI nonlinear, coupled 0.07 0.36 0.64

Fixed base, nonlinear, site effects 0.089 0.50 0.75

Figure 5.28. Fragility curves for the fixed base structure founded on rock in comparison with the

SSI model under linear and nonlinear soil behavior (left) and with the corresponding fixed base models, which consider site effects (right)

Figure 5.29. Fragility curves for the fixed base structure considering site effects and the SSI

configurations under linear (left) and nonlinear (right) soil behavior



5.4.3 Effect of soil depth and stratigraphy under nonlinear soil behavior

Table 5.5 summarizes the lognormal distributed fragility parameters (median and log-

standard deviation) in terms of PGA for the high-rise, low-code MRF considering SSI and

site effects under nonlinear soil behavior for varying soil depth and stratigraphy while

Figure 5.30 represents the corresponding fragility curves. It is seen that for both the

shallower (H=30m) and deeper (H=60m) soil medium cases, the consideration of a more

detailed stratigraphy amplifies the nonlinearities of the soil-structure systems leading

thus to higher vulnerability values. This was to be expected as it has been shown that

the layered soil profiles produce higher amplification, compared to the homogeneous

cases, in seismic response in acceleration terms at the base of the structure. The

increase in fragility of the building due to the consideration of the stratigraphy is much

more prominent for the CP limit state for both soil depth cases but is generally more

pronounced for the deeper soil medium. Regarding the influence of the soil depth,

comparing the median values of Table 5.5 as well as the fragility plots of Figure 5.30, it is

seen that the deeper soil medium (for both layered and homogeneous profiles) decreases

the vulnerability of the structure compared to the shallower one. Although for specific

earthquake cases (i.e. Campano Lucano record) the stratified deeper soil medium may

lead to higher structural drift demands due to the complex nonlinear behavior of the SSI

system, the general trend is that the increase of soil depth reduces the response and

finally the fragilities of the structure for both the homogeneous and layered soil profiles.

This may be attributed to the increased attenuation in the case of the deeper soil profile,

which reduces the seismic response at the base of the structure generally resulting to

lower drift demands in comparison to the respective shallower profile.

Figure 5.30. Fragility curves for different analyzed nonlinear SSI cases with varying soil stratigraphy for the shallower (left) and the deeper (right) soil profile



Table 5.5. Parameters of the fragility functions in terms of PGA for the analyzed structural configurations when considering the soil depth and stratigraphy under nonlinear soil behavior

Soil-structure system Median PGA (g) Dispersion β IO CP SSI-h=30m-1 layer nonlinear, coupled 0.07 0.36 0.64 SSI-h=30m-3 layers nonlinear, coupled 0.063 0.31 0.67 SSI-h=60m-1 layer nonlinear, coupled 0.09 0.62 0.71 SSI-h=60m-3 layers nonlinear, coupled 0.085 0.50 0.66

5.5 Time-dependent fragility curves under the consideration of both aging and SSI effects

Time-dependent fragility functions are derived for the three representative RC MRF

buildings considering both SSI and aging effects. For the high-rise, low-code structure

time-variant fragility curves are developed for both linear and nonlinear soil behavior.

The chloride induced corrosion model presented in Chapter 4 is adopted considering two

time-scenarios (t=0 and 50 years). The quantification of the corrosion effects on the RC

elements of the three MRF buildings under study for the 50-year corrosion scenario are

summarized in Tables 4.2, 4.3 and 4.4 of Chapter 4 regarding the loss of reinforcement,

the concrete cover strength reduction and the steel ultimate deformation reduction

respectively. Figure 5.31 presents indicative comparative plots of linear regression fit of

the logarithms of the PGA-maxISD extracted from the IDA for the high-rise, low-code

MRF building considering linear and nonlinear soil behavior respectively for the

considered time scenarios.

Figure 5.31. Comparative PGA - maxISD relationships for the SSI configurations of the high-rise, low-code MRF under linear (left) and nonlinear (right) soil behavior for the initial (t=0 years)

and the 50-year corrosion scenario (t=50 years)



Figure 5.32 depicts comparative plots of fragility curves for the three representative

buildings derived as a function of PGA for the fixed-base and SSI models always for the

different corrosion scenarios. A great increase in fragility is observed for the SSI models

with respect to the fixed base structures founded on rock. This trend holds true for both

the initial and 50-year corroded structures with the latter showing higher vulnerability. In

addition, for the high-rise building designed with low seismic code provisions, Figure 5.33

shows the derived graphs of time-dependent fragility functions for the SSI configurations

in the light of linear and nonlinear soil behavior respectively in comparison with the fixed

based structure for the initial and corroded scenario. It is shown that the SSI model,

which considers soil nonlinearity is less vulnerable compared to the SSI system where

linear elastic soil behavior is taken into account. This observation is more noticeable for

the CP damage limit state and for the initial time scenario (t=0 years).

Table 5.6 summarizes the estimated median and β(t) values of the different damage

states (e.g. IO, CP) as a function of PGA for all the considered building configurations and

time scenarios. Finally, Table 5.7 presents the time variant fragility parameters for the

different considered SSI configurations of the analyzed high rise, low code building.

Table 5.6. Parameters of the fragility functions in terms of PGA for the considered structural

configurations and corrosion scenarios




IO CP


Fixed base –outcropping rock

0 0.10 0.73 0.74

50 0.09 0.59 0.73

SSI models- Vs=200 m/sec

0 0.06 0.44 0.65

50 0.05 0.37 0.67

High rise MRF-low code

Fixed base - outcropping rock

0 0.14 0.68 0.65

50 0.13 0.59 0.65


0 0.07 0.28 0.68

50 0.06 0.26 0.71



0 0.10 1.31 0.78

50 0.10 1.13 0.77


0 0.08 0.75 0.64

50 0.08 0.67 0.64



Figure 5.32. Time-dependent fragility curves in terms of PGA for the analyzed fixed base and

SSI structural configurations



Table 5.7. Time-dependent fragility parameters in terms of PGA for the high rise, low code building considering fixed base and SSI (for linear or nonlinear soil behavior) structural

configurations




IO CP

High rise MRF-low

code


0 0.14 0.68 0.65

50 0.13 0.59 0.65


0 0.07 0.28 0.68

50 0.06 0.26 0.71

Fully nonlinear SSI model- Vs=300 m/sec

0 0.07 0.36 0.64

50 0.06 0.28 0.62

Figure 5.33. Time-dependent fragility curves in terms of PGA for the high rise, low code building when considering fixed base and SSI structural configurations under linear and nonlinear

soil behavior

5.6 Conclusions

The seismic vulnerability of three representative RC frame buildings designed according

to different seismic code levels, has been assessed taking into account SSI effects.

Consideration of SSI has been achieved by applying the direct one-step coupled

approach, which accounts simultaneously for inertial and kinematic interaction schemes.

The different soil-structure systems have been analyzed considering at first linear soil

behavior. For the high-rise building designed with low seismic code provisions, for which

soil-structure interaction was more pronounced, both linear elastic and nonlinear soil

behavior have been considered to gain further insight into the influence of SSI and site

effects on fragility analysis. Soil nonlinearity has been introduced through the use of a

pressure-independent multi yield surface incremental plasticity model. A two-step

uncoupled approach has been also applied which considers the modification of ground

motion due to site effects on the response of the fixed base structure. In this way, the



importance and relevant contribution of site and SSI effects have been investigated.

Moreover, to examine more thoroughly the effect of SSI on the seismic performance and

fragility of the building under nonlinear soil behavior, the coupled soil-structure systems

have been further analyzed for varying soil depth and stratigraphy. Finally, time-

dependent fragility functions were derived for all three MRF structures considering both

SSI and chloride induced corrosion effects for a 50-year time scenario.

Comparative dynamic analyses were conducted for the fixed base models (considering

or not site effects) and the soil-structure systems under linear and nonlinear soil

behavior for selected test earthquake records to demonstrate the influence of SSI and

site effects on the seismic response and vulnerability. Results in terms of acceleration

time histories at the base of the structure, interstorey drifts and stress-strain hysteretic

loops at various soil depths for the nonlinear soil-structure configurations highlighted the

significant role of SSI and site effects in modifying the ground motion imposed at the

base of the structure and finally its structural dynamic response. The level of this

modification depends on the ground motion characteristics (frequency content, duration),

the dynamic properties of the soil and the structure itself.

IDA was performed by applying 15 multiply scaled input motions for all considered

models. Finally, probabilistic fragility functions have been derived in terms of rock

outcropping PGA for the IO and CP limit states. It was shown that the consideration of

SSI and site effects under both linear and nonlinear soil behavior may significantly affect

the structural performance increasing considerably the structure’s seismic vulnerability

compared to the reference case where the structure is assumed as fixed base and no SSI

or site effects are taken into account. When soil nonlinearity is introduced these effects

are generally expected to have lower impact on structure’s fragilities for higher levels of

seismic loading. When the soil behavior is assumed linear elastic the fragility curves

derived for the coupled SSI approach have practically no difference with the uncoupled

fixed base model where site effects are taken into account. On the other hand, nonlinear

SSI leads to an increase of the structure’s vulnerability compared to the corresponding

fixed base model. The latter could be attributed to the complex nonlinear behavior of the

underlying soil that may introduce additional translation and rotation effects to the

structure yielding to higher drift demands. Overall, among the analyzed cases, the

uncoupled fixed based model where site effects are linearly modeled shows the highest

vulnerability. Thus, while avoiding the computational cost introduced by the coupled SSI

models, the use of the fragility curves for the fixed based model where site effects are

modeled linearly would lead to conservative results. However, this is valid only for the

analyzed cases and should not be regarded as a general conclusion.



Furthermore, nonlinear SSI leads to an increase in fragility of structure when the

stratigraphy of the soil profile is taken into account, as the step-like layered soil medium

may amplify the imposed input motion at the base of the structure in comparison to the

homogeneous soil cases. On the other hand, it is seen that nonlinear SSI may decrease

the seismic vulnerability of the structure for deeper homogeneous and layered soil

profiles. This may be attributed to the increase of attenuation levels. However it

generally depends on the considered soil depth and stratigraphy as well as on the

characteristics of the input motions in relation to the dynamic properties of the soil and

the structure itself.

Regarding the consideration of aging effects on the seismic vulnerability of the soil-

structure systems, as expected based on the results of Chapter 4, chloride induced

corrosion leads to an overall increase of the seismic fragilities with time.

Overall, the aim of the present study is to prove that the conventional way of

calculating building fragility with the hypothesis of fixed base structure may lead to

unconservative results. SSI and site effects are very important to be ignored. The work

presented herein provides an insight into the influence of SSI and site effects on the

seismic performance and vulnerability of RC frame buildings under linear and nonlinear

soil behavior. Based on the results of this study and in order to enhance the reliability in

seismic vulnerability assessment studies, further research is necessary for the

development of generalized fragility functions applicable to a variety of RC building

typologies which would take into account SSI and site effects for a variety of soil

conditions. Moreover vulnerability functions derived for the same building should be

related to varying subsoil conditions and different Intensity Measures.




CHAPTER 6

Time-building specific vulnerability assessment of RC buildings using field

monitoring data

6.1 Introduction

In the context of seismic vulnerability assessment of reinforced concrete (RC) buildings,

the use of field monitoring data constitutes a significant tool for the representation of the

actual structural state, reducing uncertainties associated with the building configuration


thus the reliability in the risk assessment procedure. In the present chapter, the seismic

vulnerability of existing RC buildings is evaluated combining through a comprehensive

methodology, the numerical analysis and field monitoring data. The proposed

methodology is highlighted through the derivation of “time-building specific” fragility

curves for an eight-storey RC structure (hospital building), built almost five decades ago,

that is composed by two adjacent units separated through a structural joint. The

assessment of the dynamic characteristics is performed using ambient noise

measurements recorded by a temporary seismic network which was deployed inside the

hospital. The modal identification results are used to update and better constrain the

initial finite element model of the building, which is based on the available design and

construction documentation plans. Three-dimensional incremental dynamic analysis is

performed to derive the fragility curves for the initial as built model (“building-specific”)

and for the real structures as they are nowadays (“time-building specific”). The initial

“building specific” curves are evaluated through their comparison with conventional

generic curves that are commonly used in risk assessment studies. Moreover, in order to

validate and enhance the reliability of the obtained results, the “time-building specific”

fragility curves, are compared to time-dependent curves derived for the hospital units

applying the analytical methodology proposed in Chapter 4 adopting an appropriate for

the specific case study corrosion scenario. Results derived from both approaches indicate

Chapter 6: Time-building specific vulnerability assessment of RC buildings using monitoring data198


that the consideration of the actual state of structures may significantly alter their

expected seismic performance leading to higher vulnerability values. Part of the research

presented in this chapter has been published in Bulletin of Earthquake Engineering (Bindi

et al., 2014a) scientific journal.

6.2 Application study: AHEPA hospital

6.2.1 Structural description

The AHEPA general hospital in Thessaloniki is one of the largest hospitals in northern

Greece located in the campus of Aristotle University. It is a major teaching and research

hospital and part of the National Healthcare System of Greece. It covers all possible

specializations of a large-scale major hospital (surgical, pathology, psychiatry etc.). The

hospital complex (illustrated in Figure 6.1) consists of 40 buildings of various functions

and typologies, 2 electrical substations, a gas distribution network and an underground

water supply system. Many of these buildings were built before 1985 and are classified

as low seismic code structures. In case of an emergency its central location in the city of

Thessaloniki makes it one of the most important medical care centers for an efficient

crisis management.

Figure 6.1. General view of the AHEPA hospital complex



The target building hosts both administration and hospitalization activities. It was

constructed in 1971 and is considered representative of structures that have been

designed according to the old 1959 Greek seismic code (‘Royal Decree’ of 1959), where

the ductility and the dynamic features of the constructions are ignored. During the 1978

Thessaloniki earthquake (M=6.5, R=26.7km, Papazachos et al., 1979; Soufleris et al.,

1982), which generally caused extensive damages and the collapse of one high-rise

residence structure, the hospital building suffered only slight damage. It is an eight

storey infilled structure and its special feature is that it is composed of two adjacent tall

building units that are separated through a structural joint as illustrated in Figure 6.2(a).

The separation gap is approximately equal to 5cm and potential pounding phenomena

(hammering effects) between the to units may occur during a strong earthquake event.

UNIT 1 covers a rectangular area of 29m by 16m while UNIT 2 has a trapezoidal cross

section of 21m by 27m by 16m. The total height of the building with respect to the

foundation level is 28.6m with a constant inter-storey height of 3.4m except for the

second floor where the height increases to 4.8m due to the presence of a middle floor

level which covers only a part of the typical floor plan (Figure 6.2(a)). From the structural

point of view the building’s force resisting mechanism comprises longitudinal and

externally transverse reinforced concrete moment resisting frames. The columns have

variable dimensions along the height of the building starting from 0.45m x 0.70m at the

lowest level (basement) and resulting to 0.35m x 0.35m at the upper floor. In the

longitudinal direction the outer and inner columns are connected by beams with cross-

section of 0.20m x 0.60m and 0.35m x 0.40m respectively. In the transverse direction

on the other hand only the exterior columns are connected by beams with dimensions of

0.20m x 0.95m. The presence of beam to beam connections at all floor levels near the

staircases and elevator shafts, constitute a complex structural system which is

particularly evident in the middle floor where the RC beams are inverted. Reinforced

concrete walls are present in both building units, surrounding partially the staircases and

the lift shafts; they are not specially detailed for seismic performance. More specifically

there are two walls in the transverse and one in the longitudinal direction of UNIT 1 and

only one wall in the transverse direction of UNIT 2. The RC walls are 0.20m thick while

their length is decreasing significantly along the structure’s height. Moreover a perimeter

reinforced concrete wall with dimensions of 0.20m x 3.00m has been constructed at top

of the building. Figures 6.3 and 6.4 present the geometrical properties of the sections

and the reinforcement details of the structural elements respectively. Moreover Figure

6.5 illustrates the diameters and position of the reinforced bars of walls and columns for

the different floor levels. It is observed that the reinforcement of the second and upper

floor columns is greater than for the first floor elements probably due to the presence of



the middle floor which leads also to an increase of the height of the second floor. In-situ

testing on materials, structural details and non-structural components were not possible

to be conducted. The material properties and the structural details used for the numerical

modeling of the building units, are defined based on the information of the available

blueprints. More specifically concrete B225 (fc=14MPa) is used for all beams and columns

while two steel classes StIII (fy=500MPa) and StI (fy=220MPa) are utilized for the

reinforced bars. Steel class StI is used for the reinforcement of all beams (longitudinal

and transverse) and for most column elements. In Figure 6.5, it can be seen for which

cases StIII is utilized. The mass properties are deduced from the available blueprints

based on the structural elements and the prescriptions of the national loading standards.

Table 6.1 summarizes the main characteristics of the two building units according to the

design and construction plans, namely the mass, the characteristic strength values of

concrete (fc) and reinforcement steel (fy). The two building units do not have common

foundation. The foundation system of UNIT 1 consists of simple footings of variable

geometries without tie-beams whereas in UNIT 2 the footings are combined partially with

a raft foundation. Figure 6.2(b) represents a typical cross-section of the hospital with the

foundation soil profile and the average shear wave velocities Vs,ave estimated from cross-

hole and down-hole tests (Raptakis et al., 1994). The soil consist of a stiff clay with

average Vs,ave of about 400-450m/sec. The rock basement (schist) is found at 30 to 35m

depth having Vs velocities greater than 750m/sec. The foundation soil at the hospital

building can be characterized as soil type B according to EC8 soil classification.

Regarding the non-structural components, besides the three existent elevators, an

electricity generator is also installed in the basement of UNIT 1, which in case of a

general shut down (e.g. due to a strong earthquake event) constitutes the only source of

electricity supply for the entire hospital. Finally it should be noted that no significant

interventions or retrofitting works have been carried out over the years according to the

Technical service of the hospital, that would allow deviations from the available design

and construction plans.

Using the SYNER-G taxonomy (Pitilakis et al., 2014a) for RC structures to describe

the typology of the hospital building, it may be considered typical of high-rise infilled

moment resisting frame buildings designed with low seismic code level.

Table 6.1. Main characteristics of the hospital building units (fc and fy represent the strength of concrete and reinforcement steel respectively)

RC building Total mass (t) fc (MPa) fy (MPa)

UNIT 1 3804.0 14.0 220.0 and 500.0

UNIT 2 3144.0 14.0 220.0 and 500.0



(a)

(b)

Figure 6.2. (a) Typical floor plan and middle floor with the structural joint and (b) typical soil profile of AHEPA hospital building (dimension in m)



Figure 6.3. Geometrical properties of the element sections of UNIT 1 and UNIT 2 presented in

section A-A’ along the longitudinal direction of the hospital building (dimensions in m)

Figure 6.4. Reinforcement layout of UNIT 1 and UNIT 2: red and blue correspond to the beam and column reinforcement respectively (diameters in mm)



Basement 1st floor

2nd floor 3rd floor

Figure 6.5. Diameters and position of the column reinforced bars of the different floor levels for both UNIT 1 and UNIT 2 (diameters and dimensions in mm)



4th floor 5th floor

6th floor 7th floor

Figure 6.5. (Continued) - Diameters and position of the column reinforced bars of the different floor

levels for both UNIT 1 and UNIT 2 (diameters and dimensions in mm)



6.2.2 Instrumentation arrays

Permanent and temporary instrumentation arrays (Figure 6.6) have been implemented

under the responsibility of the Soil Dynamics and Geotechnical Earthquake Engineering of

the Aristotle University of Thessaloniki (SDGEE-AUTH) and in close cooperation with

Helmholtz Centre Potsdam, German Centre for Geosciences (GFZ). The permanent

accelerometric array (SOSEWIN network) operates in AHEPA hospital since May 2012. In

addition to the SOSEWIN network, various temporary networks have been deployed

inside the hospital to evaluate the risk of the building for various earthquake scenarios.

The permanent network is installed for the long term building monitoring. It is composed

by sensing units where the building motion is measured in real time through MEMS

sensors. It is mainly intended to monitor the building response to earthquakes.

Furthermore the earthquake recordings from the permanent instrumentation array are

used to develop an operational framework for Early Earthquake Warning (EEW) and rapid

post-earthquake damage assessment. Ambient noise measurements on the other hand

are used for the dynamic characterization of the building deploying a denser network of

stations equipped with velocimeters, which have a better amplitude resolution and a

lower internal noise than the MEMS. The description of both permanent and temporary

network provides a complete view of the instrumentation arrays that have been installed

in the hospital building.

6.2.2.1. Permanent array

The SOSEWIN network constitutes of 13 triaxial accelerometers (MEMS ADXL203 chip)

installed in the basement (S02FC), the first (SB4D4) and the fourth (SB6C4, SB688,

SB5E8, SB27C) floor (SB6C4, SB688, SB5E8, SB27C) and the roof (SB0F8, SB22C,

SB260, SB278, SB110, SB6BC, SB11C) as presented schematically in Figure 6.6. One

more accelerometer is installed on the roof of a nearby building and used as bridge node

for the data transmission to the two gateways installed outside of the SDGEE-AUTH as

illustrated in Figure 6.7. Several earthquake events have already been recorded and the

instrumentation array continues to transfer data streams to the Seiscomp3 server

installed at SDGEE-AUTH premises. In Figure 6.8 SOSEWIN recordings for a local

earthquake (Volvi Earthquake 11.10.2013, Mw=4.7, R=10km) are shown.



Figure 6.6. Floor plans of the basement, 1st and 4th floors and the roof with the permanent and temporary instrumentation. All SXXXX are accelerometers of the permanent network, all RE-XX

and T4D50 are seismometers of the temporary networks operating for short period of time inside the hospital. Photos of the SOSEWIN stations at the 4th floor near the structural joint (RE-39) and

at roof (SB0F8)

Target-13 sensors

Bridge node1 sensor

Data centerGateway nodes

Figure 6.7. Permanent network array of AHEPA hospital



Figure 6.8. Earthquake data for the longitudinal (east-west, EW), transverse (north-south, NS) and

vertical (V) components recorded at SOSEWIN sensors at the 4th floor and the roof from the 11.10.2013 Volvi Earthquake (Mw=4.7, R=10km)

6.2.2.2. Temporary array

In February 2013 a two-day ambient noise experiment was conducted in the hospital

building in cooperation with GFZ Potsdam. During the first day, a temporary array of 39

triaxial seismometers was deployed in the two building units. In order to capture the

translational and torsional modes of the building, the sensors were installed in every floor

with the configuration illustrated in Figures 6.6 and 6.9. Each floor was instrumented

with four stations, which were installed along the middle corridor of the building near and

far the structural joint (Figure 6.9). The instruments were Mark Products short-period

seismometers (L4C-3D, 1Hz natural frequency) coupled to EarthData recorders EDL

(PR6-24). The seismic sensors are passive seismic sensors with 1Hz corner frequency,

connected to 24bit digitizers. Even in the free field, the internal noise of such equipment

allow to record ambient noise to about 0.2Hz (e.g. Strollo et al., 2008a; 2008b). At four

locations, a second station equipped with Güralp broadband seismometers (CMG-40T,

30sec natural period) coupled to Reftek recorders (DAS-130) was also deployed for

instrumental comparison purposes. GPS antennas guaranteed the time synchronizations

among all instruments. The sensors recorded along the two orthogonal horizontal and

along the vertical directions (three components). The two horizontal components are

oriented along the longitudinal and transversal direction of the building. Ambient noise

was recorded simultaneously for about 4 hours in all stations with a sampling rate of 500

Hz and gain 10. In the second day, 51 stations were used (44 EDL and 7 Reftek), adding

one station at certain floors. Table 6.2 summarizes the serial codes and locations of the

employed instruments for both days of experiment. As illustrated in Figure 6.10 the

amplitude of the time series is increasing as the noise waveforms are propagating from

the basement to the roof of the building.



Figure 6.9. Sections A-A΄ and B-B΄ along the longitudinal and transverse direction of the hospital building with the temporary instrumentation

Table 6.2. Serial number and position of all the stations used in the two-day ambient noise experiment

1st day 2nd day Station position UNIT 1 UNIT 2 UNIT 1 UNIT 2

Basement RE-07, RE-03 RE-30, RE-02 RE-38, T4K21*, RE-05, RE-02 RE-10, RE-31

1st floor RE-29, RE-41 RE-01, RE-10 RE-01, RE-43 RE-09, RE-21

2nd floor RE-09, RE-31 RE-38, RE-05 RE-07, RE-11, RE-03 RE-28, RE-36

3rd floor RE-22, RE-25 RE-18, RE-14 RE-25, T4D50*, RE-18, RE-16 RE-14, RE-22

4th floor RE-45,RE-39 T4D50* RE-34, RE-12 RE-39, RE-45

T4D50, T4K19* RE-12, RE-34

5th floor RE-15, RE-44 RE-26,RE-35, T4K20*

RE-26, RE-35 T4K20*, RE-37 RE-15, RE-44

6th floor RE-17, RE-20 RE-08,RE-33, T4D78*

RE-17, RE-33, RE-41

RE-20,RE-08, T4D78*

7th floor RE-27, RE-23 RE-32,RE-42, T4D49*

RE-42, RE-27, RE-29

RE-23,RE-32 T4D49*

Roof RE-06, RE-24, RE-13 RE-04, RE-40 RE-13, RE-27,

RE-06 RE-19, RE-24,

RE-40 *: broad-band seismometers (CMG-40T)



Figure 6.10. Synchronized ambient noise recordings for the longitudinal component. All the

records have the same amplitude scale (y-axis)

6.3 Description of the methodological framework

A schematic flowchart of the proposed methodological framework that has been adopted

for the derivation of the ”time-building specific” fragility curves of the hospital building

units based on field monitoring data is presented in Figure 6.11. Ambient noise

measurements are used to derive the experimental modal model of the hospital building

and identify its modal properties based on operational modal analysis (OMA). The modal

identification results are used to update and better constrain the initial finite element

model of the building, which is based on the design and construction documentation

plans. In the absence of any structural geometry modification since 1971 when the

building was constructed, only the variation in the material properties is taken into

account in the present study. An eigenvalue sensitivity analysis of the elastic numerical

modal models is performed to identify the most sensitive parameters influencing the

structural modes of interest which are used in the manual updating process to define the

optimal analytical models that reflect the experimental results. The selection of the best

updated finite element (FE) model for the two building units is made by evaluating an

appropriate response correlation function between experimental and numerical results.

Three-dimensional incremental dynamic analyses (IDA) (Vamvatsikos and Cornell, 2002)

of the nonlinear updated models are performed using real ground motion accelerograms

that are selected based on the regional seismic hazard, to derive the “time-building

specific” fragility curves that correspond to the actual state of the hospital building units.



Monitoring dataExperimental modal model

(Operational Modal Analysis)

Design and construction plansInitial FE model

Building-time specific vulnerability assessment using field monitoring data

Nonlinear analytical simulation of the updated models: Material inelasticityGeometrical nonlinearity

Building-time specific fragility curves generation

3D nonlinear incremental dynamic analysisEDP: maximum interstory drift

Earthquake demand:Regional seismic hazard (SHARE)

Methodology for fragility curve generation:Incorporation of uncertainties in limit state definition, capacity and demand

Manual updating process

Comparison between experimental and numerical modal model: evaluation of response function

Eigenvalue sensitivity analysis

Sensitivity in material properties

Selection of the “best” updated FE model

Figure 6.11. Methodological framework adopted in the present study

6.4 Operational modal analysis (OMA) using field monitoring data

6.4.1 Modal identification methods

System identification is the process of building a mathematical model of a physical

system based on experimental data (Ljung, 1999). From an engineering point of view the

goal of system identification is to predict the physical quantities of a system based on its

mathematical model (Kim, 2011). Research on linear system identification evolved in the

late 1960s on the basis of control engineering (Gevers, 2006).

