Advances in Engineering Software 45 (2012) 213–231

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Advances in Engineering Software

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The behavior of masonry assemblages and masonry-infilled R/C frames subjectedto combined vertical and cyclic horizontal seismic-type loading

G.C. Manos ⇑, V.J. Soulis, J. ThauamptehAristotle University of Thessaloniki, School Of Engineering, Department of Civil Engineering, Division of Structural Engineering, Laboratory of Strength of Materialsand Structures, Earthquake Simulator Facility, Thessaloniki, Greece

a r t i c l e i n f o

Article history:Received 19 July 2011Received in revised form 25 September 2011Accepted 25 September 2011Available online 1 December 2011

To the memory of George Nitsiotas, ProfessorEmeritus of Aristotle University ofThessaloniki, Greece.

Keywords:Masonry infillsReinforced concrete frames with masonryinfillsMasonry assemblagesHorizontal seismic-type cyclic loadingExperimental and numerical predictions

0965-9978/$ - see front matter � 2011 Elsevier Ltd. Adoi:10.1016/j.advengsoft.2011.10.017

⇑ Corresponding author. Tel.: +30 2310 995653; faxE-mail address: gcmanos@civil.auth.gr (G.C. Mano

a b s t r a c t

The present systematic study aims to propose valid numerical models that can realistically approximatethe shear behavior of masonry assemblages and the hysteretic behavior of masonry infilled reinforcedconcrete (R/C) frames when they are subjected to combined vertical and horizontal cyclic loads. Success-ful numerical simulations are developed for the non-linear shear behavior of masonry joints and the non-linear behavior and ultimate strength of relatively weak Greek masonry piers; these are finally used, withthe same materials and geometry, as infills in the R/C frames. A valid numerical model is proposed thatcan capture successfully the various observed non-linear response mechanisms that develop within themasonry infilled R/C frames when they are subjected to combined vertical and cyclic horizontal loads.

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1. Introduction

This paper presents summary results of a numerical and exper-imental investigation that had the following objectives:

� To propose and validate different modeling techniques for thenumerical simulation of the non-linear behavior of masonrymortar joints under shear loading.

� To investigate the possibility of applying commercial software[10] for simulating the non-linear in-plane shear behavior ofunreinforced masonry piers made with relatively weak mortarin traditional Greek masonry constructed with clay bricks.

� To apply micro-modeling and macro-modeling techniques [9]utilizing this commercial software [10] for this type of unrein-forced masonry in order to predict failure modes, and load-carrying capacity observed experimentally when these masonrypiers are subjected to in-plane diagonally compressive orcombined vertical and cyclic horizontal loading.

� To examine next the behavior of masonry infilled frames. Toextend the proposed numerical simulation for masonry-infilledR/C frames and to validate it by comparing the numerical pre-

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dictions with results obtained from a corresponding experimen-tal study, where R/C masonry-infilled frame specimens aresubjected to in-plane combined vertical and cyclic horizontalloading.

� To study the influence of different forms of interface betweenthe masonry infill and the surrounding R/C frame and to exam-ine the influence that this interface exerts, in terms of stiffness,load bearing capacity, and failure mechanisms of the masonryinfill and the R/C frame, when such structural formations aresubjected to in-plane combined vertical and cyclic horizontalloading.

Many researchers in the past have attempted validations ofnumerical simulations of the non-linear behavior of mortar jointssimilar to the ones that are tried here, employing non-commercialsoftware. A brief summary is given in what follows. Jukes and Ridd-ington [7], developed a program to study the influence of variousfactors on the ultimate strength of masonry triplets. Laboratory re-sults from triplet samples, formed from different combinations ofmortar and bricks together with different loading conditions, wereused for the verification of the numerical results. Shear bond testson triplets have also been carried out, by Roberti et al. [20]. Van Zijland Rots [29], applied a discrete numerical modeling approach, cap-turing the most important failure modes on micro-shear clay-brick

214 G.C. Manos et al. / Advances in Engineering Software 45 (2012) 213–231

specimens. Lourenco [9], proposed a numerical model that com-bines the tension cut-off criterion, the Coulomb friction criterionand an elliptical cap mode. This model is incorporated into a finiteelement simulation of a masonry wall subjected to combined in-plane compressive and shear loading. Lourenco [9], used experimen-tal results of racking tests of masonry walls from Raijmakers andVermeltfoort [16] to validate the numerical approach he proposed.A 2-D finite element simulation was utilized by Riddington andJukes [17], for the prediction of the behavior of a brickwork panelsubjected to combined horizontal and vertical compressive loads. Fi-nally, Bosiljkov et al. [1], conducted a numerical and experimentalstudy on the influence of different mortar types on the behavior ofmasonry under uni-axial compressive loading. Karapitta et al. [8]proposed recently a simple smeared-crack numerical model forunreinforced masonry walls that are subjected to horizontal cyclicloading. Three different total strain-based constitutive relationswere proposed for the initiation of tensile, compressive and sheardamage and the corresponding stress–equivalent strain cycliccurves for each type of damage. It was demonstrated that the pro-posed numerical model yields a reasonably accurate prediction ofthe hysteretic behavior of unreinforced masonry walls under cyclichorizontal load. Da Porto et al. [4], carried out an extensive experi-mental program employing small masonry assemblages and sub-jecting them to uni-axial and diagonal compression tests as wellas in-plane cyclic shear-compression tests, aimed at defining thein-plane cyclic behavior of three types of load bearing masonry wallsassembled with perforated clay units and various types of head andbed joints. In their study the experimental behavior was modeledwith four types of non-linear finite element models. The proceduresadopted for model calibration established the reliability of the vari-ous modeling strategies. Moreover, Da Porto et al. [3], investigatedexperimentally three typologies of load-bearing un-reinforced ma-sonry walls; namely masonry made with thin layer joints, masonrymade with ordinary bed joint and interlocking units, and masonrymade with ordinary bed joint and units with pockets for mortar, sub-jected to in-plane cyclic loads. From the analysis of the experimentalcyclic behavior and of the corresponding envelope curves for thethree typologies of tested masonry, an analytical model was pro-posed, based on non-dimensional variables, which was defined bya symmetrical envelope curve dictating the hysteretic behavior.

