Investigation of Seismic Behavior of Infill Wall Surrounded by … · Then, my family especially my...

University of Minho

School of Engineering

Onur ONAT

Investigation of Seismic Behavior of Infill

Wall Surrounded by Reinforced Concrete

Frame

Doctoral Thesis

Civil Engineering

Work performed under the supervision of

Professor Paulo B. Lourenço

Co-Supervisor

Assoc. Prof. Dr. Ali Koçak

Yıldız Technical University, Istanbul, TURKEY

October 2015

vii

DECLARATION

Name: Onur Onat

E-mail: [email protected]

Phone number: (+90) 535 527 0108

Doctoral thesis title: Investigation of Seismic Behaviour of

Infill Wall Surrounded by Reinforced

Concrete Frame

Supervisor: Professor Doutor Paulo José Brandão

Barbosa Lourenço

Co-Supervisor: Assoc. Prof. Dr. Ali Koçak (Turkey)

Year of conclusion: 2015

Area of knowledge: Civil Engineering

THE INTEGRAL REPRODUCTION OF THIS DISSERTATION IS ONLY

AUTHORIZED FOR RESEARCH EFFECTS, AFTER WRITTEN DECLARATION

OF THE INTERESTED PARTY, TO WHICH IT PLEDGES TO COMPLY.

University of Minho, October 2015

iii

ACKNOWLEDGMENTS

The research of a PhD thesis is a great and long journey. During this long experience, I

want to give my great pleasures to my individuals around me.

First of all I want to give my great pleasure to Allah (God) to create for me an

opportunity to study my PhD thesis in Portugal.

Second, thanks to my supervisor Professor Koçak to accept me as a PhD student when I

was following a professor to study PhD.

Third, I would like to express a great thanks to Prof. Lourenço to accept me as a PhD

student. For sharing his time and his great scientific knowledge with me without doubt.

Then, my family especially my mother and my friends; Dr. Erkut Sayın, Dr. Burak Yön,

Dr. Nuno Mendes from Portugal, all LNEC engineers and staff in Lisbon. My PhD

thesis progress jury members; Prof. Dr. Yusuf AYVAZ and Prof. Dr. Tülay AKSU

ÖZKUL.

Finally, I wish to express my gratitude to my mother and all friends.

v

ABSTRACT

90 % of Turkey territory is under earthquake threat. Many earthquake struck the country

in the last 20 years. Large earthquakes can be listed like 1993 Erzincan, 1995 Afyon

Dinar, 1996 Adana Ceyhan, 1999 Gölcük, 1999 Düzce, 2003 Bingöl and last three years

8 Mart 2010 Elazığ Kovancılar, 2011 Van Tabanlı and then 2011 Van Edremit. It was

experienced with these earthquakes that life loss and economic loss of Turkey is

extremely high. It was also understood that defects and problems of failure are focused

on main bearing elements namely reinforced concrete elements. Finally, life and

economic loss can also occur even without completely failed structures, only with

partially failed structures. A possible reason for these losses is the collapse of masonry

infill wall.

The main, and one of the most important, reason of economic and life loss during

earthquakes is related to infill walls behavior, both in-plane and out-of-plane. In a

sismic activity, the expected behaviour of structure is to follow nonlinear post-peak

behaviour under earthquake load until the end of seismic activity, without total collapse

to prevent life loss. This study is focused on the behavior of infilled structures along

combined in-plane and out-of-plane directions. For this purpose, masonry solutions in

Turkey and rest of Europe are investigated. In particular, the out-of-plane beahvior of

unreinforced infill wall was studied with and without bed joint reinforcement.

The purpose of this thesis is to investigate seismic behaviour of infill wall surrounded

by reinforced concrete frame. The seismic effect that causes both in-plane and out-of-

plane behaviour of infill wall was performed on the shake table. This in-plane and out-

of-plane force was applied bidirectional at simultaneously. Numeric and experimental

studies were performed in terms of crack propagation and failure modes of infill wall.

This dissertation is divided into two main parts. In Part A, one reinforced concrete

frame with two leaf cavity brick wall (TLCW) simulated with a finite element software.

TLCW model was scaled 1:1.5 according to Cauchy Froude similitude law. After

modelling of this structure; firstly model updating was performed on material properties

according to dynamic identification test. The purpose of model updating is to verify

material properties that obtained experimentally before performance analysis of the

structure. Then, pushover analysis was performed on the mentioned structure. After that

nonlinear time history analysis was performed. After both of the nonlinear analysis,

interstorey drift curves were plotted. These plottted interstory curves were evaluated

with experimental curves according to ASCE SEI 41/06. In addition to TLCW model,

an imaginary reinforced concrete sturcture with unreinforced brick wall (URM) model

was used in pushover and nonlinear time history analysis to see the effect of infill wall

thickness on performance curve. The size of complete URM structure is the same as

TLCW model except infill wall thickness. In this URM model single layer 13 cm

thickness infill wall was used. DIANA software was used in numeric part of this thesis.

Second part of the thesis composed of three one bay one storey reinforced concrete

frame with unreinforced infill wall and reinforced infill wall. The scale of the specimens

were 1:1 due to real dimensions of isolated prototype and the size of the specimens were

6.4x3.25m. 1:1 scale is a common scale for isolated particular prototype test specimen.

These specimens were exposed to simultaneous bidirectional earthquake load on shake

table. During the test in-plane and out-of-plane behaviour of infill walls were

considered and evaluated together. The tested specimens were prototype simulation of

vi

7th floor of 8 storey building. Roof and 8th storey loads were considered as prestressed

reinforcement in columns and beams. These prototype specimens were exposed to

bidirectional earthquake load on shake table. The properties of the seismic load is

narrow band low frequency along in-plane direction and narrow band high frequency

along out-of-plane direction. During the first test there was an incomplete boundary

condition problem due to a 2 mm gap on the strut. For this reason the specimen has not

damaged enough along in-plane direction as expected. The specimen had a different

failure mode due to this boundary condition problem. After experience of this test, test 1

repated with new strut mechanism. Successful results were obtained from repeated test.

Then, in-plane failure mode and damage map were determined. After that test 2 was

performed with reinforced concrete frame with bed joint reinforcement. Bed joint

reinforcement is a reinforcing technique to prevent life and economic loss during the

earthquake. After test 2, succesfull results were obtained as expected. Force – drift

curves were plotted, in-plane and out-of-plane damage maps were drawn and out-of-

plane simulation curves were plotted for test 2. Limit bearing loads were calculated for

both experimental models according to formulas in literature and regulations. These

calculated limit loads were compared with experimental results.

…

Keywords: Infill wall, model calibration, pushover analysis, time history analysis,

shake table, retrofit of infill wall, finite element, out-of-plane behaviour

vii

RESUMO

90% do território da Turquia está sob ameaça terremoto. Muitos terremoto atingiu o

país nos últimos 20 anos. Grandes terremotos podem ser listados como Erzincan 1993,

1995 Afyon Dinar, 1996 Adana Ceyhan, 1999 Gölcük, 1999 Düzce, 2003 Bingöl e

último três anos 8 Mart 2010 Elazığ Kovancılar, 2011 Van Tabanlı e, em seguida, 2011

Van Edremit. Foi experimentado com estes terremotos que a perda de vida e perda

econômica da Turquia é extremamente alta. Ele também foi entendido que os defeitos e

problemas de insucesso estão focados em elementos de apoio principais, nomeadamente

elementos de betão armado. Finalmente, a vida ea perda econômica também pode

ocorrer mesmo sem estruturas completamente falidas, apenas com estruturas

parcialmente falhou. Uma possível razão para essas perdas é o colapso da parede de

alvenaria de enchimento.

O principal, e um dos mais importantes, devido a perdas económicas e vida durante

terramotos está relacionada com o comportamento de enchimento paredes, tanto no

plano e fora do plano. Em uma atividade sísmica, o comportamento esperado da

estrutura é seguir o comportamento pós-pico não linear sob carga terremoto até o final

da atividade sísmica, sem colapso total para evitar perda de vida. Este estudo é focado

sobre o comportamento das estruturas infilled juntamente combinado no plano e fora do

plano instruções. Para este efeito, as soluções de alvenaria na Turquia e resto da Europa

são investigados. Em particular, o comportamento fora do plano da parede de

enchimento sem reforço foi estudada com e sem cama reforço da articulação.

O objetivo desta tese é investigar o comportamento sísmico de parede de enchimento

rodeado por estrutura de concreto reforçado. O efeito sísmica que faz com que tanto no

plano e fora do plano da parede de conduta de enchimento foi realizada sobre a mesa de

trepidação. Este e out-of-plane força foi aplicada no plano bidirecional no

simultaneamente. Estudos numéricos e experimentais foram realizados em termos de

propagação de trincas e modos de falha parede de enchimento. Esta dissertação está

dividida em duas partes principais. Na Parte A, uma estrutura de concreto armado com

dois parede de tijolo cavidade folha (TLCW) simulado com um software de elementos

finitos. Modelo TLCW foi escalado 1: 1,5 acordo com a lei similitude Cauchy Froude.

Depois da modelação desta estrutura; Em primeiro lugar a actualização do modelo foi

realizado em propriedades do material de acordo com o teste de identificação dinâmica.

O objectivo do modelo de actualização é para verificar as propriedades dos materiais

obtidos experimentalmente que, antes da análise da estrutura de desempenho. Em

seguida, a análise foi realizada em tarefa simples a estrutura mencionada. Depois que a

análise não linear história tempo foi realizada. Depois de tanto da análise não linear, as

curvas de deriva interstorey foram plotados. Estas curvas interstory plottted foram

avaliados com curvas experimentais de acordo com a ASCE SEI 41/06. Além de

modelo TLCW, um sturcture concreto imaginário reforçado com parede de tijolo sem

reforço modelo (URM) foi usado na tarefa simples e análise da história não-linear de

tempo para ver o efeito da espessura da parede de enchimento na curva de desempenho.

O tamanho da estrutura URM completa é a mesma como modelo TLCW excepto

espessura de parede de enchimento. Neste modelo URM foi usada parede de

enchimento única camada 13 cm de espessura. DIANA software foi usado em parte

numérica desta tese.

viii

Segunda parte da tese composto por três um compartimento de um piso de concreto

reforçado com a parede de enchimento sem reforço e parede de enchimento reforçado.

A escala dos espécimes foram 1: 1 e o tamanho dos espécimes foram 6.4x3.25m. Estas

amostras foram expostas a carga terremoto bidirecional simultânea na tabela shake.

Durante o teste no plano e fora do plano comportamento de paredes de enchimento

foram consideradas e avaliadas em conjunto. Os espécimes testados foram simulação

protótipo do 7º andar de 8 andares. Telhado e oitavo andares cargas foram consideradas

como reforço pré-esforçado em colunas e vigas. Estas amostras de protótipos foram

expostos a carga terremoto bidirecional na tabela shake. As propriedades da carga

sísmica é baixa frequência de banda estreita ao longo da direção no plano e estreito de

alta frequência da banda ao longo da direção out-of-plane. Durante o primeiro teste foi

um problema de condição de limite incompleta devido a um intervalo de 2 mm sobre o

suporte. Por esta razão, a amostra não tenha danificado o suficiente ao longo da direção

no plano conforme o esperado. A amostra tinha um diferente modo de falha devido a

este problema condição de contorno. Após a experiência deste teste, teste de 1 repated

com novo mecanismo de suporte. Bons resultados foram obtidos a partir de ensaio

repetido. Em seguida, foram determinados modos de falha e danos mapa in-plane.

Depois que o teste 2 foi realizado com estrutura de cimento armado com cama de

reforço da articulação. Cama reforço conjunta é uma técnica de reforço para evitar a

vida e perdas econômicas durante o terremoto. Após o teste 2, foram obtidos resultados

succesfull como esperado. Force - curvas de deriva foram plotados, no plano e fora do

plano mapas de danos foram sorteados e out-of-plane curvas de simulação foram

plotados para o teste 2. limite cargas de rolamento foram calculadas para ambos os

modelos experimentais de acordo com fórmulas na literatura e regulamentos . Estas

cargas limite calculados foram comparados com os resultados experimentais.

…

Palavras-chave: Parede de enchimento, calibração do modelo, análise pushover,

Análise História tempo, mesa vibratória, retrofit de parede de enchimento, elemento

finito, out-of-plane comportamento

ix

ÖZET

Yüzde doksanı deprem tehlikesi altında olan ülkemizde son 20 yıl içinde olan

depremlere bakıldığında bunlar; 1993 Erzincan, 1995 Afyon Dinar, 1996 Adana

Ceyhan, 1999 Gölcük, 1999 Düzce, 2003 Bingöl ve son üç yıl içerisinde ise 8 Mart

2010 Elazığ Kovancılar, 2011 Van Tabanlı köyü ve akabinde 2011 Van’ın Edremit

ilçesi olan 5.6 büyüklüğündeki son deprem meydana gelmiştir. Deprem tehlikesini çok

yoğun yaşayan ülkemizdeki bu depremlerden elde edilen tecrübeler göstermiştir ki can

ve mal kaypları ciddi oranlarda olmaktadır. Bunları azaltmak için ülkemizde taşıyıcı

sistem elemanlarına sürekli önem verilip hata ve kusurların sadece bu elemanlarda

olduğu düşünülmektedir. Oysaki can ve mal kayıpları hasarlı olup kısmi göçmüş ama

toptan göçme olmamış bir binada da olabilmektedir ve bunların sebepleri de taşıyıcı

olmayan ama yapının rijitliğine ciddi katkısı olan duvar elemanlardır.

İki kısımdan oluşan bu tezde, deprem etkisindeki betonarme çerçeveli dolgu duvarların

sismik davranışı incelenmişir. Düzlem içi ve düzlem dışı davranışların oluşumuna sebep

olan sismik etki eş zamanlı olarak sarsma tablasında simule edilmiş olup, dolgu

duvardaki çatlak ilerlemeleri ve göçme metodları hem sayısal hem de deneysel olarak

incelenmiştir. Bu tez kapsamında öncelikli olarak Cauchy-Froude benzetim kanununa

göre 1:1.5 oranında ölçeklendirilmiş iki katmanlı betonarme çerçeveli dolgu duvarlı bir

yapının, bir sonlu elemanlar programında simülasyonu yapılarak daha önce yapılan

sarsma tablası deneyinden elde edilmiş verilere göre; model kalibrasyonu yapılmıştır.

Model kalibrasyonun yapılmasındaki amaç, deneysel olarak elde edilmiş olan malzeme

parametrelerinin doğruluğunu saptamak ve yapılacak olan performans analizlerinden

doğru sonuçlar elde etmek. Model kalibrasyondan sonra itme analizi ile sayısal

çalışmaya devam edilmiş, akabinde ise lineer olmayan zaman tanım alanında yapılan

çözüm yapılmıştır. Hem itme analizinin hem de lineer olmayan zaman tanım alanındaki

çözümünden elde edilen katlar arası göreli ötelenme ASCE SEI 41/06 yönetmeliğine

göre deneysel verilerle birlikte kıyaslanmıştır. Duvar kalınlığının sistemin

performansına olan katkısını göstermek için deneysel sonuçları olan çift katmanlı

duvara ait sayısal çalışma, herhangi bir deneysel verisi olmayan ama deneye tabi

tutulmuş olan model ile aynı boyutlarda olacak şekilde betonarme elemanlara sahip

fakat 13 cm kalınlığındaki güçlendirmesiz tek tabakalı duvarı olan hayali bir model ile

performans eğrileri ve göreli kat deplasmanları açısından kıyaslanmıştır. Birinci kısıma

konu olan çalışmalar, DIANA sonlu elemanlar programıyla modellenmiştir.

İkinci kısım çalışmalar ise tek katlı, tek açıklıklı 1:1 ölçeğinde gerçek yapıdan izole

edilmiş 6.4x3.25m boyutlarına sahip prototip yapı, güçlendirmesiz ve derz donatı ile

güçlendirilmiş tuğla duvarların sarsma tablasında suni eş zamanlı çift yönlü deprem

kuvvetlerine maruz bırakılarak düzlem içi ve düzlem dışı davranışları aynı anda

incelenmiştir. Teste tabi tutulan bu yapı 8 katlı ve üç açıklıklı bir yapının 7. Katını

temsil eden prototipi olarak düşünüşmüştür. 1:1 ölçek oranı, bu tür gerçek yapıdan izole

edilmiş prototip yapıların deneysel çalışması için kullanılan yaygın ölçek türüdür.

Prototip numunelerin kolon ve kirişleri üzerindeki diğer katların ağırlığını temsil etmesi

için öngermeli donatılar yerleştirilmiştir. Prototip numune, eş zamanlı çift yönlü suni

deprem kuvvetine sarsma tablası üzerinde maruz bırakılmıştır. Numunelere uygulanan

deprem kuvvetleri düzlem içinde dar bantlı düşük frekanslı, düzlem dışı ise dar bantlı

yüksek frekanslıdır. İlk numune olan güçlendirmesiz duvar ile yapılan deneysel çalışma

esnasında, tamamlanmamış mesnet şartlarından dolayı numune, düzlem içi yeteri kadar

hasar almamıştır. Beklenen kuvvet-deplasman değerleri yakalanamamıştır. Sistem

x

beklenen hasarı göstermediği için literatürden farklı bir göçmeye sebep vermiştir.

Tamamlanmamış sınır şartı problemi; sistemin düzlem içinde hasar almasını sağlayan

gergi elemanın bağlantılarının deney esnasında yeterli rijitliği sağlayamaması. Daha

sonra bu deney tekrar edilmiş ve başarılı sonuçlar alınmıştır. Alınan sonuçlar ile düzlem

içi hasar ve göçme haritası belirlenmiştir. Düzlem dışı ise göçme mekanizması adım

adım simüle edilmiştir. Derz donatılı ikinci numune ile yapılan ve beklenen sonuçların

alındığı diğer deneyle düzlem içi ve düzlem dışı kuvvet-deplasman, kıyaslaması

yapılmıştır. Ayrıca ikinci numunenin de düzlem içi ve düzlem dışı hasar göçme

haritaları belirlenerek, düzlem dışı davranışları simüle edilmiştir. Son olarak düzlem

dışı, iki numunenin de taşıyabileceği limit yükler literatürdeki formüllere göre

hesaplanmış ve deneysel sonuçlardan elde edilen limit yüklerle yakınsaklıkları

kıyaslanmıştır.

Anahtar Kelimeler: Dolgu duvarlar, modal kalibrasyon, itme analizi, zaman tanım

alanında çözüm, sarsma tablası, güçlendirme, sonlu elemanlar, DIANA

ix

TABLE OF CONTENTS

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

Abstract ............................................................................................................. v

Resumo ............................................................................................................ vii

Özet .................................................................................................................. ix

Table of Contents ............................................................................................. ix

List of tables ................................................................................................... xiii

List of figures ................................................................................................. xiv

1 Introduction

1.1 Literature Review ................................................................................................... 1

1.1.1 Seismicity of Turkey ....................................................................................... 1

1.1.2 Seismicity of the World ................................................................................... 9

1.1.3 In-plane Behaviour of Infill Wall .................................................................. 10

1.1.4 Out-of-plane Behaviour of Infill Wall ........................................................... 18

1.1.5 Retrofitting Techniques of Infill Wall ........................................................... 26

1.2 Objective of the thesis ........................................................................................... 28

1.3 Hypothesis ............................................................................................................ 29

1.4 Outline of the Thesis ............................................................................................. 29

1.5 References ............................................................................................................. 30

2 Part A: Preparation of Numeric Model & Model Updating of Two Leaf

Cavity Wall Reinforced Concrete Structure

2.1 Introduction ........................................................................................................... 36

2.2 Model Calibration Indicators ................................................................................ 38

2.2.1. Modal Assurance Criterion (MAC) ............................................................... 38

2.2.2. Coordinate Modal Assurance Criterion (COMAC)....................................... 39

2.2.3. Normalized Modal Differences (NMD) ........................................................ 40

x

2.3. Model Updating Techniques ................................................................................. 40

2.3.1. Douglas-Reid Method ................................................................................... 40

2.3.2. Robust Method .............................................................................................. 41

2.4. Finite Element Simulation of Two Leaf Cavıty Wall Reinforced Concrete

Structure ........................................................................................................................... 42

2.5. Model Calibration of Two Leaf Cavity Wall Reinforced Concrete Structure ...... 47

2.5.1. Calibration Number 1 .................................................................................... 53





2.6. Conclusion ............................................................................................................ 65

2.7. References ............................................................................................................. 65

3 Part A: Pushover Analysis of Reinforced Concrete Structures with Two

Leaf Cavity Wall and Unreinforced Brick Wall

3.1. Introduction ........................................................................................................... 68

3.2. Parameterization ................................................................................................... 70

3.2.1. Total Strain Crack Model (Fixed and Rotating) ............................................ 71

3.2.2. Combined Cracking Shear Crush .................................................................. 72

3.3. Pushover Analysis ................................................................................................. 77

3.3.1. Regular Newton-Raphson Method ................................................................ 79

3.3.2. Analysis of the Results for TLCM ................................................................ 80

3.3.3. Analysis of the Results for URM .................................................................. 85

3.3.4. Comparison between TLCW and URM for Push-Over Curve...................... 89

3.3.5. Comparison of Drift Levels with Codes ........................................................ 95

3.3.6. Evaluation of the Stiffness ............................................................................. 98

3.3.7. Crack patterns ................................................................................................ 99

3.4. Conclusion .......................................................................................................... 108

3.5. References ........................................................................................................... 108

4 Part A: Time History Analysis of Reinforced Concrete Structures with

Two Leaf Cavity Wall and Unreinforced Masonry Wall

4.1 Introduction ......................................................................................................... 111

xi

4.2 Input Signals ....................................................................................................... 113

4.3. Secant Analysis Method (Quasi Newton Method) ............................................. 116

4.3.1. Broyden ....................................................................................................... 118

4.3.2. BFGS ........................................................................................................... 118

4.3.3. Crisfield ....................................................................................................... 119

4.4. Time History Analysis of TLCW Model ............................................................ 119

4.5. Time History Analysis of URM Model .............................................................. 129

4.6. Comparison of Time History Analysis Results .................................................. 132

4.7. Conclusion .......................................................................................................... 136

4.8. References ........................................................................................................... 137

5 Part B: Shake Table Test Setup

5.1. Introduction ......................................................................................................... 138

5.2. Prototype Definition ........................................................................................... 140

5.3. Infill Wall for URM ............................................................................................ 143

5.4. Test Setup and Related Apparatus Definition ..................................................... 145

5.5. Instrumentation ................................................................................................... 149

5.5.1. Accelerometer .............................................................................................. 150

5.5.2. Hamamatsu Displacement Measuring Device ............................................. 151

5.5.3. Krypton Displacement Measuring Device .................................................. 152

5.5.4. LVDT Displacement Measuring Device ..................................................... 153

5.6. References ........................................................................................................... 154

Model 0: Unreinforced Brick Wall (Failed Test)

6.1. Input Signals and Characterization of Model-0 .................................................. 155

6.2. Mode Shapes and Mode Frequencies ................................................................. 158

6.2.1. Longitudinal Frequencies and Mode Shapes ............................................... 158

6.2.2. Transversal Frequencies and Mode Shapes ................................................. 159

6.3. Analyses and Results .......................................................................................... 160

Model 1: Unreinforced Brick Wall (Successful Test)

7.1. Input Signals and Accelerations for Test 1 ......................................................... 172

7.2. In-plane Curves ................................................................................................... 174

7.3. Out-of-Plane Curves and Behavior ..................................................................... 175

xii

7.4. Crack Patterns and Damage Maps ...................................................................... 188

7.5. Modal Frequencies and Damage Indicator ......................................................... 191

Model 2: Bed Joint Reinforcement Brick Wall

8.1. Brief Definition of Infill Wall ............................................................................. 194

8.2. Input Signals and Accelerations for Test 2 ......................................................... 195

8.3. In-plane results .................................................................................................... 196

8.4. Out-of-plane Results ........................................................................................... 197

8.5. Crack Patterns and Failure Mechanism of Test 2 ............................................... 208

8.6. Modal Frequencies and Damage Indicator of Test 2 .......................................... 209

Comparison of Results and Discussion of Experiments ............................... 211

Conclusion & Recommendation ................................................................... 217

xiii

LIST OF TABLES Table 1. 1 R1 Values for Different Height/Thickness Ratio (Angel, 1994) ................................................ 20

Table 1. 2 𝜆2 values to calculate q in Eqn. 2.12 (FEMA 273, 1997) ......................................................... 26

Table 2. 1 Engineering Properties of Concrete and Infill belong to FE TLCW Model .............................. 48

Table 2. 2 Eigenvalue analyses results for model selection........................................................................ 51

Table 2. 3 Parameter importance table for modal updating ........................................................................ 53

Table 2. 4 Updating summary for calibration 1 .......................................................................................... 54

Table 2. 5 Updating Summary for Calibration 2 ........................................................................................ 58




Table 3. 1 Return periods and maximum acceleration of earthquakes exposed to TLCW structure (Leite et

al., 2011; Leite, 2014) ........................................................................................................................... 80

Table 3. 2 Engineering properties of concrete and infill belong to TLCW ................................................ 82

Table 3. 3 Engineering properties of interface belong to TLCW ............................................................... 83

Table 3. 4 Dissipated energy of fine meshed model ................................................................................... 88

Table 3. 5 Dissipated energy of coarse meshed model ............................................................................... 88

Table 3. 6 Experimental energy dissipation capacity ................................................................................. 89

Table 3. 7 Performance levels for primary elements of reinforced concrete frames (ASCE/SEI 41-06,

2007) ..................................................................................................................................................... 95

Table 3. 8 Stiffness of fine meshed model ................................................................................................. 98

Table 3. 9 Stiffness of coarse meshed model ............................................................................................. 98

Table 4. 1 Brief Summary of Shake Table Experiments .......................................................................... 113

Table 4. 2 Displacement Comparison of Experimental Structure and Finite Element Model at 100%

Earthquake Load: Node Number 95 for 1st story, 255 for 2

nd story .................................................... 124

Table 4. 3 Displacement Summary TLCW Model at Stage 4 .................................................................. 128

Table 4. 4 Displacement summary TLCW model at Stage 5 ................................................................... 129

Table 5. 1 Properties of shaking table test machine at LNEC .................................................................. 142

Table 6. 1 Parameters to determine response spectrum for shake table tests ........................................... 156

Table 6. 2 Mode frequencies for longitudinal directions .......................................................................... 158

Table 6. 3 Mode frequencies for transversal direction ............................................................................. 159

Table 6. 4 Target and applied load percent in both directions .................................................................. 160

Table 7. 1 Target and Applied Earthquake Loads in Percentage (%) ....................................................... 172

Table 7. 2 Force and Drift (mm) values of Model-1 during Shake Table ................................................ 174

Table 7. 3 Summary of out-of-plane behavior of infill wall ..................................................................... 178

Table 7. 4 Natural vibration periods of specimen 1 after each two test step in transversal direction ....... 191

Table 7. 5 Natural vibration periods of specimen 1 after each two test step in longitudinal direction ..... 191

Table 8. 1 Target and Applied Loads During Test 2 ................................................................................ 196

Table 8. 2 Natural vibration periods of specimen 2 after each test step in transversal direction .............. 209

Table 8. 3 Natural vibration periods of specimen 2 after each test step in longitudinal direction ............ 209

xiv

LIST OF FIGURES

Figure 1. 1 Seismicity map of Turkey (AFAD, 2015) .................................................................................. 2

Figure 1. 2 Out-of-plane collapse of infill wall during 1999 Marmara earthquake (Bruneu, 2002) ............. 3

Figure 1. 3 Seismicity of NAF (Kocak,2010) ............................................................................................... 3

Figure 1. 4 Out-of-plane failure of brick infill wall (Doğangün, 2006)........................................................ 4

Figure 1. 5 Out-of-plane failure of gabble wall (Doğangün, 2006) .............................................................. 5

Figure 1. 6 Out-of-plane failure of adobe house (Celep et al., 2010) ........................................................... 6

Figure 1. 7 Out-of-plane failure of infill wall during Kovancılar earthquake (Celep et al., 2010) ............... 6

Figure 1. 8 Out-of-plane failure of infill wall during Van earthquake in 2011 (Kızılkanat et al., 2011; Yön,

2014) ....................................................................................................................................................... 7

Figure 1. 9 Failure of infill wall due to out-of-plane behavior during Van earthquake (photo belong to

author) ..................................................................................................................................................... 8

Figure 1. 10 Out-of-plane failure of infill wall during L’Aquila earthquake (Leite, 2015) .......................... 9

Figure 1. 11 Talha administration building (Elnashi et al., 2010) .............................................................. 10

Figure 1. 12 Partial story collapse of O’Higgins tower (Elnashi et al., 2010) ............................................ 10

Figure 1. 13 Collapse mechanism of solid infill masonry with reinforced concrete frame (Shing and

Mehrabi, 2002) ..................................................................................................................................... 13

Figure 1. 14 Failure mechanisms of infills with eccentric openings (Kakaletsis and Karayannis, 2007) .. 15

Figure 1. 15 Prototype and shake table to assess out-of-plane action by Hashemi (Hashemi and Mosalam,

2006) ..................................................................................................................................................... 17

Figure 1. 16 Prototype and shake table to assess out-of-plane action by Stavridis (Stavridis et al., 2012) 17

Figure 1. 17 Experimental Test Up and Specimen Constructed by Dawe and Seah (Dawe and Seah, 1989)

.............................................................................................................................................................. 18

Figure 1. 18 Experimental Test Setup Used by Angel (Angel, 1994) ........................................................ 19

Figure 1. 19 In-plane Damage Classification by Angel (Angel, 1994) ...................................................... 20

Figure 1. 20 Tested Specimens by Calvi and Bolognini (Calvi and Bolognini, 2001) ............................... 22

Figure 1. 21 Airbag Test Setup Used by Griffith et al. (2007) ................................................................... 22

Figure 1. 22 Damage Maps of Tested Solid Specimens by Griffith (2007) ............................................... 23

Figure 1. 23 Test Setup Used by Komaraneni (2009) ................................................................................ 23

Figure 1. 24 In-plane and Out-of-plane Action of Test (Komaraneni, 2009) ............................................. 24

Figure 1. 25 Test Setup Used by Pereira (Pereira, 2013) ........................................................................... 25

Figure 2. 1 CL18B three nodes curved beam element ................................................................................ 43

Figure 2. 2 CQ40S eight nodes curved shell element ................................................................................. 43

Figure 2. 3 CQ40L eight nodes layered curved shell element .................................................................... 44

Figure 2. 4 CL24I three nodes line to shell interface element a) Topology, b) Displacement ................... 44

Figure 2. 5 Full view of model after constructing FEM; a, c, e and g View of FEM, b, d, f and h Drawing

of Structure ........................................................................................................................................... 47

Figure 2. 6 Solid View of the TLCW structure .......................................................................................... 47

Figure 2. 7 Experimental Modes of Reinforced Concrete Structure with Two Leaf Cavity Infill Wall ..... 48

xv

Figure 2. 8 Elastic Foundation Properties used under Foundation ............................................................. 50

Figure 2. 9 Modes of FE model .................................................................................................................. 52