The typical scheme of the identification process for a linear time-invariant vibrating

structure is presented in Figure 6.12. Based on the knowledge of the system’s

experimental response (output data) to an excitation source (input data) a parametric

modal model can be derived that is defined by a set of modal parameters

(eigenfrequencies, mode shapes, damping ratios). There are several deterministic or

stochastic techniques developed over the past years that can be used to build the

mathematical model of the dynamic structural systems in frequency or time domain

based on measured data. A modal model of an artificially excited structure can be

obtained based on Experimental Modal Analysis (EMA); however in case of real scale civil

structures applying an artificial excitation might be difficult from technical and



economical point of view. Therefore, Operational Modal Analysis (OMA) is generally

preferred to forced vibration measurements since the same modal parameters can be

obtained from vibration data in operational rather than laboratory conditions by modeling

the interaction between the structure and its environment (e.g. wind, traffic, etc).

Ambient vibration measurements are usually used to perform OMA and indentify the

modal parameters of a structure. In contrast to Experimental Modal Analysis, the

properties of ambient excitation in Operational or Output- Only Modal Analysis are

difficult or impossible to be measured. Therefore stochastic identification techniques

have been developed by the assumption that the response is a realization of a stochastic

process with unknown white Gaussian noise as input (Figure 6.12) characterized by a flat

spectrum in the frequency range of interest. Based on this assumption the excitation

input is considered to have the same energy level at all frequencies implying that all

modes are excited equally (Van Overschee and De Moor, 1996; Peeters, 2000).

Figure 6.12. Stochastic Output-Only Identification

There are different stochastic identification techniques to extract the modal

parameters of a structural system, namely the parametric and non-parametric methods.

In non-parametric methods the modal parameters are estimated directly by post-

processing the measured data whereas in the parametric methods the dynamic

characteristics are extracted based on a parametric model that is updated to fit the

recorded data. The two methods are described in more detail in the following paragraphs.

Non-parametric algorithms are traditionally associated with the Discrete Fourier

Transform and the computation of auto and cross power spectra. They are widely used

due to their simplicity and intuitiveness. Two of the most commonly used non-parametric

methods for the modal parameters estimation of the identified system are (a) the Basic

Frequency Domain or the Peak Picking (PP) method (Bendat and Piersol, 1993) and (b)

the Frequency Domain Decomposition (FDD) (Brincker et al., 2000). Both methods are

based on correlations of the power spectra between the outputs and the reference

outputs and on decomposition of the stochastic power spectral density (PSD). In the first

method the frequency peaks from the average spectra are selected that are derived

based on the output recordings of the sensors. The FDD method is considered to be an

improved version of the PP method and consists of decomposing the system’s power

spectral density into its singular values. It is shown that taking the Singular Value

Decomposition SVD of the spectral matrix, the latter is decomposed into a set of auto



spectral density functions each corresponding to a single degree of freedom (SDOF)

system (Brincker et al., 2000).

The output PSD, Gyy(jω), at discrete frequencies is decomposed by taking the Singular

Value Decomposition SVD of the matrix:

Hyy i i iG ( j ) U S U (6.1)

where Ui=[ui1, ui2,….., uim] is a unitary matrix including the singular vectors uij and Si is a

diagonal matrix including the scalar singular values sij. If only one mode is dominating

close to the peak then the first singular vector is an estimate of the mode shape. If two

modes are dominating at this frequency peak then the two first singular vectors are

estimates of the corresponding mode shapes (Figure 6.13).

These results are exact under the following conditions:

the loading is white noise

the structure is lightly damped and

the mode shapes of close modes are geometrically orthogonal.

Disadvantages of the nonparametric methods are the subjective selection of the

eigenfrequencies, the lack of accurate damping estimates and the determination of

operational deflections shapes instead of mode shapes since no modal model is fitted to

the data (Peeters and De Roeck, 1999).

Figure 6.13. Frequency Domain Decomposition (FDD) method

Stochastic subspace identification SSI (Van Overschee and De Moor, 1991) works in

time domain and is one of the most commonly applied parametric identification methods.

The SSI techniques involve the selection of a mathematical model whose parameters are

adjusted to the model so that it fits to the measured data. The goal of this model

calibration is to minimize the deviation between the predicted and measured system

response. The number of the parameters plays a significant role in the identification

process. In case a too small number is defined, the modal parameters may be not

modeled statistically correctly. On the other hand, if the number is defined to be too

high, then the model becomes over-specified resulting in unnecessary high statistical

uncertainties of the model parameters. An advantage of the parametric over the non-



parametric techniques is the direct estimation of the system’s damping ratio from the

identification process.

SSI is based on a state space description of the dynamic problem. In fact, the second

order dynamic problem, expressed through the differential equation of motion, is

converted into two first order problems, namely the “state equation” and “observation

equation”. The stochastic state-space model of a discrete–time, linear, time invariant

system is mathematically described by the following set of equations (Ewins, 1984;

Peeters and De Roeck, 1999):

k 1 k kx Ax w (6.2)

k k ky Cx v (6.3)

with

p T Tq q pqT

p

w Q SE w u

u S R

(6.4)

where yk l is the measurement vector at time instant k of the l outputs; kx n is the

state vector at discrete time instant k and contains the numerical values of n states; vk l and wk

n are unmeasurable vector signals that are assumed to be zero mean,

stationary, white noise vector sequences; A n n is the state matrix that describes the

dynamics of the system by its eigenvalues whereas C l n is the output matrix. The

matrices Q n n , S n l and R l l are the covariance matrices of the noise sequence wk

and vk. The matrix pair A, C is assumed to be observable, which means that all modes

of the system can be observed in the output yk and can thus be identified. E is the

expected value operator and δpq is the Kronecker delta. During the stochastic

identification the parametric model is defined to determine the following parameters:

the order n of the unknown system

the system matrices A and C as well as Q, S and R so that the

predicted and the measured output of the model are equal.

The output measurements are gathered and rearranged in a block Hankel (data

driven SSI) or Toeplitz (covariance driven SSI) matrix as past (reference) and future

blocks. The Hankel or Toeplitz matrix is a matrix where each antidiagonal or diagonal

consists of the repetition of the same element respectively. More specifically for the

predicted output response time series expressed as a discrete data matrix the block

Hankel and Toeplitz matrices are defined accordingly as:



Hankel matrix Toeplitz matrix

1 2 n 2s

2 3 n 2s 1

ps s 1 n s 1

s 1 s 2 n s f

s 2 n s 1

2s 2s 1 n

y y y

y y y

Hy y yH

y y y Hy y

y y y

Tf pT H H

s s 1 1

s 1 s 2

2s 1 2s 2 s

R R R

R R RT

R R R

(6.5)

where H 2sl ( n 2s ) and T ls ls , s is the number of block rows and n-2s the number of

block columns. The subscripts p and f stand for past and future and the matrices Hp and

Hf are defined by splitting the Hankel matrix into two parts of s blocks. Rs are the

covariance matrices between all outputs and references and are defined as T

k s kRs E y y . The key step of SSI is the projection of the row space of the future

outputs into the row space of the past outputs (Van Overschee and De Moor, 1996). The

idea behind the projection is that it retains all the information in the past that is useful to

predict the future resulting to a data order reduction. The main theorem of SSI (Van

Overschee and De Moor, 1996) states that the projection can be factorized as the

product of the observability matrix (that is based on the matrix pair A, C) and the

Kalman filter state sequence. The aim of the Kalman filter (Van Overschee and De Moor,

1996; Peeters and De Roeck, 1999; Ljung, 1987; Juang, 1994) is to produce an optimal

prediction for the state vector xk+1 by making use of the observations of the outputs up

to time k and the system matrices combined with the noise covariances. Introducing a

QR-factorization to the Hankel or Toeplitz matrix the projection matrix can be computed.

Continuously the projection matrix is decomposed into its singular values (Singular Value

Decomposition SVD) revealing the order of the system. Finally based on the estimated

system order, the observability matrices and the Kalman filter state sequences, the

system matrices can be calculated. Knowing the outputs, the system order and the

system matrices the identification problem is solved and the modal parameters can be

extracted (Figure 6.14).



Figure 6.14. Stochastic subspace identification (SSI) method

6.4.2 Operational modal analysis using ambient noise measurements

To evaluate the dynamic characteristics of the hospital building, namely the natural

frequencies and mode shapes, system identification and Operational Modal Analysis were

performed using MACEC 3.2 software (Reynders et al., 2011) for the two adjacent

building units separately (UNIT 1 and UNIT 2) as well as for the entire hospital building

complex, analyzed as a single building taking into account the interaction of the two

building units due to their connection with the structural joint (BUILDING). MACEC 3.2 is

a Matlab based code that offers extensive functionalities for the visualization and

processing of the data, the identification of system models and the determination and

visualization of the structural modal parameters. Operational modal analysis consists of

three distinct steps which are: (1) the collection of the data and preprocessing, (2)

system identification and (3) the determination of the modal parameters from the

identified system model. Thus the term “modal analysis” can be defined at two different

levels: (i) the whole procedure of obtaining modal parameters from measurements (steps

1, 2 and 3) and (ii) the determination of the modal parameters from the identified

system model (step 3). MACEC toolbox clearly differentiates between system

identification and modal analysis of level (ii).

The geometrical characteristics of the models introduced and analyzed in MACEC 3.2

are illustrated in Figure 6.15. Operational modal analysis is performed considering only

the horizontal components of the measurements. The grid of the models is built so that

the defined nodes correspond to nodes that have been actually measured. The sensors

that were used for the identification process are illustrated in Figure 6.9. A total duration

of 1800 sec (30min) is used for OMA as tests for stability of the results showed that 30

minutes are enough to get reliable results. Before identification the data were decimated

with a factor of 10 and filtered with a low-pass anti-aliasing filter with a cut-off frequency

of 25Hz and re-sampled at 50Hz reducing thus the number of data from 900000 to



90000 points avoiding thus unnecessary computational burden in the modal analysis

where the frequencies of interest are smaller than 25Hz.

UNIT 1 UNIT 2 BUILDING

Figure 6.15. Visualization of the building’s geometry in MACEC 3.2

In order to verify and enhance the modal identification results for the different

systems under study (UNIT 1, UNIT 2 and BUILDING), analyses have been conducted

using both non-parametric and parametric identification techniques. More specifically the

stochastic (or output-only) system identification methods that have been applied in

MACEC 3.2 are the following:

nonparametric PSD+ estimation using the correlogram method in frequency

domain

reference-based covariance-driven stochastic subspace identification in time

domain.

In the non-parametric methods, system identification is based on the calculation of

the Positive Power Spectral Density (PSD+) matrix at discrete frequency lines. For the

PSD+ estimation of the measured outputs collected from all channels, the correlogram

method was applied. In the correlogram approach, the auto and cross-PSDs of one or

two quasi-stationary ergodic sequences is estimated as the Laplace transform of the auto

or cross correlation functions respectively (Reynders, 2012). In Figures 6.16 and 6.17

indicative plots of estimated auto and cross correlation PSDs are illustrated

corresponding to stations installed at the basement and the top of the hospital building

near and far from the structural joint.

Modal analysis of the identified non-parametric models has been conducted based on

the Peak Picking (PP) and Frequency Domain Decomposition (FDD) methods. In the PP

method the averaged normalized power spectral density (ANPSD) is computed and the

well separated modes are estimated by picking the peaks in the ANPSD. In the FDD



method, the singular values are obtained from the decomposition of the PSD matrix and

the modal parameters are estimated by picking the peaks of the first singular value.

(a) (b)

Figure 6.16. Indicative auto-correlation PSDs+ for time series recorded at stations near the joint, (a) station installed at the basement and (b) station installed at the top

(a) (b)

Figure 6.17. Indicative cross-correlation PSDs+ between time series recorded at stations of the basement and roof (a) near the joint and (b) far from the joint

Modal identification based on parametric methods was conducted by applying the

reference-based covariance-driven stochastic subspace method. The number of block

rows in Toeplitz matrix was selected as 2x(expected system order)/number of outputs).

After the QR and singular value decomposition step of the SSI algorithm (Figure 6.14),

the real system order was estimated based on the singular values (Figure 6.18). For

noiseless data, the system order equals the number of nonzero singular values while for

noisy data the noise causes some singular values to be different of zero. Due to the fact

that the noise is present in the recorded ambient vibration data, the identified system

description contains both system and noise dynamics. A common approach in modal

analysis is then to over-specify the model order (Peeters et al., 1999) such that the true

system modes (physical modes) are separated from the noise modes (mathematical

modes) (Reynders et al., 2011). In general the selection of the model order for the



construction of the stabilization diagrams for the SSI method depends on the number of

modes of interest as well as the number of sensors. For the construction of the

stabilization diagrams a model order range from 2 to 150 in steps of 2 was selected for

UNIT 1 and UNIT 2, whereas for BUILDING the upper limit of the model order was

increased to 200. The increase of the model order for BUILDING was required due to the

analysis of a much larger data set as data from 36 stations were used for the

identification analysis in contrast to UNIT 1 and UNIT 2 where data from only 18 sensors

were used. The aim is to use the stabilization diagrams to detect the columns of stable

modes that satisfy the defined stabilization criteria and continuously select a

representative mode from each column.

Figure 6.18. Singular values of Covariance-driven SSI method in decreasing order of

magnitude

The results of the nonparametric and parametric analyses for the two adjacent

buildings analyzed separately (UNIT 1 and UNIT 2) and as one single building

(BUILDING) are presented in Figure 6.19. In Table 6.3 the eigenfrequencies computed

with the different system identification methods are summarized. It should be noted

herein that potential effects of the non-structural components did not influence the

identification results. The electricity generator was not operating during the experiment

while other non structural elements, such as elevators and medical devices, are

operating in high frequencies (f>10Hz) and are not affecting thus the frequency range of

interest (f<10Hz).



UNIT 1-PP

UNIT 2-PP

BUILDING-PP

UNIT 1 - FDD

UNIT 2 - FDD

BUILDING - FDD

UNIT 1 - SSI/COV

UNIT 2 - SSI/COV

BUILDING - SSI/COV

Figure 6.19. Modal identification applying the Peak Picking (PP), Frequency Domain Decomposition (FDD) and the reference-based covariance-driven Stochastic Subspace Identification (SSI-cov)

methods using ambient noise measurements

Table 6.3. Modal identification results for UNIT 1, UNIT 2 and BUILDING estimated using

parametric and non-parametric identification techniques

Mode type UNIT 1 UNIT 2 BUILDING

PP(Hz)/ FDD (Hz)

SSI (Hz, ξ %)

PP(Hz)/ FDD (Hz)

SSI (Hz, ξ %)

PP(Hz)/ FDD(Hz)

SSI (Hz, ξ %)

Mode1: Coupled

translational 1.65/1.65 1.65 0.8 1.65/1.65 1.65 0.9 1.65/1.65 1.65 0.8

Mode 2: Coupled

translational 1.91/1.90 1.91 1.3 1.91/1.91 1.91 1.1 1.91/1.91 1.91 0.8

Mode 3: Torsional 2.33/2.33 2.33 3.6 2.35/2.35 2.33 3.5 2.35/2.35 2.33 3.2

Mode 4: 1st

Longitudinal 3.50/3.50 3.47 5.4 3.58/3.58 3.52 5.8 3.54/3.58 3.51 6.4

Mode 5: 2nd

Longitudinal 5.20/5.20 5.15 3.0 5.20/5.22 5.16 1.1 5.20/5.20 5.15 2.1



Comparing the results between the different techniques, it is observed that the

estimated frequency values for the five well separated modes are very close to each

other (practically the same for the first three modes) for the two identification methods

applied as well as for the different system models identified. Similar orders and shape

types of the modes are estimated for the different system models (UNIT 1, UNIT 2 and

BUILDING) implying that the dynamic characteristics of the complex hospital building are

possible to be captured by monitoring and analyzing the two adjacent building units

separately. The mode shapes corresponding to the identified modes are presented in

Figures 6.20, 6.21 and 6.22. The building is exhibiting coupled sway and torsional modes

in the frequency range of interest, which are expected in case of geometric and structural

irregularities or eccentricities between the center of mass and center of rigidity. The

highly coupled obtained mode shapes confirm the complex vibrational characteristics of

the building especially for the first two identified frequencies. Figure 6.23 represents

indicatively for UNIT 1 the contribution of the transverse, longitudinal and torsional

motion in the first two modes.

The resonant frequencies of the two adjacent units are very close which may be

attributed to their similar mass and stiffness properties. In order to gain insight of the

modal behavior of the two units and to investigate the correlation between their mode

shapes, the modal assurance criterion (Allemang and Brown, 1982) for the identified

modes is quantified as:

Tj Ei

ij T Tj i Ej Ei

MAC

(6.6)

where φj is the eigenvector j from the experimental modal model of UNIT 1 and φEi the

eigenvector i from the experimental modal model of UNIT 2. MAC values are calculated

higher than 0.8 for the first, third and the fourth modes, approximately equal to 0.60 for

the fifth mode while for the second mode MAC value is found to be lower than 0.60.

Based on the MAC results, it is seen that mode shapes for the two building units are

identical for the first, third and fourth modes. For the second and fifth modes which

correspond to the same frequencies for both units, the mode shapes are not identical for

the UNIT 1 and UNIT 2 although being of similar type. This may be attributed to the

different geometrical and structural configurations of the two units. An interesting aspect

is also the fact that mode 3 is identified for both units as torsional, however the mode

shapes for the two structures are out of phase. Based on the above considerations the

two units cannot be considered as an entire monolithic building neglecting the influence

of the structural joint as they do not present a common modal behavior. In fact the

identified mode shapes reveal a coupling of the two building units under low vibration



(operational conditions). The first and second mode shapes are identified as coupled

translational modes mainly in the transverse direction. The difference between the two

first modes is the fact that for both units the torsional component in the second mode

shape is much more pronounced in comparison to the first one (Figure 6.23). Under no

interaction, the second mode shape would be expected to be a coupled translational

mode mainly in the longitudinal direction. Under strong ground motion however, due to

the strong nonlinearities which the systems are expected to experience and taking into

account the fact that the two units do not have common foundation, the interaction

between the two units may be completely different affecting consequently their seismic

response. For the above reasons the seismic vulnerability assessment is performed

considering the two units separately. The aim of the updating procedure presented

continuously is to calibrate the numerical models in order to reflect the elastic modal

behavior of the two separate structural units as identified through the analysis of the

noise measurements. Damping values are not considered in the implemented updating

formula as their computation includes high levels of uncertainties and are presented

herein only for the sake of completeness.

1st mode: 2nd mode: 3rd mode: 4th mode: 5th mode: Coupled

translational Coupled

translational Torsional 1st Longitudinal 2nd Longitudinal

Figure 6.20. Mode shapes corresponding to the five first indentified frequencies for UNIT 1




Figure 6.21. Mode shapes corresponding to the five first identified frequencies for UNIT 2






Figure 6.22. Mode shapes corresponding to the five first indentified frequencies for BUILDING

Mode shape 1 Mode shape 2

Figure 6.23. Contribution of the lateral components in the first two modes in the longitudinal and transverse direction for UNIT 1



6.4.3 System identification and operational modal analysis using seismic

recordings

Operational modal analysis has been performed using besides the ambient noise

measurements, also the earthquake events recorded by the permanent accelerometric

network. The seismic events recorded since the SOSEWIN network started to operate in

May 2012, which have been used for the analyses, are presented in Table 6.4. It should

be noted herein that no significant earthquake, in terms of damage potential, has

occurred within the time frame of the operating period.

The grid of the systems analyzed in MACEC varies depending on the earthquake and

more specifically on the sensors of the two building units that actually recorded the

seismic events. Only these sensors are used for the identification process and the modal

analysis for each earthquake. In Figures 6.24, 6.26 and 6.27 the grid models and the

modal identification results are presented indicatively for the Limnos earthquake case

(Limnos 24/5/2014, M=6.2, R=12.8km) based on both FDD and SSI methods. In ANNEX

B the grid models and analyses results of all earthquake events are summarized. For

specific seismic events (NW from Lake Langada 6/12/2013, Limnos 24/5/2014,

Kalamaria 16/7/2014, West from Kassandra peninsula in Halkidiki 22/8/2014) a broad

band seismometer was operating on the ground floor of UNIT 1 recording thus the input

motion. For these cases the corresponding input accelerograms and response spectra are

also presented (Figure 6.25 for the Limnos earthquake event 24/5/2014). Table 6.5

summarizes the modal identification results in terms of resonance frequencies for all

recorded earthquake events which are also compared to the corresponding results using

the noise measurements (FDD method). Results show that using the earthquake data it

is not possible to capture all frequencies of the structural systems. For almost all seismic

events, only the first, second and third modes are systematically identified. It is also

noticed that for most cases the frequencies are found slightly smaller in relation to the

identification results using noise measurements. It should be noted however that

ambient noise measurements were conducted at the building deploying a denser network

of stations equipped with velocimeters, which have a better amplitude resolution and a

lower internal noise than the MEMS, providing thus more accurate results regarding the

dynamic characterization of the building. In order to derive reliable results and determine

how the characteristics of real ground motion recordings (frequency content, duration)

affect the dynamic behavior of the monitored structural systems, more earthquake data

need to be collected and analyzed.



Table 6.4. Earthquake events used for OMA of the hospital building

Date Event Time Lateral Longitudinal Depth (km)

Magnitude (M

L)

12.5.2012 Thessaloniki 22:48:12.8 40.564 22.841 7.4 4

11.10.2013 Volvi, Thessaloniki 8:15:48 40.689 23.410 10 4.7

26.10.2013 West from Kassandra peninsula in Halkidiki 17:07:14:30 40.227 23.102 8.1 3.6

6.12.2013 NW from Lake Langada 17:00:52:2 40.799 22.938 9.5 2.6

24.5.2014 Limnos 09:25:02:1 40.286 25.375 12.8 6.2

16.7.2014 Kalamaria 16:14:58:0 40.569 22.948 12.2 3

22.8.2014 West from Kassandra peninsula in Halkidiki 4:27:54 39.935 23.431 13.5 5


Figure 6.24. Grid models of the different systems analyzed in MACEC for the earthquake events: Limnos 2014



Figure 6.25. Input acceleration in the longitudinal and transverse direction recorded at the

base of UNIT 1 and the corresponding elastic acceleration response spectra for Limnos, 24.05.2014 event

Figure 6.26. Modal identification applying the Frequency Domain Decomposition (FDD) and the Stochastic Subspace Identification (SSI) methods using earthquake recordings of Limnos, 24.05.2014

event




f1=1.60Hz f1=1.60Hz f1=1.60Hz

f2=1.88Hz f2=1.88Hz f2=1.88Hz

f5=5.15 f5=5.12 f5=5.12

Figure 6.27. Mode shapes of the identified modes of UNIT 1, UNIT 2 and BUILDING for the earthquake event of Limnos, 24.05.2014 event.

Chapter 6: Time-building specific vulnerability assessment of RC buildings using monitoring data 227


Table 6.5. Modal identification results for the recorded earthquake events compared to the corresponding results for the noise measurements (FDD)

EQ Thessaloniki 12/5/2012

Volvi, Thessaloniki 11/10/2013

West from Kassandra peninsula in Halkidiki

26/10/2013

NW from Lake Langada 6/12/2013

(Hz) UNIT 1 UNIT 2 BUILDING UNIT 1 UNIT 2 BUILDING UNIT 1 UNIT 2 BUILDING UNIT 1 UNIT 2 BUILDING

f1 1.60 1.61 1.61 1.60 1.60 1.60 1.60 1.60 1.60 1.64 1.64 1.64

f2 - - - 1.80 1.80 1.80 1.92 - 1.92 1.92 1.92 1.92

f3 - - - - - - - - - - - -

f4 - - - - - - - - - - - -

f5 5.10 5.10 5.09 5.08 5.10 5.10 5.10 5.08 5.08 5.04 5.04 5.04

EQ Limnos 24/5/2014

Kalamaria 16/7/2014

West from Kassandra peninsula in Halkidiki

22/8/2014 Noise measurements

(Hz) UNIT 1 UNIT 2 BUILDING UNIT 1 UNIT 2 BUILDING UNIT 1 UNIT 2 BUILDING UNIT 1 UNIT 2 BUILDING

f1 1.60 1.60 1.60 1.64 1.64 1.64 1.64 1.64 1.64 1.65 1.65 1.65

f2 1.88 1.88 1.88 - - - 1.96 1.96 1.96 1.90 1.91 1.91

f3 - - - - - - - - - 2.33 2.35 2.35

f4 - - - - - - - - 4.20 3.50 3.58 3.58

f5 5.15 5.12 5.12 5.7 5.7 5.7 5.16 5.16 5.16 5.20 5.22 5.20



6.5 Finite element model updating

Model updating aims at the “correction” or “update” of the initial finite element model

based on data processing, obtained from measurements conducted on the test structure

(Mottershead and Friswell, 1993). The main purpose is to modify iteratively updating

parameters to result in structural models that better reflect the measured data than the

initial ones. One of the key issues during the updating process is the selection of the

appropriate updating parameter. In general, if not serious geometrical modifications are

identified, as in the present test case, structural features, such as material or mass

properties, are likely to be selected as updating parameters in order to increase the

correlation between the observed dynamic response of the structure and the predicted

from the numerical modal model (Scodeggio et al., 2012). Other parameters such as soil-

structure interaction, condition and aging of the foundations after a strong earthquake,

the connection between structural elements which influence the modal properties, may

contribute in the updating process, however include high uncertainty levels and

additional tests may be required for their determination (e.g. non-destructive tests). For

the AHEPA case study, soil-structure interaction effects are not expected to be

pronounced as the soil is characterized as stiff clay with an average shear wave velocity

over the upper 30-35m equal to 450m/s (Figure 6.2). Besides, for the extracted modes

(particularly for the three first modes) that are used in the updating procedure, the

modal displacements extracted from the ambient vibration measurements corresponding

to the basement nodes are much smaller in comparison to the top floor nodes for both

buildings allowing the fixed base assumption. On the other hand the evaluation of the

condition and aging of the foundations after the Thessaloniki earthquake or the quality of

the connections between structural elements is not indicated as limited information is

provided by the blueprints and data from non-destructive tests are not available. An

extensive parametric study of the hospital buildings considering the variation in structural

parameters (e.g. modulus of elasticity) is conducted, investigating the sensitivity of the

model to material properties, and how the latter may affect the overall stiffness of the

structure. A manual updating scheme is applied considering only a limited number of

parameters, which however allows a good observation of the process in order to gain

complete insight on the effects of the sensitivity parameters on the structural behavior.

The initial numerical modal model of the buildings under study is based on the design

and construction documentation plans. The numerical modeling is conducted for the two

adjacent units separately using OpenSees finite element platform (Mazzoni et al., 2009).

Elastic beam-column and truss elements are employed to model the linear RC elements

(beams and columns) and masonry infills respectively. For the linear modeling of the



masonry infills a double strut model is adopted to represent the in-plane behavior of the

infill panel. Fixed base conditions are assumed for both structural models.

The updating procedure is performed not only to improve the frequencies of the

considered modes of the initial numerical model presented in Tables 6.6 and 6.7, but also

to calibrate the numerical mode shapes in order to fit the experimental data. Only the

third mode of the numerical modal model was identical to the respective experimental

one for both units. One the other hand the mode shapes of the first and second modes

needed to be updated in order to capture the coupled sway modes reflecting thus the

experimental results preserving at the same time the torsional mode shape of the third

mode. As sensitivity parameter for the updating procedure, the compressive strength of

the masonry infill, fm, is selected to take into account the uncertainties of the material

behavior as well as the possible heterogeneity between the material properties of the

different infill parts. Besides the masonry strength of the infills, also the sensitivity in the

concrete strength has been investigated as well as the combination of both parameters.

The updating procedure using the concrete strength showed that frequencies and mode

shapes were not affected significantly. Thus it was preferred to use only one sensitivity

parameter, namely the compressive strength of the infill panels, in order to avoid

complicated updating schemes and allow a better observation of the updating procedure.