In the present work, as will be outlined, various numerical toolswere employed, utilizing commercial software, for the simulationof the in-plane cyclic behavior of relatively weak unreinforced ma-sonry, which was part of the examined R/C masonry infilled assem-blages. The proposed methodology offers a numerical way that canrealistically predict the masonry infill state of stress and the dam-age potential for such seismically loaded infill R/C frames. Conse-quently, the proposed methodology can be utilized to predict theseismic vulnerability of masonry infills under a strong earthquakeand thus expose the fact that such masonry infills sometimes con-stitute inherently dangerous structural elements. Moreover, theproposed methodology can also be used to investigate how effec-tive are measures that are intended to upgrade a R/C framed struc-tural system that also includes masonry infills and reduce thevulnerability of its constituents. The following step by step proce-dure was used in the validation process of these numerical tools.Initially, two different numerical simulations are outlined and val-idated for approximating the non-linear behavior of masonry mor-tar joints under shear. Both simulations utilize the micro-modelingtechnique. In particular, experimental and numerical results fromthe study of Riddington et al. [19], were used to validate the pro-posed non-linear numerical simulations for masonry mortar joints.It is shown that both these micro-modeling techniques can suc-cessfully predict the shear strength and the propagation of failureof masonry mortar joints studied by Riddington et al. [19]. Threetypes of numerical simulations are tried next for the numerical

approximation of the behavior of single-leaf unreinforced masonrypanels tested under diagonal compression [25]. Two of thesenumerical simulations utilize the micro-modeling representationsof the mortar–brick interface, which were used before in the Ridd-ington, Fong, and Jukes study [19]. In addition, a macro-modelingsimulation is utilized for the numerical representation of masonrypanels under diagonal compression. The experimental results ob-tained from diagonal compression tests on square masonry panelswith different mortar types (V1, H) are used to validate the pro-posed numerical models. These square, masonry panels, tested un-der diagonal compression, had the same mechanical characteristicsas the masonry infills used for the construction of masonry-infilledR/C frames that will be studied next [25]. It is shown that themacro-modeling simulation proposed in this study for approxi-mating masonry behavior can successfully predict the shearstrength and failure mechanism obtained experimentally in ma-sonry panels tested under diagonal compression. The samemacro-model, which was proposed for these masonry panelstested under diagonal compression, is next utilized for the numer-ical simulation of the hysteretic behavior of masonry piers testedunder combined in-plane vertical and horizontal cyclic loading.The masonry piers tested experimentally are of the same materialproperties as the masonry panels tested under diagonal compres-sion [25]. This proposed macro-model can again predict success-fully the hysteretic behavior of these masonry piers.

Once one becomes confident that the proposed numerical sim-ulations of masonry under different types of loading can success-fully capture the non-linear behavior that is observedexperimentally, an effort is made to validate one of these numeri-cal simulations for approximating the behavior of masonry-infilledR/C frames. In this effort the same macro-model validated before isselect to be used in the numerical simulation of the masonry infillR/C frame behavior including stiffness and strength degradation.This is done by numerically simulating the non-linear behavior ofthe masonry infill itself, the formation of plastic hinges for theR/C frame at pre-defined locations and the sliding or the separationof the masonry infill from the surrounding R/C frame.

Styliniades [23,24], conducted an extensive experimental pro-gram with 16 single storey one bay 1/3 scaled masonry infilledR/C frame models. These specimens were very similar to the in-filled R/C frame specimens that are used here for the validationof the numerical model proposed in this study. The influence of avery important parameter was investigated in this study; that isthe level of interaction between the masonry infill and the sur-rounding R/C frame. Eight specimens had an interface betweenthe infill and the internal surface of the surrounding R/C framemade of mortar. Two different mortar types were used for the con-struction of these specimens both for the masonry infills and thesurrounding mortar interface, one strong and one weak. Theremaining eight specimens had a 1 mm wide gap between the ma-sonry infill and the beam of the R/C frame. It was suggested thatthe well compacted strong mortar interface between infill and sur-rounding R/C frame resulted in an increase of the initial stiffness,ultimate strength, and energy dissipation of these masonry infilledR/C frame specimens when they were subjected to combined ver-tical and horizontal cyclic loading. Moreover, Valiasis [28], hasexamined experimentally the cyclic behavior of 20 single storeyone bay 1/3 scaled masonry infilled R/C frame models also verysimilar to the infilled R/C frame specimens that are used here forthe validation of the numerical model proposed in this study. Fi-nally, a number of single-story one-bay R/C frame scaled speci-mens with masonry infills have been constructed and tested atthe strong reaction frame of the Laboratory of Strength of Materialsof Aristotle University of Thessaloniki [25]. These specimens havethe same overall geometry, the same structural details and areconstructed with the same materials as the in situ ‘‘unit’’ frame,

G.C. Manos et al. / Advances in Engineering Software 45 (2012) 213–231 215

forming the 5-story building at the European Test Site at Volvi-Greece [11,12]. The emphasis in this paper is on the employednumerical simulation for approximating the observed in-planecyclic response of three of these specimens and the comparisonof the numerical predictions with the recorded experimentalbehavior. The validation of the proposed numerical approach isdone through: (a) the comparison between the numerical andexperimental cyclic total behavior of the infilled R/C frames underthe combination of vertical cyclic horizontal loads, (b) the compar-ison of the damage patterns predicted numerically and observedexperimentally, (c) the comparison of the shear behavior of ma-sonry infills themselves, assuming different interface and levelsof interaction between the infills and the surrounding R/C frame.The masonry infill–R/C frame interaction has also been investi-gated experimentally by Stylianides [23,24], Valiasis [28], Valiasisand Stylianides [26], Valiasis et al. [27] and by Parducci and Mezzi[13]; they examined the influence of the interface between ma-sonry infill and the surrounding frame in a broad way. Carydiset al. [2] pointed out the significant influence on the observedbehavior exercised by the gap (0.5–1 cm) between the masonry in-fill and the surrounding R/C frame which resulted from shrinkageduring the construction period of the masonry infill. In the presentstudy this influence arising from the masonry infill R/C frame inter-action at the interface is more specifically examined employingthree types of interface (e.g. mortar V1, mortar H, and cork) withproperties defined through certain measured parameters in thelaboratory. The significance of the out-of-plane behavior of the ma-sonry infills is pointed out by Carydis et al. [2], as it is also seenfrom damage observations after strong earthquake events. How-ever, in all these studies as well as in the present investigation onlythe in-plane behavior is examined.

