bauforschung und baupraxis pptx

The modem calculation methods, tne high performance computers and the advanced software packages are the major research tools in his concern, ‘The present thesis concems to develop and i

đt thản

Bquforschung und Baupraxis

From Research to Practice in Construction

COLLAPSE ANALYSIS OF MASONRY STRUCTURES UNDER EARTHQUAKE ACTIONS

Tammam Bakeer

“ehflentehe destehzfuhl rogivefsgldnung deTU resđen ona

‘Publication Seis of he Chok of srcturol Design of U Dresden vot

Schriftenreihe des Lehrstuhls Tragwerksplanung, TU Dresden Publication Series of the Chair of Structural Design, TU Dresden

Bauforschung und Baupraxis

From Research to Practice in Construction

Heftvol 8

COLLAPSE ANALYSIS OF MASONRY STRUCTURES

UNDER EARTHQUAKE ACTIONS

Tammam Bakeer

Bauforschung und Baupraxis

From Research to Practice in Construction

Herausgegeben von Prof Dring, Wolam Jager und Doz Dr.-Ing Todor Vassily Lehrstuhl Tragwerespanung Fakuta archer

‘Technische Universitat Dresden

01062 Dresden Tol +49 (0) 251 145.33 50 10 Fox +49(00351 146 3977 13 emai LetrstuhTreqwerksplanung@msibox tu dresden de

Herstolung: Ainoa Digaldruck GmbH, Dresden (SEN, 978-9-86760-120.0

"` 19 Dresden 2008

tn dor Schitontoihe “‘Baufrschung und Baupraxis" werden Abeiton und Botrage des Lotrstus

‘Tragworkspanung der TU Dresdon ebenso wi selche von Wissenschaften und Praktker de mìt đem Lenrtuh in Vertingungstenen verbfntien Aniegan it e, neu Ergebnisse aus dor Forschung und Latve voreustalen und anderersats Verretem aus dar Praxis dle Moghenikt 7

‘geben, ber interessante Vorhaben, Plsnungen id Technken eder Technwlogien zu betehten, ES Sol dam der informationsaustausch zwischen den Wissenseratlor, Injenouten und Shodonlen

‘gelerden sowie Ergebnisse und Erahiungen fr se wotere Anwendung dokumenven und Doreigestolt worden,

COLLAPSE ANALYSIS OF MASONRY STRUCTURES

UNDER EARTHQUAKE ACTIONS

Dissertation

‘genehmigt von der Fakultt Architektur der

“Technischen Universitat Dresden zur Erlangung des akademischen Grados eines Doktors der Ingenieurwissenschaften

(Dr-ing)

Dipl.-Ing Tammam Taher Bakeer

‘eb am 01.01.1880 n Homs, Syilen

Tag der Disputabon: 29 05.2009

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To my Rama and Rana

| dedicate this work

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‘Acknowledgements

The frst interest to develop this work originates from the need to preserve masonry monuments in my homeland Syria, the land that is well known as the cradle of vilzations

The research repor in this thesis is carted out atthe chair of structural design, Faculty

of Architecture, Dresden Univerely of Technology The experimental data of large scale swuelwes in this thesis have been provided by the European research project ESECMaSE The major tool that used to develop the numerical models is LS-DYNA software ver, S71, a5 well as itis used to implement the proposed algorthms, The Calculations of large scale structures have been carried out in the high performance

‘Computing centre of Dresden Universty of Technology,

| consider my few years in Dresden to be a crucial period in my life, where | introduced

to many challenging problems, in one of the most attractive place to study masonry structures, First and foremost | would fk to express my sincere and deep gratitude towards my supervisor Prof Dr-Ing Wolfram Jager for is generosity, wisdom,

‘outstanding support throughout my research af Dresden Universi of Technology

| would tke fo record my thanks to the team of ZIM (high performance computing center

of Dresden Univesity of Technology) for ther fast help and great attention As wel as,

my thank goes fo the team of ELSA the European Laboratory for Structural Assessment in JRC the Joint research centre, 'spraialy) and particulary to Dr Amelie Anthoine for providing the necessary experimental data which used in hs thesis

| am very grateful for the fruitful colaboration | had with Dipl-Ing Peter Schéps His encouragement, valuable discussions and great attention are never forgotten Besides, |

‘owe my gratitude to Dring Sang Ha Nguyen for his suggestions and the valuable time {gave to me, | am deeply indebted to my colleagues at the chair of siructural design for ther great suppart and continuous scientie discussions for provcing a stimulaing and fun environment in the chair | also wish to express my sincere appreciation to Prof Gassan Nader & Prof Eido Shannat for their united suppon and encless encouragement They are of those professors wel remembered by students

Lasty and most importanty, | am extremely grateful fo my parents who have been the souree of encouragement and inspiration throughout my life

pope

Tammam Bakeer Dresden, August 2008

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Abstract

Earthquake actions are by far the major risk that causes the collapse of masonry Structures, The assessment of the seismic performance of large scale masonry Structures remains a chalanging task despite the progress achieved by means of

‘experimental studies, Due fo tne capacity linstatio of shaking tables and other dynamic testing devices, the large scale computer modeling appears to be a very efficient altemative The modem calculation methods, tne high performance computers and the advanced software packages are the major research tools in his concern,

‘The present thesis concems to develop and investigate computer-aided techniques to simulate the behaviour of large scale masonry structures under earthquake actions staring from elaste linear behaviour to the progression af damage up to the point of collapse

The numerical models have been developed by means of exalic finite element code LS- DYNA The numencal techniques which allow the emergence of clscantinuties have been adopted and the combined Finite-Discrete Element Method, capable of processing large deformations and discontiulies has been applied for the purpose of collapse analysis, The abilly of mash free methods, lke smontned particles hycrodynamic, have been examined for simulation the failure modes and the fragmentation ofthe materia The necessary background ofthe constitutive models of masonry constituents has been given and the major features, shortcomings and challenging problems have been Fighighted An interface cohesive model based on the smoalhnees of the yelé surface has been proposed and implementad The acopted models have been vaidated by

