investigation of seismic behavior of infill wall surrounded by … · then, my family especially my...
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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
2.5.2. Calibration Number 2 .................................................................................... 57
2.5.3. Calibration Number 3 .................................................................................... 59
2.5.4. Calibration Number 4 .................................................................................... 61
2.5.5. Calibration Number 5 .................................................................................... 63
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 2. 6 Updating Summary for Calibration 3 ........................................................................................ 60
Table 2. 7 Updating Summary for Calibration 4 ........................................................................................ 62
Table 2. 8 Updating Summary for Calibration 5 ........................................................................................ 64
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
transversal direction .............................................................................................................................. 86
Figure 3. 14 Force-Displacement curves of TLCE and URM infill structures (Coarse Mesh) along
longitudinal direction ............................................................................................................................ 87
Figure 3. 15 Force-Displacement curves of TLCE and URM infill structures (Fine Mesh) along
transversal direction .............................................................................................................................. 87
Figure 3. 16 Force-Displacement curves of TLCE and URM infill structures (Fine Mesh) along
longitudinal direction ............................................................................................................................ 88
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
Figure 3. 30 Crack pattern of TLCW in transversal directions with fine mesh before failure (Loading
Type: Negative Transversal) ............................................................................................................... 102
Figure 3. 31 Crack pattern of TLCW in transversal directions with fine mesh before failure (Loading
Type: Negative Longitudinal) ............................................................................................................. 102
Figure 3. 32 Crack pattern of TLCW in transversal directions with coarse mesh before failure (Loading
Type: Positive Transversal) ................................................................................................................ 102
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
Type: Negative Transversal) ............................................................................................................... 103
Figure 3. 35 Crack pattern of TLCW in longitudinal directions with coarse mesh before failure (Loading
Type: Negative Longitudinal) ............................................................................................................. 104
Figure 3. 36 Crack pattern of URM in transversal directions with fine mesh at the time of failure (Loading
Type: Positive Transversal) ................................................................................................................ 105
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
Type: Negative Longitudinal) ............................................................................................................. 106
Figure 3. 40 Crack pattern of URM in transversal directions with coarse mesh before failure (Loading
Type: Negative Transversal) ............................................................................................................... 107
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
Figure 4. 7 Crack Propagation of TLCW Model at the End of Stage 2 .................................................... 121
Figure 4. 8 Crack Propagation of TLCW Model at the End of Stage 3 .................................................... 122
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. 16 Numeric Crack Propagation for URM Model at Stage 2 ..................................................... 131
Figure 4. 17 Numeric Crack Propagation for URM Model at Stage 3 ..................................................... 132
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. 11 Out-of-plane movements of infill wall and RCF at 61% eq. load Test 1 ............................. 180
Figure 7. 12 Out-of-plane movements of infill wall and RCF at 95% eq. load Test 1 ............................. 181
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. 17 Relative displacements of infill wall and RCF at 61% eq. Load Test 1 ............................... 183
Figure 7. 18 Relative displacements of infill wall and RCF at 95% eq. Load Test 1 ............................... 184
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. 22 Out-of-plane acceleration amplification of infill wall and RCF at 28% eq. load Test 1 ...... 186
Figure 7. 23 Out-of-plane acceleration amplification of infill wall and RCF at 61% eq. load Test 1 ...... 187
Figure 7. 24 Out-of-plane acceleration amplification of infill wall and RCF at 95% eq. load Test 1 ...... 187
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. 10 Out-of-plane movements of infill wall and RCF at 48% eq. load Test 2 ............................. 200
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. 14 Relative displacements of infill wall and RCF at 10% eq. load Test 2 ................................ 202
Figure 8. 15 Relative displacements of infill wall and RCF at 33% eq. load Test 2 ................................ 203
Figure 8. 16 Relative displacements of infill wall and RCF at 48% eq. load Test 2 ................................ 203
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. 19 Out-of-plane acceleration amplification of infill wall and RCF at 10% eq. load Test 2 ...... 205
Figure 8. 20 Out-of-plane acceleration amplification of infill wall and RCF at 33% eq. load Test 2 ...... 205
Figure 8. 21 Out-of-plane acceleration amplification of infill wall and RCF at 48% eq. load Test 2 ...... 206
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.