Figure 2. 10 COMAC values for 4 modes .................................................................................................. 55

Figure 2. 11 NMD values for 4 modes ....................................................................................................... 56

Figure 2. 12 MAC values for 4 modes ....................................................................................................... 56

Figure 2. 13 Frequency comparison FE TLCW model .............................................................................. 57

Figure 3. 1 Performance curve of a typical structure (Ghobarah, 2001) .................................................... 69

Figure 3. 2 Propagation of cracks at two leaf cavity wall model just before collapse (Leite, 2010) .......... 71

Figure 3. 3 Coloumb friction model combined with tension cut-off and elliptical compression cap ......... 72

Figure 3. 4 Hardening and softening rule for interface element’s compression cap ................................... 77

Figure 3. 5 Flow chart of iteration steps during the nonlinear static analysis ............................................. 78

Figure 3. 6 Iteration type of Regular Newton-Raphson Method ................................................................ 80

Figure 3. 7 Hysteric curves of experimental earthquake data belongs to 4 stages in transversal direction 81

Figure 3. 8 Hysteric curve of experimental earthquake data belongs to 4 stages in longitudinal direction 82

Figure 3.9 Fine mesh (Onat et al., 2015) .................................................................................................... 84

Figure 3.10 Coarse mesh (Onat et al., 2015) .............................................................................................. 84

Figure 3. 11 Force – Displacement curve of TLCW reinforced concrete frame fine and coarse mesh along

transversal direction .............................................................................................................................. 84

Figure 3. 12 Force – Displacement curve of TLCW reinforced concrete frame fine and coarse mesh along

longitudinal direction ............................................................................................................................ 85

Figure 3. 13 Force-Displacement curves of TLCW and URM infill structures (Coarse Mesh) along


Figure 3. 14 Force-Displacement curves of TLCE and URM infill structures (Coarse Mesh) along


Figure 3. 15 Force-Displacement curves of TLCE and URM infill structures (Fine Mesh) along


Figure 3. 16 Force-Displacement curves of TLCE and URM infill structures (Fine Mesh) along


Figure 3. 17 Force ratio-Displacement curves of TLCE and URM along transversal direction (Fine Mesh)

.............................................................................................................................................................. 90

Figure 3. 18 Force ratio-Displacement curve of TLCE and URM along longitudinal direction (Fine Mesh)

.............................................................................................................................................................. 91

Figure 3. 19 Force ratio-Displacement curves of TLCW and URM along transversal direction (Coarse

Mesh) .................................................................................................................................................... 92

Figure 3. 20 Force ratio-Displacement curve of TLCE and URM along longitudinal direction (Coarse

Mesh) .................................................................................................................................................... 93

Figure 3. 21 Comparison of pushover curve belong to fine and coarse mesh along transversal direction

(Onat et al., 2015) ................................................................................................................................. 94

Figure 3. 22 Comparison of pushover curve belong to fine and coarse mesh along longitudinal direction

(Onat et al., 2015) ................................................................................................................................. 94

xvi

Figure 3. 23 Storey Level - % Drift in Transversal Direction .................................................................... 95

Figure 3. 24 Storey Level - Drift (%) in Longitudinal Direction (Onat et al., 2015) .................................. 96

Figure 3. 25 Maximum displacements (mm) along storey height in transversal direction at maximum

force ratio .............................................................................................................................................. 97

Figure 3. 26 Changes of maximum displacement (mm) along storey height in longitudinal direction ...... 97

Figure 3. 27 Experimental crack propagation of TLCW before stage 4 (Leite, 2014) ............................... 99

Figure 3. 28 Crack pattern of TLCW in transversal directions with fine mesh before failure (Loading

Type: Positive Transversal) ................................................................................................................ 100

Figure 3. 29 Crack pattern of TLCW in longitudinal directions with fine mesh before failure (Loading

Type: Positive longitudinal) ................................................................................................................ 101


Type: Negative Transversal) ............................................................................................................... 102


Type: Negative Longitudinal) ............................................................................................................. 102

Figure 3. 32 Crack pattern of TLCW in transversal directions with coarse mesh before failure (Loading


Figure 3. 33 Crack pattern of TLCW in longitudinal directions with coarse mesh before failure (Loading

Type: Positive Longitudinal) .............................................................................................................. 103

Figure 3. 34 Crack pattern of TLCW in transversal directions with coarse mesh before failure (Loading


Figure 3. 35 Crack pattern of TLCW in longitudinal directions with coarse mesh before failure (Loading


Figure 3. 36 Crack pattern of URM in transversal directions with fine mesh at the time of failure (Loading


Figure 3. 37 Crack pattern of URM in longitudinal directions with fine mesh at the time of failure

(Loading Type: Positive Longitudinal) ............................................................................................... 105

Figure 3. 38 Crack pattern of URM in transversal directions with fine mesh before failure (Loading Type:

Negative Transversal) ......................................................................................................................... 106

Figure 3. 39 Crack pattern of URM in longitudinal directions with fine mesh before failure (Loading


Figure 3. 40 Crack pattern of URM in transversal directions with coarse mesh before failure (Loading


Figure 3. 41 Crack pattern of URM in longitudinal directions with coarse mesh before failure (Loading

Type: Negative longitudinal) .............................................................................................................. 107

Figure 4. 3 Input Acceleration of 100 % Earthquake in Transversal Direction ........................................ 115

Figure 4. 4 Input Acceleration of 100 % Earthquake in Longitudinal Direction ...................................... 116

Figure 4. 5 Quasi-Newton Iteration .......................................................................................................... 117

Figure 4. 6 Crack Propagation of TLCW Model at the End of Stage 1 .................................................... 120



xvii

Figure 4. 9 Control Points during the Time History Analysis to Compare Results .................................. 123

Figure 4. 10 Instrumentation of Accelerometer to Measure Two Way Acceleration ............................... 123

Figure 4. 11 Comparison of Displacements along Transversal Direction: Node Number 95 (100%

Earthquake Load) ................................................................................................................................ 125

Figure 4. 12 Comparison of Displacements along Longitudinal Direction: Node Number 32 (100%

Earthquake Load) ................................................................................................................................ 126

Figure 4. 13 Crack Propagation of TLCW Model at the Time of Collapse at Stage 4 ............................. 127

Figure 4. 14 Heavy Damages and Heavy Cracks of Model at Stage 5 (225% Earthquake Load) ............ 128

Figure 4. 15 Numeric Crack Propagation for URM Model at Stage 1 ..................................................... 130



Figure 4. 18 Relative Displacement Comparison of Two Models with Experimental Results at Stage 3 133

Figure 4. 19 Interstory Drift in Transversal Direction .............................................................................. 133

Figure 4. 20 Interstory Drift in Longitudinal Direction ............................................................................ 134

Figure 4. 21 Base Shear – Roof Displacement (mm) ............................................................................... 135

Figure 5. 1 Simulated multistory structure and considered part of imaginary structure for TIM Test ..... 141

Figure 5. 2 Test specimen and surrounded steel apparatus ....................................................................... 142

Figure 5. 3 Shake table test setup at LNEC .............................................................................................. 143

Figure 5. 4 Used brick masonry for all tests ............................................................................................. 143

Figure 5. 5 General overview of URM specimen ..................................................................................... 144

Figure 5. 6 Production of reinforced concrete frames .............................................................................. 144

Figure 5. 7 Reinforced concrete frame before constructing infill wall ..................................................... 145

Figure 5. 8 Reinforced concrete frame with infill wall ............................................................................. 145

Figure 5. 9 Steel connections to support specimen ................................................................................... 146

Figure 5. 10 Steel frames around the specimen ........................................................................................ 147

Figure 5. 11 Roller boundary condition for specimen .............................................................................. 148

Figure 5. 12 Strut between specimen and south reaction wall .................................................................. 149

Figure 5. 13 Supplementary apparatus ..................................................................................................... 149

Figure 5. 14 Accelerometers ..................................................................................................................... 150

Figure 5. 15 Accelerometer instrumentation on infill wall ....................................................................... 151

Figure 5. 16 a) Hamamatsu Camera, b) Laser Reader .............................................................................. 151

Figure 5. 17 Main unit of Krypton ........................................................................................................... 152

Figure 5. 18 Switch and collector cables of Krypton ............................................................................... 153

Figure 5. 19 LVDT ................................................................................................................................... 153

Figure 6. 1 Longitudinal impulses for dynamic identification ................................................................. 157

Figure 6. 2 Transversal impulses for dynamic identification ................................................................... 157

Figure 6. 3 Signals of characterization ..................................................................................................... 158

Figure 6. 4 First 2 Modes of longitudinal direction .................................................................................. 159

Figure 6. 5 First 2 modes of transversal direction .................................................................................... 160

Figure 6. 6 Force – Drift (%) curve in both direction ............................................................................... 161

xviii

Figure 6. 7 Mode frequencies belong to first experiments (Model 0) ...................................................... 161

Figure 6. 8 Instrumentation of Accelerometers to Measure Out-of-Plane Accelerations ......................... 162

Figure 6. 93D Out-of-Plane Graphs a) 1st step earthquake load, b) 2

nd step earthquake load, c) 3

rd step

earthquake load ................................................................................................................................... 163

Figure 6. 10 Instrumentation of Krypton on the infill wall....................................................................... 164

Figure 6. 11 Displacement of infill wall measured by Krypton ............................................................... 165

Figure 6. 12 Location of correct measurement at last stage (Model 0) .................................................... 165

Figure 6. 13 PGA v.s. Displacement along HA3 (Model 0) ..................................................................... 166

Figure 6. 14 Acceleration amplification of HA3 line (Model 0) .............................................................. 167

Figure 6. 15 Instrumentation of Krypton and considered line numbers of Krypton (Model 0) ................ 167

Figure 6. 16 Displacement amplification of infill wall versus PGA (Model 0) ........................................ 168

Figure 6. 17 Displacements and damage of specimen after Step 3 (Front Side) ...................................... 169

Figure 6. 18 Damage of Step 3: 63 % earthquake load (Back Side)......................................................... 169

Figure 6. 19 Damage of specimen after 100 % earthquake load .............................................................. 170

Figure 6. 20 Step 5: Deformation after 263 % earthquake load ............................................................... 170

Figure 7. 1 PGA versus Number of Stages for URM Wall (Test1) .......................................................... 173

Figure 7. 2 In-plane Force – Drift curve (mm and %) Test 1 ................................................................... 174

Figure 7. 3 Distances between two Hamamatsu camera and location of Hamamatsu cameras ................ 175

Figure 7. 4 Out-of-Plane Forces – Drift curve at North side .................................................................... 176

Figure 7. 5 Out-of-Plane Force – Drift curve at South side ...................................................................... 176

Figure 7. 6 Location of accelerometers that considered calculating average out-of-plane displacement of

infill wall in transversal direction ....................................................................................................... 177

Figure 7. 7 Out-of-Plane mid-displacement of infill wall according to mid-accelerometers ................... 178

Figure 7. 8 Instrumentation for out-of-plane evaluation (For Displacement) ........................................... 179

Figure 7. 9 Out-of-plane movements of infill wall and RCF at 10% eq. load Test 1 ............................... 179

Figure 7. 10 Out-of-plane movements of infill wall and RCF at 28% eq. load Test 1 ............................. 180



Figure 7. 13 Average out-of-plane displacements for all stages at Test 1 ................................................ 181

Figure 7. 14 Instrumentation to evaluate relative displacement for out-of-plane movement of infill wall

and reinforced concrete structure ........................................................................................................ 182

Figure 7. 15 Relative displacements of infill wall and RCF at 10% eq. Load Test 1 ............................... 182

Figure 7. 16 Relative displacements of infill wall and RCF at 28% eq. load Test 1 ................................ 183



Figure 7. 19 Average relative out-of-plane displacement of infill wall and reinforced concrete frame for

left line all stages Test 1 ..................................................................................................................... 185

Figure 7. 20 Average relative out-of-plane displacement of infill wall and reinforced concrete frame for

right line all stages Test 1 ................................................................................................................... 185

Figure 7. 21 Out-of-plane acceleration amplification of infill wall and RCF at 10% eq. load Test 1 ...... 186

xix




Figure 7. 25 Crack propagation at 28% eq. load Test 1 ............................................................................ 188

Figure 7. 26 Crack propagation and damage map for 61% eq. load Test 1 West side ............................. 189

Figure 7. 27 Crack propagation and damage map for 95% eq. load Test 1 West side ............................. 190

Figure 7. 28 Damage map for 292% eq. load Test 1 West side ................................................................ 190

Figure 7. 29 Damage map for 217% eq. load Test 1 East side ................................................................. 191

Figure 7. 30 Damage Indicator for Test 1; Infill Wall (URM) ................................................................. 193

Figure 8. 1 Bed Joint Reinforcement (BJR) and Construction Phase ....................................................... 195

Figure 8. 2 Dimension Detail and Position of Mortar Joints in the Mortar .............................................. 195

Figure 8. 3 PGA versus Number of Stages for Bed Joint Reinforcement ................................................ 196

Figure 8. 4 In-plane Force – Drift Curve (For Both mm and %) Test 2 ................................................... 197

Figure 8. 5 Out-of-plane Force – Drift Curve (For both mm and % Drift) for RCF at Test ..................... 197

Figure 8. 6 Force – Mid-displacement of Infill Wall at Test 2 ................................................................. 198

Figure 8. 7 Instrumentation, horizontal and vertical alignments for Test 2 .............................................. 198

Figure 8. 8 Out-of-plane movements of infill wall and RCF at 10% eq. load Test2 ................................ 199

Figure 8. 9 Out-of-plane movements of infill wall and RCF at 33% eq. load Test 2 ............................... 199


Figure 8. 11 Out-of-plane movements of infill wall and RCF at 105% eq. load Test 2 ........................... 200

Figure 8. 12 Out-of-plane movements of infill wall and RCF at 180% eq. load Test 2 ........................... 201

Figure 8. 13 Horizontal and vertical alignments to calculate relative displacements for Test 2............... 202




Figure 8. 17 Relative displacements of infill wall left line and RCF along all steps at Test 2 ................. 204

Figure 8. 18 Relative displacements of infill wall right line and RCF along all steps at Test 2 ............... 204




Figure 8. 22 Out-of-plane acceleration amplification of infill wall and RCF at 105% eq. load Test 2 .... 206

Figure 8. 23 Out-of-plane acceleration amplification of infill wall and RCF at 180% eq. load Test 2 .... 207

Figure 8. 24 Removed instruments at Test 2 Step 4 (180 % Eq. Load) .................................................... 207

Figure 8. 25 Crack propagation and failure mechanism of specimen at Test 2 ........................................ 208

Figure 8. 26 Damage indicator for Test 2; infill wall with BJR ............................................................... 210

Figure 9. 1 Comparison of Force – Drift curves for both models In-plane direction ............................... 212

Figure 9. 2 Comparison of Force – Drift curves of RCF for both models along out-of-plane direction .. 213

Figure 9. 3 Force – mid-displacement (mm) of infill walls ...................................................................... 214

Figure 9. 4 Force – mid-displacement curve for both model until 100% eq. load.................................... 215

xx

Chapter 1 – Introduction

1

Chapter 1 1 INTRODUCTION

1.1 LITERATURE REVIEW

1.1.1 Seismicity of Turkey

The biggest natural challenge of Turkey is the earthquake. There are two main active

faults that divide Turkey into two parts; North and South. One is the long active fault

that lays from East part to West part, passing by the Black sea region. This fault is

called the North Anatolian Fault (NAF). The other, active fault starts in the NAF,

South-East part and ends in the Mediterranean region (SAF). The seismicity map of

Turkey can be seen in Figure 1.1.

Investigation of Seismic Behavior of Infill Wall

2

Figure 1. 1 Seismicity map of Turkey (AFAD, 2015)

One of the biggest and the most disastrous earthquake in Turkey’s history is Erzincan

earthquake. Erzincan was struck by a devastating earthquake in 1939. The magnitude of

this earthquake was 8.0 and 6600 houses were destroyed. After many years, Erzincan

was struck by another earthquake in 1992. The magnitude of this earthquake was 6.8

and the epicenter of this last earthquake was only 7.7 km far from city center. The

unofficial total death toll was about 3000 and hundreds of houses were destroyed

(Bruneu and Saatcioglu, 1994). But the 1999 Marmara and Düzce earthquakes were the

biggest tragedy for Turkish people; as 17.000 people were killed (Bruneu, 2002) and

much damage was experiences, see Figure 1.2.


3

Figure 1. 2 Out-of-plane collapse of infill wall during 1999 Marmara earthquake

(Bruneu, 2002)

İstanbul is located at the end of the NAF zone. The seismicity of this fault is very high

as shown in Figure 1.3.

Figure 1. 3 Seismicity of NAF (Kocak,2010)


4

The performance of structures damaged by the 1999 Marmara earthquake was studied

by many researchers like Koçak (2010) (Kocak, 2010) and Sezen et al. (2002) (Sezen et

al., 2003). It was emphasized by Koçak that most of the buildings damaged by Marmara

earthquake is 6 storey’s high. A tragic reality revealed by Koçak was that concrete

quality for 28 % of the buildings is C14 or less, and 75 % of the buildings do not fulfill

the strength requirements of Turkish Earthquake Code (Sezen et al., 2003). Sezen et al.

listed errors such as strong beam – weak column, soft and weak stories, and poor quality

concrete (Doğangün, 2004). Only 4 years later, a 6.7 magnitude other earthquake on the

NAF struck Bingöl city for 10 s. The maximum PGA of 5.45 m/sn2 was recorded for

this earthquake. 1351 buildings were destroyed, 5617 buildings were heavily damaged,

900 people were killed and 700 people were injured seriously (Doğangün, 2004). The

observed structural deficiencies were nearly the same as with Marmara earthquake.

However, there was a new deficiency concept that came into the picture with this

earthquake “Infill Wall Failure” (Doğangün, 2006). The infill deficiencies were called

in this earthquake “Large and heavy overhangs and unconfined infill walls” (Doğangün,

2006). Out-of-plane failure of infill walls can be seen in Figure 1.4 and Figure 1.5

respectively.

Figure 1. 4 Out-of-plane failure of brick infill wall (Doğangün, 2006)


5

Figure 1. 5 Out-of-plane failure of gabble wall (Doğangün, 2006)

Large earthquakes hit Turkey nearly every year. After Bingöl earthquake Ağrı,

Doğubeyazıt was struck by an earthquake in 2007. Many masonry houses were

damaged by this earthquake, although this is a moderate magnitude (5.1) earthquake

(Bayraktar et al., 2007). 1000 buildings were affected and 18 people were killed due to

collapse of masonry buildings (Bayraktar et al., 2007). There were successive

earthquakes at Bala in 2007, with magnitude 5.5 and 5.7 respectively. Out-of-plane

failure took part as a new concept and wide discussion topic in literature with these

earthquakes in Turkey. However, the concept was discussed only for masonry and

adobe building with these structures. Bala region is very close to the capital city of

Ankara and this earthquake was also triggered by NAF (Ural et al., 2012). In the year

2010, Kovancılar, one of the districts of Elazığ city was struck by an earthquake with

the magnitude of 6.0. This district is very close to the starting point of NAF and SAF.

This earthquake damaged many rural adobe and masonry buildings as seen in Figure 1.6

and Figure 1.7 respectively.


6

Figure 1. 6 Out-of-plane failure of adobe house (Celep et al., 2010)

Figure 1. 7 Out-of-plane failure of infill wall during Kovancılar earthquake (Celep et al.,

2010)

The last earthquake tragedy for Turkey, very close to present time, is Van and Edremit

(Van) earthquakes. These earthquakes struck Van city and its district Edremit on 23

October 2011 and 9 November 2011. The magnitude of former was 6.6 and former the

earthquake lasted 25 s. The magnitude of the latter was 7.2. Absolute maximum ground

acceleration (PGA) was 195 cm/sn2 for Van earthquake. After these earthquakes 604

people were killed, 1301 people seriously injured and 2307 multistory structures were

collapsed (Kızılkanat et al., 2011). There were many structural deficiencies found but

one for them became prominent with these earthquakes. This structural deficiency was


7

weak behavior of infill wall along out-of-plane direction. Failure of building due to out-

of-plane behavior of infill wall can be seen in Figure 1.8 and Figure 1.9.

Figure 1. 8 Out-of-plane failure of infill wall during Van earthquake in 2011 (Kızılkanat

et al., 2011; Yön, 2014)


8

Figure 1. 9 Failure of infill wall due to out-of-plane behavior during Van earthquake

(photo belong to author)

In-plane and out-of-plane interaction is very complicated and should be analyzed well

for this phenomenon. For low-rise and mid-rise Unreinforced Masonry (URM) infilled

RC frames, ground story infill walls are expected to be damaged firstly. Because, they

are subjected to highest in-plane demands. However, under the effect of bidirectional

loading, where the two components of a ground motion are equally significant, infill

walls of the upper stories may fail under the combination of in-plane and out-of-plane

effects. The in-plane demand reduces at the upper stories, while that of out-of-plane

forces increases due to the increase of accelerations (Mosalam et al., 2015).

As seen from the figures above, the out-of-plane behavior of infill walls during the

earthquake play one of the most important roles about dissipating earthquake energy,

collapse mechanism, life and economic loss. The motivation of this thesis is out-of-

plane behavior of infill wall and contribution to structural mechanism during seismic

activity. To gain a better perspective, the seismicity of the world should also be

considered in terms of this aspect.


9

1.1.2 Seismicity of the World

In the last 10 years there were many hazardous earthquakes in the world, from Asia to

Europe. For instance, Sumatra earthquake that struck Indonesia in 29 December 2004.

The magnitude of this earthquake was 9.3. 226.226 people died and 49.648 people were

missing. Moreover, this earthquake triggered a tsunami that hit Indonesia and this

earthquake affected 12 countries (Rosetto et al., 2007). L’Aquila earthquake hit Italy in

the year 2009 and caused considerable amount economic loss and many deaths. Infill

wall contribution to reinforced concrete frame was emphasized and soft storey

mechanisms were found (Verderame et al., 2010). During this earthquake many

building suffered out-of-plane failure of infill walls as seen in Figure 1.10 (Leite, 2014).

a)Out-of-plane failure of

infill walls at upper stories

b)Out-of-plane failure of

infill walls at lower stories

c)Out-of-plane failure of

infill wall along

longitudinal direction

Figure 1. 10 Out-of-plane failure of infill wall during L’Aquila earthquake (Leite, 2015)

An 8.8 Magnitude earthquake struck Maule in Chile in the year 2010. It is predicted that

800.000 people are victim of this earthquake due to loss of their life, missing, injured

and house loss. This earthquake triggered a tsunami whose wave height was estimated

to reach 12 m in some places. Totally, 370.051 houses were damaged from this

earthquake (Elnashi, et al., 2010). Retrofitting of infill walls played an important role

during this earthquake. After the 8.8 magnitude earthquake in Chile, the behavior of

infill walls can be seen in Figure 1.11 and Figure 1.12 respectively below.


10

Figure 1. 11 Talha administration building (Elnashi et al., 2010)

Figure 1. 12 Partial story collapse of O’Higgins tower (Elnashi et al., 2010)

1.1.3 In-plane Behaviour of Infill Wall

The studies on increasing stiffness of structures due to masonry infill date back to 1954

in the world. In Turkey this kind of studies dates back to 1971. The first experimental

study in Turkey was implemented by Ersoy and Üzsoy (1971) (Ersoy and Üzsoy, 1971).

In this study, it was reported that nine one bay one storey reinforced concrete structures

with masonry infills were exposed to monotonic increasing cyclic load. Results of these

experiments showed that lateral stiffness of the structure increased 700 % and the


11

interstorey drift ratio decreased 65 % when compared with the bare frame (Ersoy and

Üzsoy, 1971).

Two reinforced concrete structures were tested by Liauw and Kwan (Liauw and Kwan ,

1992). In this study two specimens with four storey were prepared, one of them was

reinforced concrete with infill wall another of them was reinforced concrete with shear

wall from bottom to top. It is emphasized that these specimens were scaled 1:3 and their

earthquake performance were compared. Both specimens were exposed to El Centro

earthquake with time history analysis. It was reported that even if these two specimen

have nearly the same static strength, they had different base shear. On the base of this

study, it was emphasized that structure with infill wall had more lateral capacity than

the structure with shear wall (Liauw and Kwan, 1992).

Fourteen one bay, two storey infilled frames were tested by Altın et al (1992) under

reversed cyclic load. This experimental study had been done to investigate infill type,

connection type and flexural bearing capacity of reinforced concrete frame with infill.

This study used diagonal reinforcement, vertical pre-stressed reinforcement, dowel clips

at connection point and grid reinforcement. Superior performance was shown when

clips dowels connecting the infill and frame member are used (Altın et al., 1992).

12 one-bay, one-storey 1:2 scaled reinforced concrete frames with infill were tested by

Mehrabi et al. (1997). Nine of these specimens were designed 1:1.5 according to h/L

ratio and 3 of them were designed 1:5 according to h/L ratio. It was reported that there

is a considerable amount of stiffness increase like 30 % with increasing vertical load

among all specimens. Another output of this study was that the specimens with 1:5 h/L

ratio had shown 17 % more capacity while compared with the specimen with 1:2 h/L

ratio. The specimens which had the same h/L ratio but had different strength of infill

compared each other and reported that higher strength infill frame showed better

capacity with 28% higher strength against lateral loads

(Mehrabi et al. 1997a).

Mehrabi et al. (1997) were used a smeared crack model finite element model to present

a precise behavior of masonry mortar joints and cementious interface. This study

emphasized how important numerical simulation is with respect to adopting the correct

model and parameters. Compressive hardening behavior and bond slip behavior were

taken into consideration in this study. It was reported that bond slip behavior had an

important role on the response of bare frame but had not the same effect on the infilled


12

frames. Also, a main output of this study was a good correlation between the

experimental and numeric studies (Mehrabi et al., 1997b).

Mosalam et al. (1997) investigated infilled steel frame without openings, infilled steel

frame with openings and infilled steel frame with eccentric openings. The conclusion of

this study can be listed as follows;

Effect of number of bays on the infill; it was reported that there is 10 %

differences between the two bays and one bay specimens under lateral load.

Effect of openings on stiffness of structure; it was emphasized that openings

caused 40 % decrease at stiffness of the structure on pre-cracking behavior.

However these openings caused more ductile behavior at post-cracking behavior

(Mosalam et al., 1997a).

Mosalam et al. (1997) evaluated adding infill walls to reinforced concrete frames on the

basis of seismic fragility curves in their studies. This numeric study also proved that

strength and stiffness differences between complete structures and single bay, single

storey reinforced concrete structures can be change at different ratio levels. It was

reported that this ratio can be change from 15 % to 30 % (Mosalam et al., 1997b).

Flagananand and Bennett (1999) stated in their studies that obviously, designing a

reinforced concrete structure against bidirectional effect of seismic load result in

capacity decrease. Moreover it was reported that out of plane behavior of the structure is

mostly related to shear strength capacity of bed joint materials.

Buonopane and White (1999) implemented a pseudo dynamic experiment to investigate

performance of half scaled, two bay two storey, infill masonry based on Taft ground

motion. In this research that there were no openings at first storey but there were

window and door openings at second storey. The specimens were exposed to four

different levels of earthquake load. At the end of the first three ground motions, the

interstorey drifts were nearly equal at the first floor. However, it was reported that the

second floor had larger displacement. It was concluded that due to opening at second

floor, stiffness of the second storey was lower than first floor. Moreover, at last ground

motion, the top floors reached their capacity due to openings. It was concluded that, at

last stage of loading, specimens collapsed due to soft storey.

Shing and Mehrabi (2002) investigated in-plane and out-of-plane effects of the infill

wall on collapse mechanism. It was shown that the collapse mechanism completely


13

depends on strength of masonry infill and reinforced concrete. The in-plane collapse

mechanisms were idealized as seen in Figure 1.13 (Shing and Mehrabi, 2002).

Figure 1. 13 Collapse mechanism of solid infill masonry with reinforced concrete frame

(Shing and Mehrabi, 2002)

Also in this study, the ratio of openings in infill masonry was investigated and it was

emphasized that a 50 % opening causes a reduction of its strength around 20-30 %.

However, even if there is a decrease at stiffness of structure, it was reported that the

structure shows a more ductile behavior with a larger opening (Shing and Mehrabi,

2002).

Al-Chaar et al. (2002) implemented a series of experiments with five ½ scaled

reinforced concrete structure composed of infill and concrete masonry unit (CMU).

Outputs of this study were shared by authors like below;

The maximum load of two bay structure composed of infill masonry was

reported bigger than strongly designed single bay CMU unit.

The maximum resistivity load of three bay structure was 1.2 times bigger than

single bay structure.


14

The maximum lateral strength of single bay CMU unit infill wall is 24 times

bigger than single bay frame and the maximum lateral stiffness of infill wall is

18 times bigger than single bay frame.

Stiffness of two bay specimen composed of CMU unit is bigger than single bay

(Al-Chaar et al., 2002)

Anıl and Altın (2007) conducted an experimental study to investigate single bay single

storey reinforced concrete filled with partially of fully shear wall. These specimens

were casted at 1/3 scale and were exposed cyclic lateral loads. According to the reports,

the purpose of this study was to explain the behavior of partially filled shear wall into

reinforced concrete structure. It was reported that specimen which had window opening

at middle of the structure showed lower strength (28 %) while compared with solid

specimens. Moreover, it was emphasized that the specimen with opening collapsed due

to short column effect. Other contribution of this study is to clarify that after crushing of

corners, specimens were collapsed brittleness increased with the Lw/Hw ratio. It was

also observed that the pushover curve is overestimated, if the cyclic nature of lateral

loads is ignored (Anıl and Altın, 2007)

Kakaletsis and Karayannis (2007) conducted a series of tests to discuss the behavior of

a structure produced single bay 1/3 scaled. Openings in infill masonry structures were

located eccentrically. It was reported that the location of openings has no effect on the

serviceability limit. But if openings are located in the middle, peak load limit decreases.

Location of openings has more effect on energy absorption capacity than strength. It

was also reported that if openings are located very close to column, they dissipates more

energy than any other case. It was emphasized that at the end of experiment there were

some failure mechanism idealized as seen in Figure 1.14. Collapse mechanism is mostly

related to these strut mechanisms (Kakaletsis and Karayannis, 2007).


15

Figure 1. 14 Failure mechanisms of infills with eccentric openings (Kakaletsis and

Karayannis, 2007)

Pujol and Fick (2010) conducted an experiment with full scale reinforced concrete

structure. It was reported that this full scale three storey structure first was exposed

ground motion only with bare frame after that reinforced with infill masonry. The

authors indicated that brick masonry increased the stiffness of the structure by 100 %. In

this study to observe out of plane behavior, infill masonry was constructed with small

dimension brick. It was emphasized that infill masonry keeps interstorey drift ratio

under control. Infill masonry walls increased the stiffness of the structure by 500 %

(Pujol and Fick, 2010).

Varela-Rivera et al. (2011) tested six full scale confined masonry with different

boundary conditions. These experiments were implemented with airbag pressure.

