Sensitivity Analysis of Nonlinear Behaviour of Infill ... · 1. INTRODUCTION Infill panels are constructed of masonry which is a heterogeneous material with a wide range of strength,

1. INTRODUCTIONInfill panels are constructed of masonry which is aheterogeneous material with a wide range of strength,deformation and energy dissipation properties. Thematerial non-homogeneity, wide range of materialproperties, the inherent nonlinear behaviour and the variety of local construction methods make theunderstanding of masonry behaviour and hence theinfill-frame more challenging.

A comparison made by Priestley et al. (2007) ofdifferent masonry materials used in existing Italianbuildings indicated that the compressive strength of thedifferent materials can vary by a factor of 5 to 10.Benjamin and Williams (1958) reported coefficients ofvariation of up to 100% in the compressive strength andmodulus of rupture, even though they used the sameclay bricks and mortar mix in their infill-framespecimens. By comparing different tests on infill-

Advances in Structural Engineering Vol. 16 No. 10 2013 1729

Sensitivity Analysis of Nonlinear Behaviour of Infill-

Frames Under In-Plane and Out-of-Plane Loading

Alireza Mohyeddin1,*, Helen M Goldsworthy2 and Emad F Gad3

1School of Engineering, Edith Cowan University2Department of Infrastructure Engineering, The University of Melbourne

3Faculty of Engineering and Industrial Sciences, Swinburne University of Technology

(Received: 11 March 2013; Accepted: 3 July 2013)

Abstract: This paper addresses the sensitivity of the in-plane and out-of-planebehaviour of reinforced-concrete (RC) frames with masonry infill panels to a selectnumber of material related parameters. Instead of general conclusions, the intention isto facilitate a deeper insight into the behaviour of infill-frames at a micro level over awide range of drift values. A script, which has recently been developed, is used togenerate the finite element (FE) models of an infill-frame with desired geometric andmechanical properties. Also, the same three-dimensional FE model is used for both in-plane and out-of-plane analyses of infill-frames. The sensitivity analyses areconducted in three sequential parts: the analyses of a masonry bare wall under one-waybending, the analyses of an infill-frame under out-of-plane loading and the sensitivityanalyses of an infill-frame under in-plane loading. A simple method is delineated toovercome convergence issues which are related to the highly nonlinear finite elementmodels to be solved using the Newton-Raphson algorithm.

Key words: finite element method, infill-frame, masonry, reinforced-concrete, sensitivity analysis.

frames and their theoretical results, Fiorato et al. (1970)concluded that the variability of the test results was suchthat “it is difficult to separate the limitations of themodel from the variability possible in the test results”.Unlike other conventional construction materials suchas concrete and steel, masonry units are produced usingdifferent local materials with different shapes.

Polyokov (1956) referred to the studies by LIOnishchik in 1937 and 1939 in which he had suggestedthat a masonry panel could be considered as a“compressed diagonal strut” in the design of a frame(under in-plane loading). Later on, an equivalent crosssectional area of such a strut was proposed by Holmes(1961) for the first time. This concept has been widelystudied since then (e.g. Stafford-Smith 1962, 1966a;Mainstone 1971; Klingner and Bertero 1978; Zarnic andTomazevic 1985; Sobaih and Abdin 1988; Angel 1994;Mehrabi 1994; Zarnic 1994; Reinborn et al. 1995;

*Corresponding author. Email address: [email protected]; Fax: +61 8 6304 5811; Tel: +61 8 6304 5201.

and Kwan (1982), Dhanasekar et al. (1984), Ali andPage (1988), Riddington and Gambo (1991), Rots(1991), Lourenco and Rots (1993, 1994), Crisafulli(1997) as examples of such studies.

Based on a parametric study using a FE model,Dhanasekar and Page (1986) showed that the effect ofthe shear and tensile bond strengths of bed and headjoints on the in-plane strength of the infill-frame issignificant. These, however, are highly variable materialproperties and difficult to measure (Mohyeddin 2011).They found that the compressive strength of themasonry is influential only in the infill-frames whichfail due to corner crushing of the masonry and has littleinfluence on those with diagonal-shear mode of failure.Nevertheless, their specimens were not subjected togravity (vertical) loads and that could be a reason for theexcessive sensitivity of the results to bond strengths,and the reduced sensitivity to the compressive strength.They found the effect of any variation in Poisson’s ratioto be negligible. The FE load-deflection curvesprovided in this reference extend to a maximum drift ofapproximately 0.3% and are compared to experimentalresults of only up to 0.2%, i.e. a very low level of drift.

Based on a masonry material model and an interfacefinite-element previously proposed by Lotfi and Shing(1991, 1994), Mehrabi (1994) developed a two-dimensional FE model for the in-plane analysis of infill-RC frames. Stavridis and Shing (2010) furtherdeveloped this model and conducted a parametric studyon infill-frames to examine the effect of the variabilityof masonry and concrete material properties on the in-plane response of infill-frames.

Seah (1998) developed a two-dimensional FE modelfor analysis of infill-frames under in-plane loading. Hedefined the failure surfaces for masonry as thosespecified by Lourenco (1996). Using his FE model, he explored the effects of panel aspect ratio, strength of the infill panel-to-frame interface, the gap between theframe and the infill, mortar joint shear strength, frame(connections) rigidity, masonry strength and gravityloads on infill-steel frames (Dawe et al. 2001).

Given the inherent high variability of the masonrymaterial properties, a sensitivity analysis is deemed tobe a necessary part of any analytical study on infill-frames before any conclusion can be made on thebehaviour of such structures. On the other hand, theexisting models are applicable to either in- or out-of-plane loading, whereas in actual earthquakes they areapplied at the same time, deteriorating the structuresimultaneously.

The intention here is to investigate the sensitivity ofthe in-plane and out-of-plane behaviour of infill-framesto a select number of parameters within a certain range

1730 Advances in Structural Engineering Vol. 16 No. 10 2013

Sensitivity Analysis of Nonlinear Behaviour of Infill-Frames Under In-Plane and Out-of-Plane Loading

Saneinejad and Hobbs 1995; Crisafulli 1997; Madan et al.1997; Al-Chaar 1998; Kappos et al. 1998; Combescure2006).

Fiorato et al. (1970) conducted a comprehensivestudy of the in-plane behaviour of infill-RC frames.They carried out twenty-seven push-over tests on one-eighth scale models of infill-RC frames (they usedsmall-scale clay bricks). They confirmed that theinteraction between the frame and infill panel results ina structural response which is markedly stiffer andstronger than the sum of the individual response ofeither of the components. Ignoring this interaction notonly is a considerable strength of the structure wasted,but also there will typically be a failure to correctlylocate the critical sections within the structure.

Based on experimental results of more than 200tests on small scale mortar infill-steel frames, StaffordSmith (1966b) concluded that the in-plane stiffnessand (ultimate) strength of the infill-frame arefunctions of the relative stiffness of the frame andinfill panel. They observed that the in-plane responseof an infill-frame is distinctly different from that of apanel or a frame. However since the infill was made ofmortar only, it was assumed that the infill washomogeneous and isotropic; assumptions that arehardly applicable to a real infill panel due to existenceof bed and head joints.