‘means ofthe dynamic test results of two full scala masonry structures

‘The developed approach has been used to study the performance of heritage masonry builsings, wich involve members of diferent geometries, against the fundamental earthquake characteristics, The influences of earthquake characterises on the

‘vulnerability of ealapse have been explored by the collapse analysis of a case study of full heritage masonry bulaing

‘A theory forthe shear fature behaviour of vertically reinforced masonry shear walls has been developed, which gives an idealization forthe behaviour after the inital failure of

‘composite material wih a high level of nnomogeneity ike masonry Besides collapse Analysis has Deen employed as a tool to develop and verity the seismic rtrofiting ofthe reconstructed heritage ouikings The approach has been applied on a case study of

‘adobe masonry Dulding from Bam citadel which collapsed aflr ie earthquake of 2002,

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Rigid Badies Sping Metbod (BSM) 28

242 Discontinuous Deformation Analysis (ODA) 28 24.3 _Non-Smooth Contact Dynamics (NSCD) 29

244 Modiied Discrste Element Mathad DEM) a 24.5 Combined Finte-Diserete Elements (DEM/FEM) 30

Limit Analysis Models (LAM) at 2.4.7 Applied Element Method (AEM) 3

4.3 Contec ana CD,

44 Fine clamentcades andsolionstategies — 8&

45 Techniques of rack formation 58

452 Predetermined crack techniques

4.8 Modeling svategies for collapse simulation 14

.`_ Congllhiltvä imodiiB uc eeacueacu2sechinu.gzdtiurddueosecaiz ĐỂ, 5.1 The basics of plasticity theory Tạ

5314 “Maianhaelh talcaiiisesxplastri 8 5.1.2 Implementation nto LS-DYNA, 83 5.2 Constiuive madels ofthe interiaces 85 5.3 implementation of echesive interface material model $6 53.1 The smooth veld surface 88

5.3.4 Simulation the fragmentation using interface elements 96 5.4 Constitutive models of masonry constituents 96 5.4.1 General shape of yield surface for geo-materale 96

‘542 Ganateials constiutioe madels in LS.OVNA 0

6.3 SPH modeling of masonry in LS-DYNA t2

Full scale dynamic testing and computer modellin

Z1 Dynamic testing methods

‘Shaking table testing method (STT) 7.42 Peeude-dynamic testing method (PSD) 116

7.1.9 Real ime dynamic hybrid testing method (RTPSD) 18

5 BiAiibSc ¿c2 cese-reneieszcgeoes TA,

‘73.4 Finite element modeling 22-252 8,

‘Analysis of results for low earthquake inten: tát 7.52 Comparison wth experimental resus 144 7.53 Analysisgfresufs for moderate earthquake intensities 16 7.5.4 Analysis of results for song earthquake intensities 18 7.55 _Sensitvty of collapse process tothe bond strength 149 7.5.6 Influence of vetial ground motion 150

Earthquake characteristics and collay

82 Mosque of Takiyya ak-Sulaymanivya 155 8.2.1 Historical background and the layout of Takivya 158

8.2.3 Constuetion of the geometty and fnte element modelling, 161

841 Seismicity of the region 164 8.4.2 The response spectrum 166 8.43 Synthesis of arifeial acoelerograms 167

.e behaviour

85 Collapse analysis ofthe structure, 168

$6 Effect of earthquake characteristics 169 B7 Theduection ofthe earthquake

8.8 The frequency content ofthe earthquake 1

242 Results ofthe Gnite slement model a 9.4.9 Tensile crack opening of one side of the bed joint- Case 191 9.4.4 Shear cohesion falure of one sie ofthe bed joint Case I 193

915 Modeling strategies of reinforced masonry 195

Verification of retrofiting measures by colapse analysis 198

2.6.2 Description ofthe model 200

1 Introduction

Masonry is one of the most primitive building materials known to mankind since the beginning of earliest civiizations Masonry has been used in the constuction of the most longlasting exciing ancient monuments, artifacts, cathedrals and cies in a vast variety

Of cultures Furthermore, Masonry material is used widely in today’s structures due to the simplicity of building technique and the attracted features that characterize this maleral

Many actions are leading to the collapse

fof masonry structures and one of the

major sources of destucton is the

seismic action The ruins of many

masonry monuments are the evidence for

oor performance of masonry structures

against earthquakes, Figure 1

Many experimental methods have been showed technical limitations in dynamic testing

of large scale structures due to the high cost of such tests On the other hand, the computer modeling has been showed great efficiency and simplicity due to the

‘availablity and growing advance of fast computers and software packages

However, the creation of an elaborate model that represents the behaviour of the structure vith al stages from inital elastic near behaviour to the plastic non-linear, the tracking, the separation and then the collapse is stil raught vih đifTeules,

4.1 Masonry in architecture history

Perhaps, the first used masonry material was stonemasonry, Lourengo [109]

‘Archaeological excavations have revealed one of the earliest examples of the fist permanent slonemasonry houses near Hullen Lake (e 9,000-8,000 BC), where dc Stone huts, circular and semi-sublerranean constructions were found, Loureng [103] and Olveira (138) Stone was diftcult to shape and due its weight, transporting was sities

‘Mud brick started in use as an allemative masonry material in dray climate regions

‘where clay mud is available The first mud brick consirucions probably goes back to

Jencho', Palestine (c ð,360-7 350 BC], where many mud brick houses have founded inthe ste Ole shaped bricks have been founded in Gayond, 2 place located in the upper Tigns area in souln east Anatolia clase to Diyarbakir Indus Valley Civikeaton also used mud brick extensively, as can be seen in the runs of Mohtenor-Daro’ and Harappa

In EgypL, Fom pre-dynastc irmes (5.000 BC) unl[ the Roman occupation (50 AD) the basc meleral to buld houses was sun deed Onck, commonly of Nile mud, as can be seen in tho runs of Buhen, The pure Nila mud shrinks over 30% in the drying process

