Tesi Maria Ricamato

8/7/2019 Tesi Maria Ricamato

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Universit degli Studi di Cassino

Facolt di Ingegneria

Dottorato di Ricerca in Ingegneria Civile

XX Ciclo

Numerical and experimental analysis of

masonry arches strengthened with FRP

materials

Maria Ricamato

Cassino, Novembre 2007


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University of Cassino

Department of Engineering

Graduate School in Civil EngineeringXX Cycle - November 2007

Numerical and experimental analysis of masonry

arches strengthened with FRP materials

Maria Ricamato

Supervisor: Prof. Elio Sacco

Coordinator: Prof.ssa Maura Imbimbo


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To my mother and my father,

with love


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Acknowledgements

Three years ago this day seemed very distant, instead today I am working for

concluding my PhD thesis. At the end of this experience, first the financial supports

of the Italian National Research Council (CNR) and of The Laboratories University

Network of Seismic Engineering (RELUIS) are gratefully acknowledged.

My greatest thanks is for my Scientific fathers: Prof. Giovanni Romano for

having directed me towards the research and Prof. Elio Sacco for giving me the

opportunity to improve my scientific and technical knowledge, for the work done

under his supervision and for his useful suggestions.

I would like to thank Prof.ssa Sonia Marfia for the fruitful discussions and also

Prof.ssaMaura Imbimbo and Prof.Raimondo Luciano for their disposal.

I would like to express my gratitude to Prof. Olivier Allix of the ENS of Cachan

(France), who gave me the opportunity to spend part of my PhD under his

supervision. This period was very important for my experience, both from a

professional and personal point of view. A special thanks to Ing.Pierre Gosselet, for

his help to overcome many difficulties that I encountered with the multiscale

methods and to the LMT who hosted me for 6 months, in particular thanks to

Beatrice Faverjon who represented always a reference point also for human aspect.

I would like to express my deep and sincere gratitude to my friends and

colleaguesErnesto Grande and Veronica Evangelista, who spent several days with

me working hardly.

Many thanks toDIMSAT,LAPS and Geolab Sudstaff.

I would like to rememberall my friends for their friendship whenever I needed it.

Finally a great thank to my family: my motherFrancesca and my fatherLucio,for their love and support, my brotherNicandro for his humor that in times of

distress has been able to give me the courage to continue.

My gratitude to myFranco cannot be summarized in few rows: I will never forget

his love, his patience and his continuous support in what I do...


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INDEX

Acknowledgements.......................................................................................................4

1. INTRODUCTION ....................................................................................................9

1.1. Early static theories of the arch .......................................................................12

1.2. Motivations of the research and outline of the thesis......................................15

2. MASONRY MATERIAL.......................................................................................18

2.1. Introduction.....................................................................................................18

2.2. Mechanical behavior .......................................................................................19

2.3. Masonry modelling .........................................................................................23

2.4. No-tension material model..............................................................................25

3. FRP COMPOSITE MATERIALS FOR STRENGTHENING

MASONRY STRUCTURES......................................................................................28

3.1. Introduction.....................................................................................................28

3.2. Mechanical behavior .......................................................................................29

3.2.1. Alkaline ambient effects..........................................................................34

3.2.2. Humidity effects ......................................................................................35

3.2.3. Extreme temperature and thermal cycle effects ......................................35

3.2.4. Frost-thaw cycles effects .........................................................................35

3.2.5. Temperature effects .................................................................................35

3.2.6. Viscosity and relaxation effects ..............................................................36

3.2.7. Fatigue effects .........................................................................................36

3.3. Masonry structures reinforced with FRP materials.........................................36

3.4. Collapse mechanism for reinforced structures................................................38

4. EXPERIMENTAL PROGRAM .............................................................................40

4.1. Introduction.....................................................................................................404.2. Setup and instrumentations .............................................................................40

4.3. Preliminary experimental campaign ...............................................................42

4.4. Materials used in the experimental program...................................................44

4.5. Standard claybrick..........................................................................................44


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4.5.1. Cubic compressive test ............................................................................45

4.5.2. Indirect tensile test...................................................................................49

4.5.3. Elastic secant modulus ............................................................................53

4.6. Mortar..............................................................................................................59

4.6.1. Compressive tests ....................................................................................59

4.6.2. Elastic secant modulus ............................................................................62

4.7. Reinforcement material ...................................................................................64

4.8. Experimental test on the arches ......................................................................69

4.9. Arch laying......................................................................................................69

4.10. Arch preparation ...........................................................................................72

4.11. Experimental campaign:Arch 1....................................................................74

4.11.1. Collapse mechanism description ...........................................................76

4.11.2. Load-displacements curves ...................................................................78

4.12. Experimental campaign:Arch 2....................................................................83


4.12.2. Load-displacements curves ...................................................................85

4.13. Experimental campaign:Reinforced arch .....................................................88

4.13.1. Application of the FRP reinforcement ..................................................88

4.13.2. Test organization ...................................................................................91


4.13.4. Load-displacement curves.....................................................................95

5. MODELING AND NUMERICAL PROCEDURES..............................................99

5.1. Introduction.....................................................................................................99

5.2. Masonry constitutive models ........................................................................100

5.2.1. Model 1..................................................................................................1005.2.2. Model 2..................................................................................................103

5.3. FRP constitutive model .................................................................................105

5.4. Limit analysis................................................................................................107

5.5. Arch model....................................................................................................109


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5.5.1. Governing equation of the arch .............................................................110

5.5.2. Kinematics of the arch...........................................................................111

5.5.3. Cross section..........................................................................................111

5.6. Stress formulation .........................................................................................114

5.6.1. Complementary energy .........................................................................117

5.6.2. Arc-length technique .............................................................................120

5.7. Displacement formulation.............................................................................125

5.7.1. Kinematics.............................................................................................127

5.7.2. Finite element implementation..............................................................128

5.8. Post-computation of the shear stresses..........................................................131

5.9. Numerical results ..........................................................................................135

5.9.1. Models and numerical procedures assessment ......................................135

5.9.2. Experimental surveys numerical results................................................141

5.9.2.1. Comparison 1.................................................................................141

5.9.2.2. Comparison 2.................................................................................146

6. MULTISCALE APPROACHES ..........................................................................156

6.1. Introduction...................................................................................................156

6.2. Methods based on the homogenization.........................................................157

6.2.1. Theory of homogenization for periodic media ......................................158

6.3. Methods based on the super-position............................................................159

6.3.1. Variational multiscale method...............................................................160

6.4. Methods based on the domain decomposition ..............................................160

6.4.1. Primal approach.....................................................................................161

6.4.2. FETI method..........................................................................................165

6.4.3. Mixed method: the micro-macro approach ...........................................1666.5. Numerical results ..........................................................................................169

CONCLUSIONS ......................................................................................................175

APPENDIX: RELUIS SCHEDE..............................................................................177

NOTATIONS............................................................................................................187


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REFERENCES .........................................................................................................189


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1.INTRODUCTION Numerous ancient constructions are made of masonry material that is one of the

oldest building material. Many ancient and historical masonry buildings are

characterized by the presence of arches and vaults. In particular the arch is a

fundamental constructive element having both load-bearing and ornamental function.

The false arch was one of the first constructive elements. It was realized by flat

stones placed on top of each other that created a stepwise arch. The constructive

technique was refined during the centuries, also introducing the use of the mortar to

joint the stones or the bricks.

The Egyptian and the Babylonians introduced the use of arches in civil constructions,

the Assyrians constructed the first vaults in masonry buildings, the Etruscans used

arches in order to realize the first masonry bridges.

The Romans made large use of masonry arches and vaults for the constructions, not

only of buildings but also of roads, bridges, aqueducts and amphitheatres, as

illustrated in Fig. 1.1.

Fig. 1.1: The Colosseum, Roma.


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On the contrary, cult buildings were made using columns and architraves, as for

Greeks temples. One of the most representative cult building is the Pantheon of

Roma, characterized by the presence of a very well-known vaulted structure (Fig.

1.2).

Fig. 1.2: The Pantheon, Roma.

Moreover, Romans constructed arches also as monuments, like the triumphal

arches, e. g. the arch of Janus in Rome and the Triumphal arch in Paris (neoclassical

version of the ancient triumphal arches of the Roman Empire).

Fig. 1.3: The arch of Janus in Rome and Triumphal arch in Paris.