In the past, significant research effort has been devoted to theanalysis of masonry-infilled frames utilizing the finite elementmethod. Dhanasekar and Page [5], developed an iterative non-linear finite element model incorporating a biaxial strength enve-lope for the infill and one-dimensional joint element to modelthe interface between the infill and its surrounding frame. Zarnic[31], proposed two models, one for the simulation of the inelasticresponse to monotonous loading and the other for the simulationof the inelastic response to dynamic loading. These two modelsare based on experimental and analytical research involving 34one-bay, one-story specimens. The first model can be used forthe quick assessment of the stiffness and the load-bearing capacityof infilled frames. It assumes a tri-linear relationship betweendeformation and base shear. The second model, which is incorpo-rated in a computer program for dynamic analysis, includes frameelements, modeled as flexural joints, and masonry infills, modeledas pairs of compressive longitudinal struts. Zarnic et al. [32], devel-oped a two-dimensional plane-stress finite element model for un-reinforced and reinforced masonry infill using a Drucker–Pragertype yield surface. The behavior of reinforcement for the frame is

line of symmetry

FR

σn

(a)

fixed

σn

FR

mortar joint

mortar joint

Masonry unit

Masonry unit

Masonry unit Mas

Mas

moF

Fig. 1. (a) Triplet test loading arrangement, physical model s

idealized, using a uni-axial elasto-plastic model resisting only axialforces, whereas the contact between the frame and the masonryinfill is modeled with a 10 mm thick interface layer. Singh et al.[21], presented an inelastic finite element model to simulate theentire time history response of reinforced concrete masonry-infilled frames. This inelastic model is capable of predicting the se-quence of the formation of plastic hinges in the surrounding frameas well as that of cracks in the infills. Ghosh and Amde [6], pro-posed a finite element simulation to study the failure modes of ma-sonry infilled frames employing a variety of different frame-infillstrengths, as described by the analytical methods of previousinvestigators [18,14]. They compared their predictions with theexperimental results of previous researchers and they proposedtwo failure criteria for the masonry infill; the first includes ahomogenization approach together with the Von Mises criterionfor plane stress condition and a smeared crack model, whereas inthe second approach the mortar joints of the masonry infill aremodeled assuming a combination of the Mohr–Coulomb yield cri-terion together with a yield criterion in tension.

2. Numerical simulation of the non-linear behavior of mortarjoint under shear

The non-linear in-plane behavior of relatively weak Greek ma-sonry is believed to occur mainly at the mortar joints. Conse-quently, the numerical simulation of the non-linear behavior forthis type of masonry focuses on simulating the non-linear behaviorof the mortar joints. This is achieved by realistically simulating thefailure mechanisms that develop at the mortar joints as well as bysuccessfully predicting the in-plane load levels from which thesefailure mechanisms are initiated and from which they propagate.

Fig. 1a depicts a typical mortar joint in a triplet test that will besimulated in Section 2.1. Both numerical simulations outlined be-low are based on a combination of existing shear and normal stressfailure criteria for the mortar joints (Fig. 1b). Initially, a tripletarrangement (Section 2.1) and a diagonal compression test (Sec-tion 2.2) will be employed for the validation.

There are two modeling techniques that are generally availablefor masonry. The first is the ‘‘micro-modeling technique’’, in whicheach single constituent part of a masonry assemblage is repre-sented separately, (i.e. units, mortar, unit–mortar interface). Theadvantage of this method is that non-linearities, due to both mate-rial behavior and interface failure, can be addressed, while thebehavior of each constituent part can be checked separately. Thesecond modeling technique is the ‘‘macro-modeling technique’’where the behavior of the masonry constituents is not taken intoaccount but the masonry as a whole is considered to act as a com-posite with appropriate mechanical properties connecting theaverage masonry strains to average masonry stresses. The advan-tage of this method is that it can be applied to large masonry struc-tures providing a relatively simple and efficient simulation. Two

Shear stress along mortar joint

Normal stress along mortar joint

tension compression

τ

τoσn

(b)

support

σn

onry unit

onry unit

rtar joint R

imulated numerically. (b) Mortar joint failure envelope.

Fig. 2. Numerical simulation of triplet test: (a) Numerical simulation of mortar joint using 2-D non-linear spring elements. (b) Numerical simulation of mortar joint using acontinuum interface.

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different applications of the micro-modeling technique are em-ployed here for the numerical modeling of the mortar joint, result-ing in two different numerical simulations of the in-plane mortar-joint behavior, which are described below. These simulations donot differentiate between bed and head joints.

(a) Single line of 2D non-linear contact spring interface (Fig. 2a)

In this first type of simulation adjacent masonry units are geo-metrically expanded by the mortar joint thickness in such a way asto leave room only for a single interface between them. The ma-sonry units are represented by 8-noded continuum plane-stresselements, which are assumed to be linear-elastic in their behavior.The mortar joints are not represented by continuum elements. In-stead, a single line of 2D non-linear contact spring elements, sim-ulating in this very simple way the mortar joint, represents theinterface between the expanded brick units. This single line of2D non-linear contact spring interface simulates the non-linearbehavior and failure mechanism of the mortar joints. The stiffnessof these springs Kn and Ks are derived from the following formulas(1), and (2) for this kind of simulation:

Normal to mortar joint Kn ¼Eu � Em

hm � ðEu � EmÞð1Þ

Tangential to mortar joint Ks ¼Gu � Gm

hm � ðGu � GmÞð2Þ

where Eu and Em are the Young’s moduli, Gu, Gm are the shear mod-uli for the masonry unit and mortar respectively, hm is the actualthickness of the joint. The stiffness values of springs are derivedfrom the actual material properties of the triplets’ constituents.

(b) 2.2. A single line of 2D non-linear Mohr–Coulomb contin-uum interface (Fig. 2b)

This second type of simulation utilizes a single 2D non-linearcontinuum interface between the masonry units. A Mohr–Coulombfailure envelope is adopted for the mortar–masonry interface thatcan reproduce the crack opening and slip planes. Linear-elasticplane stress elements with 8 nodes are used for the finite elementmodeling of the brick units and the mortar, thus restricting thenon-linear behavior at the two mortar–brick interfaces for a singlemortar joint.

2.1. Numerical simulation of the behavior of triplets

The numerical simulation of this well-established experimentalprocedure is examined here whereby a simple three-brick and twomortar-joint assembly (triplet) is subjected to combined loads nor-mal and tangential to the mortar joints (see Fig. 1a and b). The val-idation of both proposed micro-models, which were describedbefore, was achieved through the comparison with correspondingnumerical results, which were obtained by Riddington et al. [19].The simulated tested triplets were formed by solid clay engineer-ing bricks with nominal dimensions 215 � 102.5 � 65 mm, andby mortar of class BS5628 (1 masonry cement:3.5 sand by weight)forming joints of 10 mm thickness. The mechanical characteristicsof the materials used in the present analysis (Table 1) are the sameas used by Riddington et al. [19].

The numerically-predicted average ultimate shear strength,which is accompanied by a slip of the mortar joint, is plotted inFig. 3, for four different pre-compression load levels, together withthe adopted Mohr–Coulomb failure envelope, which was also as-sumed by Riddington et al. [19]. In the same figure, the value of

Table 1Mechanical properties employed in the numerical simulation of the triplet test.

