Contribution to Numerical Modelling of Concrete- Masonry Interface In Concrete Framed Structures With Masonry Infill

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1 Contribution to Nuerial Modelling of Conrete- Masonry Interfae In Conrete Fraed Strutures With Masonry Infill Induprabha S.A.D, B.S.Eng.(Hons)(Moratuwa) (eail: K.G.S. Dilrukshi, B.S. Eng (Moratuwa), Ph.D. (Moratuwa), (eail: Abstrat Masonry infills have long been used as interior partitions and exterior walls in buildings. They are usually treated as non-strutural eleents, and their interation with the bounding frae is often ignored in design. Nevertheless, infill ontributes strength to a struture and will interat with the bounding frae when the struture is subeted to strong lateral seisi loads, when the infill is stressed due to oveents of an overlying slab or any other ase of in-plane or out of plane lateral loading. This interation ay or ay not be benefiial to the perforane of the struture, however, and it has been a topi of uh debate in the last few deades. The interation of the infill is governed by the relative stiffness and strength harateristis of eah individual oponent and ost iportantly the interfae harateristis that deide the degree of oposite ation. An interfae is a speial ontat plane on whih nonlinear relations between stresses and displaeent disontinuities are present. Very often initiation and propagation of raks along these interfaes are the ause of failure of the relevant strutures. Siilarly, in the ase of onrete fraed asonry asseblages, the bond between the asonry and the onrete frae is a weak link, through whih failure is possible. Therefore to siulate this behaviour, interfae eleents with a suitable onstitutive odel an be utilized. This paper explores finite eleent odels developed to siulate the behaviour of onreteasonry interfae of asonry infill. In this study, brik-onrete ouplets were atheatially odelled, using oerially available software ANSYS. The adopted nuerial strategy onsists of siplifying the onrete-asonry-ortar interfae to a zero thik interfae, odelling the brik units and the onrete units with three diensional solid brik eleents and odelling the bond using zero thikness interfae eleents with a ohesive-zone odel (CZM) for ixed-ode frature based on daage ehanis introdued by Alfano and Crisfield(2001). Key words Displaeent disontinuities, ohesive-zone odel, zero thik interfae, nuerial odelling of asonry, non-linear behaviour.

2 1. Introdution Masonry infills have long been used as interior partitions and exterior walls in buildings. They are usually treated as non-strutural eleents, and their interation with the bounding frae is often ignored in design. Nevertheless, infill ontributes strength to a struture and will interat with the bounding frae when the struture is subeted to strong lateral seisi loads, when the infill is stressed due to oveents of an overlying slab or any other ase of indued in-plane or out of plane lateral stresses. This interation ay or ay not be benefiial to the perforane of the struture, however, and it has been a topi of uh debate in the last few deades. The perforane of suh frae strutures with infill, during an earthquake has attrated aor attention. Even though frae infill interation has soeties led to undesired strutural perforane, reent studies have shown that a properly designed infilled frae an be superior to a bare frae in ters of stiffness, strength, and energy dissipation. Siilarly, in the ase of infill raking due to theral oveents of an overlying slab whih is a oon proble in a tropial ountry like Sri Lanka the interation between onrete bea and asonry wall plays a aor role. Aording to Ghassan K (2008), experiental investigations of the behavior of asonry-infilled steel and reinfored onrete fraes under in-plane and out of plane lateral loading has been the subet of any researhers. Starting bak in 1970 with the experiental studies of Fiorato et al who tested 1/8-sale non-dutile reinfored onrete as yli lateral loading the investigations were followed by the studies of any other researhers like Klingner and Bertero in 1976, Bertero and Brokken in 1983, Zarni and Toazevi in 1985, and Shidt in More reently, single-story reinfored onrete fraes with asonry infills were studied by Mehrabi et al in 1994 and 1997, Angel et al in 1994, and Al-Chaar et al in 1998 and Masonry infilled steel fraes were tested by Dkanasekar et al in 1985, Dawe and Seah in 1989, Mander et al in 1993, and any others. All experiental studies ited above have shown that the behavior of an infilled frae is heavily influened by the interation of the infill with its bounding frae. In ost instanes, the lateral resistane of an infilled frae is not equal to a siple su of the resistane of its oponents beause frae/infill interation an alter the load-resisting ehaniss of the individual oponents. At low lateral loading, an infilled frae ats as a onolithi load resisting syste and as loading inreases, the infill tends to partially separate fro the bounding frae. Due to this a opression strut ehanis is fored, as observed in any earlier studies. Due to the presene of a vast range of geoetrial and strutural onfigurations of asonry, use of physial odels to investigate asonry is ostly and diffiult. As a result finite eleent ethod (FEM) has been widely used in the analysis of onrete and steel fraed asonry strutures. A nuber of different analytial odels have been developed to evaluate these infills. Dhanasekar and Page (1986) and Liauw and Lo (1988) have used linear and nonlinear bea eleents to odel the behaviour of steel fraes, and interfae eleents to odel the interation between the infill and the frae. Dhanasekar and Page used a nonlinear orthotropi