‘wiile the addition of chopped staw and sand to the mud prevented the formation of cracks,

‘The invention ofthe burnt brick (as apposed fo the considerably earlier sun-cried mud bck) enabled the construction of permanent buildings in regions where the harsher clmate precluded the use of mud bricks

Masonry was widely used in the Plain of Shinar where famous ziggurats as hexahedral towers were efecied They were pyramidal, stepped temple towers thal has an architectural and religious structure charactestc of the major cies of Mesopetamis

"The land between the vers” The structural fom ofthe pyramids, which represents on

of the most stable structural shapes, was 2 logical development ofthe inital stone piles, The stacking of large blocks of stone in pyran form allows reaching great heights The

‘mos! famous pyramids are undoubtedly the Eoypan pyramids at Giza

‘The understanding of the structural behaviour started to play an important role in the construction of temples with the use of stone lintels to support the masonry above

‘openings in was famous example in Lion Gate at Mycenae Greece (1 300 BC ) ussd

fa stone lintel for @ span of 3 m and was loaded by 25.30 tons The lintel idea shows the beginning of he arched Behaviour fat would daminate the following milennium Olvera 138),

The arch was fist developed in the Indus Valley chlizaion and subsequently in Mesopotamia, Egypt, Assyta, Greek and Persian civilizations for underground structures such as drains and vaults However, ancient Romans were the fist to use them widely above ground

‘The Greeks played an important role in the use of structural elements, namely: columns and beams fo buidé their temples The most famous one is Parthenon’ which Fepresented an important ole forthe use of limestone in baling the sirctural elements,

‘The Romans contributed signficanty to the constuction of buildings, They bult roads, bfdgos, aqueducts and harbors Also, they introduced rotable innovations in materials, structural concepts and constuction process

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Figure 3 The development ofthe archtechture of masonry structures

Remarkable examples of the use of dry stone blocks in buildings by Romans aro the Colosseum’ in Roma and Segovia's aqueduct in Spain Romans expleited the structural form of arches to construct magnificent bridges and equeducts which are surviving unt today, such as Segovia's aqueduct’ in Spain and Pont du Gard aqueduct’ in France, Figure 2

‘Vaults and domes played a great cole in the construction of large-span roots, @ good

‘example are the elegant geometry of vauits and the comes that used in Hagia Sophia in Istanoul (6" century AD}, Ozkul etal 145] Another interesting stuctual form is the castles, which were spread ftom Europe to the Middio East The Crac des Chevaliers’ dnd Citadel of Salah Ed-Din"” are good examples of crusaders castles in the Middle East

Gothic architecture, which was originated in the 13” century, represented remarkable improvements in reducing the heaviness of Roman constructions by using framing elements (columns, arch bs, fying buttresses ane butress wall or tower) working in Comaression Two of the finest examples ofthe Gothic architecture are the Cathedral of Charves" and the Cathecral of Amens™, The history of Gothic architecture with ts Pioneering construction is also marked by failures, ecacks and permanent deformations The Renaissance architecture was intlated in Florence ang aroused a new concepts and forms Buildings were characterized by regular forms and geometrical symmetry in plane and elevation, The church of St Mania dal Fiore in Florence (bull 18” century) land tho church of St Peter in Rome (16" cantury) are remarkable examples of Renaissance architecture

During the Baroque period, no significant or innovative solutions conceming the Siructural conception were developed Important examples in Europe are St, Pauls Cathedral in London (17" century) and the Pantnéon in Pars (18” century), Figure 3

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{AB me ea aus tw a na aang, apo ata woh bu oo Spe Panta Garis an aesadut nthe mut of France conan by ma Raman Emp, anaes Yeo! 10 8G Newer excavate howeret suagest he corstuelen ik pace he mide ef he Mak Fon a0,

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sf be Gob aye of aciertuein at Ponce, Convucton was begun 118, The Cate! of Gur tac) n Ameho ( 1320-238) ee flac compete cated! Fronee, wih De

4.2 The scope and objectives

The following study deals vith both historical and today's masonry structures It focuses pemaniy on earthquake actions However, the developed models alowed to be used for Another loading regime Finite element method is the fundamental numerical tool in tis Study, and the advantages ef using other mesh free methods also have been discussed

‘The main concern of the following research focuses to develop and investigate computer-aided techniques that are able lo simulate the collapse of large scale masonry Structures under earinquake actions, which investigation can not bê carisd out in laboratory condons

‘The most relevant epecific objectives of this study ae:

to develop campuler models that ean simulate the progress of damage in masonry structures in all stages, starting from elastic near behaviour, 10 plastic nnoninear behaviour, cracking, separation up fo the colapse

~ 10 develop constitutive models for masonry constitutions, capable of mapping the real behaviour and incorporate the computaton effrency

ta verify and evaluate the developed models in comparison versus experimental resus of full seale dynamic tests

to investigate the effect ofthe diferent earthquake characteristics on the collapse mechanisms of large scale historical masonry structure

to develop 2 theory based on the variation of damage states for the falure behaviour of vertically reinforced masonry walls

Áo adopt the collapse analysis technique for developing the reinforcement of historical masonry structures

Toe second chapter is deleted to the stale ofthe art of the modelling techniques of

‘masonry, gives comprehensive study for the progress of research in numerical analysis,

‘th focus on the works in discrete methods, A classification ofthe available techniques

nd the application area is achieved, The fentures and shortcoming of each tecnnique is Giscussed, as wel

‘The third chapter investigates in depth the material properties of masonry and is constituents and the faiure mechanisms Diferent failure theories for masonry as & composite are described and discussed The expenmental setups forthe determination

Of the basic material parameters of masonry are given and the corresponding failure modes are described,

The fourth chaplor introduces the finite element method as a basic numerical too! for rmadeling mascn:y The combination of fnite element method with discrete elemant

‘method, contact analysis and soluton techniques are presented Diferent numerical Simulation techniques for crack formation reported in the iiteture are discussed Modleling strategies for masonry based on combined fnite-discrete element metho are Proposed