During the Middle-Age both the Byzantine architecture in the East and the Romanic

one in the West still adopted the Roman round arches.


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The Goths, in the 13th century, substituted the semicircular arch with the pointed

arch. A main characteristic of the Gothic structures is the lightness of the buildings,

obtained by the introduction of flying buttresses and towers. The Cathedral of Milan

is an example of Gothic structure, Fig. 1.4.

Fig. 1.4: Cathedral of Milan.

During the Renaissance, the churches assumed a great structural interest. In

particular the Church of S. Maria del Fiore in Florence and the Basilica di S. Pietro,

Fig. 1.5, represent great examples of regular shapes and geometrical symmetry due to

the use of vaults.

Fig. 1.5: S. Maria del Fiore and Basilica di S. Pietro.

Then no relevant or innovative solution concerning the structural conception were

developed, but still today the arch is a fundamental structural element and its use has


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been extended to all types of construction by the use of new material, like

reinforced concrete and steel.

1.1.Early static theories of the archThe arch is one of the most interesting structural elements in the construction history

because of its intuitive static behavior. During the centuries, many studies were

developed on the more appropriate shape of the arch, but only in the 17 th century a

static theory of the arch was proposed.

The Romans used systematically the arch realizing structure both of great value and

strong impact. The Roman scientist, Vitruvio, identified the main characteristics of

the arch and wrote ten books De Architectura, in which both the theory and the

practice concerning with the art of construction were presented. Vitruvio discussed

about the presence of the thrust of the vault on the supporting columns and walls. He

has also understood the functioning of the arched structures, suggesting to realize

strong and massive supports in order to contrast the thrust of the arches and vaults.

In the 13

th

century, Leon Battista Alberti wrote the De Re Aedificatoria, motivatingthe use of arched structures with the aim of increasing both of the spans and the

bearing capability.

A more refined theory was attributed to the constructors of the Middle-Age: its main

characteristic is the approximation of the arch shape by the thrusts line. Also the

geometrical rule to determine the thickness of the piers was attributed to them. This

theory was the only respected during the Renaissance. Leonardo Da Vinci (1452 -

1519) developed some ideas and intuitions three centuries later. He asserted arco

non altro che una fortezza causata da due debolezze imporoch larco negli edifici

composto di due quarti di circolo, I quali quarti circoli ciascuno debolissimo per se

desidera cadere e opponendosi alla ruina luno dellaltro, le due debolezze si


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convertono in ununica fortezzalarco non si romper se la corda dellarchi di fori

non toccher larco di dentro.

Fig. 1.6: Leonardos intuitive static scheme for the arch.

This theory for which the arch is assimilate to two beams was reproposed by Caplet

in the 18th century.

The first significant theory of the arch was attributed to the mathematician

astronomer Philippe de La Hire (1670 - 1718). In its treatise Trait De Mcanique,

posthumous published in 1730, he underlined the wedge mechanism of the arch.

According to him, the arch results subdivided in blocks and each block can be

considered like a piece of wedge incident on the mortar joints. Its model was the first

approach in the static theory of the arch that considers the masonry structure like a

rigid system of solids geometrically defined and with an own weight, neglecting the

frictional phenomenon. Two problems were faced by de La Hire: the vaults

equilibrium independent of its piers and the determination of the piers dimensions

considering the vault thrusts. The first problem lead, in the years, to the method of

polygon of the forces, while, concerning the second problem, he developed the basis

of the limit analysis.

In the 1785, Mascheroni, in theNuove ricerche sullequilibrio delle volte, proposed acollapse mechanism of the arch characterized by the formation of intrados cracks at

key, of extrados cracks at springers and of intrados cracks at piers extremities, as

schematically illustrated in Fig. 1.7.


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Fig. 1.7: Mascheronis collapse mechanism.

In the 19th century the method of the successive resultants was diffused. It was

adopted to study short span symmetric arches symmetrically loaded. It is based on

the definition of the thrusts line contained inside the third medium. The thrusts line

can be regarded as an indicator of stability: if it is not coincident with the center-line

of the arch, there is eccentricity and the arch thickness must be such that the

eccentricity remains inside the section.

The early method characterized by a collapse analysis was the method of Mery. This

method is based on the limit analysis and it is applicable only if the assumed collapse

mechanism occurs. It can be used if the arch is semicircular and its thickness is

constant, the maximum span of the arch is 8-10 metres, the arch is made of anhomogeneous material in order to be schematized by a rigid body, the arch is

symmetric and symmetrically loaded. The method of Mery can be applicable using

the parallelogram rule. In order to verify the part of the arch included between the

key and the springers, the arch must be subdivided in blocks of different dimensions.

Established the loads agent on each block, the resultants of loads are determined and

the thrusts line can be obtained applying the parallelogram rule again and again.

In the 1833, Moseley in the On a new principle in static called the principle of least

pressure enounced the least pressure principle for the determining the thrusts line of

the arch. In 1867 Winkler wrote a treatise on the thrusts line of the arch based on the

elasticity theory developed in those years.


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Recently, in 1982, Heyman in The masonry arches enounced the safe theorem of the

limit analysis particularized for the masonry arches. According to him, it is necessary

to determine at least one line of thrusts contained inside the thickness of the arch to

ensure that the structure is safe. On the other hand, it is sufficient a small variation in

the position of the line of thrusts, e. g. caused by loading increase, to allow the

formation of localized cracks. As consequence, the hinges formation can occur and a

kinematical mechanism can be activate. Generally, the collapse mechanism occurs

for formation of four hinges, two at extrados and two at intrados alternatively

located.

1.2.Motivations of the research and outline of the thesisThe preservation of historical and ancient buildings and monuments requires the

definition of intervention methodologies for the maintenance and consolidation. The

definition of these methods must reflect on one hand the structural safety, on the

other hand the respect of the original structure. The masonry arch is essential and

unique in the historic heritage. Some of the consolidation techniques of masonryarches, widely adopted in the recent years, can alter the nature and original structural

working of the arch and they also introduce extraneous elements not compatible with

the materials and traditional techniques. More recently, for the protection and

maintenance of ancient and historical buildings, the use of innovative materials, such

as composites, received great interest because of their possible advantages in terms

of low weight, simplicity of application, high strength in the fiber directions,

immunity to corrosion and reduced invasiveness. In particular, they appear

particularly indicated for the maintenance and rehabilitation of ancient structures

because they do not substantially violate the principles of the Carta di Venezia.

After the earthquakes of 1997 (Umbria and Marche), an intensive research activity

was developed for the definition of some rules for the design of the strengthening of


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masonry arches by FRP. In 2003 the CNR, The National Council of Researches,

established that it was necessary to elaborate a text containing the instructions for the

Design and Construction of Externally Bonded FRP Systems for Strengthening

Existing Structures, in order to give to engineers the guidelines for the use of fiber-

composite materials for the reinforcement of concrete and masonry structures. In the

year 2004 a full text CNR DT/200 was published in Italian and then in English

with the name. It could be emphasized that the DT200 is the first code in the world

which contains a Chapter completely dedicated to the use of FRP for the

strengthening of masonry structures.

The present PhD thesis is aimed to derive and to develop some simple strategies to

study the response of unreinforced and reinforced masonry arches. In particular, the

aim is to formulate simple and effective procedures that the engineers can use for the

design of the reinforcements of masonry arches, evaluating the safety of the

structure. In order to validate the effectiveness of the developed models and

procedures, an experimental campaign on un-reinforced and reinforced masonry

arches is conduced. Moreover, a more sophisticate numerical procedure, based on the

multiscale analysis, is developed.

Finally, the dissertation concerns with three macro-arguments: the experimental

program, the modeling and numerical procedures development and the multiscale

analysis.

In Chapter 2 a general overview on the modeling of masonry material is given. The

different modeling strategies are also discussed, underlining the main advantages of

each approach.

Chapter 3 analyzes the FRP properties. In particular an excursus on FRP material

history is made and its physical and mechanical characteristics are presented.Chapter 4 contains the description of the experimental program. In order to

characterize the nonlinear behavior of the masonry material, the physical and

mechanical properties of masonry material constituents are investigated through

experimental test. Moreover an experimental campaigns is realized on unreinforced


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and reinforced masonry arches. The adopted procedure for testing the arches is

described and the experimental results are discussed.