The selection of the particular parameter is made as its definition includes high

uncertainty levels due to the fact that no data were available from the design and

constructions plans. A suite of numerical modal models is generated assuming a normal

distribution for fm and defining possible scenarios adopting different infill masonry

compressive strength values and configurations (Scodeggio et al., 2012). The random

properties of the masonry compressive strength, namely the mean value μ=3MPa and its

covariance COV=20% are defined according to Mosalam et al. (1997). For the initial

finite element models the compressive masonry strength is considered equal to the mean

value μ=3MPa. The different values of compressive strength for the considered updating

scenarios are subsequently computed based on the mean and standard deviation σ

according to the adopted normal distribution considering a limit range for the mean value

of μ-3≤ fm≤ μ+3 Then the elastic modulus in compression, Em, which is used as input

parameter to simulate the masonry infills, is estimated based on the adopted mean value

for the compressive strength according to the relation Em= 1000fm (Paulay and Priestley,

1992).

To take into account the heterogeneity of the masonry mechanical properties as well

as the possible variation between the material properties and the modulus of elasticity of

the different parts, several updating scenarios are investigated. In particular five

different scenarios are defined based on the variation in fm (or Em) and the considered



configurations of the masonry infills for the selection of the best model as illustrated in

Figure 6.28.

- Scenario 1: single value of elastic modulus for all the perimeter of the two buildings

Em

- Scenario 2: different values of elastic modulus for (a) the longitudinal Emlong and (b)

the transverse Emtransv infills

- Scenario 3: different values of elastic modulus for (a) the longitudinal infills

depending their location Emlong1 and Emlong2, (b) the transverse infills far from the joint

Emtransv1 and (c) the transverse infills close to the joint Emtransv2

- Scenario 4: different values of elastic modulus for (a) the longitudinal and (b) the

transverse infills building by building (UNIT1: Emlong1, Emtransv1 / UNIT2: Emlong2, Emtransv2).

- Scenario 5: different values of elastic modulus for all infills along the perimeter

regardless their location (Emlong1, Emlong2, Emlong3, Emlong4, Emtransv1, Emtransv2, Emtransv3,

Emtransv4).

Scenario 1 Scenario 2 Scenario 3

Em Em

Em

EmEm

Em Em Em

Emlong

Emtransv

Emlong

Emlong Emlong

Emtransv Emtransv

Emtransv

Emlong1

Emtransv1

Emlong1

Emlong2 Emlong2

Emtransv2 Emtransv2

Emtransv1

Scenario 4 Scenario 5

Emlong1

Emtransv1

Emlong2

Emlong1 Emlong2

Emtransv1 Emtransv2

Emtransv2

Emlong1

Emtransv1

Emlong2

Emlong3 Emlong4

Emtransv2 Emtransv3

Emtransv4

Figure 6.28. The different updating scenarios adopted within this study

Modal analyses for all the derived numerical modal models are performed in

OpenSees for the three dimensional elastic linear finite element models of the two

adjacent buildings separately (UNIT 1 and UNIT 2). Only one among them is considered

as the best model representing the measured dynamic response. The selection of the

best model is based on the evaluation of the Modal Assurance Criterion-MAC defined

according to Equation 6.6, where φj is the eigenvector j from numerical modal model and

φEi the eigenvector i from field monitoring test. The computation of the MAC values and

the correlation of the responses between the experimental and numerical modal models

are made at 18 nodes (2 nodes per floor corresponding to the sensor locations) for each

building unit. A good correlation between the two tested modes is considered to be



achieved for MAC values greater than 0.8. The scenario that represents most accurately

the experimental results for the modes under investigation is found to be the one

corresponding to the updating scenario 3. The elastic moduli in compression of masonry

infills adopted for this scenario were the following: Emlong1=3GPa (fm=μ=3MPa),

Emlong2=1.8GPa (fm=μ-2σ=1.8MPa), Emtransv1=3GPa (fm=μ=3MPa) and Emtransv2=4.8GPa

(fm=μ+3σ=4.8MPa).

Due to the complexity of the structure under study only the first three modes are

considered in the updating process, which represent the fundamental deformation modes

of the structure and activate approximately 80% of the total mass of the building units.

In Tables 6.6 and 6.7 the results of the updating methodology for UNIT 1 and UNIT 2 are

presented respectively. The eigenfrequencies and mode shapes of the updated finite

element models are compared to the initial ones as well as to the experimental results. It

is seen that for UNIT 1 the updated finite element model correlates well with the

experimental results for all the modes under investigation (MAC>0.8). For UNIT 2 on the

other hand, MAC values are high for the 1st and 3rd mode, indicating the satisfactory

correlation between analytically and experimentally calculated modal parameters,

whereas for the 2nd mode it was not possible to achieve MAC values greater than 0.8.

This may be attributed to the fact that the structural configuration of UNIT 2 (trapezoidal

plan section) did not allow to capture the 2nd mode shape and probably another

sensitivity parameter related not only to the structural stiffness (such as the masonry

compressive strength) but also to the storey mass or a combination of several

parameters related to both stiffness and mass, would be more appropriate. Given

however the difficulties in proper asserting the mass properties of the complex hospital

building (e.g. distribution of mass along height and floor), this parameter is not used in

the updating procedure as the associated uncertainties may reduce the accuracy of the

results.



Table 6.6. Comparison of the updated finite element model of UNIT 1 with the initial model and the experimental results (T: period, f: frequency)

Initial FEM T (sec)/f(Hz)

Mode shape of updated FEM T (sec)/f(Hz)

Mode shape of experimental model T(sec)/f(Hz) MAC

Coupled translational T1=0.69sec/f1=1.46Hz

0.96

T1=0.64sec/f1=1.56Hz T1=0.61sec/f1=1.65Hz


0.94

T2=0.53sec/f2=1.89Hz T2=0.52sec/f2=1.91Hz

Torsional T3=0.37sec/f3=2.70Hz

0.97

T3=0.37sec/f3=2.70Hz T3=0.43sec/f3=2.33Hz

Table 6.7. Comparison of the updated finite element model of UNIT 2 with the initial model and the experimental results (T: period, f: frequency)

Initial FEM T (sec)/f(Hz)

Mode shape of updated FEM T (sec)/f(Hz)

Mode shape of experimental model

T(sec)/f(Hz) MAC


0.98

T1=0.65sec/f1=1.54Hz T1=0.61sec/f1=1.65Hz


<0.8 due to the particular structural

configuration T2=0.53sec/f2=1.89Hz T2=0.52sec/f2=1.91Hz

Torsional T3=0.36sec/f3=2.77Hz

0.94

T3=0.35sec/f3=2.86Hz T3=0.43sec/f3=2.33Hz



6.6 Nonlinear finite element modeling

The nonlinear numerical modeling of the initial and updated structure is conducted using

OpenSees finite element platform (Mazzoni et al., 2009). Inelastic force-based

formulations are employed for the simulation of the nonlinear three-dimensional, with six

degrees of freedom, beam-column frame elements. The applied formulations allow both

geometric and material nonlinearities to be captured. Distributed material plasticity along

the element length is considered based on the fiber approach to represent the cross-

sectional behavior. Each fiber is associated with a uniaxial stress-strain relationship; the

sectional stress-strain state of the beam-column elements is obtained through the

integration of the nonlinear uniaxial stress-strain response of the individual fibers in

which the section is subdivided. For both initial and updated units, the material strength

properties for concrete and steel summarized in Table 6.1, are used for the definition of

the stress-strain relationship. It should be noted that the consideration of the characteristic

strength values of the concrete and steel materials for the analyses may lead to conservative results.

However since in-situ tests were not conducted in order to extract reliable mean values of the

materials’ strength and as the main goal was to identify the material properties (concrete and

masonry) through the updating procedure, it was decided to proceed the analyses considering the

characteristic strength values. The Popovics concrete model (Popovics, 1973) is used to

define the behavior of the concrete fibers, yet different material parameters are adopted

for the confined (core) and the unconfined (cover) concrete. Due to the fact that the

building units are designed according to low seismic code provisions with non sufficient

transverse reinforcement, the element sections are considered to be unconfined. The

uniaxial ‘Concrete04’ material is used to construct a uniaxial Popovics concrete material object

with degraded linear unloading/reloading stiffness according to the work of Karsan and

Jirsa (Karsan and Jirsa, 1969) with zero tensile strength. The steel reinforcement is

modeled using the uniaxial ‘Steel01’ material to represent a uniaxial bilinear steel

material with kinematic hardening described by a nonlinear evolution equation. For the

nonlinear modeling of the masonry infills inelastic struts are used to represent infill walls

as they provide sufficient accuracy to capture key characteristics of the force-

displacement response. The nonlinear behavior of the infill panels is reflected by assigned

axial load hinges on the diagonal struts whose characteristics are determined as given in

FEMA-356 (FEMA, 2000). Each strut is assigned an elasto-plastic force displacement

relationship representing initial stiffness and peak strength behavior of the masonry. The

infill material strength for the initial models is taken equal to the mean value adopted for

the updating procedure (μ=3MPa) while for the updated models the masonry strength is

defined based on the selected updated scenario described in the previous section. The

structural models do not include any contribution from non-structural components or



from gravity-load resisting structural elements that are not part of the lateral resisting

system. Since non-destructive tests were not possible to be conducted and details for the

formation of the beam-column joints were not available from the blueprints, rigid

connection is considered for the modeling of the joints between beam and column. To

take into account the rigidity against the in-plane deformation of the floor slabs,

diaphragm constraint is employed. For both structural models fixed base conditions are

assumed.

6.7 Selection of the input motion

A representative set of accelerograms is selected to perform the non-linear incremental

dynamic analysis. The selected earthquake scenario consists of a set of 15 real ground

motion records (Table 6.8) obtained from the European Strong-Motion Database

(http://www.isesd.hi.is). They are all referring to stiff soil conditions classified as soil type B

according to EC8 (CEN, 2004) with moment magnitude (Mw) and epicentral distance (R)

that range between 5.8<Mw<7.2 and 0<R<45km respectively. Soil type B is the soil

category of the foundation soil according to a detailed geotechnical survey performed in

the site (Anastasiadis et al., 2001). In order to eliminate potential source of bias in

structural response, the selection of pulse-like records is avoided. The primary selection

criterion was the average acceleration spectra of the set to be of minimal “epsilon”

(Baker and Cornell, 2005) at the period range of 0<T<2sec with respect to the regional

acceleration spectrum adopted from SHARE for a 475 year return period

(http://portal.share-eu.org:8080/jetspeed/portal/). The optimization procedure was performed

making use of the REXEL software (Iervolino et al., 2010). The mean normalized elastic

response spectrum of the records is illustrated in Figure 6.29 in comparison with the

corresponding reference spectrum adopted from SHARE. It is observed that a good fit

between the two spectra is achieved. Before applying the selected records, the real

seismic records are first subjected to baseline correction and filtering. In particular, a

Butterworth bandpass 4th order filter type in the frequency range from f1=0.25 Hz to

f2=10 Hz and a linear type baseline correction were applied to all records using

Seismosignal software (Seismosoft, Seismosignal 2011). ANNEX C summarizes the

acceleration time histories as well as the elastic acceleration response spectra of the

seismic records used as input motion.



Figure 6.29. Normalized average elastic acceleration response spectrum of the input motions

compared with the corresponding reference spectrum adopted from SHARE for a 475 year return period (http://portal.share-eu.org:8080/jetspeed/portal/)

Table 6.8. List of records used for the IDA

Earthquake Name Station ID Date Mw R

[km] PGA_X [m/s2]

PGA_Y [m/s2]

Waveform ID

Friuli (aftershock) ST28 15/9/1976 6.0 14 1.3841 2.3189 000147 Izmit

(aftershock) ST3265 13/9/1999 5.8 23 1.8983 1.2837 006959

Montenegro (aftershock) ST76 24/5/1979 6.2 21 1.6273 1.3034 000231

South Iceland ST2488 17/6/2000 6.5 17 3.9202 2.3852 004676 Kalamata ST164 13/9/1986 5.9 10 2.1082 2.9095 000413

Izmir ST162 6/11/1992 6.0 41 0.6527 0.8007 000549 Potenza ST99 3/2/1998 5.8 36 0.7848 0.8544 000944

Ano Liosia ST1101 7/9/1999 6.0 17 1.171 1.0661 001314 Tithorea ST166 18/11/1992 5.9 25 0.3709 0.2744 000550

Ano Liosia ST1258 7/9/1999 6.0 14 2.3842 2.1588 001714 South Aegean ST1310 23/5/1994 6.1 45 0.5976 0.4023 001881

Ano Liosia ST1255 7/9/1999 6.0 20 0.8549 0.7604 001711 Valnerina ST83 19/9/1979 5.8 39 0.3855 0.2303 000244

Friuli (aftershock) ST35 15/9/1976 6.0 21 4.6466 4.9562 000126 Duzce 1 ST3134 12/11/1999 7.2 11 1.0914 0.7137 006494

6.8 Incremental dynamic analysis (IDA)

The IDA procedure (Vamvatsikos and Cornell, 2002) is used to determine the seismic

performance and assess the seismic vulnerability of the initial and updated finite element

models of UNIT 1 and UNIT 2. Within this study the damage measure is expressed in

terms of maximum interstorey drift ratio, which is generally used as engineering demand

parameter in assessment studies of frame buildings as it relates well to dynamic

instability and structural damage (Rossetto and Elnashai, 2003). More specifically, the

maximum peak SRSS drift, maxISD (i.e. the maximum over all stories of the peak of the

square-root-sum-of-squares of each storey’s drift) in the two principal directions is

selected (Wen and Song, 2002). The seismic intensity is described using peak ground



acceleration (PGA) recorded on soil type B according to EC8 (CEN, 2004). PGA is selected

as intensity measure due to the fact that the derived curves are incorporated in an

operational tool for Early Earthquake Warning and rapid post-event damage assessment

that will be used by the civil protection authority of the hospital. In this context, PGA is

considered appropriate due to its simple computation in real-time and its efficient use by

the authorities.

IDA is conducted for the structural models by applying the 15 progressively scaled

records of Table 6.8. In particular, a PGA-stepping tracing algorithm is applied for each

record with an initial step of 0.1g, a step increment of 0.1g and a first elastic run at

0.05g. For certain records it was necessary to reduce the step size of the algorithm to

increase the accuracy close to the flatline of the IDA curve. The minimum number of

converging runs is allowed to vary from 10 to 15 per record depending on the

characteristics of the structure and the record itself.

The fiber based approach that has been adopted for the nonlinear modeling of the

structures simulates sidesway collapse associated with strength and stiffness degradation

along the total length of beams and columns. The section and reinforcement details

presented in Figures 6.3 and 6.4 reveal stronger columns – weaker beam formations.

The analysis model does not directly capture column shear failure as the columns in this

study are expected to yield first in flexure rather than experiencing direct shear failure,

as in the case of squat non-ductile RC columns. Collapse modes for the particular building

units are related to column flexural failures in the lower storeys which are defined for

each ground motion based on the intensity (peak ground acceleration) of the input

ground motion that results in structural collapse, identified in the analysis by excessive

interstorey drifts.

By interpolating the derived pairs of PGA and maxISD for each individual record 15

continuous IDA curves for each structural model are derived. Figure 6.30(b) illustrates

representative IDA curves for each record in terms of PGA for the updated finite element

models of UNIT 1 and UNIT 2. For the purpose of the present study, two limit states are

defined in terms of interstorey drift ratio, representing the immediate occupancy (IO)

and collapse or near collapse prevention (CP) performance levels. The first limit state,

namely the Immediate Occupancy corresponds to the yielding point where the elastic

branch gives place to the post-elastic branch. The second limit state is assigned at a

point where the IDA curve is softening towards the flat line, but at low enough values of

maxISD so that we still trust the structural model (Vamvatsikos and Cornell, 2004). Thus

different IO and CP limit state values are chosen on the IDA curves for the same

structure depending on the reference finite element model (initial or updated) and the

individual record. For both initial and updated models of UNIT 1 and UNIT 2 the median



of the first limit state is found equal to 0.1%, which is in line also with the proposed limit

value of HAZUS for moment resisting infilled frame buildings. The median of the defined

CP limit states in terms of SRSS interstorey drift (maxISD) is used to define the CP limit

state of the structure, which for both structures is found to be equal to 1.4% and 1.1%

for the initial and updated models respectively. The assignments of the IO and CP limit

state points on the IDA curves of the updated units are presented in Figures 6.30(a) and

(b). The dispersion that is observed in the definition of the collapse prevention limit value

may be attributed on one hand to the record-to-record variability in terms of frequency

content and duration and on the other hand to the fact that PGA is used as intensity

measure as in this case the seismic response and vulnerability depends on the input

ground motion sets (Kwon and Elnashai, 2007).

(a)

(b)

Figure 6.30. Assignments of the immediate occupancy (IO) and collapse prevention (CP) limit damage state points on the IDA curves for the updated units



6.9 Derivation of fragility curves

The results of the IDA (PGA - maxISD values) are used to derive the fragility curves for

both analyzed buildings, expressed as a two-parameter lognormal distribution functions.

Equation 6.7 represents the cumulative probability of exceeding a damage state DS

conditioned on a measure of the seismic intensity IM:

ln ln

/IM IM

P DS IM

(6.7)

where, Φ is the standard normal cumulative distribution function, IM is the intensity

measure of the earthquake expressed in terms of PGA (in units of g), IM and β are the

median values (in units of g) and log-standard deviations respectively of the building

fragilities and DS is the damage state. The median values of PGA corresponding to the

prescribed performance levels are determined based on a regression analysis of the

nonlinear IDA results (PGA – maxISD pairs) for both building units. More specifically a

linear regression fit of the logarithms of the PGA – maxISD data which minimizes the

regression residuals is adopted in the analysis cases. Figure 6.31 presents the PGA -

maxISD relationships for the updated models of both UNIT 1 and UNIT 2, where it is

noticed that the results show similar distribution and curve fitting.

Three primary sources of uncertainties are generally taken into account for the

estimation of the total variability associated to each damage state for conventionally

derived fragility curves, namely the variability associated with the definition of the

damage states, the capacity of the structure and the seismic demand. Demand

uncertainties are associated to the effects of ground motion record-to-record variability

on building response. Capacity uncertainty reflects the variability of structural properties

as well as the fact that the modeling procedures are not perfect. Damage state definition

uncertainties are due to the fact that the thresholds of the damage indices or parameters

used to define damage states are not known (Selva et al., 2013). In the present study

the uncertainty associated with the demand is taken into consideration by calculating the

dispersion of the logarithms of PGA – maxISD simulated data with respect to the

regression fit. The log-standard deviation value in the capacity is assumed to be 0.3 for

the low code structures following the HAZUS prescriptions (NIBS, 2004). Uncertainties in

how well the nonlinear simulation model represents the behavior of the real building as

well as the highly nonlinear structural behavior near collapse are incorporated in the

collapse assessment and are reflected in the fragility curves through the consideration of

the capacity uncertainty. As far as the uncertainty in the definition of the damage states

is concerned, the damage limit values are defined on the IDA curves and since they are



considered building-specific, the additional uncertainty related to the definition of the

damage states is not taken into consideration. Based on the above considerations, the

definition of the limit state values is implicitly related to the material properties and

structural modeling and is therefore incorporated in the uncertainty associated with the

capacity. As discussed in (Michel et al., 2012) and (Perrault et al., 2013) in-situ tests and

vibration measurements may improve the knowledge of the building’s response and its

seismic behavior reducing thus the epistemic uncertainties associated with the capacity.

In the present study the use of ambient noise measurements to improve the knowledge

regarding the elastic behavior of the structure may reduce the epistemic uncertainties for

the IO limit state, however for the definition of the CP state, there are significant

underlying uncertainties which cannot be neglected as nonlinear behavior of structures

under strong ground motion introduces variations of the modal parameters and

influences their seismic response. Therefore the uncertainty in the capacity is not further

reduced. Under the assumption that the log-standard deviation components of demand

and capacity are statistically independent, the total log-standard deviation is estimated

as the root of the sum of the squares of the component dispersions. The herein

computed log-standard deviation β values of the curves vary from 0.6 to 0.68 for the

considered finite element models of the adjacent building units.

Fragility curves are derived for the initial and updated finite element models of UNIT 1

and UNIT 2. The initial as built numerical models are based on the available design plans

and correspond to the initial state of the structures (“building-specific”), whereas the

updated models reflect the measured responses and therefore represent their actual

state (“time-building specific”).

The calculated “building-specific” fragility curves of UNIT 1 and UNIT 2 that

correspond to their initial state are evaluated through their comparison with conventional

curves from the literature (Pitilakis et al., 2014a) that are derived for representative

models of the same typology (high-rise, regularly infilled, moment resisting frame

structures designed with low seismic provisions). More specifically, in Figure 6.32 the

derived curves are compared with the generic curves proposed by Kappos et al. (2003;

2006) for the specific typology. It is noted that most of the work presented in Kappos et

al. (2003) was carried out by the same authors within the framework of the RISK-UE

project. The differences between the results (given in terms of fragility functions) of

Kappos et al. (2003) and Kappos et al. (2006), are probably due to slight geometric

differences adopted for the studied RC building typologies. A good match between the

curves is observed for the IO limit state as both generic curve sets are very close to the

calculated ones. However for the CP state it is seen that the “building-specific” curves

corresponding to the as-built state of the hospital case study are comparable only with



the curves of Kappos et al. (2003) and differs significantly with the respective curves of

Kappos et al. (2006), which is indicative of the non negligible variability that may be

observed between generic fragility curves.

The initial fragility curves are further validated through the computation of the

expected damage probability of the hospital building for the 1978 destructive earthquake

in Thessaloniki (Penelis et al., 1988) as they are considered to better reflect the state of

the structure at the time of the event which occurred quite soon after their construction

(in 1971). For a representative intensity value for the specific seismic event equal to 0.3g

the probabilities of slight damage (IO state) and collapse (CP state) according to Figure

6.32 are approximately estimated to 99% and 1% respectively. These probabilities are

consistent with the actual reports of that time that no considerable earthquake damage

was observed for the specific building.

In Figure 6.33 the updated numerical models are compared with the initial ones for

both building units. The updated curves present a shift to the left in comparison to the

initial ones, indicating an increase in the structures’ vulnerability which is more

noticeable for the CP limit state and for higher intensities. Since this difference in the

fragility between the initial and updated models is not attributed to geometrical

modifications but to the variation and distribution of material properties, it could be

assumed that the increase in the buildings’ fragility is in fact an evidence of potential

degradation of the structure over time. As no significant damages have been reported for

the specific building during past earthquake events, the structural deterioration may be

related to aging effects, which are further analyzed in the following section.

Figure 6.31. PGA-maxISD relationships for updated finite element models of UNIT 1 and UNIT 2



Figure 6.32. Comparative plots of the initial fragility curves derived for the two adjacent building units with the corresponding fragility curves provided by Kappos et al. (2003;2006)

Figure 6.33. Comparative plot of the “building-specific” fragility curves derived for the initial and updated models of UNIT 1 and UNIT 2

6.10 Comparison with the time-dependent fragility curves of the hospital building units

6.10.1 Deterioration modeling due to corrosion

Time-dependent fragility curves are derived for both hospital units considering aging

effects due to rebar corrosion following the analytical methodology presented in Chapter

4. Corrosion may affect an RC structure in a variety of ways (e.g. cover spalling, loss of

steel-concrete bond strength, loss of steel cross sectional area) resulting to loss of

ductility, reduction of load bearing capacity and finally to more brittle failure

mechanisms. The aim of the present application is twofold: to apply the proposed

methodology on a real building case and to compare the “time-building specific” fragility

curves derived in the previous section with the time-dependent curves increasing the

reliability of the methodologies and results.



The probabilistic model proposed by FIB- CEB Task Group 5.6 (2006) is adopted for

the computation of the corrosion initiation time, Tini, due to chloride ingress. The

statistical characteristics of the parameters involved in the computation of Tini (Table

6.9), adopted in the corrosion model of Chapter 4 for a relatively high corrosion scenario

are considered appropriate also for the coastal city of Thessaloniki. For a cover depth

equal to 20mm, the mean value of Tini is estimated approximately equal to 7 years.

Table 6.9. Statistical characteristics of parameters affecting the chloride induced corrosion of RC elements adopted in the present study (according to the methodology of Chapter 4)

Parameter Mean Coefficient of variation (cov) Distribution

Cover Depth (mm) α 20 0.40/0.32 Lognormal Environmental function ke 0.67 0.17 Normal

Chloride migration Coefficient (DRCM,0) (m2/s) 1.58E-11 0.20 Normal Aging exponent n 0.362 cov=0.677 , a=0.0, b=0.98 Beta

Critical Chloride Concentration (Ccrit) wt % cement 0.6 cov=0.25, a= 0.2, b=2.0 Beta

Surface Chloride Concentration (Cs) wt % cement 1.283 0.20 Normal

Rate of Corrosion (icorr) mA/cm2 2 0.25 Normal

A 45-year corrosion scenario is adopted, which is considered representative of the

current state of the hospital building units. The chloride induced corrosion effects that are

taken into account, are the section area loss of reinforced bars (Ghosh and Padgett,

2010) and the concrete cover strength reduction (Coronelli and Gambarova, 2004;

Simioni, 2009). The effects of corrosion are assumed to be distributed uniformly around

the perimeter and along the concrete members. Table 6.10 summarizes the mean

percentages (%) of reinforcement area loss and cover concrete strength reduction due to

corrosion for the different RC elements of the structures under study within the elapsed

time (t-Tini). Results show that beams seem to be more affected regarding the steel area

loss in comparison to columns. On the other hand similar concrete cover reduction values

are observed for both beams and column elements.

Table 6.10. Loss of reinforcement (%) and concrete cover strength reduction (%) for the considered corrosion scenario (t=45 years)

UNIT 1 UNIT 2

Steel area loss (%) Concrete cover reduction (%) Steel area loss (%) Concrete cover

reduction (%)

Beam 14 59 13 59

Column 8 59 8 56



6.10.2 Derivation of the time-dependent fragility curves and comparison with

“time-building specific” curves

Using the seismic records of Table 6.8, IDA analysis is performed for the corroded

building units following the same procedure as described in Chapter 3, Section 3.6 for the

initial and updated models. The median IO limit value is defined based on the IDA results

and is found equal to 0.1% for UNIT 1 and UNIT 2 respectively. The median of the

defined CP values is estimated equal to 1.0% for both corroded units, which is a slightly

lower value compared to the 1.1% estimated for the updated models. The assignments

of the IO and CP limit state points on the IDA curves of the corroded units are presented

in Figure 6.34. The median PGA values for the two damage states are computed based

on the regression analysis of Figure 6.35 while the standard deviation is calculated

accounting for the variability associated with the definition of the limit state value, the

capacity of each structural type and the seismic demand.

