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Strengthening of Masonry Arches with Fiber-ReinforcedPolymer Strips

Paolo Foraboschi1

Abstract: This paper deals with masonry arches and vaults strengthened with surface fiber-reinforced polymer~FRP! reinforcement inthe form of strips bonded at the extrados and/or intrados, considering strip arrangements that prevent hinged mode failure, sofailure modes are:~1! crushing,~2! sliding, ~3! debonding, and~4! FRP rupture. Mathematical models are presented for predictinultimate load associated with each of such failure modes. This study has shown that the reinforced arch is particularly susfailure by crushing, as a result of an ultimate compressive force being collected by a small fraction of the cross section. Fdebonding at the intrados may also be an issue, especially in the case of weak masonry blocks or multiring brickwork arches.sliding has to be considered if the reinforcement is at the extrados and loading is considerably nonsymmetric.

DOI: 10.1061/~ASCE!1090-0268~2004!8:3~191!

CE Database subject headings: Arches; Masonry; Fiber reinforced polymers; Reinforcement; Mathematical models; CruFailure modes.

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Introduction

Numerous historical constructions are still in service all overworld and a significant part of them are of cultural and artvalue. Many historical constructions contain masonry archebarrel vaults, cross or groin vaults, cloist vaults, and domes~i.e.,masonry shells!, which play an important part in public and redential buildings, as well as in road, rail, and waterway infrasttures.

Modern-day loads are far higher than the ones initially conered. A masonry shell with either tie-rods or nonslender pierscollapses if its loading is severely nonsymmetrical. The sacondition of a common masonry shell consequently dependon the level of loading, but on the live-to-dead loads ratio. Ifratio is low, modern loads are supported because of the outsing combination of mechanical properties that masonry shellrely on to carry symmetrical loads. If the ratio is high~i.e., iftoday’s live loads are severe!, because the live loads distributimay not be symmetrical, modern loads have the potentiacausing masonry shells to collapse, in fact, the failure of masshells is not unusual.

Substantial alterations often have to be made to masbuildings to meet present architectural requirements. Suchations can lead to a significant reduction in the safety margimasonry shells~e.g., buttresses or tie-rods may be removed,columns or walls may be rested on the shell’s extrados, opemay be cut, the spandrel fill may be removed or replacedlighter material, etc.!. As a result, the current usage of many m

1Professor, Dipt. di Costruzione dell’Architettura~DCA!, IUAV–Univ. degli Studi di Venezia, ex Convento delle Terese, Dorsoduro 230123–Venice, Italy. E-mail: [email protected]

Note. Discussion open until November 1, 2004. Separate discusmust be submitted for individual papers. To extend the closing daone month, a written request must be filed with the ASCE ManaEditor. The manuscript for this paper was submitted for review andsible publication on April 11, 2002; approved on May 14, 2003. Tpaper is part of theJournal of Composites for Construction, Vol. 8, No.
3, June 1, 2004. ©ASCE, ISSN 1090-0268/2004/3-191–202/$18.00.
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sonry shells either satisfies present needs but fails to fulfilrequirements of modern codes, or it satisfies the codes bunable to meet the present building, road, rail, or waterway istructural demands. Structural engineers consequently oftento assess masonry shells. When the safety margins of a mashell are no longer assured or prove inadequate for new demthen strengthening is needed.

Strengthening masonry shells poses serious concerns bthe vast majority is of considerable architectural and histovalue. Traditional reinforcement techniques may guarantee aequate increment in strength, stiffness, and ductility, but areshort-lived and labor-intensive, and they usually violate aestrequirements or conservation or restoration needs. Such prohave recently led researchers~Hamid et al. 1994; Modena 199Saadatmanesh 1994; Ehsani et al. 1997; Kolsch 1998; Trialou 1998a, b; Tinazzi et al. 2000; Albert et al. 2001; Meier 20Tong Li et al. 2001; Valluzzi et al. 2001! to suggest strengthenimasonry shells with fiber-reinforced polymer~FRP! compositein the form of bonded surface reinforcements.

Reinforcements epoxy-bonded to the masonry surface emasonry structures to bear substantial tensile stresses, elimitheir greatest mechanical shortcoming at an acceptable costernally bonded reinforcements may be made of steel, but themuch more effective if they are made of FRP. The benefits ofover conventional reinforcement materials include its adaptato curved and rough surfaces, such as historical masonry tebe.

To ensure adequate masonry permeability and complyrestoration requirements, most of the boundary has to be leftout reinforcement. To minimize the amount of FRP whileensuring an adequate safety margin, reliable methods are nfor the structural analysis of reinforced shells.

The main events leading to the collapse of a masonryinclude severe cracking patterns. Cracking splits the shellslices, ultimately converting it into a one-dimensional thrusstructure, since the slices behave like arch segments. The ulload is therefore carried by a system of masonry arches w
geometry depends on the cracking pattern. Thus the ultimate
MPOSITES FOR CONSTRUCTION © ASCE / MAY/JUNE 2004 / 191

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Reinforcement cannot prevent masonry from crackingcracks may form also at a reinforced boundary, but they caopen because the reinforcement stitches the crack. Thus threinforcement is incapable of modifying the pattern of crackinthe masonry, and the reinforced shell carries the ultimate loameans of the same system of arches as the unreinforcedFRP reinforcement can, however, modify the failure mode omasonry shell and significantly increase the load-carrying caity, provided that the reinforcement changes the ultimate behof the masonry arches into which the masonry shell convertsmasonry arch simulation considered herein is therefore alsoable for describing reinforced masonry shells, hence the theical models presented in this paper can be applied equally wall masonry shells.