Chapter 1 – Introduction
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)
Investigation of Seismic Behavior of Infill Wall
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)
Chapter 1 – Introduction
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.
Investigation of Seismic Behavior of Infill Wall
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
Chapter 1 – Introduction
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)
Investigation of Seismic Behavior of Infill Wall
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.
Chapter 1 – Introduction
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.
Investigation of Seismic Behavior of Infill Wall
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
Chapter 1 – Introduction
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
Investigation of Seismic Behavior of Infill Wall
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
Chapter 1 – Introduction
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.
Investigation of Seismic Behavior of Infill Wall
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).
Chapter 1 – Introduction
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).
Investigation of Seismic Behavior of Infill Wall
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).
Chapter 1 – Introduction
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)
Investigation of Seismic Behavior of Infill Wall
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)
Chapter 1 – Introduction
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.
Investigation of Seismic Behavior of Infill Wall
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.
Chapter 1 – Introduction
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.
Investigation of Seismic Behavior of Infill Wall
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.
Chapter 1 – Introduction
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.
Investigation of Seismic Behavior of Infill Wall
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.
Chapter 1 – Introduction
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).
Investigation of Seismic Behavior of Infill Wall
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
Chapter 1 – Introduction
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
Investigation of Seismic Behavior of Infill Wall
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
Chapter 1 – Introduction
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.
Investigation of Seismic Behavior of Infill Wall
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.
1.5 REFERENCES
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Chapter 1 – Introduction
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2008
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frames. Engineering Structures, 50, pp. 43-45, 2013
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Infilled Frame Test Data, PMFSEL Report No:95-1, March, Universit of Texas
Austin, USA, 1995
Bayraktar, A., Coşkun, N., Yalçin, A., Damages of masonry buildings during the july
2004 Doğubeyazıt (Ağrı) earthquake in Turkey. Engineering Failure Analysis,
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Binici, B., Ozcebe, G., Ozcelik, R., Analysis and Design of FRP Composites for Seismic
Retrofit of Infill Walls in Reinforced Concrete Frames, Composite Part B:
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Bruneu, M., Saatçioğlu, M., Behaviour of unreinforced masonry structures during the
1992 Erzincan, Turkey, earthquake. TMS Journal, pp. 79-87, 1994.
Bruneu, M., Building damage from the Marmara, Turkey earthquake. Journal of
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concrete frame. Journal of Structural Engineering, ASCE, 125(6), pp. 578-589,
1999
Calvi, G., Bolognini, D., Seismic Response of Reinforced Concrete Frames Infilled With
Weakly Reinforced Masonry Panels, Journal of Earthquake Engineering, 5:2,
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Investigation of Seismic Behavior of Infill Wall
32
Celep, Z., Erken, A., İlki, A., Taşkın, B., 8 March 2010 Kovancılar-Elazığ earthquake
pre-engineering report. İTÜ Press, Istanbul, 2010
Dawe, J. L., Seah, C. K., Out-of-plane Resistance of Concrete Masonry Infilled Panels,
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.
Elnashai, A. S., Gençtürk, B., Kwon, Oh-S., Al-Qadi, I. L., Hashash, Y., Roesler, J. R.,
Kim, S. J., Jeong, S. H., Dukes, J., Valdivia, A., The Maule (Chile) earthquake
February 27, 2010: Consequence assessment and case studies. Mid-America
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Ersoy, U., Üzsoy, S., The behaviour and strength of infilled frame. TÜBİTAK MAG-
205, Technical Report, 1971
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
Hendry, A. W., The Lateral Strength of Unreinforced Brickwork, The Structural
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
Chapter 1 – Introduction
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
Kızılkanat, A., Coşar, A., Koçak, A., Güney, D., Selçık, M. E., Yıldırım, M., 23
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
Mosalam, K., Günay, M. S., Progressive collapse analysis of RC frames with URM
infill walls considering In-plane/Out-of-plane interaction. Earthquake Spectra,
31(2), pp. 921-943, 2015.