Results were compared with different methods: yield line, failure line and compressive

strut method. In theory, the failure line method was not adequate for quasi-brittle

materials like masonry but it was used. It was reported that maximum stresses

concentrated on three or four sided specimens. It was emphasized that failure pressure

was estimated very close with failure line method. The maximum pressure was

estimated lower with the yield line method (Varela-Rivera et al., 2011).


16

Baloevic et al. (2013) modeled two bay planar reinforced concrete structure with infill.

In this study both macro and micro models were used. In this study phase analysis was

used to simulate original constructing facilities. At first the reinforced concrete structure

was modeled. Afterwards, nonlinear analysis with self-weight infill masonry was added

to model. Between these two phases, the displacements of bare frame were kept

constant until the end of phase 1. In this study, the smeared crack model was used. It

was reported that micro model gave closer results to the experiments than macro model.

Sigmund and Penava carried out a series of experiments to see the effect of openings in

the infill wall in terms of strength, stiffness, energy dissipation capacity and failure

modes. 1:2.5 scaled specimens were used and it was reported that the opening presence

and orientation has no influence on infill until 1 % drift level. However, after 1 % drift

level, the contribution of these changes become important. Furthermore, it was shown

that door gap is less desired than window gap because of the early loss of strength

(Sigmund and Penava, 2014).

In another study 1:2.5 scaled 10 one bay, one storey specimens were exposed to

constant vertical and lateral cyclic load test to compare the contribution of different

infill type. It was reported that linear monolithic behavior observed at 0.1 % drift level.

Specimens reached their capacities at 0.3 % drift level and maintained them until 0.75

% drift level. This study showed that after 0.75 % drift level, infill was heavily damaged

and contribution of infill should be neglected. Then this paper concluded that the

contribution of all types of masonry infill was approximately the same (Zokvic et al.,

2013).

Hashemi and Mosalam (2006) conducted a shake table experiments on a substructure

composed of middle bays of a 5-storey reinforced concrete prototype to assess out of

plane failure. These specimens were scaled ¾ due to dimension restriction of shake

table. Prototype and test specimen can be seen in Figure 1.15 (Hashemi and Mosalam,

2006).


17

a) Prototype structure

b) Shake table and specimen

Figure 1. 15 Prototype and shake table to assess out-of-plane action by Hashemi

(Hashemi and Mosalam, 2006)

It was reported that cracks occurred as a horizontal lines at mid of the infill panel under

mild action. However, failure occurred near the boundary of reinforced concrete and

infill panel [34]. Other prototypes and shake table experiments were implemented by

Stavridis, Koutromanos and Shing (2012). Three storey, two bay 2/3 scaled reinforced

concrete structure with infill wall was exposed to shake table experiment. Motivation

for this study was many buildings in California constructed in years 1920 and later

(Stavridis et al., 2012). Specimen and prototype for these experiments can be seen in

Figure 1.16.

a) Prototype structure

b) Shake table and specimen

Figure 1. 16 Prototype and shake table to assess out-of-plane action by Stavridis

(Stavridis et al., 2012)


18

It was concluded that at 43 % shake level, there was some repairable cracks on the

specimen. After 83 % excitation, 1.03 % interstorey drift was reported. However, this

ratio is limited with 0.3 % by ASCE 41-06 (Stavridis et al., 2012, ASCE/SEI 41-06,

2006)

1.1.4 Out-of-plane Behaviour of Infill Wall

The out-of-plane behavior of infill walls is very important for a structure to resist the

imposed external load. The carrying capacity and stiffness of the whole structure against

the earthquake load is mostly depending on this behavior. This behavior is controlled in

a large extent by an arching effect, as indicated by McDowell (McDowell and McKee,

1956) and Hendry (Hendry, 1973). There a few important parameters that are affect out-

of-plane behavior of infill wall. These are compressive strength of masonry and

stiffness of the enclosure main bearing elements. The first analytical methods were

developed by Hendry (Hendry, 1973) and Anderson (Anderson, 1984). Then Dawe and

Seah (1989) used airbags to characterize the out-of-plane behavior of infill wall and the

maximum load carrying capacity (Dawe and Seah, 1989). The setup constructed by

Dawe and Seah can be seen in Figure 1.17.

a)Physical Geometry of Specimen

b)Test Set up

Figure 1. 17 Experimental Test Up and Specimen Constructed by Dawe and Seah

(Dawe and Seah, 1989)

Dawe and Seah (Dawe and Seah, 1989) proposed equations to calculate out-of-plane

capacity of infill walls. These equations can be seen in Eqn. 1.1, Eqn. 1.2 and Eqn. 1.3.

𝑞 = 4.5 𝑓𝑚′ 0.75𝑡2(

𝛼

𝑙2.5 +𝛽

𝑙2.5) (1.1)


19

𝛼 =1

𝑕(𝐸𝐼𝑐𝑕

2 + 𝐺𝑠𝐽𝑐𝑡𝑕)0.25 < 50 (1.2)

𝛽 =1

𝑙(𝐸𝐼𝑏 𝑙2 + 𝐺𝑠𝐽𝑏𝑡𝑙)0.25 < 50 (1.3)

In these equations 𝑓𝑚′ is the compressive strength of masonry. t, h and l are the

thickness, height and length of the infill wall, respectively. E is elastic modulus of the

concrete; Ic and Ib are the inertia moments of the column and beam sections,

respectively. Jc and Jb are the torsional constants of the beam and column (Dawe and

Seah, 1989).

It was also realized that in-plane damage has considerable effect on the out-of-plane

behavior of infill wall. For this purpose, Angel (1994) tested eight full scale one storey

and one bay reinforced concrete frames filled with concrete masonry and brick masonry

wall. He firstly applied in-plane load then this action stopped and out-of-plane load was

applied by airbag to specimen until a certain drift level. The test set up used by Angel

can be seen in Figure 1.18 below.

a)In-plane Test Setup

b)Out-of-plane Test Setup

Figure 1. 18 Experimental Test Setup Used by Angel (Angel, 1994)

Angel proposed equations for the out-of-plane capacity of infill walls. These equations

can be seen in Eqn. 1.4, Eqn. 1.5 and Eqn. 1.6.

𝑞 =2𝑓𝑚

′

(𝑕

𝑡)𝑅1𝑅2𝜆 (1.4)

𝑅2 = 0.357 + 2.49 ∗ 10−14𝐸𝐼 ≤ 1.0 (1.5)

𝜆 = 0.154 ∗ 𝑒−0.0985𝑕

𝑡 (1.6)

He classified the in-plane damage to use in the formulation like in Figure 1.19. R1 is the

in-plane reduction capacity coefficient calculated by ∆

∆𝑐𝑟 and selected from Table 1.1.


20

Figure 1. 19 In-plane Damage Classification by Angel (Angel, 1994)

Table 1. 1 R1 Values for Different Height/Thickness Ratio (Angel, 1994)

𝑕

𝑡

R1 value equivalent to ∆

∆𝑐𝑟

∆

∆𝑐𝑟= 1

∆

∆𝑐𝑟= 2

5 0.997 0.994

10 0.946 0.894

15 0.888 0.789

20 0.829 0.688

25 0.776 0.602

30 0.735 0.540

35 0.716 0.512

40 0.727 0.528

In 1999, Flaganan and Bennett, proposed a modified equation after Dawe and Seah.

This modification was done by eliminating the torsional effect (Torsion effect was the

second part of terms defined in Eqn. 1.1, 1.2 and 1.3), as torsion effect has minor effect

and unnecessary complexity. Other analytical solution was proposed by Klinger

(Bashandy et al., 1995). Klinger modified the equations proposed by Cohen and Laing

(1956). Arch effect was considered by Klinger due to main effect of this behavior

(Bashandy et al., 1995). This equation can be seen in Eqn. 1.7, 1.8 and 1.9.


21

𝑞 =8

𝑕2𝑙 𝑀𝑦𝑣 𝑙 − 𝑕 + 𝑕𝑙𝑛 2 + 𝑀𝑦𝑕(

𝑥𝑦𝑣

𝑥𝑦𝑕)ln(

𝑙

𝑙−𝑕

2

) 𝑙 (1.7)

𝑀𝑦𝑣 =0.85𝑓𝑚

′

4(𝑡 − 𝑥𝑦𝑣 )2 (1.8)

𝑥𝑦𝑣 =𝑡𝑓𝑚

′

1000𝐸 1−𝑕

2 (𝑕2

)2+𝑡2

(1.9)

In Eqn. 1.7, 1.8 and 1.9 𝑓𝑚′ is the compressive strength of infill wall; h is the height, l is

the length and t is the thickness of the infill wall. Xyv is the maximum displacement of

the infill wall in the vertical direction. Myh is calculated by substituting Xyv by Xyh in

Eqn. 1.8 then l and h in Eqn. 1.9 (Bashandy et al., 1995).

To see behavior of infill wall along out-of-plane direction for unreinforced masonry and

retrofitted walls, Calvi and Bolognini (2001) tested three 1:1 scale specimens.

Dimensions of the prototype specimens were 4.5 m length and 3.0 m height. These

specimens were constructed to simulate first storey of 4 storey building. The specimens

can be assumed like unreinforced masonry wall, infill wall with bed joint reinforcement

and infill wall with wire mesh (Calvi and Bolognini, 2001). Out-of-plane load was

applied in the middle of the infill panel. Firstly, in-plane load was applied then out-of-

plane load was applied to specimens. It was emphasized that bed joint reinforcement

decreased in-plane damage Wire mesh increased the out-of-plane capacity of the

specimens. Specimens which were studied by Calvi and Bolognini (Calvi and

Bolognini, 2001) can be seen in Figure 1.20 below.


22

a)URM Specimen

b)Bed Joint Reinforcement

Specimen

c)Wire Mesh Specimen

Figure 1. 20 Tested Specimens by Calvi and Bolognini (Calvi and Bolognini, 2001)

Griffith et al. (2007) focused also on out-of-plane behavior of infill wall with airbag

test. They tested eight full scale specimens. Their test set up can be seen in Figure 1.21.

Figure 1. 21 Airbag Test Setup Used by Griffith et al. (2007)

During the test vertical load was applied to the specimens to simulate vertical pre-

compression. The authors emphasized that applying vertical load increased the out-of-

plane capacity and draw damage maps to explain the test results in detail as seen in

Figure 1.22.


23

a)Damage Map for Inside Face of

Specimen with External Load

b)Damage Map for Outside Face of

Specimen with External Load

c)Damage Map for Inside Face of

Specimen without External Load

d)Damage Map for Outside Face of

Specimen without External Load

Figure 1. 22 Damage Maps of Tested Solid Specimens by Griffith (2007)

Komaraneni (2009) tested three 1:2 scaled reinforced concrete frame with infill wall to

see out-of-plane damage under unidirectional load. For this purpose, special test setup

was developed as seen in Figure 1.23 below.

a)Transversal Side View

b)Front View of Setup

Figure 1. 23 Test Setup Used by Komaraneni (2009)

Testing of the specimen can be seen in Figure 1.24 below during the in-plane and out-

of-plane action.


24

a)In-plane Action

b)Out-of-plane Action

Figure 1. 24 In-plane and Out-of-plane Action of Test (Komaraneni, 2009)

Slenderness of the infill played a very important role in this study (Komaraneni, 2009).

Varela-Rivera et al. (2012) tested three confined masonry walls by airbag test to see

out-of-plane behavior of infill wall. Dimensions of tested specimens are 3.7 m length

and 2.7 m height. Thickness of the wall is 0.15 m. It was concluded that maximum out-

of-plane pressure of the wall increases with the increasing vertical load. It was

emphasized that snap through failure type was observed at specimen with vertical load

and crushing was observed for the wall without vertical load (Varela-Rivera et al.,

2012).

The last known study for out-of-plane action of infill wall was carried out by Pereira

(Pereira, 2013). Pereira used the airbag method to assess out-of-plane behavior of infill

wall and three specimens, as Calvi and Bolognini used before. Test setup of Pereira can

be seen in Figure 1.25.


25

Figure 1. 25 Test Setup Used by Pereira (Pereira, 2013)

Pereira suggested also in his thesis the equations below.

𝑞 =𝑓𝑐𝑚

𝑕𝑤𝑡𝑤

𝑅1𝑅2𝜆 0.77𝐶𝑓

𝑕𝑤

𝑙𝑤 + 0.34𝐶𝑓 (1.10)

𝐶𝑓 =𝑓𝑥1

𝑖

𝑓𝑥1(𝑟𝑒𝑓 1) (1.11)

In Eqn. 1.10 and 1.11 a few parameters are unknown these are 𝐶𝑓 which is a coefficient,

𝑓𝑥1𝑖 which is the flexural strength in the direction parallel to the bed joints and 𝑓𝑥1(𝑟𝑒𝑓 1)

which is the flexural strength in the direction parallel to the bed joints of the wall to be

taken as a reference that is the unreinforced masonry wall.

FEMA 273 (1997) also suggests a few equations to calculate out-of-plane capacity of

infills. These equations can be seen in Eqn. 1.12 and 1.13 below.

𝑞 =0.7∗𝑓𝑚

′ ∗𝜆2

(𝑕𝑖𝑛𝑓

𝑡𝑖𝑛𝑓)

∗ 144 (1.12)

Here, 𝜆2 is the coefficient corresponding to certain slenderness for using Eqn. 1.12. This

coefficient can be chosen in Table 1.2 below (FEMA 273, 1997).


26

Table 1. 2 𝜆2 values to calculate q in Eqn. 2.12 (FEMA 273, 1997))

Slenderness 5 10 15 35

𝜆2 0.129 0.030 0.034 0.013

Eurocode 6 (2005) also suggests equations for out-of-plane capacity of infill wall as

seen in Eqn. 1.13

𝑞 = 𝑓𝑚′

𝑡𝑤

𝑙

2

(1.13)

1.1.5 Retrofitting Techniques of Infill Wall

Seismic retrofit is an important issue for post peak behavior of structure after an

earthquake. Many retrofitted techniques were studied to increase structural life and

provide adequate safety levels. Low rise masonry and concrete structures were

retrofitted with steel strips by Taghdi et al. (2000). It was reported that using steel strips

prevented rotations and this technique increased the lateral capacity of specimens by

550%, when constructed with masonry infill, and by 291%, when constructed by

concrete shear wall (Taghdi et al., 2000).

Retrofitting of walls against blast effect was studied by Samoush et al. (2001). This

study adopted FRP on the external surface of the walls. Although, strength was

increased 1000% for the out-of-plane behavior with this application, in-plane shear

failure could not be prevent according to authors (Samoush et al., 2001).

Hamoush et al. (2002) studied the out-of-plane behavior of surface reinforced walls

using eighteen compact masonry wall panels. Static out-of-plane load was applied to

specimens and mesh S-glass fiber-reinforcing system was used for retrofitting. Failure

load, mid-span deflection and fiber-end slippage was investigated. It was emphasized

that wrapped more than one layer increased the structural integrity if layers extends

until supports. Flexural performance of out-of-plane behavior of infill wall was

increased with this method (Hamoush et al., 2002).

Binici et al. used FRP composites to retrofit mid-rise reinforced concrete structures

infill walls to resist lateral loads (Binici et al., 2007). This FRP sheets were applied by

FRP anchors. This experimental study was also modeled by Binici et al. FRP anchors


27

were modeled with equal struts. It was reported that FRP anchors showed satisfied

results in terms of collapse prevention state. Before retrofit 77% of the columns reached

the Collapse Prevention Limit State. However, after retrofit this ratio was decreased to

30%. Interstory drift was decreased from 1.2% to 0.8% (Binici et al., 2007).

CFRP strips were used by Altin et al. An experimental study conducted on one bay one

story 1/3 scaled perforated clay brick infilled wall reinforced concrete frame to see the

effect of width and arrangements of CFRP strips on the retrofitted specimen. l/h ratio of

infill walls were 1.73. 10 specimens were tested. It was reported that two sides CFRP

strips increased lateral strength 2.61 times than one sides. Ultimate lateral load was

increased 1.57 times with one side CFRP strips and this ratio was increased 1.85 times

with two sides’ strips (Altın et al., 2008a). One bay two storey non-ductile frames were

reinforced with Altin et al. Two retrofit techniques were used for this experimental

study. One of them is wire mesh, other of them is constructing new columns on both

sides. It was reported that these local retrofit techniques prevented successfully local

failures. Local failure is prevented especially with lap splice part (Altın et al., 2008b).

Kyriakides (2011) developed a new Engineering Cementitious Composites (ECC)

called as Sprayable ductile fiber-reinforced cement based material. Four 1/5 scaled non-

ductile reinforced concrete frame with infill wall was used. However, one of these

specimens was unreinforced and three of infill wall specimens were reinforced with

ECC and then exposed to quasi static cyclic load. It was reported that thin layer of ECC

on the specimen increased 10 times of deformation capacity through a rocking motion.

Then, Kyriakides tested 2/3 scale two-bay three-story non-ductile reinforced concrete

frame with infill wall by shake table. It was reported that ECC material improved

significantly performance of this type of structure under dynamic excitation. It was

concluded by author that strength and stiffness of specimens were increased by 45-53 %

by ECC. Moreover, flexural experiments proved that 13 mm thick ECC layer improved

load carrying capacity 35 times (Kyriakides, 2011; Kyriakides and Billington, 2014).

Leite tested 3 1/1.5 scaled reinforced concrete structures with brick infill wall to assess

out-of-plane movement with shake table. Two types of retrofit techniques were used.

These are bed joint reinforcement and wire mesh. Control structure was composed of

two leaf cavity wall reinforced concrete structure. Two leaf cavity wall reinforced

concrete structure was collapsed due to soft storey mechanism and also this structure

showed brittle failure during the 150% earthquake load. This structure was designed


28

according to Portugal standard (REBAP). The second structure with bed joint

reinforcement infill wall did not collapse. This structure resisted strong ground motion.

None of the infill wall collapsed due to out-of-plane movement. Model 3 which one is

composed of wire mesh resisted also 150% earthquake load with light cracks. This

model also prevented high damage and total collapse (Leite, 2014).

1.2 OBJECTIVE OF THE THESIS

This thesis addresses the investigation of seismic behavior of infill wall surrounded by

reinforced concrete frame under bidirectional simultaneous earthquake load.

Assessment of in-plane and out-of-plane behavior of infill wall was performed under

simultaneous dynamic in-plane (drift) motion and out-of-plane motion of infill wall. For

this purpose thesis divided into two main part. Part A composed of numeric part of the

thesis especially focused on the global behavior of infill wall constructed with full

structure but not full scale. This numeric model was tested before shake table

experiment. Firstly, after modeling with finite element software, model updating was

performed on the numeric model. Then pushover analysis was performed on the

structure to simulate global behavior of infill wall under lateral incremental load. Two

finite element model was considered. One of them is TLCW reinforced concrete

structure, other of them is reinforced concrete frame with unreinforced brick wall

(URM). Second model has not any experimental results. The infill wall orientation of

URM model is single layer 13 cm thickness. The main purpose is to compare these two

models is to see the effect of wall thickness on performance of the structure. Results of

the pushover curves were evaluated on the base of ASCE/SEI 41-06. Then nonlinear

time history analysis was performed on both models to compare each other with

experimental results. Second main part of the thesis, this is Part B, is composed of

experimental part of three shake table experiments. These experiments were focused on

the out-of-plane behavior of infill wall under bidirectional seismic load. The effect of

in-plane damage is evaluated on out-of-plane failure mechanism of infill wall during

this extreme action. Three shake table experiments were implemented with two different

specimens. First experiment was unsuccessful due to incomplete boundary condition.

Specimen of first experiment is called as Model-0. Second and third experiments were

successful. Test specimens of these successful tests were called Model-1 and Model-2

respectively. Model-1 was considered as reinforced concrete frame with unreinforced


29

conventional type of brick infill wall and Model-2 was considered as reinforced

concrete frame with reinforced brick infill. Bed Joint Reinforcement was used as

reinforcing technique between each horizontal brick line. And then reinforced and

unreinforced brick wall tests were compared each other. Main purpose of this

comparison is to see energy dissipation capacity, maximum drift capacity and maximum

load bearing capacity of infill walls. Finally, out-of-plane bearing capacities of infill

walls were calculated and compared each other according to current codes and adapted

formulas.

1.3 HYPOTHESIS

The motivation of this thesis is the behavior of infill walls during the low or high

amplitude earthquakes, which causes severe damage due to out-of-plane behavior of

infill walls. This out-of-plane movement usually leads to severe economic and life loss.

Several previous studies for this purpose have been carried out. However, earthquake

loads were applied not concurrently. The novelty of this study is the application of

earthquake bidirectional load at the same time. Furthermore, the contribution of infill

wall with and without retrofitting is tested and evaluated.

It is also noted that in a building with torsional irregularities, large magnitude of in-

plane acceleration of external seismic force in one direction can affect the out-of-plane

behavior during bidirectional seismic action. In that case, what is the effect e.g. of bed

joint reinforcement on reinforced plaster on the out-of-plane failure of infill brick wall?

Such reinforcement should keep the wall in-plane direction more stable and infill wall

should behave more ductile during the seismic event.

1.4 OUTLINE OF THE THESIS

In order to address the study of seismic behavior of infill walls, this thesis is divided

into ten chapters like below;

Chapter 1 addresses the literature review of the thesis, objective of the thesis and

hypothesis of the thesis.

Chapter 2 discusses the model updating of the finite element model of TLCW

reinforced concrete structure.


30

Chapter 3 presents pushover analysis of TLCW and URM model to simulate global

behavior of infill wall and performance level of both structures. After analysis,

interstorey drift results were evaluated according to ASCE/SEI 41-06

Chapter 4 includes nonlinear time history analysis of the both finite element TLCW and

URM model. After analysis, interstorey drift results were evaluated according to

ASCE/SEI 41-06.

Chapter 5 presents shake table test setup for Part B, experimental part of the thesis.

Casting of specimens, dimensions of specimens, placed instruments on the wall were

taken into account in this chapter.

Chapter 6 discusses lessons and learned from unsuccessful test of Model-0.

Chapter 7 presents the input signals of Test-1, dynamic identification and test results of

reinforced concrete structure with unreinforced brick wall in terms of force drift curves.

Moreover, out-of-plane behavior of infill wall was simulated according to load steps. In

addition to these, out-of-plane failure of infill was expressed.

Chapter 8 presents the properties of Bed Joint Reinforcement, production techniques,

input signals of Test-2, dynamic identification and test results of reinforced concrete

frame with Bed Joint Reinforcement infill brick wall. Furthermore, out-of-plane

behavior of infill wall was simulated according to load steps. In addition to these, out-

of-plane failure of infill was expressed.

Chapter 9 addresses shake table results and discussion of Test 1 and Test 2. Results

were plotted in the same graph and presented. Out-of-plane bearing capacity of infill

walls were calculated according to current regulations and formulas in the literature.

Chapter 10 presents the main conclusion of the thesis and future studies.

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frames. Engineering Structures, 50, pp. 43-45, 2013

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2004 Doğubeyazıt (Ağrı) earthquake in Turkey. Engineering Failure Analysis,

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Canadian Journal of Civil Engineering, 16:854-864, 1989

Doğangün, A., Performance of reinforced concrete buildings during the May 1, 2003

Bingöl earthquake in Turkey. Engineering Structures, 26, pp. 841-856, 2004.

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Kim, S. J., Jeong, S. H., Dukes, J., Valdivia, A., The Maule (Chile) earthquake

February 27, 2010: Consequence assessment and case studies. Mid-America

Earthquake Center, Report No:10-04, USA, 2010.

Ersoy, U., Üzsoy, S., The behaviour and strength of infilled frame. TÜBİTAK MAG-

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FEMA 273, Guidelines for the Seismic Rehabilitation of Buildings, Applied Technology

Council (ATC-43) and Federal Emergency Management Agency, USA, 1997

Flaganan, R. D., Bennett, R. M., Bidirectional behaviour of structural clay tile infilled

frames. Journal of Structural Engineering, ASCE, 125(3), pp. 236-244, 1999

Griffith, M. C., Vaculik, J., Lam, N. T. K., Wilson, J., Lumantarna, E., Cyclic Testing of

Unreinforced Masonry Walls in Two-Way Bending, Earthquake Engineering

and Structural Dynamics, 36:801-821, 2007

Hashemi, A., Mosalam, K. M., Shake table experiment on reinforced concrete structure

containing masonry infill wall. Earthquake Engineering and Structural

Dynamics, 35, pp. 1827-1852, 2006

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Engineer, 51(2), 43-50, 1973

Hamoush, S. A., McGinley, M. W., Mlakar, P., Scott, D., Murray, K., Out-of-plane

Strengthening of Masonry Walls with Reinforced Composites, Journal of

Composites for Construction, 5:139-145, 2001

Hamoush, S., McGinley, M., Mlakar, P., Terro, M. J., Out-of-plane Behavior of

Surface-Reinforced Masonry Walls, Construction and Building Materials,

16:341-351, 2002

Kakaletsis, D., Karayannis, C., Experimental investigation of infilled R/C frames with

eccentric openings. Structural Engineering and Mechanics, 26(3), pp. 231-250,

2007


33

Komaraneni, S., Out-of-plane Seismic Behavior of Brick Wall Masonry Infilled Panels

With Prior In-plane Damage, PhD Thesis, Ilt Kanpur University, Department

of Civil Engineering, India, 2009

Kyriakides, M. A., Seismic Retrofit of Unreinforced Masonry Infills in Non-ductile

Reinforced Concrete Frames Using Engineered Cementitious Composites, PhD

Thesis, Civil and Environmental Engineering, Stanford University, USA, 2011

Kyriakides, M. A., Billington, S. L., Behavior of Unreinforced Masonry Prisms and

Beams Retrofitted with Engineered Cementitious Composites, Materials and

Structures, 47:1573-1587, 2014

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October 2011 Van earthquake technical investigation report. Yıldız Technical

University Press, Istanbul, 2011.

Koçak, A., A study with a purpose to determine structural defects and faults: The

seismic risk of the existing buildings in various districts of Istanbul/Turkey.

Scientific Research and Essays, 5(5), pp. 468-483 1980, 2010

Leite, J., Seismic behaviour of masonry infill walls: Test and design. PhD Thesis,

Minho University, Guimaraes, Portugal.

Liauw, T. C., Kwan, A. K. H., Experimental study of shear wall and infilled frame on

shake table. Earthquake Engineering 10th

World Conference, pp. 2659-2663,

1992, Balkema, Rotterdam

McDowell, E. L., KcKee, K. E., Arching action theory of masonry walls. Journal of

Structural Division, ASCE, 82(ST2), pp. 915.911-915.918, 1956.

Mehrabi, A., Shing, P. B., Schuller, M. P., Noland, J. L., Experimental evaluation of

masonry-infilled RC frames. Journal of Structural Engineering, ASCE, 122, pp.

228-237, 1997a

Mehrabi, A., Shing, P. B., Finite element modelling of masonry-infilled RC frames.

Journal of Structural Engineering, ASCE, 123, pp. 604-613, 1997b

Mosalam, K., Ayala, G., White, R. N., Roth, C., Seismic fragility of LRC frames with

and without masonry infill walls. Journal of Earthquake Engineering, 1(4), pp.

693-720, 1997

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34

Rosetto, T., Peiris, N., Pomonis, A., Wilkinson, S. M., Re, D. Del., Koo, R., Gallocher,

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Seismic Zone Map of Turkey. Disaster and Emergency Management Authority, Turkey

10.03.2015.

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seismic design and construction practices in Turkey. Engineering Structures,

25, pp. 103-114, 2003

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Progress in Structural Engineering and Materials, 4, pp. 320-331, 2002

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response of infilled R-C frames. Journal of Earthquake Engineering, 18(1), pp.

113-146, 2014

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reinforced concrete frame with masonry infill walls. Earthquake Engineering

and Structural Dynamics, 41, pp. 1089-1108, 2012

Pereira, M. F. P., Avaliçao do Desempenho das Envolventes dos Edificios Face a Acçao

dos Sismos (in Potuguese), PhD Thesis, Minho University, Civil Engineering

Department, Guimaraes, Portugal, 2013

Pujol, S., Fick, D., The test of a full-scale three storey RC structure with masonry infill.

Engineering Structures, 32, pp. 3112-3121, 2010

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Concrete Walls Using Steel Strips, Journal of Structural Engineering, 126:9,

1017-1025, 2000

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buildings during the 2007 Bala, Turkey earthquakes. Natural Hazards, 60, pp.

1013-1026, 2012.

Valera-Rivera, J. L., Navarrete,-Macias, D., Fernandez-Baqueiro, L. E., Moreno, E. I.,

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35

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Structural Dynamics, 42, pp. 1131-1149, 2013

Chapter 2 – Part A: Preparation of Numeric Model & Model Updating

36

Chapter 2 2 PART A: PREPARATION OF NUMERIC MODEL &

MODEL UPDATING OF TWO LEAF CAVITY WALL

REINFORCED CONCRETE STRUCTURE

2.1 INTRODUCTION

At present, the adequacy of Finite Element (FE) simulation methods for different

structural analysis problems has been verified and widely accepted. But the reliability of

a model, analyzed with finite element software, depends mostly on the input parameters.

Using available measured data and improving the correlation between the FE simulation

and the data is known as model calibration or model updating (Atamtürktür and Laman,

2010). The aim of this process is to use model calibration to improve the accuracy of the

engineering properties of the model and to validate the modeling assumptions of FE

representations (Sevim et al., 2011). In other words, the main purpose of the model

calibration is to overcome imprecise and uncertain aspects of the numerical simulation

on the base of actual measurements (Cunha and Caetano, 2006).


37

It is well known that prediction and validation of numerical models using experimental

results can be difficult. This can be due to modeling errors as listed below;

Errors in the Model of the Structure; this type of error is encountered when the

model has deficiencies of physical (or geometrical) definition or the adopted

behavior for the material model is incorrect because data is insufficient or

incorrect.

Errors in the Constitute Model; this type of error is encountered when the

simplifying assumptions of material model adopted are incorrect.

Errors in the Computational Representation of the Structure; this type of errors

occurs in the inadequate discretization of complex systems during creation of

the finite element mesh (Cunha and Caetano, 2006; Mottershead and Friswell,

1993), or structural model in general.

During model calibration, the most important thing is determining the calibration type

and parameters. There are two types of calibration; one of them is Deterministic Model

Calibration; another of them is Stochastic Model Calibration, as follows;

Deterministic Model Calibration is the most conventional and widely used

calibration type when a numerical model tries to match experimental data. For

this reason reliability and predictability of Finite Element Model updating

naturally gets higher day by day.

Stochastic Model Calibration is a kind of approach arising from uncertain

physical measurements. In this type of calibration the parameters are determined

with a probabilistic approach. Stochastic Model calibration needs robust

statistical background or evaluation (Friswell et al., 2001).

However accuracy and compatibility between experimental and numerical data of

model calibration is the most important issue during this process. So, carefully selected

parameters have to be considered. In the context of dynamic identification and dynamic

structural analysis, data like natural frequencies, mode shapes, mass matrix and

damping factors play an important role. In model calibration, aimed at increasing the

reliability of the numeric model and at obtaining a good match between experimental

and numerical data, a process of trial and error, or optimization, is usually required


38

involving multiple calculations (Friswell et al., 2001; Mottershead and Friswell, 1993).