Review of Failure Modes of Masonry Arch

Failure by crushing is unlikely in a masonry arch, since themate normal action provided by the cross section can baeven very severe external loads, i.e., the crushing load gexceeds the hinged mode loads~mechanism loads!. There arefew exceptions, e.g., an extremely flat arch with tie-rods aspringing, made of poor-quality masonry and loaded symmcally ~in this case, geometrical nonlinearities have to be takenaccount too!.

Failure by sliding between components could only occuunrealistically thick arches, but does not happen in real lifefact, sliding is caused by the excessive inclination of the linthrust with respect to the cross section. In this case, howeveline of thrust is unable to be defined within the masonry’s thness and each intersection of the line of thrust with the bouncorresponds to a pin. This means that the sliding load drastexceeds the hinged mode loads.

So the masonry arch can fail primarily due to a mechanconsisting of a set of portions of arch joined by pins. Kinemcally, a pin behaves like a hinge. Two fundamental differeexist, however, between a pin and a beam-hinge, such as thused in steel and concrete members, namely:~1! position, and~2!rotation. The pin’s position is on the boundary of the structi.e., either at the extrados or intrados of the arch, whereaposition of a beam-hinge is along the axis of the member.rotation of a pin is unilateral, i.e., only the relative opening oftwo pinned sections is possible, whereas both rotations aresible in a beam-hinge. Consequently, the compatibility condidepend on whether the hinge is on the extrados or intradfurther difference exists between a pin and a plastic hinge, thcontrary to the latter, the former does not display any plastic

As a consequence of the compatibility conditions, theretwo possible shapes for mechanisms, namely~Fig. 1!: ~1! the archdisplacement mechanism~shape 1!, and ~2! the overall archabutment displacement mechanism~shape 3!. Shape 2 is unreaistic in practice because for real loads and structures, shapeoccur instead. Likewise, shape 4 is insignificant, since it canresult from a lateral movement of the ground or the collapselateral structure in the case of multibay arches.

The flat arch, i.e., the arch with height span-to-rise ratio,hibits a supplementary shape for mechanisms with respectsemicircular arch. The extra-shape consists of the reverse of2: the springing hinges are on the intrados, the haunch hinge
on the extrados, and the crown hinge is on the intrados. According
192 / JOURNAL OF COMPOSITES FOR CONSTRUCTION © ASCE / MAY/J

.

to this shape of mechanism, the haunches of the circulardescend and the crown ascends, while the springing sectionot move.

Collapse Tests on Masonry Prototypes

The experimental procedure consisted of loading full-scale ptypes of brickwork arches, vaults, and domes, with and witvarious types of FRP reinforcement, up to failure~Figs. 2–11!.More than 50 specimens were tested. A complete discussithe whole experimental program has been presented else~Faccio et al. 2000; Foraboschi 2001a, b, c; Faccio and Forchi 2002!, so only a brief overview is provided here.

In Fig. 2, the reinforcement consisted of three 180° intrastrips. The load was applied at a quarter span. After debondthe reinforcement due to ripping of the brick, the arch failedthe four-hinge mechanism. In Fig. 3, 11 ribbed barrel vaultstested for three strip arrangements. In all the tests, a quarteline-load was applied to the extrados, and the springingsprevented from translating horizontally. The three strip arraments were as follows. Strip arrangement 1~two specimens!:three 28° strips, 50 mm wide, 2,050 mm spaced, were attachthe intrados of the loading line. The arches failed by the fhinge mechanism, but the position of the hinges differed fromcase of the unreinforced specimen, and the ultimate loadconsequently 14.3 times greater. Strip arrangement 2~two speci-mens!: three 180° strips, 50 mm wide, 2,050 mm spaced,attached to the whole extrados~outside the ribs!. The archefailed by sliding under a load 7.8 times the ultimate load ofunreinforced specimen. Strip arrangement 3~seven specimens!:four 180° strips, 600 mm wide, 1,538 mm spaced, were attato the whole intrados of three specimens and two 180° stripmm wide, 3,075 mm spaced, were attached to the whole intof four specimens. All the specimens failed by crushing, anthe crushing loads were considerably greater than the h

Fig. 1. Shapes of collapse mechanism of semicircular masonry

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In Fig. 4, the specimen was unreinforced. The load wasplied to the center of a web. Failure was dictated by the inscient buttressing action of the webs adjacent to the loaded wFigs. 5 and 6, the two specimens were reinforced on 45 andof the extrados, respectively. The load was applied to the cena web. Failure was dictated by crushing of the loaded web.ultimate loads were, respectively, 2.5 and 2.1 times the ultiload of the unreinforced specimen. In Figs. 7 and 8, the specwas reinforced with an annular strip at the springing. Thewas applied at the crown. The dome split into four slicesfailed by shape 1 collapse mechanism. Accordingly, the ultiload was supported without availing of any contribution fromstrip. In Fig. 9, the specimen was reinforced with four ann

Fig. 4. Prototype of brickwork cross-vault

Fig. 5. Prototype of brickwork cross-vault with extrados reinforment ~grid arrangement!

Fig. 2. Prototype of brickwork arch bridge tested up to collapse.internal span was 5,015 mm. Three 180° strips, 55 mm wide anmm spaced, were attached to the intrados.

Fig. 3. Eleven ribbed barrel vaults, with and without various typefiber-reinforced polymer reinforcement, were tested up to faiThis specimen collapsed by the four-hinge mechanism~see the foucracks!. Other specimens failed by crushing.