This folowed by an ilustation of plasticity theory and the implementation of @ material rmadel into the expict solr of LS-DYNA inthe fith chapter, The constitute models that serve for the proposed modeling stategies are described and discussed A constitutive model for a cohesive interface element based an smaoth yield surlace is

‘developed and validated

The features of applying mesh free methods are presented in the sich chapter, where the smeothed particle hydredynamc is employed

‘The seventh chapter reports the experimental results of two dynamic tests Two rumerical models correspond to each test have been created The objained numerical results compared with hat from experiments, Furhhermore, adaional studies concerning the simulation of the collapse of the structure under higher earinquake intensites are performed, where such stidies can nat be achieved in laboratory

Inthe eighth chapter, a lacge scale historical masonry stuctuee is used as a case study

to explore the performance for different earthquake characteristics, The effect of earthquake direction, as well as the frequency content ofthe accelecogram is studied

‘The ninth chapter dovoted for reinforced masonry stuctures A review of the current slate of esearch is reported and a navel faire theory for verbally reinforced masonry

is presented The possible modeling strategies for reinforcement modelling are Aiscussed, and the colapse analysis is use to develop the reinforcement for a case study of historical masonry structure

The tenth chapter summarizes the major conclusions obtained inthis research, and also suggests recommendations for future research works The 14 appendices present In etal the results of numerical simulations

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2 The state of research in masonry modelling

Masonry achieved 2 great progress in the last few decades, Many research efforts for masonry structures were carried cut all over the world o understand the stuctural Behaviour, ether through laboratory lasts or by using validated numerical models

Masonry researches are benefited from the enormous progress in other Buiding materials However, the methodologies that are used fr the analysis and design of other building materials are stil lacking for_ masonry Furthermore, numerical modeling

‘methods are stil raught wih citcultes, Ths is due to the complexity ofthe behaviour of

‘masonry structure, which is determined by the interaction of the ndvigual behaviours of Several parts of he structure, ofan wit aiforent material characteristics

Several models and methods have been proposed inthe erature In order to study the mechanical behaviour of masonry This chapter is devoted to give an overview insight the [atest upsiocdate progress in modeling of masonry and numerical simulation of collapse

2.1 Modelling strategies of masonry

Masonry s a composite material, and its overall behaviour is stetly dependent on the arrangement and properties of is diferent consttuents The engineerng Merature on Tadeling of masonry is enormous and the research in the field Is widespread, Numerical models may be based on two methodolagias, Massart [124] Fist mesoscopic detalles descriptions consider masonry as a heterogeneous siucture wih Separate descriptions of each constituent, Second, models intended for large-scale suetural calculations are generally of a phenomenological nature, and represent the collacive behaviour of canstituents by closed:farm macroscopic consttufvs equations The three principle modeling strategies are correspond io three diferent scales of complexity which have been identified by Lourenco [108] and Rots [187], Figure 4 1+ Micro modeling or to phase material model: staring from the knowledge of single constituents Each component of the masonry structure has its ovm behaviour which might be comalex This modeling sistegy is categorized inte (2) Detaiied micro-madeling whereby unis and mortar represented as Continuum, withthe univmartar interfaces modelled using discontinuous interface elements as potential crack, sip and crushing lanes;

(©) Simpiifed micro-modeling through the adoption of “geometrically expanded masonry units wih a single “averagec” interface representing the mortar and the two mortarlunt interfaces This model requires the material model of the expanded unit and masonry joints

2: Macro:madeling or single phase material model, the quasi-periodic nature of masonry has prompted io Investigate the use of homogenization techniques,

‘where all masonry components are smeared by an equivalem homogenized Continuum One-phase material models are treating masonry as an ideal homegencous material with constiutwe equations that differ fam these of the compenents

22 Made tanto 2

Figure 4 The three principal modeling strategies of masonry

The decision about the suitable technique depends on required accuracy and the size of the model

Micro modeling gives more realistic representation of the structural behaviour, but itis relatively prohibiive to be used due to the great number of the degrees of freedom, Fequire more input deta, and their failure cteron has an elaborated form due fo the it:

‘mortar interaction The constitutive equations of the components have narmally @ simple form, and they are appropriate forthe study ofthe local Behaviour of masonry

‘The constitutive models on macro level are relatively simple to use, require less input data, and he fale erterion has normally a simple form, Itrequires a priv definitions of constitutive prescriptions The consitulive equations are relatively complicated and are Suitable for the study of the overall behaviour of the entire masonry structure to reduce the numerical caleulation,

2.2 Methods of analysis

2 large variety of numerical modeling frameworks have been employed to analyse the

‘mechanical behaviour of masonry Despite many numerical methods have the abilty to analyse the mechanical behaviour forthe early stages of failure, the ability to study the Performance near and after the collapse is stil limited and presents challenging Tmadeling problems As witnessed by the extensive study ofthe literature two numerical

approaches are widely descrited for analysing the mechanical behaviour of masonry Figure 5:

1) Continuum methods: the model is based on continuum material equations The finite element method (FEM) isthe typical example of this approach Smeared crack approach can be adopted in zones where separation occurs between structural elements

2) Discrete methods (or distinct methods): assumes that the geometry of cracks propagation is predefined before the analysis

Figure 5 The numerical analysis methods for masonry structures

Continuum approach has been widely used for many application areas, but the use of this approach isnot applicable to collapse analysis Nevertheless, combining continuum approaches with discrete approaches produces more powerful and accurate methods Moreover, continuum methods are more capable of simulating the behaviour before the collapse review of these two methods is given inthe folowing sections

2.3 Continuum methods

‘There are @ wide range of applications involve materials or systems that showing đisconlinufy at some level Despite that some systems are ininsicaly discontinuous thay are well approximated by a continuum This approximation is possible ifthe scale of the objects of interest is large enough Finite element method (FEM) and boundary element method (BEM) are well suited for representing of continuum media The interest

to develop continuous model for the discrete structure of masonry is due to computalon efficiencies gained by this model while the ciserelo type of analyses is very computer time consuming Furthermore, masonry often has periodic nature where the application

of the homogenized continuum model would allow for more elegant and efficient solution, Cerrlaza etal [41] and Sulem et al (177)