First type of simulation Numerical simulation of mortar joint utilizing 2-D non-linear spring elements

Elastic mechanical characteristicsMasonry unit E = 28500 N/mm2 v = 0.13

Normal stiffness Kn (N/mm3) Tangential stiffness Ks (N/mm3)Mortar joint 1273.096 529.43

Mortar joint (Mohr–Coulomb envelope) Non-linear mechanical characteristicsLocal bond shear strength so (N/mm2) Local coefficient of friction l Bond tensile strength ft (N/mm2)1.75 0.95 0.9

Second type of simulation Numerical simulation of mortar joint utilizing 2-D non-linear continuum interface

Elastic mechanical characteristicsMasonry unit E = 28500 N/mm2 v = 0.13Mortar joint E = 8800 N/mm2 v = 0.18

G = 3730 N/mm2

Mortar joint (Mohr–Coulomb envelope) Non-linear mechanical characteristicsLocal bond shear strength so (N/mm2) Local coefficient of friction l Bond tensile strength ft (N/mm2)1.75 0.95 0.9

Fig. 3. Shear strength of mortar joint at the initiation and at the complete failure ofmortar joint under four different pre-compression load levels.

G.C. Manos et al. / Advances in Engineering Software 45 (2012) 213–231 217

shear stress when initiation of failure was indicated is also plotted,for four different pre-compression load levels. The shear and nor-mal stress distribution is measured along the center of the mortarjoint, utilizing the second type of simulation (Fig. 4a). Failure is ini-tiated when the combination of shear stress and normal stress ap-proaches the failure criteria (limit stress levels and Mohr–Coulombenvelope) that were assumed in the non-linear analysis. Fig. 4bshows the normal and shear stress distribution at the initiationof failure. As can be seen in this figure, during the initiation of fail-ure the stress distribution of shear and normal stress is far fromuniform along the length of the joint. This is true for the two typesof simulation. The distribution for both the shear and normal stres-ses is relatively more uniform at the central part of the mortar-joint than at the edges. After the initiation of slip failure and asthe loading sequence progresses by slowly increasing the imposedhorizontal displacement in the non-linear analysis process, theshear stress distribution becomes more uniform than that whichis shown in Fig. 4b. At the same time, the slip failure propagatesalong the mortar joint from the initial failure point towards thecenter. At the ultimate load, the shear stress distribution alongthe mortar-joint becomes uniform and the slip failure spreadsthroughout along the interface (Fig. 4c). As can be seen, the twotypes of simulation are in good agreement with the simulation em-ployed by Jukes and Riddington [7] for the triplet tests. The predic-tions obtained from the first and second type of simulations will be

utilized for the subsequent validation of the in-plane diagonalcompression test.

2.2. Simulation of diagonal compression test behavior

The validation of the numerical simulation to realistically mod-el the shear behavior of masonry panels was next achieved throughthe comparison of numerical results with experimental results onsquare masonry panels that were subjected to a diagonal compres-sion test arrangement. The square masonry panels tested underdiagonal compression had the same mechanical characteristics asthe masonry infills used for the construction of masonry-infilledR/C frames, which are examined in Section 3. Both, the diagonalcompression tests and the infilled R/C frame tests, which are sim-ulated, were performed at the Laboratory of Strength of Materialsand Structures of Aristotle University of Thessaloniki [25]. Twodiagonal compression masonry specimens were tested withdimensions 580 mm � 550 mm � 58.5 mm. Two different mortartypes were used for the construction of the mortar joints of thesespecimens; a weak mortar type H, and a normal mortar type V1,having a mortar joint thickness of 10 mm. The first type of diagonalcompression numerical simulation (with 2-D non-linear springelements for the mortar joint) is depicted in Fig. 5. In Fig. 6 the sec-ond type of diagonal compression numerical simulation (2-D non-linear continuum interface for the mortar joint) is also shown. In anadditional third type of diagonal compression simulation, themacro-modeling technique is adopted together with the isotropicmodified Von Mises failure criterion, where the whole masonry pa-nel is simulated utilizing 2-D continuum elements with no differ-entiation between the masonry units and mortar joints of themasonry panel (Fig. 7). The mechanical properties employed inthese three different types of the diagonal compression testnumerical simulation are listed in Table 2.

In Figs. 8 and 9 typical measured shear stress–strain curves (s–c) for masonry panels under diagonal compression are depictedwith mortar joints either V1 or H, respectively. In the same figures,the shear stress–strain curves obtained numerically, utilizing thesethree types of numerical simulation, are also shown. The experi-mentally observed and numerically predicted failure regions, uti-lizing these three different types of numerical simulation, arepresented in Fig. 10a–d for the masonry panel with V1 mortarjoints, and in Fig. 11a–d for the masonry panel with H mortar joint.

All examined types of diagonal compression numerical simula-tion can satisfactorily predict, up to a point, the bearing capacity, in

Fig. 4. Numerical simulation of triplet test: (a) Cross section along mortar joint utilizing the second type of simulation. (b) Distribution of stresses at the initiation of failurepredicted by the second type of simulation and by Riddington et al. [19]. (c) Distribution of stresses at failure.

Fig. 5. Numerical simulation of masonry wall under diagonal compression utilizing 2-D non-linear spring elements for the mortar joints.

218 G.C. Manos et al. / Advances in Engineering Software 45 (2012) 213–231

terms of shear strength, and the failure mechanism observedexperimentally for the tested masonry panels. Consequently, thenumerical simulation utilizing the macro-modeling, despite itssimplicity when compared with the micro-modeling of masonry,is selected as a valid alternative for the modeling either of masonrypiers or of masonry infills subjected to compressive and shear-state of stress. In this relatively simple numerical simulation the

linear and non-linear behavior can be satisfactorily defined by asingle material law (modified von Mises) using a relatively coarsefinite element discretization leading to relatively short durationsolutions. It must be pointed out that all the examined numericalsimulations cannot successfully capture the behavior observedexperimentally in the large non-linear displacement range afterthe ultimate load has been reached (Figs. 8–11).

Fig. 6. Numerical simulation of masonry wall under diagonal compression utilizing 2-D non-linear continuum interface for the mortar joints.

Fig. 7. Numerical simulation of masonry wall under diagonal compression utilizing 2-D non-linear continuum elements combined with a single failure criterion.

Table 2Mechanical properties employed in the numerical simulation of the diagonal compression test.