3 odel to siulate the behaviour of brik infills, and Liauw and Lo used a siple seared rak odel to siulate the behavior of iro-onrete infills. Shidt (1989) used seared rak eleents to odel both reinfored onrete fraes and brik infills. In all those analyses, infill panels have been odelled as a hoogenous aterial before frature, and the effets of ortar oints have been seared out. These odels for onrete-asonry fraed strutures have a aor defiieny of suffiient attention not being paid to siulate the interation through the onrete bea and asonry infill untion. Further in Engineering pratie soe of the oonly used interfae types at the bea wall untion inlude (i) leaving a gap between the frae and the infill in order to avoid transfer of load between frae and infill (ii) breaking of bond between frae and infill (no bond/non integral) (iii) onneting the frae and the infill by provision of shear onnetors (integral interfae) (iv) onneting the frae and the infill by eent ortar (onventional type) and (v) using of non-strutural aterials like lead sheet, ork et. Therefore a nuerial approah has to be adopted to siulate the onrete asonry infill interfae behaviour and to explore the effet of bond between onrete and asonry infill on the global behaviour of these fraed strutures. An interfae is a speial ontat plane on whih nonlinear relations between stresses and displaeent disontinuities are present. Therefore to siulate this behaviour interfae eleents with a suitable onstitutive odel an be utilized and essentially this should be verified with adequate experiental data. The failure ehaniss of Couplets under diret tension and shear loading an be differentiated in to the following two kinds of rupture: Rupture ourring along the ortar/brik interfae for ahine ade briks and soe of the hand-ade brik speiens (see Figure 1), Rupture beginning along the interfae and rossing through the ortar layer and rushing of brik (see Figure 2). Figure 1: Rupture odes in ouplet speiens with ahine ade briks Figure 2: Rupture odes in ouplet speiens with hand-ade briks The interfae odels used should be able to siulate these situations. An interfae ay be treated as a opletely bonded interfae or an inopletely bonded interfae (Song and Kawakai 1998). The opletely bonded interfaes should prevent large relative displaeent fro ourring at the ontat plane. The inoplete bonded interfaes ay have the behaviours of sliding, de-bonding and re-bonding, rotation et.

4 Further, in the ontext of the finite eleent ethod, there are two aor groups of interfae eleents/odels known as the zero thikness interfae eleent and thin layer interfae eleents. Athanasios (2003) has onduted a detailed study about these tehniques of odelling interfaes in disontinuous systes. Aording to hi, the expliit representation of disontinuities by eans of FEM and the so alled interfae eleent goes bak to the work of Goodan, Zienkiewiz, Mahtabh and Gaboussi in the 1970s. Aording to Rots (1997) the ethod was first developed and applied to solid asonry by Page in Several interfae odels have been proposed in literature to study rak propagation in these inopletely bonded eentitious aterials and at biaterial interfaes. Aording to the studies of G. Alfano (2006), soe of these reent advaneents of the interfae odelling are results of the work of any researhers as Carol et al, Ce rvenka et al, Ruiz et al, Alfano and Crisfield, Marfia and Sao and Cohetti et al. Aong the, Alfano and Crisfield have presented an interfae odel for ixed-ode frature based on daage ehanis whih has appliations in the delaination analysis of lainated oposites and whih therefore provides the theoretial bakground for the daage and debonding odel of interfae eleents in several oerial software as ANSYS[[ANSYS 12.0, Theory referene anual]. In the iro odelling of asonry speial attention has been paid to odel the brik-ortar oint interfae. A nuber of plastiity-based ontinuous-interfae odels have been developed to odel the tension and shear behaviour of asonry ortar oints (Rots 1997, Loreno and Rots 1997). Those odels aount for the interation between noral opression and shear as well as the shear dilatation often observed in experients. Mehrabi and Shing (1997) have developed an interfae odel for analyzing asonry infills that aounts for the inrease of ontat stress due to oint losing, the geoetri shear dilatation, and the plasti opation of a ortar oint. The failure surfae of the odel is based on a hyperboli funtion proposed by Lotfi and Shing (1994), and is apable of odelling daage auulation at ortar oints under inreasing displaeent and yli loading. This is refleted by shear strength redution and ortar opation (loss of aterial) at interfaes. The odel has been used to analyze the infilled fraes tested by Mehrabi et al. (1994). The appliation of these odels to siulate the onrete asonry interfae is yet to be explored. Also, studying about the effet of onreteasonry interfae on the perforane of asonry has beoe subet of any researhes. Attepts have been ade nuerially (Ibrahi and Suter, 1990, Mehrabi et. al., 1997, Asteris, 2008) as well as experientally (Dias 2005). This paper explores finite eleent odels developed to siulate the behaviour of onreteasonry interfae of asonry infill. In this study, brik-onrete ouplets were atheatially odelled, using oerially available software ANSYS. The adopted nuerial strategy onsists of siplifying the onrete-asonry-ortar interfae to a zero thik interfae, odelling the brik units and the onrete units with three diensional solid brik eleents and odelling the bond using zero thikness interfae eleents with a ohesive-zone odel (CZM) for ixed-ode frature based on daage ehanis introdued by Alfano and Crisfield(2001).