‘An attempt has been made to take info account the characteristics of masoncy materials fof micro-polar continuum, such as Cosserat continuum, instead of classical Cauchy Continuum, inorder to gel better representation forthe effec of particle rotation Masiani [122] and Masiani [123] present procedures to develop a Cosserat continuum to provide

a description of the mechanical behaviour of masonry with reguiar texture

“The plasticity theory has been employed to develop macro material models fr in plane behaviour of masonry Lourengo [108] proposed an anisotropic model of two surfaces Rankine/Mil, Massart [124] developed two-dimensional anisotropic damage model in a

“mult-plane framework Schlegel {164} showed an implementation of the material mode!

of Ganz theory (Ganz [62)) in ANSYS software Mister [132] used the shear failure theory of Mann & Miller ((117] and {116} to implement a material model for masonry panels in ANSYS,

Attempts also have been made to understand the behaviour of rubble and eyclopean masonry from natural stones (Mann [118], Warnecke [196] and Schlegel [164]) based on Morr-Caulomb criteria, The behaviour of mult:leaf masonry has been considered ss

‘wall, Egermann [51] and Schlegel (184)

(Church of eur ladies (Frauenkirche), Dresden, Stoll et al [178

Macro-modeling strategy has been often used in Iiterature for continuum models Some Continuum medels were buit using micro-madeling strategy (Schlegel [164)), where material models for mortar and unis considered separately with continuous Tite tlemant mesh on uni-mortar interfaces,

In continuum method the softening and local cracking of material considered by the

‘smeared crack approach, Rots [158], The smeared crack approach was frst developed for use in concrete structures and has been extended to masonry structures, Loft etal [106] In this approach cracks are modelled in an average sense by modifying the Taterial properties at the integration points of finite elements, Smeared cracks are Convenient when the crack orentations are not known beforehand, because the formation of a crack involves ne remeshing or new degrees of freedom However, the

smeared erack models can not be able fo simulate the final stage of softening process in

‘masonry material, i the fill separation of the continuum can not be accomplished by means of smeared crack models,

The modeling of masonry structures as continuum is far from being @ good representation of thei real behaviour due to the great number of discontinutes While

‘his approach suffers @ computationally traclable problem, a continuum model offers & {quite crude approximation of what is really a mico-mechanical phenamencn,

Many complications arise with continuum approach forthe highty nonlinear behaviours, either from material or geometrical perspectives For instance, i is very dificult or tunfeasiple to use the continuum approach to study the behaviour of materials or Siructures that change their status from continuum state to entirely discrete state, Ike behaviour of structures before and during collapse

Lourengo et.al [107] used FEM model with interface elements for simulation of uniaxial Compression tests of masonry prisms A fictitious micro-stucture composed of inear elastic particles separated by non-linear interfaces was adapted to model units and

‘mortar in quarter of the basic masonry cel, Cavichi etal 40] used limit analysis with interface elements to determine inal falure of masonry bridge considering arch-fI interaction

Interface elements were introduced to consider the discontinuty at planes of failures However, with this technique itis enly possible to show small displacements before the failure The interface elements have limitations to simulate the large displacements at the collapse ofthe structure

Figure 7 FEM made! wih interface elements for simulation of uniaxial (a) tensile and

(b) compression tests of masonry prisms, Lourengo et.al (107}

Discrete element method goes back tothe pioneering work of Cundall et al 46}, where itwas originally used to model jointed and fractured rock masses, The proposed method Showed high effciency to describe siscontinuous phenomena and dynamical prablems oftarge deformations, Occurrence and propagation of fracture have been natursly taken inte account wih a ciscrete model, Later, this approach was extended to others felds of engineering, where the elaborate study of joints is requred, 6 @ soils and other granular materials, Ghaboussi and Barbosa (64) This numerical technique 1s also used for the rmadeling of masonry stuctures, Lemos et al (99), Sineraian [174] and Lemos [98 The early formulation of the ciscrete element method has been orginally termed distinct element method DEM (Cundal (45) and nas been invented for rigid circular bocies in twa dimensions with deformable contacts, The overall soluion scheme forthe DEM has been formulated in an explicit time-stepping format Movements of bodies have been

‘ven by extamal forces and varying contac! forcas, The methed considers each body in tum and at any given time determines all forces (extemal forces or contact forces) that are acting on it Out of balance forces induce accelerations which then determine the movement of that body during the next time step The discrete element method Comprises diferent techniques which are proper for the simulation of éynamic behaviour

Of systems of multple separated bodies These bodies wil be subjected to continuous changes in contact status and varying contact forces which in tum influence the subsequent movement ofthe bodies Such problems are non-smooth in space (separate bodies) and in time jumps in velecitas upon colisions) and the unilateral constraints (on-penetrabiiy) must be consisered

In case of rigid bodies, the constitutive law of contact interaction ls only needed, while the continuum constitutive law (eg elastcty plasticity, camage and fractunng) must be included for deformable bodies Computational modeling of muli-body contacts represents the dominant feature in ciscree element methads as ihe number of booies Considered might be very large According to the nature of the problem and level of Accuracy, the bodies of the system can be considered as rigic, simply deformable (pseudo-ngid) or uly deformable

Many computer codes are formulated for discrete element methods The fst code was

‘orginally formulated by Cundal [46] to simulate the response of discontinuous media subjected to either static or dynamic lading and has been futher developed by Lemos

ft al [100], Nowadays, a vast range of open source, non-commercial and commercial software are available such as: UDEC, BALL & TRUBAL, QUAKE & DAMSEL, NESSI FRIP, FLAC, 3DEC, PFC30, REBOP, EDEM, GROMOS, ELFEN, MIMES PASSAGE/DEM, and TRIDEC

Many existing metheds belong te the discrete element computational formwork could appear under diferent names and each of em has been developed ini own right