The effect of the surrounding frame on out-of-planestability of the masonry infill was first explained byThomas (1953). The out-of-plane strength of amasonry infill is mainly dependent on its slenderness.As reported by Shing and Mehrabi (2002) manystudies on out-of-plane behaviour of infill-framesindicate that infill panels restrained by frames candevelop significant out-of-plane resistance as a resultof an arching effect. Dawe and Seah (1989) concludedthat prior to cracking the behaviour of the infill-frameis governed by flexural action whereas thepostcracking behaviour is governed by arching action.

One of the issues is the similarity between the crackpatterns of in- and out-of-plane loading which canhave acumulative effect on each other (Angel 1994).The interaction between in- and out-of-plane loadinghas been largely ignored due to difficulties in bothexperiments and theoretical modelling, and hencethere is only limited research on such an interaction(e.g. Angel 1994; Flanagan and Bennett 1999; Calvi etal. 2004).

Many researchers have applied the finite elementmethod to the analysis of masonry and infill-framestructures. One can refer to Karamanski (1966), Mallickand Severen (1967), Riddington and Stafford Smith(1977), Page (1978), Arya and Hegemier (1978), Liauw

of material variation using the same three-dimensionalFE model. This will be a step forward towards the futureresearch on the interaction between the two, which, insome previous earthquakes, has been found to besubstantial (e.g. Kafle et al. 2008).

2. FE MODEL OF THE INFILL-FRAMEDue to the complexity of the geometry of an infill-framemodel, the preprocessing phase of an infill-frame FEanalysis is prohibitively time-consuming; this will aggregate when a series of parametric/sensitivityanalyses is to be carried out. In order to facilitate suchanalyses, a script, which has been developed in a macrofile, is utilised. This macro file can be used to generatea generic three-dimensional FE model of a one-storeyone-bay reinforced-concrete frame with/without aninfill panel. All of the geometric and mechanicalproperties of the infill-frame (such as frame span, frameheight, beam/column dimensions, the amount oflongitudinal reinforcement/stirrups, concrete cover,number of masonry rows in the infill panel, number ofmasonry units in a single row, mortar joint thickness,masonry unit dimensions, existence of a gap betweenthe beam and masonry panel, the width of such a gap,masonry and/or concrete material properties,frictional/debonding properties at bed and head joints)can be easily changed. A complete version of this script(macro file), which is to be executed within ANSYS,can be found in Mohyeddin (2011). The detaileddiscussions on this model can also be found inMohyeddin et al. (2013); a general description of themodel as well as its limitations is explained below.

2.1. General Aspects of the FE ModelThe finite element which is used to model the reinforced-concrete and masonry materials, has smearedreinforcement and smeared cracking capabilities alongthree orthogonal directions. The nonlinear behaviour ofthe material in compression is considered through anappropriate stress-strain relationship (see sections below),and the tensile stress is limited by the material tensilestrength. The failure surface is implemented such that atension cut-off is added to the von Mises failure surface.This is similar to the model proposed by Lotfi and Shing(1991), which has also been applied to later studies(Mehrabi 1994; Al-Chaar and Mehrabi 2008; Stavridisand Shing 2010); however, one of the advantages of thefailure surface of the constructed model is implementedin a three-dimensional stress space.

2.2. Reinforced-Concrete Material ModellingThe cross sections of the beam, columns and theirconnections are meshed such that the longitudinal

rebars are smeared over a limited number of elementsrather than the whole cross-section. This is to locatethe reinforcement in the appropriate location; nolongitudinal reinforcement is smeared across theelements of the cross-section representing the plainconcrete cover and concrete core. The same strategy isused for the transverse rebars along the memberswhich in turn represent the spacing between thestirrups. Figure 1 shows how this is implemented; inthis figure a generic FE mesh of a frame is plottedwithout the plain concrete core and concrete coverelements.

The capability of the combination of smeared cracks(instead of individual cracks) and smearedreinforcement (representing stirrups; see Figure 1) toreplicate the actual confinement of concrete was subjectto a series of sensitivity analyses. Since cracking doesnot occur gradually in the constructed FE model (i.e. anelement is either cracked at an integration point, or not),microcrack formation/propagation cannot be properlyrepresented. To this end, different stress-strainrelationships proposed for confined and unconfinedconcrete were examined (e.g. Kent and Park 1971; Scottet al. 1982; Mander et al. 1988; CEB-FIP Model Code1993; Eurocode 2 2005). Figure 2(a) includes agraphical example of some of the abovementionedmodels for f’c = 30.9 MPa, where f’c is thespecified/characteristic compressive strength of theconcrete. This value is the concrete strength recorded inthe experiment used for verification of reinforced-concrete FE modelling (Mohyeddin 2011). Figure 2(b)contrasts the force-drift curves of a bare frame whichwas analysed using different stress-strain relationships.The results show that the modified Kent and Park offersthe best match with the experimental results. It furthershows that the influence of confinement shouldexplicitly be included within the material constitutive


Alireza Mohyeddin, Helen M Goldsworthy and Emad F Gad

XY

Figure 1. FE mesh without concrete core and concrete cover to

show the arrangement of elements accommodating longitudinal and

transverse reinforcement

model. Taucer et al. (1991) also found this model as agood balance between simplicity and accuracy. Furtherresults on the sensitivity analyses of this non-ductileframe can be found in Mohyeddin et al. (2010). Thisframe is similar to that of the infill-frame consideredlater for the in-plane analyses except that thecompressive and tensile strengths of concrete are 30.89 MPa and 6.76 MPa, respectively.

A bi-linear stress-strain relationship is assumed forthe smeared reinforcement material. The modulus ofelasticity of steel, Es, is assumed to be 200 GPa, and thesecondary stiffness, E2, (also known as the “tangentstiffness”) is assumed to be 2.5% of Es. As it isapplicable to most metals, the von Mises failure surfacewith a total stress range of twice the yield stress(Bauschinger effect) is used here for the reinforcingsteel.

2.3. Masonry Material ModellingSince the masonry modelling proposed in this paper isused in the context of infill-frames, the relationshipproposed by Angel (1994) is used to represent thenonlinear behaviour of masonry material incompression:

Em = 750 f ′cm (2)

in which σm and εm are the compressive stress and strain,respectively, f’cm is the maximum compressive strengthof the masonry, εcrm is the maximum strain of themasonry before it fails and Em is the modulus ofelasticity of masonry. One of the issues with theequation proposed by Angel is that where εcrm is smallerthan 0.003 or greater than 0.0048 the second derivativeof the equation is positive, leading to unrealistic resultswhen matched against experimental curves. For thisreason, for any such extreme values, the equationproposed by Hendry (1990) is used (Figure 3):

(1)

σε

εε

ε

mcm crm

crmm

cm cr

f

f

=−

+−

′

′

27 250 1

4

27 1 333 3

33( )

( . mm

crmm m mE

)

4 22

εε ε+



50

40

30

20

10

00 0.005 0.01 0.015 0.02

Code 90-ConfinedMander al-ConfinedKent & Park-ConfinedKent & Park-Unconfined

Strain

120

100

80

60

40

20

00 1 2 3 4

Drift (%)

(a)

(b)

ExperimentalConfined (Kent & Park)Un-confined (Kent & Park)Confined (Mander et al.)Confined (Code 90)

Str

ess

(MP

a)La

tera

l for

ce (

kN)

Figure 2. A comparison between different: (a) stress-strain

relationships for confined concrete; (b) FE results using different

material models

Initial part, up to 0.00044, withpositive second derivative

Positive second derivative

Angel

Hendry

12

9

6

3

0

12

9

6

3

0

0 0.001 0.002

0 0.002 0.004

e0m

e0m

Strain (mm/mm)

Strain (mm/mm)

Str

ess

(MP

a)S

tres

s (M

Pa)

Figure 3. A comparison between the two equations given by

Hendry (1990) and Angel (1994) for ε0m = 0.0013 (εcrm = 0.0020),

and ε0m = 0.0034 (εcrm = 0.0051)

(3)

in which ε0m is the strain at which the maximum stress,f’cm, occurs.