First type of simulation Numerical simulation of mortar joint utilizing 2-D non-linear spring elements

Elastic mechanical characteristicsMasonry unit E = 4316 N/mm2 v = 0.13Mortar joint Normal stiffness Kn (N/mm3) Tangential stiffness Ks (N/mm3)V1 209.718 125.774H 102.37 60.88

Mortar joint (Mohr–Coulomb envelope) Non-linear mechanical characteristicsLocal bond shear strength so (N/mm2) Local coefficient of friction l Bond tensile strength ft (N/mm2)

V1 0.20 0.20 0.12H 0.14 0.52 0.12

Second type of simulation Numerical simulation of mortar joint utilizing 2-D non-linear continuum interface

Elastic mechanical characteristicsMasonry unit E = 4316 N/mm2 v = 0.13Mortar jointV1 E = 200 N/mm2 G = 120 N/mm2 v = 0.18H E = 100 N/mm2 G = 59 N/mm2 v = 0.18

Mortar joint (Mohr–Coulomb envelope) Non-linear mechanical characteristicsLocal bond shear strength so (N/mm2) Local coefficient of friction l Bond tensile strength ft (N/mm2)

V1 0.20 0.20 0.12H 0.10 0.52 0.10

Third type of simulation Numerical simulation of masonry wall utilizing 2-D non-linear continuum elements combined with asingle failure criterion

Masonry panel Elastic mechanical characteristicsV1 E = 1000 N/mm2 v = 0.13H E = 800 N/mm2 v = 0.13

Non-linear mechanical characteristicsCompressive strength fc (N/mm2) Tensile strength ft (N/mm2)

V1 1.2 0.20H 0.6 0.15Non-linear behavior E = �5 N/mm2

G.C. Manos et al. / Advances in Engineering Software 45 (2012) 213–231 219

Fig. 8. Numerically predicted and measured diagonal compression test behavior,masonry panel with mortar joint V1.

Fig. 9. Numerically predicted and measured diagonal compression test behavior,masonry panel with mortar joint H.

220 G.C. Manos et al. / Advances in Engineering Software 45 (2012) 213–231

2.3. Simulation of racking test masonry behavior

The previously validated macro-model representation of amasonry panel is further checked, utilizing experimental resultsobtained by Thauampteh [25], whereby masonry piers were sub-jected to combined in-plane vertical and cyclic horizontal loading(racking test). Fig. 12 depicts the testing layout whereby a masonrypier with overall dimensions 1590 mm (length) � 845 mm(height) � 58.5 mm (thickness) is placed within a steel reaction

Dama(a) (b)

Fig. 10. (a) Experimental for masonry panel (mortar joint V1). (b) 2-D non-linear spring ejoints. (d) 2-D non-linear continuum elements combined with a single failure criterion.

frame [25]. The vertical load was kept almost constant at a prede-termined level, varied from 20 kN to 100 kN. The horizontal forceapplied at the top of the pier was varied in a cyclic manner, bycontrolling the imposed horizontal displacement at this point ina predetermined way. As already mentioned, these masonry pierswere made with the same brick units and mortar that were alsoused for the diagonal compression tests, mentioned in Section 2.2before and the masonry infilled R/C frames of Section 3. The mortarhead joint thickness was 15 mm, while the bed joint thickness was10 mm.

The obtained behavior for two such masonry piers in terms ofan average cyclic horizontal load–horizontal displacement enve-lope curve, is depicted in Fig. 13a and b. Fig. 13a is for the 1st pier(W2NV1) constructed with normal mortar type V1, whereasFig. 13b is for the 2nd pier (W4NH) constructed with weak mortartype H. As mentioned before, only the results from the third type ofnumerical simulation utilizing the macro-modeling is shown here.The same material properties, stiffness, limit stress levels of themodified Von Mises envelope that were used for the diagonal com-pression test (presented in Section 2.2), are utilized again here.Fig. 13a and b depict the comparison of measured and numericallypredicted behavior, in terms of cyclic horizontal load and horizon-tal displacement, for the 1st (W2NV1) and 2nd piers (W4NH)respectively. As can be seen in Fig. 13a, there is reasonable agree-ment between predicted and measured values for the initial stiff-ness and the bearing capacity for the 1st pier (W2NV1). For the2nd pier (W4NH), as can be seen in Fig. 13b, there is again reason-ably good agreement between the predicted and measured valuesfor the initial stiffness and the bearing capacity. The numericalsimulations of the 1st (W2NV1) and 2nd pier (W4NH) is not so suc-cessful in the large non-linear displacement range as the testedspecimens degrade more rabidly than is predicted numerically.Reasonable agreement is seen between the experimentally ob-served and numerically predicted damage, which is presented inFig. 14a and b for the masonry pier with mortar joint V1(W2NV1), and in Fig. 14c and d for the masonry pier with mortarjoint H(W4NH).

3. Numerical simulation of the behavior of masonry-infilled R/Cframes subjected to cyclic horizontal and vertical in-plane loads

A series of R/C infilled frame specimens were subjected to cyclichorizontal loading during the experimental investigation that tookplace in the Laboratory of Strength of Materials, in the University ofThessaloniki [25]. The group of frames include one-bay one-story1/3-scale models with overall external dimensions 1720 mm

ge patterns(c) (d)

lements for the mortar joints. (c) 2-D non-linear continuum interface for the mortar

Damage patterns(a) (b) (c) (d)

Fig. 11. (a) Experimental for masonry panel (mortar joint H). (b) 2-D non-linear spring elements for the mortar joints. (c) 2-D non-linear continuum interface for the mortarjoints. (d) 2-D non-linear continuum elements combined with a single failure criterion.

Fig. 12. Experimental arrangement for testing masonry piers subjected to horizontal and vertical in-plane loads.

Fig. 13. (a) Experimental–numerical comparison for masonry pier W2NV1. (b) Experimental–numerical comparison for masonry pier W4NH.

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(length) � 1000 mm (height) and a length over height ratio equalto 1.7 (l/h = 1.7, Fig. 15).

As the validation of the proposed numerical simulation was donedirectly with the results obtained from the 1/3 scaled specimens anyinfluences arising from scaling were ignored. It is expected thatsuch influences cannot be significant as the used masonry infillswere constructed with prototype burnt clay units togetherwith prototype mortar mixes and mortar joints that were

approximately 9–10 mm thick, which is close to the thicknessof prototype mortar joints. This type of weak masonry employedas masonry infill was dominated by the compression–shear (fric-tional) non-linear mechanism that developed at these joints.

The cross-section of the columns was 110 mm � 110 mmmand that of the beam 100 mm � 155 mm and reinforcement ratioequal to 0.00785 (q = 0.785%). Axial load equal to 50 kN was ap-plied at the top of each column by a hydraulic actuator and was

Fig. 14. (a) Damage pattern of 1st pier W2NV1 under horizontal and vertical load. (b) Damage pattern (x) predicted numerically. (c) Damage pattern of 2nd pier W4NH underhorizontal and vertical load. (d) Damage pattern (x) predicted numerically.

Fig. 15. Masonry infilled R/C frame specimen and design details.

