NUMERICAL SIMULATION OF URM WALLS RETROFITTED WITH CABLE BY DISTINCT ELEMENT METHOD

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1 10 th Canadan Masonry Symposum, Banff, Alberta, June 8 12, 2005 NUMERICAL SIMULATION OF URM WALLS RETROFITTED WITH CABLE BY DISTINCT ELEMENT METHOD Y. Zhuge 1 1 Senor Lecturer, School of Natural and Bult Envronments, Unversty of South Australa, Mawson Lakes Campus, SA 5095, Australa, yan.zhuge@unsa.edu.au ABSTRACT The hstory of past earthquakes has shown that masonry buldngs have suffered the maxmum damage. Also, the Australan love of hertage buldngs (most of them beng of unrenforced masonry) means that greater attenton s requred to secure ther performance under sesmc loadng n the future. Therefore, to retroft and strengthen exstng masonry structures to resst potental damage from earthquakes has become an mportant ssue. A research project was carred out at the Unversty of South Australa amed at developng a smple and hgh strength sesmc retrofttng technque for masonry structures. A seres of expermental tests on unrenforced masonry (URM) walls retroftted wth an nnovatve cable system have been conducted. The results ndcated that both the strength and ductlty of the tested specmens were sgnfcantly enhanced wth the technque. In ths paper, an analytcal model based on Dstnct Element Method (DEM) has been developed to smulate the behavour of URM walls before and after retrofttng. KEYWORDS: dstnct element method, walls, retrofttng, cable. INTRODUCTION The Newcastle earthquake n 1989 led to the creaton of a new set of gudelnes for earthquake resstant desgn n Australa. Ths new code has resulted n the need to retroft structures that do not comply wth the new gudelnes systematcally. Masonry structures are one of the most common constructon types n Australa. Although the hstory of past earthquakes has shown that masonry buldngs have suffered the maxmum damage and also accounted for the maxmum loss of lfe, they contnue to be popular. Most of the hstorcal buldngs throughout Australa are unrenforced masonry (URM), hghlghtng the need to mprove ther performance by retrofttng and strengthenng to resst potental earthquake damage. Two types of falure are commonly observed n load bearng URM walls subjected to sesmc loads. These are n-plane falure characterzed by a dagonal tensle crack pattern, and out-ofplane falure, where cracks are prmarly along the mortar bed jonts. The current research project s amed at ncreasng the n-plane load carryng capacty of URM walls. A seres of expermental tests on URM walls retroftted wth an nnovatve cable system have been

2 conducted. The results ndcated that both the strength and ductlty of tested specmens were sgnfcantly enhanced wth the technque. In ths paper, an analytcal model whch s based on Dstnct Element Method (DEM) has been developed to smulate the behavour of URM walls before and after retrofttng. In the dstnct element method, a sold s represented as an assembly of dscrete blocks. Jonts are modelled as nterfaces between dstnct bodes. The DEM s a dynamc process especally desgned to model the behavour of dscontnutes. By usng DEM, the response of dscontnuous meda, such as unrenforced masonry, under both statc and dynamc loadng can be smulated. The DEM model was successfully appled to smulate the response of URM shear wall panels n prevous studes [1, 2]. In the current study, a new user defned FISH functon has been developed to model the structural behavour of cable. The results between dstnct element model and experments are compared and dscussed. OUTLINE OF DISTINCT ELEMENT METHOD The Dstnct Element Method has been progressvely developed over the past two decades. Cundall [3] frst ntroduced the Dstnct Element Method to smulate progressve movements n block-lke rock systems and the model has been mplemented subsequently nto the computer program UDEC. In the DEM method, a sold s represented as an assembly of dscrete blocks. Jonts are modelled as nterfaces between dstnct bodes. The contact forces and dsplacements at the nterfaces of a stressed assembly of blocks are found through a seres of calculatons, whch trace the movements of the blocks [4]. At all the contacts, ether rgd or deformable blocks are connected by sprng-lke jonts wth normal and shear stffness k n and k s respectvely. Smlar to the Fnte Element Method (FEM), the unknowns n the DEM are also the nodal dsplacements and rotatons of the blocks. However, unlke FEM, DEM s a dynamc process and the unknowns are solved by the equatons of moton. The speed of propagaton depends on the physcal propertes of the dscrete system. The soluton scheme used by DEM s the explct tme marchng scheme and t uses fnte contact stffness. If the blocks are rgd, block dsplacements are calculated from the out of balance moment and forces appled to the centre of gravty of each block. Resultant forces F nclude boundary forces appled to the edges of the block and gravty. Newton's second law of moton s appled for each block: ( t ) ( t) u& F = t m where u& s the velocty, m s the mass, and t s the tme. Equaton 1 Followng the central dfference ntegraton scheme, Equaton 1 can be transformed nto: ( t) ( t+ t / 2) ( t t / 2) F u& = u& + t Equaton 2 m