Many studies performed related to this purpose. However, one of last studies performed

by Altunışık et al. (2013) performed experimental modal analysis on highway bridges

by ambient and forced vibration test. It was emphasized that Enhanced Frequency

Domain Decomposition and Stochastic Subspace Identification methods are very useful

to identify mod shapes. However, it was reported that revealed damping ratios are

different (Altunışık et al, 2013). Şahin and Bayraktar (2014) used forced vibration test

on a steel footbridge. It was mentioned that measured data processed through band-pass

filter to obtain frequency-response functions, auto power spectra, cross power spectra,

spectrograms and power spectral densities. It was reported that special software was

used this is SignalCAD then modal calibration was started. Finally, reliable structural

properties were obtained (Şahin and Bayraktar, 2014a). To make modal calibration

process far better than conventional type of calibration, special optimization based

software was developed by Şahin and Bayraktar called as FemUP. Sequential Quadratic

Programming (SQP) was explored and used. Then, reliability of this software was

experienced by a few examples. It was reported that developed software is very

effective and reliable (Şahin and Bayraktar, 2014b). Vibration based damage

identification was performed on concrete arch dams. It was reported that modal

calibration revealed production defects like segregation at crest level. It was concluded

that this type of damage detection is reliable for safety evaluation (Türker et al., 2014)

2.2 MODEL CALIBRATION INDICATORS

2.2.1. Modal Assurance Criterion (MAC)

The Modal Assurance Criterion (MAC) is a statistical and powerful indicator. The

historical development of MAC dates back to 1970s. This criterion was developed to

check if mode shapes are consistent or not, on the basis of orthogonality .If the

frequency response function matrix does not have enough information, predicting the

modal vector under different conditions plays an important role and becomes a

confidence factor to evaluate experimental data (Allemang, 2003). The purpose of MAC

is to measure the correlation between numeric and experimental mode shapes as seen in

Eq. 2.1.

MACe,n= {𝜑𝑖

𝑒}𝑇{𝜑𝑖𝑛 }

2

{𝜑𝑖𝑒}𝑇{𝜑𝑖

𝑒}{𝜑𝑖𝑛 }𝑇{𝜑𝑖

𝑛 } (2.1)


39

In equation 2.1 {𝜑𝑖𝑒} and {𝜑𝑖

𝑛} are the mode vectors of two different models. The

superscript e indicates experimental the subscript n indicates numerical. The range of

MAC value between 0 to 1, where zero means no match between the mode shapes and

one means perfect correlation between the experimental and numerical modes. If MAC

is small this means that;

The system is non-stationary; this happens if the system is nonlinear and two

data sets have been obtained at different times or excitation level.

There is noise on the reference modal vector; this situation occurs in case of

input of a frequency response function measurement.

The modal parameter estimation is invalid; this happens in case of an

inconsistent data set or unrelated mode shape vectors.

Although the parameter evaluation MAC is sensitive to magnitudes, higher magnitudes

have a dominant effect. So, erroneous points will have minor effect, unless they are

distributed well in the structure (Allemang, 2003).

2.2.2. Coordinate Modal Assurance Criterion (COMAC)

Coordinate Modal Assurance Criterion (COMAC) is an extended version of the Modal

Assurance Criterion. The COMAC values determine the positive or negative

contribution of each reference node to the MAC value. MAC is a single value, but there

are more than one COMAC node on the numeric model on the basis of the recorded

data. COMAC is evaluated by a set of mode pairs, e.g. calculated (numerical) versus

experimental. Two modal vectors indicate the same modal vector in each mode pair, but

the set of mode pairs indicate all modes of interest in a given frequency. For each data

location point / degree of freedom i, a value of COMAC is obtained for the two set of

modes. Then, the COMAC value can be calculated with Equation 2.2 as seen below

(Allemang, 2003).

COMACi,e,n= 𝜑𝑖 ,𝑗

𝑒 𝜑𝑖 ,𝑗𝑛

2𝑛𝑖

(𝜑𝑖 ,𝑗𝑒 )2 (𝜑𝑖 ,𝑗

𝑛 )2𝑛𝑖

𝑛𝑖

(2.2)


40

2.2.3. Normalized Modal Differences (NMD)

Normalized Modal Differences (NMD) is a parameter that is calculated from the MAC

value to check the discrepancy of two mode shape vectors. The difference from MAC is

to that the parameter is more sensitive to higher values of MAC, as seen from equation

2.3. During a modal updating process if a MAC value is obtained below 0.9, NMD

value will be high. As an example 0.99 MAC value corresponds to 0.10 NMD value. A

value lower than 0.33 for the NMD is assumed as a good correlation (Ramos, 2007).

NMDe,n= 1−𝑀𝐴𝐶𝑒 ,𝑛

𝑀𝐴𝐶𝑒 ,𝑛 (2.3)

2.3. MODEL UPDATING TECHNIQUES

2.3.1. Douglas-Reid Method

This type of modal updating method is based on the minimization of differences

between two modal quantities. Selecting variables and constructing a mathematical

model is not enough for this procedure. Considering uncertainty conditions, upper and

lower limit of estimations are also as important and partly control the update. Douglas

and Reid proposed the equation below (Douglas, and Reid, 1982).

𝜔𝑗𝐹𝐸 𝑋1, 𝑋2, … … , 𝑋3 = 𝐶𝑗 + [𝐴𝑖𝑘𝑋𝑘 + 𝐵𝑖𝑘 (𝑋𝑘)2]𝑛

𝑘=1 (2.4)

Where Xk (k=1,2,……., n) are variables to calibrate and Aik, Bik and Ci are constants.

These (2n+1) constants must be calculated from the system of equations below;

𝜔𝑗𝐹𝐸 𝑋1

𝐵 , 𝑋2𝐵 , … … , 𝑋𝑛

𝐵 = 𝐶𝑗 + [𝐴𝑖𝑘𝑋𝑘𝐵 + 𝐵𝑖𝑘 (𝑋𝑘

𝐵)2]𝑛𝑘=1


𝐿 , 𝑋2𝐵 , …… , 𝑋𝑛

𝐵 = 𝐶𝑗 + [𝐴𝑖𝑘𝑋𝑘𝐿 + 𝐵𝑖𝑘(𝑋𝑘

𝐵)2]𝑛𝑘=1


𝑈 , 𝑋2𝐵 , … … , 𝑋𝑛

𝐵 = 𝐶𝑗 + [𝐴𝑖𝑘𝑋𝑘𝑈 + 𝐵𝑖𝑘 (𝑋𝑘

𝐵)2]𝑛𝑘=1

.

. (2.5)

.

.

.


41


𝐵 , 𝑋2𝐵 , … … , 𝑋𝑛

𝐿 = 𝐶𝑗 + [𝐴𝑖𝑘𝑋𝑘𝐿 + 𝐵𝑖𝑘(𝑋𝑘

𝐿)2]𝑛𝑘=1


𝐵 , 𝑋2𝐵 , … … , 𝑋𝑛

𝑈 = 𝐶𝑗 + [𝐴𝑖𝑘𝑋𝑘𝑈 + 𝐵𝑖𝑘 (𝑋𝑘

𝑈)2]𝑛𝑘=1

Where 𝑋𝑘𝐵 is the initial value of each variable to be calibrated, and 𝑋𝑘

𝐿 and 𝑋𝑘𝑈vare lower

and upper limits for each variable, respectively (Douglas and Reid, 1982).

After calculation of the constants, the least square minimization is applied on the

numeric frequencies 𝜔𝑗𝐹𝐸 and the experimental 𝜔𝑗

𝐸𝑋 , as;

π = 𝑤𝑖𝑚𝑖=1 𝑒𝑖

2 (2.6)

εi= 𝜔𝑖𝑒𝑥 − 𝜔𝑖

𝐹𝐸(𝑋1, 𝑋2, … , 𝑋𝑛)𝑚𝑖=1 (2.7)

Where π is the objective function, εi is the residual function, 𝑤𝑖 is the weight constant

and m is the number of frequencies mentioned for modal updating (Douglas and Reid,

1982).

2.3.2. Robust Method

The so-called robust method is used by (Ramos, 2007), which uses an objective

function π and the errors between numeric and experimental frequencies given by 𝜔𝑖𝐸

and 𝜔𝑖𝐹𝐸 andthe differences between numeric and experimental mode shapes indicated

by ∅𝑖 ,𝑗 ,𝐸 and ∅𝑖 ,𝑗 ,𝐹𝐸. Equation 2.8 is constructed by using these variables;

π=1

2[𝑊𝑤 (

𝜔 𝑖𝐹𝐸

2− 𝜔𝑖

𝐸 2

𝜔 𝑖𝐸

2 )2 + 𝑊∅ (∅𝑖 ,𝑗 ,𝐹𝐸

2−∅𝑖 ,𝑗 ,𝐸2

∅𝑖 ,𝑗 ,𝐸2 )2𝑛

𝑗 =1𝑚𝑖=1

𝑚𝑖=1 ] (2.8)

In equation 3.8, 𝑊𝑊 and 𝑊∅are the weight constants of natural frequencies and mode

shapes respectively. Furthermore, m and j are the number of modes and the modal

displacement respectively (Ramos, 2007).

This updating process is again done on the basis of optimization techniques. This

optimization must be implemented by using a Jacobian sensitivity matrix composed of i

rows and j columns, where the Gradient ∇𝜋(𝜃) is constructed. The Jacobian matrix is

calculated by first order partial derivative of the residual functions, as shown in equation

2.9.


42

J(θ)ji=𝜕𝜋 (𝜃)

𝜕𝑥 𝑖 (2.9)

After calculating the Jacobian matrix, the Hessian Matrix G is calculated from the

second partial order derivatives of the residual functions (Ramos, 2007), as:

G(θ)jk=𝜕2휀𝑖(𝜃)

𝜕𝑥 𝑖𝜕𝑥 𝑗 (2.10)

Here,휀is are the residual functions and θ are the updated variables. The Hessian and

Gradient are the objective functions, given by;

∇𝜋(𝜃)=J(θ)T 𝜋(𝜃) (2.11)

∇2𝜋(𝜃)=J(θ)T J(θ)+Q(θ) (2.12)

where

Q(θ)= 𝜋𝑖(𝜃)𝐺𝑖𝑚𝑖=1 (𝜃) (2.13)

2.4. FINITE ELEMENT SIMULATION OF TWO LEAF CAVITY WALL

REINFORCED CONCRETE STRUCTURE

The numeric model of a Two Leaf Cavity Wall Reinforced Concrete Structure (RC)

tested by Pereira (Pereira, 2013) and Leite (Leite, 2014) is constructed next to

subsequent nonlinear push-over analysis and time history analysis. During the

construction of FE model for this structure, columns, beams and foundation were

modeled with class-III beam elements in software DIANA 9.4.4 (TNO, 2012), which is

CL18B composed of three nodes. CL18B beam element can be seen in the Figure 2.1.


43

Figure 2. 1 CL18B three nodes curved beam element

Interpolation polynomial is related to displacement of the CL18B beam element can be

seen in equation 2.14.

𝑢𝑖 𝜉 = 𝑎𝑖0+ 𝑎𝑖1

𝜉 + 𝑎𝑖2𝜉2 (2.14)

Moreover, geometric function is related to rotation of beam element can be seen in

equation 2.15.

ø𝑖 𝜉 = 𝑏𝑖0+ 𝑏𝑖1

𝜉 + 𝑏𝑖2𝜉2 (2.15)

In equation 2.14 and 2.15 there are a few notations. These are u and ø. These are

displacement and rotation respectively. i represent the direction x, y and z. There are two

Gauss integration point on the beam element.

The slab was modeled with eight nodes quadrilateral curved shell element called as

CQ40S, which can be seen in Figure 2.2. This element can only be used for linear

elastic analysis, as it is pre-integrated in the thickness direction.

Figure 2. 2 CQ40S eight nodes curved shell element

The polynomials for translation u and rotation ø expressed as in Equation 2.16 and 2.17

respectively. These are general polynomials for curved shell element valid for also

CQ40L.


44

𝑢𝑖 𝜉, 𝜂 = 𝑎0 + 𝑎1𝜉 + 𝑎2𝜂 + 𝑎3𝜉𝜂 + 𝑎4𝜉2 + 𝑎5𝜂2 + 𝑎6𝜉2𝜂 + 𝑎7𝜉𝜂2 (2.16)

ø𝑖 𝜉, 𝜂 = 𝑏0 + 𝑏1𝜉 + 𝑏2𝜂 + 𝑏3𝜉𝜂 + 𝑏4𝜉2 + 𝑏5𝜂2 + 𝑏6𝜉2𝜂 + 𝑏7𝜉𝜂2 (2.17)

The default in ζ direction (thickness), there are three Simpson integration point. There

are two Gauss integration points along other two directions.

All of walls of the structure were modeled with eight nodes quadrilateral layered curved

shell element known as CQ40L can be seen in Figure 2.3. This element allows

introducing any non-linear material model in each of the layers.

Figure 2. 3 CQ40L eight nodes layered curved shell element

Interface elements were considered to model the connection between the infill and the

RC frame. Three nodes line to surface interface element was used. The name of this

element is CL24I can be seen in Figure 2.5.

Figure 2. 4 CL24I three nodes line to shell interface element a) Topology, b)

Displacement

There are three point Newton-Cotes integration scheme in longitudinal direction, ξ and

there are three point Simpson scheme in the “thickness” direction ζ.

During the construction of the finite element model of the two leaf cavity wall

reinforced concrete structure, a problem was found. Since beam elements and shell

elements were used, the geometry of the structural elements was only represented by

their axis line. Naturally, there will be a space between the infill and the reinforced

concrete frame. This space was allowed using the TYINGS command. Displacements

and rotations of interfaces element around infill and reinforced concrete frame were


45

made compatible by appropriate constraints. This process is done in order not to change

the geometry of the infill. Different views of the structure can be seen in Figure 2.5. A

3D perspective of the FE model is shown in Figure 2.6.

a)South Face of the Structure FEM

b) South Face of the Structure Drawing

c) North Face of the Structure FEM d)North Face of the Structure Drawing


46

e)West Face of the Structure FEM

f)West Face of the Structure Drawing

g)East Face of the Structure FEM h)East Face of the Structure Drawing


47

Figure 2. 5 Full view of model after constructing FEM; a, c, e and g View of FEM, b, d,

f and h Drawing of Structure

Figure 2. 6 Solid View of the TLCW structure

2.5. MODEL CALIBRATION OF TWO LEAF CAVITY WALL REINFORCED

CONCRETE STRUCTURE

In this case study, the calibration process is done by using MATLAB with a least square

algorithm minimization of the objective function (MATLAB, 2006). To obtain the best

match, 10-6

is used as a tolerance in the objective function between nth

and (n-1)th

iteration numbers. When this tolerance is reached, the updating process is stopped

automatically. Calibration process is carried on together with MATLAB (MATLAB,

2006) and DIANA (TNO, 2012).

During the model updating process, at first, a rigid foundation was used. After

calculating the eigen values, it was realized that the first three modes were wrongly

sorted. According to the experimental results, the first mode is transversal, the second

mode is longitudinal, and the third mode is rotational, while fourth and fifth modes are

mixed. Experimental modes and frequencies can be seen in Figure 2.8 (Leite, 2014)


48

a)Experimental Mode-I (f1=7,7

Hz)

b) Experimental Mode-II

(f2=9,6 Hz)

c) Experimental Mode-

III (f3=26,9 Hz)

d) Experimental Mode-IV (f4=32,8 Hz)

e) Experimental Mode-V (f5=39,4 Hz)

Figure 2. 7 Experimental Modes of Reinforced Concrete Structure with Two Leaf

Cavity Infill Wall

The material properties from the building, namely Young’s modulus of the infill Einf,

Possoin’s ratio of the infill υinf, specific weight of concrete ρconc, specific weight of infill

ρinfill and compressive strength of concrete fcm, are obtained by an experimental study

(Pereira, 2013). These parameters can be seen in table 3.1. Econc was calculated on the

base of Eurocode 2 recommendations (EN1992-1-1, 2004).

Table 2. 1 Engineering Properties of Concrete and Infill belong to FE TLCW Model

Econc

(MPa) υcon ρconc (kg/m

3)

Einf

(MPa) υinf

ρinf

(kg/m3)

fcm (MPa)

30450 0.20 2200 3600 0,21 1590 29.5


49

Computation of interface stiffness located between the reinforced concrete and infill

wall is more complicated, as no tests on the interface can be carried out. For its first

estimation, the existing render, the thickness of the joint and the interface thickness

itself are considered. KN and KS, respectively normal and tangential (Lourenço, 1996).

The resulting stiffness of the interface element can then be estimated as;

𝐾𝑁 =𝐸𝑢 ∗𝐸𝑚

𝑡𝑚 ∗ 𝐸𝑢 −𝐸𝑚 (2.18)

Then, the KS value can be calculated by Lourenço (Lourenço, 1996);

𝐾𝑆 =𝐾𝑁

2𝑥(1+𝜐) (2.19)

In this formula, the Poisson’s ratio υ is assumed equal to 0.15. So, KS value is calculated

as 75 N/mm3. After calculation of normal and tangential stiffness of interface, an

eigenvalue analysis was done with rigid foundation. It was realized that with a rigid

foundation, the first two modes were shift with respect to the experimental values. To

find an agreement with the mode shapes, an elastic foundation was used. This situation

mostly emerged due to the connection between the RC foundation and shaking table,

which is not perfect due to execution difficulties of making a perfectly straight

foundation. The RC foundation is connected to the shaking table by pre-stressed steel

bolts and gaps can be observed. In addition, the shaking table can be also affecting the

measured modes, not providing an infinitely rigid foundation.

This lack of agreement between experimental and numerical modes was eliminated by

using an elastic foundation. Two different elastic foundation properties were used under

the foundation to simulate the shaking table, in order to replicate the observed modes.

One set of the properties was used in the North and South direction, while another set

was used in the West and East direction, by trial and error. Location of elastic

foundation and selected parameters can be seen in Figure 2.8.Correct mode shapes and

acceptable frequencies can be seen in Figure 2.9 after using elastic foundation before

modal updating, before a more detailed calibration is made below.


50

Figure 2. 8 Elastic Foundation Properties used under Foundation

Before starting model calibration suitable and more realistic mesh number was

determined. This is called as model selection. To select suitable model, different mesh

numbers were determined and eigenvalue analyses were performed on each model.

These analyses results can be seen in Table 2.2.


51

Table 2. 2 Eigenvalue analyses results for model selection

MODE

NUMBER

EXP.

FREQUENCIES

(Hz)

696

ELEMENT

ERROR

(%)

2008

ELEMENT

ERROR

(%)

6784

ELEMENT

ERROR

(%)

9744

ELEMENT

ERROR

(%)

13416

ELEMENT

ERROR

(%)

1 7.71 7.9 2.5 7.95 3.1 8.06 4.5 8.14 5.6 8.2 6.4

2 9.62 10.0 4.0 9.89 2.8 9.92 3.1 9.87 2.6 10.2 6.0

4 32.84 37.4 13.9 36.5 11.1 36.1 9.9 35.79 9.0 37 12.7

5 39.4 42.1 6.9 41.1 4.3 40.8 3.6 40.8 3.6 41 4.1

AVERAGE 6.8 5.3 5.3 5.2 7.3


52

As seen from Table 2.2, lowest average error belongs to last model composed of 9744

element. This model was used further study.

a) FEM Mode-I (f1=8,1

Hz)

b) FEM Mode-II (f2=9,8

Hz)

c) FEM Mode-III (f3=23,9

Hz)

d) FEM Mode-IV (f4=35,8 Hz)

e) FEM Mode-V (f5=40,8 Hz)

Figure 2. 9 Modes of FE model

As seen from Figure 2.9c, 3rd

mode could not replicate correctly even if using elastic

foundation. This is a torsion mode and seems more difficult to measure experimentally

and to replicate numerically. For this reason, model updating was focused on the other

four modes; first transversal, first longitudinal and (fourth and fifth) mixed modes. Six

different modal calibrations were done aiming at close fitting the experimental

frequencies. While determining the calibrated parameters, potential sources of

uncertainties were clarified and determined with Parameter Importance Table shown in

Table 2.3.


53

Table 2. 3 Parameter importance table for modal updating

Parameter Reason Decision

Elastic Modulus of

Concrete

Contribution to total

mass of the structure is

77 %

Due to experimental

value, 2nd

priority

calibration

Elasticity Modulus of

Infill

Contribution to total

mass of the structure is

less but this parameter is

mostly affected by

interface

Due to experimental

value, 2nd

priority

calibration

KN and KS values of

interface stiffness

No mass contribution but

behavior of modal shape

is mostly effected by this

parameter

Parameters calculated

by formula, 2nd

priority calibration

KN(W-E), KN(N-S) and

KS(ALL) Stiffness of

elastic foundation

No mass contribution but

correct mode shape is

obtained by this

parameters

1st priority for

calibration

As seen from the Parameter Importance Table, mode shapes were affected by many

parameters, particularly the stiffness of the elastic foundation. For this reason, at first,

modal calibration was focused on the elastic foundation. Another important factor is

movement capability of structure was restricted due to distinct number of KN(W-E), KN(N-S)

and KS(ALL). For this reason, model updating process was enlarged from 1st degree

priority important parameters to 2nd

degree important parameters.

2.5.1. Calibration Number 1

In this calibration, only normal stiffness of North and South face of the elastic

foundation were calibrated and results of calibration are tabulated in Table 2.4.


54

Table 2. 4 Updating summary for calibration 1

VARIABLES INITIAL

VALUES

UPDATED

VALUES

EXPERIMENTAL

FREQUENCIES (1)

INITIAL

FREQUENCIES (2)

ERROR

BETWEEN

1&2

UPDATED

FREQUENCIES (3)

ERROR

BETWEEN

1&3

KN(W-E) 1x10

4

KN/m3

4.3x103

KN/m3

7.7 8.1 5.6 % 7.5 2.5 %

KN(N-S) 1x10

5

KN/m3

9.2x104

KN/m3

9.6 9.8 2.6 % 9.7 0.4 %

32.8 35.8 9.0 % 35.8 8.9 %

39.4 40.8 3.6 % 40.8 3.5 %

Average 5.2 % Average 2.8 %


55

As seen from Table 2.4 that there were not so much difference between frequencies of

4th

and 5th

modes. The updating process was successfully done but calibration did not

make any differences as seen from Figure 2.10, Figure 2.11 and Figure 2.12. Average

COMAC values along transversal direction is 0.725 over 1.0 and along longitudinal

direction is 0.7 over 1.0 as seen in Figure 2.10. However, NMD values are extremely

good for 1st and 2

nd modes but this value is very high for 4

th and 5

th modes. NMD results

can be seen in Figure 2.11. MAC values are very high for first two modes but a little bit

low for last two modes. However, these are also acceptable for boundary condition

problem. Another calibration process was done on the base of Parameter Importance

Table to see change of parameters.

Figure 2. 10 COMAC values for 4 modes


56

Figure 2. 11 NMD values for 4 modes

Figure 2. 12 MAC values for 4 modes


57

Figure 2. 13 Frequency comparison FE TLCW model


In this calibration, in addition to KN(W-E) and KN(N-S) shear stiffness of elastic foundation

was also considered during the updating process. Results are tabulated in Table 2.5.


58

Table 2. 5 Updating Summary for Calibration 2

VARIABLES INITIAL

VALUES

UPDATED

VALUES

EXPERIMENTAL

FREQUENCIES (1)

INITIAL

FREQUENCIES (2)

ERROR

BETWEEN

1&2

UPDATED

FREQUENCIES (3)

ERROR

BETWEEN

1&3

KN(W-E) 1x104

KN/m3

0.75x104

KN/m3

7.7 8.14 5.6 % 7.6 0.9 %

KN(N-S) 1x105

KN/m3

0,86x105

KN/m3

9.6 9.87 2.6 % 9.5 0.7 %

KS(ALL) 1x105

KN/m3

0.97x105

KN/m3

32.8 35.79 9.0 % 35.7 8.8 %

39.4 40.8 3.6 % 40.7 3.3 %



59

Since Table 2.5 was inspected carefully and compared with Table 2.4, it will be seen

that first two modes converged less than 1 % error but this calibration process also did

not make a good match for fourth and fifth mode. COMAC, NMD, MAC and frequency

comparison graphs were the same as in calibration 1. For this reason, they are not

shown here.


As seen in the first two calibrations, since the number of calibrated parameters

increased, extremely good correlation was obtained for the two frequencies and modes.

On the basis of this assumption, interface normal and shear stiffness were considered as

variables in this calibration 3 for a good match even for frequency number 4 and 5.

Results were tabulated in Table 2.6.


60


VARIABLES INITIAL

VALUES

UPDATED

VALUES

EXPERIMENTAL

FREQUENCIES (1)

INITIAL

FREQUENCIES (2)

ERROR

BETWEEN

1&2

UPDATED

FREQUENCIES (3)

ERROR

BETWEEN

1&3

KN(W-E) 1x104

KN/m3

0,05x104

KN/m3

7.7 8.14 5.6 % 7.4 3.8 %

KN(N-S) 1x105

KN/m3

1.1x105

KN/m3

9.6 9.87 2.6 % 9.6 0.3 %

KS(ALL) 1x105

KN/m3

5x105

KN/m3

32.8 35.79 9.0 % 34.2 4.0 %

KN(interface) 1.75x108

KN/m3

10.5x108

KN/m3

39.4 40.8 3.6 % 39.5 0.1 %

KS(interface) 75.52x107

KN/m3

10.1x107

KN/m3



61

Table 2.6 gives a good match between the experimental and numeric frequencies. These

good relations are the most important demonstration of the modal updating. These

relations also reveal the importance of modal updating process.MAC, COMAC, NMD

and Frequency Error graphs were similar to the calibration number 1. For this reason

new graphs are not shown.


Even if experimental data were available from other tests, there are still uncertain ties

regarding Einf, normal and shear stiffness of the infill, which were also updated in this

calibration phase. The main reasoning of this calibration phase is the differences of

material parameters between small specimens and whole structure. Results of this

updating process can be seen in Table 2.7.


62


VARIABLES INITIAL

VALUES

UPDATED

VALUES

EXPERIMENTAL

FREQUENCIES (1)

INITIAL

FREQUENCIES (2)

ERROR

BETWEEN

1&2

UPDATED

FREQUENCIES (3)

ERROR

BETWEEN

1&3

Einf 3.6x106

KN/m2

3.1x106

KN/m2

7.7 8.14 5.6 % 8.1 5.1 %

KN(interface) 1.7x108

KN/m3

10.5x108

KN/m3

9.6 9.87 2.6 % 9.7 0.6 %

KS(interface) 75.2x107

KN/m3

231.8x107

KN/m3

32.8 35.79 9.0 % 34.4 4.6 %

39.4 40.8 3.6 % 39.0 0.98 %



63

Table 2.7 shows that the calibration of Einf and stiffness values of interface element did

not bring out a better correlation after updating process. This updating process was

focused on only second and fifth modes. First and fourth mode shapes nearly stayed the

same. But under these conditions, average frequency errors decreased from 5.2% to

2.8%, which is in the same range of previous calibrations.


Finally, in this calibration process, only Einf and Econc were considered. The main

purpose in this calibration is to see what could be the improvement in changing both the

expected value for concrete and masonry. The results were tabulated in Table 2.8.


64


VARIABLES INITIAL

VALUES

UPDATED

VALUES

EXPERIMENTAL

FREQUENCIES (1)

INITIAL

FREQUENCIES (2)

ERROR

BETWEEN

1&2

UPDATED

FREQUENCIES (3)

ERROR

BETWEEN

1&3

Einf 3.6x106

KN/m2

3.3x106

KN/m2

7.7 8.14 5.5 % 8.0 3.7 %

Econc 3.04x107

KN/m2

2.35x107

KN/m2

9.6 9.87 2.6 % 9.5 0.7 %

32.8 35.79 9.0 % 33.9 3.2 %

39.4 40.8 3.6 % 38.5 2.3 %



65

Table 2.8 shows that this calibration process also has not so much influence on the

variables like calibration 3. But this calibration was also considered another alternative

of solution to overcome this problematic condition. Average error decreased around half

of the initial error, as in the previous results. Again, MAC, COMAC, NMD and

Frequency Error graphs are nearly the same as in Calibration 1.

2.6. CONCLUSION

In this chapter, model updating was done to a test on “Two Leaf Cavity Wall

Reinforced Concrete Structure”. Before starting model calibration elastic foundation

was used under the structure. Because, it was seen that first three modes were incorrect

with rigid foundation after eigenvalue analysis. This situation occurred mostly because

of the imperfect geometry of the boundary condition and the connection with steel bolts.

These connection points decreased the vertical stiffness of the structure. To overcome

this problematic situation elastic foundation was used. In the model updating, the

calibration process was divided into five steps. At the end of this process, it can be seen

easily from the summary table belong to each calibration that there were not so much

differences between each stage. Five calibration were considered, it can be concluded

that average error after updating is only 2.7 %. The frequency error was 5.2 % before

updating, meaning that his amount was decreased almost to the half after updating. This

is a good match between the experimental and numeric values. The better match is

calibration 3 and this calibration process includes elastic foundation parameters and

interface stiffness. The first two modes of the structure were nicely fit but the third

mode could not be corrected, as well as higher modes. Still, it can be concluded that the

dynamic response is globally reasonably replicated by the proposed numerical model.

2.7. REFERENCES

Atamtürktür, S., Laman, J, A. Finite Element Model Correlation and Calibration of

Historic Masonry Monuments: Review, The Structural Design of Tall and

Special Buildings, 21, 96-113, 2010

Atamtürktür, S., Verification and Validation under Uncertainty Applied to Finite

Element Models of Historic Masonry Monuments, Proceedings of the IMAC-

XXVII, Orlando, Florida USA, 2009


66

Altunişik, A. C., Bayraktar, A., Sevim, B., Analytical and Experimental Modal Analyses

of a Highway Bridge Model, Computers and Concrete, 12(6):803-818, 2013

Allemang, J. R., The Modal Assurance Criterion – Twenty Years of Use and Abuse,

Journal of Sound and Vibration, 37:14-21, 2003

Cunha, A., Caetano, E., Experimental Modal Analysis of Civil Engineering Structures,

Journal of Sound and Vibration. 6:12-20, 2006

Douglas B. and Reid W., Dynamic Tests And System Identification of Bridges, Journal

of the Structural Division, 108(10):2295-2312, 1982

EN 1996-1-1, Eurocode 6: Design of Masonry Structures – Part 1-1, General Rules for

Reinforced and Unreinforced Masonry Structures, European Committee for

Standardization, 2005

Eurocode 2, Design of concrete structures - Part 1-1: General Rules And Rules for

Buildings, EN 1992-1-1, December, 2004

Friswell, M. I., Mottershead J. E., Ahmadian, H., Finite-Element Model Updating Using

Experimental Test Data: Parameterization and Regularization, The Royal

Society, 359:169-186, 2001

Sevim, B., Bayraktar, A., Altunışık, A. C., Atamtürktür, S., Birinci, F., Finite Element

Model Calibration Effects on the Earthquake Response of Masonry Arch

Bridges, Finite Element in Analysis and Design, 47:621-634, 2011

Mottershead J. E., Friswell, M. I., Modal Updating in Structural Dynamics: A Survey,

Journal of Sound and Vibration, 167(2):347-375, 1993a

Mottershead J. E., Friswell, M. I., Modal Updating in Structural Dynamics: A Survey,

Journal of Sound and Vibration, 167(2):347-375, 1993b

Lourenço, P. B., Computational Strategies for Masonry Structures, PhD Thesis.