The tensile strength of the masonry, f’tm, isconsidered to be 10% of the uniaxial compressivestrength. This is based on the suggestions given byCrisafulli (1997) for masonry units based on acomparison between different experimental results.Poisson’s ratio of masonry is considered equal to 0.2.

In the FE models constructed here, the mortar jointthickness is broken into two halves. This is similar to“simplified micro modelling” based on the classificationby Rots (1991) and Lourenco (1996). This methodreduces the number of interface elements and decreasesthe computational costs and convergence problems. Eachhalf is attached to the adjacent masonry unit from oneside, and interacts with the other half of the mortar jointand its adjoining masonry unit through interface (surface-to-surface frictional contact) elements [Figure 4(a)]. Thesame type of contact elements are used to represent theinterface between the infill panel and frame members.

Both shear and tensile debonding are modelled usingthe “cohesive zone model (CZM)”. This is based on a

σεε

εεm cm

m

m

m

mf= −

′ 20 0

2 linear elastic fracture mechanics (LEFM) methodproposed by Alfano and Crisfield (2001), assuming alinear softening branch for the stress-strain curve.

Earlier analyses of the constructed model showed thatif all of the mortar elements possessed a nonlinear materialmodel along with cracking/crushing capability, some ofcontact elements (which are attached to mortar elements)would deform in such a way that they would become ill-shaped. As a result, the complete loss of contact betweenthe two adjacent masonry FE units would occur, leading toa disrupted load path. Such a discontinuity in the modelcould lead to a premature failure, which would not only beunrealistic, but also progressive and fatal. Anotherconsequence of such behaviour would be convergenceissues. In order to provide a stable underlying platform forsome of contact elements and protect the “masonry FEunits” [Figure 4(b)] from an extensive deformation and/orpenetration, a central band of mortar [Figure 4(b)] isassumed to behave in a linearly elastic manner.Incorporating an elastic central mortar band, however,may raise some questions on accuracy of the results andwhether they would prevent or postpone some of thefailure modes of masonry. Therefore, their overall effecton the behaviour of the masonry panel needed furtherinvestigation. The results of this investigation, which hasbeen explored in detail by Mohyeddin (2011), will besummarised in the next section.

2.4. Limitations of the Constructed ModelThere are limitations in the constructed FE model whichcan be summarised as follows:

(1) One of the shortcomings is associated with thefailure surfaces used for concrete and masonrymaterial. Even though the von-Mises failuresurface with a tension cut-off has already beenused in the literature for both concrete andmasonry materials (see “General aspects of theFE model), it is a source of discrepancy betweenthe experimental and FE results;

(2) There are inadequacies in the capability of thecontact elements in terms of the tensile andshear bond and more accurate models, e.g.Hordijk (1991), Pluijm (1992) and Rots (1997),could improve the overall model;

(3) The tensile stress-strain relationship formasonry and concrete is a linear one whichcould be improved by incorporating moresophisticated models (e.g. van Mier 1986;Lourenco 1996; Bazant and Becq-Giraudon2002; Wittmann 2002);

(4) There is no debonding between the reinforcementand concrete; this is to reduce the number ofelements and the nonlinearity of the model.



Mortar rims with nonlinearmaterial properties

Elastic mortar band in the middle to providea more stable platform for contact elements

One set of contact elements representing theinterface midway between the head joint

One set of contact elements representing theinterface midway between the bed joint

(a)

(b)

Figure 4. (a) The location of the interface (contact) elements in the

masonry; (b) “Masonry FE unit” used in analyses comprising a

nonlinear masonry block surrounded by nonlinear mortar rims and

a central elastic mortar band

However, the model could be adapted to includethe debonding between the reinforcing bars andconcrete;

(5) Stability of contact elements in cases wherethe underlying elements fully crack/crush; thiswas rectified by inserting an “elastic mortarband” to stabilise the contact elements and toreduce the likelihood of convergenceproblems. Even though the elastic mortar banddoes not influence most of the masonry failuremodes (viz. sliding along the joints, crackingof the masonry blocks in direct tension,diagonal cracking of the units where there issufficient normal stress to develop friction inthe joints, and masonry crushing), it may havesome confining effect on the masonry unit inthe mid part. This effect, however, is notsubstantial; this is because any excessive stressin the elastic band would be followed by extrastresses in the masonry units leading tocracking/crushing of the units. Hence, thisundesired effect will diminish rapidly. Theother effect is that elastic bands may cause adiscontinuity of cracks where the cracks formin the middle of a masonry FE unit. Again, interms of vertical cracks (even though theelastic band in the middle would remainintact), the load path would be interrupted bythe cracks in the masonry unit; therefore theeffect would not be major. However, in thecase of diagonal cracks, they cannot grow to acontinuous crack across adjacent rows, if theyform in the middle of the masonry. This failuremode would be delayed until the nearby headjoint fails or the crack is redirected to adjacentmortar elements (rims) with nonlinear materialproperties (Figure 4).

3. SOLUTION OF HIGHLY NONLINEARMODELS

Mohyeddin (2011) introduced a method to overcomeconvergence problems associated with the highlynonlinear models constructed here. This is important inview of the fact that when the Newton-Raphson methodis used for solution of a nonlinear (structural) model, itoften leads to convergence difficulties which in manycases results in a termination of the analysis. A commonsymptom of this behaviour is that substeps start to bisect(if automatic time-stepping is activated) to reduce thenonlinearity, and the number of iterations increases toattempt to achieve convergence; these strategies maynot always be successful. The proposed method relieson the assumption that for an infinitesimal substep

(which means the load/displacement increment isinfinitesimal) the tangent stiffness gives a goodapproximation to the actual stiffness without anyiterative procedure being required. This means that theconvergence criterion can be disregarded for aninfinitesimal substep.