The fragility curves of the initial, updated and corroded models of both UNIT 1 and

UNIT 2 are compared in Figure 6.36, while the fragility parameters (median and log-

standard deviation) of the different cases are summarized in Table 6.11. As it can be

seen, the vulnerability of the structures increases over time due to corrosion, as

expected. This increase is more noticeable for the CP limit state. Comparing the fragility

between corroded and updated models, it is seen that for the IO limit state, no significant

difference between the curves is observed. For the CP state however, the curves

corresponding to the corroded models present a greater shift to the left in comparison to

the respective curves of the updated models indicating that the analytical procedure

considering aging effects results to higher fragility. In particular the difference in the

median PGA values corresponding to the CP state for the corroded models in relation to

the updated ones is in the order of 8-13% for UNIT 1 and UNIT 2. The 1978 Thessaloniki

event is used again for the evaluation of the damage probabilities for the different cases

that are investigated. For the IO state (slight damage level), no significant differences

are observed in comparison to the initial state of the building as the probability is high for

all cases (approximately 95%). For the CP state however the probability of occurrence is

increased compared to the as built state of the structure from 1% to 3% and 5%

respectively for the updated and corroded case.



a).

b). Figure 6.34. Assignments of the IO and CP limit damage state points on the IDA curves for

the corroded units

Figure 6.35. PGA-maxISD relationships for the corroded (t=45years) hospital buildings UNIT 1 and UNIT 2



Figure 6.36. Comparative plots of the fragility curves corresponding to the initial, updated and corroded models of UNIT 1 and UNIT 2

Table 6.11. Parameters of the derived fragility curves for the initial and updated finite element models for UNIT 1 and UNIT 2

RC building Finite Element Model Median PGA (g)

Dispersion IO CP

UNIT 1 Initial 0.059 1.49 0.67

Updated 0.057 1.21 0.64 Corroded 0.050 1.11 0.61

UNIT 2 Initial 0.074 1.35 0.68

Updated 0.065 0.99 0.6 Corroded 0.073 0.86 0.63

6.11 Discussion and Conclusive remarks

The “time-building specific” or actual seismic vulnerability of one of the main buildings of

the most important hospital in Thessaloniki (AHEPA) has been assessed based on

ambient noise field monitoring data. The special feature of the target building is that it is

composed of two adjacent tall units that are connected with a structural joint. Ambient

noise measurements were used to derive the experimental modal model of the two

adjacent buildings first separately, and then for the entire building analyzed as one,

taking into account the interaction of the two building units and identify their modal

properties based on system identification and OMA respectively. The identified modal

parameters were found very close for the different identification methods (non-

parametric and parametric) applied as well as for the different system models analyzed,

implying that the dynamic characteristics of the hospital building analyzed as one are

possible to be captured by monitoring and analyzing the two adjacent buildings

separately.

The modal identification results based on ambient noise measurements were used to

update and better constrain the initial finite element models of the two adjacent units,

which were based on the design and construction documentation plans provided by the

Technical Service of the hospital. A sensitivity parameter related to the structural



stiffness was adopted for the updating procedure, namely the compressive masonry infill

strength. In general a good correlation with the experimental results was achieved for

both building units.

Incremental dynamic analysis was performed for the initial and updated structural

models to evaluate the seismic performance of the building units when their actual state

is taken into account. The fragility functions were derived for the IO and CP limit states in

terms of PGA for both units. It was shown that the use of conventional generic fragility

curves, although appropriate for assessing fragility and losses in a regional/urban scale,

may lead to inaccurate fragility and loss estimates in the case of individual building

assessment, which constitute crucial components in the framework of decision making

and risk mitigation strategies (e.g. seismic safety and rehabilitation costs). Moreover, an

overall increase in the structures’ fragility for the updated models is observed in

comparison to the ones corresponding to their initial state, which is attributed to

deterioration phenomena affecting progressively the building over time. In order to

increase the reliability of the derived results, the updated “time-building specific” fragility

curves are compared with the time-dependent curves where aging effects due to rebar

corrosion are taken into account through the analytical simulation of steel area loss and

concrete cover strength reduction for a 45-year corrosion scenario adopting the

methodology presented in detail in Chapter 4. Although the applied methodologies are

quite different approaches for assessing the actual structural condition, both result to an

increase of the seismic vulnerability in comparison to the initial, “as built” state of the

hospital building. In general, a good correlation between the “time-building specific” and

time-dependent fragility curves is observed. The fact that for the CP state, the structures’

fragilities appear to be higher for the corroded case may be attributed to the relatively

high rate of corrosion that was considered indicating that a conservative corrosion

scenario/model was adopted for the hospital building case. Combining the analytical

methodology with in-situ visual inspections would allow a more realistic quantification of

the corrosion effects on the different elements instead of considering these effects to be

uniformly distributed. For example a distinction between the external and the internal

elements should be accounted for as the latter are much less exposed to corrosion

phenomena. In any case, results indicate that potential degradation mechanisms that

may affect the structural condition over time should not be ignored especially in the case

of buildings with strategic interest (e.g. hospital) as this may lead to an underestimation

of their real vulnerability.

Overall the study presented in this chapter, provides further insight on the

assessment of the “time-building specific” seismic vulnerability of typical RC buildings

using ambient noise field monitoring data, presenting an integrated methodology where



the actual state of the structure is taken into account (degradation due to time, possible

pre-existing damages, changes in geometry and mass distribution etc). Thus the

presented methodology can be used to yield more reliable structural models with respect

to their real conditions in terms of structural detailing, mass distribution and material

properties. However the analysis results of monitoring data (e.g. ambient noise

measurements) should be used with caution when trying to extract information for the

instrumented building such as the dynamic properties.

It should be noted herein that ambient vibration measurements may provide

information regarding the impact of degradation phenomena (such as corrosion) on the

global behavior by tracking changes in modal parameters (frequencies, mode shapes)

with time. In order to quantify locally aging (corrosion) effects on the RC elements, also

non-destructive tests are required in order to gain insight regarding the effects on a

component level. Furthermore the proposed methodology should be extended for “real-

time” risk assessment and post-seismic fragility updating. As an example, by exploiting

the computing power of the strong motion sensing units installed in AHEPA, the “time-

building specific” fragility curves derived in this study allow the implementation of

building-customized alerting procedure suitable for performing an automatic building

tagging (Bindi et al., 2015b; Parolai et al., 2015). In this context, the use of field

monitoring data will contribute in reducing the uncertainties associated with the risk

assessment procedure improving seismic safety and allowing the development of robust

real time assessment tools and appropriate risk mitigation strategies.




CHAPTER 7

Conclusions – Limitations – Recommendations for future research

7.1 Summary of findings and contributions

An efficient seismic risk assessment tool that could be utilized by decision makers, civil

protection authorities and scientists in order to establish emergency plans and mitigation

strategies on a regional or site-specific scale, requires the reliable vulnerability

assessment of the structures. However, in most of the existing studies assessing the

vulnerability of reinforced concrete (RC) buildings, it is assumed that the structures are

optimally maintained during their lifetime neglecting the impact of progressive

deterioration due to various time-dependent mechanisms. Moreover RC buildings are

considered fixed to their base ignoring the presence of the soil beneath their foundation,

which may be realistic only when the structure is founded on rock or very stiff soil. A

better understanding on the effects of deterioration mechanisms acting during the

structure’s lifetime as well as the influence of the base conditions on the structural

performance, is therefore essential to reduce a great deal of uncertainty associated with

the seismic vulnerability assessment of RC buildings. The probabilistic treatment of these

uncertainties through the use of the so-called fragility (or vulnerability) curves allows the

efficient integration of the physical vulnerability components to the risk assessment

study. In this context the use of field monitoring data for identifying the actual state and

vulnerability of existing structures becomes an attractive tool for reducing uncertainties

involved within the risk assessment procedures and rapid damage assessment

frameworks.

Stemming from the general lack of seismic vulnerability assessment studies for RC

buildings that take into consideration the effects of progressive deterioration and soil-

structure interaction (see Chapter 2), one of the most significant contributions of the

present research is the proposition and quantification of an analytical methodology to

estimate the physical vulnerability of RC frame buildings subjected to seismic motion

CHAPTER 7:Conclusions – Limitations – Recommendations for future research 250


taking into account aging (Chapter 4) and SSI effects (Chapter 5). Overall, more than

10,000 nonlinear dynamic analyses were performed for the different structural

configurations and time scenarios.

Aging and SSI effects are incorporated in the analytical vulnerability assessment

methodology of RC buildings described in Chapter 3. In order to derive generic fragility

curves and increase the reliability of the results, seven RC moment resisting frame

buildings were selected of varying typologies designed to different seismic code levels.

The proposed methodological framework for the fragility curve generation was

highlighted analyzing the intact, fixed base reference frame buildings. Moreover in order

to investigate the impact of infill panels on the response of RC frames, representative

models of different height and code design classes were analyzed considering regularly

and irregularly contributed infills along the height of the structures. The derived fragility

curves showed that the highest fragility values were observed for the buildings with no

seismic code provisions. Even when compared with the models designed with low seismic

code level the median values of the latter were considerably higher being thus less

vulnerable. The probability of exceeding especially the collapse prevention state

decreases significantly when the buildings are designed with high seismic code

provisions. It is also seen that the seismically designed bare frames are more vulnerable

for both damage states compared to the infilled ones as the presence of the infill walls

significantly increases the strength and stiffness of the structures. In particular, the

regularly infilled buildings present lower vulnerability values with respect to the ones with

a pilotis. Thus, as expected, the presence of the soft ground storey has a less favorable

effect on the overall capacity of the structures due to the localization of inelastic

displacement demand at the bottom bare storey. However, the irregularly infilled frames

may have either a favorable or detrimental effect in fragility of reference bare frames

depending on the structural typology and code design level (e.g. seismically or non-

seismically designed frames). The derived fragility curves of the bare frame and infilled

structures were validated through their comparison with literature curves for the same

building typologies. In general the comparison between the proposed and the literature

curves is judged satisfactory. The scatter observed between the curves reveal the high

aleatory and epistemic uncertainties associated with the different fragility curves found in

the literature. The high scatter of the curves corresponding to the collapse prevention

damage state can be attributed to the fact that the structural behavior near collapse is

highly nonlinear and depends significantly on the modeling assumptions and analysis

methods that have been adopted in each study. Furthermore the variability between the

curves corresponding to the adopted damage states is noticed to be higher for the infilled

structures as the modeling techniques adopted for the simulation of the infill panels and



the definition of their material properties may vary significantly between the different

studies affecting thus the vulnerability results. Based on the previous findings it becomes

evident that although conventional generic fragility curves, derived usually for simplified

finite element models, may be appropriate for seismic fragility and loss assessment on a

regional/urban scale, their use in the case of individual building assessment may not

always lead to reliable fragility and loss estimates, which have significant impact on the

seismic safety and rehabilitation costs especially for buildings with strategic interest.

Traditionally the structural vulnerability implicitly refers to the intact, as-built state of

the structures assuming an optimum plan of maintenance. However different time-

dependent mechanisms acting on the structures during their lifetime, may lead to

significant deterioration levels when they are not subjected to the required interventions.

This issues become even more crucial in the presence of seismic hazard. In Chapter 4,

time-dependent probabilistic fragility functions were derived considering chloride induced

corrosion effects. Three main aspects for corrosion were included in the analysis, namely

the loss of reinforcement cross-sectional area, the degradation of concrete cover and the

reduction of steel ultimate deformation. Different corrosion initiation times were

estimated depending on the structural characteristics. Thus, it was seen that corrosion

starts to affect the buildings designed with no or low seismic code provisions much earlier

(Tini7years) compared to the structures designed with high seismic code levels

(Tini14years). It was shown that for the given corrosion scenario, beams were more

affected compared to the columns as their reinforcement layout included steel bars of

lower diameters. In general the consideration of corrosion effects led to an increase the

fundamental period of the structures with time implying decreasing progressively the

stiffness of the systems. Pushover analyses that were conducted for the different

structures and time scenarios under study, showed that due to effects of aging, the

structures undergo a progressive strength and stiffness degradation as well as a loss of

ductility over time. Moreover the comparative dynamic analysis that was performed for

the structural models at different points in time, showed that that corrosion effects may

result to the variation of the failure mechanisms over time reducing the resistance and

loading bearing capacity of the structures. Furthermore the definition of the collapse

prevention limit state based on the IDA results for the considered time scenarios

revealed a decrease of the CP limit values over time for the different structures analyzed.

Overall, a significant increase in the seismic fragility of the structures was observed over

time due to corrosion for both bare frame and infilled buildings, highlighting the

importance of considering the deterioration effects due to aging on the seismic

vulnerability of structures. Results show that the increase in the structures’ fragility is

much more pronounced for the bare frame models and the CP limit state resulting to an



average decrease of the corresponding median intensity measure value (Sa(T1, ξ%)) up

to 40% after 75 years due to corrosion. Buildings designed only for gravity loads are

expected to experience greater increase in fragility over time in comparison to the

structures which have been designed according to seismic code provisions. The

consideration of regularly infilled walls was shown to yield a substantial decrease in

fragility of both the initial as-built and corroded bare frame structures. Finally for the

bare frame models, simple time-dependent models were introduced for the efficient

assessment of the time-dependent shift in the fragility parameters for each damage state

due to corrosion, allowing the estimation of the fragility parameters at any point in time

without conducting complete fragility analyses.

Besides aging, other important effects that can significantly contribute to the

building’s seismic fragility are the soil condition affecting the foundation compliance and

the soil-structure interaction. Due to the fact that the incorporation of SSI phenomena in

the analysis is generally believed to reduce the seismic demand and consequently the

corresponding structural damage, their effects in fragility modeling is generally

neglected. In Chapter 5, probabilistic fragility functions were derived considering SSI

and site effects for both linear and nonlinear soil behavior. In general, it was shown that

the conventional way of calculating building fragility with the hypothesis of fixed base

structure may lead to unconservative results. In particular the consideration of SSI and

site effects under both linear and nonlinear soil behavior may significantly affect the

structural performance increasing considerably the structure’s seismic vulnerability

compared to the reference case where the structure is assumed as fixed base and no SSI

or site effects are taken into account. When soil nonlinearity is introduced these effects

are generally expected to have lower impact on the structure’s fragilities for higher levels

of seismic loading. Moreover it was shown that for linear soil behavior, the fragility

curves derived for the coupled SSI approach have practically no difference with the

uncoupled fixed base model where site effects are taken into account. On the other hand,

nonlinear SSI leads to an increase of the structure’s vulnerability compared to the

corresponding fixed base model. The latter could be attributed to the complex nonlinear

behavior of the underlying soil that may introduce additional translation and rotation

effects to the structure yielding higher drift demands. Overall, among the analyzed cases,

the uncoupled fixed based model where site effects are linearly modeled shows the

highest vulnerability. Thus, while avoiding the computational cost introduced by the

coupled SSI models, the use of the fragility curves for the fixed based model where site

effects are modeled linearly would lead to conservative results. However, this is valid

only for the analyzed cases and should not be regarded as a general conclusion.

Furthermore, nonlinear SSI leads to an increase in fragility of structure when the



stratigraphy of the soil profile is taken into account, as the step-like layered soil medium

may amplify the imposed input motion at the base of the structure in comparison to the

homogeneous soil cases. On the other hand, it is seen that nonlinear SSI may decrease

the seismic vulnerability of the structure for deeper homogeneous and layered soil

profiles. This may be attributed to the increase of attenuation levels. However it

generally depends on the considered soil depth and stratigraphy as well as on the

characteristics of the input motions in relation to the dynamic properties of the soil and

the structure itself. Regarding the consideration of aging effects on the seismic

vulnerability of the soil-structure systems, as expected chloride induced corrosion leads

to an overall increase of the seismic fragilities with time, resulting to an average

decrease of the median intensity value (PGA) corresponding to the collapse prevention

state up to 14% after 50 years.

In the context of seismic vulnerability assessment of reinforced concrete (RC)

buildings, the use of field monitoring data constitutes a significant tool for the

representation of the actual structural state, reducing uncertainties associated with the

building configuration properties as well as many non-physical parameters (age,

maintenance, etc.), enhancing thus the reliability in the risk assessment procedure. In

Chapter 6 a comprehensive methodology was proposed for the evaluation of the seismic

vulnerability of existing buildings combining the numerical analysis and field monitoring

data. The proposed methodology was highlighted through the derivation of “time-building

specific” fragility curves for a high-rise hospital building designed according to low

seismic code provisions using ambient noise measurement. The special feature of the

target building is that it is composed of two adjacent tall units that are separated through

a structural joint. Operational modal analysis was conducted to identify the experimental

modal models. The identified modal parameters were found very close for the different

identification methods (non-parametric and parametric) applied as well as for the

different system models analyzed, implying that the dynamic characteristics of the

hospital building analyzed as one are possible to be captured by monitoring and

analyzing the two adjacent buildings separately. The modal identification results reveal a

coupling of the two building units under operational conditions. However it was decided

to perform the vulnerability assessment study separately for the two units due to the fact

that under strong ground motion, their interaction may be completely different due to the

severe nonlinearities that are expected to be experienced by the systems affecting

consequently their seismic response. The modal identification results based on ambient

noise measurements were used to update and better constrain the initial finite element

models of the two adjacent units, which were based on the design and construction

documentation plans provided by the Technical Services of the hospital. A sensitivity



parameter related to the structural stiffness was adopted for the updating procedure. In

general a good correlation with the experimental results was achieved for both building

units. Three-dimensional incremental dynamic analyses were conducted to assess the

seismic performance of the two building units and derive the fragility curves for the initial

(“building-specific”) and for the updated (“time-building specific”) models. It was shown

that the use of conventional generic fragility curves, although appropriate for assessing

fragility and losses in a regional/urban scale, may lead to inaccurate fragility and loss

estimates in the case of individual building assessment, which constitute crucial

components in the framework of decision making and risk mitigation strategies (e.g.

seismic safety and rehabilitation costs). Moreover, an overall increase in structures

fragility for the updated models was observed in comparison to the ones corresponding

to their initial state, which was attributed to deterioration phenomena affecting

progressively the building over time. In order to increase the reliability of the derived

results, the updated “time-building specific” fragility curves were compared with the

time-dependent curves where aging effects due to rebar corrosion were taken into

account through the analytical simulation of steel area loss and concrete cover strength

reduction for a 45-year corrosion scenario adopting the methodology presented in detail

in Chapter 4. Although the applied methodologies are quite different approaches for

assessing the actual structural condition, both resulted to an increase of the seismic

vulnerability in comparison to the initial, “as built” state of the hospital building. Results

indicate that potential degradation mechanisms that may affect the structural condition

over time should not be ignored especially in the case of buildings with strategic interest

(e.g. hospital) as this may lead to an underestimation of their real vulnerability.

7.2 Limitations and recommendations for future work

The work of the present thesis has certain limitations and should be extended through

additional research in the following areas:

Future study should aim at the validation of the proposed time-dependent fragility

curves with field post earthquake surveys and adequate field experiments while

large scale laboratory tests in prototype structures or building components is

certainly warranted to enhance their reliability and robustness and finally to

ensure their efficient implementation in seismic vulnerability assessment studies.

The proposed vulnerability assessment method considering SSI and site effects

and the corresponding fragility curves are appropriate for predicting the structural

damage of the soil-structure systems assuming rigid foundation and full contact

between the soil and structures’ nodes forbidding thus any relative movement

between the structure and the soil. Further research should be addressed



investigating the influence of a compliant foundation where detachment and

sliding is allowed.

Significant effort should be devoted for the development of generalized fragility

functions applicable to a variety of RC building typologies which would take into

account SSI and site effects for a variety of soil conditions.

It is also suggested to increase the applicability band of the proposed

methodological framework through the development of supplementary fragility

curves considering aging and SSI effects for other structural typologies (e.g. for

dual RC buildings)

The proposed updating procedure that is used for the calibration of the numerical

models in order to match the experimental results extracted analyzing field

monitoring data, should be further developed in order to yield more reliable

models with respect to their real conditions in terms of structural detailing, mass

distribution and material properties.

The methodology proposed for the seismic vulnerability assessment of RC

buildings using filed monitoring data, should be extended for “real-time” risk

assessment and post-seismic fragility updating. As an example, by exploiting the

computing power of the strong motion sensing units installed in AHEPA, the “time-

building specific” fragility curves derived in this study allow the implementation of

building-customized alerting procedure suitable for performing an automatic

building tagging (Bindi et al., 2015b; Parolai et al., 2015). In this context, the use

of field monitoring data will contribute in reducing the uncertainties associated

with the risk assessment procedure improving seismic safety and allowing the

development of robust real time assessment tools and appropriate risk mitigation

strategies.




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ANNEX A

Seismic input motion

A.1 Seismic input motion

The acceleration records and response spectra of the earthquake events which have been

used for the seismic vulnerability assessment of RC buildings considering aging and soil-

structure interaction effects. The response spectrum of each record is compared to the

reference spectrum of Ambraseys et al., 1996.

ANNEX A: Seismic input motion 286


Figure A.1. Accelerograms of the real seismic records used as input motion for the IDA



Figure A.1. Accelerograms of the real seismic records used as input motion for the IDA (continued)



Figure A.1. Accelerograms of the real seismic records used as input motion for the IDA (continued)



Figure A.2. Normalized elastic response spectra of the seismic records in comparison to the corresponding median predicted spectrum of Ambraseys et al., (1996)



Figure A.2. Normalized elastic response spectra of the seismic records in comparison to the corresponding median predicted spectrum of Ambraseys et al., (1996) (continued)



Figure A.2. Normalized elastic response spectra of the seismic records in comparison to the corresponding median predicted spectrum of Ambraseys et al., (1996) (continued)




ANNEX B

Modal identification results of AHEPA hospital using earthquake data

B.1 Grid models in MACEC

The grid of the systems analyzed in MACEC varies depending on the earthquake and

more specifically on the sensors of the two building units that actually recorded the

seismic events. Only these sensors are used for the identification process and the modal

analysis for each earthquake. ANNEX C summarizes all grid models that have been

introduced for the identification analysis in MACEC for all recorded earthquake cases.

ANNEX B: Modal identification results of AHEPA hospital using earthquake data 294



Figure B.1. Grid models of the different systems analyzed in MACEC for the earthquake events: NW from Lake Langada 2013, West from Kassandra peninsula in Halkidiki 2014


Figure B.2. Grid models of the different systems analyzed in MACEC for the earthquake events: Thessaloniki 2012


Figure B.3. Grid models of the different systems analyzed in MACEC for the earthquake events:

Thessaloniki 2013





Kalamaria 2014, Limnos 2014



West from Kassandra peninsula in Halkidiki 2013



B.2 Seismic input motion

For specific seismic events (NW from Lake Langada 6/12/2013, Limnos 24/5/2014,

Kalamaria 16/7/2014, West from Kassandra peninsula in Halkidiki 22/8/2014) a broad

band seismometer was operating on the ground floor of UNIT 1 during the earthquake

occurrence, recording thus the input motion. For these cases the corresponding input

accelerograms and response spectra are also summarized in the present ANNEX.



Figure B.6. Input acceleration in the longitudinal and transverse direction recorded at the

base of UNIT 1 and the corresponding elastic acceleration response spectra for the NW from Lake Langada, 6.12.2013 event

Figure B.7. Input acceleration in the longitudinal and transverse direction recorded at the base of UNIT 1 and the corresponding elastic acceleration response spectra for Limnos,

24.05.2014 event




base of UNIT 1 and the corresponding elastic acceleration response spectra for the Kalamaria, 16.7.2014 event


base of UNIT 1 and the corresponding elastic acceleration response spectra for the West from Kassandra peninsula in Halkidiki, 22.8.2014 event



B.3 Modal identification

In the following figures the modal identification of the different analyzed systems is

presented based on both Frequency Domain Decomposition (FDD) and Stochastic

Subspace Identification (SSI) methods for all earthquake cases.



Figure B.10. Modal identification applying the Frequency Domain Decomposition (FDD) and the Stochastic Subspace Identification (SSI) methods using earthquake recordings of the Thessaloniki,

2012 event

Figure B.11. Modal identification applying the Frequency Domain Decomposition (FDD) and the Stochastic Subspace Identification (SSI) methods using earthquake recordings of the Thessaloniki,

2013 event



Figure B.12. Modal identification applying the Frequency Domain Decomposition (FDD) and the Stochastic Subspace Identification (SSI) methods using earthquake recordings of N West from

Kassandra peninsula in Halkidiki, 26.10.2013 event

Figure B.13. Modal identification applying the Frequency Domain Decomposition (FDD) and the Stochastic Subspace Identification (SSI) methods using earthquake recordings of NW from Lake

Langada, 6.12.2013 event



Figure B.14. Modal identification applying the Frequency Domain Decomposition (FDD) and the Stochastic Subspace Identification (SSI) methods using earthquake recordings of Limnos, 24.05.2014

event

Figure B.15. Modal identification applying the Frequency Domain Decomposition (FDD) and the Stochastic Subspace Identification (SSI) methods using earthquake recordings of Kalamaria,

16.07.2014 event



Figure B.16. Modal identification applying the Frequency Domain Decomposition (FDD) and the Stochastic Subspace Identification (SSI) methods using earthquake recordings of the West from

Kassandra peninsula in Halkidiki, 22.08.2014 event




ANNEX C

Seismic input motion – AHEPA hospital

C.1 Seismic input motion

ANNEX B summarizes the acceleration records and response spectra of the earthquake

events that have been used for the seismic vulnerability assessment of the AHEPA

hospital building units. The response spectrum of each record is compared to the

reference spectrum adopted from SHARE for a 475 year return period

(http://portal.share-eu.org:8080/jetspeed/portal/).

ANNEX C: Seismic input motion – AHEPA hospital 306


Figure C.1. Accelerograms of the real seismic records used as input motion for the IDA



Figure C.1. Accelerograms of the real seismic records used as input motion for the IDA (continued)












Figure C.2. Normalized elastic response spectra of the seismic records in comparison to the corresponding reference normalized spectrum adopted from SHARE for a 475 year return period




(continued)




(continued)




(continued)




(continued)



Σωτηρία Καραπέτρου – ∆ιδακτορική ∆ιατριβή

ΕΚΤΕΝΗΣ ΠΕΡΙΛΗΨΗ

I.1 Εισαγωγή

Τις τελευταίες δεκαετίες το ενδιαφέρον της επιστημονικής κοινότητας των μηχανικών

επικεντρώνεται όχι μόνο στην ανάλυση και το σχεδιασμό νέων κατασκευών αλλά κυρίως

στην αποτίμηση της συμπεριφοράς των υφισταμένων. Οι καταστρεπτικές συνέπειες

ισχυρών σεισμών σε κοινωνικό αλλά και οικονομικό επίπεδο, όπως στις πρόσφατες

περιπτώσεις της Ιαπωνίας (Tohokou, 2011) και της Ν. Ζηλανδίας (Christchurch, 2011)

έχουν καταστήσει επιτακτική την ανάγκη της διεξαγωγής όλο και περισσότερων

προσεισμικών ελέγχων και μελετών εκτίμησης των αναμενόμενων απωλειών λόγω

σεισμού κυρίως για έργα υψηλής σπουδαιότητας, όπως νοσοκομεία, σχολεία, λιμενικές

εγκαταστάσεις κτλ. Σε χώρες υψηλής σεισμικής επικινδυνότητας (όπως η Ελλάδα)

ενδέχεται κατά τη διάρκεια ενός ισχυρού σεισμού να εμφανιστούν σοβαρές βλάβες σε

κτηριακές και όχι μόνο δομές, οι οποίες ιδιαίτερα στην περίπτωση κτηρίων υψηλής

σπουδαιότητας μπορεί να οδηγήσουν σε σημαντικές απώλειες τόσο σε κοινωνικό αλλά και

σε οικονομικό επίπεδο. Στο πλαίσιο της μείωσης της σεισμικής διακινδύνευσης, η έρευνα

διεθνώς επικεντρώνεται τόσο στο αντικείμενο της σεισμικής διακινδύνευσης όσο και της

δομικής τρωτότητας καθώς και της σύζευξης αυτών.