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strips from the springing to the crown. The strips did not chathe dome splitting into slices, but they changed the mode ofure from the hinge mechanism to crushing of the masonry. In10, the annular strip did not change the vault splitting intoslices, but it changed the mode of failure from the hinge menism to rupture of the FRP in the annular strip, and consequincreased the ultimate load. The annular strip at the haun~Foraboschi 2001c! proved more effective than the strip atcrown ~Fig. 10!. In fact, the ultimate load of the specimen wthe haunch annular strip was 2.1 times greater than that witConversely, the four meridian strips proved useless~the corneribs were subjected to a prevailing axial force!. In Fig. 11, the

Fig. 6. Prototype of brickwork cross-vault with extrados reinforment ~four-sided annular reinforcement!

Fig. 7. Prototype of brickwork dome


specimen was reinforced with narrow strips at the intrados.specimen failed by masonry ripping that caused the strip tocome detached.In the present context, only the following experimental resand interpretations are of interest.1. Five modes of failure were observed, namely:~1! mecha

nism ~i.e., hinged mode!; ~2! masonry crushing;~3! sliding~slipping! along a mortar joint;~4! debonding of the FRreinforcement; and~5! tension rupture of the FRP reinforcment.

2. Each failure by mechanism is due to the hinging behavithe pins, each located at the boundary opposite thewhere the cracks open.

3. A crack still develops even on a reinforced boundary,therefore also a pin still develops on the opposite bounbut the reinforcement prevents the hinging behavior ofpin. The hinges of a reinforced structure that fails by menism are consequently located in sections different fromendemic hinging sections of the unreinforced structure.

4. Masonry crushing takes place in sections that are crabut stitched by the reinforcement. In order to develop astantial tension force in the strip, the bricks on whichstrip is bonded have to rotate rigidly around the bounopposite the strip. The opposite boundary thus behavespin ~but not like a hinge!. The pin localizes the contact btween the units that rotate around it. Consequently, the sprofile lies at a limited depth,y ~Fig. 12!. The pin’s behaviois one of the two reasons why the strengthened arch isticularly susceptible to failure by crushing. Despite the rforcement, the sections liable to hinging in the unreinfomasonry are still the binding sections, albeit to a consably lesser degree.

5. Masonry crushing was monitored by numerous sgauges. In Fig. 13 the compression strains,«m , measured amasonry crushing in two barrel vaults are represented~aver-age «m of the two specimens!. The values of«m are ex-pressed with respect to the compression strain correspoto the peak of the masonry constitutive law,«m1 . The measurements recorded by the strain gauges showed thportions,W, of masonry in front of the reinforcement str~Fig. 12! exhibit great compressive strains, while the reming fraction of the masonry cross section exhibits only mginal compressive strains. Accordingly, the ultimate cpressive force is generated by a series of masonry reglabeled theworking area, whose position is in front of thFRP strips@Fig. 12~a!#. The localization of the cross sectiis the other reason why the reinforced arch is particususceptible to failure by crushing.

6. The working area depends on the width and spacing ostrips, as well as on the masonry’s texture, but it is subtially independent of the strip’s axial stiffness or of the msonry’s elasticity modulus. To be more specific, the meaments recorded by the strain gauges show thatboundaries of the working area vary with the materproperties, but the area they embrace does not~i.e., y•W isconstant!. The greater the reinforcement’s axial stiffness wrespect to the masonry’s elasticity modulus, the lessepin’s rotation; i.e., the greater the depthy of the workingarea. Conversely, the greater the reinforcement’s axialness with respect to the masonry’s elasticity modulussharper the cross section’s localization; i.e., the narrowewidth W of the working area. As a result, the working adepends very little on the material’s stiffness, unlike
boundaries of said area.
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7. Subsequent processing of the experimental results shthat each working area in front of a strip can be reproduby a rectangle, whose [email protected]., sidesy and W, Fig.12~b!# correspond in width~i.e., W! to the blocks~units! towhich the strip is bonded plus one block, and in depth~i.e.,y! to one-third of the thickness. This rectangle reprodunot the shape of the working area, but the areaAw of thesurface it embraces.

8. Sliding consists of the slipping of one part in relationanother along a layer of mortar and is due to the inabilitthe friction mechanism to provide the cross section withshear action needed to balance the shear demand of tternal load. In asymmetrical loading conditions, the csection most likely to slide is the springing on the leloaded side.

9. Debonding of the reinforcement consists in either the ripof a layer of brick or stone, or the detachment of a blfrom the brickwork~pull-out!, while the FRP reinforcemeand the bonding layer both remain intact. Debondingaffected reinforcement at the intrados, not at the extrad

Fig. 8. Failure o

Fig. 9. Prototype of brickwork dome with four annular reinforments

f the specimen in Fig. 7

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-

Fig. 10. Prototype of brickwork cloist vault reinforced by an annustrip at the crown and four meridian strips along the joints ofwebs~from the crown to the haunches!


Fig. 11. Detachment of the fiber-reinforced polymer strip due to the ripping of the brick

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Fig. 12. ~a! Cross section of the reinforced arch~cylindrical vault!. The shaded rectangles represent the working area. The width,W ~crosssection localization!, and the depth,y ~pin localization! of each working area is shown.~b! Shaded rectangle~working area! represents the fractioof masonry cross section involved in balancing the tension force in the reinforcement.

196 / JOURNAL OF COMPOSITES FOR CONSTRUCTION © ASCE / MAY/JUNE 2004

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11. In all the tests, crushing, sliding, debonding, and FRPture were observed only if the reinforcement preventethe hinged modes from occurring, whereas the specimfailed by mechanism whenever this possibility remaineven if the hinges were far from their endemic positioThis means that the ultimate loads for crushing, sliddebonding, and FRP rupture always exceed the ultiload for the mechanisms.