Cundall & Hart [45] wore defined four classes of discrete element methods: Distinct Element Methods (OEM), Modal methods, Discontinuous deformation analysis (ODA), Momentum-exchange methads The other classifcations of the discrete methods are based on the manner these methods address, Bicani¢ [20], ie.: detection of contacts, tteatment of contacts (rigi, deformable, defarmabilty, (constitutive aw) of bodies in contact (gd, deformable, elastic, elasto-plastic, etc) large displacements and large fotations, number (small or large) andior distnbution (loose or dense packing) of interacting bodies considered, consideration of the model Doundares, possible Subsequent fracturing or fragmentation and me-stepping integration schemes (explicit impli,

The heterogeneous nature of masonry and the discontinuity at block interfaces ean be

‘well descried by discrete element approach This approach is well suited for collapse Simulation of masonry structures, where good qualty resulls have been achieved Azevedo et al [11] was used UDEC (Universal Distinct Element Code) to simulate the collapse of monumental masonry sirctures due to seismic actions, Figure 8 Furher

‘examples can be seen in he works of Robert et al, 15], Psychars etal, [148]

Extensive research work was devoted to analysis masonry structures using other versions of DEM such as; Rigid Bodies ‘Spring Method RESM, discontinuous eformation analysis ODA, combined discretesinite elements, non-smooth contact ynamiee NSCD and Modified Disunet Element Method (MDEM),

Figure 8 Collepse analysis of masonry structures using the discrete element method

(a) masonry arch bridge (Lemos (97); (0) Simulation of an aqueduct pila, {Lemos (98) (c) ry stone masonry pedestal sustaining a stafve (Sincraian 1174), (a) Collapse sequence for the S Giorgio bell ower in Trignano,

‘Azevedo, eta [T1]

2.4.1 Rigid Bodies Spring Method (RBSM)

The Rigid Bodies Spring Method or (rigid block spring model) RBSM was proposed early

as a generalized limit plastic analysis framework Sold stuctures are assumed to be assembles of rigid blocks interconnected by discrete deformable interfaces with tstnibuted (elastic) normal and tangential springs

ASM has been used for studying the seismic behaviour of masonry walls Caso etal {33} was proposed a computational model using RBSM for evaluating the dynamical Fesponse and the damage of large masonry walls subjected to out of plane seismic actions Besides, Cascio [38] was proposed a rigid block spring model for inplane behaviour of masonry walls made of regular textures, where quadtlateral giane rigid flements were used and connected by normal springs and one shear spring on each Side In the work af Casolo etal [37] the RBSM has been adopted for seismic analysis

of in plane dynamic behaviour of masonry walls considering hysteretic energy tissipation and mechanical deterioration,

An experimental and analytical studies were made by Nerlo et a [137] for earthquake Fesistance of confined concrete block masonry structures The wall specimens made of concrete blocks have been tested under cyclic lateral load and simulated by a RBSM The noninear behaviour has been modelled by using rigid bodies and boundary springs As a result of the study RBSM has been showed goad conformity for analysing this type of structures However, analysis using the RBSM is unattainable up to complete collapse of he structure,

Figure 9 Scheme of an iegular masonry and the unit ce’ defined by four rigid

elements in RSM, Casoto etal [B7]

2.4.2 Discontinuous Deformation Analysis (0DA)

‘The method of discontinuous deformation analysis (ODA) is based on discrete element approach which uses implicit integration scheme DDA is a displacement-based method

‘veloped during the 1980's, Shi etal [171], Shi [173] and Shi [172] for solving stess- lisplacement problems of a jointed rock mass Jun et.al [91] was extended the eriginal

20 DDA formulation of Shi and Goodman 10 3D ODA formulation DDA has been typicaly formulated as a work-energy method It can be derived using the principle of

‘minimum potential energy (ing [B8)) or by Hamiton's principle, Once the equations of

‘motion are eseretzed, a steponise linear time marching scheme in the Newmark family Can be used for the solution of the equations of motion Step-wise linear imalict time

‘marching alows the so-called quasi-static solution, where step-wise velocities are never

Used, Quasistatic analysis i useful for examining slow or eceeping failures The relation between acjacent blocks is govemed by equations of contact inerpenetration and tneten

This method is capable of analysing a system of discrete, discontinuous blocks under {general stalic or dynamic loading, with block deformations and rigid body movements

‘curing simultaneously The onginal DDA framework was based on simply deformable blocks and the technique was futher developed and used for several applications including masonry structures In algonthmic terms, the method has been seen as an alterative way of introducing solid deformabilty into discrete element framework where block sliding and separation is considered along predetermined disconinuiy planes, Bieanié et al [21] The DDA has been further employed in Bicani¢ etal, [23] and Bicanié eta [22] for modeling of masonry arch bridges

Figure 10 Edinburgh arch bridge deformed shape following BDA, with simply

deformable Blocks, Biganié et a [23]

Later, the DDA has been extended to the Lagrangian discontinuous deformation

‘analysis (LODA) and used to simulate of dynamic process of earthquakes Cai etal (33) Doolin et al {49} developed DDA markup language (ODAML) to provide a practical engineering platform for ciscontinuous deformation analysis,

2.4.3 Non-Smooth Contact Dynamics (NSCD)

‘The Non Smeath Contact Dynamics method or shorly contact dynamics (NSCD) was Initiated by Jean etal [86] and developed within FORTRAN software LMGC In NSCD,

‘Signorni elation fer unilateral conditions and Coulomb faw as a dry fiction law has been Adopted together with an impli algorithm scheme for the dynamical equation NSCD Uses few lage time steps, deals with numerous simultaneous contacts and needs much iteration at each time step

NSCD was used to simulate masonry as a large collection of bodies under unilateral Constraints and triconal contact, Chetouane etal (42), Acary etal [3] and Acary etal Ki

«

Figure 11 (a) Cumulated shear at the end of the dynamic loading of masonry wall

‘modelled by NSCD using the LMGC90 code, Chetouane et al [42]: (|

‘Stresses in masonry arch bridge after a settlement of ground modelled using NSCD, Acary t a (3)