5 2. Methodology 2.1 Modelling assuptions and the nuerial odels used in the study A typial asonry brik- onrete blok ouplet was onsidered. The briks were of the standard size of 210x105x50 and the grade 25 onrete blok odelled was of a siilar size. The thikness of the ortar oint was onsidered as 10 whih is oonly used in onstrution pratie. One iro odel was reated with solid eleents to odel the brik, onrete blok and the ortar oint separately as show in Figure 3. In this no interfae eleents were used for the interfaes between the ortar-onrete and ortar-brik and the untions were onsidered to be fully bonded (odel Type1). The other was reated with zero thikness ontat target eleents and fully bonded option (odel Type 2) as given in Figure 5. The two types of odels for ouplets were analysed for the ases of diret shear and diret tension. All degrees of freedo at the botto of the brik and the two faes in the diretion parallel to the load appliation in diret shear test were restrained in order to odel the diret shear test ethod boundary onditions (Figure 5). In the ase of the ouplet under diret tension only the botto surfae was onsidered fixed (Figure 6). Figure 3: Miro odel Type1 Figure 4: Miro odel Type2 (With interfae) Figure 5: Boundary onditions for shear Figure 6: Boundary onditions for diret tension

6 2.2 Nuerial odelling of raking A three diensional eight noded isoparaetri eleent SOLID65 was eployed for the odelling of both onrete and asonry eleents. The eleent is apable of raking (in three orthogonal diretions), rushing, plasti deforation and reep. The aterial odel of SOLID 65 in ANSYS, having a five paraeter Willias-Warnke failure riterion [ANSYS 11.0, Theory referene anual], is ipleented to easure raking or rushing of the aterial (Figure 7) sybols are defined in ANSYS 11.0, Theory referene anual. Sine there is no possibility of raking of the onrete eleents, those eleents were reated without the rak odel. The SOLID65 eleent has eight Gauss integration points at whih raking and rushing heks are perfored. The eleent behaves in a linear elasti anner until either the speifi tensile or opressive strength is exeeded. If raking or rushing ours at an integration point, the raking is odeled through an adustent of aterial properties whih effetively treats the raking as a seared band of raks. In nuerial routines the foration of a rak is represented by the odifiation of the stress-strain relationships of the eleent to introdue a plane of weakness in a diretion noral to the rak fae. Also, a shear transfer oeffiient is used to represents a shear strength redution fator for those subsequent loads that indue sliding aross the rak. Figure 7: The failure surfae desribed in three diensional prinipal stress spae 2.3 Nuerial odelling of interfae The total behaviour of the ouplet is governed by the relative stiffness and strength harateristis of eah individual oponent. Out of these fators the interfae harateristis are the vital ones that deide the degree of oposite ation. ANSYS provides two ethods to odel separation of interfaes - i.e. an interfae eleent with ohesive zone aterial odel and a ontat eleent with bonded ontat option and a ohesive