In Chapter 5 the modeling of masonry materials and FRP and the developed

numerical procedures are illustrated. In particular the masonry material is assumed as

a no-tensile material with a limited compressive strength, while the reinforcement is

considered as an linear elastic material. Two different approaches are developed: a

stress formulation, based on the complementary energy, and a displacement

formulation, characterized by the implementation of a three node beam finite element

based on the Timoshenkos theory. Several numerical analysis are conduced in order

to validate the models and the developed numerical procedure. The numerical results

are also put in comparison with experimental results both available in literature and

obtained during the experimental campaign.

Chapter 6 illustrates a brief introduction to the multiscale methods; in particular the

domain decomposition methods are analyzed.

At the end, a summary and final conclusions, which can be deduced from this

research, are given.


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2.MASONRY MATERIAL

2.1.IntroductionThe masonry material is one of the oldest building material, as confirmed by the

historical heritage. The development of adequate stress analyses for masonry

structures represents an important task not only to verify the stability of masonry

constructions, as old buildings, historical town and monumental structures, but also

to properly design effective strengthening and repairing works. In fact, many of

masonry structures have been suffered from the accumulated effects of material

degradation, aging, overloading and foundation settlements. For this reason, the

rehabilitation and the maintenance of existing masonry structures represent an

important topic. In the years several studies have been developed related to masonry

structures, i.e. [1] - [38], mainly devoted to the development of new restoration

technologies and, moreover, to the definition of effective computational procedure

for reliable stress analyses.It could be emphasized that the analysis of masonry structures is not simple at least

for several reasons:

the masonry material can be considered as a composite material obtained byassembling bricks by means of mortar joints;

the masonry material presents a strongly nonlinear behavior, so that linearelastic analyses generally cannot be considered as adequate;

the structural schemes which can be adopted for the masonry structuralanalyses are more complex than that adopted for concrete or steel framed

structures, as masonry elements are often modeled by two- or three-

dimensional elements.


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As a consequence, the behavior and the analysis of masonry structures still represent

one of the most important research field in civil engineering, receiving great attention

from the scientific and professional community; for instance, in Reference [1]

several specific problems related to the design and behavior of old and mainly new

masonry constructions are discussed.

In this chapter a brief discussion on the main aspects concerning the mechanical

behavior of the masonry material, i.e. [2] - [5], is reported.

2.2.Mechanical behavior

The mechanical behavior of the masonry material presents complex aspects due to

the fact that it is a composite material made of units of natural or artificial origin

(irregular stones, ashlars, adobes, bricks and blocks) jointed by dry or mortar joints

(commonly clay, lime or cement based mortar). The units can be jointed together

using mortar or just by simple superposition obtaining different combinations that

can be classified [6] in stone masonry and bricks masonry, as illustrated in Fig. 2.1

and Fig. 2.2, respectively.

Fig. 2.1: Stone masonry (a) rubble masonry, (b) ashlar masonry, (c) coursed ashlar masonry.

(a) (b) (c)


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Fig. 2.2: Brick masonry, (a) common bond, (b) cross bond, (c) Flemish bond, (d) stack bond, (e)

stretcher bond.

The heterogeneity of the masonry material, which depends on the assemblage of its

constituents (brick and mortar, as previously seen), leads to a complex structural

behavior. Generally, the behavior of the masonry is intermediate between the

behavior of the brick and mortar, as shown in Fig. 2.3.

Fig. 2.3: Qualitative stress-strain diagram in uniaxial tension and compression.

In Tab. 2.1 the mechanical characteristics of the masonry constituents are reported.

Mortar

MasonryBrick


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Mortar Brick

Compression

Strength [MPa]

3.0 - 30.0 6.0 - 80.0

Tensile Strength

[MPa]

0.2 - 0.8 1.5 - 9.0

Tensile Modulus

[MPa]

(8.0 - 20.0)

103.0

(15.0 - 25.0)

103.0

Poissons coefficient 0.10 - 0.35 0.10 - 0.25

Tab. 2.1: Mortar and brick mechanical characteristics.

While the bricks properties are generally defined on the base of brick type, the

mortar mechanical properties depend strongly as much on the natural materials of

which it is constituted as on the procedures of manufacturing; indeed, the mortar

strength is influenced a lot by the binder and the dosage. According to the Italian

Code 20/11/1987 (Norme tecniche per la progettazione, esecuzione e collaudo degli

edifici in muratura e loro consolidamento) and the previous and successive rules,

four classes of mortar have been specified, as reported in Tab. 2.2.

Cement Common

lime

Water

lime

Sand Pozzolana

M4 Grout - - 1 3 -

M4 Pozzolana

mortar

- 1 - - 3

M4 Cement lime 1 - 2 9 -

M3 Cement lime 1 - 1 5 -

M2 Mortar of

cement

1 - 0.5 4 -

M1 Mortar of

cement

1 - - 3 -

Class Kind of

Mortar

Composition

Tab. 2.2: Mortar classes.


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Subjected to a uniaxial load, the masonry material has a stress-strain curve that

presents a brittle failure, characterized by a compression stress failure value greater

than the tensile one, as illustrated in Fig. 2.4. In particular, it can be individuated the

following characteristic features:

compressionOA that is essentially linear; AB characterized by a nonlinear behavior,

increasing until the maximum value of the compression stress; BC,

decreasing feature with nonlinear behavior and softening;

tensionOI very short feature that has a linear behavior and IL decreasing feature.

Moreover, the point B represents the peak load and the point C represents the point

in correspondence of which the masonry material collapses in compression.

Fig. 2.4: Stress - strain masonry curve.

An important feature, common to all cohesive materials, is the occurrence of

softening, which is defined as a progressive decrease of the mechanical strength

under continuous imposed displacement, after the load peak. Softening behavior is

experimentally observed in uniaxial compressive, tensile and shear failure.

B

A

I L

O

C


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relationship of the masonry, accounting in a suitable manner for the

mechanical properties of each material component. Moreover, this approach

can lead to effective models, with reduced computational effort for a

structural analysis (i.e. Luciano and Sacco [13], Milani et al. [14], [15]). On

the other hand, the non-linear homogenization procedure required to recover

a macro model could induce some theoretical or computational difficulties

[16].

Macro-models are based on the use of phenomenological constitutive lawsfor the masonry material; i.e. the stress-strain relationships adopted for the

structural analysis are derived performing tests on masonry, without

distinguishing the blocks and the mortar behaviour. A phenomenological

model could be unable to describe in a detailed manner some micro-

mechanisms occurring in the damage evolution of masonry, but it is very

effective from a computational point of view when structural analyses are

performed [17], [18].

The linear elastic model is the simplest approach to the analysis of masonry

structures. In the linear elastic model the material exhibits an infinite linear elastic

behavior, both in compression and tension. The structural response obtained under

the hypothesis of linear elastic behavior, although often not completely reliable for

ancient constructions [19], can be of great help; in fact, the linear analysis requires

few input data and it is less demanding, in terms of computer resources and

engineering time used when compared with non-linear models. Moreover, for

masonries characterized by significant tensile strength, linear analysis can provide a

reasonable description of the process leading to the crack pattern.


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2.4.No-tension material modelBecause of the very low tensile strength of many masonries with respect to the

compressive strength, a no-tension model is often adopted; it is based on the

assumption of zero the tensile strength of the material, as illustrated in Fig. 2.5,.

The no-tension material (NTM) model (i.e. [20] and [21]) leads to a realistic

approximation for the evaluation of the mechanical response of the masonry

material. In fact, the collapse mechanism of old masonry constructions is often due to

the opening of cracks in tensile zones. The use of the no-tension model allows to

compute the limit carrying load for masonry structures invoking the limit analysis

theorems.

Fig. 2.5: Linear elastic model with no tensile strength.

The no-tension material model is based on the fundamental hypothesis that the

tensile strength is zero while it considers a linear elastic behavior in compression.The no-tension model presents the following very special properties: a convex strain

energy function governing the stress-strain relationship exists, thus the constitutive

law results to be reversible and there is no energy dissipation for the crack formation

and evolution.

O


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The question regarding the safety of the no-tension approach with respect the

fracture mechanics solution was discussed by Bazant [22], who proved that the no-

tension model is not always safe with respect to the fracture mechanics approach.

The problems considered by Bazant concern the case of fractured rocks,

characterized by the presence of a preexistent localized crack; for old masonry

structures, which present sufficiently densely distributed microcracks, the no-tension

model can be considered reliable.