Based on direct observations of the solution phaseof many nonlinear analyses performed with differentconvergence tolerances, an idea evolved as follows: ifit was possible to jump over a specific substep thatblocks the solution from being pursued any further,here called the “convergence hurdle point” (CHP), itwould be likely that convergence would not beproblematic for the rest of the analysis, or until anotherCHP is reached. If this is true, it means that theiterative Newton-Raphson method would be able toproceed after passing the local CHPs, instead of theanalysis being terminated. In order to implement thismethod when there is a CHP:

1) Solution is stopped;2) The analysis is allowed to progress for a few

infinitesimally small substeps, by manipulatingconvergence criteria (e.g. by overwriting thecalculated norm of the out-of-balance force(residual) vector with a large figure, in the case of convergence being checked based onforce, i.e. “MINREF” command of ANSYS2009);this is to temporarily deactivate anyconvergence check and the iterative Newton-Raphson procedure;

3) The solution will be stopped again after a fewinfinitesimal substeps when the norm of theresidual force vector is small enough to pass theinitial (default) convergence criterion. It hasbeen observed (Mohyeddin 2011) that if thesolution is allowed to proceed for say 50infinitesimal substeps (which could beequivalent to 0.005% of the total solution timespan), CHP will be passed and the Newton-Raphson algorithm can be set to its initial set-up;

4) The solution is restarted (multi-frame restartmethod of ANSYS 2009) for the second timeand continued with the initial convergencecriteria (i.e. the usual solution features providedby the programme such as automatic time-stepping are employed again for a faster (lessexpensive) solution and to benefit from theiterative Newton-Raphson procedure).

The accuracy of the results of nonlinear models,which were analysed using the above method andverified by experimental results (Mohyeddin 2011),confirm that this method can confidently beemployed.



4. SENSITIVITY ANALYSESThe verification of the constructed FE model isexplained in Mohyeddin (2011) and Mohyeddin et al.(2013). The FE model was verified against theexperimental results of a test conducted on a bareframe under in-plane lateral load (Mehrabi 1994),two masonry walls under one-way (out-of-plane)bending (Doherty 2000), two infill-frames under in-plane lateral loading (Mehrabi 1994) and an infill-frame under two-way (out-of-plane) loading(Angel,1994). The results of the sensitivity analyses on theselected bare frame are explained in Mohyeddin et al.(2010).

4.1. Out-of-Plane One-Way Bending of MasonryWalls

One of push-over static tests conducted by Doherty(Doherty 2000), namely Specimen No. 3 is used inthis section. This is one of the two specimensconsidered by Mohyeddin (2011) for the masonry FEmodelling verification. Standard Australian three-holeextruded clay bricks having dimensions of76*110*230 mm (thickness*width*length) were usedwhich were laid with 1:1:6 (cement : lime : sand)mortar mix. The specimen is 1485 mm high, 110 mmthick and 950 mm wide. As for the out-of-planeloading, a hand pump driven hydraulic actuator wasused at the mid-height of the wall. The averagecompressive strength of masonry prisms is 13.3 MPa,which is used as the input for Eqn 1, assuming ε0m is0.0017. The shear bond strength, τ0, and mode IIfracture energy of the interface, GII

F, do not contributeto out-of-plane failure of the tested specimen, andhence their effect can be neglected in the FE analyses.In FE models here, the coefficient of friction isassumed to be 0.7. Due to expected poor quality of thehead joints, the friction coefficient at head joints isconsidered to be one third of that of bed joints.

4.2. Results of the Se.nsitivity Analysis of theMasonry Wall

There are a number of issues with regard to themodelling of shear and tensile bond strengths betweenthe mortar and the masonry unit. Some of these issues,which are summarized as follows, will be discussedlater in this section:

a) Small intervals for data saving: Debondingoccurs over a very short time interval, and hencea results file with a reasonably fine resolution isrequired to capture the exact instance at whichdebonding occurs. The same applies torecording of experimental data. It is very likely

that a part of the discrepancy between theexperimental and analytical curves can beattributed to insufficient resolution of theavailable experimental data;

b) Difference between the nature of debonding in aFE model and an experimental test: In a FEmodel all of the bed and head joints are typicallyin contact and bonded. This is contrary to anactual masonry specimen where the net bondingarea must be distinguished from the gross crosssectional area of a mortar layer (Pluijm 1992;Park 2001);

c) Scatter of data: The available material data formasonry is highly scattered, i.e. there arecoefficients of variation of up to 100% (Pluijm1992);

d) No sensitivity to debonding in some cases:Where the masonry specimens are confined (byeither gravity loads or the surrounding frame)there is less sensitivity to debondingparameters. Therefore, it appears that in somecases, the inclusion of debonding parametersjust adds to uncertainties in the model instead ofimproving it;

e) Convergence: This can be an issue sincedebonding is a highly nonlinear behaviour and,when combined with other nonlinearitiesinvolved in the model, variations in thedebonding parameters can sometimes result inan unconverged solution.

f) Limited available experimental results: Theavailable data is limited to a small number ofmasonry unit/mortar types, and hence notdirectly applicable to all types of masonry.

Table 1 summarizes the values that are chosen tostudy the effect of the variation of tensile bond strengthand Mode I fracture energy on the behaviour of a



Table 1. Variables in one-way bending analyses

Tensile Mode IAnalysis Bond Fracture Energy ∆tNo. f ’

t0(MPa) GI

F(N/mm) (mm)a

FE (MW) 1 0.35 0.01 0.1FE (MW) 1a 0.35 0.01 0.02FE (MW) 1b 0.35 0.01 1.2FE (MW) 2 0.35 0.02 0.02FE (MW) 3 0.35 0.05 0.02FE (MW) 4 0.50 0.01 0.02FE (MW) 5 0.50 0.05 0.02FE (MW) 6 1.00 0.05 0.02

Note: “MW” stands for Masonry Wall.a “∆t” represents the increments at which results were saved.

masonry wall; these values are within the rangerecommended by Pluijm (1992).

Figure 5 shows a generic deflected shape for thisspecimen. On should note that there is no overburden onthe wall. As depicted in this figure, two separate rigidblocks of masonry have formed, and a crack hasdeveloped along the bed joint in the middle of the wall(where the lateral load is applied). There is no evidenceof masonry cracking and/or crushing in this specimen,and hence the failure mode is purely attributed to thetensile debonding along the bed joint.

In Figures 6(a) to 6(c) the results of the same analysiswith the tensile bond strength, f’t0, set equal to 0.35 MPaand mode I fracture energy of the interface, GI

F, equal to0.01 N/mm, but with different data resolutions, areprovided. This figure shows that even by saving theresults at 0.1 mm steps, i.e. Analysis FE (MW) 1, thepeak load cannot be captured. In the analysis shown inFigure 6(d), GI

F is double that used in the previousanalyses and is equal to 0.02 N/mm. A comparisonbetween Figures 6(b) and 6(d) shows that as a result ofincreasing GI

F, the peak load has slightly increased(3.9 kN versus 4.2 kN). However, the displacement atwhich debonding is completed and the load has levelledoff has not changed (i.e. equal to 1 mm (0.07% drift) inboth cases. In Figure 6(e) the effect GI

F is morepronounced. It is shown that by increasing GI

F to 0.05N/mm, the peak load has reached as high as 5.3 kN.Also, the displacement at which the load has levelled offhas increased to 2.2 mm (0.15% drift). A comparison ofFigures 6(f) and 6(b) shows that increasing f’t0 from0.35 MPa to 0.5 MPa results in an increase in the peakload from 3.9 kN to 4.4 kN. However, the displacementat which the load ceased to drop has slightly decreased(0.8 mm versus 1.0 mm). A comparison between Figures6(f) and 6(g) shows that by increasing GI

F from 0.01N/mm to 0.05 N/mm and keeping f’t0 constant at 0.5

MPa, both the peak load and the displacement at whichthe load has levelled off have increased (viz. 4.4 kN and0.8 mm versus 5.8 kN and 1.6 mm). Figure 6(h) showsthat by doubling f’t0 in comparison to that of assumed inFigure 6(g) and keeping GI

F constant at 0.05 N/mm thepeak load has gone up even further to 8.8 kN. Thisvariation has not affected the displacement at which theload has levelled off.