Investigation of Seismic Behavior of Infill Wall
34
Rosetto, T., Peiris, N., Pomonis, A., Wilkinson, S. M., Re, D. Del., Koo, R., Gallocher,
S., The Indian Ocean tsunami of December 26, 2004; Observations in Sri
Lanka and Thailand. Natural Hazards, 42, pp. 105-124, 2007
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Sezen, H., Whittaker, A. S., Elwood, K. J., Mosalam, K. M., Performance of reinforced
concrete buildings during the August 17, 1999 Kocaeli, Turkey earthquake and
seismic design and construction practices in Turkey. Engineering Structures,
25, pp. 103-114, 2003
Shing, P. B., Mehrabi, A. B., Behaviour and analysis of masonry-infilled frames.
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
Stavridis, A., Koutromanos, I., Shing, P. B., Shake-table test of a three-storey
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.,
Out-of-plane behaviour of confined masonry walls. Engineering Structures, 33,
pp. 1734-1741, 2011
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Masonry Walls Subjected to Combined Axial Loads and Out-of-Plane Uniform
Pressures, Canadian Journal of Civil Engineering, 39:439-447, 2012
Chapter 1 – Introduction
35
Verderame, G. M., Luca, F. D., Ricci, P., Manfredi, G., Preliminary analysis of a soft
storey mechanism after the 2009 L’Aquila earthquake. Earthquake Engineering
& Structural Dynamics, 40, pp. 925-944, 2010.
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loads. PhD Thesis, Fırat State University, 2014
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frames with various types of masonry infill. Earthquake Engineering and
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).
Chapter 2 – Part A: Preparation of Numeric Model & Model Updating
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
Investigation of Seismic Behavior of Infill Wall
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)
Chapter 2 – Part A: Preparation of Numeric Model & Model Updating
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)
Investigation of Seismic Behavior of Infill Wall
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
𝜔𝑗𝐹𝐸 𝑋1
𝐿 , 𝑋2𝐵 , …… , 𝑋𝑛
𝐵 = 𝐶𝑗 + [𝐴𝑖𝑘𝑋𝑘𝐿 + 𝐵𝑖𝑘(𝑋𝑘
𝐵)2]𝑛𝑘=1
𝜔𝑗𝐹𝐸 𝑋1
𝑈 , 𝑋2𝐵 , … … , 𝑋𝑛
𝐵 = 𝐶𝑗 + [𝐴𝑖𝑘𝑋𝑘𝑈 + 𝐵𝑖𝑘 (𝑋𝑘
𝐵)2]𝑛𝑘=1
.
. (2.5)
.
.
.
Chapter 2 – Part A: Preparation of Numeric Model & Model Updating
41
𝜔𝑗𝐹𝐸 𝑋1
𝐵 , 𝑋2𝐵 , … … , 𝑋𝑛
𝐿 = 𝐶𝑗 + [𝐴𝑖𝑘𝑋𝑘𝐿 + 𝐵𝑖𝑘(𝑋𝑘
𝐿)2]𝑛𝑘=1
𝜔𝑗𝐹𝐸 𝑋1
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.
Investigation of Seismic Behavior of Infill Wall
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.
Chapter 2 – Part A: Preparation of Numeric Model & Model Updating
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.
Investigation of Seismic Behavior of Infill Wall
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
Chapter 2 – Part A: Preparation of Numeric Model & Model Updating
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
Investigation of Seismic Behavior of Infill Wall
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
Chapter 2 – Part A: Preparation of Numeric Model & Model Updating
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)
Investigation of Seismic Behavior of Infill Wall
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
Chapter 2 – Part A: Preparation of Numeric Model & Model Updating
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.