7 zone aterial (ANSYS 11.0, Contat tehnology guide). In this study ontat eleent with bonded ontat option and a ohesive zone aterial was used to odel interfae. For the odelling of the asonry-onrete interfae, the surfae to surfae ontat eleent of CONTAC173 with target eleent TARGE170 was used. ANSYS provides two ohesive zone aterial odels with bilinear behaviour to represent debonding. The aterial behaviour, defined in ters of ontat stresses (noral and tangential) and ontat separation distane (noral gap and tangential sliding), is haraterized by linear elasti loading followed by linear softening. Debonding allows three odes of separation; 1. Mode I debonding for noral separation 2. Mode II debonding for tangential separation 3. Mixed ode debonding for noral and tangential separation. Debonding is also haraterized by onvergene diffiulties during aterial softening. Artifiial daping is provided to overoe these probles. After debonding is opleted, the surfae interation is governed by standard ontat onstraints for noral and tangential diretions. The ohesive zone aterial odel with bilinear behaviour is defined as: P K U 1 d, K U 1 d and K U 1 d n n y t y z where; P- Noral ontat stress (tension), τ y - tangential ontat stress in Y diretion, τ z - tangential ontat stress in Z diretion, K n - Noral ontat stiffness, K t - Tangential ontat stiffness, U n - Contat gap, U y - Contat slip distane in Y diretion, U z -Contat slip distane in Z diretion, d - Debonding paraeter. The following aterial onstants were used (see Table 1) in order to define the aterial behaviour with tration and separation. t z Table 1: Material onstants for defining interfae behaviour Constant Sybol Meaning C1 σ ax Maxiu noral ontat stress C2 Contat gap at the opletion of debonding C3 τ ax Maxiu equivalent tangential ontat stress C4 U t Tangential slip at the opletion of debonding C5 η Artifiial daping oeffiient C6 β Flag for tangential slip under opressive noral ontat stress Here U n and U t were defined in ANSYS as; U n U n = 6U n and U t = 6U t.

8 For brittle aterials like onrete, U n and U t are the displaeents orresponding to σ ax and τ ax respetively. The values for K n, K t, σ ax and τ ax were the sae as the values defined earlier in this hapter. The values of η and β were defined aording to the instrutions of ANSYS anual as; η = 1000 x odulus of elastiity and β = Siplifiation of onrete bea asonry infill untion in to a zero thikness interfae The ethod developed by Rots (1997) to odel the asonry-ortar interfae was used in this study to odel the onrete asonry interfae. In this odel the onstitutive behaviour of the unit is desribed by stress-strain relations for the ontinuu eleent. In the linear elasti range, the stress (σ) vs the strain (ε) relationship an be desribed aording to Hooke s law. The presene of a 10 thik ortar layer between onrete and asonry was assued in this siulation. The siplifiation of the onrete-asonry-ortar interfae to a zero thik interfae is illustrated in Figure 5 Figure 8: Siulation of the onrete-asonry oint Case 1 (Figure 8) shows the atual situation with adhesive areas on both sides of the ortar layer. In Case 2 (Figure 8) a opound interfae has been reated, aounting for both adhesion areas and the ortar layer. Finally in Case 3 (Figure 8) the onrete and asonry units were blown up to reate an interfae with zero thikness but with the properties of the adhesion area-ortar layer-adhesion area obination. The total lengthening aross half the units and oint should be equal in both Case 2 (over a length l ) and Case 3 (over a length l / ) For Case 2 h 2E h E h 2E

9 where h, h and h are the thiknesses and E, E and E are the oduli of elastiity of the onrete, asonry and oint respetively. For Case 3 (the siplified odel) / / / h 1 h / / 2E kn 2E however, Δl should be equal to Δl / and we have also assued that blown up units have the sae / / E value as the real units (i.e E E and E = E ) Also, h h h and 2 / h h / h Therefore the noral stiffness, k n, of the interfae eleent will beoe: k n h 4E E 4 E E E E E E E Siilarly the shear stiffness, k t, of the interfae eleent is given by: 2 k t where h 4G G E G G G G G G G G 2.5 Material Properties and Loading The aterial properties (See Table 2) were taken fro earlier studies done on nuerial odelling of raking in asonry (Dilrukshi & Dias 2008). Table 2: Material properties Conrete Masonry Mortar Weight per unit volue (kn/ 3 ) Modulus of elastiity (kn/ 2 ) 25x10 6 1x10 6 1x10 6 Poisson ratio The tensile and shear strength of ortar oint was onsidered as 0.2 N/ 2 and 0.13 N/ 2 respetively. The self load was applied at the first load step and a diret shear load of 275kg with no preopression was then applied to the ouplets at a nuber of sub steps for Case1. In Case 2 for both odels with and without interfae eleents, additional to the self load a diret tensile load of 40kg was applied. The analysis was perfored at eah sub step and results of eah sub step were reorded.