3 For blocks n two dmensons where several forces are assumed to act on the block (ncludng gravty loads), the velocty (Equaton 2) can be re-arranged to nclude the angular velocty of block: u& θ & ( t+ t / 2) ( t+ t / 2) = u& = θ& ( t t / 2) ( t t / 2) + ( + ( F m M I ( t) ( t) + g ) t ) t Equaton 3 where θ & = the angular velocty of the block; I = the moment of nerta of the block; u& = the velocty components of block centrod; ΣM (t) = the total moment actng on the block; ΣF (t) = the total force actng on the block; and g = the components of gravtatonal acceleraton. Assumng the veloctes are stored at the half-tme pont of the step, the new veloctes n Equaton 3 can be used to determne the new block locaton: x θ ( t+ t) ( t+ t ) = x = θ ( t) ( t) ( t + u& ( t + θ& + t / 2) + t / 2 t t Equaton 4 where θ = the rotaton of the block about ts centrod; and x = the coordnates of block centrod. The new poston of the block nduces new condtons at the block boundares and thus new contact forces. Resultant forces and moments are used to calculate the lnear and angular acceleratons of each block. The calculaton scheme summarsed above by Equaton 1 to Equaton 4 s repeated untl a satsfactory state of equlbrum or contnung falure s reached for each block. It should be noted that tme has no real physcal meanng f a statc analyss s beng performed. If the blocks are deformable, they wll frst be nternally dscretsed nto fnte dfference trangular elements before the equatons of moton are formulated at each grd pont. The mortar jonts are represented numercally as a contact surface between two block edges. The consttutve laws appled to the contacts are: σ = k u Equaton 5 s n s n s n τ = k u Equaton 6 where k n and k s are the normal and shear stffness of the contact, σ n and τ s are the effectve normal and shear stress ncrements, and u n and u s are the normal and shear dsplacement ncrements. Stresses calculated at grd ponts located along contacts are submtted to the selected falure crteron. For unrenforced masonry shear wall panels, Coulomb frcton s formulated:

4 τ s C + σ n tanφ = τ max Equaton 7 where C s the coheson and φ s the frcton angle. There s also a lmtng tensle strength f t for the jont. If the tensle strength s exceeded, then σ n = 0. Modellng drect tensle splttng of brck s a more delcate subject. In order to smplfy the problem, the brck unt materal s modelled wth a Mohr-Coulomb falure crteron wth a tenson cutoff. The shear flow rule s non-assocated and the tensle flow rule s assocated. A detaled dscusson of the model can be found n Zhuge and Hunt [3]. SUMMARY OF EXPERIMENTAL PROCEDURES Three full-scale clay brck masonry walls retroftted wth the cable system have been tested under combned compresson and rackng cyclc loads. An unrenforced masonry wall was also tested under the same loadng condton for comparson. The proposed retrofttng systems am to mprove the performance of walls by ncreasng shear strength above flexural strength and by ncreasng ductlty and energy dsspaton capablty. All specmens were chosen wth an aspect rato of 1.0 to ensure that most of the unretroftted walls would exhbt shear-nduced damage. Therefore, n-plane falure would domnate. The dmensons of the wall were 940 mm long x 940 mm hgh x 110 mm wde (11 courses hgh and 4 brcks n each course). The wall was constructed on a concrete foundaton beam to smulate a house footng. The type of cable used for the experment was Ronstan typcal grade 316 stanless steel wre rope (19 sngle strands, dameter 10mm, breakng load 71 kn). The endngs for the cable were seafast threaded swage termnals (RF1513M1010). The anchorage for the connecton plate to the foundaton beam was a Ramset Chemset Anchor (M 16 x 190 mm, desgn tensle and shear load 8.5 kn per anchor and Chemset 800 seres). The cables were fxed on one sde of the wall only. Retroft was accomplshed by addng two 10 mm dameter cables (wre ropes) to one sde of the wall face, as shown n Fgure 1. Ideally cables should be added on both sdes of the wall to prevent an eccentrc stffness and strength dstrbuton that may cause twstng of the retroftted walls. The cable dameter was chosen to ensure that the wall would fal earler than the cable. The anchor was desgned to transfer the load from the cable to the foundaton wthout falure before the cable was broken. The tested walls were subjected to a constant vertcal compressve stress σ m = 0.2 MPa. To smulate earthquake loadng, a seres of horzontal dsplacement reversals of ncreasng ampltude were appled to the walls. Each wall was cycled twce at each of the ncrementally ncreasng dsplacement ampltudes untl falure. The specmens were nstrumented for dsplacement, rotaton and stran measurements. Stran gauges were used to measure strans n cable.

5 Fgure 1 URM Wall Retroftted wth Cable [5] NUMERICAL SIMULATION OF MASONRY WALLS RETROFITTED WITH CABLE The cable conssts of a number of wres or strands and has hgh tensle strength, lghtness and hgh corroson resstance. These materals can absorb tensle stress and ncrease overall element stffness, ductlty and bearng capacty. Usng a cable system for sesmc retrofttng applcatons has other advantages such as archtectural versatlty, low cost and fast constructon, durablty, and no loss of valuable space. Furthermore, t does not add a sgnfcant mass to the exstng buldng, leavng the dynamc propertes of the structures vrtually unchanged. Numercal smulaton of URM walls retroftted wth a cable s not an easy task. Frst, masonry s not a smple materal, as t s composed of two materals n a geometrc array - an assemblage of brcks set n a mortar matrx. The nfluence of mortar jonts and bond as a plane of weakness s a sgnfcant feature. A complcated two-phase fnte element mcro-model has been used by some researchers n recent years [6, 7, 8] but such a model would make ths analyss very complex. On the other hand, DEM s fully dynamc and deals wth pseudo-statc problems by allowng the dynamc behavour to reach equlbrum wth notonal tme. It s specally desgned to model the behavour of dscontnutes. Therefore, DEM s well suted for masonry structures. The DEM has been appled by the author to analyse the structural behavour of unrenforced masonry [3, 9]. Intally, a stress boundary was used, where the horzontal load was monotoncally ncreased. However, nether the falure pattern nor the prncpal stress dstrbuton compared well wth expermental or fnte element results. An mproved model was then ntroduced, where the stress boundary was replaced by a progressvely ncreased dsplacement boundary. The model was appled to smulate the response of unrenforced masonry shear wall panels wth and wthout an openng, where expermental test results are avalable. In general, good agreement was observed n the comparson [3]. Although DEM has been successfully appled to smulate URM walls subject to n-plane load, addng a cable s not straghtforward. A specal cable element was created n the model to smulate the axal behavour of the cable renforcement whch only carres unaxal tensle force. The ncremental axal force, t F, s calculated from the ncremental axal dsplacement by