∆εδομένου του σημαντικού οικονομικού και κοινωνικού διακυβεύματος, πολλές

επιστημονικές μελέτες έχουν επικεντρωθεί στην ανάπτυξη μεθοδολογιών για την

αποτίμηση της σεισμικής τρωτότητας κτηρίων. Η συνήθης πρακτική κατά την αποτίμηση

της σεισμικής τρωτότητας των κατασκευών είναι η θεώρηση της πλήρους πάκτωσης

αγνοώντας ταυτόχρονα οποιοδήποτε φαινόμενο γήρανσης. Έτσι δε λαμβάνονται υπόψη

παράγοντες που σχετίζονται με τις συνθήκες του περιβάλλοντος των κατασκευών οι οποίοι

ωστόσο είναι δυνατόν να προκαλέσουν σημαντικές φθορές σε αυτές με αποτέλεσμα τη

μείωση της λειτουργικότητας και της αντοχής τους. Ένας από τους πιο σημαντικούς

παράγοντες της κατηγορίας αυτής αποτελεί η διάβρωση του σκυροδέματος, ένα φαινόμενο

που οφείλεται στη διείσδυση των χλωριόντων της ατμόσφαιρας (Ghosh and Padgett,

2010). Επίσης σημαντική επίδραση στη σεισμική τρωτότητα των κτηρίων ασκεί και το

Εκτενής Περίληψη 318


φαινόμενο της αλληλεπίδρασης εδάφους – κατασκευής. Η επίδραση του φαινομένου

μπορεί να είναι άλλοτε θετική και άλλοτε αρνητική καθώς εξαρτάται τόσο από τα δυναμικά

χαρακτηριστικά του εδάφους και του υπό μελέτη συστήματος όσο και από τα

χαρακτηριστικά (συχνοτικό περιεχόμενο, πλάτος, διάρκεια) της σεισμικής διέγερσης (Sαez

et al., 2011). Κατά την αποτίμηση υφισταμένων κτηρίων απαιτείται επίσης να λαμβάνονται

υπόψη διάφορες παράμετροι οι οποίες μπορεί να οδηγήσουν σε απομείωση της

δυσκαμψίας στο χρόνο και να επηρεάσουν τη σεισμική συμπεριφορά τους. Τέτοιες

παράμετροι μπορεί να είναι η φθορά των κατασκευών λόγω φαινομένων γήρανσης καθώς

και πιθανές προϋπάρχουσες βλάβες λόγω προηγούμενων ισχυρών σεισμών. Σε αυτές τις

περιπτώσεις η ενοργάνωση των κτηρίων και η χρήση των μετρήσεων πεδίου μπορεί να

αποτελέσει ένα σημαντικό εργαλείο για την εκτίμηση της πραγματικής δυναμικής

συμπεριφοράς και σεισμικής τρωτότητας των κατασκευών.

Στόχος της παρούσας διατριβής είναι η διερεύνηση όλων των ανωτέρω επιμέρους

θεμάτων προτάσσοντας μια ολοκληρωμένη μεθοδολογία βελτιωμένης αξιοπιστίας για την

αποτίμηση της σεισμικής τρωτότητας κτηρίων οπλισμένου σκυροδέματος στην οποία θα

συνεκτιμώνται φαινόμενα τα οποία μέχρι τώρα έχουν αντιμετωπιστεί μόνο επιμεριστικά,

όπως η γήρανση των υλικών, η αλληλεπίδραση εδάφους – κατασκευής και η συνεκτίμηση

της δυναμικής συμπεριφοράς βάσει μετρήσεων πεδίου. Μια συνοπτική περιγραφή των

μεθοδολογιών που έχουν εφαρμοστεί καθώς και των αποτελεσμάτων/συμπερασμάτων που

έχουν εξαχθεί παρουσιάζεται στις ενότητες που ακολουθούν.

I.2 Μεθοδολογία αποτίμησης της τρωτότητας

Η διδακτορική διατριβή επικεντρώνεται στην αποτίμηση της τρωτότητας κτηρίων

οπλισμένου σκυροδέματος (Ο/Σ) που υπόκεινται σε σεισμικές διεγέρσεις λαμβάνοντας

υπόψη τη γήρανση των υλικών και την αλληλεπίδραση εδάφους-κατασκευής. Η

τρωτότητα εκφράζεται μέσω αθροιστικών λογαριθμοκανονικών συναρτήσεων τρωτότητας

που περιγράφουν την πιθανότητα υπέρβασης της κάθε οριζόμενης στάθμης βλάβης

συναρτήσει μιας η περισσότερων παραμέτρων που χαρακτηρίζουν την ένταση του

πιθανού σεισμού. Το Σχήμα I.1 απεικονίζει το γενικό πλαίσιο της προτεινόμενης

μεθοδολογίας. Για την κατασκευή των καμπυλών τρωτότητας λαμβάνοντας υπόψη τη

γήρανση των υλικών και τη δυναμική αλληλεπίδραση εδάφους-κατασκευής, μελετήθηκαν

διδιάστατα πλαισιακά κτηριακά προσομοιώματα διαφορετικής γεωμετρίας και δυσκαμψίας,

σχεδιασμένα βάσει διαφορετικών επιπέδων αντισεισμικών κανονισμών τα οποία

περιγράφονται στην αμέσως επόμενη υποενότητα. Η «ικανότητα» της κατασκευής ορίζεται

από την τυπολογία του κτηρίου (γεωμετρία, δυσκαμψία), τις ιδιότητες των υλικών και την

προσομοίωση της πλαστικότητας των μελών. Η γήρανση και η αλληλεπίδραση εδάφους-

κατασκευής ενσωματώνονται στη μεθοδολογία της αποτίμησης όπως περιγράφεται στο



Σχήμα I.1 και περιγράφονται στις ενότητες Ι.3 και Ι.4 αντίστοιχα. Η σεισμική απαίτηση

ορίζεται βάσει πραγματικών σεισμικών καταγραφών που χρησιμοποιούνται ως κινήσεις

εισαγωγής για τη διεξαγωγή των βήμα προς βήμα επαυξητικών δυναμικών αναλύσεων με

διαφορετικά χαρακτηριστικά ως προς το συχνοτικό περιεχόμενο και τη διάρκεια κίνησης. Η

παράμετρος απόκρισης η οποία μελετάται και βάσει της οποίας ορίζονται οι στάθμες

βλάβης (ή επιτελεστικότητας) είναι το μέγιστο σχετικό βέλος ορόφου. Ορίζονται δύο

αντιπροσωπευτικές στάθμες επιτελεστικότητας, της άμεσης χρήσης μετά το σεισμό (ΑΧ)

και της αποφυγής κατάρρευσης (ΑΚ). Κατασκευάζονται διαφορετικά σετ καμπυλών

τρωτότητας, τα οποία εκφράζονται συνερτήσει είτε της φασματικής επιτάχυνσης που

αντιστοιχεί στη θεμελιώδη ιδιοπερίοδο των κατασκευών είτε της μέγιστης εδαφικής

επιτάχυνσης.

Κτηριακά προσομοιώματα- πλαισιακά κτήρια Ο/Σ σχεδιασμένα με βάση διαφορετικών επιπέδων κανονισμών.

Αναλυτική προσομοίωση των φορέων- γεωμετρία και δυσκαμψία- ιδιότητες υλικού- προσομοίωση πλαστικότητας

Σεισμική απαίτηση- επιλογή σεισμικών κινήσεων εισαγωγής

Επαυξητικές δυναμικές αναλύσεις- παράμετρος απόκρισης: μέγιστο σχετικό βέλος ορόφου- μηχανισμός αστοχίαςΟρισμός σταθμών

βλάβης- σε όρους μέγιστου σχετικού βέλους ορόφου Μεθοδολογία κατασκευής

καμπυλών τρωτότητας- στατιστική ανάλυση- αβεβαιότητες στη σεισμική απαίτηση, τη διαθέσιμη απόκριση, τον ορισμό σταθμών βλάβης

Κατασκευή καμπυλών τρωτότητας-σε όρους φασματικής επιτάχυνσης που αντιστοιχεί στη θεμελιώδη ιδιοπερίοδο περίοδο των κατασκευών- σε όρους μέγιστης εδαφικής επιτάχυνσης

Σχήμα I.1. ∆ιάγραμμα ροής της μεθοδολογίας για την αποτίμηση της σεισμικής τρωτότητας κτηρίων οπλισμένου σκυροδέματος

I.2.1 Περιγραφή των υπό μελέτη φορέων

Στα πλαίσια της παρούσας διατριβής, επιλέχθηκαν επτά κτήρια Ο/Σ αμιγούς πλαισιακής

λειτουργίας, τα οποία έχουν σχεδιασθεί με βάση διαφορετικά επίπεδα αντισεισμικών

κανονισμών. Η περιγραφή και η ταξινόμηση των διαφορετικών κτηριακών τυπολογιών

έγινε βάσει του πλαισίου ταξινόμησης κατά SYNER-G (www.syner-g.eu) (e.g. Crowley et

al., 2011). Έτσι επιλέχθηκαν δύο αντιπροσωπευτικά κτήρια χαμηλού και μέσου ύψους, τα

οποία έχουν σχεδιασθεί μόνο για να παραλαμβάνουν κατακόρυφα φορτία βαρύτητας,

χωρίς αντισεισμική προστασία (Χαμηλό κτήριο – Χωρίς Κανονισμό; Μέσου ύψους κτήριο –

Χωρίς Κανονισμό). Επίσης επιλέχθηκαν δυο πλαισιακά συστήματα, συγκεκριμένα ένα



μέσου ύψους και ένα υψηλό κτήριο, σχεδιασμένα με βάση τον Ελληνικό Αντισεισμικό

Κανονισμό του 1959 (Μέσου ύψους κτήριο – Χαμηλό επίπεδο Κανονισμό; Υψηλό κτήριο –

Χαμηλό επίπεδο Κανονισμού). Τέλος χρησιμοποιήθηκαν για τις αναλύσεις τρία κτήρια

αμιγούς πλαισιακής λειτουργίας σχεδιασμένα βάσει σύγχρονων Αντισεισμικών

Κανονισμών. Συγκεκριμένα επιλέχθηκαν δύο κτήρια χαμηλού και μέσου ύψους

σχεδιασμένα με βάση τον Ελληνικό Αντισεισμικό Κανονισμό ΕΑΚ (Χαμηλό κτήριο – Υψηλό

επίπεδο Κανονισμού; Μέσου ύψους κτήριο – Υψηλό επίπεδο Κανονισμού Ελλάδας) καθώς

και ένα επιπλέον κτήριο μέσου ύψους το οποίο έχει σχεδιασθεί βάσει των σύγχρονων

αντισεισμικών διατάξεων του Κανονισμού της Πορτογαλίας (Μέσου ύψους κτήριο – Υψηλό

επίπεδο Κανονισμού Πορτογαλίας). Ο Πίνακας I.1 παρουσιάζει συγκεντρωτικά βασικά

χαρακτηριστικά των φορέων σε όρους μάζας, αρχικής θεμελιώδους ιδιοπεριόδου Τ1,

αντοχής σκυροδέματος fc και χάλυβα fy. Στο Σχήμα I. παρουσιάζονται τα γεωμετρικά

χαρακτηριστικά καθώς και οι λεπτομέρειες όπλισης των υπό μελέτη πακτωμένων

κατασκευών.

Πίνακας I.1. Κύρια χαρακτηριστικά των κτηριακών προσομοιωμάτων πλαισιακής λειτουργίας

Κτήριο Ο/Σ Συνολική Μάζα [t]

Αρχική θεμελιώδης ιδιοπερίοδος T1 [sec] fc [MPa] fy [MPa]

Χαμηλό κτήριο – Χωρίς Κανονισμό 207 0.98 24 276

Μέσου ύψος κτήριο - Χωρίς Κανονισμό 198 0.66 16 343

Μέσου ύψος κτήριο – Χαμηλό επίπεδο Κανονισμού 135 0.58 14 400

Υψηλό κτήριο – Χαμηλό επίπεδο Κανονισμού 334 0.89 14 400

Χαμηλό κτήριο – Υψηλό επίπεδο Κανονισμού 35 0.40 20 500

Μέσου ύψος κτήριο – Υψηλό επίπεδο Κανονισμού (Ελλάδας) 130 0.66 20 400

Μέσου ύψος κτήριο – Υψηλό επίπεδο Κανονισμού (Πορτογαλίας) 266 0.48 28 460

Σχήμα I.2. Σχηματική αναπαράσταση των γεωμετρικών (διατομές) και των κατασκευαστικών (λεπτομέρειες όπλισης) χαρακτηριστικών των πακτωμένων φορέων



Σχήμα I.2. (Συνέχεια)-Σχηματική αναπαράσταση των γεωμετρικών (διατομές) και των κατασκευαστικών (λεπτομέρειες όπλισης) χαρακτηριστικών των πακτωμένων φορέων



Σχήμα I.2. (Συνέχεια)-Σχηματική αναπαράσταση των γεωμετρικών (διατομές) και των κατασκευαστικών (λεπτομέρειες όπλισης) χαρακτηριστικών των πακτωμένων φορέων

Η αριθμητική προσομοίωση των φορέων έγινε στο πρόγραμμα πεπερασμένων

στοιχείων OpenSees (Mazzoni et al., 2009). H ανελαστική προσομοίωση των δοκών και

των υποστυλωμάτων έγινε χρησιμοποιώντας στοιχεία δοκού-υποστυλώματος με βάση τη

μέθοδο των δυνάμεων. Η πλαστικότητα προσομοιώνεται ως κατανεμημένη σε όλο το

μήκος των δομικών στοιχείων μέσω ινών που περιγράφουν τη συμπεριφορά των διατομών

του κάθε μέλους βάσει μη-γραμμικών νόμων τάσεων – παραμορφώσεων. Για την

περιγραφή της συμπεριφοράς του σκυροδέματος σε θλίψη χρησιμοποιήθηκε το μοντέλο

των Kent and Park (Scott et al., 1982) με γραμμική μείωση της δυσκαμψίας υπό

ανακυκλιζόμενη φόρτιση και μηδενική εφελκυστική αντοχή (‘Concrete01’), με

διαφοροποίηση αντοχής και παραμορφωσιμότητας για το περισφιγμένο και το

απερίσφιγκτο σκυρόδεμα. Για την προσομοίωση του χάλυβα θεωρήθηκε διγραμμικός



ελαστοπλαστικός νόμος με κινηματική κράτυνση (‘Steel01’). Η μάζα θεωρείται

ομοιόμορφα κατανεμημένη κατά μήκος των δομικών στοιχείων.

Τα κτηριακά προσομοιώματα μελετώνται αρχικά ως «γυμνά» πλαισιακά συστήματα. Για

τη μελέτη της επιρροής τοιχοπληρώσεων στη σεισμική απόκριση και τρωτότητα των

φορέων, επιλέχθηκαν τρία αντιπροσωπευτικά προσομοιώματα, τα οποία αναλύθηκαν και

για την περίπτωση πλαισιακών τοιχοπληρωμένων συστημάτων (Χαμηλό κτήριο – Χωρίς

Κανονισμό; Υψηλό κτήριο – Χαμηλό επίπεδο Κανονισμού; Μέσου ύψους – Υψηλό επίπεδο

Κανονισμού). Η προσομοίωση της τοιχοποιίας στο OpenSees πραγματοποιείται βάσει του

μοντέλου του διπλού θλιπτήρα (Holmes, 1963; Stafford-Smith, 1962; 1966;

Thiruvengadam, 1985; Chrysostomou, 1991; Hashemi and Mosalam, 2007) που αποτελεί

ικανοποιητική προσέγγιση της αλληλεπίδρασης της τοιχοπλήρωσης με το περιβάλλον

πλαισιακό σύστημα και ως προς την πολυπλοκότητα του προσομοιώματος και ως προς το

υπολογιστικό κόστος (απαιτούμενος χρόνος ανάλυσης). Τα τοιχοπληρωμένα πλαίσια

μελετήθηκαν για την περιπτώσεις ομοιόμορφης καθ’ ύψος κατανομής της τοιχοποιίας

καθώς και για την περίπτωση ύπαρξης pilotis. Στον Πίνακα I.2 παρουσιάζονται

συγκεντρωμένα τα κύρια χαρακτηριστικά των τοιχοπληρωμένων πλαισίων.

Πίνακας I.2. Κύρια χαρακτηριστικά των τοιχοπληρωμένων πλαισιακών κτηριακών προσομοιωμάτων

Κτήριο Ο/Σ

Θεμελιώδης ιδιοπερίοδος

τοιχοπληρωμένων πλαισίων-pilotis

Tpil [sec]

Θεμελιώδης ιδιοπερίοδος ομοιόμορφης καθ’ ύψος

τοιχοπλήρωσης Tinf [sec]

Θλιπτική αντοχή

fm [MPa]

∆ιατμητική αντοχή

vme [MPa]

Μέτρο Ελαστικότητας

Em [MPa]

Χαμηλό κτήριο – Χωρίς Κανονισμό

0.69 0.25 1.2 0.62 660

Υψηλό κτήριο – Χαμηλό επίπεδο Κανονισμού

0.48 0.33 3 1 3000

Μέσου ύψος κτήριο – Υψηλό

επίπεδο Κανονισμού

(Πορτογαλίας)

0.23 0.15 3 1 3000

I.2.2 Σεισμικές διεγέρσεις εισαγωγής

Για τη διεξαγωγή των μη γραμμικών δυναμικών αναλύσεων επελέγησαν 15 πραγματικές

σεισμικές καταγραφές από την ευρωπαϊκή βάση δεδομένων ισχυρής εδαφικής κίνησης

(“European Strong-Motion Database” http://www.isesd.hi.is) (Πίνακας I.3). Οι

επιλεγείσες διεγέρσεις είναι στο σύνολό τους καταγραφές σε επιφανειακή έξαρση βράχου

και αντιστοιχούν σε κατηγορία εδάφους Α σύμφωνα με τον Ευρωκώδικα 8 με μέγεθος

(Mw) και επικεντρική απόσταση (R) που κυμαίνονται μεταξύ των 5.8<Mw<7.2 και

0<R<45km αντίστοιχα. Το βασικό κριτήριο επιλογής ήταν το μέσο φάσμα επιταχύνσεων



των καταγραφών για ένα εύρος περιόδου 0.00<T<2.00sec να προσεγγίζει κατά το

δυνατόν το στοχευόμενο φάσμα αναφοράς (Ambraseys et al., 1996) χρησιμοποιώντας τις

μέσες τιμές των Mw και R για τα ορισθέντα παραπάνω όρια. Η παραπάνω διαδικασία για

την επιλογή των διεγέρσεων πραγματοποιήθηκε με τη βοήθεια του προγράμματος REXEL

(Iervolino et al., 2010). Στο Σχήμα I.3 απεικονίζονται συγκριτικά το μέσο

κανονικοποιημένο φάσμα των καταγραφών σε σχέση με το στοχευόμενο μέσο

κανονικοποιημένο φάσμα του Ambraseys et al. (1996) όπου παρατηρείται πολύ καλή

σύγκλιση.

Πίνακας I.3. Σεισμικές διεγέρσεις για τη διεξαγωγή των ανελαστικών δυναμικών αναλύσεων

Σεισμός Σταθμός Ημερομηνία Mw R (km) PGA (m/s2) Κωδικός Friuli ST20 6/5/1976 6.5 23 3.499 000055xa

Montenegro ST64 15/4/1979 6.9 21 1.774 000198xa

Montenegro (aftershock) ST68 24/5/1979 6.2 30 0.667 000234xa

Valnerina ST225 19/9/1979 5.8 5 1.51 000242xa

Valnerina ST61 19/9/1979 5.8 22 0.6 000246xa

Campano Lucano ST93 23/11/1980 6.9 23 1.363 000287xa



Golbasi ST161 5/5/1986 6 29 0.538 000410ya

Golbasi ST161 6/6/1986 5.8 34 0.167 000412xa

Izmit (aftershock) ST575 13/9/1999 5.8 15 0.714 001243xa

Mt. Vatnafjoll ST2483 25/5/1987 6 42 0.131 005271ya

Kozani ST1320 13/5/1995 6.5 17 1.396 006115ya

South Iceland ST2497 17/6/2000 6.5 34 0.386 006269xa

Firuzabad ST3293 20/6/1994 5.9 39 0.216 007158xa

Σχήμα I.3. Σύγκριση μέσου κανονικοποιημένου ελαστικού φάσματος καταγραφών με το

στοχευόμενο μέσο κανονικοποιημένο φάσμα των Ambraseys et al. (1996)



I.2.3 Μη γραμμικές ανελαστικές βήμα προς βήμα δυναμικές αναλύσεις

∆ιεξάγονται μη γραμμικές ανελαστικές βήμα προς βήμα δυναμικές αναλύσεις όπου τα υπό

μελέτη συστήματα υποβάλλονται σε µία (ή περισσότερες) καταγραφές εδαφικής

κίνησης, η καθεµία από τις οποίες κλιµακώνεται σε διάφορα επίπεδα έντασης

καλύπτοντας το εύρος από την ελαστικότητα μέχρι και τη δυναμική αστάθεια της

κατασκευής (Vamvatsikos and Cornell, 2002). Παράγονται έτσι µία (ή περισσότερες)

καµπύλες απόκρισης του κάθε συστήματος που εκφράζουν τη σχέση μεταξύ της

παραμέτρου βλάβης και του επιπέδου έντασης. Στα πλαίσια της παρούσας εργασίας ως

παράμετρος βλάβης επιλέγεται το μέγιστο σχετικό βέλος ορόφου maxISD ενώ ως μέτρο

έντασης η φασματική επιτάχυνση που αντιστοιχεί στην αρχική θεμελιώδη ιδιοπερίοδο των

φορέων Sa(T1,5%).

Οι βήμα προς βήμα επαυξητικές δυναμικές αναλύσεις διεξήχθησαν για όλα τα

προσομοιώματα για τις 15 προοδευτικά κλιμακούμενες σεισμικές διεγέρσεις. Η κλιμάκωση

των καταγραφών έγινε εφαρμόζοντας κατάλληλο αλγόριθμο έτσι ώστε για κάθε

καταγραφή να επιτρέπεται μέγιστος αριθμός 12 αναλύσεων με αρχικό βήμα ίσο με 0.01g,

επαυξητικό βήμα ίσο με 0.05g και μια πρώτη ελαστική ανάλυση για 0.005g και 0.01g για

τα κτήρια σχεδιασμένα χωρίς ή με χαμηλό επίπεδο αντισεισμικού Κανονισμού και για τα

κτήρια σχεδιασμένα με βάσει σύγχρονο αντισεισμικό κανονισμό αντίστοιχα.

Τα ζεύγη Sa(T1,5%)-maxISD για κάθε καταγραφή χρησιμοποιήθηκαν για τη κατασκευή

των καμπυλών απόκρισης με παρεμβολή των ενδιάμεσων σημείων. Στο Σχήμα I.4

φαίνονται οι 15 παραχθείσες καμπύλες απόκρισης καθώς και οι ποσοστιαίες καμπύλες

16%, 50% (διάμεσος) και 84% για τον πακτωμένο υψηλό κτήριο Ο/Σ σχεδιασμένο με

βάση χαμηλού επιπέδου αντισεισμικό κανονισμό.

Το επόμενο βήμα για την κατασκευή των καμπυλών τρωτότητας είναι ο ορισμός των

σταθμών βλάβης. Επιλέγονται δυο οριακές τιμές του μέγιστου σχετικού βέλους ορόφου

maxISD αντιπροσωπευτικές των σταθμών επιτελεστικότητας που αντιστοιχούν στη άμεση

χρήση (ΑΧ) μετά το σεισμό και της αποφυγής κατάρρευσης (ΑΚ). Η πρώτη τιμή ορίζεται

σύμφωνα με τις προδιαγραφές κατά HAZUS (NIBS, 2004), ενώ η δεύτερη ορίζεται πάνω

στη διάμεσο (50% ποσοστημόριο) καμπύλη απόκρισης του κάθε φορέα. Για τον αξιόπιστο

ορισμό της οριακής τιμής ΑΚ επιλέγεται ένα σημείο στο τμήμα “χαλάρωσης” πριν το πλατό

της καμπύλης που σηματοδοτεί την έναρξη της δυναμικής αστάθειας της κατασκευής

(Vamvatsitkos and Cornell, 2004). Ενδεικτικά παρουσιάζεται στο Σχήμα I.4 ο ορισμός των

σταθμών βλάβης ΑΧ και ΑΚ επάνω στη διάμεσο καμπύλη απόκρισης που έχει εξαχθεί για

την περίπτωση του υψηλού κτηρίου σχεδιασμένο με βάση αντισεισμικό κανονισμό.



Σχήμα I.4. Ορισμός των επιπέδων βλάβης «Άμεση Χρήση μετά το σεισμό ΑΧ» και «Αποφυγή Κατάρρευσης ΑΚ» επάνω στη διάμεσο καμπύλη απόκρισης των βήμα προς βήμα δυναμικών αναλύσεων για την περίπτωση του υψηλού κτηρίου σχεδιασμένου με βάση χαμηλό επίπεδο

αντισεισμικού κανονισμού

I.2.4 Κατασκευή καμπυλών τρωτότητας

Οι καμπύλες τρωτότητας περιγράφουν την πιθανότητα για δεδομένη σεισμική ένταση, η

βλάβη μιας κατασκευής να είναι ίση ή μεγαλύτερη από ένα ορισμένο επίπεδο. Τα

αποτελέσματα των βήμα προς βήμα δυναμικών αναλύσεων (Sa(T1,5%)-maxISD ή PGA-

maxISD) χρησιμοποιούνται για την κατασκευή των καμπυλών τρωτότητας που

περιγράφουν την κατανομή της πιθανότητας υπέρβασης της κάθε στάθμης βλάβης και

εκφράζονται βάσει της ακόλουθης κανονικής λογαριθμικής κατανομής:

In IM In IM

P DS IM

/ Φ

(I.1)

όπου Φ: η τυπική κανονική αθροιστική συνάρτηση, DS: η στάθμη βλάβης, ΙΜ: το μέτρο

έντασης που στην παρούσα εργασία εκφράζεται σε όρους μέγιστης εδαφικής επιτάχυνσης,

IM και β: η διάμεσος (εκφρασμένη σε g) και η λογαριθμοκανονική τυπική απόκλιση των

καμπυλών τρωτότητας αντίστοιχα. Οι τιμές των διαμέσων τιμών Sa(T1,5%) ή PGA που

αντιστοιχούν στις στάθμες επιτελεστικότητας ΑΧ και ΑΚ, υπολογίζονται με ανάλυση

παλινδρόμησης των αποτελεσμάτων των βήμα προς βήμα δυναμικών αναλύσεων (ζεύγη

Sa(T1,5%)-maxISD, PGA-maxISD). Στο Σχήμα I.5 παρουσιάζεται ενδεικτικά ο

υπολογισμός των διαμέσων τιμών του μέτρου έντασης Sa(T1,5%) που αντιστοιχούν στα

επίπεδα βλάβης ΑΧ και ΑΚ για την περίπτωση του υψηλού κτηρίου σχεδιασμένου με

χαμηλό επίπεδο κανονισμού.



AXSa AKSa

(α) (β)

Σχήμα I.5. Ανάλυση παλινδρόμησης για τον υπολογισμό των διαμέσων τιμών του μέτρου έντασης που αντιστοιχούν στις θεωρούμενες στάθμες βλάβης για την περίπτωση του υψηλού κτηρίου σχεδιασμένου με βάση χαμηλό επίπεδο αντισεισμικό κανονισμό: (α) Σχέσεις Sa (T1, 5%) – maxISD σε λογαριθμική κλίμακα και (β) υπολογισμός των διαμέσων τιμών του μέτρου έντασης για τις ΑΧ και ΑΚ στάθμες

βλάβης

Οι αβεβαιότητες που υπεισέρχονται στον υπολογισμό της τρωτότητας, εκφράζονται

μέσω της διασποράς της λογαριθμοκανονικής κατανομής β, η οποία αποτελείται από

τρεις επιμέρους όρους που εκφράζουν την αβεβαιότητα που αφορά στη σεισμική

απαίτηση, στη διαθέσιμη απόκριση και στον ορισμό των σταθμών βλαβών. Η

αβεβαιότητα στη σεισμική απαίτηση υπολογίζεται από τη διασπορά των αποτελεσμάτων

Sa(T1,5%)-maxISD ή PGA-maxISD των βήμα προς βήμα δυναμικών αναλύσεων ενώ για

τις άλλες πηγές αβεβαιοτήτων υιοθετήθηκαν οι προτεινόμενες τιμές κατά HAZUS (NIBS,

2004) ίσες με 0.25/0.3 (υψηλού/χαμηλού επίπεδου αντισεισμικός κανονισμός) και 0.40

αντίστοιχα. Η συνολική διασπορά υπολογίζεται ως το άθροισμα των τετραγώνων των

επιμέρους αβεβαιοτήτων.