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kept constant during the cyclic horizontal loading. The results ofthe full study are included in the work by Thauampteh [25],where the behavior of all ten (ten) ‘‘bare’’ and masonry infilledspecimens is examined in detail. Moreover, the extensive com-parison of various numerical simulations with the behavior ob-served by Thauampteh [25], as well as by Styliniades [24],Valiasis [28], and Yasin [30] for the masonry infilled R/C framesis included in the work by Soulis [22] where the conclusions ofthe corresponding extensive validation, utilizing the results of all

these experimental studies are also presented. Due to space lim-itations, in this paper the validation of the proposed numericalsimulations presented is based on the comparison of experimen-tal and numerical cyclic response of three specimens investi-gated by Thauampteh [25]. These are the ones designated withthe code names F1N(R2f,0w)s, F2N, F3NP. Brief information onthese three selected masonry infilled R/C specimens is shownin Table 3 and Figs. 15 and 16. The members of these R/C framespecimens were designed and constructed to prohibit any shear

Table 3Outline of three masonry infilled R/C specimens selected for the present validation [25].

TestNo.

Frame codename infill state

Technical description of masonry infill Technical description of theinterface between frame and infill

1 F1N(R2f,0w)s(Virgin)

Mortar V1, thickness 58.5 mm Cork thickness 5 mm (withoutplaster)

2 F2N (Virgin) Mortar V1, thickness 58.5 mm Mortar V1 thickness 10 mm(without plaster)

3 F3NP (Virgin) Virgin infill constructed using mortar V1, and frame–infill interface using mortar V1, thickness10 mm, initially reinforced by reinforced plaster, that is in contact with the surrounding framethickness 78.5 mm

Fig. 16. (a) Test set up of frame with virgin masonry infill (F2N). (b) Test set up of frame whereby the masonry infill had both its faces covered with reinforced plaster (F3NP).(c) Loading sequence for frame F2N. (d) Loading sequence for frame F3NP.

Table 4Strengths of masonry infills and concrete.

Masonryinfill

Masonry infillthickness(mm)

Compressivestrength of masonry(N/mm2)

Shear strength of masonryunder diagonal compression(N/mm2)

Compressive strength ofmasonry units (N/mm2)

Compressivestrength of concrete(N/mm2)

Compressive strength ofmortar cylinders (N/mm2)

Virgin infillV1 58.5 2.765 0.180 6.50 25.9 1.125

Reinforced infillV1 78.5 3.75 0.44 6.50 25.9 1.125

Table 5Mechanical characteristics of frame’s reinforcement.

A/a Yield stress fsy (N/mm2) Ultimate strength fsu(N/mm2) Strain at yield esy (%) Strain at ultimate stress esu (%) Young modulus (N/mm2)

U5.5 (Longitudinal) 311 425 0.8 22.0 6.5 � 104

U5.5 (Transverse) 360 542 0.6 20.0 6.5 � 104

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mode of failure. Consequently, the numerical simulationpresented here deals only with mode of failures linked withthe flexural behavior of these R/C members. The possibility ofthese R/C structural elements developing shear mode of failureshould also be investigated as such a mode of failure is in many

practical cases a realistic possibility. This is being currentlyinvestigated; however, it cannot be easily validated due to lackof available experimental data.

As already mentioned, the influence exerted by the interface be-tween the masonry infill and the surrounding frame was examined

Fig. 17. Finite element simulation of masonry infilled R/C model.

Fig. 18. (a) Cross section of column with the reinforcement and the simulation of plastic hinge. (b) Combination of joint elements used in Lusas 13.3 [10] for the estimation ofmoment–rotation curve for column cross section.

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extensively in both studies by Thauampteh [25] and by Soulis [22].The validation presented here, although using only the selectedthree specimens is well representative of the most important

conclusive observations found in all these studies where all therelevant results are also included Thauampteh [25], Styliniades[24], Valiasis [28], Yasin [30]. Tables 4 and 5 list the mechanical

Fig. 19. (a) Cross section of beam with the reinforcement and the simulation of plastic hinge. (b) Rotational joint element used in Lusas 13.3 [10] for the estimation ofmoment–rotation curve for beam cross section.

Fig. 20. (a) Moment–rotation curve for beam cross section. (b) Moment–rotation curve for column cross section.

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properties of the materials used in the construction of these RCframes and their masonry infills.

The cyclic loading was applied gradually through an imposedcyclic horizontal displacement sequence. For the masonry infilledframe specimens F1N(R2f,0w)s, F2N this was done with a six-stepsequence (Fig. 16c) employing three full reversals for each step upto the level where the angular distortion for the tested framereached the value of 8.6‰. For the masonry infilled frame speci-men F3NP (Fig. 16d), three full load-reversals for each displace-ment level were employed with a 10-step sequence, up to thelevel where the angular distortion for the tested frame reachedthe value of 26.73‰.

It must be recognized that if the loading was applied as actualearthquake load in real time the R/C frame–masonry infill responsemay differ in terms of stiffness, strength or hysteretic dampingfrom what was measured during the presented experimentalsequence whereby the cyclic load was introduced in quasi-staticway. However, at this point in time the experimental data availabledo not provide information from real time earthquake load in asystematic way to be used in the proposed numerical simulation.The numerical simulation focused so far to achieve good agree-ment between the predicted and observed variation in terms ofstiffness and strength; the numerical simulation of the hystereticenergy absorption by the infill did not exhibit the same satisfactorydegree of accuracy. In this way, if one was to perform a timehistory dynamic analysis would be faced with this deficiency.

3.1. Simulation of the beam/column R/C elements and the plastic hingeformation

The finite element simulation employed for the R/C frame withthe masonry infill is shown in Fig. 17. In the numerical model of thesurrounding R/C frame the beam and the two columns are simu-lated, together with the locations of possible plastic hinge forma-tion at the ends of each element (Fig. 17, detail Nos. 4 and 5).Thick beam elements, able to deform and rotate in plane, were em-ployed for both the columns and the beam. Rigid beam elementswere also employed to simulate the corner connection betweenthe beam and the column (Fig. 17, detail No. 4). The formation ofplastic hinges at each end of the beam is achieved by a numberof flexural non-linear 2-D joint elements simulating the flexuralmoment against the elastic/plastic rotation at this location(Fig. 17, detail No. 4, Fig. 19a and b). A number of non-linear 2-Djoint elements are also employed at the ends of each column(Fig. 17, detail No. 5 and Fig. 18a and b). This time not only the flex-ural behavior is simulated, by the moment versus the elastic/plas-tic rotation (with the presence of axial load) relationship, but alsothe slip of the reinforcement. These non-linear 2-D joint elementsare also represented in Fig. 18b by the ‘‘z’’ symbol. The measuredmechanical properties of the concrete and reinforcement for thetested specimens are utilized to obtain the necessary values forthe properties of these non-linear 2-D joint elements. In Fig. 20athe calculated by a specialized software [15], moment–rotation

Fig. 21. Failure surface of masonry infill.

Fig. 22. Effective stress versus plastic strain for compressive assumed behavior.

Fig. 23. Effective stress versus plastic strain for tensile assumed behavior.

Table 6Mechanical properties of infills used in the numerical simulation.

TestNo.