The no-tension material model received and still receives great attention by many

researchers to study the behavior of old masonry structures. Indeed, the statement

no tension material was proposed by Zienkiewicz et al. [23] to study the behavior

of fractured rocks. Then, several studies were developed regarding the NTM from a

mechanical, i.e. [24] - [28], mathematical [29] and computational point of view,

developing displacement, i.e. [30] - [32], as well as stress and mixed variational

formulations, i.e. [33] - [35]. It could be emphasized that, although the NTM presents

and apparent simplicity, its numerical treatment is not trivial.

The assumption of a masonry linear elastic behavior in compression can be

considered adequate only when the evaluation of the load carrying capacity of the

structure occurs for a collapse mechanism accompanied by very low compressive

stresses; on the contrary, when the compression strength plays a significant role in

the evaluation of the structural collapse load, the no-tension model appears

inadequate. This case may occur, for instance, for shear masonry panels, building

walls and strengthened arches, where the presence of

the reinforcement can prevent the formation of hinges.

A first proposal of a no-tension model with limited compressive strength has been

presented in Reference [36]. The model proposed by Lucchesi and coworkers is based on two fundamental assumptions: the stress-strain relation is again

hyperelastic, so that the crushing of the material is considered to be reversible, and

the inelastic strain in compression is always orthogonal to the fracture strain. Indeed,

the crushing strain is quite irreversible in character and it could not also be


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orthogonal to the fracture strain, during the whole loading history. As matter of fact,

the compression failure is affected by progressive damage and inelastic irreversible

strain. In order to derive a simple and effective model, Marfia and Sacco [18]

developed a no-tension model which accounts for the inelastic behavior in

compression, considering a plasticity model which neglect the damage and softening

effects. The derived model appears appropriate for the description of the material

crushing when limited values of the compressive strain arise.

The elasto - plastic model is characterized by a first linear elastic feature OA and a

plateau with a constant stress DE, as schematically illustrated in Fig. 2.6.

Fig. 2.6: Elasto - plastic model.

A delicate point is the determination of the point D: it can be fixed to avoid to

underestimate the masonry stress and to ensure a safe state, far from point E. The

possibility to determine the collapse load of masonry and the irreversible nature of

strains in the plateau DE for cyclic load are the principal characteristics of this model[37].


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3.FRP COMPOSITE MATERIALS FORSTRENGTHENING MASONRY STRUCTURES

3.1.IntroductionIn the last decades the use of innovative materials, such as composites, received great

interest because of their possible advantages in terms of low weight, simplicity of

application, high strength in the fibers direction, immunity of corrosion and quite

reduced invasiveness. The use of Fiber Reinforced Polymers (FRP), that are a class

of composite materials characterized by the combination of high-strength fibers and a

matrix, is growing in the different fields of the engineering. Initially adopted for

applications in aircraft and space industries, FRP have been used in the medical,

sporting goods, automotive and small ship industries (see Fig. 3.1) due to their high

strength in the fibers direction.

Fig. 3.1: Ordinary FRP devices and appliances.


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The greater reduction of the fibers prices, due to their increasing use and to an

optimization of the production processes, have recently concurred to their diffusion

also in the field of the civil constructions. In particular, they appear particularly

indicated for the maintenance and rehabilitation of ancient structures because they do

not substantially violate the principles of the Carta di Venezia, as they can be

considered (quite) reversible and distinguishable.

3.2.Mechanical behaviorThe FRP are composite materials constituted by two phases: polymeric matrix and

high-strength fibers. The two phases are visible at microscope and they present

mechanical and geometrical properties sufficiently different, as consequence the

composite has mechanical properties different from those of the constituents ones.

The nature of every phase influences significantly the final properties of the

composite; however, in order to obtain a composite with a high mechanical

resistance, it is not sufficient to use only resistant fibers: it is also necessary to

guarantee a good adhesion between the matrix and the reinforcement. The adhesionis usually guaranteed by the employment of a third component, called interface or

interphase, applied in a much thin layer on the surface of fibers, between fibers and

matrix, as schematically illustrated in Fig. 3.2.


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Fig. 3.2: FRP phases.

The interphase, whose characteristics are fundamental for the good use of thematerial in structural applications, is usually a thin and monoatomic layer. In fact, the

lack of adhesion between fiber and matrix is one of the causes of the structural

yielding of the composite materials.

The organic matrices guarantee the transfer of the stresses between the surrounding

structure and the fibers embedded in it, protecting these last ones from the

aggressions of the external agents and from mechanical hit. The matrices, more used

for the fabrication of FRP, are the polymeric ones made up of thermosetting resins.

These resins are available in shape partially polymerized and they are liquid or dense

at ambient temperature. The resins, mixed with an opportune reagent, polymerize

until becoming a vitreous solid material. The matrices have various advantages: they

are characterized by capacity of impregnation of the fibers, by optimal adhesive

properties, by good resistance to the chemical agents. Their main limitations are the

temperatures of exercise, limited from the upper by the vitreous transition

temperature, the brittle failure, the sensibility to the humidity in phase of application

on the structure. The epoxy resins are the more utilized: they have a good resistance

to the humidity and the to chemical agents and optimal adhesive property.

INTERFACE

FIBERMATRIX


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The fibers more used for composite materials employed in the applications of the

civil engineering are: glass (Fig. 3.4), carbon (Fig. 3.3), and aramidic (Fig. 3.5)

fibers.

Fig. 3.3: Carbon fibers at microscope.

Fig. 3.4: Glass fibers.

Fig. 3.5: Aramidic fiber.

The glass fibers have an elevated resistance to the corrosion, an elastic modulus

lower than those of carbon and aramidic fibers, a quite reduced resistance to the

abrasion, a discreet strength to plastic slip and to fatigue. In order to promote the

adhesion between fibers and matrix and to protect fibers from the action of the

alkaline agents and from the humidity, the fibers undergo special treatments. In the


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operations of manipulation before the phase of impregnation great caution is

necessary. For their easy damage during the treatments, they are covered from a

protecting film that inhibit the installation of acid dioxides contained in the air,

which, otherwise, would penetrate in the microscopic voids present on the surface.

The aramidic fibers are of organic nature and they are characterized by an elevated

resistance to the manipulation operations. The modulus and the tensile strength are

intermediate between those of carbon and glass fibers, while the compressive

resistance is approximately equal to 1/8 of the tensile one. They are characterized

also by an elevated degree of anisotropy that favors the localized rupture with

consequent instability. They can be degraded for extended exposure to the solar light

and it is preferable not to use them at temperatures greater than 150C for problems

of material oxidation. Moreover, they are sensitive to the humidity.

The carbon fibers are used for the fabrication of composite materials with elevated

performances; they are distinguished for the high modulus and resistance. They

exhibit a behavior with brittle failure. The crystalline structure of the graphite is

hexagonal, with carbon atoms organized in structures essentially planar, tied from

interaction transverse forces of van der Waals.

The precursors of carbon fibers are the polyacrylonitrile (PAN) and the Rayon fibers.

Starting from these, through a process of carbonization combined with thermal

processes and the sizing process, two types of carbon fibers are produced: the High

Strength (HS) and the High Modulus (HM).

The carbon fibers are often dealt with epoxy materials that prevent the abrasion,

increase the workability and realize a good compatibility with the matrices made up

of epoxy resins. The principal properties, as tensile modulus and tensile strength, of

some fibers used for composite materials are reported in Tab. 3.1.


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Tensile

modulus [Gpa]

Tensile strength

[Mpa]

Failure

strain [%]

Coefficient of

thermal expansion

Density

[g/cm^3]

Fiber E-glass 72 - 80 3445 4.8 5 - 5.4 2.5 - 2.6

Fiber S-glass 85 4585 5.4 1.6 - 2.9 2.46 - 2.49

Graphite fiber (high modulus) 390 - 760 2400 - 3400 0.5 - 0.8 -1.45 1.85 - 1.9

Graphite fiber (low modulus) 240 - 280 4100 - 5100 1.6 - 1.73 -0.6 - -0.9 1.75

Aramid fiber 62 - 180 3600 - 3800 1.9 - 5.5 -2 1.44 - 1.47

Polymeric matrix 2.7 - 3.6 40 - 82 1.4 - 5.2 30 - 54 1.10 - 1.25

Steel 206 250 - 400 (yield)

350 - 600 (failure)

20 - 30 10.4 7.8

Tab. 3.1: Properties of FRP constituents.