Based on the out-of-plane one-way bending analysesof the masonry wall considered here, it can beconcluded that increasing the tensile bond strength, f’t0,results in increasing the peak load, while it has littleinfluence on the displacement at which the load levelsoff. On the other hand, increasing mode I fractureenergy, GI

F, leads to an increase in both the peak loadand the displacement at which the load levels off.Moreover, it was shown that, since debonding occursover a very short time interval, a results file with areasonably fine resolution is required to capture theexact instance at which debonding occurs. It is alsolikely that the actual maximum load might not becaptured adequately during an experimental test, if thesampling rate is too low.

4.3. Infill-Frame under Out-of-Plane Two-WayBending

One of eight tests conducted by Angel (1994), namelySpecimen 1, is considered here for the purpose of theinfill-frame sensitivity analysis under out-of-planeloading. Angel’s research was conducted to investigatethe interaction between in- and out-of-plane loadings onductile RC frames with both clay brick and concreteblock masonry infill panels. In this test, an axial force of222.4 kN was applied and maintained on each columnthroughout the test. The out-of-plane pressure was thenapplied. The beam includes the flanges shown in Figure7 which replicate the contribution of an RC slab in theactual structures. This has also been considered in theFE model.

Figure 7 shows the FE model of this specimen withsome of the geometric properties of the infill-frame. Theinfill panel has a slenderness ratio (hI/t) of 34 (hI and tare the height and thickness of an infill panel,respectively). The infill panel was built using reclaimedChicago common clay bricks (reclaimed fromdemolishing sites, also known as old Chicago bricks)with a mortar mix of 1:1:6 (cement : lime : sand). Thecompressive strength of the masonry is 11.5 MPa andthe tensile bond was measured as 0.22 MPa. The RCframe was designed and constructed in accordance withACI-318 (1989). The compressive and tensile (modulusof rupture) strength of concrete were measured as 55.4 MPa and 4.8 MPa, respectively. The yield stress of



Figure 5. A typical deformed shape of the masonry wall

longitudinal and transverse reinforcement was reportedas 475 MPa and 450 MPa, respectively. The coefficientof friction for the bed joints is assumed to be 0.4 basedon experimental results; this coefficient is assumed to be

33% and 75% of that of the bed joint for head joints andthe interface between the infill panel and frame,respectively. Mode I fracture energy, GI

F, is assumed tobe 0.01 N/mm.



(a) (b)

(g) (h)

(c) (d)

(f)

ExperimentalFE (MW) 1: f′t0 = 0.35; GI

F = 0.01; ∆t = 0.1

5.0

4.0

3.0

2.0

1.0

0.00.0 1.0 2.0 3.0 4.0

Draft (%)

ExperimentalFE (MW) 1a: f′t0 = 0.35; GI

F = 0.01; ∆t = 0.02

5.0

4.0

3.0

2.0

1.0

0.00.0 1.0 2.0 3.0 4.0

Draft (%)


F = 0.02; ∆t = 0.02

5.0

4.0

3.0

2.0

1.0

0.00.0 1.0 2.0 3.0 4.0

Draft (%)


F = 0.01; ∆t = 0.02

5.0

4.0

3.0

2.0

1.0

0.00.0 1.0 2.0 3.0 4.0

Draft (%)


F = 0.05; ∆t = 0.02

0.0

6.0

8.0

4.0

2.0

0.0 1.0 2.0 3.0 4.0

Draft (%)

ExperimentalFE (MW) 1b: f′t0 = 0.35; GI

F = 0.01; ∆t = 1.2

0.0

5.0

4.0

3.0

2.0

1.0

0.0 1.0 2.0 3.0 4.0

Draft (%)

(e)


F = 0.05; ∆t = 0.02

0.0

5.0

6.0

4.0

3.0

2.0

1.0

0.0 1.0 2.0 3.0 4.0Draft (%)


F = 0.05; ∆t = 0.02

0.0

5.0

6.0

4.0

3.0

2.0

1.0

0.0 1.0 2.0 3.0 4.0

Draft (%)

Late

ral f

orce

(kN

)La

tera

l for

ce (

kN)

Late

ral f

orce

(kN

)La

tera

l for

ce (

kN)

Late

ral f

orce

(kN

)La

tera

l for

ce (

kN)

Late

ral f

orce

(kN

)La

tera

l for

ce (

kN)

Figure 6. A comparison between the experimental results and FE analyses with different values of f’t0 and GIF

In order to accommodate for partial filling of the topbed joint and a relatively loose contact between the infillpanel and the frame as explained by Angel, thecompressive and tensile strength of the top bed joint,and the contact stiffness at the interface of the top bedjoint and the beam are considered to be 10% of thevalues used in the rest of the model.

The out-of-plane pressure was applied using anairbag. Angel applied the concept of virtual work toconvert the measured pressure from the airbag, pa, to anequivalent uniformly distributed pressure on totalsurface area of the panel, pI. He concluded that fordifferent tests, pI is approximately 5-10% less than themeasured values of pa. Angel did not report the exactvalues of pa, nor did he report the exact values ofconversion factors for each individual test. Figure 8(a)shows a comparison between the pressure-drift curvesfrom FE and that of the experiment as reported by Angel(OP in this figure stands for out-of-plane). In this figurethe results of two analyses are compared; the solid linerepresents an analysis in which the out-of-plane load hasbeen applied on an area equal to the deflated area of theairbag (2337*1422 mm2), whereas the dotted line showsthe results of the analysis in which the infill panel has

been exposed to a uniformly distributed pressure on thetotal surface area of the panel (2438*1626 mm2). TheFE results show that the difference between thepressure-drift curves for the two pressures, pa

(pressure on the deflated area of the airbag) and pI

(pressure on the total surface area of the panel), isalmost negligible. Based on these results, if we increasethe pressure-drift curve given by Angel (1994) by say7.5% (i.e. the average of 5% and 10%) to compensatefor the “correction” that was made by Angel, thedifference between the FE and experimental results willbe even less. This is shown in Figure 8(b). Even thoughthe reduced values presented in Figure 8(b) appear to bemore reliable, the FE results in this paper are comparedwith the original pressure-drift curve provided by Angel(1994). It should be noted that the out-of-plane pressureis applied on the whole area of the infill panel during theanalysis.

Table 2 shows the key parameters that are selectedfor the sensitivity analyses. For force-controlled out-of-plane analyses the model is only capable of predictingthe behaviour of the structure up to the point where themaximum load is reached (limitations imposed by theNewton-Raphson method (Mohyeddin 2011)).