University of Delft, Netherlands, 1996

MATLAB, MATLAB: The language of technical computing, The MathWorks, Release

7.2, USA, 2006

Mendes, N., Seismic Assessment of Ancient Masonry Buildings: Shaking Table Tests

and Numerical Analysis, PhD Thesis, University of Minho, Guimaraes,

Portugal, 2013

Ramos L. F., Damage Identification on Masonry Structures Based on Vibration

Signatures, PhD Thesis, Universidade do Minho, Guimarães, Portugal, 2007


67

Şahin, A., Bayraktar, A., Forced-Vibration Testing and Experimental Modal Analysis of

a Steel Footbridge for Structural Identification, Journal of Testing and

Evaluation, 42(3):1-18, 2014a

Şahin, A., Bayraktar, A., Computational Finite Element Model Updating Tool for

Modal Testing of Structures, Structural Engineering and Mechanics, 51(2):229-

248, 2014b

TNO, DIsplacement method ANAlyser. User’s Manual, Release 9.4.4, Netherlands,

2012

Türker, T., Bayraktar, A., Sevim, B., Vibration Based Damage Identification of

Concrete Arch Dams by Finite Element Model Updating, Computers and

Structures, 13(2):209-220, 2014


68

Chapter 3 3 PART A: PUSHOVER ANALYSIS OF REINFORCED

CONCRETE STRUCTURES WITH TWO LEAF CAVITY

WALL AND UNREINFORCED BRICK WALL

3.1. INTRODUCTION

Push-over analysis led to the idea of the so-called “Performance Based Design”. Nearly

for two decades, push-over analysis has been widely used by engineers to estimate the

behavior of complex structures. In seismic engineering push-over analysis is estimated

to fulfill the demand requirements of structure, by incrementing horizontal static forces

in the nonlinear regime, which somehow replicate the dynamic action. For the sake of

credible push-over analysis, it is necessary to emphasize that;

The structural model has to be realistic,

Analysis procedures have to be reliable,

Modes and frequencies had to identified realistic.

Structures have dominant engineering characteristics such as deformation capacity,

stiffness and strength, which control three performance levels: serviceability, damage

control and collapse prevention. However it has to be determined well which of the

Chapter 3 – Part A: Pushover Analysis

69

characteristics is more effective, and it is difficult to evaluate the stiffness during

changing loading conditions. Criteria have to be clear and have to reflect the actual

behavior of the structure. The force-displacement diagram is an important feature of the

response, as shown in Figure 3.1 (Ghobarah, 2001).

Figure 3. 1 Performance curve of a typical structure (Ghobarah, 2001)

The main purpose to plot a push-over curve is to evaluate the lateral bearing capacity of

a structure. This graph can give an idea to the analyst related to the performance of the

structure during a future earthquake. This performance can be determined by the

maximum displacement of the roof level versus base shear (Reinhorn, 1997; İrtem et al.,

2004). The level of damage in a structure at this target displacement point is considered

representative of the damage of the building (Moghadam, 2000).

Much research was done to estimate the correct damage mechanisms. For example, Tso

and Moghadam (1996) developed a method to estimate the correct damage pattern of

multistory and eccentric structures. According to this study, during failure, the first

mode shape has more influence than other mode shapes (Tso and Moghadam, 1996).

Kilar and Fajfar (1997) developed a method for nonlinear static analysis. This method

applies a constant incremental lateral load to the structure. In this study the authors

accepted that the structure is a planar macro element, and base shear and roof

displacement were taken into considered for a better relation (Kilar and Fajfar, 1997).

Krawinkler and Seneviranta (1998) evaluated the basic principles of nonlinear static

analysis with constant incremental load ratio (Krawlinker and Seneviranta, 1998).

Additionally, Chopra and Goel (2001) developed a new analysis method including


70

higher modes of the structure. The basic calculation principles of this method are based

on seismic demand of the structure composed of each storey’s inertial moment (Chopra

and Goel, 2001). Based on these studies, diverse performance levels to estimate

structural damage are available in different codes, such as Vision 2000 (Ronald, 1997),

ATC-40 (ATC, 1996), FEMA-273 (NEHRP, 1997), FEMA-274 (NEHRP, 1997),

Eurocode-8 (EN 1998-1, 2004) and TEC 2007 (Ministry of Construction, 2007).

3.2. PARAMETERIZATION

In this chapter before starting a numerical analysis, nonlinear parameters were

calculated by means of Eurocode-8 (EN 1998-1, 2004). There are three different

materials in the numeric model: concrete, interface and infill. For each of them,

different nonlinear properties were used. These properties were selected based on the

crack propagation during shake table experiments and literature review. The Total

Strain Fixed Crack model was used for reinforced concrete due to lateral crack

propagated during experiment. Basic properties of Total Strain Fixed Crack were

calculated by CEB-FIP 2010 (CEB-FIB, 2012) and Eurocode-2 (EN 1992-1-1, 2004).

The Total Strain Rotating Crack model was used for the masonry infill due to the fact

that no reinforcement is presented; see also Figure 3.2 with crack propagation in the

infill.


71

Figure 3. 2 Propagation of cracks at two leaf cavity wall model just before collapse

(Leite, 2010)

Combined Cracking Shear Crush material model was used for interface element to

simulate fracture, frictional slip and crushing. This material model is also known as the

composite interface model (Lourenço and Rots, 1997; Lourenço et al., 1998).

3.2.1. Total Strain Crack Model (Fixed and Rotating)

This material model describes compression and tensile behavior of material with one

stress-strain relationship. The material model based on total strain is developed along

the lines of the Modified Compression Field Theory (Vecchio and Collins, 1986). The

total strain based crack models follow a smeared approach for the fracture energy

(Selby and Vecchio, 1993). The fundamental difference between the two concepts

(Fixed and Rotating) is the direction of the maximum tensile principal stress according

to local coordinates. Propagation of a fixed crack predetermines to local coordinates

once the crack is initiated. However, propagation of a rotation crack changes

continuously during the cracking process by using global coordinates. The strain vector,

εxyz in the element coordinate system x, y, z, is updated with the strain increment Δεxyz.

In the fixed concept, the strain transformation matrix is kept fixed and the behavior is

evaluated in a fixed coordinate system determined by the initial crack directions. The


72

strain transformation matrix is determined by calculating the eigenvectors of the strain

tensor, with the Jacobi method. The strain tensor can be seen in Equation 3.1.

E=

휀𝑥𝑥 휀𝑥𝑦 휀𝑥𝑧

휀𝑦𝑥 휀𝑦𝑦 휀𝑦𝑧

휀𝑧𝑥 휀𝑧𝑦 휀𝑧𝑧

(3.1)

The eigenvectors are stored in the rotation matrix R which can be read in Equation 3.2

below.

R= 𝑛 𝑠 𝑡 =

𝑐𝑥𝑛 𝑐𝑥𝑠 𝑐𝑥𝑡

𝑐𝑦𝑛 𝑐𝑦𝑠 𝑐𝑦𝑡

𝑐𝑧𝑛 𝑐𝑧𝑠 𝑐𝑧𝑡

(3.2)

In Equation 3.2, 𝑐𝑥𝑛 = 𝑐𝑜𝑠ø𝑖𝑗 this cosine is between i and j axes (global and local). And

then the strain transformation matrix can be calculated by substituting the appropriate

values in Equation 3.2 (Vecchio and Collins, 1986; Selby and Vecchio, 1993).

3.2.2. Combined Cracking Shear Crush

This interface model was formulated by Lourenço and Rots (Lourenço and Rots, 1997)

for plane stress and further developed by Van Zijl (Zijl, 2000). This interface model is

based on multi-surface plasticity, including a Coulomb Friction model together with a

tension cut-off and an elliptical compression cap, as seen in Figure 3.3 below.

Figure 3. 3 Coloumb friction model combined with tension cut-off and elliptical

compression cap


73

Softening acts in all three modes and is preceded by hardening in the case of the cap

mode. The interface model is derived in terms of the generalized stress and strain

vectors like shown in Equation 3.3 and 3.4 below.

σ= 𝜎𝜏 (3.3)

ε= 𝑢𝑣 (3.4)

𝜎 is the stress and 𝑢 is the relative displacement at normal direction in interface model,

whereas 𝜏 is the shear stress and 𝑣 is the relative displacement in shear direction. In

elastic region, the constitutive behavior is described by Equation 3.5.

σ=D ε (3.5)

The stiffness matrix D, see Equation 3.6, is diagonal with the normal and shear

stiffness, kn and ks, respectively (Vecchio and Collins, 1986; Zijl, 2000).

D=diag[kn,ks] (3.6)

3.2.2.1. Shear Slipping

The Coulomb friction yield criterion is;

f= 𝜏 + 𝜎 ∗ Φ − 𝑐 (3.7)

this equation describes shear slipping with Φ, the friction coefficient equal to tan(ø) of

the friction angle, and 𝑐 is the adhesion. Both adhesion softening and friction softening

are in action with Equation 3.8 as seen below;

𝑐 𝜎, 𝜅 = 𝑐0𝑒−

𝑐0

𝐺𝑓𝐼𝐼𝜅

(3.8)

Where 𝑐0 the initial adhesion of brick-mortar is interface and 𝐺𝑓𝐼𝐼 is the shear slip

fracture energy. The friction softening is coupled to the adhesion softening like

Equation 3.9 below;

Φ 𝜎, 𝜅 = Φ0 + Φr − Φ0 (𝑐0−𝑐)

𝑐0 (3.9)


74

Where Φr and Φ0 are initial and residual friction coefficients. The adhesion and friction

parameters are found by linear regression of the joint shear experimental data, whereas

fracture energy is determined by appropriate integration of stress-crack response. This

process produces the total energy dissipated by both adhesion and friction softening like

Equation 3.10 as seen below.

𝐺𝑓𝐼𝐼∗ = 𝐺𝑓

𝐼𝐼(1 +𝜎

𝑐0 Φr − Φ0 ) (3.10)

Experimentally obtained linear relation between the fracture energy and normal

confining stress is obtained as seen in Equation 3.11 below;

𝐺𝑓𝐼𝐼 =

𝑎𝜎 + 𝑏; 𝑖𝑓 𝜎 < 0𝑏, 𝑖𝑓 𝜎 ≥ 0

(3.11)

Where 𝑎 and 𝑏 are the constants determined by linear regression of the experimental

data (Vecchio and Collins, 1986; Zijl, 2000).

3.2.2.2. Dilatancy

For the dilatancy parameter, the rule is like below;

휀𝑝 = 𝑢𝑝

𝑣𝑝 =⋋

𝜕𝑔

𝜕𝜎 (3.12)

after apotential function, given by equation 4.13;

𝜕𝑔

𝜕𝜎=

Ψ𝑠𝑖𝑔𝑛(𝜏)

(3.13)

Ψ is the dilatancy coefficient obtained by tan(ψ). And then;

Ψ=𝑢𝑝

𝑣𝑝 𝑠𝑖𝑔𝑛(𝜏) (3.14)


75

By integration of the shear-slip, the induced normal uplift is found to be in Equation

3.15 below.

𝑢𝑝 = Ψd ∆𝑣𝑝 (3.15)

This is experimental evidence that dilatancy depends on confining stress and shear slip.

A dilatancy formulation of separate dilatancy is in Equation 3.16.

Ψ = Ψ1 𝜎 Ψ2(𝑣𝑝) (3.16)

This equation simplifies the curve fitting and ensures convexity of the potential function

g as seen in Equation 3.17 below.

g= (𝜕𝑔

𝜕𝜎)𝑇 𝑑𝜎 = 𝜏 + Ψ2(𝑣𝑝) Ψ1 𝜎𝑑𝜎 (3.17)

So, expression of normal uplift is on shear-slipping is chosen like in Equation 3.18

below.

𝑢𝑝 =

0 𝑖𝑓 𝜎 < 𝜎𝑢

Ψ0

𝛿 1 −

𝜎

𝜎𝑢 (1 − 𝑒−𝛿𝑣𝑝 ) 𝑖𝑓 𝜎𝑢 ≤ 𝜎 < 0

Ψ0

𝛿(1 − 𝑒−𝛿𝑣𝑝 ) 𝑖𝑓 𝜎 ≥ 0

(3.18)

Equation 4.18 yields differentiation and then Equation 3.19 is obtained like below.

Ψ =

0 𝑖𝑓 𝜎 < 𝜎𝑢

Ψ0 1 −𝜎

𝜎𝑢 𝑒−𝛿𝑣𝑝 𝑖𝑓 𝜎𝑢 ≤ 𝜎 < 0

Ψ0𝑒−𝛿𝑣𝑝 𝑖𝑓 𝜎 ≥ 0

(3.20)

The dilatancy Ψ0is obtained at zero normal confining compression stress and shear slip,

and the compression stress 𝜎𝑢 is where dilatancy becomes zero, are obtained by

experimental data (Vecchio and Collins, 1986; Zijl, 2000).


76

3.2.2.3. Softening

Strain softening hypothesis is valid in which the softening is governed by shear-slipping

like Equation 3.21.

Δ𝜅 = Δ𝑣𝑝 = Δ ⋋ (3.21)

Where Δ𝜅 and Δ ⋋ are the plastic strain increment during the analyzing the system with

Newton-Raphson method (Zijl, 2000).

3.2.2.4. Tension Cut-Off

The yield function of cut-off is;

𝑓2 = 𝜎 − 𝜎𝑡 (3.22)

Where 𝜎𝑡 is brick-mortar tensile bond strength. The softening is exponential.

𝜎𝑡 = 𝑓𝑡𝑒−

𝑓𝑡

𝐺𝑓𝐼 𝜅2

(3.23)

Where 𝑓𝑡 is the bond strength and 𝐺𝑓𝐼 is the Mode I fracture energy.

3.2.2.5. Compression Cap

Compression Cap is one of the yield criteria, formulated by Equation 4.24 below.

𝑓3 = 𝜎2 + 𝐶𝑠𝜏2 − 𝜎𝑐

2 (3.24)

𝐶𝑠is the parameter which control shear stress failure.

The shear surface hardens by a parabolic softening. The peak strength 𝑓𝑐 is reached at

the maximum plastic strain 𝜅𝑝 . Finally, if a softening branch is considered, the fracture

energy, 𝐺𝑓𝑐, is given by Figure 3.4 below.


77

Figure 3. 4 Hardening and softening rule for interface element’s compression cap

𝜎İ =1

3𝑓𝑐 (3.25)

𝜎𝑚 =1

2𝑓𝑐 (3.26)

𝜎𝑟 =1

7𝑓𝑐 (3.27)

3.3. PUSHOVER ANALYSIS

In this chapter nonlinear static analysis was carried out for two structures composed of

different types of masonry and a single bay reinforced concrete (RC) frame. One of

these structures is a Two Leaf Cavity Wall (TLCW) and another one is an unreinforced

single leaf 13 cm thickness wall (URM). The structure which has Two Leaf Cavity

masonry wall has experimental hysteric curve exposed to earthquake at LNEC in

Lisbon, and serves as validation. The other structure, which has single leaf 13 cm thick

masonry wall, has no experimental values and serves as a traditional structural in

Turkey. This structure was modeled with the same condition and the same parameters

with the two leaf cavity wall. The main purpose of this comparison is to see the

contribution of two leaf cavity wall for the in-plane and out of plane behavior of RC

structures. Verification of elastic parameters belongs to TLCW numeric model was

made by modal updating in the previous chapter. In addition to the elastic properties,


78

the nonlinear properties of the structural model are presented here on the basis of the

theoretical approach mentioned above.

This nonlinear analysis was made with Regular Newton-Raphson method and a

convergence criterion based on an internal energy tolerance equal to 10-3

. During the

analyses, the lateral force was applied proportional to the total mass, in each direction

both positive and negative, and the arc-length control method was used. This is an

indirect displacement control method. These analyses were done also with a line search

algorithm. The force ratio was obtained by Equation 3.28 at each iteration step.

𝛼𝑥 ,𝑧 = 𝐻𝑜𝑟𝑖𝑧𝑜𝑛𝑡𝑎𝑙 𝐵𝑎𝑠𝑒 𝑆𝑕𝑒𝑎𝑟

𝑆𝑒𝑙𝑓𝑤𝑒𝑖𝑔 𝑕𝑡 𝑜𝑓 𝑆𝑡𝑟𝑢𝑐𝑡𝑢𝑟𝑒 (3.28)

The iterative solution procedure is the most important aspect during the analysis and the

general flowchart can be seen below.

Figure 3. 5 Flow chart of iteration steps during the nonlinear static analysis

During the iteration, the total displacement increment is adapted until reaching the

tolerance of energy variation. The successive iteration steps are calculated like equation


79

𝑢𝑖+1 = 𝑢𝑖 + 𝑢𝑖+1 (3.29)

The iterative increments are calculated by the use of the stiffness matrix “K”, which

provides the relation between the force vector and displacement vector. This matrix

changes at each iteration. The calculated stiffness at each step is shown in Equation

3.30.

𝑢𝑖 = 𝐾𝑖−1𝑔𝑖 (3.30)

In Equation 3.30, 𝑔𝑖 is the out of balance force vector at the start of increment.

Variation of iteration procedures was adapted according to the arc-length control

method.

3.3.1. Regular Newton-Raphson Method

The Newton-Raphson method is usually divided into two groups, one of them is the

Regular and the other is Modified. Both of them are used to determine the update in the

displacement vector in an increment. In both analysis types, the stiffness matrix is the

tangential stiffness of the structure but in Regular Newton-Raphson method, the

stiffness is updated at each step. This prediction is done by the last calculated value,

even if the equations are not at equilibrium state. In the Modified version, the stiffness

is only update at the beginning of the step.


80

Figure 3. 6 Iteration type of Regular Newton-Raphson Method

The Regular Newton-Raphson Method converges with a quadratic convergence rate,

when it is close to the solution. Quadratic convergence means that the method

converges in a few iterations to solution.

3.3.2. Analysis of the Results for TLCM

According to the experimental data, TLCW structure had a brittle collapse during stage

4. This stage and other stages were classified according to return periods shown in

Table 3.1 below. On the basis of these ground motions, hysteric curves were plotted as

seen in Figure 3.7 transversal and Figure 3.8 longitudinal.

Table 3. 1 Return periods and maximum acceleration of earthquakes exposed to TLCW

structure (Leite et al., 2011; Leite, 2014)

Step

Number

Return Period

(Years)

PGA (m/s2)

Transversal Longitudinal

Step1 225 1.33 1.73

Step2 475 2.13 2.92

Step3 2475 7.25 10.27

Step4 1.5*2475 9.64 10.51


81

Figure 3. 7 Hysteric curves of experimental earthquake data belongs to 4 stages in

transversal direction


82

Figure 3. 8 Hysteric curve of experimental earthquake data belongs to 4 stages in


As seen from the figures, stage 4 was plotted in two parts because this structure

collapsed at the beginning of the stage 4. For this reason, stage 4 was plotted with

maximum values only, as an upper and lower limit boundary for transversal direction.

However, there is no record for longitudinal direction at stage 4.

Before the numerical analysis, nonlinear parameters were calculated and defined to the

system according to Eurocode 2 (EN 1992-1-1, 2004). These nonlinear parameters were

tabulated in Table 3.2 and Table 3.3 respectively below.

Table 3. 2 Engineering properties of concrete and infill belong to TLCW

Type of

Material

Compressive

Strength 𝒇𝒄

(MPa)

Compressive Fracture

Energy 𝑮𝒄 (N/mm)

Tensile

Strength𝒇𝒕

(MPa)

Mode-I

Fracture

Energy 𝑮𝒇𝑰

(N/mm)

Concrete 29.5 47.2 2.32 0.051

Infill 1.26 2.0 0.20 0.013


83

Interface properties were the most relevant parameters controlling the response.

Therefore, these parameters were calculated carefully. Firstly, the cohesion, friction

angle and dilatancy coefficient were determined as seen in Table 3.3, with mode-I

fracture energy adopted as 0.012 N/mm (CUR, 1994). Furthermore, for mode-II fracture

energy, a value of 1/10 of the cohesion (in N/mm2), is adopted according to CUR (CUR,

1994). Compressive strength of interface element used is the value of the infill wall,

1.26 MPa, and the shape of the cap was the one recommended by Lourenço (Lourenço,

1996). Young’s modulus for Infill and Reinforced concrete values which were used for

pushover, adopted based on the experimental study [76]. So, before performing the

pushover analysis, calibration of this parameter was done to obtain the correct push-

over curve. Finally, nonlinear properties of interface element are seen as Table 3.3

below.

Table 3. 3 Engineering properties of interface belong to TLCW

Kn

Normal

Traction

(N/mm3)

Ks Shear

Tarction

(N/mm3)

Tensile

Stregth𝒇𝒕𝒓

(MPa)

Mode-I

Fracture

Energy

𝑮𝒇𝑰

(N/mm)

Mode-II

Fracture

Energy

𝑮𝒇𝑰𝑰

(N/mm)

Compressive

Fracture

Energy 𝑮𝑭𝑪

(N/mm)

Friction

Coefficients

c Ø Ψ

175 75 0.3 0.012 0.030 8 0.6 0.75 0.01

After parameterization, the push-over analysis was performed to compare experimental

and numeric hysteric curve. This first analysis was performed by a fine mesh, with a

total number of nodes equal to 28562. This pushover analysis also performed with a

coarse mesh, composed only of 2821 nodes. The purpose of this second analysis is to

assess the sensitivity of the response to mesh refinement, between the coarse mesh and

fine mesh, so that a coarse mesh can be used for time history analysis, see Figure 3.9

and Figure 3.10.


84

Figure 3.9 Fine mesh (Onat et al., 2015)

Figure 3.10 Coarse mesh (Onat et al., 2015)

Figure 3.11 presents the fine and coarse mesh of TLCW model. Fine mesh dissipates

1817.68 KNmm in positive direction and 1625.67 KNmm in negative direction.

Furthermore, coarse mesh model of TLCW model dissipate 1657.72 in positive

direction and 1462.73 KNmm in negative direction.

Figure 3. 11 Force – Displacement curve of TLCW reinforced concrete frame fine and

coarse mesh along transversal direction

-400

-300

-200

-100

0

100

200

300

400

-10 -8 -6 -4 -2 0 2 4 6 8 10

FO

RC

E (

KN

)

DISPLACEMENT (mm)

FE TLCW FINE MESH (+)

FE TLCW FINE MESH (-)

FE TLCW GROSS MESH (+)

FE TLCW GROSS MESH (-)


85

Figure 3. 12 Force – Displacement curve of TLCW reinforced concrete frame fine and

coarse mesh along longitudinal direction

Only TLCW model is evaluated in Figure 3.12. Fine mesh dissipates 1567.62 KNmm in

positive direction and 1363.51 KNmm in negative direction. Furthermore, coarse mesh

model of TLCW model dissipates 1628.52 in positive direction and 1168.27 KNmm in

negative direction.

3.3.3. Analysis of the Results for URM

TLCW reinforced concrete structure is compared with URM reinforced concrete in

terms of performance. Again, there is not any experimental results belonging to URM

structure but this structure was modeled with the same condition and parameters.

Consequently, this evaluation strategy shows best comparison related to reinforced

technique. The purpose of this comparison is to show how far the performance of

TLCW from URM structures is. As a construction technique, 13 cm uniform thickness

infill wall is commonly used by most of the countries especially in Turkey. Two

analyses were performed by URM. The numbers of elements are the same with TLCW

model. Nonlinear static analysis of these two structures was plotted in the same chart as

seen in Figure 3.13 along transversal and Figure 3.14 along longitudinal direction with

fine mesh.

TLCW model was compared with URM model in Figure 3.13. Pushover analysis was

performed on these models with coarse mesh. Energy dissipation capacity of TLCW

-300

-200

-100

0

100

200

300

-10 -5 0 5 10 15

FO

RC

E (

KN

)

DISPLACEMENT (mm)

FE TLCW FINE MESH (+)

FE TLCW FINE MESH (-)

FE TLCW GROSS MESH (+)

FE TLCW GROSS MESH (-)


86

model in positive and negative side 1114.32 KNmm and 1431.9 KNmm respectively.

Furthermore, energy dissipation capacity of URM model is 604.43 KNmm and 705

KNmm in positive and negative direction respectively in transversal direction.

The result of pushover analysis with coarse mesh was plotted in Figure 3.13 along

longitudinal direction. TLCW model dissipated 1622.35 KNmm in positive direction

and 1308.18 KNmm in negative direction. However, URM model dissipated less energy

naturally like 604.43 KNmm in positive direction and 705 KNmm in negative direction.

Figure 3.14 presents comparison of two model in terms of Force – Displacement. This

comparison is done for fine mesh. TLCW model showed better performance and

dissipated 2054.2 KNmm energy in positive direction and 2063.1 KNmm energy in

negative direction. However, URM model dissipated 890.86 KNmm and 646.5 KNmm

energy in negative direction.

Figure 3. 13 Force-Displacement curves of TLCW and URM infill structures (Coarse

Mesh) along transversal direction

-400

-300

-200

-100

0

100

200

300

400

-8 -6 -4 -2 0 2 4 6

FO

RC

E (

KN

)

DISPLACEMENT (mm)

TLCW FE GROSS MESH

URM FE GROSS MESH


87

Figure 3. 14 Force-Displacement curves of TLCE and URM infill structures (Coarse

Mesh) along longitudinal direction

Figure 3. 15 Force-Displacement curves of TLCE and URM infill structures (Fine

Mesh) along transversal direction

-300

-200

-100

0

100

200

300

-15 -10 -5 0 5 10

FO

RC

E (

KN

)

DISPLACEMENT (mm)

TLCW FE GROSS MESH

URM FE GROSS MESH

-300

-200

-100

0

100

200

300

400

-10 -8 -6 -4 -2 0 2 4 6 8 10FO

RC

E (

KN

)

DISPLACEMENT (mm)

TLCW FE FINE MESH

URM FE FINE MESH


88

Figure 3. 16 Force-Displacement curves of TLCE and URM infill structures (Fine

Mesh) along longitudinal direction

Longitudinal direction, TLCW model dissipated 1720.51 KNmm in positive direction

and 1005.7 KNmm in negative direction. Naturally, URM model dissipated 584 KNmm

in positive direction and 822 KNmm in negative direction. Dissipated energies can be

seen in Table 3.4 and Table 3.5

Table 3. 4 Dissipated energy of fine meshed model

Direction TLCW (KNmm) URM

Positive Negative Positive Negative

Transversal 1817.68 1625.67 890.86 646.5

Longitudinal 1567.62 1363.51 584.0 822.0

Table 3. 5 Dissipated energy of coarse meshed model

Direction TLCW (KNmm) URM (KNmm)


Transversal 1657.72 1462.73 604.43 705.0

Longitudinal 1628.52 1168.27 600.0 1000.16

-250

-200

-150

-100

-50

0

50

100

150

200

250

-15 -10 -5 0 5 10 15

FO

RC

E (

KN

)

DISPLACEMENT (mm)

TLCW FE FINE MESH

URM FE FINE MESH


89

3.3.4. Comparison between TLCW and URM for Push-Over Curve

As seen from the figures, TLCW model shows higher strength but more brittle behavior.

Because when the structure is forced to move laterally with lateral force, plastic hinges

occur at columns, with larger rotations, when compared with TLCW. These hinges

force the structure to collapse. This problem can be solved during the design phase.

URM structure showed more ductile behavior but lower strength, as predicted. Initial

stiffness of structures was also different. To compare numeric energy dissipation

capacity with experimental, Table 3.6 can be seen.

Table 3. 6 Experimental energy dissipation capacity

Direction Step1 (KNmm) Step2 (KNmm) Step3 (KNmm)

Transversal 69.86 144.1 1002.2

Longitudinal 81.47 150.6 1737.6

As seen from Table 3.6, experimental energy dissipation capacity at step3 has a good

match between coarse mesh of TLCW model in negative side along transversal

direction and coarse mesh of TLCW model in positive side along longitudinal direction.

The difference between experimental energy dissipation capacity and numeric energy

dissipation capacity is 27% in transversal direction and 8% in longitudinal direction.

Performance curves also can be seen from Figure 3.17 and Figure 3.18 on the base of

experimental hysteric curves with fine mesh.


90

Figure 3. 17 Force ratio-Displacement curves of TLCE and URM along transversal

direction (Fine Mesh)

The purpose of plotting Figure 3.17 is to see easily the differences between fine meshed

model of TLCW and URM in transversal direction. Until 0.2g, both models show the

same behavior and then URM model starts to fail due to starting cracks. However, after

first crack of infill wall, TLCW model continue to resist lateral load in transversal

direction. 0.35g is the critical for URM model. After this force ratio, infill wall was

failed and RC frame continued resisting lateral load.


91

Figure 3. 18 Force ratio-Displacement curve of TLCE and URM along longitudinal

direction (Fine Mesh)

As seen in Figure 3.18, there is not any certain infill wall failure for TLCW model. All

structure fails together with all structural and non-structural elements around 10 mm

roof displacement in positive transversal direction. However, there is a certain failure

area for URM model. After failure of infill wall, RC frame continue resisting of seismic

load itself without infill wall. Figure 3.17 and Figure 3.18 proves that TLCW model

shows brittle behavior, URM model shows ductile behavior.

Results of coarse mesh also can be seen from Figure 3.19 and Figure 3.20.


92

Figure 3. 19 Force ratio-Displacement curves of TLCW and URM along transversal

direction (Coarse Mesh)

There is a strange difference in Figure 3.19 on behalf of URM model. This bizarre point

is the demonstration of heavy cracks of in positive transversal direction. This strange

part is the presence of double hill at performance curve of URM model. This is the

demonstration of firstly heavy cracks of infill wall along in-plane direction. After these

cracks, structural and non-structural members continue resisting lateral load together.

After small increasing lateral performance of the model, infill walls were failed

completely. Then RC frame resisted rest of the seismic action without infill wall.

TLCW model showed very brittle behavior. Because, this model collapsed earlier than

expected. However, stiffness of numeric TLCW model shows good match with

experimental TLCW model. Post-peak behavior of TLCW model is not clear in Figure

3.19.


93

Figure 3. 20 Force ratio-Displacement curve of TLCE and URM along longitudinal

direction (Coarse Mesh)

In Figure 3.20, especially post-peak behavior of numeric TLCW model is clear. Along

this direction, TLCW model showed ductile behavior. One of the most important point

is lateral bearing capacity of URM model. Lateral bearing capacity of URM model is

nearly 33% less than TLCW model in longitudinal direction.

In terms of force ratio-displacement curve, Figure 3.21 presents the comparison of all

pushover analysis and experimental result along transversal direction, and Figure 3.22

along longitudinal direction can be seen below. As seen from the figures, along the

transversal direction, the maximum load factor of experimental value is 0.662g at

positive X direction and 0.67g at negative X direction. Furthermore numerical values

are also compatible with experimental values. Numerical values are 0.64g at positive X

direction and 0.62 at negative X direction. However, there is no experimental value

belonging to stage 4. The reason for this is the strong impact along the longitudinal

direction.