The most common shape for the composite materials is the laminate one. The

laminates are constituted by two or more overlapped thin layers, called lamina, (see

Fig. 3.6).

1

2 x=1

2

x

1

2

z

Y

X

x

Fig. 3.6: Laminate constituted by more laminas.

The main advantage of laminates is the maximum freedom in the disposition of

fibers. In each plane, the direction of fibers can be chosen in order to obtain the

desired physical and mechanical characteristics of the laminates. On the basis of the

mechanical properties that have to be conferred to the laminate, different types offibers can be adopted. For instance, hybrid laminates are obtained by assembling

layers of epoxy resin reinforced by aramidic and carbon fibers, or by alternating

layers of epoxy resin with aramidic or aluminum fibers. The orientation of fibers is

one of the main aspects that determines the behavior of the composite material. A


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disposition of unidirectional fibers, as schematically illustrated in Fig. 3.7, leads to

an orthotropic response of the lamina.

Fig. 3.7: Laminate with unidirectional fibers.

With this type of disposition, the best mechanical properties is obtained in the

direction of fibers. A bidirectional disposition confers to the composite mechanical

characteristics which depends on the chosen fiber direction.

Beyond to the orientation also the length, the shape, the composition and the

percentage in volume of fibers, the mechanical properties of the resin and the

interface influence the response of the composite.

The mechanical properties (strength, strain, tension modulus) of some FRP systems

degrade in presence of determined environmental conditions, i.e. alkaline ambient,

extreme humidity, temperatures, thermal cycles.

3.2.1.Alkaline ambient effectsThe pores of the material that must be reinforced content water that can degrade the

resin and the interphase. It is necessary that the resin complete the curing before the

exposition to alkaline ambient.


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3.2.2.Humidity effectsThe main effects connected to the absorption of humidity regard the resins; they are

plasticization, reduction of vitreous transition temperature, strength and stiffness

reduction. The absorption of humidity depends by the kind of resin, the composition

and number of laminas, the curing conditions, the interphase and the processing.

3.2.3.Extreme temperature and thermal cycle effectsThe main effects of temperature are connected to the viscous answer of the

composite. At the service temperature of most structures, the resins are stable, but

when the temperature increases, the resin breaks down and evaporates; the composite

performances strongly decrease when the temperature exceeds the vitreous transition

one. The thermal cycle have not deleterious effects, even if they can favor the

formation of micro-fractures.

3.2.4.Frost-thaw cycles effectsThe exposition to frost-thaw cycles do not influence the performance of the

composites, but can reduce those of the resin and the interphase, because of the

separation between fibers and matrix.

3.2.5.Temperature effectsThe increasing of the temperature involves a gradual degradation of the mechanical

properties of composite in terms both of tensile strength and stiffness.


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3.2.6.Viscosity and relaxation effectsIn a composite material, viscosity and relaxation depend from the properties of resin

and fibers. The presence of fibers reduces the viscosity of the resin; the worse effect

occurs when the load is applied in the direction orthogonal to the fibers or when the

composite is characterized from one low percentage in volume of fibers. The

viscosity can be reduced if it is assured a low stress in exercise.

3.2.7.Fatigue effectsThe performances of FRP under fatigue are very good and they are connected to the

composition of matrix. In the unidirectional composites, fibers have got little defects

and, consequently, they contrast the formation of fractures. Moreover the

propagation of eventual fractures is limited from the action explicated from the fibers

staying in the adjacent zones.

3.3.Masonry structures reinforced with FRP materialsIn the last years, a significant research activities has been performed to investigate on

the possibility to adopt composite materials as reinforcement of the masonry

buildings. Starting from the earliest works, Triantafillou and Fardis [38], several

studies have been devoted to the evaluation of the advantages in terms of resistance

and ductility, for the use of FRP for the strengthening of masonry constructions.

Indeed, researches demonstrate that the use of FRP for the strengthening of masonry

structures is very effective for different structural elements as masonry panels, but

also arches and vaults.


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Several researches have been oriented to the analysis of masonry walls reinforced by

FRP sheets or laminates, subjected to in-plane and out-of-plane loads. The possibility

of adopting FRP composites for strengthening of masonry was initially investigated

by Croci et al. [39]. They presented the results of experimental tests performed on

wall specimens reinforced by vertical FRP materials. Experimental investigations on

the use of epoxy-bonded glass fabrics were developed by Saadatmanesh [40] and by

Ehsani [41]. Luciano and Sacco [13], [42] and Marfia and Sacco [43] proposed

micromechanical models to study the behavior of masonry elements reinforced with

FRP sheets. Cecchi et al. [44] developed a homogenization technique to evaluate the

overall behavior of reinforced masonry walls.

Experimental tests, performed by Schwegler [45] and Laursen et al. [46],

demonstrated the significant improvement of the in-plane shear capacity and the

important increase of the ductility of masonry walls strengthened with FRP

laminates. Triantafillou [47] and Velazquez et al. [48] developed experimental

studies, showing that the flexural capacity of masonry walls can be drastically

increased strengthening the panels with FRP laminates. Olivito and Zuccarello [49]

presented the durability of masonry structures reinforced by FRP subjected to low

cycle fatigue.

In the last few years great interest was devoted to the reinforcement of masonry

arches and vaults, probably as a result of the recent Umbria- Marche seismic events.

In fact, aramidic fiber reinforced composites were adopted to restore the vaults of the

Basilica di S. Francesco dAssisi [50] and the Chiesa di San Filippo Neri, in Spoleto

[51]. Como et al. [52] applied the limit analysis theorems in order to evaluate the

collapse of reinforced arches. Olivito and Stumpo [53] proposed a numerical and

experimental analysis of vaulted masonry structures subjected to moving load.Briccoli Bati and Rovero [54] and Aiello et al. [55] developed experimental

investigations on reinforced masonry arches, emphasizing that the application of

sheets or laminates of composite materials significantly increases the strength of the

structure, modifying the collapse mechanism and the corresponding collapse load.


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Chen [56] presented a method to calculate the limit load-bearing capacity of masonry

arch bridges strengthened with FRP. Experimental tests and finite element analyses

of masonry arches made of blocks in dry contact and reinforced by FRP materials

have been developed by Luciano et al. [57], demonstrating the effectiveness of

strengthening. Foraboschi [58] presented mathematical models for studying the

possible failure modes of masonry arches and vaults with FRP reinforcement.

Ianniruberto and Rinaldi [59] investigated on the influence of the presence of FRP to

the collapse behavior of the structure when reinforcements are placed at the extrados

or at the intrados of the arch.

It can be emphasized that the collapse of masonry elements is generally induced by

the opening of fractures due to the limited strength in tension. The presence of the

FRP reinforcement, placed in the tensile zones of the masonry structure, inhibits the

opening of the fractures; thus, a compression state can occur for bent elements, and

the failure for crushing can be activated. As a consequence, a suitable masonry

model for reinforced masonry should take into account the possibility of the collapse

for compression, i.e. a limited compressive strength for the masonry material should

be considered.

3.4.Collapse mechanism for reinforced structuresWhen a masonry structure is reinforced, the collapse mechanism changes with

respect to the unreinforced one. Indeed, the collapse of a reinforced masonry

structure can occur for the activation of different failures: opening of cracks in the

masonry for tensile stresses, crushing of masonry in compression, shear failure of the

masonry, decohesion of the FRP from the masonry and failure of the reinforcement,

i.e. [54], [60] and [61]. While the unreinforced masonry collapses generally for

activation of mechanisms due to the very limited tensile strength of the masonry or

for shear failure, for reinforced masonry the limited compressive strength of the


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masonry and the delamination phenomenon can play fundamental roles in the overall

collapse of the structure.

Crushing of masonry in compression and reinforcement failure are strictly connected

to the mechanical properties of masonry and reinforcement fibers respectively, while

the decohesion phenomenon regards the interface masonry-FRP. The adhesion

between masonry and composite is a very relevant factor in the masonry

reinforcement by laminas or woven. The debonding can regard both laminas and

woven applied on the extrados or intrados surface of the reinforced element. The

understanding of the debonding mechanism is very important for the successful

application of the external FRP reinforcement; it is necessary to know when

debonding initiates and the parameters that influence it. The decohesion can be

classified in Plate-end debonding (it initiates at a plate-end and propagates inwards)

and Intermediate crack debonding (it initiates at a crack in the structure mid-span

zone and then it propagates towards the nearest zones).