Investigation of Seismic Behavior of Infill Wall
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.
Chapter 2 – Part A: Preparation of Numeric Model & Model Updating
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
Chapter 2 – Part A: Preparation of Numeric Model & Model Updating
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.
Chapter 2 – Part A: Preparation of Numeric Model & Model Updating
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.
Chapter 2 – Part A: Preparation of Numeric Model & Model Updating
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 %
Chapter 2 – Part A: Preparation of Numeric Model & Model Updating
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
Investigation of Seismic Behavior of Infill Wall
56
Figure 2. 11 NMD values for 4 modes
Figure 2. 12 MAC values for 4 modes
Chapter 2 – Part A: Preparation of Numeric Model & Model Updating
57
Figure 2. 13 Frequency comparison FE TLCW model
2.5.2. Calibration Number 2
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.
Chapter 2 – Part A: Preparation of Numeric Model & Model Updating
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 %
Average 5.2 % Average 3.4 %
Chapter 2 – Part A: Preparation of Numeric Model & Model Updating
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.
2.5.3. Calibration Number 3
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.
Chapter 2 – Part A: Preparation of Numeric Model & Model Updating
60
Table 2. 6 Updating Summary for Calibration 3
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
Average 5.2 % Average 2.0 %
Chapter 2 – Part A: Preparation of Numeric Model & Model Updating
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.
2.5.4. Calibration Number 4
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.
Chapter 2 – Part A: Preparation of Numeric Model & Model Updating
62
Table 2. 7 Updating Summary for Calibration 4
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 %
Average 5.2 % Average 2.83 %
Chapter 2 – Part A: Preparation of Numeric Model & Model Updating
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.
2.5.5. Calibration Number 5
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.
Chapter 2 – Part A: Preparation of Numeric Model & Model Updating
64
Table 2. 8 Updating Summary for Calibration 5
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 %
Average 5.2 % Average 2.4 %
Chapter 2 – Part A: Preparation of Numeric Model & Model Updating
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
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66
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Buildings, EN 1992-1-1, December, 2004
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Lourenço, P. B., Computational Strategies for Masonry Structures, PhD Thesis.
University of Delft, Netherlands, 1996
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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
Chapter 2 – Part A: Preparation of Numeric Model & Model Updating
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
Chapter 2 – Part A: Preparation of Numeric Model & Model Updating
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
Investigation of Seismic Behavior of Infill Wall
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.
Chapter 3 – Part A: Pushover Analysis
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
Investigation of Seismic Behavior of Infill Wall
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
Chapter 3 – Part A: Pushover Analysis
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)
Investigation of Seismic Behavior of Infill Wall
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)
Chapter 3 – Part A: Pushover Analysis
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).
Investigation of Seismic Behavior of Infill Wall
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.
Chapter 3 – Part A: Pushover Analysis
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,
Investigation of Seismic Behavior of Infill Wall
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 𝑆𝑒𝑎𝑟
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
Chapter 3 – Part A: Pushover Analysis
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.
Investigation of Seismic Behavior of Infill Wall
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
Chapter 3 – Part A: Pushover Analysis
81
Figure 3. 7 Hysteric curves of experimental earthquake data belongs to 4 stages in
transversal direction
Investigation of Seismic Behavior of Infill Wall
82
Figure 3. 8 Hysteric curve of experimental earthquake data belongs to 4 stages in
longitudinal direction
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
Chapter 3 – Part A: Pushover Analysis
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.
Investigation of Seismic Behavior of Infill Wall
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 (-)
Chapter 3 – Part A: Pushover Analysis
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 (-)
Investigation of Seismic Behavior of Infill Wall
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
Chapter 3 – Part A: Pushover Analysis
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
Investigation of Seismic Behavior of Infill Wall
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)
Positive Negative Positive Negative
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
Chapter 3 – Part A: Pushover Analysis
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.
Investigation of Seismic Behavior of Infill Wall
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.