Relationships between Fiber-Reinforced PolymerArrangement and Failure Modes

The boundary opposite an FRP strip is prevented from hinThe compatibility conditions~Foraboschi 2000, 2001a! require:~1! the hinges of a mechanism to alternate~extrados-intradosetc.!, and ~2! the distance between two consecutive hinges tgreater than the arch’s thickness. Reinforcing the majority~notall! of the extrados or intrados consequently prevents failurthe arch displacement mechanism~shape 1 and 2 of Fig. 1!. Re-inforcing most of the intrados also prevents the overall aabutment displacement mechanism~shape 3 of Fig. 1!, whereasthis shape of mechanism can still occur even if all of the extrare reinforced, though this significantly reduces the lateral th

The same results may be achieved by discontinuouslyforcing the boundary, e.g., with two strips on the extrados~on thehaunches, maybe! and one on the intrados~on the crown!.

The following conclusion can thus be drawn. To assuremasonry shell the greatest possible load-bearing capacity,forcement has to prevent all mechanisms from occurring, sothe only feasible types of failure that remain are due to:~1!Crushing,~2! sliding, ~3! debonding, or~4! FRP rupture.

When the reinforced arch’s failure is dictated by the menism, the ultimate load analysis can be done by adaptingmethods typically used for the unreinforced arch. A new verof the lower and upper bound theorem~Foraboschi 2001a! can be

Fig. 13. Diagram represents~closed circles! the measures of«m withrespect to«m1 ~experimentally determined as well!. The open circlein the lower representation indicate the position in the masonry wthe measurements were taken.

used for this purpose. When failure is dictated by a mode other

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than a mechanism, however, the analysis calls for specific mods ~Triantafillou 1998a, b; Valluzzi et al. 2001!.

Failure Analysis by Crushing, Sliding, Debonding,and Fiber-Reinforced Polymer Rupture

The distribution of the external loads is given. Accordingly,loading is governed only by a load factor, i.e., the scalar valq.To assess the ultimate load factor,qu , hereafter the bending mment is taken with respect to the external reinforcement, inof the centroid of the cross sections. LetM 8 be such an internaction. It should be noted that hereafter all the internal actionexpressed per unit of the arch’s width.

Crushing

Pin behavior~see experimental results 4! is due to the elasticitmodulus of the FRP reinforcement. The crushing mode loathe reinforced arch exceeds the hinged mode load of the uforced arch~see experimental results 11!, so in order to reach thcrushing load, the reinforcement has to provide the arch’s secwith a tension force; i.e., the reinforcement has to be extenThe ultimate tensile strain of the FRP reinforcement is at1.2–1.5%, while the masonry cracks at a strain of less0.030%. The tension force in the FRP is thus the resultsubstantial relative rotation of the bricks to which the stribonded. In particular, the lower the FRP elasticity modulusgreater the rotation, and as a result the depth of the stresswill be shallower.

The cross-section localization~see experimental results 5 a6! is due to a compressive behavior that is typical of tdimensional masonry structures. Consider a brickwork paneported continuously at the base and loaded by a concenforce at the top~Fig. 14!. If the magnitude of the force is low, tforce spreads into the panel at a certain angle of diffusion. Dsion implies a field of tension stresses normal to the comprestresses~and thus also to the force!. If the magnitude of the forcis higher, said tension stresses lead to cracks parallel to thepressive stresses, followed by cracks normal to the compre

Fig. 14. Stress diffusion in a masonry wall composed of linelastic no-tension blocks~bricks!

stresses, and these cracks prevent diffusion. In this latter case, the


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force is collected by a vertical strut~chord! just under the forcecomprising a limited number of units~i.e., blocks!.

To define the number of blocks involved in adsorbingforce, let us suppose that the mortar joints consist of bedunilateral~no-tension! springs that are linear-elastic~in compression!, while the bricks consist of rigid blocks. Such an assumpimplies ~block equilibrium! that the force is collected by a stwith a width equating to three blocks~shaded block, Fig. 14!. Ifthe compression constitutive law for the joints allows for a ceplasticity to be displayed, then the width of the strut is enarrower.

The phenomenon described for the masonry panel explaincross-section localization observed for the test prototypes.only difference between the reinforced shell and the previouample of a panel is that, for the shell, the phenomenon isgenerated by a localization of normal stresses~as it is for thepanel!, but is the result of tension forces collected by narreinforcements with wide gaps between them. The phenomentherefore generated by a localization of shear stresses thbalanced by compressive forces similarly localized in thesonry ~as the compressive force of the wall in Fig. 14!, and thistogether with the pin localization, leads to crushing.

Finally, crushing failure of the reinforced shell is causedgoverned by two opposing phenomena, namely,~1! the pin local-ization, which is due to the bricks’ rotation and governed bystitching action of the strip; and~2! the cross-section localizatiowhich is due to annular and longitudinal cracking in the mas~that prevents stress diffusion!, and is governed by the interfashear stresses.