Frame codename

E Youngmodulus (N/mm2)

Poissonratio

fc Assumed compressivestrength of masonry (N/mm2)

ft Assumed tensile strength ofmasonry (N/mm2) (as % of fc)

Esc Softening modulusunder compression (N/mm2)

Est Softening modulusunder tension (N/mm2)

1 F1N(R2f,0w)s 1000 0.2 1.2 0.2 (16.7%) �10 �102 F2N 1000 0.2 1.2 0.2 (16.7%) �10 �103 F3NP 3500 0.2 4.5a 1.5 (33.3%) �5 �5

a Includes reinforced plaster.

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relationship for the beam cross-section, based on its particulardetailing and material properties, is compared with the corre-sponding behavior produced by this non-linear 2-D joint elementsimulation. Similar comparison is made in Fig. 20b for the columncross-section with the axial load level equal to 50 kN; this axialload level was employed for all the R/C masonry infilled specimens.As can be seen, these non-linear 2-D joint elements successfullysimulate the calculated, by means of a specialized software [15],flexural moment–elastic/plastic rotation. Thus, they are expectedto simulate in a realistic way the non-linear flexural behavior ofthe critical sections of the examined reinforced concrete frameelements.

3.2. Simulation of the masonry infill

Plane stress elements are used for simulating the masonry infill(Fig. 17, detail No. 1); they are connected to the surrounding frameby a different series of 2-D joint elements that simulate the ma-sonry infill to R/C frame interface (peripheral mortar joint), as de-scribed below. The selection of size of these plane stress elementswas decided in a way that minimizes the computational cost butattains a satisfactory degree of accuracy for the simulation of themasonry infill behavior, as presented in the previous Sections 2.2and 2.3. The same macro-modeling that was used in these Sections2.2 and 2.3 for simulating the masonry behavior under diagonalcompression or under horizontal and vertical loading was also em-ployed here. It is assumed that a single material law including anisotropic modified Von Mises failure criterion governs the behaviorof the masonry infill. The mechanical elastic and post-elastic prop-erties of the different masonry panels that are utilized in thisnumerical simulation are listed in Table 6.

The assumed in this analysis initial yield surface is shown inFig. 21. The compressive assumed behavior is modeled by astress–strain relationship shown in Fig. 22, which includes a soft-ening branch to simulate masonry crushing. The tensile assumedbehavior upon cracking is modeled by a stress–strain relationshipshown in Fig. 23 where a softening branch is also employed. Thestrength properties and the plastic strain degradation used forthe numerical simulation of the masonry infill as indicated byFigs. 21–23 and Table 6, are based on the corresponding propertiesused for the successful numerical simulation of the masonrybehavior when subjected to either diagonal compression (Sec-tion 2.2) or racking (Section 2.3).

3.3. Simulation of interface between the R/C frame and the masonryinfill

The interaction between the R/C frame and the masonry infillhas a critical role, as it asserts an important influence on the result-ing state of stress of the masonry infill and contributes to thedevelopment of the various masonry failure modes. For this pur-pose, two sets of non-linear 2-D joint elements are used to simu-late the separation and slip between frame and infill as well asthe transfer of compression and shear for the three different types

of interface. The first set of these 2-D joint elements (Fig. 17, detailNos. 2 and 3) is active in the a direction transverse to the interface;it is of a frictional type, where the value of friction coefficient isintroduced (Table 7) which was shown to yield reasonably goodbehavior during the numerical simulations of the diagonal com-pression (see Section 2.2).

Table 7Mechanical properties of the interface used to simulate the mortar joint between infill and surrounding frame (cork, V1, strong interface).

A/a

Simulation of jointinterface between frameand infill

E Youngmodulus (N/mm2)

G Shearmodulus (N/mm2)

fc Measured compressivestrength of mortar (N/mm2)

ftn Assumed tensile strengthof mortar (N/mm2) (as % of fc)

so Local bond shearstrength of mortar (N/mm2)

l Frictioncoefficient

1 Cork 5 (Lowstiffness)

2 0.18 0.018 (10%) 0.03 –

2 V1 mortar 150 (Mediumstiffness)

65 1.20 0.12 (10%) 0.18 0.2

3 Reinforced plaster incontact with R/C frame

1000 (Highstiffness)

440 40 4.00 (10%) 5.20 –

Fig. 24. Comparison of experimental and numerical cyclic response infilled frameF1N(R2f,0w)s.

Fig. 25. Comparison of experimental and numerical cyclic response infilled frameF2N.

Fig. 26. Comparison of experimental and numerical cyclic response infilled frameF3NP.

Fig. 27. Measurement of the horizontal displacement of the infilled frame.

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The second set of non-linear joint elements (Fig. 17, detail Nos.2 and 3) is active in both the transverse and the normal to theinterface directions. In the normal to the interface direction thesejoint elements have elastic and post-elastic force/displacementproperties based on measured compressive strength values listedin Table 7 (resulting from the corresponding interface area) to-gether with an assumed post-elastic softening behavior. Similarly,the elastic and post-elastic force/displacement properties of thesejoint elements in the transverse direction are based on assumed lo-cal bond shear strength with a softening nature (Table 7). Boththese two sets of non-linear 2-D joint elements are placed in theperimeter of the masonry infill–R/C interface as shown in Fig. 17by the symbol ‘‘z’’ (Fig. 17, detail Nos. 2 and 3). For specimensF1N(R2f,0w)s, where cork was used in the interface, and for spec-imen F3NP, where the reinforced plaster of the masonry infill wasin full contact with the surrounding R/C frame the value of the

coefficient of friction for the first set of joint elements was assumedto be equal to zero (see Table 7). Rigid beam elements were intro-duced to link the thick beam elements representing the R/C framebeam and columns with these non-linear joint elements approxi-mating numerically in this way the interface between masonry in-fill and R/C frame.

3.4. Validation of the proposed numerical simulation for the masonryinfilled R/C frame

The validation of this proposed numerical simulation of the ma-sonry infill–R/C frame behavior is presented here by comparing thenumerically-predicted with the observed behavior in terms of: (a)load–displacement hysteretic curves, (b) shear stress-shear defor-mation curves of the infill behavior when different interface is used

Fig. 28. Measurement of the diagonal deformation of the masonry infill. Fig. 30. The influence of the interface between masonry infill and frame on theshear behavior of masonry infill, Comparison of the behavior F1N(R2f,0w)s–F2N.

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between the masonry infill and the surrounding frames, (c) thedamage of the masonry infills.

The comparison of experimental and numerical cyclic responsefor the masonry infilled R/C frames F1N(R2f,0w)s, F2N, F3NP is de-picted in Figs. 24–26. The employed numerical simulations predictsuccessfully the strength and load–displacement hystereticbehavior that are observed experimentally for all the examinedspecimens (see also conclusive observations 4, 5 and 6).