94

Figure 3. 21 Comparison of pushover curve belong to fine and coarse mesh along

transversal direction (Onat et al., 2015)

Figure 3. 22 Comparison of pushover curve belong to fine and coarse mesh along

longitudinal direction (Onat et al., 2015)


95

3.3.5. Comparison of Drift Levels with Codes

The results are compared firstly with ASCE/SEI 41-06 (ASCE/SEI 41-06, 2007).

According to ASCE/SEI 41-06 performance levels are tabulated in Table 3.7

Table 3. 7 Performance levels for primary elements of reinforced concrete frames

(ASCE/SEI 41-06, 2007) Item Collapse Prevention (CP) Life Safety (LS) Immediate Occupancy (IO)

Primary Extensive cracking and

crushing; portions of face

course shed.

Extensive cracking and some

crushing but wall remains in

place. No falling units.

Extensive crushing and

spalling of veneers at corners

of openings.

Minor cracking of masonry infills

and veneers. Minor spalling in

veneers at a few corner openings.

Secondary Extensive cracking and

crushing; some walls dislodge

Same as primary Same as primary

Drift 0.6 % transient or permanent 0.5 % transient, % 0.3

permanent

0.1 % transient, negligible

permanent

On the basis of ASCE/SEI 41-06, performance levels of structure were plotted in Figure

3.22 in transversal direction and Figure 3.23 in longitudinal direction.

Figure 3. 23 Storey Level - % Drift in Transversal Direction

In transversal direction 1ststorey of TLCW with fine mesh nearly reached the 0.3 % drift

capacity in negative direction, whereas this storey showed more conservative behavior

along positive direction so this floor stayed about LS line. Experimental results proved

that behavior of this model is ductile at both storey’s. Because, during the test structure

moved more than desired on the shake table due to flexible boundary condition.

Performance of tested structure is located between IO and LS. TLCW fine mesh model

is showed extremely good match between experimental results in positive and negative

0

2

4

-0.4 -0.2 0 0.2 0.4

STO

REY

LEV

EL (

m)

DRIFT (%)

TLCW FINE MESH

TLCW COARSE MESHURM FINE MESH

URM COARSE MESHEXPERIMENTAL

IO

LS


96

direction along transversal direction at first storey. However, finite element analysis is

performed under perfect boundary condition for this reason drift of second storey

showed differences between experimental results. The rest of the results belong to other

model for fine and coarse mesh can be seen in Figure 3.23.

Figure 3. 24 Storey Level - Drift (%) in Longitudinal Direction (Onat et al., 2015)

In longitudinal direction, 1ststorey performance of the TLCW model showed a good

match between experimental and numeric drift along negative direction. For positive

direction, numeric model showed more ductile behavior and passed beyond the LS line

and experimental drift. However, 1ststorey performance of numeric TLCW model is

very close to experimental drift along negative direction. This performance is located

between IO and LS for both models. Second storey performance is near IO level. The

differences between experimental and numeric drift at second storey proved that

structure failed due to soft storey of first floor. Performance of fine and coarse mesh of

URM model can be seen in Figure 3.22 and Figure 3.23.

0

2

4

-0.4 -0.2 0 0.2 0.4 0.6

STO

REY

LEV

EL (

m)

DRIFT (%)

TLCW FINE MESH

TLCW COARSE MESHURM FINE MESH

URM COARSE MESHEXPERIMENTAL

IO

LS


97

Figure 3. 25 Maximum displacements (mm) along storey height in transversal direction

at maximum force ratio

Figure 3. 26 Changes of maximum displacement (mm) along storey height in


As seen from the Figures 3.25 and 3.26 displacements of experimental values of TLCW

is overlapped with Finite Element model of this structure along transversal direction.

0

2

4

0 2 4 6

ST

OR

EY

LE

VE

L (

m)

DISPLACEMENT (mm)

EXPERIMENTAL

FINE MESH TLCW

FINE MESH URM

GROSS MESH TLCW

GROSS MESH URM

0

2

4

0 2 4 6 8 10

ST

OR

EY

LE

VE

L (

m)

DISPLACEMENT (mm)

EXPERIMENTAL

FINE MESH TLCW

FINE MESH URM

GROSS MESH TLCW

GROSS MESH URM


98

Coarse mesh of TLCW model stayed behind the experimental and fine mesh of TLCW

model due to failure of coarse particle of finite elements. However, there is a difference

in longitudinal direction in terms of displacement. This difference shows that relative

displacement of model in longitudinal direction completely depends on the mesh

number of the model. Furthermore, there is a certain prediction in terms of relative

displacement in transversal direction.

3.3.6. Evaluation of the Stiffness

Stiffness of the models are also evaluated separately and presented in Table 4.8 and

Table 3.8 below. While calculating stiffness, derivation of formula belongs to force

displacement curve was considered. Stiffness of the model was evaluated until first

crack.

Table 3. 8 Stiffness of fine meshed model

Direction TLCW (KN/mm) URM (KN/mm)


Transversal 128.43 183.96 108.12 118.98

Longitudinal 100.59 92.88 78.13 57.49

There is a 15 % difference in positive and 35% difference in negative direction between

TLCW and URM model along transversal in terms of stiffness. Moreover, there is 22%

difference in positive and 38% difference between TLCW and URM model in

longitudinal direction. This evaluation is related to fine meshed model.

Table 3. 9 Stiffness of coarse meshed model

Direction TLCW (KN/mm) URM (KN/mm)


Transversal 128.43 183.96 114.1 167.35

Longitudinal 100.59 92.88 104.82 89.36

Table 3.9 presents stiffness evaluation for coarse meshed model. Stiffness difference

between TLCW and URM model in transversal direction 11% for positive direction and

9% for negative direction. In addition to transversal, longitudinal direction showed

lower difference like around 5% for positive and 4% for negative direction.


99

3.3.7. Crack patterns

After evaluation of force, displacement, relative displacement, drift and then stiffness

parameters, Figure 3.27 presents crack propagation of experimental model below.

a)North

b)South

c)East

d)West

Figure 3. 27 Experimental crack propagation of TLCW before stage 4 (Leite, 2014)

Crack propagation of numeric model can be seen for TLCW model and URM model.

There are four types of loading for both analysis mentioned before. Crack propagation

of these loadings can be seen below.


100

Figure 3. 28 Crack pattern of TLCW in transversal directions with fine mesh before

failure (Loading Type: Positive Transversal)


101

Figure 3. 29 Crack pattern of TLCW in longitudinal directions with fine mesh before

failure (Loading Type: Positive longitudinal)


102


failure (Loading Type: Negative Transversal)


failure (Loading Type: Negative Longitudinal)

Nonlinear analysis results of TLCW with coarse mesh are demonstrated below.

Figure 3. 32 Crack pattern of TLCW in transversal directions with coarse mesh before

failure (Loading Type: Positive Transversal)


103

Figure 3. 33 Crack pattern of TLCW in longitudinal directions with coarse mesh before

failure (Loading Type: Positive Longitudinal)

Figure 3. 34 Crack pattern of TLCW in transversal directions with coarse mesh before



104

Figure 3. 35 Crack pattern of TLCW in longitudinal directions with coarse mesh before


As seen from the figures crack patterns are compatible with experimental values. These

cracks were calculated by maximum tensile principle strains. On the base of cracks and

experimental data, structure showed a brittle failure mechanism along first transversal

mode. In terms of photos and numeric images, major cracks were occurred at first floor

bottom part of the window through east and west direction. However at south part of

structure, diagonal cracks loosen the bearing capacity of the structure at first floor as

seen negative and positive transversal loading. These mentioned parts were working as

a diagonal tension strut. The weak area is between the window and the door at the first

floor at north part of the structure. In addition, URM structure has very close failure

pattern to experimental specimen like TLCW as shown below.


105

Figure 3. 36 Crack pattern of URM in transversal directions with fine mesh at the time

of failure (Loading Type: Positive Transversal)

Figure 3. 37 Crack pattern of URM in longitudinal directions with fine mesh at the time

of failure (Loading Type: Positive Longitudinal)


106

Figure 3. 38 Crack pattern of URM in transversal directions with fine mesh before


Figure 3. 39 Crack pattern of URM in longitudinal directions with fine mesh before



107

Figure 3. 40 Crack pattern of URM in transversal directions with coarse mesh before


Figure 3. 41 Crack pattern of URM in longitudinal directions with coarse mesh before

failure (Loading Type: Negative longitudinal)


108

3.4. CONCLUSION

This chapter presents the nonlinear static analysis for two case studies of reinforced

concrete frames with masonry infill. One of them has a double leaf cavity wall (TLCW)

and the other has a single leaf wall (URM). Both models have been analyzed with a

coarse and a fine mesh, and differences about 10% have been found between the

models, even the coarse mesh uses about 1/10 of the degrees of freedom. It is also noted

that the TLCW model shows higher base shear ratio capacity than the URM in terms of

resisting lateral loads, but also showed a more ductile behavior. The differences in terms

of base shear are about 35%. Moreover, TLCW model dissipated more energy than

URM model about 50 %. There is 10 % difference between fine and coarse mesh in

terms of energy dissipation capacity. More energy dissipation capacity of TLCW model

is obvious evidence to consider superior property to use construction industry.

Furthermore, stiffness difference between two models is 30 % in both directions until

first crack. TLCW reinforced concrete frames, or in the presence of excessively strong

infill which is named double leaf model proved that this type of infill solution can resist

more lateral loads than conventional type of infill orientation that is unreinforced single

leaf wall. However, while design phase it is strongly suggested that soft storey collapse

should be considered and designer should take prevention.

3.5. REFERENCES

American Society of Civil Engineers, Seismic Rehabilitation of Existing Building:

ASCE SEI 41/06, USA, 2007

ATC–40, Seismic Evaluation and Retrofit of Concrete Buildings‖ Applied Technology

Council. California, USA, 1996

CEB-FIP, Model Code 2010, Final draft, vol. 1. Comité EuroInternational du Béton,

2012

Chopra, A., K., Goel, R., K., A Modal Pushover Analysis Procedure for Estimating

Seismic Demands For Buildings, Earthquake Engineering and Structural

Dynamics, 31:561–582, 2001

CUR, Structural Masonry: An Experimental/Numerical Basis for Practical Design

Rules (in Dutch). Report 171, CUR, Gouda, The Netherlands, 1994


109

EN 1998-1, Eurocode 8: Design of Structures for Earthquake Resistance-General

Rules, Seismic Actions and Rules for Buildings, European Committee for

Standardization, 2004

Eurocode 2: Design of concrete structures - Part 1-1: General rules and rules for

buildings, EN 1992-1-1, December, 2004

FEMA–273, NEHRP Guidelines for the Seismic Rehabilitation of Buildings‖ Federal

Emergency Management Agency, Washington, USA, 1997

FEMA–274, NEHRP Guidelines for the Seismic Rehabilitation of Buildings‖ Federal

Emergency Management Agency, Washington, USA, 1997

Ghobarah, A., Performance-Based Design in Earthquake Engineering: State of

Development. Engineering Structures, 23:878-884, 2001

Reinhorn, A., M., Inelastic Analysis Techniques in Seismic Evaluations, Proceedings of

International Workshop on Seismic Design Methodologies for the Next

Generation of Codes, 277-287 Slovenia, 1997

Irtem, E., Türker, K., Hasgül, U., Performance Evaluation of Reinforced Concrete

Structure Designed by Turkish Code, 6th International Congress on Advances

of Civil Engineering, 6-8 October 2004, İstanbul, Turkey

Kilar, V., Fajfar, P., Simple Push-Over Analysis of Asymmetric Buildings, Earthquake

Engineering and Structural Dynamics, 26:233-249, 1997

Krawinkler, H., Seneviranta, G., D., P., K., Pros and Cons of a Pushover Analysis Of

Seismic Performance Evaluation, Engineering Structures, 20:452-464, 1998

Leite, J., Pereira, M., P., Lourenço, P., B., Infill Masonry: Seismic Behaviour of

Reinforced Solutions, 7th International Conference AMCM2011, Krakow,

Poland, 2011

Leite, J., Innovative Solutions for Weak Infill Walls, Technical Report, Minho

University, Guimaraes, Portugal, 2012

Leite J., Design of Masonry Walls for Building Enclosures Subjected to Extreme

Actions, PhD Thesis, Minho University, Guimaraes, Portugal, 2014

Leite, J., Soluções Inovadoras para paredes de Alvenaria Não Resistentes‖ Scientific

ProgressReport, University of Minho, Portugal, 2010

Lourenço, P., B., Rots, J., G., A Multi-Surface Interface Model for the Analysis of

Masonry Structures, Journal of Structural Engineering, ASCE 123(7) 660-668,

1997


110

Lourenço, P., B., Rots, J., G., Blaauwendraad, J., Continuum Model for Masonry:

Parameter Estimation and Validation, Journal Structural Engineering, ASCE

124, 6, 1998

Lourenço, P. B., Computational Strategies for Masonry Structures, PhD Thesis. Delft,

Netherlands, 1996

Moghadam, A., S., Tso, W., Pushover Analysis for Asymmetric and Set-Back Multi-

Story Buildings, 12th WCEE, 1093-1101, 2000

Ronald, O., A Framework for Performance-Based Earthquake Resistivity Design,

EERC-CURE Symposium, 31 January-1 February 1997 California, Berkeley,

1997

Selby, R., G., Vecchio, F., J., Three-Dimensional Constitutive Relations For Reinforced

Concrete, Technical Report 93-02, University of Toronto, Department of Civil

Engineering, Toronto, Canada, 1993

Tso W., K., Moghadan, A., S., Damage Assessment of Eccentric Multistorey Buildings

Using 3-D Pushover Analysis, 11th World Conference on Earthquake

Engineering, 997-1005, 1996

Turkish Ministry of Construction, Earthquake Disaster Prevention 2007, Ankara, 2007

Vecchio, F., J., Collins, M., P., The Modified Compression Field Theory for Reinforced

Concrete Elements Subjected To Shear, ACI Journal 83(22) 219-231, 1986

Zijl, V., G., P., A., G., Computational Modelling of Masonry Creep and Shrinkage, PhD

thesis, Delft University of Technology, 2000

Chapter 4 – Part A: Time History Analysis

111

Chapter 4 4 PART A: TIME HISTORY ANALYSIS OF REINFORCED

CONCRETE STRUCTURES WITH TWO LEAF CAVITY

WALL AND UNREINFORCED MASONRY WALL

The purpose of this chapter is to discuss the time history analysis of the strictures

analyzed in the previous chapter with pushover analysis. Before starting the analyses,

the numerical parameters were transferred directly from the previous pushover analysis.

Next, the analysis type is described briefly and then the results are discussed.

4.1 INTRODUCTION

Shake table experiments were implemented by many researchers to see realistic

behavior of complete or scaled structures. Liauw and Kwan implemented shake table

experiment on two 1:3 scaled structures. Both of them are 4 storeys. One of them is

constructed using a reinforced concrete shear wall and another of them is made using an

infill wall. The first structure resisted until 0.95g but heavily damaged, while the second

structure collapsed at 0.835g. It was emphasized that structure with infill wall dissipated


112

energy better than the structure with shear wall. Another important point is that the infill

wall structure collapsed due to soft storey mechanism at first floor. Another important

aspect is that the structure with infill wall resisted a base shear 6 % higher than the

structure with shear wall (Liauw and Kwan, 1992).

Ile et al. carried out a shake table experiments on light reinforced concrete frame and

reinforced wall with current design practice in France. Numerical and experimental

results were compared between each other. It was emphasized that damage was

concentrated at the bottom part of the specimens at both experimental and numerical

simulation. Then authors found good match between experimental and numerical results

in terms of failure mode (Ile et al., 2008).

Toranzo et al. investigated confined masonry rocking wall effect with steel

supplementary hysteric damping. For this purpose 40 % scaled wall-frame system was

used to validate the system. The specimen was exposed to 60 ground motions and a

maximum 2.5 % drift was achieved. With supplementary damping, damping ratio was

increased to 14 % and then it was emphasized that with these study lateral demand

capacity was increased between 33% and 50% (Toranzo et al., 2009).

2/3 scaled 3 storey one bay reinforced concrete structure with brick infill wall was

tested by Stavridiset et al. to analyze the combinedin-plane and out-of-plane behavior of

infill wall. For this purpose, a prototype model was used. Stavridiset et al. used non-

ductile reinforcement detailing during construction phase. 14 scaled historical

earthquake ground motion was used in this test. Stavridiset et al. found acceptable

results in terms of dynamic response, load resistance and failure mechanism (Stavridis

et al., 2012).

Shake table experiments were implemented for different purposes as mentioned above.

These results should be verified with Time History Analysis to verify the agreement of

test results and numeric model parameters, and to better understand the experimental

results. This chapter presents the time history analysis of double leaf cavity wall

reinforced concrete structure and an unreinforced wall reinforced concrete structure,

which is typical of Turkish construction. The material parameters adopted previously

for pushover analysis have been now used in time history analysis.


113

4.2 INPUT SIGNALS

Shake table experiments were implemented in four steps (Leite, 2014). These four steps

are briefly explained in Table 4.1 below.

Table 4. 1 Brief Summary of Shake Table Experiments

Step Number Return Period (Years) PGA (m/sn

2)

Transversal Longitudinal

Step1 225 1.33 1.73

Step2 475 2.13 2.92

Step3 2475 7.25 10.27

Step4 1.5x2475 9.64 10.51

Design spectrum of all stages according to Eurocode 8 (EN 1998-1, 2004) in transversal

and longitudinal directions can be seen in Figure 4.1 and Figure 4.2 respectively.

Figure 4. 1 Design Spectrums of Input Signals in Transversal Direction According to

Eurocode-8


114

Figure 4. 2 Design Spectrums of Input Signals in Longitudinal Direction According

Eurocode-8

Step3 was considered as 100 % earthquake load acceleration ratio of this stage is 0.74g

in transversal direction and 1.05g in longitudinal direction. Input signals of stage 3 are

presented in Figure 4.3 and Figure 4.4 below.


115

Figure 4. 1 Input Acceleration of 100 % Earthquake in Transversal Direction


116

Figure 4. 2 Input Acceleration of 100 % Earthquake in Longitudinal Direction

4.3. SECANT ANALYSIS METHOD (QUASI NEWTON METHOD)

Nonlinear time history analysis was performed with the Secant method. Newton

methods failed due to severe changes in stiffness matrix, from loading to unloading, and

reverse. A Quasi-Newton method, also called Secant Method, essentially uses the

information of previous solution vectors and out-of-balance force vectors during the

increment to achieve an approximation of the stiffness matrix. Unlike Regular Newton

Raphson, the Quasi-Newton method does not set up a completely new stiffness matrix

at each iteration as seen in Figure 4.5 below.


117

Figure 4. 3 Quasi-Newton Iteration

In this case the stiffness of the structure is determined from the quantities known at the

equilibrium path. If the iterative displacement increment is called 𝛿𝑢𝑖 and the change in

out-of-balance force vector 𝛿𝑔𝑖related to this increment can be shown in Eqn. 4.1.

𝛿𝑔𝑖=𝑔𝑖+1-𝑔𝑖 (4.1)

So, the Quasi Newton relation can be seen in Eqn. 4.2.

𝐾𝑖+1*𝛿𝑢𝑖=𝛿𝑔𝑖

(4.2)

With a matrix Ki that fulfills the next iterative increment is calculated from Eqn. 3.30.

For a system with more than one degree of freedom, the secant stiffness matrix K is not

unique. The methods implemented in DIANA are known as Broyden, Broyden-

Fletcher-Goldfarb-Shanno (BFGS) and the Crisfield methods. By substitution it can be

seen that the following two matrices fulfill the Quasi-Newton relation as seen Eqn. 4.3

and Eqn. 4.4.


118

𝐾𝑖+1 = 𝐾𝑖 + 𝛿𝑔𝑖−𝐾𝑖𝛿𝑢𝑖 ∗𝑐

𝑇

𝑐𝑇∗𝛿𝑢𝑖 (4.3)

𝐾𝑖+1 = 𝐾𝑖 + 𝛿𝑔𝑖−𝐾𝑖𝛿𝑢𝑖 ∗𝑐

𝑇+𝑐∗(𝛿𝑔𝑖−𝐾∗𝛿𝑢𝑖)𝑇

𝑐𝑇∗𝛿𝑢𝑖−

(𝛿𝑔𝑖−𝐾∗𝛿𝑢𝑖)𝑇∗𝛿𝑢𝑖∗𝑐∗𝑐𝑇

(𝑐𝑇𝛿𝑢𝑖)2 (4.4)

In Eqn. 4.3 and Eqn. 4.4 the vector c can be selected freely. The Quasi-Newton methods

can be used efficiently because the inverse of the stiffness matrix can be derived directly

from the previous secant stiffness and the update vectors.

4.3.1. Broyden

If in Eqn. 4.3 c substituted by 𝛿𝑢and 𝐾𝑖+1 is inverted, the Broyden method results in

Eqn. 4.5

𝐾𝑖+1−1 = 𝐾𝑖

−1 +(𝛿𝑢𝑖−𝐾𝑖

−1𝛿𝑔𝑖)𝛿𝑢𝑖𝑇𝐾𝑖

−1

𝛿𝑢𝑖𝑇𝐾𝑖

−1𝛿𝑔𝑖 (4.5)

4.3.2. BFGS

The inverse secant stiffness matrices are not calculated explicitly, but the iterative

displacements 𝛿𝑢 are calculated directly by substitution of Eqn. 4.5. in Eqn. 4.6. Then

Eqn. 4.6 is obtained like below.

𝐾𝑖+1−1 = 𝐼 +

𝛿𝑢𝑖𝛿𝑔𝑖𝑇

𝛿𝑢𝑖𝑇𝛿𝑔𝑖

∗ 𝐾𝑖−1 ∗ 𝐼 −

𝛿𝑔𝑖𝛿𝑢𝑖𝑇


+𝛿𝑢𝑖𝛿𝑢𝑖

𝑇


(4.6)

By successive application of Eqn. 4.5 and Eqn. 4.6, the correct secant stiffness can be

calculated from the stiffness K0 that was used at the start of increment and an update

vector for every iteration. For every intermediate iteration one additional update vector

is to be stored with size number of degrees of freedom. The lighter the iteration number,

the more additional storage is needed and the more additional vector calculations are to

be performed (TNO, 2012).


119

4.3.3. Crisfield

To avoid increasing storage and computation time requirements for the Broyden and

BFGS methods, Crisfield (Crisfield, 1991) suggested using only the most recent

correction vector. For a one dimensional situation this method still behaves as in Figure

4.5 above. All three Quasi-Newton methods can be used irrespectively of the stiffness

matrix K0 used for the first prediction. This could be a tangential stiffness matrix, as

used in Figure 4.5, or the linear elastic stiffness matrix. These methods usually have a

convergence rate between that of the Regular Newton-Raphson and the Modified

Newton-Raphson. For the Broyden and the BFGS schemes the memory and the time

consumption will increase with the number of iterations.

4.4. TIME HISTORY ANALYSIS OF TLCW MODEL

The Secant Crisfield method was used during the time history analysis to prevent

excessive time and memory consumption, as emphasized above. The two other methods

were tested in preliminary analysis and results were the same, as expected. The

nonlinear time history analysis was implemented for Two-Leaf Cavity Wall (TLCW)

and Unreinforced Brick Wall (URM) models and results were compared with

experimental results. Internal energy tolerance of 10-3

was used as convergence

criterion.

The time history analysis was performed in four steps. After analysis of TLCW model,

displacements and crack patterns were compared with experimental results. Major

cracks of the specimen on the shake table can be seen in Figure 3.27 at Stage 3. Crack

propagation of numeric model belongs to TLCW model can be seen in Figure 4.6 for

Stage 1, in Figure 4.7 for Stage 2 and Figure 4.8 for Stage 3.


120

a)South

b)North

c)East

d)West

Figure 4. 4 Crack Propagation of TLCW Model at the End of Stage 1


121

a)South

b)North

c)East

d)West


As seen from Figure 4.7, cracks are given from maximum principle strain. The

maximum value of these strains for Stage 1 and Stage 2 is about 10-2

. However, the

structure was heavily damaged end of Stage 3, and the maximum principle strains

reached up to 10-1

as seen in Figure 4.8 below. To plot the maximum strain values, the

envelope of the complete analysis (along the full time history) was considered.


122

a)South

b)North

c)East

d)West


The structure which was exposed to load in the laboratory collapsed at the beginning of

Stage 4. The numeric model of this structure finished time history analysis at Stage 4

successfully. However, at the end of this analysis, the numeric model was heavily

damaged, with too large displacements, meaning that collapse was indeed obtained.

There is also a good match between experimental and numerical displacements. Four

points were considered during the analysis to compare numerical and experimental

analysis. These four nodes and node numbers can be seen in Figure 4.9 below.


123

Figure 4. 7 Control Points during the Time History Analysis to Compare Results

Hamamatsu devices located to these points in real model to measure displacement

during the experiments. This instrumentation can be seen in Figure 4.10.

Figure 4. 8 Instrumentation of Accelerometer to Measure Two Way Acceleration

Measured acceleration from these control points were integrated into displacements, and

then compared with experiments. Brief comparison of displacements can be seen in

Table 4.2 below.


124

Table 4. 2 Displacement Comparison of Experimental Structure and Finite Element

Model at 100% Earthquake Load: Node Number 95 for 1st story, 255 for 2

nd story

Experimental

(Transversal)

Numeric

(Transversal)

Match

(%)

Experimental

(Longitudinal)

Numeric

(Longitudinal)

Match

(%)

Stage1

Positive

2nd

Floor 0.90 0.75 83.0 0.99 0.90 91.0

1st

Floor 0.50 0.45 90.0 0.70 0.55 79.0

Stage1

Negative

2nd

Floor -0.80 -0.68 85.0 -0.80 -0.82 97.5

1st

Floor -0.58 -0.40 69.0 -0.69 -0.50 73.0

Stage2

Positive

2nd

Floor 1.90 1.50 79.0 1.50 1.40 93.0

1st

Floor 0.90 0.75 83.0 1.00 0.80 80.0

Stage2

Negative

2nd

Floor -1.65 -1.35 82.0 -1.35 -1.20 89.0

1st

Floor -1.05 -0.85 81.0 -1.20 -0.92 77.0

Stage3

Positive

2nd

Floor 5.63 5.25 93.0 7.41 7.42 99.0

1st

Floor 2.90 3.40 83.0 5.66 5.22 92.0

Stage3

Negative

2nd

Floor -5.41 -5.50 98.0 -6.21 -6.67 93.0

1st

Floor -3.63 -3.92 92.0 -4.52 -4.48 99.2

As seen from Table 4.2, displacements showed a good match between experimental

results and finite element calculation. 100 % earthquake analysis was the critical

analysis. Because, the structure was damaged not collapsed. The comparison between

numerical and experimental displacement are shown in Figure 4.11 and Figure 4.12.


125

Figure 4. 9 Comparison of Displacements along Transversal Direction: Node Number

95 (100% Earthquake Load)


126

Figure 4. 10 Comparison of Displacements along Longitudinal Direction: Node Number

32 (100% Earthquake Load)

Then, analysis of Stage 4 was performed on numeric model to see displacement and

crack pattern.


127

a)South

b)North

c)East

d)West

Figure 4. 11 Crack Propagation of TLCW Model at the Time of Collapse at Stage 4

Displacements are obtained from calculated signals and absolute maximum

displacements were considered. Finite element model reached an absolute maximum

13.89 mm displacement at node number 255 in longitudinal direction, which is about

the double when compared with stage 3. Moreover, finite element model reached 8.91

mm in transversal direction at the node 279. Displacement summary of stage 4 was

tabulated in Table 4.3.


128

Table 4. 3 Displacement Summary TLCW Model at Stage 4

Node Number Transversal (mm) Longitudinal (mm)

32 2.45 9.46

95 6.78 7.57

255 3.19 13.89

2479 8.91 10.56

Numerically, still a Stage 5 was performed on TLCW model to check the evolution of

the response. To generate input signal of Stage 5, Stage 4 was multiplied by 1.5 scales

and then a 225% earthquake load was generated. Crack patterns of whole model were

demonstrated in Figure 4.14.

a)Front b)Back

Figure 4. 12 Heavy Damages and Heavy Cracks of Model at Stage 5 (225% Earthquake

Load)

As seen in Figure 4.14 above, there are major and heavy cracks on the model.

Maximum principle strain was plotted 0.1-1

and 0.1-2

to see heavy crack of model.

Displacements of stage 5 were presented in Table 4.4 below, which are now even more

absurd.


129

Table 4. 4 Displacement summary TLCW model at Stage 5

Node Number Transversal (mm) Longitudinal (mm)

32 5.20 23.28

95 16.71 19.04

255 7.29 31.94

2479 21.29 23.99

As seen from the Table 4.4, stage 5 generated nearly 5 times bigger displacement than

stage 3 and 3 times bigger displacements than stage 4. After this analysis, new time

history analysis was performed on URM model to see especially displacement

differences, because crack propagations are nearly the same.

4.5. TIME HISTORY ANALYSIS OF URM MODEL

Nonlinear time history analysis was performed on URM model to check again the

performance level of the typical masonry infill solution in Turkey. Stage1, Stage2,

Stage3 and Stage 4 inputs were applied again to URM model respectively. The same

material properties were used during the analysis. Stage 1 crack propagations can be

seen in Figure 4.13 below, for the same strain level of TLCW model.


130

a)North b)South

c)East d)West

Figure 4. 13 Numeric Crack Propagation for URM Model at Stage 1

Afterwards, stage 2 load was applied to model and cracks were monitored at maximum

displacement step. Crack propagation of stage2 can be seen in Figure 4.16 below.


131

a)North b)South

c)East d)West


Cracks were monitored strain level between 0.1-3

and 0.1-2

for Stage 1 and 2. However,

there are bigger cracks at Stage 3 and 4 and for this reason the upper limit of strain level

was extended to 0.5-2

as seen in Figure 4.17 for Stage 3.


132

a)North b)South

c)East d)West


As seen from Figure 4.17, URM model was heavily damaged at the end of Stage 3.

Crack propagation is similar to experimental model. Experimental cracks can be seen in

Figure 4.26 at previous chapter. Relative displacements, drifts and base shear forces are

compared with experimental and TLCW model in the following section.

4.6. COMPARISON OF TIME HISTORY ANALYSIS RESULTS

After nonlinear time history analysis, TLCW model showed better performance than

URM model in terms of displacement, resisting loads. However, URM model was

heavily damaged after 100% load. This heavy damage is irreversible, so structure

cannot be repaired for further use. However, under 0.7g or 0.8g load TLCW model can

be use after repair or any other effective retrofit technique. TLCW model showed very

good match between experimental results as seen in Figure 4.19 for both directions.


133

a)Relative displacements in transversal

direction

b)Relative displacements in longitudinal

direction

Figure 4. 16 Relative Displacement Comparison of Two Models with Experimental

Results at Stage 3

URM model exhibited displacements higher than desired. This model was more prone

to collapse under severe earthquake loads than TLCW model as seen in Figure 5.18

above. Interstory drift ratios of these models are presented in Figure 4.19 in transversal

direction and Figure 4.20 in longitudinal direction. Numerical results are also compared

with experimental results in Figure 4.20 and Figure 4.21.