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4.EXPERIMENTAL PROGRAM

4.1.IntroductionThe experimental program was realized at LAPS, Laboratories of Structural Analysis

and Design of University of Cassino, with the collaboration of the Geolab Sud of San

Vittore del Lazio. The experimental tests were performed at the Geolab laboratory

and part of the instrumentation was supplied by them.

In order to determine the correct setup of the used instrumentation it was necessary

to perform a preliminary experimental campaign on a steel beam.

4.2.Setup and instrumentationsSeveral instrumentations were necessary to perform the experimental program; in

particular, the devices to determine displacements, the strain gauges, the hydraulic jack to apply the external load, the load cells and the data acquisition system were

used. Two instruments were adopted to determine the displacements: comparators

and potentiometers.

The comparator used in the experimental program is a dial gauge; the instrument

bases its functionality on the displacement of a cylindrical rod that can be flow into a

tubular guide for a maximum value of 100 mm. It is positioned on the interested

surface, so the tracer point is in contact with the surface of the specimen subjected to

the measurement.

The potentiometer has the same performances of the dial gauge; it is composed by a

cylindrical rod that can move into a tubular guide until 100 mm. On the extremity of


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the rod there is a magnet that fixes the potentiometer to the interested surface on

which a metallic element has been previously glued.

The load was applied by an hydraulic jack and it was measured by two electric load

cells. The load cells have a maximum value of 50 kN and 500 kN respectively; they

are constituted by an inox steel body with an electronic device that allows to convert

the mechanical tensile or compressive load into an electric signal. There is an

optional plate that allows a more homogeneous load repartition on the body cell. The

electronic device is constituted by resistive strain-gauges connected by an electric

Wheatstone bridge.

In the experimental program, two electric digital data acquisition systems,Leane and

Wshay, were used. When it is subjected to load, each load cell emits an electric

differential signal which is transmitted by a connector to the data acquisition system;

the aim of data acquisition system is the data elaborations, i.e. the conversion of the

electric signal into mechanical engineering quantities. So the data acquisition system

allows the measurement by the manual or automatic data acquisition. The Washay is

a model P3 Strain Indicator and Recorder; it is portable and alimented by battery; its

data acquisition is manual. The measurements obtained by this data acquisition

system were used to verify the correct working of theLeane data acquisition system.

Leane is a portable data acquisition system characterized by electric and battery

alimentation. The data acquisition system has seven modules and four channels for

each one; in total it is possible to have 28 acquisitions at the same time. In the

experimental program, Leane was used for the acquisition in continuous of the

potentiometers and of the cell load of 5 t. TheLeane acquisitions are transmitted to a

PC by a cable and then, the results can be worked out by a software given by the

Leane.


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4.3.Preliminary experimental campaignThis preliminary experimental campaign was necessary to validate the data

acquisition systemLeane, in particular to verify that the in continuous displacements

acquisition did not depend on the potentiometers position on the data acquisition

system channel and they were not different from the displacements measured using

the comparators. It was necessary to calibrate a new load cell of 50 kN, called in the

following as small load cell. The load values of the 50 kN load cell acquired with the

Leane are in accordance with those measured by the 500 kN load cell, called in the

following as great load cell, acquired with the Wshay. The specimen of preliminary

tests campaign was a steel beam and the tests were organized in TEST A

(potentiometer calibration and displacement acquisition crosscheck), TEST B (small

load cell calibration) and TEST C (small load cell acquisition by Leane crosscheck).

TEST A

The aim of the test A was the potentiometers calibration and the crosscheck of the

correct displacements acquisition obtained by the potentiometer connection to the

different channels ofLeane.

The potentiometers were connected to data acquisition system Leane to have the

displacements in correspondence of each load variation, in continuous. As previously

seen, withLeane it is possible to have 28 acquisitions; the steel beam was subjected

to 6 load cycles, called Test 1, Test 2, Test 3, Test 4, Test 5 and Test 6, characterized

by the same load steps. In every load cycle, the potentiometer position on the data

acquisition system module was changed to validate the different acquisitions

obtained for every module and to validate the acquisitions obtained for every

different channel of each module.

In the Test A it can be pointed out that the difference between the various

displacement acquisitions is in all the cases lower than 0.1 mm. The channel 4 of the


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module 1 does not work. The difference between the displacement values registered

by potentiometers and comparators is satisfactory.

TEST B

This campaign had the aim to calibrate the new small load cell. It was possible to put

in comparison the acquisitions obtained from the small load cell and the acquisitions

obtained by the great load cell, both connected with the data acquisition system

Wshay.

The maximum error of test resulted equal to 1%; thus, it can be pointed out that the

new small cell works in good accordance with the normalized great one.

TEST C

This campaign had the aim to verify the correct functionality of the small cell

connected with the data acquisition systemLeane.

The Test C puts in evidence that the difference between the manual and automatic

acquisition of the load is, on average, lower than 2%.


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4.4.Materials used in the experimental programThe determination of the physical and mechanical properties of the materials used in

the experimental program is necessary to understand the behavior of reinforced

masonry arches. In the following the properties of the masonry material constituents

and of the reinforcement are presented.

The masonry material is composed by standard clay bricks and mixed mortar. At

LAPS, Laboratories of Structural Analysis and Design of University of Cassino, with

the collaboration of the Geolab Sud of San Vittore del Lazio, an experimental

program both on standard clay brick and mortar was performed.

For what concerns the reinforcement, it is composed by carbon fibers and epoxy

matrix and their properties were given by the manufacturer.

4.5.Standard claybrickIn the experimental program, standard clay bricks (Fig. 4.1) were used.

Fig. 4.1: Standard clay brick.


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In order to determine its main mechanical properties, the standard clay brick was

subjected to several experimental tests. In particular, a cubic compressive test, an

indirect shear test and a test to individuate the elastic secant modulus were

performed.

4.5.1.Cubic compressive testStandard clay brick cubic specimens were prepared in order to determinate the

compressive strength, in accordance with UNI 8942/3. This code gives the guidelines

for the determination of the unitary load of compressive failure strength, that has to

be determined on a fixed number of specimens with prefixed geometric

characteristics. According to the code, the tests have to be performed on cubic

specimens with orthogonal faces and parallel plane of the bedding plane, as


Fig. 4.2: Cubic specimen extrapolated by standard clay brick.

The specimens were located on the Galdabini SUN 60 that is a universal testing

machine with a 600 kN nominal capacity, used in displacement control. A series of

pre-loading tests finalized to set the machine and to position the specimens into its

slabs were realized before the compressive test. The failure load was obtained from


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the yielding load of every specimen. Then the other parameters necessary to

characterize the test results were determined:

average compressive strength:

1

n

bi

ib

f

fn

==

(4.1)

wherebi

f is the result of the single test and n is the number of test results;

standard deviation:

( )2

1

n

b bi

i

f f

sn

=

=

(4.2)

variation coefficient:

v

b

sc f= (4.3)

characteristic value:

( )1bk b vf f kc= (4.4)

where k is the fractile coefficient, fixed by normative in function of the number oftested specimens.

The compressive test was realized on 6 cubic specimens extracted by one of the

series of the standard clay brick; their dimensions are reported in Tab. 4.1.


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Specimen

[number]

Deep

[mm]

Length

[mm]

Heigth

[mm]

1 55 56 55

2 55 55 54

3 56 55 55

4 55 55 55

5 55 55 54

6 55 55 55

Tab. 4.1: Specimens size.

A carton layer was interposed at the top of the specimen in order to distribute the

compressive stress. The specimen was allocated into the press, Fig. 4.3.

Fig. 4.3: Specimen positioning.

The specimen was subjected to an axial load acting perpendicular to the bedding

plane until its failure, Fig. 4.4.


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Fig. 4.4: Typical failure of the specimen.

The failure load and the compressive strength were determined for each specimen, as

reported in Tab. 4.2

Specimen

[number]

Area

[mm2]

Failure

load [kN]

Compressive

strength (fb)

[kN/mm2]

1 3080 127.883 0.0415

2 3025 107.918 0.0357

3 3080 125.144 0.0406

4 3025 104.944 0.0347

5 3025 110.894 0.0366

6 3025 126.239 0.0417

Tab. 4.2: Compressive test results.