2.4.4 Modified Discrete Element Method (MDEM)

‘The original DEM was considered the material 2s an assembly of particles at which ao resistant forces exis! against traction, Elastic springs and dashpots were added by

‘Wiliams et a [198] 19 give continuity to the discrete numerical model it has bean showed that DEM can be viewed as a generalized fie element method, This method is called the modified DEM or extended DEM, The model behaves as continuous

‘macium while the springs are intact After tha breakage of some springs, iis possible to trace the movement of tne individual parts which separated ffom each other to destroy the structure's unity Using this method, becomes possible to analyse the fracture developing processes,

“The MDEM is capable fo follow the structural behaviour from initial loading up to the compleie collapse, However, he accuracy of EDEM in the range of smal deformation Is Tees than thatin FEE

2.4.5 Combined Finite-Discrete Elements (DEM/FEM)

For the problems, where the state of stresses and transition from continuum to discontnuum are important the Combined Finite-Discrefe Element (FEMIDEM) technique has been intoduced to combine the advantages of the FEM and DEM,

In the early 1990s, the combined finteiscrete element method was mostly an

‘cadamic subject In the last ten years, the frst commercial codes Rave been developed

‘and many commercial finite element packages have been increasingly adopted the Combined fnite-diserete element method, The hear ofthe DEM concerne the automatic Comlact detection between surfaces of separate block components Global search algorithms have been used to provide shortlists of potential contacts Local search algorithms have been then implemented to identiy the actual contact potenbal, Finally Using the penaiy method and the defined interface properties, the normal and tangential forces between the biocks have been resolved,

By combining FEM and DEM, the homogeneous material within each discrete body can

be modelled, facitaling elastic and non-inear maternal behaviour During the deformation of the bodies falure enitrion can be applied to detect ifthe stessistain Sate reaches the defined limit at which the fracture may ocour When these thresholds

are exceeded the FEM/DEM technique allows the fracture of discrete bodies (see Owen fetal [144], Munjza et al [135], Munjza (134), Frangin et al (61] and Komodromas (83)

2.46 Limit Analysis Models (LAM)

‘The Method of Limit Analysis Models is orginaly based on the rigt-perfectly plastic

‘matenal modeling in order to evaluate the load bearing capacily and the failure

‘mechanism ofthe structure The applicabilty of limit analysis to masonry structures that are modelled as assemblages of rigid blocks depends on some basic hypotheses, Ordutia et a4], [142], [140] and [139]

“The limit analysis can be regarded as a practical computational tool since only requires @ reduced number of materal parameters and it can provide a good insight nto the failure pattern and limit load Ordufa [143] presents an investigation about the capabiltes of limit analysis of rigid block assemblages in structural assessment of ancient masonry constructions Fems and Tin-Loi [57] suggested simple numerical scheme for sohing limit analysis problems for large-scale block structures

©

Figure 13 (a) Out of plane loaded wall supported at one edge, Ordua et al [141]; (0)

‘Masonry pile (c) 20 Bridgemill with the spandrel wall, Ordufa etal [143]

2.4.7 Applied Element Method (AEM)

Applied Element Method (AEM) was developed at the University of Tokyo by Meguro et

a [127] and Meguro et al [130] for analysing and visualizing the response of structures under extreme loading condtions The research on AEM is started since 1995 Many esearch efforis and validation tests have been conducted and published to introduce the AEM's breakthroughs: aulo-element separation, auto-element contact detection, realise element modeling and simplified super-slement meshing AEM is currently Ulized in numerous industries where the analysis and visualizaton of stuctures under extreme loading conditions is cruciat seismic engineering, vunerabiliy assessment emoltion, blast analysis, rocKal engineering (Meguro et al (127], (128), (128) [130] and Mayorea etal 126)

“The major advantages of the AEM are the simple modelling and programming, and high accuracy of the results wih relatively short CPU time Using AEM, the stuctural behaviour can be carried out from inital loading, to crack ination and propagation, separation of structural members and up to complete collapse in reasonable time with reliable accuracy and relatively simple material models,

By this method the structure is modelled as an assemblage of small elements that are made by dividing of the structure vitually as shown in Figure 14, where the two elements are assumed to be connected by normal and shear springs that are placed at interfaces and distributed around the element surfaces, The springs totally represent the siresses and deformations of a certain volume ofthe studied elements,

For modeling of masonry structures, each unit ls represented by a set of elements,

‘where mortar joints are placed at the corresponding contact surfaces, Meguro et al [127] and Guragain et al [72] One shortcoming of this method is that, there is no flexibility to mode! irregular geometies lke infinite element method

\

Figure 14 Masonry discretization and AEM modeling, the AEM ilustration tothe right

‘rom Meguro etal [128]

2.5 Concluding remarks

Modeling of masonry has been attracted a great amount of research works in the few last decades Most of research activites in this feld were focused on representing masonry as continuum using homogenization theory The plasticty theory has been Played a big role in developing material madels for continuum models ef masonry,

‘Attompls algo have been deveted in he fed of discrete modeling However, the works

in this oiection were less than fat in continuum modeling, and this were limited fo small scale structures

‘The reasons fr appiying continuum models in many research works are:

Easy handling of the problem for macro models by plasticity theory

= Most of commercial finite element codes proside a possibilty o implement &

‘material adel into thew codes, whereas the implementation of discret

‘modeling techniques into these codes is often not possible

The limitation in computer resources, where the discrete models need considerable amount of resources for large scale structures

= The generation of discrete models sometimes is complicated tke in case of rubble masonry

The ciserele models which developed for masonry are based on using specie rumerical tachriques lke contacts or springs to define the interfaces between te Giscrte elements The failures of the imorfaces signify inal the ciscrate elements go large displacements The simulation of large displacements is ted for some discret method, a8 well asthe discrete methods sil challenging for large scale structures,

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3 Mechanical behaviour and failure of masonry