Στο Σχήμα I.6 παρουσιάζονται οι καμπύλες τρωτότητας για το υψηλό κτήριο

σχεδιασμένο με βάση χαμηλό επίπεδο αντισεισμικού κανονισμού σε όρους Sa(T1,5%) για

τις στάθμες βλάβες που αντιστοιχούν στην Άμεση Χρήση μετά το σεισμό «ΑΧ» και την

Αποφυγή Κατάρρευσης «ΑΚ». Βάσει των καμπυλών υπολογίζεται για ένα επίπεδο έντασης,

π.χ. 0.4g, η πιθανότητα υπέρβασης των επιπέδων βλάβης ΑΧ και ΑΚ ίση με 97% και 20%

αντίστοιχα. Για το ίδιο επίπεδο έντασης, η πιθανότητα το κτήριο να μην εμφανίσει βλάβες

είναι ίση με 2%. Οι πιθανότητες όμως ο φορέας να παρουσιάσει βλάβες που να

αντιστοιχούν στις στάθμες επιτελεστικότητας ΑΧ και ΑΚ είναι 77% και 20% αντίστοιχα.



PAK

PAX

Σχήμα I.6. Καμπύλες τρωτότητας του υψηλού κτηρίου σχεδιασμένου με βάση χαμηλού επιπέδου κανονισμό σε όρους Sa(T1, ξ=5%) για τις στάθμες βλάβης που αντιστοιχούν στην Άμεση Χρήση «ΑΧ»

μετά το σεισμό και την Αποφυγή Κατάρρευσης «ΑΚ»

I.2.5 Αξιολόγηση των καμπυλών τρωτότητας

Στόχος αυτής της ενότητας είναι η επαλήθευση της αξιοπιστίας των καμπυλών τρωτότητας

που έχουν εξαχθεί με βάση την παραπάνω μεθοδολογία για τα θεωρούμενα πακτωμένα

πλαισιακά κτήρια. Για το σκοπό αυτό πραγματοποιήθηκαν συγκρίσεις των καμπυλών με

αντίστοιχες καμπύλες της βιβλιογραφίας για τις υπό μελέτη τυπολογίες κτηρίων Ο/Σ με τη

βοήθεια κατάλληλου υπολογιστικού εργαλείου που αναπτύχθηκε στα πλαίσια του

ερευνητικού προγράμματος Syner-G (http://www.vce.at/SYNER-G/), όπου σημαντικό

κομμάτι των εργασιών επικεντρώθηκε στον εντοπισμό των κύριων τυπολογιών κτηρίων

στην Ευρώπη και στη συγκέντρωση των αντίστοιχων καμπυλών τρωτότητας (κτήρια από

οπλισμένο σκυρόδεμα και τοιχοποιία). Επιχειρήθηκε η εναρμόνιση των καμπυλών με

τέτοιο τρόπο ώστε να αναφέρονται στις μεταξύ τους συγκρίσεις σε ίδια μορφή έντασης,

επιπέδων βλαβών και τυπολογίας κτηρίων. Αυτό επιτυγχάνεται βάσει σχέσεων της

διεθνούς βιβλιογραφίας, οι οποίες έχουν συμπεριληφθεί σε κατάλληλο λογισμικό το οποίο

εκτελεί αυτομάτως τις απαιτούμενες μετατροπές (Fragility Function Manager). Για τις

ανάγκες της παρούσας διατριβής η εναρμόνιση ως προς την ένταση επιτελείται θεωρώντας

την φασματική επιτάχυνση που αντιστοιχεί στη θεμελιωμένη ιδιοπερίοδο της κατασκευής

ενώ ως προς τις στάθμες βλάβης, η εναρμόνιση διεξάγεται για δύο στάθμες βλάβης: της

διαρροής και της ολικής κατάρρευσης.

Στο Σχήμα I.7 παρατίθενται ενδεικτικά συγκριτικά διαγράμματα των εναρμονισμένων

καμπυλών με τις αντίστοιχες σεισμικές καμπύλες τρωτότητας της βιβλιογραφίας για το

υψηλό κτήριο σχεδιασμένο με βάση χαμηλό επίπεδο κανονισμού. Συνολικά, οι

προσεγγιστικές αυτές συγκρίσεις θεωρούνται αρκετά ικανοποιητικές. Φανερώνουν,



ωστόσο, τη μεγάλη αβεβαιότητα που σχετίζεται με τις διαφορετικές καμπύλες τρωτότητας

που συναντώνται στη βιβλιογραφία.

Σχήμα I.7. Σύγκριση των εναρμονισμένων καμπυλών τρωτότητας σε όρους Sa για την περίπτωση του υψηλού μη τοιχοπληρωμένου κτηρίου σχεδιασμένου βάσει χαμηλού επιπέδου αντισεισμικό

κανονισμό με τις αντίστοιχες καμπύλες των Kappos et al. (2003; 2006) που αντιστοιχούν στην ίδια τυπολογία φορέα



I.3 Χρονικά εξαρτώμενη σεισμική τρωτότητα κτηρίων Ο/Σ λαμβάνοντας υπόψη τη γήρανση των υλικών

Η συνήθης πρακτική των μεθοδολογιών αποτίμησης είναι η θεώρηση της τρωτότητας ως

«αμετάβλητης» στο χρόνο αγνοώντας οποιοδήποτε φαινόμενο γήρανσης. Έτσι δε

λαμβάνονται υπόψη παράγοντες που σχετίζονται με τις συνθήκες του περιβάλλοντος των

κατασκευών οι οποίοι ωστόσο είναι δυνατόν να προκαλέσουν σημαντικές φθορές σε αυτές

με αποτέλεσμα τη μείωση της λειτουργικότητας και της αντοχής τους. Παρά τις

προσπάθειες κάποιων ερευνητών να ενσωματώσουν την παράμετρο του χρόνου ως βασική

συνιστώσα στη μεθοδολογία της αποτίμησης γεφυρών και κτηρίων Ο/Σ (π.χ. Ghosh and

Padgett, 2010; Choe et al., 2010; Yalciner et al., 2012; Fotopoulou et al., 2012), η

χρήση χρονικά εξαρτώμενων συναρτήσεων τρωτότητας δεν είναι αρκετά διαδεδομένη έως

σήμερα.

Ένας από τους πιο σημαντικούς παράγοντες της κατηγορίας αυτής αποτελεί η

διάβρωση του σκυροδέματος που μπορεί να οδηγήσει σε σημαντική μείωση της αντοχής

και της λειτουργικότητας της κατασκευής. Οι παράγοντες που την επηρεάζουν είναι είτε

φυσικοί (κλιματολογικές συνθήκες περιβάλλοντος, τοπογραφία) είτε εξωγενείς (κακός

σχεδιασμός). Κύριες αιτίες που την προκαλούν είναι η ενανθράκωση του σκυροδέματος

και η διείσδυση χλωριόντων, διαδικασίες που δεν είναι τελείως ανεξάρτητες μεταξύ τους.

Στην παρούσα διατριβή η γήρανση των υλικών κτηρίων Ο/Σ λαμβάνεται υπόψη

ενσωματώνοντας στη μεθοδολογία της αποτίμησης πιθανοτικά προσομοιώματα

υπολογισμού της χρονικής στιγμής έναρξης της διάβρωσης του οπλισμού λόγω της

διείσδυσης χλωριόντων. Συγκεκριμένα υιοθετείται το πιθανοτικό προσομοίωμα κατά FIB-

CEB Task Group 5.6 (2006) με βασικές παραμέτρους τη συγκέντρωση των χλωριόντων

και την επικάλυψη του σκυροδέματος. Η μεθοδολογία εφαρμόσθηκε και για τα επτά

πλαισιακά κτήρια Ο/Σ που παρουσιάστηκαν στην προηγούμενη ενότητα εξετάζοντας ένα

δυσμενές διαβρωτικό περιβάλλον με ένα σχετικά υψηλό ρυθμό διάβρωσης (Stewart,

2004), ο οποίος θωρείται σταθερός κατά τη διάρκεια ζωής των κατασκευών (Ghosh and

Padgett, 2010). Ο χρόνος έναρξης της διάβρωσης υπολογίστηκε ίσος με 7.01 χρόνια για

τα κτήρια που έχουν σχεδιασθεί χωρίς ή με βάση χαμηλού επιπέδου αντισεισμικό

κανονισμό (πάχος επικάλυψης 20mm) ενώ για τα κτήρια σχεδιασμένα με βάση σύγχρονο

κανονισμό ο χρόνος έναρξης της διάβρωσης προσδιορίστηκε στα 14.11 χρόνια (πάχος

επικάλυψης 25mm).

Κατά τη φάση έναρξης της διάβρωσης δεν παρατηρείται αμέσως απομείωση της

αντοχής των υλικών, αρχίζει όμως να αποσταθεροποιείται η υπάρχουσα προστατευτική

μεμβράνη λόγω της διείσδυσης των χλωριόντων και του διοξειδίου του άνθρακα της

ατμόσφαιρας. Όταν η συγκέντρωση των χλωριόντων ή του διοξειδίου του άνθρακα



υπερβεί μία κρίσιμη τιμή η μεμβράνη αδρανοποιείται σημαίνοντας την έναρξη του

φαινομένου. Ως επιπτώσεις της διάβρωσης στην κατασκευή θεωρηθήκαν η μείωση της

διατομής των ράβδων οπλισμού (Ghosh and Padgett, 2010), η μείωση της αντοχής του

σκυροδέματος της επικάλυψης (Coronelli and Gambarova, 2004) και η μείωση της

μέγιστης εφελκυστικής παραμόρφωσης του χάλυβα (Rodriguez and Andrade, 2001) και

υπολογίστηκαν για κάθε κτήριο συναρτήσει του ρυθμού και του χρόνου έναρξης της

διάβρωσης. Τα «γυμνά» μη τοιχοπληρωμένα πλαίσια μελετήθηκαν για τέσσερα χρονικά

σενάρια t=0, 25, 50 και 75 χρόνια ενώ τα τοιχοπληρωμένα κτήρια για τα χρονικά σενάρια,

t=0 και 50 χρόνια. Σε κάθε περίπτωση οι επιπτώσεις της διάβρωσης φαίνεται να είναι

σημαντικότερες για τις δοκούς σε σύγκριση με τους στύλους που αποδίδεται στο γεγονός

πως αποτελούνται από μικρότερης διαμέτρου οπλισμούς. Παρατηρείται επίσης αύξηση της

ιδιοπεριόδου των «γυμνών» και τοιχοπληρωμένων (ομοιόμορφα καθ’ ύψος και pilotis)

πλαισίων με τον χρόνο, καθώς οι επιπτώσεις της διάβρωσης οδηγούν σε σταδιακή

απομείωση της δυσκαμψίας.

Η επιρροή της γήρανσης στη δυναμική απόκριση των κτηρίων μελετήθηκε αρχικά

εφαρμόζοντας ανελαστικές στατικές υπερωθητικές αναλύσεις των προσομοιωμάτων για τα

θεωρούμενα χρονικά σενάρια. Στο Σχήμα I.8 παρουσιάζονται ενδεικτικά αποτελέσματα

καμπυλών αντίστασης όπως έχουν προκύψει από τη στατική υπερωθητική ανάλυση του

υψηλού κτηρίου σχεδιασμένο με βάση χαμηλό αντισεισμικό Κανονισμό για τις περιπτώσεις

«γυμνού» και τοιχοπληρωμένου πλαισίου και για τα διάφορα χρονικά σενάρια. Το

τοιχοπληρωμένο (ομοιόμορφη κατανομή καθ’ ύψος και pilotis) σε σύγκριση με το «γυμνό»

πλαισιακό σύστημα παρουσιάζει σημαντικά αυξημένη δυσκαμψία και χαρακτηρίζεται από

υψηλότερες τέμνουσες βάσης και μικρότερες μετακινήσεις οροφής. Σε όλες τις

περιπτώσεις όμως λόγω των φαινομένων της γήρανσης τα κτήρια (τοιχοπληρωμένα και

μη) παρουσιάζουν μείωση της αντοχής και της δυσκαμψίας καθώς και απώλεια της

πλαστιμότητας στο χρόνο.

Για τα πλαισιακά συστήματα (τοιχοπληρωμένα και μη) διεξήχθησαν μη γραμμικές

ανελαστικές βήμα προς βήμα δυναμικές αναλύσεις για την κατασκευή των χρονικά

εξαρτώμενων λογαριθμοκανονικών καμπυλών και επιφανειών τρωτότητας. Κρίσιμο βήμα

αποτελεί ο ορισμός των επιπέδων βλάβης. Η οριακή τιμή της πρώτης στάθμης βλάβης που

αντιστοιχεί στην «Άμεση Χρήση μετά το σεισμό» (ΑΧ) ορίζεται ίση με 0.5% και 0.1%

ακολουθώντας τις οδηγίες κατά HAZUS (NIBS, 2004). Η δεύτερη στάθμη βλάβης

αντιστοιχεί στην «Αποφυγή Κατάρρευσης» (ΑΚ) η οριακή τιμή της οποίας ορίζεται βάσει

των αποτελεσμάτων των δυναμικών αναλύσεων. Οι Πίνακες I.4 και I.5 παρουσιάζουν

συγκεντρωμένες τις χρονικά μεταβαλλόμενες οριακές τιμές ΑΚ για τα θεωρούμενα πλαίσια

(τοιχοπληρωμένα και μη αντίστοιχα).



Σχήμα I.8. Καμπύλες αντίστασης του «γυμνού» και τοιχοπληρωμένου (ομοιόμορφη καθ’ ύψος κατανομή, pilotis) υψηλού κτηρίου σχεδιασμένο με βάση χαμηλό επίπεδο Κανονισμού για τα

θεωρούμενα χρονικά σενάρια

Πίνακας I.4. Οριακές τιμές της στάθμης βλάβης «Αποφυγή Κατάρρευσης» όπως έχουν υπολογισθεί

για τα «γυμνά» πλαίσια και τα θεωρούμενα χρονικά σενάρια

Χρονικό σενάριο

(έτη)

Χαμηλό κτήριο – Χωρίς

Κανονισμό

Μέσου ύψος κτήριο - Χωρίς

Κανονισμό

Μέσου ύψος

κτήριο – Χαμηλό επίπεδο

Κανονισμού

Υψηλό κτήριο – Χαμηλό επίπεδο


Χαμηλό κτήριο – Υψηλό επίπεδο


Μέσου ύψος κτήριο – Υψηλό επίπεδο

Κανονισμού (Πορτογαλίας)

Μέσου ύψος

κτήριο – Υψηλό επίπεδο

Κανονισμού (Ελλάδας)

0 0.028 0.014 0.013 0.0225 0.049 0.025 0.039

25 0.025 0.014 0.012 0.021 0.046 0.022 0.037

50 0.024 0.011 0.011 0.02 0.043 0.02 0.033

75 0.021 0.009 0.0095 0.017 0.037 0.019 0.03



Πίνακας I.5. Οριακές τιμές της στάθμης βλάβης «Αποφυγή Κατάρρευσης» όπως έχουν υπολογισθεί για τα τοιχοπληρωμένα πλαίσια και τα θεωρούμενα χρονικά σενάρια

Χρονικό σενάριο

(έτη)

Χαμηλό κτήριο – Χωρίς Κανονισμό

Υψηλό κτήριο – Χαμηλό επίπεδο Κανονισμού

Μέσου ύψος κτήριο – Υψηλό επίπεδο Κανονισμού

(Πορτογαλίας) ομοιόμορφη κατανομή καθ’ ύψος

pilotis ομοιόμορφη κατανομή καθ’

ύψος pilotis

ομοιόμορφη κατανομή καθ’

ύψος pilotis

0 0.005 0.019 0.005 0.023 0.003 0.03

50 0.0045 0.0175 0.0045 0.0225 0.0025 0.028

Στο Σχήμα I.9 παρουσιάζονται συγκεντρωτικά για τα επτά μη τοιχοπληρωμένα

πλαισιακά συστήματα οι χρονικά εξαρτώμενες καμπύλες τρωτότητας συναρτήσει της

φασματικής επιτάχυνσης που αντιστοιχεί στη θεμελιώδη ιδιοπερίοδο των κτηρίων. Στο

Σχήμα I.10 δίνονται επιπλέον τυπικά αποτελέσματα υπό τη μορφή χρονικά

μεταβαλλόμενων επιφανειών τρωτότητας συναρτήσει της Sa(T1,5%) για το υψηλό κτήριο

σχεδιασμένο με βάση χαμηλού επιπέδου αντισεισμικό κανονισμού.



Σχήμα I.9.Χρονικά εξαρτώμενες καμπύλες τρωτότητας συναρτήσει του Sa(T1, 5%) για τα πακτωμένα, μη τοιχοπληρωμένα πλαισιακά κτήρια



Σχήμα I.10.Επιφάνειες τρωτότητας συναρτήσει του χρόνου και Sa(T1, 5%) για τις στάθμες βλάβης που αντιστοιχούν στην «Άμεση Χρήση μετά το σεισμό» (αριστερά) και της «Αποφυγή Κατάρρευσης» (δεξιά) για την περίπτωση του μη τοιχοπληρωμένου υψηλού κτηρίου σχεδιασμένο με βάση χαμηλό επίπεδο

αντισεισμικό κανονισμό

Τα αποτελέσματα φανερώνουν γενικά μια αύξηση της σεισμικής τρωτότητας με τον

χρόνο. Η αύξηση αυτή φαίνεται να είναι πιο έντονη για το επίπεδο βλάβης που αντιστοιχεί

στην «Αποφυγή Κατάρρευσης». Πιο συγκεκριμένα η αύξηση της διαμέσου Sa(T1,5%) για

τα επίπεδα βλάβης «Άμεση Χρήση μετά το σεισμό» και «Αποφυγή Κατάρρευσης»

υπολογίζεται σε 20% και 40% αντίστοιχα για σχεδόν όλα τα υπό μελέτη κτήρια. Πάντως η

μεγαλύτερη και μικρότερη αύξηση αναμένεται για τα προσομοιώματα «Μέσου ύψους

κτήριο - Χωρίς Κανονισμό» και «Μέσου ύψους κτήριο – Υψηλό επίπεδο Κανονισμού

(Ελλάδας)» αντίστοιχα.

Το Σχήμα I.11 συγκεντρώνει τις αντίστοιχες χρονικά εξαρτώμενες καμπύλες

τρωτότητας για τα τοιχοπληρωμένα πλαίσια με ομοιόμορφη κατανομή τοιχοποιίας καθ’

ύψος και με pilotis. Σε σύγκριση με τα «γυμνά» πλαισιακά κτήρια Ο/Σ, τα τοιχοπληρωμένα

πλαίσια φαίνεται να είναι λιγότερο τρωτά ειδικά για τις περιπτώσεις εκείνες που τα κτήρια

έχουν σχεδιασθεί με υψηλό επίπεδο αντισεισμικού κανονισμού. Πιο συγκεκριμένα τα

πλήρως τοιχοπληρωμένα κτήρια με ομοιόμορφη κατανομή της τοιχοποιίας καθ’ ύψος

παρουσιάζουν τη μικρότερη τρωτότητα όλων των υπό μελέτη τύπων («γυμνά» πλαίσια,

πλήρως τοιχοπληρωμένα, pilotis) με τα κτήρια με pilotis να ακολουθούν. Σε αυτή την

περίπτωση τα «γυμνά» πλαίσια είναι τα πιο τρωτά συστήματα τα οποία υπό ισχυρή

σεισμική διέγερση αναμένεται να παρουσιάσουν τις μεγαλύτερες βλάβες. Ωστόσο όσον

αφορά στο χαμηλό κτήριο σχεδιασμένο χωρίς αντισεισμικό κανονισμό, τη μεγαλύτερη

τρωτότητα παρουσιάζει το προσομοίωμα με pilotis ενώ το λιγότερο τρωτό σύστημα είναι

εκείνο του πλήρους τοιχοπληρωμένου προσομοιώματος. Τα συμπεράσματα αυτά ισχύουν

και για το αρχικό σενάριο (t=0 έτη) καθώς και για το χρονικό σενάριο των 50 ετών.



Σχήμα I.11.Χρονικά εξαρτώμενες καμπύλες τρωτότητας συναρτήσει του Sa(T1, 5%) για τα πακτωμένα, τοιχοπληρωμένα πλαισιακά κτήρια (ομοιόμορφη καθ’ ύψος κατανομή και pilotis)



Για την περίπτωση των «γυμνών» πλαισιακών φορέων, που έχουν μελετηθεί για

περισσότερα των δύο χρονικών σεναρίων, η χρονικά εξαρτώμενη διάμεσος των καμπυλών

μπορεί να αναπαρασταθεί επαρκώς με μια πολυωνυμική συνάρτηση δευτέρου βαθμού. Στο

Σχήμα I.12 παρουσιάζεται ενδεικτικά η χρονικά εξαρτώμενη διάμεσος σε όρους Sa(T1,

5%) για την περίπτωση του μη τοιχοπληρωμένου υψηλού κτηρίου σχεδιασμένο με

χαμηλού επιπέδου κανονισμό και για τη στάθμη βλάβης ΑΚ. Με τον ίδιο τρόπο μπορούν να

αναπαρασταθούν και οι αντίστοιχες τυπικές αποκλίσεις. Έτσι αναπαριστώντας τις βασικές

παραμέτρους των καμπυλών τρωτότητας μέσω απλών σχέσεων, δίνεται η δυνατότητα της

άμεσης εκτίμησης της τρωτότητας του δεδομένου κτηρίου και για το συγκεκριμένο

σενάριο διάβρωσης για οποιαδήποτε στιγμή στο χρόνο, εφόσον είναι γνωστή η

τρωτότητας της κατασκευής στην αρχική της κατάσταση (t=0 έτη).

Υψηλό κτήριο –Χαμηλό επίπεδο Κανονισμού

Σχήμα I.12. Αναπαράσταση της χρονικά εξαρτώμενης διαμέσου (σε όρους Sa(T1, 5%)) των καμπυλών με πολυώνυμο δευτέρου βαθμού για την περίπτωση βλαβών που αντιστοιχούν στη

στάθμη επιτελεστικότητας ΑΚ, για το μη τοιχοπληρωμένο υψηλό κτήριο σχεδιασμένο βάσει χαμηλού επιπέδου κανονισμό



I.4 Επιρροή της δυναμικής αλληλεπίδρασης εδάφους – κατασκευής στην εκτίμηση της σεισμικής τρωτότητας κτηρίων Ο/Σ

Η συνήθης πρακτική κατά την αποτίμηση της σεισμικής τρωτότητας των κατασκευών

οπλισμένου σκυροδέματος (Ο/Σ) είναι η θεώρηση πλήρους πάκτωσης αγνοώντας το

φαινόμενο της δυναμικής αλληλεπίδρασης εδάφους-κατασκευής (∆ΑΕΚ). Πρόσφατες

μελέτες ωστόσο έχουν δείξει πως η επίδραση του φαινομένου μπορεί να παίξει

καθοριστικό ρόλο στη σεισμική απόκριση και τρωτότητα κτηρίων Ο/Σ. Η ∆ΑΕΚ αφορά στην

αμοιβαία αλληλεπίδραση του εδάφους και της κατασκευής με αποτέλεσμα τη

διαφοροποίηση της απόκρισης του συστήματος σε δυναμική φόρτιση. Για τα συνήθη

κτήρια αναμένεται γενικά μείωση των σεισμικών δράσεων. Ωστόσο είναι δυνατόν να

σημειωθεί σημαντική επαύξηση των μετακινήσεων λόγω ενδεχόμενης ενίσχυσης

δευτερογενών καταπονήσεων (π.χ. φαινόμενα P-delta) και των επιπρόσθετων

παραμορφώσεων που εισάγουν (Kramer, 1996). Παρόλο που υπάρχουν διαθέσιμες

καμπύλες τρωτότητας για κτήρια που λαμβάνουν υπόψη την επιρροή των τοπικών

εδαφικών συνθηκών (ΕΤΕΣ) για διάφορους εδαφικούς σχηματισμούς (NIBS, 2004), δεν

συμβαίνει το ίδιο για τη ∆ΑΕΚ που γενικά θεωρείται πως δρα ευνοϊκά μειώνοντας τη

σεισμική δράση των γραμμικών ελαστικών συστημάτων. Ωστόσο η ενδοσιμότητα του

εδάφους σε συνδυασμό με τη ∆ΑΕΚ για μη γραμμικά ανελαστικά συστήματα μπορεί να έχει

άλλοτε θετική και άλλοτε αρνητική επίδραση καθώς εξαρτάται τόσο από τα δυναμικά

χαρακτηριστικά του εδάφους και του υπό μελέτη συστήματος όσο και από τα

χαρακτηριστικά (συχνοτικό περιεχόμενο, πλάτος, διάρκεια) της σεισμικής διέγερσης (Sαez

et al, 2011).

Στόχος της παρούσας διατριβής αποτελεί η περεταίρω διερεύνηση της ∆ΑΕΚ στην

αποτίμηση της σεισμικής τρωτότητας πλαισιακών κτηρίων Ο/Σ. Για το σκοπό αυτό

επιλέγονται τρία αντιπροσωπευτικά πλαίσια σχεδιασμένα με διαφορετικά επίπεδα

αντισεισμικού κανονισμού, που αναλύθηκαν και ως πακτωμένα συστήματα λαμβάνοντας

υπόψη φαινόμενα γήρανσης όπως περιγράφηκε στην προηγούμενη ενότητα. Συγκριμένα

επιλέγονται τα ακόλουθα προσομοιώματα: Χαμηλό κτήριο – Χωρίς Κανονισμό, Υψηλό

κτήριο – Χαμηλό επίπεδο Κανονισμού, Μέσου ύψους κτήριο – Υψηλό επίπεδο Κανονισμού

(Ελλάδας). Για την προσομοίωση του φαινομένου της ∆ΑΕΚ εφαρμόζεται η άμεση μέθοδος

όπου η ανάλυση των υπό μελέτη συστημάτων πραγματοποιείται σε ένα υπολογιστικό βήμα

για ελαστική συμπεριφορά εδάφους. Με αυτόν τον τρόπο λαμβάνονται υπόψη και η

αδρανειακή και η κινηματική αλληλεπίδραση.

Για το υψηλό κτήριο Ο/Σ σχεδιασμένο με βάση παλιό αντισεισμικό κανονισμό, όπου

αναμένεται το φαινόμενο της αλληλεπίδρασης να είναι πιο έντονο, η ∆ΑΕΚ ερευνάται

εκτός από ελαστική και για ανελαστική συμπεριφορά του εδάφους. Επιπλέον διερευνάται



και η επιμέρους επιρροή των τοπικών εδαφικών συνθηκών (ΕΤΕΣ) και της ∆ΑΕΚ

εφαρμόζοντας την προσέγγιση των αποσυζευγμένων συστημάτων όπου λαμβάνεται υπόψη

μόνο η ΕΤΕΣ στη δυναμική απόκριση του πακτωμένου φορέα ενώ αγνοείται το φαινόμενο

της αλληλεπίδρασης. Τέλος για την περίπτωση ανελαστικής συμπεριφοράς εδάφους,

πραγματοποιούνται αναλύσεις ευαισθησίας ως προς την επιρροή του βάθους και της

διαστρωμάτωσης του εδάφους στη σεισμική τρωτότητα του συστήματος εδάφους –

κατασκευής. Τα διάφορα προσομοιώματα απεικονίζονται στα Σχήματα I.13 και I.14.