10 3. Results and Disussion The results of the two representations of the ouplets for both load ases are aording to the Figures 9-18 and Table 3 suarises the stresses transferred to the top of the brik surfae through the onrete blok-brik interfae. It is observed that no signifiant variations in the results have ourred for both odels. 3.1 Couplet behaviour under diret shear Figure 9: X diretion stresses for odel Type1 Figure 10: X diretion stresses for odel Type2 Figure 11: X diretion stresses at top of brik surfae for odel Type1 Figure 12: X diretion stresses at the top surfae of the brik for odel Type2 Figure 13: 1 st priniple stresses at top of brik surfae for odel Type1 Figure 14: 1 st priniple stresses at the top surfae of the brik for odel Type2

11 3.2 Couplet behaviour under diret tension Figure 15: Y diretion stresses for odel Type1 Figure 16: Y diretion stresses for odel Type2 Figure 17: Y diretion stresses at top of brik surfae for odel Type1 Figure 18: Y diretion stresses at the top surfae of the brik for odel Type2 Table 3: The stresses at a point in the iddle of the top of the brik surfae for both load ases Model Type and load ase X diretion stresses (N/ 2 ) Y diretion stresses (N/ 2 ) 1 st Priniple stresses (N/ 2 ) Diret Shear for odel Type E Diret Shear for odel Type E Diret Tension for odel Type E E E-01 Diret Tension for odel Type E E E-01 (For the Shear ase the stresses are for the final load step of a diret shear load of 275kg. For the tensile ase the stresses are for the final load step of a diret tensile load of 40kg) Results do not show signifiant variation of stresses for both types of odels. Therefore the opatibility between the two odels is verified for the ase of fully bonded interfae. The use of the ethod developed by Rots (1997) to siplify the asonry-ortar interfae in to a zero thikness interfae is valid for this ase.

12 The deforations at the brik surfae fro one edge to the other of the brik along the longitudinal axis for both load ases at nodes of 10 interval are as shown in Figure 19 and 20. Figure 19: Horizontal deforations along the brik surfae for diret shear load ase Figure20: Vertial deforations along the brik surfae for diret tensile load ase The vertial and horizontal deforations along the brik surfae are shown in Figures 19 and 20. The differenes in both types of deforations for the onsidered ases are less than 10% and hene onsidered aeptable. 4. Conlusions The use of the ethod developed by Rots (1997) to siplify the asonry-ortar interfae in to a zero thikness interfae is valid for this ase.

13 Aknowledgeent The authors would like to extend their sinere gratitude to the Senate Researh Counil, University of Moratuwa for the finanial support, and ivil Engineering departent of University of Moratuwa for their provision of lab failities for this investigation. We also aknowledge the olleagues who helped throughout the researh work. Referenes Alfano G, Marfia S, Sao E. A ohesive daage frition interfae odel aounting for water pressure on rak propagation. Coputer Methods and Appliations, Meh. Engrg., 2006: ANSYS Strutural analysis guide. (2007). Douentation for ANSYS 11.0, ANSYS In. Athanasios D.T. Finite eleent odelling of raks and oints in disontinuos strutural systes. 16th ASCE Engineering ehanis onferene. University of Washington, Atkinson R.H, Aaidei B.P, Saeb S, Sture S (1989). RESPONSE OF MASONRY BED JOINTS. Journal of Strutural Engineering, Vol.115, No. 9, Biani N., Stirling C. & Peare C.J. (2000). Disontinuous odelling of strutural asonry. Fifth World Congress on Coputational Mehanis,Viana, Australia. Chairoon K, A. M. (2007). Modeling of unreinfored asonry walls under shear and opression. Engineering Strutures 29, Chong V L, M. I. (1991). An investigation of laterally loaded asonry panels using non-linear finite eleent analysis. In M. J, & P. G. N, Coputer ethod in Strutural asonry (pp ). UK: Books and Journals International Ltd. Dias J.L (2007). Craking due to shear in asonry ortar oints and arround the interfae between asonry walls and reinfored onvrete beas. Constrution and building aterials 21, Dilrukshi KGS, Dias WPS. Field survey and nuerial odelling of raking in asonry walls due to theral oveents of an overlying slab, Journal of National Siene Foundation Sri Lanka 2008; 36(3): El-Sakhawy N R, R. H. (Marh 2002). Shearing behaviour of oints in load bearing asonry wall. Journal of Materials in Civil Engineering, Fouhal F, L. F. (2009). Contribution to the odelling of interfaes in asonry onstrution. Constrution and Building Materials 23,

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