‘Masonry is a composite materisl that consists of units and mortar lis overall behaviour

le sticly dependent on the arrangement and mechanical properties of its different constituents

It is quite signiteant before studying the colapse behaviour of masonry structure to Understand the failure behaviour of masonry materal

‘Tne present chapter focuses on the experimental research works which carried out to explore the mechanical characteristics of masonry matenal ands failure behaviour 3.1 Masonry constituents

A wide variety of materials were used in past centuries for building masonry Constructions Materials that are available in the vicinty were conceivably the most commen in cansirucion work When civilizations developed in river plains, the alluvial Geposits were used to produce brick constructions and w¬en chílzatsn existed in the afea of mountains, rocky oulerops and stones were used, Hamid et al (76)

‘Stones produced by nature were the frst units used to bulld masonry stuctures, Stones

‘ware widely avaiable from natural rocks lke igneous rocks, sedimentary and metamorphic rocks, Table 1

Main Group | Sub-group Examples

| Gite Dove Gee stones z sere ones : orn Basa, Vesa it

Re sgo4n ve srtngroệc - 52M950€ gid le

Sedimentary ES

Boginecus seaientay cones Secu siete Wmestne Metamorphic | Deviapea uncer nin resare | Chtaine nt, anos

stones: Tre hạt teresreve roe

Table 1 Classification of natural stones according tots formation, Muller [133] The fist stone masonry structure was bull using crude units As proficiency improved stone units were shaped inte polygonal or squared unils 50 that closefiting joints were biained,

Clay bricks wore in use for at least 10,000 years Sur-driod bricks (adobe masonry")

‘were widely used in Babylon, Egypt, Spain, South America, the Incian lands of the

" wade usage ste by te word “adobe ghi snow meapoaed inthe Engsh anguage bts a spanah ed barea onthe Srabowora at memingsn-ned wk,

United States and elsewhere The earlest bnck£ were made by pressing mud or clay into smal lumps, sometimes cigar-shaped, and letting them 0 dry in the air or the sun, Mortar is the material linking the units in masonry that closes the gaps and makes masonry monolithic In histocal masonry, itis usually compased of washed sand and ther aggregates vith 2 binder fo protect from erosion bythe vind and rain

‘The first mortars were made from cay bitumen or clay-straw mixtures It was pray Used to fil cracks and to afford uniform bedding for masonry uns In addition, the usage ofthe thin mortar joins was improved the ducabiy

‘The forerunners of modem mortars date to the use of calcined gypsum, time and natural pozzclans The Egyptians ullized calcines gypsum mortars to lbricate the beds of large Stones when they were being moved inlo postion It was discavered that lmestone wen burnt and combined with water, produced a material thal would harden with age

‘The eatiest documented usage of lime as a construction material was aporoximately

4000 BC when was used in Egyp for plastering the pyramids The mixing of ground lime

‘ith volcanic ash was prosiiced what became known as pozzolenic cement The Coliseum in Rome is an example øf 4 Roman structure that pozzolanic cement mortar Used as bonder and ithas been well survived aver many centuries, Hamid etal (76)

No significant developments in cements and mortars took place unt the eighteenth century when John Smeaton in the reconstuction of the Eddystone Lighthouse in England, mixed pazzolana with limestone containing a high proportion of cay to produce

8 durable morta that would set and harden under water

‘The next important development was the manufacture and patenting of Portland cement

by Joseph Aspain in England in 1824 The combination of Portland cement wih sand, lime and water produces much stronger mortar than what previously possible and ths, rmartar would also set and harden under water

In most historical masonry structures lime was used as mortar (Non-hydraulic ime, lime pully, dry-slaked lime, bag lime, hydraulc lime, Pozzolanic kme) Other mortars algo Used as natural pozzolana and brick powder, Mathows [125] Lime mortar crates good bending stength for masonry units, Besides, it increases the load bearing capacty particularly in flexural loacing ike what occurs during an earthquake

3.2 Failure behaviour of masonry

‘The fallure behaviour of masonry is fundamentally dominated by the propenies of ts components and the arrangement of units and thei interaction together tis therefore crucial fo realize the mechanical behaviour of the incvidual masonry components, units

ng mofar

When behaviour of masonry component needs to be investigated, the fst though is to

‘examine the constluenis disjointedly However, this is possible only for masonry units because the properties of mertar are influenced considerably by the interaction between

‘mortar and unt during hardening, Schubert [168] and Vermettfoort etal, (192)

3.2.1 Uniaxial failure behaviour of masonry unit

‘The earlier research works on he behaviour of masonry units were greatly Ieamed from the stusies in rock mechanics and concrete material inat were widely examined

Masonry units are heterogeneous materials belong to quasi-bitle materials which have

2 cisordered intemal structure It contains a large number of randomly onanted zones of potential failure inthe form of grain boundaries The designation “quasi-bitle® behaviour Feter to the transferred foree whch does not immediately drap back to zero, ather than

‘gradually decreases, Such behaviour is often denoted with softening, The softening auses localization of deformations that causes quick growtn of microcracks into Tacrooracks and finally to fully apen cracks

In recent decades, many experimental studies wore caried cut to understand the mechanical behaviour of masonry units The modern masomy unds received great

‘Studies in Iterator, for standardization and classification purposes The experimental Fecords forthe charactersic values of điferent masonvy uils ean be found in Marzann [120] Schuber [67], Schubert (185], Mann [118] Some mechanical properties for ferent natural stones are given in Table 2, Huster [83]

‘Quarzke sandstone vo200 {60250 [1220 [720 [2070 | 10-70

Meares vardsnes [2080 [8120 [o-8 eo |

Denes inetne wee | — |em se

Msrelsnostsimadose |2038 | com 4070 | 320

Table 2 Selected values of mechanical properties fr diferent natura stones

(i=Schubert(TB8] 2=IMamecke [186), tom Hustor (83)

= The mechanical properties of racks, lke compressive stength of elastic modulus are grealy dependent on physical properties of tne rocks such as porosily and Sensi

= Weathering conditions

= Petrography, mineralogical characteristics and grain size