Πακτωμένο μοντέλο, βράχος

Επιφανειακήεμφάνιση βράχου

Ελαστικό υπόβαθρο

Μοντέλο ∆ΑΕΚ

Ελεύθερο πεδίο

Ελαστικό ή ανελαστικόεδαφικό προφίλ

Μοντέλο 2 βημάτων

Σχήμα I.13. Σχηματική απεικόνιση των εφαρμοσμένων προσομοιωμάτων για τη μελέτη της

επιμέρους επιρροής της ∆ΑΕΚ και των τοπικών εδαφικών συνθηκών για την περίπτωση του υψηλού κτηρίου σχεδιασμένο βάσει χαμηλού επιπέδου κανονισμό

Vs,ave=300m/sec H=30m,60m

Βραχώδες υπόβαθρο (α)

Vs1=250m/sec

Vs2=290m/sec

Vs3=350m/sec

H1=H/6

H2=H/2

H3=H/3

Βραχώδες υπόβαθρο (β)

Σχήμα I.14. Σχηματική απεικόνιση των υπό μελέτη περιπτώσεων που εξετάζουν την επιρροή (α) του βάθους και (β) της διαστρωμάτωσης του εδαφικού προφίλ για ανελαστική συμπεριφορά

εδάφους για την περίπτωση του υψηλού κτηρίου σχεδιασμένο βάσει χαμηλού επιπέδου κανονισμό

Το έδαφος προσομοιώθηκε με επιφανειακά τετράκομβα πεπερασμένα στοιχεία επίπεδης

παραμόρφωσης. Το πλάτος και το μήκος του εδαφικού προφίλ για τα προσομοιώματα

«Χαμηλό κτήριο – Χωρίς Κανονισμό» και «Μέσου ύψους κτήριο – Υψηλό επίπεδο

Κανονισμού» θεωρήθηκαν 30m και 120m ενώ για το «Υψηλό κτήριο – Χαμηλό επίπεδο



Κανονισμού» το μήκος του προφίλ αυξήθηκε σε 220 ώστε να εξασφαλιστούν στα άκρα

του συνθήκες ελευθέρου πεδίου. Για όλες τις περιπτώσεις υιοθετήθηκε πυκνή

διακριτοποίηση βάσει της συχνότητας ενδιαφέροντος (10Hz) με τετράπλευρα στοιχεία

1m×1m. Το ελαστικό υπόβαθρο (Vs,bedrock=900m/sec) βρίσκεται σε βάθος 30m. Για την

αποφυγή της ανάκλασης των σεισμικών κυμάτων στη βάση του καννάβου εφαρμόσθηκε

κατάλληλος ιξώδης αποσβεστήρας για την προσομοίωση της απόσβεσης ακτινοβολίας.

Αρχικά διεξήχθησαν αναλύσεις για τους πακτωμένους φορείς θεμελιωμένους σε βράχο

για τις σεισμικές διεγέρσεις σε συνθήκες ‘οιονεί’ βράχου. Στη συνέχεια ακολούθησαν

αναλύσεις των υπό μελέτη συστημάτων εδάφους-κατασκευής που λαμβάνουν υπόψη τη

∆ΑΕΚ για ελαστικό έδαφος. Για το ελαστικό εδαφικό προφίλ θεωρήθηκε μια μέση ταχύτητα

διατμητικών κυμάτων Vs,30 ίση με 200m/sec ώστε να αντιστοιχεί σε έδαφος τύπου C

σύμφωνα με τις κατηγορίες εδάφους που προτείνονται στον Ευρωκώδικα 8.

Για το υψηλό πλαισιακό κτήριο, για το οποίο μελετήθηκε η ∆ΑΕΚ καθώς και η ΕΤΕΣ για

ελαστικό και ανελαστικό έδαφος, η μη γραμμική ανελαστική συμπεριφορά του εδάφους

προσομοιώθηκε με σύνθετο μη-γραμμικό καταστατικό νόμο (Yang et al., 2008).

Συγκεκριμένα, κατά τη διάρκεια της στατικής ανάλυσης η συμπεριφορά του εδάφους

θεωρείται γραμμική ελαστική ενώ κατά τη δυναμική ανάλυση μετατρέπεται σε

ελαστοπλαστική όπου η σχέση τάσεων-παραμορφώσεων εκφράζεται μέσω ενός

καταστατικού προσομοιώματος που συνδυάζει κινηματική κράτυνση με συσχετισμένο νόμο

πλαστικής ροής, με το κριτήριο διαρροής Von Mises και πολλαπλές επιφάνειες διαρροής.

Έτσι λαμβάνεται υπόψη η διάχυση της υστερητικής ενέργειας καθώς και η δημιουργία

πλαστικών παραμορφώσεων κατά τη διάρκεια της ισχυρής εδαφικής κίνησης. Η σκελετική,

μη γραμμική καμπύλη περιγράφεται βάσει του μοντέλου Masing για τη βαθμονόμηση του

οποίου χρησιμοποιούνται οι καμπύλες G-γ-D του Darendeli (2001) για αργιλικό έδαφος με

δείκτη πλαστικότητας PI=30 και ατμοσφαιρική πίεση p’0=1atm. Το έδαφος θεωρήθηκε

ομογενές συνεκτικό με αστράγγιστη διατμητική αντοχή Cu=110kPa.

Τέλος για τη διερεύνηση της επιμέρους ΕΤΕΣ και της ∆ΑΕΚ διεξάγονται αναλύσεις των

αποσυζευγμένων υποσυστημάτων εδάφους και κατασκευής. Αρχικά πραγματοποιούνται

αναλύσεις ξεχωριστά για το θεωρούμενο (ελαστικό και ανελαστικό) εδαφικό προσoμοίωμα

και η απόκριση που υπολογίζεται στην επιφάνειά του (ελεύθερο πεδίο) χρησιμοποιείται

ακολούθως ως κίνηση εισαγωγής για τη δυναμική ανάλυση του πακτωμένου φορέα. Έτσι

λαμβάνεται υπόψη μόνο η ΕΤΕΣ στη διαφοροποίηση των χρονοϊστοριών και κατ’ επέκταση

στη δυναμική απόκριση της κατασκευής αγνοώντας το φαινόμενο της αλληλεπίδρασης.

Οι δυναμικές αναλύσεις των υπό μελέτη συστημάτων εδάφους - κατασκευής

διεξάγονται με το πρόγραμμα OpenSees. Ως παράμετρος βλάβης επιλέγεται το μέγιστο

σχετικό βέλος ορόφου maxISD ενώ ως μέτρο έντασης η μέγιστη εδαφική επιτάχυνση PGA

σε συνθήκες «οιονεί» βράχου ή για έδαφος Α σύμφωνα με τον Ευρωκώδικα 8. Για τη



διεξαγωγή των μη γραμμικών ανελαστικών βήμα προς βήμα δυναμικών αναλύσεων

χρησιμοποιούνται οι σεισμικές διεγέρσεις του Πίνακα I.3. Τα αποτελέσματα των δυναμικών

αναλύσεων, συγκεκριμένα τα ζεύγη PGA-maxISD για κάθε καταγραφή, χρησιμοποιήθηκαν

για την κατασκευή των καμπυλών απόκρισης με παρεμβολή των ενδιάμεσων σημείων. Για

τον ορισμό των επιπέδων βλάβης, επιλέγονται δυο οριακές τιμές του μέγιστου σχετικού

βέλους ορόφου maxISD, αντιπροσωπευτικές των σταθμών επιτελεστικότητας που

αντιστοιχούν στην άμεση χρήση μετά το σεισμό «ΑΧ» και στην αποφυγή κατάρρευσης

«ΑΚ». Η πρώτη τιμή ορίζεται 0.5% σύμφωνα με τις προδιαγραφές κατά HAZUS (NIBS,

2004) ενώ η δεύτερη ορίζεται επάνω στη διάμεσο καμπύλη απόκρισης των πακτωμένων

φορέων όπως περιγράφηκε στην ενότητα Ι.3. Οι οριακές τιμές «ΑΚ» για τα υπό μελέτη

συστήματα αυτής της ενότητας, αντιστοιχούν στις τιμές maxISD του Πίνακα I.4 για το

χρονικό σενάριο των t=0 ετών.

Τα αποτελέσματα των βήμα προς βήμα δυναμικών αναλύσεων (PGA-maxISD)

χρησιμοποιούνται για την κατασκευή των καμπυλών τρωτότητας. Στο Σχήμα I.15

παρουσιάζονται συγκριτικά οι καμπύλες τρωτότητας των τριών πλαισιακών φορέων σε

όρους PGA για συνθήκες «οιονεί» βράχου, για την περίπτωση των πακτωμένων

συστημάτων θεμελιωμένων σε βράχο και για τα αντίστοιχα προσομοιώματα που

λαμβάνουν υπόψη τη ∆ΑΕΚ. Παρατηρείται σημαντική αύξηση της σεισμικής τρωτότητας

όταν λαμβάνονται υπόψη τα φαινόμενα της αλληλεπίδρασης εδάφους-κατασκευής. Όπως

αναμενόταν, η αύξηση αυτή φαίνεται να είναι μεγαλύτερη για το υψηλό κτήριο.

Συγκεκριμένα για το κτήριο αυτό υπολογίζεται αύξηση των διαμέσων τιμών PGA

υπολογίζεται κατά 52% και 57% για τις στάθμες βλάβης «ΑΧ» και «ΑΚ» αντίστοιχα. Σε

κάθε περίπτωση τα αποτελέσματα αναδεικνύουν τη σημαντική επίδραση των φαινομένων

∆ΑΕΚ στη δυναμική συμπεριφορά και τρωτότητα των κατασκευών, καθιστώντας

απαραίτητη τη θεώρησή τους στις μεθοδολογίες αποτίμησης.

Για την περίπτωση του υψηλού πλαισιακού φορέα σχεδιασμένο με χαμηλό επίπεδο

αντισεισμικού κανονισμού, όπου η επιρροή των φαινομένων της ∆ΑΕΚ ήταν πιο έντονα σε

σύγκριση με τα υπόλοιπα κτήρια, πραγματοποιήθηκαν επιπλέον αναλύσεις διερευνώντας

την επιμέρους επιρροή της ∆ΑΕΚ και των τοπικών εδαφικών συνθηκών υπό ελαστική και

ανελαστική συμπεριφορά εδάφους. Στο Σχήμα I.16 φαίνονται συγκριτικά οι καμπύλες

τρωτότητας του πακτωμένου υψηλού κτηρίου θεμελιωμένο σε βράχο με τις αντίστοιχες

καμπύλες των προσομοιωμάτων αλληλεπίδρασης εδάφους-κατασκευής (αριστερά) και των

πακτωμένων φορέων που λαμβάνουν υπόψη την επιρροή των τοπικών εδαφικών

συνθηκών (δεξιά). Όταν το έδαφος θεωρείται ανελαστικό η τρωτότητα του συστήματος

εδάφους-κατασκευής μειώνεται σε σύγκριση με τη θεώρηση ελαστικού εδάφους ιδιαίτερα

για την οριακή κατάσταση ΑΚ. Η μείωση αυτή είναι ακόμη πιο έντονη για την περίπτωση

του πακτωμένου φορέα που λαμβάνει υπόψη την ΕΤΕΣ. Σε κάθε περίπτωση όμως η ∆ΑΕΚ



καθώς και η ΕΤΕΣ οδηγούν σε σημαντική αύξηση της σεισμικής τρωτότητας σε σχέση με

τον πακτωμένο φορέα θεμελιωμένο σε βράχο. Η επιρροή επομένως της ∆ΑΕΚ καθώς και

των τοπικών εδαφικών συνθηκών είναι σημαντική και πρέπει να λαμβάνεται υπόψη κατά

την αποτίμηση της σεισμικής συμπεριφοράς της κατασκευής.

Στο Σχήμα I.17 από την άλλη συγκρίνονται οι καμπύλες τρωτότητας του μοντέλου

αλληλεπίδρασης εδάφους-κατασκευής και του πακτωμένου μοντέλου που λαμβάνει υπόψη

την ΕΤΕΣ για ελαστική και ανελαστική συμπεριφορά του εδάφους όπου τα αποτελέσματα

φαίνεται να διαφοροποιούνται σημαντικά. Πιο συγκεκριμένα όταν το έδαφος θεωρείται

ελαστικό το μοντέλο δυναμικής αλληλεπίδρασης εδάφους-κατασκευής φαίνεται πρακτικά

να έχει την ίδια τρωτότητα με το πακτωμένο μοντέλο. Αντίθετα, όταν το έδαφος

προσομοιώνεται ως μη γραμμικό ανελαστικό, τότε η τρωτότητα του μοντέλου

αλληλεπίδρασης εδάφους-κατασκευής παρουσιάζεται σημαντικά αυξημένη σε σύγκριση με

τον πακτωμένο φορέα. Το αποτέλεσμα αυτό πιθανόν να οφείλεται στο γεγονός ότι η

ανελαστική συμπεριφορά του εδάφους είναι δυνατό να εισάγει επιπρόσθετες

παραμορφώσεις που οδηγούν σε επαύξηση της απαίτησης μετακινήσεων στην κατασκευή.

Σχήμα I.15. Καμπύλες τρωτότητας των πακτωμένων προσομοιωμάτων θεμελιωμένων σε βράχο σε σύγκριση με τα προσομοιώματα ∆ΑΕΚ για ελαστική συμπεριφορά εδάφους. Οι καμπύλες τρωτότητας αναφέρονται και στα τρία υπό μελέτη πλαισιακά κτήρια και εκφράζονται σε όρους

μέγιστης εδαφικής επιτάχυνσης PGA σε συνθήκες «οιονεί» βράχου



Σχήμα I.16. Καμπύλες τρωτότητας του πακτωμένου υψηλού κτηρίου θεμελιωμένο σε βράχο και των προσομοιωμάτων ∆ΑΕΚ (αριστερά) καθώς και των πακτωμένων προσομοιωμάτων που

λαμβάνουν υπόψη την ΕΤΕΣ (δεξιά) για ελαστικό και ανελαστικό έδαφος

Σχήμα I.17. Καμπύλες τρωτότητας του πακτωμένου μοντέλου λαμβάνοντας υπόψη την ΕΤΕΣ και

των μοντέλων ∆ΑΕΚ για ελαστικό (αριστερά) και ανελαστικό (δεξιά) έδαφος

Στο Σχήμα I.18 παρουσιάζονται τα γραφήματα των καμπυλών τρωτότητας σε όρους

PGA για το υψηλό κτήριο σχεδιασμένο με χαμηλό επίπεδο κανονισμού, λαμβάνοντας

υπόψη τη ∆ΑΕΚ και την ΕΤΕΣ για ανελαστικό, μη γραμμικό έδαφος, καθώς και την

επιρροή του βάθους και της διαστρωμάτωσης του εδαφικού προφίλ. Παρατηρείται πως για

τις περιπτώσεις του μικρότερου (Η=30m) αλλά και του μεγαλύτερου βάθους (Η=60m)

εδαφικό προφίλ, η θεώρηση μιας πιο λεπτομερούς διαστρωμάτωσης οδηγεί σε ενίσχυση

των μη-γραμμικοτήτων των συστημάτων εδάφους-κατασκευής αυξάνοντας τη σεισμική

τρωτότητα. Η παρατήρηση αυτή αποδίδεται στο γεγονός πως ένα εδαφικό προφίλ με

πολλαπλές στρώσεις έχει ως αποτέλεσμα να προκληθούν μεγαλύτερες ενισχύσεις των



επιταχύνσεων στη βάση της κατασκευής, σε σύγκριση με ένα αντίστοιχο ομογενές έδαφος.

Η αύξηση της τρωτότητας λόγω της θεώρησης εδαφικού προφίλ με διαστρωμάτωση

φαίνεται να είναι περισσότερο αισθητή για τη στάθμη βλάβης «ΑΚ». Αυτό ισχύει για το

μικρότερου (Η=30m) αλλά και για το μεγαλύτερου βάθους έδαφος (Η=60m) με την

τελευταία περίπτωση να εμφανίζει την αύξηση αυτή ακόμη πιο έντονη. Αναφορικά με την

επιρροή του βάθους, τα συγκριτικά γραφήματα των καμπυλών τρωτότητας του Σχήματος

I.18 αποδεικνύουν πως για τα συστήματα εδάφους – κατασκευής με βαθύτερα εδαφικά

προφίλ η τρωτότητα μειώνεται. Η μείωση αυτή οφείλεται πιθανώς στα μεγαλύτερα επίπεδα

απόσβεσης που παρατηρούνται στα εδάφη μεγάλου βάθους, τα οποία οδηγούν σε μείωση

της σεισμικής απόκρισης στη βάση της κατασκευής με αποτέλεσμα τη μείωση της

απαίτησης των μετακινήσεων των κατασκευών, σε σύγκριση με μικρότερου βάθους

προφίλ

Σχήμα I.18. Καμπύλες τρωτότητας των υπό μελέτη συστημάτων ∆ΑΕΚ για ανελαστικό έδαφος με διαστρωμάτωση μικρότερου (αριστερά) και μεγαλύτερου (δεξιά) βάθους

Υιοθετώντας το σενάριο διάβρωσης της προηγούμενης ενότητας, διεξήχθησαν επιπλέον

αναλύσεις για την κατασκευή χρονικά εξαρτώμενων καμπυλών τρωτότητας λαμβάνοντας

υπόψη και την αλληλεπίδραση εδάφους-κατασκευής. Το Σχήμα I.19 αναπαριστά

συγκριτικά γραφήματα των καμπυλών τρωτότητας για τα τρία επιλεγμένα πλαισιακά

κτήρια για ελαστική συμπεριφορά εδάφους. Συγκεκριμένα οι καμπύλες του πακτωμένου

κτηρίου συγκρίνονται με τις καμπύλες που έχουν προκύψει για τα αντίστοιχα συστήματα

εδάφους – κατασκευής για τα δυο υπό μελέτη χρονικά σενάρια, t=0 και 50 ετών. Για τα

αρχικά αλλά και για τα διαβρωμένα κτήρια παρατηρείται σημαντική αύξηση της

τρωτότητας όταν λαμβάνονται υπόψη τα φαινόμενα αλληλεπίδρασης εδάφους –

κατασκευής ιδιαίτερα για τη στάθμη βλάβης που αντιστοιχεί στην «Αποφυγή

Κατάρρευσης».



Σχήμα I.19. Χρονικά εξαρτώμενες καμπύλες τρωτότητας σε όρους PGA των υπό μελέτη πακτωμένων φορέων και των αντίστοιχων συστημάτων εδάφους – κατασκευής που λαμβάνουν

υπόψη τη ∆ΑΕΚ για ελαστική συμπεριφορά του εδάφους



Επιπρόσθετα για το υψηλό κτήριο σχεδιασμένο με βάση χαμηλό επίπεδο αντισεισμικού

κανονισμού παρουσιάζονται στο Σχήμα I.20 συγκριτικά χρονικά εξαρτώμενες καμπύλες

τρωτότητας λαμβάνοντας υπόψη τα φαινόμενα ∆ΑΕΚ για ελαστικό και ανελαστικό έδαφος.

Τα γραφήματα δείχνουν πως το προσομοίωμα ∆ΑΕΚ για ανελαστικό έδαφος είναι λιγότερο

τρωτό σε σύγκριση με το αντίστοιχο προσομοίωμα θεωρώντας ελαστική συμπεριφορά

εδάφους. Η μείωση αυτή της τρωτότητας γίνεται πιο αισθητή για τη στάθμη βλάβης «ΑΚ»

και για το αρχικό χρονικό σενάριο (t=0 έτη) που ουσιαστικά δε λαμβάνει υπόψη τη

γήρανση.

Σχήμα I.20. Χρονικά εξαρτώμενες καμπύλες τρωτότητας σε όρους PGA για το υψηλό κτήριο σχεδιασμένο με βάση χαμηλού επιπέδου κανονισμό θεωρώντας συνθήκες πάκτωσης στο βράχο

καθώς και τη ∆ΑΕΚ για ελαστικό και μη γραμμικό έδαφος



I.5 Αποτίμηση σεισμικής τρωτότητας κτηρίων Ο/Σ με βάση μετρήσεις πεδίου. Εφαρμογή στο κτήριο της νευρολογικής κλινικής και διοικητικών υπηρεσιών του νοσοκομείου ΑΧΕΠΑ στη Θεσσαλονίκη

Στόχος του κεφαλαίου αυτού είναι η αποτίμηση της σεισμικής τρωτότητας κτηρίων

οπλισμένου σκυροδέματος με βάση μετρήσεις πεδίου. Κατά την αποτίμηση υφισταμένων

κτηρίων απαιτείται να λαμβάνονται υπόψη διάφορες παράμετροι οι οποίες μπορεί να

οδηγήσουν σε απομείωση της δυσκαμψίας στο χρόνο και να επηρεάσουν τη σεισμική

συμπεριφορά τους. Τέτοιες παράμετροι μπορεί να είναι η φθορά των κατασκευών λόγω

φαινομένων γήρανσης καθώς και πιθανές προϋπάρχουσες βλάβες λόγω προηγούμενων

ισχυρών σεισμών. Η συνήθης πρακτική που προτείνουν οι αντισεισμικοί κανονισμοί και

που εφαρμόζονται μέχρι και σήμερα είναι η ανάλυση των κτηρίων θεωρώντας

απομειωμένες τις παραμέτρους στιβαρότητας των δομικών στοιχείων. Από την άλλη,

υπάρχουσες οδηγίες για την αποτίμηση της σεισμικής τρωτότητας κτηρίων Ο/Σ (π.χ.

HAZUS) σε αυτές τις περιπτώσεις προβλέπουν την ενσωμάτωση συντελεστών που

συσχετίζονται είτε με τις συνθήκες συντήρησης των κτηρίων είτε με επί τόπου δοκιμές των

υλικών των δομικών στοιχείων. Οι ανωτέρω μέθοδοι παρόλο που αναγνωρίζουν την

ανάγκη να ληφθούν υπόψη φαινόμενα που οδηγούν σε υποβάθμιση των κατασκευών με

την πάροδο του χρόνου, δεν εξασφαλίζουν απαραίτητα τον αξιόπιστο προσδιορισμό της

πραγματικής κατάστασης των κατασκευών τη δεδομένη χρονική στιγμή της αποτίμησής

τους. Επιπλέον αυξάνεται όλο και περισσότερο το ενδιαφέρον τόσο σε ερευνητικό όσο και

σε επίπεδο εφαρμογής, η ανάπτυξη κατάλληλων εύχρηστων υπολογιστικών εργαλείων

αποτίμησης των κτηρίων σε πραγματικό χρόνο με σκοπό την άμεση εφαρμογή

στρατηγικών διαχείρισης σεισμικών κρίσεων και τη μείωση του σεισμικού κινδύνου. Η

ενόργανη παρακολούθηση της δυναμικής απόκρισης κατασκευών μπορεί να συμβάλλει

καθοριστικά στο πλαίσιο αυτό, αφού οι καταγραφές των δικτύων ενοργάνωσης μπορούν

να χρησιμοποιηθούν για τη δυναμική ταυτοποίηση των κτηρίων που περιλαμβάνει την

εκτίμηση των ιδιομορφικών χαρακτηριστικών (ιδιοπερίοδοι, ιδιομορφές, απόσβεση) σε

κατάσταση λειτουργίας τους (Operational Modal Analysis). Μεθοδολογίες

ταυτοποίησης/αναγνώρισης των δυναμικών χαρακτηριστικών των ενοργανωμένων

κτηρίων με βάση τις καταγραφές μόνιμων ή προσωρινών δικτύων επιτρέπουν έναν πιο

ακριβή προσδιορισμό της δυναμικής συμπεριφοράς των υφιστάμενων κατασκευών.

Τέτοιου τύπου μεθοδολογίες έχουν ένα ευρύ πεδίο εφαρμογής όπως την πρόβλεψη της

δυναμικής συμπεριφοράς (Brownjohn, 2003), την αναπροσαρμογή αριθμητικών

προσομοιωμάτων (Teughels, 2003; Jaishi and Ren, 2005; Zarate and Caicedo, 2008;

Savoia et al., 2013), την παρακολούθηση της δομικής υγείας των κατασκευών και τον

εντοπισμό βλαβών (Peeters, 2000; Farrar et al., 2001; Ramos et al., 2010; Goulet et al.,

2014), στην άμεση αποτίμηση τω βλαβών μετά από μια ισχυρή σεισμική διέγερση (Rainieri



et al., 2012) και τη χρήση πειραματικών προσομοιωμάτων βάσει μετρήσεων θορύβου στα

πλαίσια της αποτίμησης της σεισμικής τρωτότητας υφιστάμενων κατασκευών (Michel et

al., 2012).

Για την αποτίμηση της σεισμικής τρωτότητας χρησιμοποιώντας μετρήσεις πεδίου, τα

πειραματικά αποτελέσματα σε όρους ιδιομορφικών χαρακτηριστικών χρησιμοποιούνται για

την αναπροσαρμογή του αρχικού αριθμητικού προσομοιώματος του κτηρίου που έχει

προκύψει με βάση τα διαθέσιμα αρχιτεκτονικά σχέδια και ξυλοτύπους. Στη συνέχεια

πραγματοποιούνται αναλύσεις ευαισθησίας για τη βαθμονόμηση του αριθμητικού

προσομοιώματος ώστε να προσεγγίζει τα πειραματικά αποτελέσματα. Η επιλογή του

«βέλτιστου» αναπροσαρμοσμένου προσομοιώματος χρησιμοποιείται τελικά για τη

διεξαγωγή των αναλύσεων με σκοπό την κατασκευή των καμπυλών τρωτότητας. Στο

Σχήμα I.21 παρουσιάζεται η προτεινόμενη μεθοδολογία για την αποτίμηση της σεισμικής

τρωτότητας ενοργανωμένων κτηρίων με βάση μετρήσεις πεδίου.

Καταγραφές δικτύων παρακολούθησης ενοργανωμένου κτηρίου

(Πειραματικό προσομοίωμα)

Αρχιτεκτονικά σχέδια και ξυλότυποι κτηρίου(Αρχικό αριθμητικό προσομοίωμα)

Αποτίμηση σεισμική τρωτότητας κτηρίων βάσει μετρήσεων πεδίων

3∆μη γραμμική επαυξητική δυναμική ανάλυσηΠαράμετρος απόκρισης:μέγιστο σχετικό βέλος ορόφου

Μη γραμμική προσομοίωση των αναπροσαρμοσμένων προσομοιωμάτων:- Κατανεμημένη πλαστικότητα- Γεωμετρικές μη γραμμικότητες

Κατασκευή των καμπυλών τρωτότητας

Σεισμική απαίτηση:Επιλογή πραγματικών σεισμικών καταγραφών

Μεθοδολογία κατασκευής καμπυλών:Αβεβαιότητες στη σεισμική απαίτηση και στη διαθέσιμη απόκριση

Αναπροσαρμογή αριθμητικού προσομοιώματος

Σύγκριση πειραματικού και αρχικού αριθμητικού προσομοιώματος:Αξιολόγηση συνάρτησης απόκρισης

Ιδιομορφική ανάλυσηΑνάλυση ευαισθησίας στα υλικά

Επιλογή του «βέλτιστου» αναπροσαρμοσμένου αριθμητικού προσομοιώματος

Σχήμα I.21. ∆ιάγραμμα ροής της μεθοδολογίας για την αποτίμηση της σεισμικής τρωτότητας κτηρίων οπλισμένου σκυροδέματος με βάση μετρήσεις πεδίου

Στην παρούσα διατριβή η μεθοδολογία αυτή εφαρμόσθηκε για το κτήριο της

νευρολογικής κλινικής του νοσοκομείου ΑΧΕΠΑ της Θεσσαλονίκης. Το υπό μελέτη κτήριο

(ΕΝΙΑΙΟ ΚΤΗΡΙΟ) έχει κατασκευαστεί το 1971 και αποτελείται από δύο επιμέρους κτήρια



(ΚΤΗΡΙΟ Γ και ΚΤΗΡΙΟ ∆) που ενώνονται μεταξύ τους μέσω κατασκευαστικού αρμού

(Σχήμα I.22). Πρόκειται για δύο υψηλά πλαισιακά συστήματα οκτώ ορόφων από

οπλισμένο σκυρόδεμα με περιμετρική τοιχοποιία που έχουν σχεδιασθεί με βάση χαμηλού

επιπέδου αντισεισμικό κανονισμό (Βασιλικό ∆ιάταγμα ’59). Έτσι παρόλο που σε στατικό

επίπεδο θεωρείται πως λειτουργούν ανεξάρτητα, σε επίπεδο δυναμικής συμπεριφοράς υπό

ισχυρή σεισμική διέγερση αναμένεται η μεταξύ τους αλληλεπίδραση λόγω της σύνδεσής

τους μέσω του αρμού. Το ύψος των ορόφων παραμένει σταθερό και ίσο με 3.4m και για

τα δυο κτήρια με εξαίρεση τον δεύτερο όροφο όπου το ύψος του ορόφου αυξάνεται στα

4.8m λόγω της ύπαρξης μεσοπατώματος. Η θεμελίωση του κτηρίου Γ αποτελείται από

μεμονωμένα πέδιλα ενώ για την περίπτωση του κτηρίου ∆ τα πέδιλα συνδέονται μερικώς

με κοιτόστρωση. Ο Πίνακας I.6 παρουσιάζει συγκεντρωμένα τα βασικά χαρακτηριστικά

των κτηρίων σε όρους μάζας, και αντοχής των υλικών σκυροδέματος fc και χάλυβα fy.