8 #5

#3 @ 100

8 #7

305

305

Section A−A

Section B−B

305 #3 @ 130

205 3 #3#3 @ 300

102

205

1625

.630

4.8

304.

82438.4 304.8 304.8

304.8 304.8

B

B

A A

Figure 7. FE model of the infill-frame Specimen 1 tested by Angel (1994) with dimensions in mm

10

8

6

4

2

0

10

8

6

4

2

00.0 0.5 1.0 1.5

Lateral drift (%)0.0 0.5 1.0 1.5

Lateral drift (%)

ExperimentalFE (OP1): total area of the panalFE (OP1): total area of the airbag

Experimental (modified results)FE (OP1): total area of the panal

Pre

ssur

e (k

Pa)

Pre

ssur

e (k

Pa)

(a) (b)

Figure 8. Comparison between pressure-drift curves from FE and experiment considering pI/pa conversion

Therefore, the focus here is on the loading branch of thepressure-displacement curve up to where the maximumpressure is reached, and not the softening branch of thepressure-displacement curve.

Figure 9 compares the deformed shapes of the infillpanel from the first two analyses. This figure showsthat a small gap of 1 mm between the infill panel andbeam has a significant effect on the behaviour of thepanel; while the behaviour of the infill panel without agap is governed by arching action in two directions[Figure 9(a)], there is no vertical arching action in thepanel with a gap as there is no supporting effect fromthe beam on top [Figure 9(b)]. The effect of a 1 mm gapbetween the infill panel and the beam on out-of-planestrength of the panel is illustrated in Figure 10(a). Thisfigure shows that due to the presence of this gap, the

strength of the infill panel has significantly decreased.As mentioned earlier in this section, the materialproperties of the top bed joint were weakened torepresent the effect of the partial filling of the top bedjoint between the infill and the beam in Angel’s testspecimen. Figure 10(b) compares the results of twoanalyses; one representative of the test condition andthe other with no reduction in material properties of thetop bed joint. This figure shows that the out-of-planestrength of the infill-frame could be enhanced byapproximately 10%, if the upper bed joint was fullyincorporated.

The effect of masonry material strength on the out-of-plane strength of the infill-frame is illustrated in Figures 10(c) and 10(d). It is shown that the pressure-drift curve is highly sensitive to the material strength of



Table 2. Variables in out-of-plane analyses

Masonry Material

Force on Coefficient of Infill Upper bed joint

Analysis each Col. Friction f’cm f’tm f’cm f’tm

No. (kN) (fr/infill;bedj;head j) (MPa) ε0m (MPa) (MPa) ε0m (MPa)

FE (OP) 1 222.4 (0.30;0.40;0.13) 11.5 0.0027 1.15 0.1*11.5 0.1*0.0027 0.1*1.15FE (OP) 2 222.4 (0.30;0.40;0.13) 11.5 0.0027 1.15 1 mm gapFE (OP) 3 222.4 (0.30;0.40;0.13) 11.5 0.0027 1.15 11.5 0.0027 1.15FE (OP) 4 222.4 (0.30;0.40;0.13) 1.25*11.5 0.0027 1.25*1.15 0.1*11.5 0.1*0.0027 0.1*1.15FE (OP) 5 222.4 (0.30;0.40;0.13) 0.75*11.5 0.0027 0.75*1.15 0.1*11.5 0.1*0.0027 0.1*1.15FE (OP) 6 222.4 (0.30;0.40;0.13) 11.5 1.25*0.0027 1.15 0.1*11.5 0.125*0.0027 0.1*1.15FE (OP) 7 222.4 (0.30;0.40;0.13) 11.5 0.75*0.0027 1.15 0.1*11.5 0.075*0.0027 0.1*1.15FE (OP) 8 222.4 (0.30;0.40;0.13) 11.5 0.0027 1.25*1.15 0.1*11.5 0.1*0.0027 0.1*1.15FE (OP) 9 222.4 (0.30;0.40;0.13) 11.5 0.0027 0.75*1.15 0.1*11.5 0.1*0.0027 0.1*1.15FE (OP) 10 1.1*222.4 (0.30;0.40;0.13) 11.5 0.0027 1.15 0.1*11.5 0.1*0.0027 0.1*1.15FE (OP) 11 0.9*222.4 (0.30;0.40;0.13) 11.5 0.0027 1.15 0.1*11.5 0.1*0.0027 0.1*1.15FE (OP) 12 222.4 1.25*(0.30;0.40;0.13) 11.5 0.0027 1.15 0.1*11.5 0.1*0.0027 0.1*1.15FE (OP) 13 222.4 0.75*(0.30;0.40;0.13) 11.5 0.0027 1.15 0.1*11.5 0.1*0.0027 0.1*1.15

Note: “OP” stands for Out-of-Plane.

(a) (b)

Figure 9. A comparison between the deformed shape of the infill panel (a) without a gap (i.e. FE (OP) 1) and (b) with a 1 mm gap on top

(i.e. FE (OP) 2)



0

2

4

6

8

10

12

0.0 0.5 1.0 1.5

Lateral Drift (%)

ExperimentalFE (OP) 1FE (OP) 2: Gap on top

0

2

4

6

8

10

12

0.0 0.5 1.0 1.5

Lateral Drift (%)

ExperimentalFE (OP) 1FE (OP) 3: Perfect bed joint on top

Pre

ssur

e (k

Pa)

Pre

ssur

e (k

Pa)

(a)

0

2

4

6

8

10

12

0.0 0.5 1.0 1.5

Lateral Drift (%)

ExperimentalFE (OP) 1FE (OP) 4: Masonry 25% stronger

Pre

ssur

e (k

Pa)

(c)

0

2

4

6

8

10

12

0.0 0.5 1.0 1.5

Lateral Drift (%)

ExperimentalFE (OP) 1FE (OP) 6: ε0m 25% larger

Pre

ssur

e (k

Pa)

(e)

0

2

4

6

8

10

12

0.0 0.5 1.0 1.5

Lateral Drift (%)

ExperimentalFE (OP) 1FE (OP) 5: Masonry 25% weaker

Pre

ssur

e (k

Pa)

(d)

0

2

4

6

8

10

12

0.0 0.5 1.0 1.5

Lateral Drift (%)

Experimental

FE (OP) 1

FE (OP) 7: ε0m 25% lower

Pre

ssur

e (k

Pa)

(f)

(b)

0

2

4

6

8

10

12

0.0 0.5 1.0 1.5

Lateral drift (%)

ExperimentalFE (OP) 1FE (OP) 8: Masonry 25% more tensile

Pre

ssur

e (k

Pa)

(g)

0

2

4

6

8

10

12

0.0 0.5 1.0 1.5

Lateral drift (%)

ExperimentalFE (OP) 1FE (OP) 9: Masonry 25% less tensile

Pre

ssur

e (k

Pa)

(h)

Figure 10. (Continued)

the masonry. In fact, the experimental curve fallsbetween the curves representing a ± 25% variation inmaterial strength. Given the large variability of themasonry properties, this is a very good result. The effectof a 25% increase in ε0m is shown in Figure 10(e). Thisfigure shows that the out-of-plane strength of the infillpanel is very sensitive to this parameter. For instance,

25% increase in ε0m has decreased the ultimate strengthby approximately 20% at a drift of 1.5%. This is due tothe fact that a higher value of ε0m leads to a lowerstiffness of the masonry panel. Therefore, lower archingstresses would develop in the infill panel at the samelevel of drift in comparison to a stiffer panel; this, inturn, will result in a reduced out-of-plane strength.