Figure 4. 17 Interstory Drift in Transversal Direction

0

2

4

-0.80 -0.60 -0.40 -0.20 0.00 0.20 0.40 0.60 0.80

STO

REY

LEV

EL (

m)

INTERSTOREY DRIFT (%)

EXPERIMENTAL

FE TLCW MODEL

FE URM MODEL

IO

LS

CP


134

As seen in Figure 4.19, the first story drift of experimental results showed very good

correlation with TLCW model. However, second story drift is a little bit conservative

for both numeric models due to perfect boundary condition. As mentioned in chapter 3,

experimental results are highly affected by incomplete boundary condition along

transversal direction. This boundary condition problem can be seen easily from second

story drift. The drifts of TLCW model and experimental results were located between

IO and LS. Although second story drift of experimental is located in the middle of IO

and LS, the drift of TLCW model is located very close to IO level. The first story drift

of URM model is very close to CP due to high displacement under severe earthquake

load. URM model resisted design load, but this does not mean that this model can save

lives. TLCW model showed better performance for design loads in transversal direction.

Performance of models and experimental results can be seen in longitudinal direction in

Figure 5.20.

Figure 4. 18 Interstory Drift in Longitudinal Direction

Performance of the numerical model and experimental results showed nearly the same

performance in longitudinal direction. However, performance of experimental results

and TLCW model are more close to LS level. Although, the first story drift of

experimental results are located in the middle of the IO and LS level, numerical models

0

2

4

-0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8

STO

REY

LEV

EL (

m)

INTERSTOREY DRIFT (%)

EXPERIMENTAL

FE TLCW MODEL

FE URM MODEL

IO

CP


135

are more conservative for this story due to rectangular geometry. In longitudinal

direction, FE models still can be able to dissipate more energy than longitudinal

direction compared with transversal direction. As seen from drift figures, TLCW model

showed better performance than URM model.

Other important comparison parameter is the base shear for two numeric models. Base

shear roof displacement comparison can be seen in Figure 4.21 below.

Figure 4. 19 Base Shear – Roof Displacement (mm)

As seen from Figure 4.21, TLCW model resisted more load at Stage 4 like 338 KN in

transversal direction and 361 kN in longitudinal direction. Moreover, URM model

carried 300 kN in transversal direction and 310 kN in longitudinal direction. Under

lower earthquake loads like Step 1 and Step 2, both of the models showed the same

performance in terms of stiffness as seen in Figure 4.22. Then, URM model could not

resist further to strong ground motion. Cracks were increased suddenly and this

situation is a threat for life safety. On the contrary, TLCW model resisted strong ground

motion along the duration of design earthquake successfully. There is 11% difference in

transversal direction and 14% in longitudinal direction between the two models in terms

of base shear force. TLCW model displaced 9.0 mm in transversal direction and 9.1 mm

0

50

100

150

200

250

300

350

400

0 5 10 15 20

Bas

e Sh

ear

Forc

e (K

N)

Roof Displacement (mm)

TLCW Transversal

TLCW Longitudinal

URM Transversal

URM Longitudinal

EXP TLCW Trans

EXP TLCW Long


136

in longitudinal direction at Stage 4. In addition, URM model displaced 16.3 mm in

transversal direction and 18.0 mm in longitudinal direction at Stage 4.

4.7. CONCLUSION

In this chapter, nonlinear time history analysis was performed on two FE numeric

models. The Quasi Newton method was used for the global solution procedure. This

method is called as Secant Crisfield. The purpose of selecting this method is to obtain

results faster than other secant methods and, during the analysis, the selected method

produced rather less output than Broyden or BFGS.

The earthquake load was applied in four steps. These loads produced according to

Eurocode-8. While producing input signals, seismicity of Lisbon was considered and

Type 1 soil was selected. The results of numerical models were compared each other

and compared with experimental results in terms of relative displacement and drift.

According to the results, TLCW model showed perfect correlation with experimental

results in terms of displacement especially at stage 3. Stage 3 was the critical analysis

because it was the design spectrum for this structure. Displacement matches between

numerical and experimental results are on average 84% for Stage 1, 83% for Stage 2

and 94% for Stage 3, respectively. These percentages are the average values for both

positive and negative sides along transversal and longitudinal directions.

The performance of the experimental structure was between IO and LS levels at the end

of Stage 3 for both first and second story. However, there is a difference between first

and second story drift levels for both FE numerical models. Performance of the model is

mostly affected by first story performance and drift. First story drift is located between

IO and LS levels for TLCW model. Whereas, first story drift level is located between

LS and CP. TLCW model shows more conservative behavior than URM model. URM

model cannot prevent life safety under severe earthquake. TLCW model resisted 11%

more load than URM model in terms of base shear in transversal direction and TLCW

model resisted 14% more load than URM model in longitudinal direction under

dynamic analysis. As a conclusion, TLCW model seems a better application for

earthquake prone countries to resist more loads without life or economic loss, at least in

case of events stronger than the ones predicted by the code. In addition, it is also clear

that masonry infills have a strong influence on performance levels and their effect can


137

be beneficial for the assessment of existing RC structures inadequately designed or

designed according to old codes.

4.8. REFERENCES

Ile, N., Nguyen, X-H., Kotronis, P., Mazars, J., Reynouard, J. M., Shaking Table Tests

of Lightly RC Walls: Numerical Simulations, Journal of Earthquake

Engineering, 12:6, 849-878, 2008

Toranzo, L. A., Restrepo, J. I., Mander, J. B., Carr, A. J., Shake Table Test of Confined-

Masonry Rocking Walls with Supplementary Hysteric Damping, Journal of

Earthquake Engineering, 13:882-898, 2009

Stavridis, A., Koutromanos, I., Shing, P. B., Shake Table Test of a Three-Story

Reinforced Concrete Frame With Masonry Infill Walls, Earthquake

Engineering and Structural Dynamics, 41:1089-1108, 2012

Crisfield, M. A., Non-linear Finite Element Analysis of Solids and Structures, Vol:1:

Essentials, John Wiley & Sons., 1991

Leite J., Design of Masonry Walls for Building Enclosures Subjected to Extreme

Actions, PhD Thesis, Minho University, Guimaraes, Portugal, 2014

Lourenço, P. B., Computational Strategies for Masonry Structures, PhD Thesis. Delft,

Netherlands, 1996

American Society of Civil Engineers, Seismic Rehabilitation of Existing Building:

ASCE SEI 41/06, USA, 2007

Leite, J., Innovative Solutions for Weak Infill Walls‖ Technical Report, Minho

University, Guimaraes, Portugal, 2012


138

Chapter 5 5 PART B: SHAKE TABLE TEST SETUP

The best way to understand the performance, failure mechanism and behavior of a

structure subjected to earthquake loading is to carry out shake table experiments. In this

chapter the shake table test setup, prototype definitions and properties of shake table

considered in this thesis will be presented. Furthermore, infill types of reinforced

concrete structure will be defined, instrumentation will be detailed and input signal will

be presented.

5.1. INTRODUCTION

Earthquake engineering field resorts to shake table experiment to obtain more realistic

global behavior of structures and typical results for structures. This type of experiments

is important for calibration of numerical model and for further investigations. But there

are many types of experimental methods to evaluate structural performance. These

methods can be listed below;

Static monotonic test

Quasi static cyclic test

Chapter 5 – Part B: Shake Table Test Setup

139

Pseudo-dynamic test

Shake table test

The basic idea of static monotonic test is to apply an incremental load in a given

direction. Then the structural response is measured in terms of strains and displacement.

These types of tests can be controlled by displacement. However, the static monotonic

test method is less adequate to predict seismic behavior of test specimen (Vasconselos,

2005; Binda et al., 2006)

A second test method is the static cyclic test. This type of test has also a simple test

setup. Furthermore, these tests are applicable for both reduced scale specimens and full

scale specimens. The specimen is exposed to slow rate of force or load during this test.

Cyclic test is applied to structure in both test direction positive and negative. The

purpose of this test is to create realistic conditions during real ground motions. The

negative aspects of this type of experiments are that the input excitation and dynamic

response of the structure cannot be considered. Still, static cyclic tests have been used

by many authors, such as Oliveira in 2003 and Griffith in 2007 (Oliviera, 2003; Griffith

et al., 2001)

A third test type is the pseudo-dynamic test. This type of test is carried out using

displacement control and at the same time an analytic method is adopted to determine

dynamic response of the structure. Inertia forces and viscous damping can be calculated,

and introduced to the test. This type of tests is much more complicated than static

monotonic and static cyclic tests. Pinto et al. (Pinto et al., 2002) and Paquette and

Bruneau (Paquette, 2006) used this type of test.

The last type is the shaking table test. This type of experiments is the most realistic

method to estimate the real behavior of a reduced scale or full structure. Many sizes and

many types of shake table test machines are available. Six degrees of freedom is the

most powerful simulation, even if usually difficult to control and to define the input. In

this case, three degrees of freedom are for rotation and three degrees of freedom are

used for translation along three directions. These experiments are time consuming and

need very high budget. These are the negative aspect of these experiments. Shake table

experiment is frequently used by many researchers for large and (almost) full scale

structures. In many case, full scale tests are impossible due to the maximum payload of

the equipment. Moaveni et al. (Moaveni et al., 2010) and Lindt et al. (Lindt et al., 2011)

used this test for large structures.


140

This chapter presents shake table experiments carried out in the National Civil

Engineering Laboratory (LNEC) in Lisbon, Portugal. Three tests were performed in this

laboratory along this PhD thesis. All the specimens are full size one bay one story

reinforced concrete structure with an infill wall. The first test contains unreinforced

masonry infill and was unsuccessful, as the test set-up was newly developed. For this

reason this test was repeated using are constructed specimen. This was the second test,

and it was successful. The third test consisted of the same reinforced concrete structure

with an infill with bed joint reinforcement. The purpose of these tests is to understand

and determine the out-of-plane behavior of infill walls, when subjected to combined in-

plane and out-of-plane loading.

5.2. PROTOTYPE DEFINITION

The motivation of the present experiments is the expulsion of infill walls at upper

storeys due to combined in-plane and out-of-plane movement during the earthquake.

This movement is difficult to prevent and is one of the most important reasons for life

and economic loss during the earthquake. Constructing the complete structure in the

laboratory is expensive and a time consuming experiment method, required to adopt

severe scaling factors, which pose question on the representativeness of the structure.

For this reason to simulate the out-of-plane behavior of infill wall at upper storeys TIM

(Test for Infill Walls) setup was developed, compatible with the shake table. Figure 5.1

shows the basic idea of the prototype.


141

Figure 5. 1 Simulated multistory structure and considered part of imaginary structure for

TIM Test

The complete structure was defined as an 8 storey building. This imaginary building is

composed of three bays for one lateral direction and four bays for another lateral

direction. The dimensions of the complete structure are defined as 18 m along three

bays and 24 m along the full height. One bay and one story of this complete structure

was produced and the complete view of this test setup on the shake table can be seen in

Figure 5.2.


142

Figure 5. 2 Test specimen and surrounded steel apparatus

The LNEC shake table has three degrees of freedom and the maximum weight of the

test specimen is 40 tons. The rest of the properties of the shake table can be seen in

Table 5.1.The full shake table test machine can be seen in Figure 5.3 below.

Table 5. 1 Properties of shaking table test machine at LNEC

Frequency Range Hz 0.1 - 40.0

Stroke Horizontal mmpp 290/440

Vertical mmpp 290/440

Maximum Velocity (Nominal/Limit) Horizontal

Transversal cm/s 70.1/121.5

Longitudinal cm/s 41.9/72.6

Vertical cm/s 42.4/73.5

Maximum acceleration Horizontal

Transversal m/s2

18.75

Longitudinal m/s2

18.75

Vertical m/s2

31.25

Maximum Weight for Test Specimen Ton 40.0


143

Figure 5. 3 Shake table test setup at LNEC

5.3. INFILL WALL FOR URM

Three specimens were exposed to the shake table experiment. There were two types of

infill wall considered: One of them is Unreinforced Masonry and the other of them is

Bed Joint Reinforcement. Details of the URM infill are shown in Figure 5.4

Figure 5. 4 Used brick masonry for all tests

Dimensions of test specimen are 6.4 m length 3.25 m height. Also beam dimensions for

upper and lower part of the specimen is 30 cm as width and 40 cm as height. Brick

dimensions are 30x20x22 cm3, being the thickness 22 cm. The complete view of the

specimen can be seen in Figure 5.5.


144

Figure 5. 5 General overview of URM specimen

Also there are two pre-stressed reinforcement bars located in the beams and columns.

The purposes of the reinforcement bars are to simulate dead load of upper storeys. Pre-

stress force ratio of these bars for beams and columns are loaded with 180 KN/per bar

and 360 kN/per bar respectively. Before producing the reinforced concrete frame,

wooden formwork were produced and placed on the floor. Then reinforcements were

placed into the mold and cast, and then pre-stress was applied to two reinforcements for

beams and two reinforcements for columns. Production of frame is demonstrated in

Figure 5.6.

Figure 5. 6 Production of reinforced concrete frames


145

Additional apparatus were mounted on the frame with pin and steel connections.

Reinforced concrete frame can be seen in Figure 5.7 after production.

Figure 5. 7 Reinforced concrete frame before constructing infill wall

Then infill wall was constructed into the reinforced concrete frame. After this, plaster

was applied on the surface of infill wall. Final view of the specimen and dimensions can


Figure 5. 8 Reinforced concrete frame with infill wall

5.4. TEST SETUP AND RELATED APPARATUS DEFINITION

First of all before test, adaptive steel supports were placed on the shake table to fix the

specimens on the shake table. The other purpose of these adaptive steel supports is to

create pin support boundary conditions for specimen. These apparatus can be seen in

Figure 5.9.


146

Figure 5. 9 Steel connections to support specimen

During the earthquake, the supports move along transversal and longitudinal directions.

These supports allow the specimen to move on the shake table during the test like the

simulated structure. Another important component on the test set-up with specimen are

the steel frames. These frames do not allow the specimen to rotate during the

experiment. Moreover, these two steel frames keep the position of the specimen vertical

while moving along transversal direction. These steel frames can be seen in Figure 5.10.


147

Figure 5. 10 Steel frames around the specimen

There are also four roller located upper part of the specimen. These rollers are the

boundary condition between steel apparatus and specimen. These rollers allow the

specimen to move free along longitudinal direction but steel frame and specimen move

together along longitudinal direction. Details of these rollers can be seen in Figure 5.11.


148

Figure 5. 11 Roller boundary condition for specimen

One side of the specimen is free as shown in Figure 5.11; another side of specimen is

fixed to south reaction wall. South reaction wall can be seen in Figure 5.3. The main

goal of this strut is to allow specimen damaged during the experiment along in-plane

direction. Strut mechanism is another boundary condition for tested specimen. Strut

connection can be seen in Figure 5.12.


149

Figure 5. 12 Strut between specimen and south reaction wall

This strut mechanism directly measured the force in kN during the experiment along-in-

plane direction and keeps the walls fixed. After fixing the mentioned apparatus to the

specimen, another important apparatus is placed on the table between two pillars of steel

frame. This is a supplementary material to prevent the specimen from buckling. This

supplementary material can be seen in Figure 5.13.

Figure 5. 13 Supplementary apparatus

5.5. INSTRUMENTATION

After locating all apparatus and specimen on the shake table, many instruments were

attached on the wall and steel frames. These instruments are listed below;

Accelerometers

Hamamatsu displacement measuring device

Krypton displacement measuring device


150

LVDT displacement measuring device

5.5.1. Accelerometer

Accelerometers are attached on the specimen to measure directly acceleration. These

devices measure also displacement and velocity indirectly, after integration. A typical

accelerometer is shown in Figure 5.14.

Figure 5. 14 Accelerometers

44 accelerometers were attached on the specimen and enclosure apparatus.12

accelerometers directly measured the out-of-plane behavior of infill wall. 12

accelerometers measured the behavior of reinforced concrete frame, with 10

accelerometers measuring the out-of-plane behavior and 2 of them measuring the in-

plane behavior. Instrumentation of accelerometers can be seen in Figure 5.15. The rest

of the accelerometers were placed on shake table.


151

Figure 5. 15 Accelerometer instrumentation on infill wall

5.5.2. Hamamatsu Displacement Measuring Device

Hamamatsu devices are composed of two parts. One of them is the camera and the other

part is the laser reader. Hamamatsu devices measured displacements from 8 points and

they can be seen in Figure 5.16.

a) b)

Figure 5. 16 a) Hamamatsu Camera, b) Laser Reader

Hamamatsu directly measures displacements. These displacements were measured from

the corner of upper and lower beam column connection.


152

5.5.3. Krypton Displacement Measuring Device

Krypton also directly measures the displacement. This device is composed of two parts.

One of them is attached to specimen as targets / leds to collect information. 16

measuring points can be placed and the information transferred to the CPU. Krypton

measuring device can be seen in Figure 5.17.

Figure 5. 17 Main unit of Krypton

There are three lasers as seen in Figure 5.17. The combination of the three

measurements allow to obtain x, y and z coordinates. Switch unit and collector cables

can be seen in Figure 5.18.


153

Figure 5. 18 Switch and collector cables of Krypton

5.5.4. LVDT Displacement Measuring Device

LVDT’s are located on the specimen to measure relative displacements. This device can


Figure 5. 19 LVDT

4 LVDT’s were used in the experiment. Two of them are used near the actuator to

control the displacement of shake table and two of them are used to measure out-of-

plane displacement of infill wall.


154

5.6. REFERENCES

Vasconselos, G. Experimental Investigations on the Mechanics of Stone Masonry:

Characterization of Granites and Behavior of Ancient Masonry Shear Walls,

PhD Thesis, University of Minho, Portugal, 2005

Binda, L., Pina-Henriques, J., Anzani, A and Lourenço, P., A Contribution for the

Understanding of Load-Transfer Mechanisms in MultiLeaf Masonry Walls:

Testing and Modelling, Engineering Structures, 28(8), 1132-1148, 2006

Oliviera, D., Experimental and Numerical Analysis of block Masonry Structures under

Cyclic Loading, PhD Thesis, Minho University, Portugal, 2003

Pinto, A., Pegon, P., Magonette, G., Molina, J., Buchet, P., and Tsionis, G.,

Pseudodynamic Tests on Large-Scale Model of an Existing RC Bridge Using

Non—linear Sub structuring and Asynchronous Motion, Institute for the

Protection and Security of the Citizen European Laboratory for Structural

Assessment (ELSA), 2002

Paquette, J., Bruneu, M., Pseudo-dynamic Testing of Unreinforced Masonry Building

with Flexible Diaphragm and Comparison with Existing Procedures,

Construction and Building Materials, 20(4), 220-228, 2006

Moaveni, B., He, X., Conte, J., Restrepo, J., Damage Identification Study of a Seven-

Story Full Scale Building Slice Tested on the UCSD-NEES Shake Table,

Structural Safety, 32(5), 397-409, 2010

Lindt, J., Pryor, S., Pei, S., Shake Table Testing of a Full Scale SevenStory Steel-Wood

Apartment Building, Engineering Structures, 33(3), 757- 766, 2011

Chapter 6: Part B-Model 0:Unreinforced Brick Wall (Failed Test)

155

Chapter 6

MODEL 0: UNREINFORCED BRICK WALL (FAILED TEST)

In this chapter, Model-0 is described and results are presented. These experiments

started with Model-0, as the first experiment. This experiment is carried out with

reinforced concrete frame with unreinforced brick infill wall (URM). The thickness of

this wall is 22 cm. The test failed due to 2 mm gap at strut, which provided incorrect in-

plane motion. Infill wall was damaged but force displacement curve remained elastic

along longitudinal direction. First of all, dynamic identification was performed on the

structure to determine the mode frequencies and mode shapes. Then, earthquake load

was applied as incremental input.

6.1. INPUT SIGNALS AND CHARACTERIZATION OF MODEL-0

There are usually two artificial accelerogram to produce earthquake records on the base

of stochastic methods (near field and far field). These records are also adequate for

Portugal. Experiments were carried on LNEC laboratory and all earthquake parameters

were selected for seismicity of Portugal (Mendes, 2013). Response spectrum

accelerograms are compatible with Type-1 design spectrum defined in Eurocode-8 (EN

1998-1, 2004). Additional parameters are needed to create signals and one of these


156

parameters is the soil type. Soil type was selected as Type A that is Rock. Ranges of

frequencies were determined with 0.35-40 Hz. Frequencies determined on the base of

properties of shake table. Furthermore, to determine the response spectrum for test,

other parameters were calculated like return period and amplification multiplier. These

parameters are presented in Table 6.1.

Table 6. 1 Parameters to determine response spectrum for shake table tests

Probability in 50 Years Return Period Scale Factor (%)

90 22 10

50 72 34

20 224 63

10 475 100

5 975 159

2 2475 292

1 4975 464

As seen from Table 6.1, multiplier of 100 % earthquake load was considered as 1. The

return period of this earthquake load is 475 years. The probability of exceedance of this

earthquake is 10 % in 50 years. After determining these earthquake parameters,

dynamic identification was performed on the structure. To determine mode shapes and

frequencies, 1.25 mm displacement was applied to shake table to give an impulse. This

displacement was applied to both directions. Longitudinal and transversal impulse can

be seen in Figure 6.1 and Figure 6.2 respectively.


157

Figure 6. 1 Longitudinal impulses for dynamic identification

Figure 6. 2 Transversal impulses for dynamic identification


158

6.2. MODE SHAPES AND MODE FREQUENCIES

6.2.1. Longitudinal Frequencies and Mode Shapes

Mode frequencies are measured by accelerometers along longitudinal directions. These

values were processed in LNEC-SPA signal processing program and then shown below.

Mode shapes are presented in Figure 6.4.

Table 6. 2 Mode frequencies for longitudinal directions

Mode Number Frequencies (Hz) Period (S)

Mode 1 8.7 0.115

Mode 2 16.3 0.062

Mode 3 16.7 0.06

Mode 4 21.6 0.046

Mode 5 25.9 0.039

Figure 6. 3 Signals of characterization


159

Figure 6. 4 First 2 Modes of longitudinal direction

6.2.2. Transversal Frequencies and Mode Shapes

Mode frequencies were tabulated in Table 6.3 along transversal directions. Furthermore,

mode shapes are presented in Figure 6.5.

Table 6. 3 Mode frequencies for transversal direction

Mode Number Frequencies (Hz) Period (S)

Mode 1 9.1 0.110

Mode 2 10.3 0.097

Mode 3 11.4 0.088

Mode 4 17.3 0.058

Mode 5 20.1 0.050

Mode 6 29.5 0.034


160

Figure 6. 5 First 2 modes of transversal direction

6.3. ANALYSES AND RESULTS

Earthquake load was applied in five steps. Applied loads are the same with target loads

and these load ratios can be seen in Table 6.4. After applying these loads to specimen,

force displacement curve was plotted in two directions in Figure 6.6. As seen, the force

– drift curve remained elastic along in-plane direction. Furthermore, post peak part of

force – drift (%) curve along out-of-plane direction is not clear. However, it seems

slightly plastic. At the end of the test, dynamic identification was performed on the

specimen to see differences of mode frequencies. This change can be seen in Figure 6.7.

Table 6. 4 Target and applied load percent in both directions

Step Number Load Percent (%)

Step 1 10

Step 2 34

Step 3 63

Step 4 100

Step 5 292


161

a)In-plane force-drift curve b) Out-of-plane force drift curve

Figure 6. 6 Force – Drift (%) curve in both direction

Figure 6. 7 Mode frequencies belong to first experiments (Model 0)

In Figure 6.7, there are four identifications. These identifications represent the situation

before test and after tests. For instance, CAT01 was before tests, CAT02 was performed

after 63% EQ, CAT03 was performed after 100% EQ and CAT04 was performed after

end of the whole test. After shake table test, measured displacements were presented

with 3D graphs. Displacements are obtained by accelerometers. This calculation was

done by double integration as seen in Eqn. 6.1, 6.2 and 6.3


162

Peak Ground Acceleration PGA=𝑚𝑎𝑥 𝑢 𝑔(𝑡) (6.1)

Peak Ground Velocity PGV= 𝑚𝑎𝑥 𝑢 𝑔(𝑡) (6.2)

Peak Ground Displacement PGA= 𝑚𝑎𝑥 𝑢𝑔(𝑡) (6.3)

In which𝑢 𝑔(𝑡), 𝑢 𝑔(𝑡) and 𝑢𝑔(𝑡) are the time history series of accelerations, velocities

and displacements respectively.

Instrumentation of accelerometers is given in Figure 6.8. After double integration of

acceleration, displacements were obtained. Then 3D graphs were plotted in Figure 6.9.

Figure 6. 8 Instrumentation of Accelerometers to Measure Out-of-Plane Accelerations

a) 1. step 10 % Earthquake Load

b) 2. step 34 % Earthquake Load


163

c) 3. step 63 % Earthquake Load

Figure 6. 93D Out-of-Plane Graphs a) 1st step earthquake load, b) 2

nd step earthquake

load, c) 3rd

step earthquake load

As seen from the figure only three steps were recorded to simulate out-of-plane

behavior of infill wall. After 3rd

step, all instruments were removed from the wall

surface to prevent possible damage during total collapse of further excitations. In

addition to accelerometers, Krypton device also measured directly the displacements of

infill wall along out-of-plane direction. Instrumentation of Krypton device can be seen

in Figure 7.10. Krypton measured only the displacement of mid part of the wall, about

1.5 m width. Moreover, this part is located between the two steel piers.


164

Figure 6. 10 Instrumentation of Krypton on the infill wall

Krypton data were processed and plotted in 3D graphs. This graph can be seen in Figure

6.11 below. As seen from Figure 6.11, the displacement interval at first step is between

1.5 mm and 2.5 mm. Moreover, displacement interval for step 2 is around 5 mm. In

addition, at third step displacement of infill wall changes between 15 mm and 20 mm.

These ratios vary between 0.09 %, 0.22 %, 0.7 % and 0.9 % drift ratio respectively. A

few accelerometers failed measuring the data during the experiments due to high

shaking. To compare out-of-plane behavior of infill wall along a horizontal line in terms

of accelerometer instrumentation, Figure 7.13 was plotted. However, along a vertical

line only HA3 measured correct accelerations therefore correct displacements. Figure

6.12 presents the accelerometers that measured correct acceleration.


165

Figure 6. 11 Displacement of infill wall measured by Krypton

Figure 6. 12 Location of correct measurement at last stage (Model 0)


166

Figure 6. 13 PGA v.s. Displacement along HA3 (Model 0)

Acceleration amplification is also another important point of view in this experiment.

For this reason to compare well acceleration amplification was presented in Figure 6.14

along the horizontal line HA3.


167

Figure 6. 14 Acceleration amplification of HA3 line (Model 0)

Krypton device measured directly the displacement of infill wall at mid-part. This graph

can be seen in Figure 6.16. This graph gives chance to compare displacement

amplification. Firstly, instrumentation is presented in Figure 6.15 below.

Figure 6. 15 Instrumentation of Krypton and considered line numbers of Krypton

(Model 0)


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Figure 6. 16 Displacement amplification of infill wall versus PGA (Model 0)

After shake table experiment, specimen started to be damaged from 63 % earthquake

load to end. Damage maps and damage photos presented in Figure 6.17, Figure 6.18,

Figure 6.19 and Figure 6.20 respectively.


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a)Displacement of Step 3

b)Damage of Step 3

Figure 6. 17 Displacements and damage of specimen after Step 3 (Front Side)

Figure 6. 18 Damage of Step 3: 63 % earthquake load (Back Side)


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Figure 6. 19 Damage of specimen after 100 % earthquake load

a) Propagation of Out-of-Plane Behavior

b) Out-of-Plane Plastic Deformation

Figure 6. 20 Step 5: Deformation after 263 % earthquake load

Plastic deformation was 5 cm at the end of the experiment. This deformation

corresponds to 2.2% drift ratio according to FEMA 356 regulation. This deformation is

located between LS and CP. The results of this experiment proved that this test must be


171

repeated due to boundary condition problem. Following chapter contains successful

experiment results implemented with reinforced concrete structure with unreinforced

masonry infill wall (URM).


172

Chapter 7

MODEL 1: UNREINFORCED BRICK WALL (SUCCESSFUL

TEST)

7.1. INPUT SIGNALS AND ACCELERATIONS FOR TEST 1

In this chapter, the results of Model-1 were presented. Shake table experiment was

applied on Model-1, with successful results. The reason for this successful result is that

the strut mechanism was replaced by a new one and bolts were fastened tighter. This

experiment was carried on five steps. Application and target levels of these five steps

are tabulated in Table 7.1 below.

Table 7. 1 Target and Applied Earthquake Loads in Percentage (%)

Step

number

Target earthquake load in percent

(%)

Applied earthquake load in percent

(%)

Transversal Longitudinal Transversal Longitudinal

Step1 10 122 9 61

Step2 34 295 28 178

Step3 63 210 61 194

Step4 100 333 95 263

Step5 159 397 143 363

Step6 293 731 232 584

Chapter 7: Model 1-Unreinforced Brick Wall (Successful Test)

173

After inspecting Table 7.1, it is clear that earthquake load was applied low amplitude

along transversal direction and high amplitude along longitudinal direction. The purpose

of this application is to balance the effect of damage on the structure. Because, inertia of

the structure along longitudinal direction is rather high. In reverse, inertia of the

structure along transversal direction is low due to slenderness of the specimen.

Summary of test in terms of PGA can be seen in Figure 7.1. Moreover, Force and Drift

are presented in Table 7.2.

Figure 7. 1 PGA versus Number of Stages for URM Wall (Test1)

As seen from Figure 7.1, PGA values at step 2 and step 3 are very close to each other,

so step 3 will not be considered for next graphs. Because force, displacement and drift

values are very close to each other, this step is considered only out-of-plane movement.


174

Table 7. 2 Force and Drift (mm) values of Model-1 during Shake Table

STEP NUMBER FORCE (KN) DRIFT (mm)

TRANS. LONG. TRANS. LONG.

Step 1 10.1 158.2 0.50 2.41

Step 2 53.4 405.3 3.51 10.84

Step 3 77.1 418.7 3.72 14.35

Step 4 114.4 358.8 5.15 23.30

Step 5 121.0 338.6 9.00 34.60

7.2. IN-PLANE CURVES

The in-plane Force-Displacement curve can be seen in Figure 7.2 in terms of %

drift.Model-1 which is composed of Unreinforced Brick Masonry Wall (URM) carried

out a maximum of 418.7 kN in terms of lateral in-plane load. Maximum drift is

34.6mm. This value corresponds to 1.31 % drift level. Height of specimen wall was

considered as 2650 mm because there were two Hamamatsu cameras on the reinforced

concrete frame and this is the distance between these two cameras. Location of these

cameras and measured level can be seen in Figure 7.3 below.