Let us consider an arch~i.e., a cylindrical vault! reinforcedwith a single FRP strip@Figs. 12~b! and 15#. Let S be the thick

Fig. 15. Internal forces in a reinforced cross section of a masarch

ness of the arch. The cross section consequently has an are


equating toSmultiplied by the arch’s width~i.e., the length of thgeneratrices of the cylindrical vault!. Let B be the width of themasonry block~brick or stone!, andb the number of blocks wita strip attached to them. In accordance with the experimresult 7~justified by previous evaluations!, the compressive forcbalancing the tension force in the FRP strip is collectedrectangular masonry section—the working area—whose areAw

amounts to

Aw5S

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According to Eq.~1!, therefore, the fraction of the masonry crsection involved in carrying the crushing force can be calcuproviding the vault and reinforcement geometry is known. Ifreinforcement is attached to both extrados and intrados, thedos reinforcement can be ignored, since the intrados reinfment alone allows the vault to carry the maximum crushing l

Let C denote the compressive normal force per unit of wof the arch, acting on a generic cross section.C is generated bthe masonry. The ultimate value ofC is denoted asCu . Let w bethe number of reinforcement strips per unit of the arch’s wand f mc the masonry crushing stress. The experimental stresfiles at crushing exhibitf mc on each areaAw and marginal stresson the remaining fraction of the cross section. Thus the valuCu results fromf mc uniformly distributed over the working areaAccordingly,Cu amounts to

Cu5S

3•~11b!•B•w• f mc (2)

Eq. ~2! suggests a stress-block profile. Accordingly,Cu is appliedat the centroid ofAw ~i.e., atS/6 from the compressive edge, F15!.

The value ofM 8 in a generic cross section is consideredwell as the relatedC. A linear relationship is hereafter assumbetweenq and M 8. This assumption is justified by the fact tthe main source of nonlinearity betweenq and M 8 is the eccentricity e85M 8/N. In the crushing analysis,e8 is not high andabove all, it is practically independent ofq.

Let Mmax8 denote the maximum value ofM 8 in the arch, for agiven value ofq. According to the above hypothesis,Mmax8 5K•q, where the dimensional constantK depends only on the arcand so it is known. Thus

q5~1/K !•Mmax8 (3)

The moment taken with respect to the reinforcement~i.e., to theedge of the cross section! gives the following relationship btweenC andMmax8 ~Fig. 15!:

5

6•S•C5Mmax8 (4)

Eq. ~4!, in conjunction with Eq.~3!, gives the relationship btween the crushing load factor,quc , andCu :

quc5

56•S•Cu

K(5)

Substituting Eq.~2! into Eq. ~5! gives usquc

quc5

518•~11b!•B•w• f mc•S2

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Eq. ~6! solves the problem. The value ofquc depends on th
amagnitude and point of application ofCu . The magnitude ofCu
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results from the assumption of a stress-block distribution onAw .The deviations between the experimental and assumed valAw are marginal. Moreover, the observed strains are veryinside Aw , but very low outside~Fig. 13!, so only marginal deviations are likely between the actual and assumed magnituCu . The point of application ofCu stems from the depth,y, ofAw . The model assumesy5S/3. The deviations between the eperimental and assumed values ofy are negligible. A sensitivitanalysis ofquc on y was developed. SinceK does not depend oy, quc can be replaced byMmax8 . The general form ofMmax8 is

Mmax8 5Cu•S S2y

2D (7)

The ratio of the first-order term to the zero-order term ofexpansion ofMmax8 in a Taylor series about the pointy5S/3 givesus

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Fig. 17. Shear strength in a cross section of the arch, accordingof masonry arch

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f

The maximum value ofy observed in the tests wasS/2 and theminimum wasS/13. Accordingly, the greatest deviation ofy withrespect to S/3 was u3•S/39213•S/39u510•S/39. ThusI order/0 order<7.7%. As a result, the error onquc is no morethan 8%, and is therefore acceptable. The above result suthe following extrapolation. IfM 8.0 ~i.e., if the strip has telongate!, the distance between the point of application ofC andthe compressive edge can be adequately reproduced by theS/6 even ifs, f mc.

To illustrate the applicability and practicality of the propoanalysis, the model was applied~Fig. 16! to the specimens witthe third strip arrangement of Fig. 3~i.e., 180° intrados strips!,that failed by crushing. The 600 mm wide strips were attachthree bricks (11b54; w50.65), and the 35 mm wide stripsone brick (11b52; w50.33). The experimental value off mc

was 7.35 N/mm2. The application of Eq.~2! to the two striparrangements gives us Cu5(124/3)•4•245•0.65•7.355193.5 kN andCu549.1 kN, respectively. Eq.~4! written for Cu

gives usMmax8 520.00 kN m andMmax8 55.08 kN m, respectivelSince the extrados was not strengthened, at crushing the strexhibited three intrados hinges. Consequently, the crushingand internal actions were only correlated by considering eqrium ~three-hinged arch!. The experimental values ofMmax8 cantherefore be assessed directly from the experimental cruloads. The two values ofMmax8 ~i.e., the average values of the tsets of specimens! were 23.20 and 5.72 kN m, respectively. Taverage deviations between the calculated and measuredwere consequently no more than 14%, which is an accepvalue.

Sliding

The reinforced masonry withstands the shear action in theway as its unreinforced counterpart, by means of Coulomb’stion law, according to the masonry friction coefficientm'0.5~Heyman 1982!. But the resisting friction shear is generated

friction mechanism, respectively, in an unreinforced and reinforc
to the

cros

re-

ently,

x-

sng,

h the

d

-

stripcon-

-r

in-

.o thee

eyn be--

mes ofatethanently

stions,

as

theix,

FRPt canlied,n, sorce-ond-

ncenoteds ofincurs

al is

e

ad-

sonry

the resultant of the compressive stresses on the masonrysection,C, not by the normal internal actionN ~Fig. 17!.