Chapter 3 – Part A: Pushover Analysis
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.
Investigation of Seismic Behavior of Infill Wall
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.
Chapter 3 – Part A: Pushover Analysis
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.
Investigation of Seismic Behavior of Infill Wall
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)
Chapter 3 – Part A: Pushover Analysis
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
Investigation of Seismic Behavior of Infill Wall
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
Chapter 3 – Part A: Pushover Analysis
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
longitudinal direction
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
Investigation of Seismic Behavior of Infill Wall
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)
Positive Negative Positive Negative
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)
Positive Negative Positive Negative
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.
Chapter 3 – Part A: Pushover Analysis
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.
Investigation of Seismic Behavior of Infill Wall
100
Figure 3. 28 Crack pattern of TLCW in transversal directions with fine mesh before
failure (Loading Type: Positive Transversal)
Chapter 3 – Part A: Pushover Analysis
101
Figure 3. 29 Crack pattern of TLCW in longitudinal directions with fine mesh before
failure (Loading Type: Positive longitudinal)
Investigation of Seismic Behavior of Infill Wall
102
Figure 3. 30 Crack pattern of TLCW in transversal directions with fine mesh before
failure (Loading Type: Negative Transversal)
Figure 3. 31 Crack pattern of TLCW in transversal directions with fine mesh before
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)
Chapter 3 – Part A: Pushover Analysis
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
failure (Loading Type: Negative Transversal)
Investigation of Seismic Behavior of Infill Wall
104
Figure 3. 35 Crack pattern of TLCW in longitudinal directions with coarse mesh before
failure (Loading Type: Negative Longitudinal)
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.
Chapter 3 – Part A: Pushover Analysis
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)
Investigation of Seismic Behavior of Infill Wall
106
Figure 3. 38 Crack pattern of URM in transversal directions with fine mesh before
failure (Loading Type: Negative Transversal)
Figure 3. 39 Crack pattern of URM in longitudinal directions with fine mesh before
failure (Loading Type: Negative Longitudinal)
Chapter 3 – Part A: Pushover Analysis
107
Figure 3. 40 Crack pattern of URM in transversal directions with coarse mesh before
failure (Loading Type: Negative Transversal)
Figure 3. 41 Crack pattern of URM in longitudinal directions with coarse mesh before
failure (Loading Type: Negative longitudinal)
Investigation of Seismic Behavior of Infill Wall
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
Chapter 3 – Part A: Pushover Analysis
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
Investigation of Seismic Behavior of Infill Wall
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
Investigation of Seismic Behavior of Infill Wall
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.
Chapter 4 – Part A: 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
Investigation of Seismic Behavior of Infill Wall
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.
Chapter 4 – Part A: Time History Analysis
115
Figure 4. 1 Input Acceleration of 100 % Earthquake in Transversal Direction
Investigation of Seismic Behavior of Infill Wall
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.
Chapter 4 – Part A: Time History Analysis
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.
Investigation of Seismic Behavior of Infill Wall
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
𝛿𝑢𝑖𝑇𝛿𝑔𝑖
+𝛿𝑢𝑖𝛿𝑢𝑖
𝑇
𝛿𝑢𝑖𝑇𝛿𝑔𝑖
(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).
Chapter 4 – Part A: Time History Analysis
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.
Investigation of Seismic Behavior of Infill Wall
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a)South
b)North
c)East
d)West
Figure 4. 4 Crack Propagation of TLCW Model at the End of Stage 1
Chapter 4 – Part A: Time History Analysis
121
a)South
b)North
c)East
d)West
Figure 4. 5 Crack Propagation of TLCW Model at the End of Stage 2
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.
Investigation of Seismic Behavior of Infill Wall
122
a)South
b)North
c)East
d)West
Figure 4. 6 Crack Propagation of TLCW Model at the End of Stage 3
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.
Chapter 4 – Part A: Time History Analysis
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.
Investigation of Seismic Behavior of Infill Wall
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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.