Figure 7. 2 In-plane Force – Drift curve (mm and %) Test 1


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Figure 7. 3 Distances between two Hamamatsu camera and location of Hamamatsu

cameras

7.3. OUT-OF-PLANE CURVES AND BEHAVIOR

Out-of-plane force was calculated with accelerometers which were located on the infill

wall and reinforced concrete frame. During the test, out-of-plane movement of infill

wall was different at each side. One of the sides which is near the strut is called as

South, other of the side which is far from the strut is called as North. These two parts

were considered separately due to strut mechanism. Strut kept the South side of the

specimen a little bit stiff. So that North side of the specimen moved more than

Southside. The Force–Displacement curve for out-of-plane behavior can be seen in

Figure 8.4 and Figure 7.5 respectively.


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Figure 7. 4 Out-of-Plane Forces – Drift curve at North side

Figure 7. 5 Out-of-Plane Force – Drift curve at South side

Drift ratio was obtained from Hamamatsu camera which is located on the reinforced

concrete frame as mentioned before. Figure 7.4 and Figure 7.5 were plotted on the basis

of these readings from reinforced concrete frame. However, to see directly out-of-plane

displacement of infill wall, the mid part of displacement was also considered. For this


177

purpose 2 symmetric accelerometers were considered to calculate average displacement.

These accelerometers are shown in Figure 7.6.

Figure 7. 6 Location of accelerometers that considered calculating average out-of-plane

displacement of infill wall in transversal direction

The drift can be seen in Figure 7.7. To calculate the drift for out-of-plane displacement

of infill wall, only infill wall height was considered. This height is 2.25 m. On behalf of

this knowledge, force – drift (%) of infill wall can be seen in Figure 7.7. Note that there

are only three values in Figure 7.7. The reason for this is the removal of instruments at

the last two steps to prevent possible instrument damage at total collapse phase.

Summary of out-of-plane displacement of infill wall in terms of mid-displacement,

force and earthquake load percent can be seen detailed in Table 7.3.


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Figure 7. 7 Out-of-Plane mid-displacement of infill wall according to mid-

accelerometers

Table 7. 3 Summary of out-of-plane behavior of infill wall

Step

Number

EQ

Percent

Force

(KN)

Mid-Displacement of

Infill Wall Drift (%)

1 10 10.1 1.19 0.053

2 28 53.4 4.00 0.178

3 61 54.0 8.53 0.379

4 95 77.1 13.00 0.578

5 143 114.4 INSTRUMENTS

REMOVED

INSTRUMENTS

REMOVED

6 232 121.0 INSTRUMENTS

REMOVED

INSTRUMENTS

REMOVED

Out-of-plane movement was evaluated in four steps but these steps are not the ones in

Table 7.3. Out-of-plane movement was considered as 10%, 28%, 61% and 95%

respectively. Moreover, cracks and damage occurred due to different movement of wall,

as seen from Figure 7.9 to Figure 7.12. To define the out-of-plane displacement of infill


179

wall and reinforced concrete structure, some basic calculations were done according to

instrumentations in Figure 7.8.

Figure 7. 8 Instrumentation for out-of-plane evaluation (For Displacement)

Figure 7.8 presents acceleration instrumentation to calculate out-of-plane displacement

of infill wall and reinforced concrete specimen. Displacements of mid-part on the wall

were calculated. During these calculations, four lines were considered for displacement

and only absolute maximum values were considered. The first stage of the displacement

can be seen in Figure 7.9.

Figure 7. 9 Out-of-plane movements of infill wall and RCF at 10% eq. load Test 1


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In Figure 7.9, average displacement of the tested specimen is around 1.2 mm for both

infill wall and reinforced concrete frame at 10% earthquake load.


At 28% earthquake load, top-part of the infill wall was displaced more than 10 mm.

This displacement is occurred very close to free end of the infill wall. However, average

infill wall displacement is between 5-6 mm.


In Figure 7.11, out-of-plane movement of infill wall displaced more than 10 mm even if

total test specimen is displaced average 8 mm. The displacement difference of tested

specimen and maximum out-of-plane displacement is around 2.5 mm.


181


Maximum out-of-plane displacement of infill wall along Line2 is around 17 mm, this

line displaced more than average. The reason for this is the location of Line2. Line2 is

located between steel pier and strut. After that average of these four steps were

calculated and plotted to discuss the behavior of the mid-part of the specimen for out-of-

plane displacements. This graph can be seen in Figure 7.13 below.

Figure 7. 13 Average out-of-plane displacements for all stages at Test 1

Finally, the relative out-of-plane displacements were evaluated to see the displacement

differences between mid-part of infill wall and edge line of infill wall. Instrumentation

to evaluate relative displacement can be seen in Figure 7.14.


182

Figure 7. 14 Instrumentation to evaluate relative displacement for out-of-plane

movement of infill wall and reinforced concrete structure

Evaluation was done like this; to calculate relative displacement of HA2 for left line,

displacement of accelerometer 7 was subtracted by displacement of accelerometer 8. In

the same manner, to calculate HA0 for left line, displacement of accelerometer 3 was

subtracted by displacement of accelerometer 4. Then, figures were plotted below in

Figure 7.15, Figure 7.16, Figure 7.17 and Figure 7.18 respectively.

Figure 7. 15 Relative displacements of infill wall and RCF at 10% eq. Load Test 1


183

In Figure 7.15, relative displacement of infill wall is maximum at mid-part of the infill

wall, this maximum displacement is the main reason for lateral cracks but 10% eq. load

is very low amplitude for cracks.

Figure 7. 16 Relative displacements of infill wall and RCF at 28% eq. load Test 1

Figure 7.16 is the one of the best representative graph for mid part crack of specimen

due to high out-of-plane relative displacement around 9 mm.



184

Figure 7.17 shows the maximum relative out-of-plane relative displacement of infill

wall around 8 mm. This out-of-plane movement shows crack propagation and

detachment of infill wall from reinforced concrete frame.


Average out-of-plane displacements were tabulated also. Average values are evaluated

for both left and right lines. These graphs can be seen in Figure 7.18 and Figure 7.19

respectively.


185

Figure 7. 19 Average relative out-of-plane displacement of infill wall and reinforced

concrete frame for left line all stages Test 1

Figure 7.19 presents the out-of-plane movement and vulnerable part of the infill wall.

Figure 7. 20 Average relative out-of-plane displacement of infill wall and reinforced

concrete frame for right line all stages Test 1

Acceleration amplification is also an important aspect of the behavior of infill wall.

These graphs can be seen in the figures below.


186

Figure 7. 21 Out-of-plane acceleration amplification of infill wall and RCF at 10% eq.

load Test 1

Figure 7.21 shows acceleration amplification of infill wall. Line4 is the free end of the

specimen due to this reason acceleration of infill wall and rc frame is nearly the same.

But, Line1 shows detachment reason of infill wall, Line2 and Line 3 shows cracks

reason of infill wall.


load Test 1

Figure 7.22 shows the most vulnerable part of the infill wall especially Line2 and Line3.


187


load Test 1

Figure 7.23 proves that center part of the infill wall more prone to out-of-plane strike

and impact. This parts needs to be reinforced.


load Test 1

In Figure 7.24, due to high movement of RC frame, mid-part of the infill wall is stayed

behind the RC frame. This movement is also resulted in cracks. However, each vertical

slice of infill wall along vertical alignment shows different movement. This is the most

important reason of vertical cracks.


188

7.4. CRACK PATTERNS AND DAMAGE MAPS

As seen from the figures, cracks started to propagate from mid-part of the infill

specimen with horizontal cracks. Then, many new cracks occurred diagonally, from the

corner to the mid-part. These horizontal cracks can be seen in Figure 7.25 for west side

and in Figure 7.26 for east side.

Figure 7. 25 Crack propagation at 28% eq. load Test 1

In Figure 7.25 horizontal cracks can be seen. The reason for this lateral cracks are

relative displacement increase due to high shaking. This relative displacement increase

can be seen in Figure 7.16. Due to high displacement increase of upper part and low

displacement of lower part of infill wall, lateral cracks occurred along longitudinal

direction of infill wall.


189

Figure 7. 26 Crack propagation and damage map for 61% eq. load Test 1 West side

In Figure 7.26, right top part of the specimen detached and plaster was split out due to

maximum 8 mm out-of-plane displacement. During 61% earthquake load, detachment

of infill wall started. Due to high shaking of infill wall, lateral cracks propagated and

plasters toppled. However, infill wall is still resisting lateral forces.


190

Figure 7. 27 Crack propagation and damage map for 95% eq. load Test 1 West side

Figure 7. 28 Damage map for 292% eq. load Test 1 West side

Figure 7.28 shows the damage map of infill wall after 292% eq. load. After this

amplitude eq. local failures observed. These local failures composed of partially failure

of bricks and nearly complete failure of plaster and heavy lateral cracks of infill wall.


191

Figure 7. 29 Damage map for 217% eq. load Test 1 East side

Figure 7.29 shows East side of the specimen end of the test. Experimental test is

finished at this stage to prevent complete failure of infill wall in order not to damage

steel piers around infill wall. Total out-of-plane plastic deformation of infill wall is

around 7 cm.

7.5. MODAL FREQUENCIES AND DAMAGE INDICATOR

Then, a damage indicator was calculated on the basis of dynamic identification test.

Dynamic identification test results can be seen in Table 7.4 and Table 7.5.

Table 7. 4 Natural vibration periods of specimen 1 after each two test step in transversal

direction

Mod Number INITIAL After ST2 After ST4 END

1st Mode 9.0 8.2 8.0 3.1

2nd

Mode 12.4 12.0 11.6 8.5

3rd

Mode 16.3 16.1 15.6 12.5

4th

Mode 19.0 19.0 17.7 16.6

5th

Mode 27.0 26.1 25.7 24.0

Table 7. 5 Natural vibration periods of specimen 1 after each two test step in


Mod Number INITIAL After ST2 After ST4 END

1st Mode 8.4 8.2 7.4 7.2

2nd

Mode 10.2 10.0 10.0 9.5

3rd

Mode 15.6 14.6 14.2 13.4

4th

Mode 23.6 22.7 22.0 20.8

5th

Mode 31.5 30.2 30.0 27.0


192

After evaluating data in terms of acceleration, velocity and displacement for out-of-

plane movement, structural vulnerability was considered. This vulnerability is important

to evaluate damage between the each stage. There is a basic relation between damage

indicator and mass, stiffness and frequency of a single degree of freedom system.

Damage indicator can be formulated like below;

𝜔𝑖 ,𝑛2 =

𝐾𝑖 ,𝑛

𝑀𝑖 ,𝑛 (7.1)

(2𝜋𝑓𝑖 ,𝑛)2 =𝐾𝑖 ,𝑛

𝑀𝑖 ,𝑛 (7.2)

In Equation 7.1 and 7.2, 𝜔 is the natural frequency, 𝐾 is the stiffness of the single

degree of freedom element, 𝑀 is the mass of the single degree of freedom element and f

is the frequency of mode n in the dynamic identification test i. It is assumed that

damage is isotropic between first and nth dynamic identification.

𝐾𝑖 ,𝑛 = (1 − 𝑑2,𝑖 ,𝑛)𝐾𝑖,0 (7.3)

The d2 damage indicator of the model I in the dynamic identification n is equal to:

𝑑2,𝑖 ,𝑛 = 1 −𝑀𝑖 ,𝑛 𝑓𝑖 ,𝑛

2

𝑀𝑖 ,0𝑓𝑖 ,02 (7.4)

It was also assumed that during the test mode shapes do not change significantly, thus

damage indicator d2 can be formulated by;

𝑑2,𝑖 ,𝑛 = 1 − (𝑓𝑖 ,𝑛

𝑓𝑖 ,0)2 (7.5)

In formula 7.5 the damage indicator d2 is proportional to the quadratic ratio between the

frequency of the n and the first dynamic identification. To generalize this damage

assessment with a formulation for simplicity, damage indicator d is assumed to be

linearly proportional to the ratio between the frequencies n and the first frequency.

Equation 7.6 can be written,


193

𝑑𝑛 = 1 −𝑓𝑛

𝑓0 (7.6)

Equation 7.6 clearly presents damage indicator on the base of first identification before

test and without damage. First dynamic identification is the reference for other

identifications. In this terms 0 means no damage, 1 means total collapse. Results of

seismic vulnerability can be seen in Figure 7.30 below.

Figure 7. 30 Damage Indicator for Test 1; Infill Wall (URM)

As seen from Figure 7.30, when earthquake load is applied bidirectional to specimen,

URM model damaged heavily. Vulnerability index for transversal direction is 0.66.

Moreover, this index for longitudinal direction is 0.16.


194

Chapter 8

MODEL 2: BED JOINT REINFORCEMENT BRICK WALL

8.1. BRIEF DEFINITION OF INFILL WALL

In this chapter, the results of second test are presented. In this test, the infill wall

composition is different from the first test. Bed joint reinforcement (BJR) was placed on

the brick wall along horizontal direction. The type of reinforcement is Bekaert Murfor

RND/Z 5-200. Characteristic tensile strength is 500 MPa. Application of bed joint

reinforcement can be seen in Figure 8.1.

Chapter 8: Model 2-Bed Joint Reinforcement Brick Wall

195

a) Bed Joint Reinforcement

b) During Construction

Figure 8. 1 Bed Joint Reinforcement (BJR) and Construction Phase

Dimension detail and position of mortar joints in the mortar can be seen in Figure 8.2.

Figure 8. 2 Dimension Detail and Position of Mortar Joints in the Mortar

8.2. INPUT SIGNALS AND ACCELERATIONS FOR TEST 2

This test was implemented in five steps. These steps and PGA can be seen in Figure 8.2

below. Targets and Applied loads can be seen in Table 8.3 below.


196

Figure 8. 3 PGA versus Number of Stages for Bed Joint Reinforcement

Table 8. 1 Target and Applied Loads During Test 2

Step

Number

Target Earthquake Load in Percent

(%)

Applied Earthquake Load in Percent

(%)

Transversal Longitudinal Transversal Longitudinal

1 10 45 9.84 40

2 34 478 33 287

3 63 535 48 436

4 63 535 56 486

5 292 584 180 537

8.3. IN-PLANE RESULTS

At the end of the test, data were evaluated and then Force – Drift curve was plotted

along in-plane direction of specimen 2 in Figure 8.4 below. Instrumentation on the

specimen was the same as in previous test.


197

Figure 8. 4 In-plane Force – Drift Curve (For Both mm and %) Test 2

8.4. OUT-OF-PLANE RESULTS

Out-of-plane direction is the most important part of this test. Graphs were plotted in two

steps. The out-of-plane drift response can be seen in Figure 8.5 below. Mid-

displacement of infill wall was also evaluated. This graph can be seen in Figure 8.6

below.

Figure 8. 5 Out-of-plane Force – Drift Curve (For both mm and % Drift) for RCF at

Test


198

Figure 8. 6 Force – Mid-displacement of Infill Wall at Test 2

Then out-of-plane behavior of infill wall was tabulated according to displacement only.

Displacements were evaluated on the base of instrumentation of Figure 8.6.

Figure 8. 7 Instrumentation, horizontal and vertical alignments for Test 2

Out-of-plane movements were tabulated according to their applied earthquake percent.

Figures belong to all stages can be seen in figures below.


199

Figure 8. 8 Out-of-plane movements of infill wall and RCF at 10% eq. load Test2

Figure 8.8 presents out-of-plane displacement of infill wall constructed by bed joint

reinforcement. The effect of reinforcement between brick layers limited displacement

capacity of infill wall. Average out-of-plane displacement is around 0.8 mm at 10% eq.

level. Out-of-plane displacement of URM model (Test-1) was more than 1.2 mm at the

same eq. level.



200

Figure 8.9 prove that out-of-plane movement capacity of infill wall was restricted by

bed joint reinforcement. Therefore, during seismic action, infill wall stayed behind the

RC frame.


Especially, bed joint reinforcement lines keep the infill wall stable as seen in Figure

8.10 above. Average mid-displacement is around 8 mm. This ratio is less than

displacement of RC frame.



201

At 105% load level, infill wall was still resisting out-of-plane load. But a few

instruments were removed due to local damage of infill wall. The maximum out-of-

plane displacement at 105% level is around 38 mm at upper part of the specimen as seen

in Figure 8.11.


Displacement increment is also another important aspect to assess out-of-plane

movement and failure. For this reason, relative displacements were evaluated on the

base of this theory. Relative displacements were evaluated like before test.

Instrumentation and alignments on the wall can be seen in Figure 8.13 below.


202

Figure 8. 13 Horizontal and vertical alignments to calculate relative displacements for

Test 2

Relative displacements can be seen in figures below according to steps.


Figure 8.14 indicate that the average displacement of HA1 and HA2 keeps the infill

wall behind the RC frame. The main reason of this behavior is to bed joint

reinforcements.


203


Figure 8.15 proves that even if upper and lower part of the infill wall more vulnerable to

seismic action, presence of bed joint reinforcement keeps the mid-part stable.


To see relative displacements well along experimental steps, Left and Right alignments

were tabulated one by one as seen in Figure 8.17 and Figure 8.18 respectively.


204

Figure 8. 17 Relative displacements of infill wall left line and RCF along all steps at

Test 2

Figure 8. 18 Relative displacements of infill wall right line and RCF along all steps at

Test 2

Acceleration amplification of test 2 can be seen the figures below.


205


load Test 2

Acceleration amplification of infill wall is lower than that of RC frame at early stage of

the seismic action according to Figure 8.19.


load Test 2

Beginning of detachment can be seen easily at Figure 8.20. These sensitive places are

upper and lower part of the infill walls. Especially, connection points between the RC

frame and infill wall.


206


load Test 2

Line2 shows that there is a strike at infill wall which is located to free end of the model

with high amplitude. Average acceleration line (solid line) shows that there is an

acceleration increase at mid part of the infill wall due to a strike of free end.


load Test 2

Figure 8.22 shows that there is a zigzag line along vertical line of infill wall. This

amplification is the basic reason of lateral cracks and failure of infill wall along out-of-

plane direction.


207


load Test 2

At last stage many accelerometers were removed from the wall due to damaged and

collapsed area. During high shaking, movement shape of infill wall can be seen easily in

Figure 8.23 above. This reverse movement of top and bottom part of infill wall results

heavy lateral cracks. Only three instruments were kept on the wall. Acceleration

differences between upper and lower part of the infill wall is around 9 m/sn2. Removed

instruments can be seen in Figure 8.24.

Figure 8. 24 Removed instruments at Test 2 Step 4 (180 % Eq. Load)

After step 5, experiment was lasted on one more step. The purpose of this last step is to

observe toppling of brick walls. As expected, upper part of the infill was about to fall


208

down on the shake table. But, bed joint reinforcements prevented this falling of infill

wall particles.

8.5. CRACK PATTERNS AND FAILURE MECHANISM OF TEST 2

Crack propagation and failure of infill wall can be seen in below step by step.

a)48% Earthquake load in transversal

(ST3)

b)105% Earthquake load in transversal

(ST4)

c) 180% Earthquake Load in Transversal (ST5)

Figure 8. 25 Crack propagation and failure mechanism of specimen at Test 2


209

8.6. MODAL FREQUENCIES AND DAMAGE INDICATOR OF TEST 2

Then to calculate damage with a scientific manner, Damage Indicator Factor was

calculated on the base of natural vibration periods. Natural vibration periods were done

before test and after all stages. The importance of this process is to assess damage.

Natural vibration periods can be seen in Table 8.2 for transversal direction and in Table

9.3 for longitudinal direction.

Table 8. 2 Natural vibration periods of specimen 2 after each test step in transversal

direction

Mod Number INITIAL After ST1 After ST2 After ST3 END

1st Mode 8.15 7.54 7.1 6.23 2.97

2nd

Mode 9.23 9.2 8.5 8.2 5.51

3rd

Mode 13.6 13.3 12.5 12.3 8.15

4th

Mode 16 16 16 15.5 11.5

5th

Mode 19 18.7 17.5 18.5 14.6

6th

Mode 26 ????? 25 24.1 19.6

Table 8. 3 Natural vibration periods of specimen 2 after each test step in longitudinal

direction

Mod Number INITIAL After ST 1 After ST2 After ST3 END

1st Mode 7.3 7.2 6.4 6.4 6.3

2nd

Mode 9.9 9.9 9.6 9.5 9.4

3rd

Mode 13.6 14.6 12.5 12.5 12.3

4th

Mode 17 16.6 15.7 15.5 15

5th

Mode 20 20 20 20 17

6th

Mode 27.3 27.1 26 26 25


210

Figure 8. 26 Damage indicator for Test 2; infill wall with BJR

As seen from Figure 8.26, damage indicator factor for transversal direction 0.63 and

0.12 for longitudinal direction.

Chapter 9: Comparison of Results and Discussion of Experiments

211

Chapter 9

COMPARISON OF RESULTS AND DISCUSSION OF

EXPERIMENTS

9.1. CONCLUSION FOR EXPERIMENTAL PART

In this chapter, experimental results were evaluated in terms of force – displacements,

out-of-plane displacements and vulnerability indexes. During the test earthquake load

was applied to both models in five steps. URM model carried out a maximum force of

419 kN. However, the second model, which is constructed with Bed Joint

Reinforcement, carried maximum 681 kN as seen in Figure 9.1 and 9.2 below.


212

Figure 9. 1 Comparison of Force – Drift curves for both models In-plane direction

Figure 9.1 shows that Specimen 2 which is constructed with bed joint reinforcement

carries 38 % more load than URM specimen through in-plane direction. However, these

two models reached nearly the same drift ratio along in-plane direction. BJR model

reached 1.35% drift ratio and URM model reached 1.3% drift ratio end of the test.

URM model dissipated 5510 kNmm energy, but BJR model dissipated 12400 kNmm

energy along in-plane direction. BJR model dissipated 55% more energy than URM

model along in-plane direction.


213

Figure 9. 2 Comparison of Force – Drift curves of RCF for both models along out-of-

plane direction

It can be shown that these two specimens carry nearly the same load in the out-of-plane

direction. One important point is that URM specimen reached 5.1 mm drift at 61 %

earthquake load, but BJR model reached 19.4 mm drift level at 55 % earthquake load.

After 95 % earthquake load, instruments were removed on the wall. So that, maximum

drift could not measured. However, at the end of the test BJR model can carry 6%

maximum load than URM model. However, BJR model showed more ductile behavior

than URM model as seen in figures. The maximum out-of-plane load is 121 kN for

URM model as seen from Table 7.3 and 127 kN for BJR model. Even if, these two

model have the same force capacity, displacement capacities are different due to

reinforcing technique. BJR model resisted nearly the same load but showed more

ductile behavior. Moreover, URM model dissipated 158 kNmm energy, but BJR model

dissipated 1020 kNmm along out-of-plane direction.


214

Figure 9. 3 Force – mid-displacement (mm) of infill walls

The mid-displacement of infill wall is also an important graph in terms of drift because

mid-displacements are a good performance indicator. Mid-displacement of infill wall

can be seen in Figure 9.3 above. During the test one, after 3rd

step in order not to

damage instruments, all instruments on the wall were removed. For this reason only first

three step were able to collect data. One of the most important points in terms of

resisting lateral load is dissipating energy of infill wall. Infill of URM model dissipated

182 kNmm, but infill wall of BJR model dissipated 2090 kNmm energy along out-of-

plane direction. Both models have the same stiffness until first step like 63.1 kN/mm.

After first step, BJR model continues increasing with the same stiffness until 4th

step.

However, there is a decrease in stiffness after 1st step at URM model. Stiffness is

20.6 kN/mm between 1st and 2

nd step for URM model along in-plane direction.

To discuss the out-of-plane capacity of both models, force and mid-displacement of

infill walls were evaluated until 100% earthquake load. This comparison will be more

realistic than Figure 9.3. Force and mid-displacement of infill wall can be seen in Figure

9.4 below.


215

Figure 9. 4 Force – mid-displacement curve for both model until 100% eq. load

As seen from Figure 9.4, BJR model showed more ductile behavior, when compared to

URM model. BJR model reached 109 kN at 0.6g out-of-plane and 0.52g in-plane

earthquake load, but URM model reached 77 kN at 0.59g out-of-plane load and 0.4g in-

plane earthquake load. This means that bed joint reinforcement increased carrying

capacity of the specimen during the loading cycle, even if in-plane earthquake load is

1.5 times more than URM model. URM model reached 13 mm mid displacement of

infill wall. This displacement corresponds to 0.58% drift ratio. Mid-displacement of

BJR model reached 35 mm at 105% earthquake load, which corresponds to1.56% drift.

After experiments, analytical out-of-plane forces were calculated and compared with

experimental results. These calculations can be seen in Table 9.1 below.

Table 9. 1 Experimental and analytical calculation of out-of-plane forces

Test 1

URM

Test 2

BJR

Angel

(1994)

Klinger

(1996)

Pereira

(2013)

FEMA 273

(1997)

Eurocode-6

(2006)

121 KN 127 KN 100 KN 249.5 KN 51 KN 39 KN 31 KN

As seen from Table 9.1 above, maximum forces of URM and BJR models are very

close to each other. However, the closest prediction is belonging to Angel’s

formulation, with an error of 16.5 %. Klinger’s formulation overestimates the capacity


216

nearly 100%. Pereira’s, FEMA 273 and Eurocode 6 underestimated the capacity nearly

60%, 68% and 75 % respectively.

It can be concluded that in-plane force amount has a small influence on the out-of-plane

carrying capacity of infill wall. However, in-plane force has an effect on failure mode

and crack pattern. The adopted reinforcing technique also increases significantly the

out-of-plane displacement and drift ratio.

Chapter 10: Conclusion & Recommendation

217

Chapter 10

CONCLUSION & RECOMMENDATION

The objective of this thesis is to reveal seismic behavior of brick infill walls. These

brick infill walls were surrounded by reinforced concrete frame. Earthquake load was

applied to the specimens’ bidirectional and simultaneously. Global behavior of infill

walls were evaluated by numeric study in Part A. Local behavior of infill walls was

studied experimental in Part B of this thesis. Three shake table experiments were

implemented in this main section. The purpose of these shake table experiments was to

simulate in-plane and out-of-plane behavior of infill walls under bidirectional

earthquake load. This earthquake load is applied simultaneously. Out-of-plane failure

mechanism of infill walls were evaluated and compared each other. The main

conclusion of this thesis was emphasized under two main titles below.

Numeric part of this thesis address the main outputs of global behavior of infill wall like

below;


218

During modeling of TLCW by finite element software, there was a model

structure error. This error was bypassed with elastic foundation to check the

experimental engineering properties of concrete and infill wall.

Model calibration is indispensible for all numeric study to overcome any type of

error. In this thesis model calibration is used to solve model structure error.

The reason of this problem was investigated and realized that there was stiffness

degradation between shake table and foundation of the structure.

Before model updating average error was 5.3%. After model updating, this error

was decreased minimum 2%. The lowest error was obtained with updating of

elastic foundation stiffness and interface stiffness of the numeric model.

The reason to obtain this lowest error is the randomly selected elastic foundation

and calculated interface stiffness. Since, elastic modulus of infill wall and elastic

modulus of reinforced concrete frame were considered in model updating with

elastic foundation properties and interface stiffness, average error was increased.

Pushover analysis was performed on TLCW model and URM model. Both

model modeled with fine mesh around ten thousand mesh number and one

thousand mesh number. There is a 6% difference between the experimental and

numerical lateral capacity of the TLCW model in the transversal direction and a

2% difference in the longitudinal direction. Then differences were found of

about 10% between the two FE models in terms of the force ratio and 17% in

terms of displacement, even though the coarse mesh uses about 1/10 of the

degrees of freedom.

It is also noted that the TLCW model showed a higher base shear ratio capacity

than the URM model in terms of resisting lateral loads, namely 0.64g in the

transversal and 0.5g in the longitudinal direction, but it also showed a more

ductile behavior.

The differences between the two models in terms of base shear are about 35%. 5

cm infill wall thickness differences between the models result in an average 35%

base shear and average 42% displacement at the time of the maximum force

ratio.

There is only 4% difference between the experimental and fine meshed

numerical values in the transversal direction and 2% difference in the

longitudinal direction in terms of force ratio (g).

Chapter 10: Conclusion & Recommendation

219

The fine meshed model is more conservative due to the early failure of fine

mesh elements. The experimental force ratio showed a very good match with the

fine meshed TLCW model.

Experimental crack propagation was well simulated by the fine meshed TLCW

model.

TLCW infill wall solution is a better structural application for earthquake prone

territories than URM infill wall. However, two-leaf cavity reinforced concrete

structure showed brittle behavior.

In the design phases it is strongly suggested that, to prevent soft storey collapse,

the designer should consider this vital point and include the preventive features

of the TLCW model.

TLCW model resisted 12.7% more load than URM model in transversal

direction and 16.4% more load in longitudinal direction when nonlinear time

history analysis were performed on these two models.

Finite element prediction showed a good match with experimental results nearly

90% in terms of roof displacement and lateral resistivity load.

It was realized that collapse of numeric model is the same as real structure.

Crack propagation of pushover analysis and time history analysis are the same

as real shake table collapse.

TLCW model is a better application than single layer 13 cm uniform thickness

URM model which is constructed very common in Turkey and other countries.

In experimental section local behavior of infill wall was investigated in terms of out-of-

plane behavior under bidirectional simultaneous earthquake load. This section address

the contribution listed below.

Tested specimens were the isolated prototypes to simulate 7th

floor of 8 storey

building. Two reinforcements were placed into the columns and beams.

Test-1, URM model resisted 418 KN in-plane load and 121 KN out-of-plane

load.

Test-2, BJR model resisted 681 KN in-plane load and 127 KN out-of-plane load.

Bare frame of these specimens carries the load between 275KN and 300 KN.

URM model carries nearly 50% more load than bare frame. When URM model

compared with BJR model, BJR model carries nearly half more load than URM

model.


220

Maximum in-plane drifts of both models are nearly the same. However, total

lateral bearing capacity of BJR infill wall is more than URM model. Since mid-

displacement and out-of-plane force was evaluated for both models at the same

earthquake level.

URM model carries 77 KN out-of-plane force and mid-displacement of infill

wall is 13 mm. However, BJR model carries 107 KN and mid-part of the infill

displaces 34 mm.

These results show that BJR model shows more flexible behavior than URM

model.

When damage maps and photos were studied, it can be easily seen that URM

model has many lateral cracks at early stages of seismic action.

Upper and lower parts detachment and infill fails from top part. However,

diagonal cracks occurred during the test on BJR model.

Generally, cracks were accumulated on bottom part of the BJR model. Under

severe seismic action infill wall with BJR has not totally collapsed.

BJR application prevented total collapse of infill wall and increased in-plane

resistivity of complete specimen.

Future studies will be indicated on the base of seismic behavior of infill wall. This

section presents possible future implementation related to this thesis, infill walls and

masonry walls below.

Full scale reinforced concrete structure with infill wall should be modeled with

any of software. Real earthquake record should be applied to assess response of

structure in terms of global behavior of infill walls.

Full scale reinforced concrete structure with infill wall should be modeled with

asymmetric plan geometry and response of infill wall should be investigated.

Effect of window and door openings should be investigated by shake table

experiments to see the change of opening orientation on energy dissipation

capacity of prototype with and without opening under bidirectional simultaneous

earthquake load.

Full scale historical masonry or contemporary masonry walls should be exposed

to shake table to see out-of-plane behavior of infill wall.

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