Sliding is the result of an excessive shear actionV. The ulti-mate value ofV, Vu , again expressed per unit of width, is thefore ~Fig. 17!

Vu5C•m (9)

Sliding load causes the reinforcement to elongate. Consequthe distance betweenC and the compressive edge is stillS/6.Using the cross-sectional equilibrium,C can therefore be epressed as a function ofM 8 ~Fig. 15!. ReplacingC with saidfunction in Eq.~9! yields

Vu5m•1.2•M 8/S (10)

The sliding load factor is the lowestq for which V5Vu in ageneric cross section. It is essential to note thatVu also dependon the thicknessS. To design reinforcement to prevent slidiM 8 can be controlled by the arrangement of the FRP strips.

The proposed analysis was applied to the specimens witsecond strip arrangement of Fig. 3~i.e., extrados strips!, thatfailed by sliding~Fig. 16!. The analytical value of the sliding loacoincides with the average experimental values form50.64. Sucha value ofm is more realistic thanm50.5, the latter being conservative.

Debonding

Basic theoretical evaluation proves that a reinforcementepoxy-bonded onto a curved surface involves a significantcentration of normal stresses,s, transverse~normal! to the bonding masonry boundary, denoted ass' , along with the sheastresses,t, parallel to the bonding masonry boundary. In fact~Fig.18!, the transverse equilibrium of the infinitesimal arc of re

Fig. 18. Stress transfer between the reinforcement and the maarch

forcement around a masonry crack reveals thatt are balanced


s

tangentially, but not transversally~radially!. Only a transfer ofs'

between reinforcement and masonry can balance thet transferThe thickness of the reinforcement is disregarded here, sfollowing relationship relatess' with the unit tension force in threinforcement,T

s'5T

~l•w•F !(11)

in which l denotes the radius of curvature andF5width of thestrip that exhibitsT.

Eq. ~11! shows that, since thes' are due to the curvature, thexist even if the reinforcement has a thickness of nil and caevaluated independently of thet. Eq. ~11! also shows that intrados reinforcement implies1s' ~tension!, while extrados reinforcement means2s' ~compression!. While debonding incomposite-reinforced concrete beams can also result frotstresses, in masonry shells the other than debonding modfailure induce very lowt stresses that are far below the ultimlimit of t, which corresponds to a much higher ultimate loadfor the other failure modes. Debonding analysis will consequonly be concerned with intrados reinforcement.

It can be stated beforehand that thes' only exist on the brickadjacent to cracks, so the actually or potentially cracked seci.e., the cross sections whereT.0, are considered here~i.e., M 8.0 and therefore the point of application ofC is still that of Fig.15!. The relationship that linksT with N andM 8 is ~Fig. 15!

T51.2.M 8

S2N (12)

If Eq. ~12! is used in Eq.~11! for T, thens' can be calculated

s'5

1.2•M 8S

2N

~l•w•F !(13)

However, the crucial point is to establish the limit of thes' . Forthis purpose, the theoretical analysis has fully incorporatedexperimental results. Thes' are collected by the epoxy matrnot by the fibers, but the experiments demonstrated that thecomposite as well as the epoxy layer always remain intact. Ithus be stated that, if the FRP reinforcement is properly appthe epoxy resin is stronger than the masonry under tensiofailure is always dictated by the masonry and not by the reinfoment. The experiments indicated two failure modes for debing, namely:~block! ripping and~block! pull-out.

Considering the block ripping, the experimental evideshows that the transversal tensile strength of the brick, des'

mt , is the binding quantity, since this failure mode consistthe ripping of a 3–6 mm brick layer.s'

mt can be measured bysitu tests or obtained from the technical literature. Failure oconces' reachess'

mt in a section.If the angle formed by a cross section with the horizont

denoted asu, andum5angle defining the ripping section~if theloading is symmetric, theu’s are two! obtained by solving thfollowing equation, in whichM 8 andN are functions ofu andq,andS, l, w, andF are constants:

]F1.2•M 8~u;q!

S2N~u;q!G

]u50 (14)

Eq. ~14! gives us the following expression for the ripping lo
factor qur :
UNE 2004

ver-eut,k

sences,

tered

med

ig. 2

ein-

mea-

ent inasthety tolyzed

ex-

per

tion

iluresyzedst ofh.

le abe

houtin-

truc-con-

ies ofmany

ined.Thede--

eed by

pacityrfaceends

theo thes tocha-entlytruc-aterralior.ding

isionate forvalu-

qur5l•w•F•s'

mt

1.2•M 8~um ;q51!

S2N~um ;q51!

(15)

Eq. ~15! is based on the linearity betweenq andM 8.Considering debonding by block pull-out, we let the trans

sal forceR' be the resultant of thes' on a block. It is the valuof R' applied to the block that dictates failure by block pull-onot the maximums' . Then, denotingZ as the length of a bloc~i.e., the annular side of the masonry unit!, R' results asR'5B•Z•s' . Using Eq.~13!, R' can be obtained as follows:

R'5

S 1.2•M 8S

2ND •B•Z

~l•w•F !(16)

The next step is to obtain the ultimate value ofR' , denoted aR'

u . The ultimate value,R'u , is generated by the friction betwe

each of the two radial faces of the brick and the adjoining fasince~with the exception of multiring brickwork vaults! at leashalf of the blocks cross the whole thickness. Friction is triggby the resultant of the compressive stresses,C, along with thefriction coefficient. For the latter, a value of 0.5 may be assu~Heyman 1982!. For the former~Fig. 15!, the relationC51.2•M 8/S can be used. ThusR'

u is

R'u 52•m•1.2•M 8~u!/S52.4•m•M 8~u!/S (17)

R'u turns out to be a function ofu andq, as well asR' . The lower

q for which R' equalsR'u for a genericu, i.e., for which the

right-hand terms in Eqs.~16! and ~17! are equal at au, is thepull-out load-factor.