Chapter 4 – Part A: Time History Analysis
125
Figure 4. 9 Comparison of Displacements along Transversal Direction: Node Number
95 (100% Earthquake Load)
Investigation of Seismic Behavior of Infill Wall
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.
Chapter 4 – Part A: Time History Analysis
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.
Investigation of Seismic Behavior of Infill Wall
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.
Chapter 4 – Part A: Time History Analysis
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.
Investigation of Seismic Behavior of Infill Wall
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.
Chapter 4 – Part A: Time History Analysis
131
a)North b)South
c)East d)West
Figure 4. 14 Numeric Crack Propagation for URM Model at Stage 2
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.
Investigation of Seismic Behavior of Infill Wall
132
a)North b)South
c)East d)West
Figure 4. 15 Numeric Crack Propagation for URM Model at Stage 3
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.
Chapter 4 – Part A: Time History Analysis
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
Investigation of Seismic Behavior of Infill Wall
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
Chapter 4 – Part A: Time History Analysis
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
Investigation of Seismic Behavior of Infill Wall
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
Chapter 4 – Part A: Time History Analysis
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
Investigation of Seismic Behavior of Infill Wall
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.
Investigation of Seismic Behavior of Infill Wall
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.
Chapter 5 – Part B: Shake Table Test Setup
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.
Investigation of Seismic Behavior of Infill Wall
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
Chapter 5 – Part B: Shake Table Test Setup
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.
Investigation of Seismic Behavior of Infill Wall
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
Chapter 5 – Part B: Shake Table Test Setup
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
be seen in Figure 5.8.
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.
Investigation of Seismic Behavior of Infill Wall
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.
Chapter 5 – Part B: Shake Table Test Setup
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.
Investigation of Seismic Behavior of Infill Wall
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.
Chapter 5 – Part B: Shake Table Test Setup
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
Investigation of Seismic Behavior of Infill Wall
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.
Chapter 5 – Part B: Shake Table Test Setup
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.
Investigation of Seismic Behavior of Infill Wall
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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.
Chapter 5 – Part B: Shake Table Test Setup
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
be seen in Figure 5.19.
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.
Investigation of Seismic Behavior of Infill Wall
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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
Investigation of Seismic Behavior of Infill Wall
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.
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Figure 6. 1 Longitudinal impulses for dynamic identification
Figure 6. 2 Transversal impulses for dynamic identification
Investigation of Seismic Behavior of Infill Wall
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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
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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
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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
Chapter 6: Part B-Model 0:Unreinforced Brick Wall (Failed Test)
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
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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
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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.
Investigation of Seismic Behavior of Infill Wall
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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.
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Figure 6. 11 Displacement of infill wall measured by Krypton
Figure 6. 12 Location of correct measurement at last stage (Model 0)
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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.
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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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169
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)
Investigation of Seismic Behavior of Infill Wall
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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
Chapter 6: Part B-Model 0:Unreinforced Brick Wall (Failed Test)
171
repeated due to boundary condition problem. Following chapter contains successful
experiment results implemented with reinforced concrete structure with unreinforced
masonry infill wall (URM).
Investigation of Seismic Behavior of Infill Wall
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
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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.
Investigation of Seismic Behavior of Infill Wall
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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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175
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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176
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
Chapter 7: Model 1-Unreinforced Brick Wall (Successful Test)
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
Chapter 7: Model 1-Unreinforced Brick Wall (Successful Test)
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
Investigation of Seismic Behavior of Infill Wall
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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.
Figure 7. 10 Out-of-plane movements of infill wall and RCF at 28% eq. load Test 1
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.
Figure 7. 11 Out-of-plane movements of infill wall and RCF at 61% eq. load Test 1
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.
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181
Figure 7. 12 Out-of-plane movements of infill wall and RCF at 95% eq. load Test 1
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.
Investigation of Seismic Behavior of Infill Wall
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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
Chapter 7: Model 1-Unreinforced Brick Wall (Successful Test)
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.