Fig. 29. Comparison of the shear behavior of the infill observed experime

The shear stress–strain behavior of the masonry infill when theinterface between masonry infill and the surrounding R/C frame ischanged is next examined. For this purpose, a subtraction proce-dure is employed utilizing experimental results obtained for thesame R/C frame with and without masonry infill when it is sub-jected to the same loading sequence. In this way, an estimate ofthe shear state of stress of the masonry infill can be found. Thecorresponding state of strain that develops on the masonry infillscan also be found through two different methods. This state of

ntally and predicted numerically. (a) F1N(R2f,0w)s, (b) F2N, (c) F3NP.

Fig. 31. (a) Damage pattern of masonry infill observed experimentally for infilled frame F1N(R2f,0w)s. (b) Damage pattern (x) predicted numerically.

Fig. 32. (a) Damage pattern of masonry infill observed experimentally for infilled frame F2N. (b) Damage pattern (x) predicted numerically.

Fig. 33. (a) Damage pattern of masonry infill observed experimentally for infilled frame F3NP. (b) Damage pattern (x) predicted numerically.

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strain is estimated either directly, through measurements of thediagonal displacements of the infill, designated as ‘‘diagonal sheardeformations’’ of the infill c2 (D.S.D., Fig. 28) or indirectly,through measuring the total horizontal displacements at thebeam of the specimen, designated as ‘‘total shear deformations’’c1 (T.S.D., Fig. 27). The value of shear strength (su) that is foundthrough this subtraction procedure assumes uniform distributionof shear stresses in a horizontal cross section of the masonry in-fill. It must be pointed out that the values of total shear defor-mations c1 (T.S.D) include both the deformations of themasonry infill together with the deformations of the interfacebetween infill and surrounding frame whereas the correspondingvalues of the diagonal shear deformations c2 (D.S.D) do notinclude the influence of the interface between infill and sur-rounding frame but solely the shear deformations of the ma-sonry infill itself. The results of this subtraction procedure in

terms of shear stress–strain behavior for the masonry infills isshown in Fig. 29a–c, by comparing the predicted with the mea-sured cyclic response for the three selected infilled frames spec-imens (e.g. F1N(R2f,0w)s, F2N and F3NP). Fig. 30 presents thenumerically predicted shear stress–strain behavior for the ma-sonry infills for specimens F1N(R2f,0w)s and F2N; it must bepointed out that these two specimens have masonry infills builtwith the same mortar (V1, is studied) but have different inter-face; cork is employed for specimen F1N(R2f,0w)s whereas mor-tar V1 is used for specimen F2N. The most importantobservations that can be made based on these results are listedas conclusive observations 7 and 8 in the following section.

The experimentally-observed and numerically-predicted dam-age to masonry infill is presented for frames F1N(R2f,0w)s, F2N,and F3NP in Figs. 31–33. Reasonably good agreement can be seenin these figures.

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4. Conclusive observations

1. The employed two types of numerical simulations were quitesuccessful in yielding good agreement for the non-linear behav-ior of the masonry joint, as described by other researchers(Figs. 3 and 4).

2. Three different types of numerical simulations were employedfor approximating the behavior of masonry panels tested underdiagonal compression. Both the diagonal compression strengthand the failure mechanism observed experimentally was pre-dicted successfully by all used numerical simulations (Figs. 8–11). The numerical simulation utilizing the macro-modeling isselected as the most efficient because it utilizes a smaller num-ber of finite elements without losing its accuracy; thus, it wasnext utilized for the numerical simulation of the behavior ofeither individual masonry piers or masonry infills within R/Cframes when they are subjected to combined vertical and cyclichorizontal seismic type loading.

3. The employed macro-modeling simulation successfully pre-dicts, in terms of initial stiffness and strength, the observedracking behavior of ‘‘Greek-type’’ masonry piers subjected tocombined in-plane vertical and cyclic horizontal seismic typeloading. This numerical simulation is not so successful in thelarge non-linear displacement range as the tested specimensdegrade more rabidly than is predicted numerically (Figs. 13and 14).

4. The numerical simulation of masonry-infilled R/C frames suc-cessfully predicts the strength and load–displacement hyster-etic behavior as well as the sequence of the development ofplastic hinges at the predetermined positions of columns andbeam, together with the damage patterns for the masonry infill,in terms of crack propagation. Moreover, from the obtained hys-teretic behavior it can also be seen that the dissipated energyexhibits good agreement between the numerically simulatedand the observed behavior (Figs. 24–26).

5. The employed numerical simulation of masonry-infilled R/Cframes having their infill repaired with reinforced plaster, pre-dicts successfully the observed during testing increase in stiff-ness, strength and energy dissipation due to this presence ofthe partially reinforced masonry infill (Fig. 26).

6. The numerical simulations of infilled specimens F1N(R2f,0w)sand F2N, where the masonry infills are the ‘‘same’’ but utilizedifferent interface between masonry infill and surrounding R/C frame, predict an increase of the shear strength of thesemasonry infills that can be correlated to the correspondingincrease of the ‘‘stiffness’’ of the interface (Figs. 29a and b and30).

7. The use of an interface with relatively medium stiffness similarto the stiffness of the masonry infill (as in specimen F2N) resultsin such a distribution of stresses within the infill that leads to itsdiagonal compression mode of failure. This relatively mediumstiffness of the interface also results in not very high compres-sive stresses in the regions where the masonry infill cornersmeet the R/C column to beam joint. On the contrary, very highstresses and local failure is predicted in these corner regions ofthe masonry infill of specimen F1N(R2f,0w)s where a weakinterface is used (cork); this is in agreement with the observedbehavior (Figs. 31 and 32).

8. The same effect in the corner region as the one described aboveis also predicted when the stiffness of the interface as well asthat of the masonry infill is very high, as is the case of specimenF3NP. This leads to very high localized compressive stresses inthe corners of the infill and consequently to local failure ofmasonry infill in these locations (Fig. 33). This local mode offailure at the corners was also observed during the experimen-

tal sequence and resulted to a distinct drop of the bearingcapacity of the masonry infill (Fig. 29c) as well as a degradationof the bearing capacity of the masonry infill–R/C assembly(Fig. 26).

9. The employed numerical simulation seems to represent in areasonable way the most important influences that the inter-face between masonry infill and surrounding frame exerts onthe cyclic behavior of such structural assemblies in terms ofstiffness, strength modes of failure, as it is demonstrated fromthe observed behavior. This is also true, up to a point, for thenumerical predictions of the energy dissipation and thestrength degradation that is observed for these structuralassemblies during cyclic loading (Figs. 24–26 and 29). It isbelieved, that a more successful numerical simulation of thesoftening branches of both the masonry infill and the interfacebehavior will succeed to making the numerical predictions ofthe energy dissipation and the strength degradation better thanthe ones achieved in this study.

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