ΚΤΗΡΙΟ Γ ΚΤΗΡΙΟ Δ

ΚΤΗΡΙΟ Γ ΚΤΗΡΙΟ Δ

Κατασκευαστικός αρμός

Σχήμα I.22. Νευρολογική κλινική του νοσοκομείου ΑΧΕΠΑ: τυπικός όροφος και όροφος μεσοπατώματος των δυο επιμέρους κτηρίων και η ένωσή τους μέσω του κατασκευαστικού αρμού

Πίνακας I.6. Κύρια χαρακτηριστικά των υπό μελέτη κτηρίων της νευρολογικής κλινικής

Κτήριο Συνολική μάζα (t) fc (MPa) fy (MPa)

ΚΤΗΡΙΟ Γ 3804.0 14.0 220.0 and 500.0

ΚΤΗΡΙΟ ∆ 3144.0 14.0 220.0 and 500.0

Στα πλαίσια του ερευνητικού προγράμματος REAKT (http://www.reaktproject.eu/),

διεξήχθη τον Φεβρουάριο 2013 στο υπό μελέτη κτήριο πείραμα μετρήσεων θορύβου

εγκαθιστώντας ένα προσωρινό δίκτυο 36 σεισμογράφων υπό την επίβλεψη του

Εργαστηρίου Γεωτεχνικής Σεισμικής Μηχανικής ΑΠΘ σε συνεργασία με το GFZ Potsdam

(http://www.gfz-potsdam.de/en/home/). Οι μετρήσεις θορύβου διήρκησαν 4-6 ώρες και η

διάταξη των οργάνων ήταν τέτοια ώστε να είναι δυνατή η εκτίμηση των μεταφορικών και

στρεπτικών ιδιομορφών των κτηρίων με τη μεγαλύτερη δυνατή ακρίβεια. Συγκεκριμένα σε



κάθε όροφο των επιμέρους κτηρίων εγκαταστάθηκαν τέσσερα όργανα κατά μήκος του

κεντρικού διαδρόμου όπως φαίνεται στις τομές του Σχήματος I.23. Ο ρυθμός

δειγματοληψίας ορίστηκε στα 500Hz.

Σχήμα I.23. Τομές Α-Α’ και Β-Β’ κατά τη διαμήκη και εγκάρσια διεύθυνση του νοσοκομειακού κτηρίου με τη διάταξη του προσωρινού δικτύου

Μετά από κατάλληλη επεξεργασία οι καταγραφές χρησιμοποιήθηκαν για την

ιδιομορφική ανάλυση του κτηρίου υπό συνθήκες λειτουργίας του (Operational Modal

Analysis) ώστε να εκτιμηθούν τα πραγματικά δυναμικά τους χαρακτηριστικά. Η

ιδιομορφική ανάλυση των επιμέρους κτηρίων (ΚΤΗΡΙΟ Γ και ΚΤΗΡΙΟ ∆) αλλά και του

ενιαίου κτηρίου (ΕΝΙΑΙΟ ΚΤΗΡΙΟ) πραγματοποιήθηκε με το πρόγραμμα MACEC3.2 το

οποίο λειτουργεί σε περιβάλλον Matlab (Reynders et al., 2011). Ο κάνναβος των

πειραματικών προσομοιωμάτων ορίστηκε έτσι ώστε οι κόμβοι του μοντέλου να

αντιστοιχούν στις θέσεις των οργάνων (Σχήμα I.23). Η ιδιομορφική ανάλυση των

θεωρούμενων συστημάτων έγινε με βάσει παραμετρικών (Stochastic Subspace

Identification SSI Van Overschee and De Moor, 1996) και μη παραμετρικών

μεθοδολογιών (Frequency Domain Decomposition FDD Brincker et al., 2000). Τα

αποτελέσματα των FDD και SSI μεθοδολογιών σε όρους ιδιάζουσων τιμών και

διαγραμμάτων σταθεροποίησης αντιστοίχως, παρουσιάζονται στο Σχήμα I.24. Στον Πίνακα

I.7 παρουσιάζονται συγκεντρωμένα τα αποτελέσματα της ιδιομορφικής ανάλυσης σε όρους

ιδιοσυχνοτήτων και αποσβέσεων (για την SSI μέθοδο).



ΚΤΗΡΙΟ Γ - FDD ΚΤΗΡΙΟ ∆- FDD ΕΝΙΑΙΟ ΚΤΗΡΙΟ- FDD

ΚΤΗΡΙΟ Γ - SSI ΚΤΗΡΙΟ ∆ - SSI ΕΝΙΑΙΟ ΚΤΗΡΙΟ - SSI

Σχήμα I.24. Αποτελέσματα ταυτοποίησης των υπό μελέτη συστημάτων με βάση τις μεθόδους FDD και SSI

χρησιμοποιώντας μετρήσεις θορύβου

Πίνακας I.7. Αποτελέσματα ιδιομορφικών αναλύσεων με βάση την FDD και SSI μεθοδολογία για το

ΚΤΗΡΙΟ Γ, ΚΤΗΡΙΟ ∆ και ΕΝΙΑΙΟ ΚΤΗΡΙΟ

Ιδιομορφές ΚΤΗΡΙΟ Γ ΚΤΗΡΙΟ ∆ ΕΝΙΑΙΟ ΚΤΗΡΙΟ

FDD (Hz) SSI (Hz, ξ %) FDD (Hz) SSI

(Hz, ξ %) FDD(Hz) SSI (Hz, ξ %)

1η: Συζευγμένη μεταφορική 1.65 1.65 0.8 1.65 1.65 0.9 1.65 1.65 0.8

2η: Συζευγμένη μεταφορική 1.90 1.91 1.3 1.91 1.91 1.1 1.91 1.91 0.8

3η: Στρεπτική 2.33 2.33 3.6 2.35 2.33 3.5 2.35 2.33 3.2 4η: 1η μεταφορική κατά τη διαμήκη διεύθυνση

3.50 3.47 5.4 3.58 3.52 5.8 3.58 3.51 6.4

5η: 2η μεταφορική κατά τη διαμήκη διεύθυνση

5.20 5.15 3.0 5.22 5.16 1.1 5.20 5.15 2.1

Με βάση τα αποτελέσματα της ιδιομορφικής ανάλυσης των πειραματικών

προσομοιωμάτων των μεμονωμένων κτηρίων επιχειρήθηκε η αναπροσαρμογή των

αντίστοιχων αριθμητικών προσομοιωμάτων με στόχο την όσο το δυνατόν καλύτερη

προσέγγιση των πειραματικών αποτελεσμάτων. Για το σκοπό αυτό διεξήχθησαν αναλύσεις

ευαισθησίας στο πρόγραμμα OpenSees με σκοπό τη σύγκλιση των ιδιομορφικών

χαρακτηριστικών των αριθμητικών με τα αντίστοιχα πειραματικά προσομοιώματα. Ως

παράμετρος ευαισθησίας θεωρήθηκε η θλιπτική αντοχή της εξωτερικής περιμετρικής

τοιχοποιίας. Κατά τη διαδικασία της αναπροσαρμογής των αριθμητικών προσομοιωμάτων

των μεμονωμένων κτιρίων εξετάστηκαν πέντε διαφορετικά σενάρια θεωρώντας



διαφορετική τιμή της εξεταζόμενης παραμέτρου ευαισθησίας ανάλογα με τη θέση των

τοιχοπληρώσεων στην κάτοψη του κτηρίου. Η επιλογή του βέλτιστου σεναρίου βασίστηκε

στην εκτίμηση του συντελεστή MAC (Modal Assurance Criterion, Allemang and Brown,

1982) μέσω του οποίου πραγματοποιήθηκε η συσχέτιση των ιδιομορφών μεταξύ των

πειραματικών και αναλυτικών προσομοιωμάτων. Η σύγκλιση θεωρείται ικανοποιητική για

τιμές του συντελεστή MAC μεγαλύτερες του 0.8. Στους Πίνακες I.8 και I.9 παρουσιάζονται

τα αποτελέσματα της αναπροσαρμογής των κτηρίων Γ και ∆ αντίστοιχα. Μέσω αυτής της

διαδικασίας, επιτεύχθηκε ικανοποιητική σύγκλιση των ιδιομορφών και για τα δυο κτήρια Γ

και ∆ με εξαίρεση τη δεύτερη ιδιομορφή του κτιρίου ∆ όπου ο συντελεστής MAC προέκυψε

ιδιαίτερα χαμηλός, πιθανόν λόγω της ιδιαίτερης μορφολογίας του κτηρίου αυτού. Σε αυτή

την περίπτωση πιθανώς μια άλλη παράμετρος που θα συσχετίζεται εκτός από η δυσκαμψία

και με τη μάζα του κτηρίου να ήταν καταλληλότερη. Ο λόγος που δεν επιλέχθηκε μια

τέτοια παράμετρος οφείλεται στην πολυπλοκότητα και στη δυσκολία ελέγχου των

αποτελεσμάτων καθώς και στη σημαντική αβεβαιότητα που περικλείει ο ορισμός της μάζας

για ένα τέτοιου τύπου κτήριο (π.χ. κατανομή καθ’ ύψος και όροφο).

Στη συνέχεια πραγματοποιήθηκε μια σειρά μη γραμμικών βήμα προς βήμα δυναμικών

αναλύσεων για τα μη γραμμικά αναπροσαρμοσμένα προσομοιώματα πεπερασμένων

στοιχείων των δύο κτηρίων καλύπτοντας ένα ευρύ φάσμα σεισμικών εντάσεων από την

ελαστικότητα έως τη γενικευμένη δυναμική αστάθεια των κτηρίων (Vamvatsikos and

Cornell, 2002). Για το σκοπό αυτό επιλέχθηκαν 15 πραγματικές σεισμικές καταγραφές από

τη βάση δεδομένων ESMD (http://www.isesd.hi.is) που αντιστοιχούν σε έδαφος

κατηγορίας Β σύμφωνα με τον Ευρωκώδικα 8. Η επιλογή των καταγραφών έγινε με βάση

το μέγεθος σεισμικής ροπής (5.8<Mw<7.2), την επικεντρική απόσταση (0<R<45km)

καθώς και την ελαχιστοποίηση της απόκλισης του προκύπτοντος μέσου

κανονικοποιημένου φάσματος επιταχύνσεων από το αντίστοιχο φάσμα για την περιοχή του

υπό μελέτη κτιρίου (όπως ελήφθη από το SHARE) για τιμές ιδιοπεριόδων 0<Τ<2.0sec

(Σχήμα I.25).



Πίνακας I.8. Σύγκριση του αναπροσαρμοσμένου προσομοιώματος του κτηρίου Γ με το αντίστοιχο αρχικό και πειραματικό προσομοίωμα (T: ιδιοπερίοδος, f: ιδιοσυχνότητα)

Αρχικό αριθμητικό προσομοίωμα T (sec)/f(Hz)

Αναπροσαρμοσμένο αριθμητικό προσομοίωμα

T (sec)/f(Hz)

Πειραματικό προσομοίωμα T(sec)/f(Hz) MAC

Συζευγμένη μεταφορική T1=0.69sec/f1=1.46Hz

0.96

T1=0.64sec/f1=1.56Hz T1=0.61sec/f1=1.65Hz


0.94

T2=0.53sec/f2=1.89Hz T2=0.52sec/f2=1.91Hz

Στρεπτική T3=0.37sec/f3=2.70Hz

0.97

T3=0.37sec/f3=2.70Hz T3=0.43sec/f3=2.33Hz Πίνακας I.9. Σύγκριση του αναπροσαρμοσμένου προσομοιώματος του κτηρίου ∆ με το αντίστοιχο

αρχικό και πειραματικό προσομοίωμα (T: ιδιοπερίοδος, f: ιδιοσυχνότητα) Αρχικό αριθμητικό προσομοίωμα T (sec)/f(Hz)

Αναπροσαρμοσμένο αριθμητικό προσομοίωμα

T (sec)/f(Hz)

Πειραματικό προσομοίωμα T(sec)/f(Hz)

MAC


0.98

T1=0.65sec/f1=1.54Hz T1=0.61sec/f1=1.65Hz


<0.8 Λόγω της ιδιαίτερης μορφολογίας

T2=0.53sec/f2=1.89Hz T2=0.52sec/f2=1.91Hz

Στρεπτική T3=0.36sec/f3=2.77Hz

0.94

T3=0.35sec/f3=2.86Hz T3=0.43sec/f3=2.33Hz



Σχήμα I.25. Σύγκριση μέσου κανονικοποιημένου ελαστικού φάσματος απόκρισης επιταχύνσεων των κινήσεων εισαγωγής με το αντίστοιχο κανονικοποιημένο φάσμα του SHARE για περίοδο επαναφοράς

τα 475 έτη (http://portal.share-eu.org:8080/jetspeed/portal/)

Πραγματοποιήθηκαν μη γραμμικές βήμα προς βήμα επαυξητικές δυναμικές αναλύσεις

για την κατασκευή των καμπυλών τρωτότητας των αρχικών καθώς και των

αναπροσαρμοσμένων αριθμητικών προσομοιωμάτων των δύο μεμονωμένων κτηρίων. Ως

παράμετρος βλάβης επιλέχθηκε το μέγιστο σχετικό βέλος ορόφων maxISD, καθώς

θεωρείται ότι αντιπροσωπεύει ικανοποιητικά τη δυναμική αστάθεια πλαισιακών κτηρίων.

∆εδομένου ότι οι σεισμικές διεγέρσεις εφαρμόστηκαν σε δύο διευθύνσεις, το μέγιστο

σχετικό βέλος ορόφων maxISD υπολογίστηκε ως η τετραγωνική ρίζα του αθροίσματος

των τετραγώνων των σχετικών βελών ορόφου κάθε διεύθυνσης. Ως μέτρο σεισμικής

έντασης επιλέχθηκε η μέγιστη εδαφική επιτάχυνση (PGA) λόγω της απλότητάς της. Με

βάση τα ζεύγη PGA και maxISD όπως προέκυψαν από κάθε δυναμική ανάλυση,

κατασκευάστηκαν οι καμπύλες απόκρισης των βήμα προς βήμα δυναμικών αναλύσεων

αυξανόμενης έντασης για κάθε κτήριο. Για τις ανάγκες της παρούσας εργασίας ορίστηκαν

δύο στάθμες βλάβης: της άμεσης χρήσης μετά το σεισμό «ΑΧ» και της αποφυγής

κατάρρευσης «ΑΚ», οι οριακές τιμές των οποίων υπολογίστηκαν με βάση τα αποτελέσματα

των δυναμικών αναλύσεων για κάθε κτήριο ξεχωριστά. Με τη λογική αυτή υπολογίστηκε

κοινή οριακή τιμή για τη στάθμη βλάβης ΑΧ ίση με 0.1% για τα αρχικά και τα

αναπροσαρμοσμένα προσομοιώματα ενώ η οριακή τιμή για τη στάθμη βλάβης ΑΚ

υπολογίστηκε ίση με 1.4% και 1.1% για τα αρχικά και αναπροσαρμοσμένα

προσομοιώματα αντίστοιχα (Σχήμα I.26).



(a)

(b) Σχήμα I.26. Ορισμός των οριακών τιμών ΑΧ και ΑΚ των αναπροσαρμοσμένων προσομοιωμάτων βάσει

των καμπυλών απόκρισης των δυναμικών βήμα προς βήμα επαυξητικών αναλύσεων

Στο Σχήμα I.27 παρουσιάζονται συγκριτικά οι καμπύλες τρωτότητας του αρχικού

αριθμητικού προσομοιώματος και της βιβλιογραφίας για τη συγκεκριμένη τυπολογία

κτηρίου. Συγκεκριμένα για τη σύγκριση επιλέχθηκαν οι καμπύλες των Kappos et al.

(2003;2006) για πλαισιακά τοιχοπληρωμένα υψηλά κτήρια Ο/Σ σχεδιασμένα με βάση

χαμηλού επιπέδου κανονισμό. Και για τα δυο κτήρια παρατηρείται γενικά καλή σύγκλιση

μεταξύ των καμπυλών που αντιστοιχούν στη στάθμη βλάβης ΑΧ. Για τη στάθμη βλάβης ΑΚ

παρατηρείται πως οι καμπύλες των Kappos et al. (2003) είναι πολύ πιο κοντά με τις

καμπύλες των κτηρίων Γ και ∆ σε σχέση με τις καμπύλες των Kappos et al. (2006). Η

διαφορά αυτή είναι ενδεικτική της μεγάλης διασποράς που μπορεί να εμφανίσουν μεταξύ

τους οι καμπύλες τρωτότητας γενικευμένου τύπου που αναφέρονται στις ίδιες τυπολογίες

κτηρίων. Να σημειωθεί πως η διαφοροποίηση μεταξύ των καμπυλών των Kappos et al.,

(2003) και Kappos et al. (2006) αποδίδεται σε διαφορετικά γεωμετρικά χαρακτηριστικά

των προσομοιωμάτων που αναλύθηκαν για την κατασκευή των καμπυλών αυτών.



Σχήμα I.27. Συγκριτικά γραφήματα των καμπυλών τρωτότητας για τα αρχικά αριθμητικά προσομοιώματα των δυο επιμέρους κτηρίων Γ και ∆ και των καμπυλών των Kappos et al. (2003;2006)

για την ίδια τυπολογία

Οι αρχικές καμπύλες τρωτότητας χρησιμοποιούνται για την εκτίμηση του επιπέδου

βλάβης για το σεισμό της Θεσσαλονίκης του 1978. Για την αξιολόγηση των βλαβών λόγω

του συγκεκριμένου σεισμού χρησιμοποιούνται οι αρχικές καμπύλες τρωτότητας αφού

αυτές πλησιάζουν περισσότερο στην πραγματική κατάσταση των κτηρίων την εποχή

εκείνη. Θεωρώντας ένα επίπεδο έντασης ίσο με 0.3g, οι πιθανότητες για μικρές βλάβες και

πλήρη κατάρρευση ισοδυναμούν με 98% και 2% αντίστοιχα, ποσοστά που είναι συμβατά

με τα υπάρχοντα αρχεία καταγραφής βλαβών για τον συγκεκριμένο σεισμό, για τον οποίο

δεν είχαν καταγραφεί σημαντικές βλάβες για το συγκεκριμένο κτήριο.

Στο Σχήμα I.28 οι καμπύλες τρωτότητας των αναπροσαρμοσμένων αριθμητικών

προσομοιωμάτων των δυο κτηρίων Γ και ∆ συγκρίνονται με αυτές των αρχικών.

Παρατηρείται πως η τρωτότητα των αναπροσαρμοσμένων προσομοιωμάτων είναι

μεγαλύτερη σε σύγκριση με τα αρχικά ιδιαίτερα για τη στάθμη βλάβης που αντιστοιχεί

στην αποφυγή κατάρρευσης ΑΚ. Από τη στιγμή που η αύξηση αυτή δεν αποδίδεται σε

γεωμετρικές παρεκκλίσεις αλλά σε διαφοροποίηση των υλικών (σε όρους τιμών και

κατανομών), θα μπορούσε να υποτεθεί πως τα κτήρια έχουν υποστεί φθορά στο χρόνο,

όπως για παράδειγμα λόγω φαινομένων γήρανσης.

Βάσει των παραπάνω παρατηρήσεων, για τα δυο επιμέρους κτήρια της νευρολογικής

κλινικής κατασκευάστηκαν χρονικά εξαρτώμενες καμπύλες τρωτότητας λαμβάνοντας

υπόψη τη διάβρωση του οπλισμού λόγω της διείσδυσης χλωριόντων εφαρμόζοντας το

μοντέλο της ενότητας Ι.3. Για το ίδιο σενάριο διάβρωσης και για ένα χρονικό σενάριο 45

ετών (που αντιστοιχεί στην ηλικία των κτηρίων), πραγματοποιήθηκαν μη γραμμικές βήμα

προς βήμα αναλύσεις. Οι οριακές τιμές των σταθμών βλάβης υπολογίστηκαν βάσει των

καμπυλών απόκρισης ίσες με 0.1% για την ΑΧ και 1% για την ΑΚ. Στο Σχήμα I.29

παρουσιάζονται συγκεντρωμένες οι καμπύλες τρωτότητας όλων των προσομοιωμάτων που



θεωρήθηκαν στα πλαίσια αυτής της μελέτης, δηλαδή των αρχικών, των

αναπροσαρμοσμένων και των διαβρωμένων φορέων.

Σχήμα I.28. Συγκριτικά γραφήματα των καμπυλών τρωτότητας των αρχικών και αναπροσαρμοσμένων κτηρίων Γ και ∆

Σχήμα I.29. Συγκριτικά γραφήματα των καμπυλών τρωτότητας των αρχικών, αναπροσαρμοσμένων και διαβρωμένων προσομοιωμάτων των κτηρίων Γ και ∆



I.6 Συμπεράσματα

Οι καταστρεπτικές συνέπειες των ισχυρών σεισμών σε κτήρια, υποδομές αλλά και σε

ανθρώπινες ζωές, καθιστούν επιτακτική την ανάγκη ανάπτυξης μεθοδολογιών

βελτιωμένης αξιοπιστίας για την αποτελεσματική αποτίμηση και μείωση της σεισμικής

διακινδύνευσης. Ωστόσο η ποσοτική εκτίμηση της σεισμικής διακινδύνευσης εμπεριέχει

πλήθος αβεβαιοτήτων που παρεμποδίζουν τον αντικειμενικό προσδιορισμό της. Μια από τις

πιο σημαντικές συνιστώσες, που εμπεριέχει σημαντικά επίπεδα αβεβαιοτήτων, αποτελεί η

αποτίμηση της σεισμικής τρωτότητας των κατασκευών που υπόκεινται στον κίνδυνο

σεισμικής διέγερσης. Στο πλαίσιο αυτό, ένα εκ των βασικότερων επιτευγμάτων της

συγκεκριμένης διδακτορικής διατριβής αποτελεί η διατύπωση ολοκληρωμένης

μεθοδολογίας βελτιωμένης αξιοπιστίας για την αποτίμηση της σεισμικής τρωτότητας

κτηρίων οπλισμένου σκυροδέματος με την συνεκτίμηση φαινομένων, τα οποία μέχρι τώρα

έχουν αντιμετωπιστεί μόνο επιμεριστικά, όπως η γήρανση των υλικών, η αλληλεπίδραση

εδάφους – κατασκευής και η συνεκτίμηση της δυναμικής συμπεριφοράς βάσει μετρήσεων

πεδίου. Η αξιοπιστία της γενικής αναλυτικής μεθοδολογία αποτίμησης της σεισμικής

τρωτότητας κτηρίων Ο/Σ επιβεβαιώθηκε μέσω της ικανοποιητικής σύγκρισης των

εξαχθέντων καμπυλών τρωτότητας με διαθέσιμες από τη βιβλιογραφία καμπύλες για

διάφορες τυπολογίες κτηρίων. Ένας από τους πρωταρχικούς στόχους της διατριβής ήταν η

μελέτη επιρροής του χρόνου ως βασική συνιστώσα της σεισμικής τρωτότητας

προτείνοντας χρονικά εξαρτώμενες καμπύλες και επιφάνειες τρωτότητας για κτήρια Ο/Σ

διαφόρων τυπολογιών σχεδιασμένα με διαφορετικά επίπεδα αντισεισμικού κανονισμού.

Όταν λαμβάνεται υπόψη η επιρροή της γήρανσης των υλικών και πιο συγκεκριμένα η

διάβρωση του οπλισμού λόγω διείσδυσης χλωριόντων, παρατηρείται σημαντική αύξηση

της σεισμικής τρωτότητας. Πέρα από την επιρροή της γήρανσης, προτάθηκαν επίσης

καμπύλες τρωτότητας κτηρίων Ο/Σ λαμβάνοντας υπόψη την επιρροή φαινομένων

αλληλεπίδρασης εδάφους-κατασκευής και των τοπικών εδαφικών συνθηκών.

Παρατηρείται ότι η δυναμική αλληλεπίδραση εδάφους-κατασκευής σε συνδυασμό με τις

τοπικές εδαφικές συνθήκες επηρεάζουν σημαντικά τη σεισμική απόκριση κτηρίων Ο/Σ

θεμελιωμένα σε μαλακά εδάφη, αυξάνοντας την τρωτότητά τους σε σύγκριση με τις

πακτωμένες κατασκευές εδραζόμενες σε βράχο όπου τα φαινόμενα αυτά αγνοούνται.

Όταν λαμβάνεται υπόψη η μη γραμμικότητα του εδάφους, η επίδραση των φαινομένων

αυτών αναμένεται να είναι απομειωμένη σε σχέση με την περίπτωση θεώρησης ελαστικού

γραμμικού εδάφους. Γενικά ωστόσο, η δυναμική αλληλεπίδραση εδάφους-κατασκευής υπό

τη θεώρηση είτε ελαστικού είτε ανελαστικού εδάφους αυξάνει τη σεισμική τρωτότητα της

πακτωμένης κατασκευής θεμελιωμένης σε βράχο. Το συζευγμένο σύστημα έδαφος-

κατασκευή για την περίπτωση θεώρησης ελαστικού εδάφους ουσιαστικά δεν παρουσιάζει

διαφοροποιήσεις σε σχέση με το αντίστοιχο πακτωμένο μοντέλο που συνυπολογίζει την



επιρροή των τοπικών εδαφικών συνθηκών. Αντίθετα όταν η συμπεριφορά του εδάφους

είναι ανελαστική η ∆ΑΕΚ οδηγεί σε αύξηση της τρωτότητας σε σύγκριση με τον αντίστοιχο

πακτωμένο φορέα λόγω της πολύπλοκης, μη γραμμικής συμπεριφοράς του υποκείμενου

εδάφους που εισάγει στην κατασκευή επιπρόσθετες παραμορφώσεις και αυξάνει την

απαίτηση σε μετακινήσεις. Τέλος σημαντική είναι η συμβολή της διατριβής στην αποτίμηση

της σεισμικής τρωτότητας κτηρίων βάσει μετρήσεων πεδίου. Η προταθείσα μεθοδολογία

χρησιμοποιεί κατά βάση μετρήσεις θορύβου (υπό προϋποθέσεις και σεισμικές καταγραφές

χαμηλής έντασης) για την εκτίμηση της δυναμικής συμπεριφοράς του κτηρίου τη

δεδομένη στιγμή μελέτης του. Με αυτόν τον τρόπο λαμβάνονται υπόψη όλα τα πιθανά

φαινόμενα φθοράς (λόγω γήρανσης ή προϋπαρχόντων σεισμικών βλαβών) που θα

μπορούσαν να διαφοροποιήσουν τη σεισμική απόκριση των υφισταμένων κτηρίων και να

υποτιμήσουν σημαντικά τη σεισμική τρωτότητά τους.

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