0

2

4

6

8

10

12

0.0 0.5 1.0 1.5

Lateral drift (%)

ExperimentalFE (OP) 1FE (OP) 10: 10% more gravity

Pre

ssur

e (k

Pa)

(i)

0

2

4

6

8

10

12

0.0 0.5 1.0 1.5

Lateral drift (%)

ExperimentalFE (OP) 1FE (OP) 12: 25% higher friction

Pre

ssur

e (k

Pa)

(k)

0

2

4

6

8

10

12

0.0 0.5 1.0 1.5

Lateral drift (%)

ExperimentalFE (OP) 1FE (OP) 11: 10% less gravity

Pre

ssur

e (k

Pa)

(j)

0

2

4

6

8

10

12

0.0 0.5 1.0 1.5

Lateral drift (%)

ExperimentalFE (OP) 1FE (OP) 13: 25% lower friction

Pre

ssur

e (k

Pa)

(l)

Figure 10. A comparison between different load-drift curves for out-of-plane loading

228.

630

4.8

1422

.4

177.8 177.82133.6 304.8304.8

AAB

B

#2 @ 65

8 #4

177.8

177.

8

#2 @ 75

4 #5

152.4

228.

6

Section A−A

Section B−B

Figure 11. FE model of the infill-frame Specimen 8 tested by Mehrabi (1994) with dimensions in mm

Figure 10(f) displays a similar trend such that bydecreasing ε0m the strength of the infill panel increases.Moreover, it can be concluded that the experimentalpressure-drift curve falls between the analytical curvesrepresenting a certain variation for ε0m (i.e. ± 25% in thisexample).

In order to investigate the effect of uncertainty inthe tensile strength of masonry, two analyses areconducted which include 25% increase/decrease in thisparameter. Figures 10(g) and 10(h) show that theinitial stiffness and the ultimate strength of the infill-frame are not sensitive to the value of the tensilestrength of the masonry, within the chosen range ofvalues. Nevertheless, a slight change in the strength isobserved in the middle range of the lateral drift, i.e.between 0.5% and 1.5%. Comparing these two figureswith the results from the previous section clearlydemonstrates the dominating effect of the archingaction in the infill-frame. In other words, debondingparameters have a very small effect in the presence ofarching actions. The axial deflections of the stiffcolumns in this specimen are small, and hence almostno gravity load has been transferred to the infill at thebeginning of the analysis. Also, the frame is stiffenough to develop arching stresses across the slenderinfill panel with or without any extra gravity loadbeing applied to the columns. Accordingly, anyvariation in the gravity load applied to the columnsdoes not affect the out-of-plane strength of the infillpanel. This is evident from Figures 10(i) and 10(j).Since the out-of-plane behaviour of an infill panel ismainly governed by the arching effect, it is expectedthat the out-of-plane strength of the infill panel will notbe sensitive to coefficients of friction. This is indeedthe case as shown in Figures 10(k) and 10(l).

The out-of-plane two-way bending analysesconsidered here showed that:

a) The out-of-plane strength of the infill panelcannot be accurately estimated by the simpleyield line assumptions as those made by Angel(1994) to convert airbag pressure to anequivalent uniformly distributed pressure(Figure 8). It was shown that this may result inan error of up to approximately 10% in thestrength of the infill-frame;

b) Even a small gap between the infill panel andthe beam can result in a significant reduction inthe out-of-plane strength of the panel; this isrelated to lack of support at top of the panel.Similarly if the top bed joint of the panel wassuccessfully filled with good quality mortar, thepanel could stand higher levels of out-of-planepressure;

c) Any increase/decrease in the magnitude of ε0m

(the strain at which the maximum stress occurs)within the range of ± 25% will result in asignificant opposite change (i.e. decrease/increase) in the strength of the infill panel[Figures 10(e) and 10(f)];

d) The infill panels showed little sensitivity to thetensile strength of the masonry and coefficientsof friction [Figures 10(g), 10(h), 10(k) and10(l)].

4.4. Infill-Frame under In-Plane LoadingMohyeddin (2011) utilized two specimens tested byMehrabi (1994) for the FE model verification under in-plane lateral loading. In this section Mehrabi’sSpecimen 8 is selected to investigate the sensitivity ofthe infill-frame under in-plane lateral loading. A pre-compression load of 294 kN was applied to the infill-frame; this was divided into three; one-third of the totalload was applied on the beam and each of the columns.Monotonic lateral displacement was then exerted at theend of the beam. The FE model of this specimen isshown in Figure 12. The compressive and tensilestrength of concrete of this specimen are 26.8 MPa and4.9 MPa, respectively. The masonry panel was builtusing a Type S, 1:1/2:4 1/2 (cement : lime : sand) mortarand perforated concrete blocks with the dimensions of92.1*92.1*193.7 mm (thickness*width*length); bedand head joints were 9.5 mm thick. In the bed joints,mortar was applied onto the face shells only. Theequivalent width of the perforated blocks, consideringthe holes in the block, was 46.6 mm. Masonrycompressive strength and the related ε0m are 9.5 MPaand 0.0027, respectively. In order to accommodatepartial filling and the generally poor condition of headjoints, the coefficient of friction at head joints isassumed to be approximately one third of that of bedjoints. Similarly, the coefficient of friction for theinterface between the infill panel and the frame isassumed to be 15% less than that of the bed joint. Thecoefficient of friction at the bed joints is 0.95.

The shear and tensile bond strengths are assumed tobe zero. This simplifying assumption is made for tworeasons. Firstly, there is a significant uncertainty withregard to fracture energies involved in mathematicalmodels of debonding and therefore, it is hard to justify aspecific value for these parameters. Secondly, masonryin an infill-frame is highly confined, especially in thecase of the specimen considered here where a proportionof gravity load is applied on the beam; the effect ofdebonding is more pronounced where masonry is underlower values of normal/confining stresses. Table 3shows the key parameters that are selected for the



sensitivity analyses. Amongst these analyses, onlyAnalysis FE (IP) 8 includes a geometric variation i.e. thethickness of the infill as explained under Table 3. The coefficient of friction between the frame and the

masonry panel in this analysis is slightly larger than thatof Analysis FE (IP) 1; however, the effect of thisvariation is negligible for the comparison purpose here(Mohyeddin 2011).