The considered specimens exhibited a hourglass failure, Fig. 4.5, not perfectly

symmetrical because of the heterogeneous nature of the bricks.


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Fig. 4.5: Hourglass specimens failure.

The characteristic compressive strength was determined, using equations (4.1), (4.2),

(4.3) and (4.4) and in accordance with the code for which k=2.33 ifn=6; the results

are reported in Tab. 4.3.

Average compressive

strength [N/mm2]

Standard deviation

[N/mm2]

Variation

coefficient

Characteristic

compressive strength

(fbk) [N/mmq]

38.5 7.47 0.23 14.9 Tab. 4.3: Characteristic compressive strength.

4.5.2.Indirect tensile testThe indirect tensile test was realized in accordance with UNI 8942/3, which gives the

guidelines for the determination of the yielding load of specimens subjected to a

uniform load applied on the middle surface of the specimen, as schematically



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Fig. 4.6: Indirect tensile test scheme.

The code prescribes that this test has to be performed on specimens with a low

drilling percentage (the limit is fixed at 30%). The test was performed using the

Galdabini SUN 60 and it was executed with constant load increments until the

failure. In order to diffuse the load two steel beam, whose dimensions were fixed by

the code, were interposed between the specimen faces and the steel plates of the

machine, as illustrated in Fig. 4.7.

Fig. 4.7: In direct tensile test particular.

The indirect tensile test was realized on 6 specimens whose dimensions are reported

in Tab. 4.4.

F


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Specimen

[number]

Deep

[mm]

Length

[mm]

Heigth

[mm]

1 117 255 55

2 117 255 553 117 255 55

4 117 255 55

5 117 255 55

6 117 255 55

Tab. 4.4: Specimen dimensions.

Initially a pre-loading was imposed to setup the Galdabini SUN 60 , then the constant

load increments were applied. Each specimen was subjected to compression load up

to failure. The failure occurred along the direction of load application considering the

front view, as represented in Fig. 4.8.

Fig. 4.8: Specimen failure.

Analogously to the compressive test, the following quantities were determined:

average tensile strength mean deviation variation coefficient characteristic value.

The indirect tensile strength was determined for each specimen by formula:


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2

v

tf

b h= (4.5)

where tis the external applied load in Newton; h and b are the specimen height and

length respectively, expressed in mm.

The failure load and the indirect tensile strength were determined for each specimen,

as reported in Tab. 4.5.

Specimen

[number]

Area

[mm2]

Failure

load

[kN]

Indirect tensile

strength (fv)

[kN/mm

2

]1 14025 38816 3.84

2 14025 31800 3.15

3 14025 45008 4.45

4 14025 24739 2.45

5 14025 37841 3.75

6 14025 30543 3.02

Tab. 4.5: Indirect tensile test results.

The characteristic indirect tensile strength was computed and the results are reported

in Tab. 4.6.

Average indirect tensile

strength [N/mm2]

Mean deviation

[N/mm2]

Variation

coefficient

Characteristic indirect

tensile strength (fvk)

[N/mm2]

3.44 0.71 0.21 1.79

Tab. 4.6: Characteristic indirect tensile strength.


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4.5.3.Elastic secant modulusIn order to evaluate the elastic secant modulus a test was realized in accordance with

the prescription of UNI 6556 rule. The specimens extrapolated by standard clay

bricks were prismatic; in fact, the rule prescribes that the tests has to be performed on

cylindrical or prismatic with square base specimens. The test was realized using the

universal testing machine Galdabini SUN 60.

In order to evaluate the elastic secant modulus, the code prescribes the use of 3 + 3

specimens. In particular, 3 specimens were used for evaluating the compressive

strength, and the others 3 to determine the elastic secant modulus. The test was

organized in two phases.

During the first phase, 3 specimens were obtained by standard clay brick and their

size was 5x5x15 cm. Each specimen was allocated into the universal testing machine

and it was loaded until its compressive load failure, as represented in Fig. 4.9.

Fig. 4.9: Positioning into the universal testing machine of the reference specimen.

The average failure load value of the i-th set of specimens was determined as:


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3

1

3

j

ji

f

N

N==

(4.6)

After this test, the load values representing the extremes of the loading-unloading

cycles were determined using the average failure load values, recovered by equation

(4.6). In accordance with the UNI 6556 rule, the maximum load is3

1

3

i

fN N= , the

base load is0 3

1

10N N= and the intermediate loads are 3 01

2

3

N NN

+ =

and

( )2 1 02N N N = . Consequently the load cycles are defined as

0 1 0cycle 1:N N N ,

0 2 0cycle 2:N N N and

0 3 0cycle 3:N N N .

In the second phase, further 3 specimens were tested. The bricks for evaluating the

elastic secant modulus were prepared. The brick surface was cleaned and the area,

where the strain-gauge were applied, was dry sanded, removing all the eventually

incrustations, as illustrated in Fig. 4.10.

Fig. 4.10: Brick surface preparation.


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In order to simplify the strain-gauge application, guidelines were traced on the brick

surface; then the resin was applied, as represented in Fig. 4.11, and the strain-gauge

was positioned along the guidelines previously traced, as illustrated in Fig. 4.12.

Fig. 4.11: Resin application.

Fig. 4.12: Strain-gauge application.

Each specimen was allocated into the universal testing machine and all the strain-

gauge was connected with the data acquisition system. The load cell also was

connected to the data acquisition system to know the applied load at each loading

step, as represented in Fig. 4.13.


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Fig. 4.13: Specimen positionating.

For every specimen the elastic secant modulus was determined. The procedure can

be schematically described as:

1. the base loadN0 was fixed;2. the base mean strain

0 was determined;

3. the maximum load of the cycleNi was fixed;4. loading phase was performed:

0 iN N ;

5. the mean straini

in correspondence of the maximum load was determined;

6. unloading phase was performed:0i

N N ;

7. the elastic secant modulus was determined as 00

is

i

E

=

where

A

Nii= ,

A

N00 = andA is the specimen base area.

The results elaboration for all the specimens are reported in Tab. 4.7, Tab. 4.8 and

Tab. 4.9.


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Ni

[N] [N/mm2] [N/mm

2] [N/mm

2] [N/mm

2]

4150 1.6600 0.000087

16740 6.6960 5.0360 0.000351 0.000264 19075.7576

4230 1.6920 0.000098

4230 1.6920 0.000098

28350 11.3400 9.6480 0.000616 0.000518 18625.4826 18529.5551

4330 1.7320 0.000112

4330 1.7320 0.000112

41670 16.6680 14.9360 0.000947 0.000835 17887.4251

4230 1.6920 0.000110

i sE sE

Tab. 4.7: Results elaboration for specimen 1.

Ni

[N] [N/mm2] [N/mm2] [N/mm2] [N/mm2]

4110 1.6440 0.000163

16510 6.6040 4.9600 0.000520 0.000357 13893.5574

4150 1.6600 0.000182

4150 1.6600 0.000182

28610 11.4440 9.7840 0.000912 0.000730 13402.7397 13486.40448

4070 1.6280 0.000191

4070 1.6280 0.000191

40630 16.2520 14.6240 0.001302 0.001111 13162.9163

4030 1.6120 0.000192

i sE sE


Ni

[N] [N/mm2] [N/mm

2] [N/mm

2] [N/mm

2]

4090 1.6360 0.000113

16230 6.4920 4.8560 0.000407 0.000294 16517.0068

4090 1.6360 0.000117

4090 1.6360 0.000117

27420 10.9680 9.3320 0.000669 0.000552 16905.7971 16786.7196

4130 1.6520 0.000115

4130 1.6520 0.000115

40630 16.2520 14.6000 0.000977 0.000862 16937.35504070 1.6280 0.000113

i sE sE



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The elastic secant modulus of standard clay brick was obtained as the average value

of the elastic secant modulus of every specimen and it iss

E 216000 /N mm .


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4.6.MortarThe mortar used to realize the three arches belongs to the M3 class, in accordance

with the Italian CodeMinisterial Decree of 20/11/1987. The mortar is constituted by:

2800 g of pozzolana; 933 g of lime, Calcisernia, Contrada Tiegno, Isernia; 800 g of pozzolanico cement Duracem 32.5 R, Colleferro, Roma; 1.66 l of water.

In literature this mortar is classified as mixed because it is constituted by two

binders: cement and lime.

4.6.1.Compressive testsThe specimens were realized with the mortar described previously. Three specimens

of 40x40x160 mm3 were prepared using a normalized sand, as represented in Fig.