Figure 7. 17 Relative displacements of infill wall and RCF at 61% eq. Load Test 1
Investigation of Seismic Behavior of Infill Wall
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.
Figure 7. 18 Relative displacements of infill wall and RCF at 95% eq. Load Test 1
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.
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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.
Investigation of Seismic Behavior of Infill Wall
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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.
Figure 7. 22 Out-of-plane acceleration amplification of infill wall and RCF at 28% eq.
load Test 1
Figure 7.22 shows the most vulnerable part of the infill wall especially Line2 and Line3.
Chapter 7: Model 1-Unreinforced Brick Wall (Successful Test)
187
Figure 7. 23 Out-of-plane acceleration amplification of infill wall and RCF at 61% eq.
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.
Figure 7. 24 Out-of-plane acceleration amplification of infill wall and RCF at 95% eq.
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.
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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.
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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.
Investigation of Seismic Behavior of Infill Wall
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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.
Chapter 7: Model 1-Unreinforced Brick Wall (Successful Test)
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
longitudinal direction
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
Investigation of Seismic Behavior of Infill Wall
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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,
Chapter 7: Model 1-Unreinforced Brick Wall (Successful Test)
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.
Investigation of Seismic Behavior of Infill Wall
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.
Investigation of Seismic Behavior of Infill Wall
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.
Chapter 8: Model 2-Bed Joint Reinforcement Brick Wall
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
Investigation of Seismic Behavior of Infill Wall
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.
Chapter 8: Model 2-Bed Joint Reinforcement Brick Wall
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.
Figure 8. 9 Out-of-plane movements of infill wall and RCF at 33% eq. load Test 2
Investigation of Seismic Behavior of Infill Wall
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.
Figure 8. 10 Out-of-plane movements of infill wall and RCF at 48% eq. load Test 2
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.
Figure 8. 11 Out-of-plane movements of infill wall and RCF at 105% eq. load Test 2
Chapter 8: Model 2-Bed Joint Reinforcement Brick Wall
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.
Figure 8. 12 Out-of-plane movements of infill wall and RCF at 180% eq. load Test 2
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.
Investigation of Seismic Behavior of Infill Wall
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 Relative displacements of infill wall and RCF at 10% eq. load Test 2
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.
Chapter 8: Model 2-Bed Joint Reinforcement Brick Wall
203
Figure 8. 15 Relative displacements of infill wall and RCF at 33% eq. load Test 2
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.
Figure 8. 16 Relative displacements of infill wall and RCF at 48% eq. load Test 2
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.
Investigation of Seismic Behavior of Infill Wall
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.
Chapter 8: Model 2-Bed Joint Reinforcement Brick Wall
205
Figure 8. 19 Out-of-plane acceleration amplification of infill wall and RCF at 10% eq.
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.
Figure 8. 20 Out-of-plane acceleration amplification of infill wall and RCF at 33% eq.
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.
Investigation of Seismic Behavior of Infill Wall
206
Figure 8. 21 Out-of-plane acceleration amplification of infill wall and RCF at 48% eq.
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.
Figure 8. 22 Out-of-plane acceleration amplification of infill wall and RCF at 105% eq.
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.
Chapter 8: Model 2-Bed Joint Reinforcement Brick Wall
207
Figure 8. 23 Out-of-plane acceleration amplification of infill wall and RCF at 180% eq.
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
Investigation of Seismic Behavior of Infill Wall
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
Chapter 8: Model 2-Bed Joint Reinforcement Brick Wall
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
Investigation of Seismic Behavior of Infill Wall
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.
Investigation of Seismic Behavior of Infill Wall
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.
Chapter 9: Comparison of Results and Discussion of Experiments
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.
Investigation of Seismic Behavior of Infill Wall
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.
Chapter 9: Comparison of Results and Discussion of Experiments
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
Investigation of Seismic Behavior of Infill Wall
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;
Investigation of Seismic Behavior of Infill Wall
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.
Investigation of Seismic Behavior of Infill Wall
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.