The proposed analysis was applied to the arch bridge of Fthat failed by block ripping. Tests provideds'

mt50.54 N/mm2.Eq. ~11! provides the maximum tension force in the unitary rforcement (w51.06): T50.54•55•1.06•5,015/2578.81 kN/m.Strain gauges were placed on the FRP reinforcement. Thesurements recorded at the time of ripping showT598.59 kN/m.The error of the model was 20%. Thus the same error is prespredicting the debonding load~at debonding, the structure wstatically determinate!. This error, albeit acceptable, is due tofact that masonry under tension allows for a certain plasticibe displayed. To refine the model, debonding has to be anawithin the framework of fracture mechanics, following, forample, the recent works of Boyajian et al.~2002a, b!.

Fiber-Reinforced Polymer Tension Rupture

Let TFt be the ultimate axial tension force in the reinforcementunit width of strip. FRP tension rupture occurs at the lowestq forwhich the following equation is verified in a generic cross secwhereM 8(u).0 ~Fig. 15!

1.2•M 8~u!/S5TFT•F•w (18)

Conclusions

The failure modes of a masonry arch whose hinged mode fa~mechanisms! are prevented by FRP reinforcement were analto obtain the ultimate load for each mode of failure, the lowewhich constitutes the strength of the reinforced masonry arc

There is a further, fundamental problem to solve. Whimechanism is implicitly determined statically, this may not
true of failure modes other than mechanisms. While in the former
JOURNAL OF CO

the springing thrust, and therefore alsoM 8 and N, are knowndirectly, in the latter the internal actions cannot be known witconsidering compatibility and constitutive laws. This problemvolves a low-strength material analysis on two-dimensional stures that can yield only a rough solution, which also variessiderably in time~with creep, cracking, etc.!. If the ultimate loadis dictated by a mode of failure other than mechanisms, a serhinges develops opposite the unreinforced boundaries. Incases, the hinges enable the structure to be statically determOtherwise, it is advisable to use the lower thrust of the arch.springing thrust is known to exceed said lower value, whichpends on the geometry and the loading alone~Blasi and Foraboschi 1994; Foraboschi and Blasi 1996!. The lower thrust of threinforced arch can be calculated using the method proposForaboschi~2001a!.

Parametric analyses have shown that the load-bearing cacan be increased significantly using a small quantity of suFRP reinforcement, but the entity of said increment deplargely on the arrangement of the reinforcement. It is not onlylocation of the reinforcement that influences strength, but alsspacing and the width of the strips, or the number of blockwhich a strip is bonded. Finally, to prevent the collapse menism by bonding external FRP reinforcement and consequforce the arch to fail by other less critical modes, lends the sture: ~1! a significant increase in load-bearing capacity, grethan for the hinging modes;~2! an appreciable reduction in latethrust, and~3! a more certain and predictable ultimate behav

This research will be further developed to consider debonusing the tools of fracture mechanics. Although the precachieved by the model proposed here seems to be adequdesign purposes, a refinement of the formulation would beable.

Notation

The following symbols are used in this paper:Aw 5 area of the working area~m2!;

B 5 width of the block~masonry unit, i.e., brick orstone! ~m!;

C 5 unitary compressive normal force internally actingon a masonry cross section~N/m!;

Cu 5 crushing normal actionC per unit of the arch’swidth ~N/m!;

F 5 width of a fiber-reinforced polymer strip~m!;f mc 5 masonry crushing stress~N/m2!;M 8 5 unitary bending action with respect to the reinforced

boundary~N m/m!;Mmax8 5 maximumM 8 in the [email protected]., maximum of

M 8(u)] ~N m/m!;N 5 unitary normal action~N/m!;q 5 load factor;

quc 5 crushing load factor;qur 5 ripping load factor;R' 5 transversal force applied to a brick~N!;R'

u 5 ultimate value ofR' ~N!;S 5 thickness of the arch~m!;T 5 tension force in the reinforcement for an unitary

width of the fiber-reinforced polymer strip~N/m!;TFt 5 ultimateT ~N/m!;V 5 shear action in an unitary cross section~N/m!;

Vu 5 unitary ultimate value of the shear actionV ~N/m!;
W 5 width of Aw ~m!;

,

f

e

roxide.

P.’’for

ds.,

r.,

e

ty

y.ity,

archornol-

tted

rch.e

nttonda,

o,

-art.’’-

-

nry

n.’’s.,

cedicata

c-

.ity,

f.se,

ing

c-

.

y 5 depth ofAw ~m!;Z 5 length of the block, i.e., annular dimension~m!;b 5 number of blocks with a strip attached to them;

«m 5 compression strain measured in the masonry, at thecrushing of the vault;

«m1 5 compression strain corresponding to the peak of themasonry stresses;

u 5 angle formed by a cross section with the horizontal~rad!;

um 5 ripping section~rad!;l 5 radius of curvature of the intrados of the arch~m!;m 5 masonry friction coefficient~—!;s 5 normal stress~N/m2!;

s' 5 stresses transverse to the bonding surface~N/m2!;s'

mt 5 transversal tensile strength of the brick~N/m2!;t 5 tangential stress on the bonding masonry boundary

the bonding layer, and the strip~N/m2!; andw 5 number of fiber-reinforced polymer strip

reinforcements per unit of the arch’s width.