4.14.

Fig. 4.14: Preparation of mortar.


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The mortar was prepared by mechanical mixing and successively compacted using a

normalized vibrating device as illustrated in Fig. 4.15.

Fig. 4.15: Device to mix the mortar and normalized vibrating device.

After 28 days of seasoning, the specimens were subjected to a bending test. The

specimen was allocated into the universal testing machine with a lateral face on the

support rollers and the longitudinal axis orthogonal to the supports. The vertical load

was applied on the specimen lateral face and it was uniformly increased with a

maximum ratio of 220 /Kg cm s until the failure, as represented in Fig. 4.16.


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Fig. 4.16: Bending failure of mortar specimen.

In this way two semi-prismatic specimens were obtained and they were successively

subjected to the compressive test.

In order to determine the compressive behavior of the mortar, the semi-prismatic

specimen was tested, as shown in Fig. 4.17.

Fig. 4.17: Compressive test: test setup and typical compressive failure.


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The tests were performed with the universal testing machine Galdabini SUN 60 and

the results are reported in Tab. 4.10.

Specimen

Size [cm]

Weigth [g]

1 2 3

4x4x16 4x4x16 4x4x16

432.4 430.6 430.5

Compressive strength

[N/mm2]

4.7675 4.6219 4.79754.8094 4.7038 4.7438

Tab. 4.10: Mortar compressive strength.

4.6.2.Elastic secant modulusThe elastic secant modulus of the mortar was carried out. The procedure was exactly

the same that was realized for the standard clay brick. Three reference specimens for

each mixture were tested. Therefore, the final results are schematically reported in

Tab. 4.11 and Tab. 4.12 for the mixtures one, two and three and for mixtures four,

five and six, respectively.


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0 N0 i Ni 0s N0s p e E Em0 E

[10^-6] [N] [10^-6] [N] [10^-6] [N] [10^-6] [10^-6] [N/mm^2] [N/mm^2] [N/mm^2]

-79.67 420.00 -258.67 1690.00 -88.00 420.00 -8.33 -250.33 3170.77

-88.00 420.00 -266.67 1690.00 -103.00 440.00 -15.00 -251.67 3104.30

-103.00 440.00 -475.67 3020.00 -137.33 420.00 34.33 -510.00 3186.27

-137.33 420.00 -502.33 3000.00 -158.33 460.00 -21.00 -481.33 3298.13

-150.67 440.00 -699.00 4230.00 -183.00 420.00 32.33 -731.33 3256.04

-183.00 420.00 -754.00 4290.00 -217.33 420.00 -34.33 -719.67 3360.93

-58.67 420.00 -247.67 1690.00 -83.00 420.00 -24.33 -223.33 3554.10-83.00 420.00 -244.33 1690.00 -83.33 440.00 -0.33 -244.00 3201.84

-83.33 420.00 -463.33 3060.00 -139.33 400.00 -56.00 -407.33 4081.42

-139.33 400.00 -500.33 3060.00 -157.67 420.00 -18.33 -482.00 3423.24

-157.67 420.00 -713.67 4310.00 -223.00 420.00 -65.33 -648.33 3750.00

-223.00 420.00 -747.67 4310.00 -248.33 420.00 -25.33 -722.33 3365.83

-67.00 420.00 -283.50 1670.00 -74.50 420.00 -7.50 -276.00 2830.62

-74.50 420.00 -269.50 1670.00 -80.50 420.00 -6.00 -263.50 2964.90

-80.50 420.00 -283.00 1670.00 -90.50 420.00 -10.00 -273.00 2861.72

-90.50 420.00 -500.50 2840.00 -101.50 420.00 -11.00 -489.50 3089.89

-101.50 420.00 -514.00 2840.00 -142.75 420.00 -41.25 -472.75 3199.37

-142.75 420.00 -777.50 4230.00 -212.75 420.00 -70.00 -707.50 3365.72

-212.75 420.00 -847.00 4230.00 -250.00 420.00 -37.25 -809.75 2940.72

Mixture3

Cycle 1 2885.74

3061Cycle 2 3144.63

Cycle 3 3153.22

Mixture2

Cycle 1 3377.97

Mixture1

Cycle 1 3137.54

3229

Cycle

Cycle 2 3242.20

Cycle 3 3308.49

3563Cycle 2 3752.33

Cycle 3 3557.91

Tab. 4.11: Results elaboration for mortar specimen 1.

0 N0 i Ni 0s N0s p e E Em0 E

[10^-6] [N] [10^-6] [N] [10^-6] [N] [10^-6] [10^-6] [N/mm^2] [N/mm^2] [N/mm^2]

-82.33 420.00 -330.67 1630.00 -95.00 420.00 -12.67 318.00 2378.14

-95.00 420.00 -348.67 1630.00 -108.33 420.00 -13.33 335.33 2255.22

-108.33 420.00 -570.00 2820.00 -137.00 420.00 -28.67 541.33 2770.94-137.00 420.00 -574.67 2820.00 -137.00 420.00 0.00 574.67 2610.21

-137.00 420.00 -774.67 4130.00 -175.67 420.00 -38.67 736.00 3150.48

-175.67 420.00 -806.33 4130.00 -199.00 420.00 -23.33 783.00 2961.37-69.33 420.00 -299.67 1590.00 -98.33 420.00 -29.00 270.67 2701.66

-98.33 420.00 -296.00 1590.00 -114.83 420.00 -16.50 279.50 2616.28

-114.83 420.00 -518.67 2820.00 -135.67 420.00 -20.83 497.83 3013.06

-135.67 420.00 -533.00 2820.00 -154.00 420.00 -18.33 514.67 2914.51

-154.00 420.00 -774.67 4110.00 -184.00 420.00 -30.00 744.67 3097.02

-184.00 420.00 -784.67 4110.00 -184.00 420.00 0.00 784.67 2939.15

-59.33 420.00 -243.33 1650.00 -67.83 420.00 -8.50 -234.83 3273.60

-67.83 420.00 -256.00 1650.00 -77.00 420.00 -9.17 -246.83 3114.45

-77.00 420.00 -436.67 2860.00 -108.00 420.00 -31.00 -405.67 3759.24

-108.00 420.00 -473.33 2880.00 -139.00 460.00 -31.00 -442.33 3475.89

-139.00 460.00 -741.67 4110.00 -232.67 440.00 -93.67 -648.00 3520.45

-232.67 440.00 -781.00 4110.00 -263.33 420.00 -30.67 -750.33 3056.97

Mixture4

Mixture5

Mixture6

Cycle 2

Cycle 3

Cycle 1 3194.02

33673617.56

2688Cycle 2 2690.57

Cycle 3 3055.92

2880Cycle 2 2963.78

Cycle 3 3018.08

Cycle

3288.71

Cycle 1 2658.97

Cycle 1 2316.68

Tab. 4.12: Results elaboration for mortar specimen 2.

The mortar elastic secant modulus results equal to 23100 N/mms

E .


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4.7.Reinforcement materialIn this experimental program the used reinforcement system is the woven SikaWrap-

300C NW. It is constituted by carbon fibers impregnated on-site with an epoxy resin

of type SikaDur 330.

The woven was chosen because it can be easily adapted to the curvilinear surface of

the arch. On the lateral surfaces the woven has a thin texture, that safeguards the

fibers stability during the application process, made of thermoplastic material, as

shown in Fig. 4.18.

Fig. 4.18: SikaWrap-300C NW

The fibers of the woven are unidirectional. In the following the properties of

unidirectional carbon fiber provided by the manufacturer are reported.


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The epoxy resin SikaDur 330was used both as adhesive to the masonry arch and as

matrix. The resin is constituted by two-component, it is 100% solid and grey color.

The properties of the resin are reported below.


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4.8.Experimental test on the archesThe experimental campaign on masonry arches was conduced on a set of two arches

having the same geometrical characteristics and realized with the same materials.

The aims of this campaign is the evaluation of the mechanical response of

unreinforced and reinforced arches. In particular, the main aim is the validation of

the numerical model developed to individuate the behavior of the masonry arch

reinforced by FRP.

4.9.Arch layingThe arch was realized using the standard clay brick and mixed mortar previously

seen. The laying of the arch was at LAPS, Laboratories of Structural Analysis and

Design of University of Cassino, with the colla

Tesi Maria Ricamato

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