0

50

100

150

200

250

300

0.0 0.5 1.0 1.5 2.0

Lateral drift (%)

Late

ral f

orce

(kN

)

ExperimentalFE (IP) 1FE (IP) 2: 25% higher friction

(a)

0

50

100

150

200

250

0.0 0.5 1.0 1.5 2.0Lateral drift (%)

Late

ral f

orce

(kN

)

ExperimentalFE (IP) 1FE (IP) 4: Masonry 25% stronger

(c)

0

50

100

150

200

0.0 0.5 1.0 1.5 2.0

Lateral drift (%)

Late

ral f

orce

(kN

)

ExperimentalFE (IP) 1FE (IP) 3: 25% less friction

(b)

0

50

100

150

200

250

0.0 0.5 1.0 1.5 2.0

Lateral drift (%)

Late

ral f

orce

(kN

)

ExperimentalFE (IP) 1FE (IP) 5: Masonry 25% weaker

(d)

0

50

100

150

200

0.0 0.5 1.0 1.5 2.0

Lateral drift (%)

ExperimentalFE (IP) 1FE (IP) 6: ε0m 25% larger

Late

ral f

orce

(kN

)

(e)

0

50

100

150

200

0.0 0.5 1.0 1.5 2.0

Lateral drift (%)

Late

ral f

orce

(kN

)

ExperimentalFE (IP) 1FE (IP) 7: ε0m 25% lower

(g)

0

50

100

150

200

0.0 0.5 1.0 1.5 2.0

Lateral drift (%)

Late

ral f

orce

(kN

)

ExperimentalFE (IP) 1FE (IP) 8: Infill 50% more slender

(h)

0

50

100

150

200

0.0 0.5 1.0 1.5 2.0

Lateral drift (%)

Late

ral f

orce

(kN

)

ExperimentalFE (IP) 6: ε0m 25% larger

(f)

Figure 12. A comparison between different load-drift curves for in-plane loading

The effect of an increase or a decrease in allcoefficients of friction is illustrated in Figures 12(a)and 12(b). These figures show a significant change inthe force-drift curves. This effect is more pronouncedover the first 1.0% drift. It is evident that the valuesadopted for these coefficients can substantiallyinfluence the maximum strength of the infill-frame;however, the discrepancy between the curves tends todecrease as the drift reaches higher values. Also, theinitial stiffness is slightly affected by altering thecoefficients of friction. Figure 12(c) illustratesthe significant increase in the maximum strength ofthe infill-frame, as well as some improvement in theinitial stiffness, which are gained as the result of a25% enhancement of the masonry material strength(both compressive and tensile). The effect of having a25% weaker infill panel on the overall behaviour ofthe infill-frame is illustrated in Figure 12(d). Thisfigure shows that both stiffness and strength havedegraded. Furthermore, Figures 12(c) and 12(d) depictthat the experimental force-drift curve falls betweenthe force-drift curves representing a 25% change inthe masonry material properties. One parameter thatexhibits a great deal of variability is ε0m (the strain atwhich the maximum compressive strength, f’cm,occurs). The effect of a 25% increase in ε0m isillustrated in Figure 12(e). This figure shows that byincreasing ε0m, the force-drift of the FE model willclosely match that of the experiment. The force-driftcurve from Analysis 6 is reproduced in Figure 12(f)for a clearer illustration. Figure 12(g) shows that bydecreasing ε0m, which is equivalent to assuming astiffer behaviour for masonry (and also a more brittlebehaviour in this case), results in a stiffer force-driftcurve. This is accompanied with a slight reduction in

the maximum strength and, overall, a weaker infill-frame structure. The effect of infill slenderness on thebehaviour of the infill-frame is shown in Figure 12(h).The thickness of the infill in Analysis FE (IP) 8 is68% of that of other analyses. This figure shows thatthe latter, with a more slender infill panel, becomesnonlinear at a much lower load and follows arelatively flat force-drift branch at a lower level forthe rest of the analysis.

Based on in-plane analyses, it is concluded that:a) Any percentage change within the range of

± 25% in coefficients of friction results in avariation in the same manner in the strength ofthe infill-frame. These effects are mostinfluential up to approximately 1.0% of drift[Figures 12(a) and 12(b)]. This variation doesnot have a significant effect on the initialstiffness;

b) ε0m (the strain at which the maximum stressoccurs) is an influential parameter on the force-drift curve of an infill-frame [Figures 12(e) to12(g)]; while increasing ε0m by 25% leads tostrength enhancement, it slightly decreases theinitial stiffness; also, the reduction of ε0m has anopposite effect;

c) As well established by previous research,reducing the thickness of the infill decreases thestrength of the infill-frame. A 32% reduction inthe thickness of the infill resulted in 19%reduction in the maximum strength of the infill-frame [Figure 12(h)].

5. CONCLUSIONSA generic three-dimensional FE model of a reinforced-concrete frame with an infill panel has been constructed



Table 3. Variables in in-plane analyses

Coefficient of Friction Masonry Material

Analysis (fr/infill; bed joint; f’cm f’tm

No. head joint) (MPa) ε0m (MPa)

FE (IP) 1 0.70;0.95;0.32 9.5 0.0027 0.95FE (IP) 2 1.25*(0.70;0.95;0.32) 9.5 0.0027 0.95FE (IP) 3 0.75*(0.70;0.95;0.32) 9.5 0.0027 0.95FE (IP) 4 0.70;0.95;0.32 1.25*9.5 0.0027 1.25*0.95FE (IP) 5 0.70;0.95;0.32 0.75*9.5 0.0027 0.75*0.95FE (IP) 6 0.70;0.95;0.32 9.5 1.25*0.0027 0.95FE (IP) 7 0.70;0.95;0.32 9.5 0.75*0.0027 0.95FE (IP) 8a 0.75;0.95;0.32 9.5 0.0027 0.95

Note: “IP” stands for: In-Plane.a Thickness of the infill panel is assumed to be 31.75 mm which is 68% of that of other analyses. This is only based on webs of the hollow concrete block whichare parallel to the plane of the panel.

in such a manner as to facilitate the implementation of aseries of parametric analyses. A select number of theseanalyses were discussed. In some cases, the “general”effect of variation of some of these parameters has beenthe subject of previous research. However, with theintention of providing a deeper insight into thebehaviour of infill-frames at a micro level, this researchhas scrutinized the influence of such variations on the“step-by-step” structural behaviour of infill-frames overa wide range of drift values. For the range of driftconsidered here, this could not be achieved withoutovercoming convergence issues related to theconstructed models, which was successfully resolved.

A simple method was proposed in order to overcomeconvergence hurdle points (CHP). Based on manypreliminary analyses and comparisons made with theexperimental results, it is believed that this method isnot limited to the analyses presented herein, and can beimplemented in order to overcome convergence issuesrelated to other similar highly nonlinear FE models.

The parameters being varied in this paper are not theonly parameters that could be studied using this genericFE model. There are many geometric parameters, suchas the frame span, frame height, and amount oflongitudinal and transverse reinforcement in thebeam/columns that could be changed; any perforationwithin the infill panel can also be considered. Therefore,the constructed model reduces the number ofexperimental tests that would normally be needed todraw a general conclusion on the behaviour of infill-frames.

As mentioned in Introduction, there is a lack ofresearch on the interaction between in- and out-of-planeloading. The fact that the same model can be employedfor both in-plane and out-of-plane loading simplifies thefuture research for cases where the interaction betweenthe two loads is deemed to be substantial (e.g. based onthe slenderness ratio of the infill panel).

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