References

Albert, M. L., Elwi, A. E., and Cheng, R. J. J.~2001!. ‘‘Strengthening ounreinforced masonry walls using FRPs.’’J. Compos. Constr.,5~2!,76–84.

Blasi, C., and Foraboschi, P.~1994!. ‘‘Analytical approach to collapsmechanisms of circular masonry arch.’’J. Struct. Eng.,120~8!, 2288–2309.

Boyajian, D. M., Davalos, J. F., Ray, J., and Kodkani, S.~2002a!. ‘‘TheCFRP-concrete interface subjected to sodium-sulfatate and -hydattack.’’ 17th Annual Technical Conf., ASC, West Lafayette, Ind., CT. Sun and Hyonny Kim, eds., paper 088.

Boyajian, D. M., Davalos, J. F., Ray, J., and Qiao, P.~2002b!. ‘‘Evalua-tion of interface fracture of concrete externally reinforced with FRProc. Second Int. Conf. CDCC 02, Durability of FRP CompositesConstruction, Montreal, B. Benmokrane and E. El-Salakawy, e309–320.

Ehsani, M. R., Saadatmanesh, H., and Al-Saidy, A.~1997!. ‘‘Shear be-havior of URM retrofitted with FRP overlays.’’J. Compos. Const1~1!, 17–25.

Faccio, P., and Foraboschi, P.~2002!. ‘‘Masonry cloist-vault: Collapsbehavior and rehabilation with composite materials.’’Proc. BritishMasonry Society; 6th Int. Masonry Conf., G. Thompson ed., SocieStoke-on-Trent, Penkhull-UK, 9, 121–131.

Faccio, P., Foraboschi, P., and Siviero, E.~2000!. ‘‘Collapse of masonrarch bridges strengthened using FRP laminates.’’Proc. 3rd Int. Confon ACMBS III; Ottawa, A. G. Razaqpur, ed., Carleton Univers
Ottawa, 505–512.

Foraboschi, P.~2000!. ‘‘FRP reinforcement used to upgrade masonrybridges to current live loads.’’Proc. Advanced FRP Materials FCivil Structures. Design, Quality Control and Rehabilitation, Techogy Transfer Seminar, Bologna, Italy, 109–119.

Foraboschi, P.~2001a!. ‘‘Strength assessment of masonry arch retrofiusing composite reinforcements.’’J. B. Masonry Soc.,15~1!, 17–25.

Foraboschi, P.~2001b!. ‘‘On the seismic analysis of masonry abridges.’’Proc. ARCH’01, 3rd Int. Arch Bridges Conference, Paris, CAbdunur, ed., Presses de l’e´cole nationale des Ponts et chauss´es,607–613.

Foraboschi, P.~2001c!. ‘‘Debonding of FRP external reinforcemeepoxy-bonded to masonry vaults.’’Proc. CCC2001, Int. Conf. Por(Portugal), J. Figueiras et al., eds., A. A. Balkema, Lisse, Ola583–588.

Foraboschi, P., and Blasi, C.~1996!. ‘‘Closure to ‘Analytical approach tcollapse mechanisms of circular masonry arch.’ ’’J. Struct. Eng.122~8!, 979–980.

Hamid, A. A., Mahmoud, A. D. S., and El Magd, S. A.~1994!. ‘‘Strength-ening and repair of unreinforced masonry structures: State-of-theProc. 10th Int. Brick and Block Masonry Conf., Elsevier Applied Science, London, Vol. 2, 485–497.

Heyman, J.~1982!. The masonry arch, Ellis Horwood-Wiley, West Sussex, U.K.

Kolsch, H. ~1998!. ‘‘Carbon fiber cement overlay system for masostrengthening.’’J. Compos. Constr.,2~2!, 105–109.

Meier, U.~2001!. ‘‘Advanced solutions with composites in constructioProc. CCC2001, Int. Conf. Porto (Portugal), J. Figueiras et al., edA. A. Balkema, Lisse, Olanda, 3–8.

Modena, C.~1994!. ‘‘Repair and upgrading techniques of unreinformasonry structures utilized after Friuli and Campagna/Basilearthquakes.’’Earthquake Spectra,10~1!, 171–185.

Saadatmanesh, H.~1994!. ‘‘Fiber composites for new and existing strutures.’’ ACI Struct. J.,91~3!, 346–354.

Tinazzi, D., Arduini, M., Modena, C., and Nanni, A.~2000!. ‘‘FRP-structural repointing of masonry assemblages.’’Proc. 3rd Int. Confon ACMBS III, Ottawa, A. G. Razaqpur, ed., Carleton UniversOttawa, 585–592.

Tong Li, P. F., Nanni, A., and Myers, J. J.~2001!. ‘‘Retrofit of un-reinforced infill masonry walls with FRP.’’Proc. CCC2001, Int. ConPorto (Portugal), J. Figueiras et al., eds., A. A. Balkema, LisOlanda, 583–588.

Triantafillou, T. C.~1998a!. ‘‘Strengthening of masonry structures usepoxy-bonded FRP laminates.’’J. Compos. Constr.,2~2!, 96–104.

Triantafillou, T. C.~1998b!. ‘‘Errata for ‘Strengthening of masonry strutures using epoxy-bonded FRP laminates.’ ’’J. Compos. Constr.,2~4!,203.

Valluzzi, M. R., Valdemarca, M., and Modena, C.~2001!. ‘‘Behavior ofbrick masonry vaults strengthened by FRP Laminates.’’J. Compos
Constr.,5~3!, 163–169.
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