6 EA L t t F = u Equaton 8 t where u = ut = u1t1 + u2t2. Subscrpt 1 and 2 correspond to the x-drecton and the y- drecton respectvely. The cable s assumed to be dvded nto a number of segments to pass through the jonts that are requred to be renforced, wth nodal ponts located at each segment end. Axal dsplacements are computed based on ntegraton of the laws of moton usng the computed out-of-balance axal force and a mass lumped at each nodal pont (Itasca 2000). Dfferent materal propertes were assgned to the unbonded secton and the anchorage sectons at the ends of the cable. In order to smulate the anchor connecton to the end of the cable, a hgh grout shear stffness and shear strength are assgned to the cable nodes embedded n the small blocks to whch the cable s anchored. The materal propertes of the cable are lsted n Table 1. Table 1 Materal Propertes of the Cable Cable Unbonded secton Anchorage secton E A f t kbond sbond kbond sbond (MPa) (mm 2 ) (kn) (MPa) (MN/m) (MPa) (MN/m) e Where kbond s the grout shear stffness and sbond s the cohesve strength of the grout. k n and k s of the nterfaces between the wall blocks are potentally mportant parameters n the numercal analyses of masonry walls usng DEM. Unfortunately, there are very few test data avalable on stffness propertes of mortar jonts. The only test results the authors could fnd were the experments conducted at the Unversty of Delft, the Netherlands [7]. These test results were used to valdate the numercal model of masonry shear wall panels under n-plane lateral load developed by the authors [3]. As the parametrc studes ndcated that the senstvty of the results wth respect to the estmaton of jont materal parameters was small, these values of k n and k s have been adopted agan for the current model (Table 2). Table 2 - Summary of jont materal propertes Tenson Shear Normal stffness Shear stffness f t tanφ tanψ C k n k s (N/mm 2 ) (MPa) (N/mm 3 ) (N/mm 3 ) Numercal modellng of each URM wall and URM wall retroftted wth cables was carred out usng the dstnct element code UDEC (Unversal Dstnct Element Code) [4]. The dmensons of the wall were based on the expermental program (Fgure 1). Deformable blocks were utlsed to enable force transmsson between the wall and the cable. The deformable blocks must be dscretsed nto fnte dfference trangular elements. The DEM model and a typcal dscrete element mesh are shown n Fgure 2.

7 Fgure 2 - URM Wall Retroftted wth Cable usng UDEC COMPARISON WITH EXPERIMENTAL INVESTIGATIONS The comparson between numercal and expermental load-dsplacement dagrams s shown n Fgure 3. It can be seen from the fgure that the expermental behavour s well smulated by the numercal model. The collapse load estmated by the numercal model was 40.7 kn compared to the expermental result of 39.1 kn (wall 2 n the dagram), and the average collapse load of all tested walls was 43.4 kn. The sudden load drop of around 20 kn was due to major dagonal crackng occurrng n the wall. The dagram also ndcates that the wall behaved n a qute ductle manner, whch agrees wth the expermental observatons. The force carred by the cable and the force carred by the retroftted wall are also compared n Fgure 3. The expermental results ndcated that the cable carred around 50% of the force actng on the whole wall. However, the numercal results predcted that the cable would carry around 80% of the force when the wall reached ts ultmate strength. Due to the lmtaton of the software and DEM, t s very dffcult to model a steel plate attached to URM walls. Therefore, equvalent bond stffness and strength were assgned to the cable wall connecton. Nevertheless, the ultmate load capacty of the wall s well predcted by the model. 50 Horzontal force (kn) numercal cable force-numercal expermental cable force-expermental Horzontal dsplacement (mm) Fgure 3 Comparson of Load-deflecton Behavour Durng the testng, all retroftted walls exhbted superor behavour when compared wth URM walls. The ultmate load capacty of walls retroftted wth the cable was ncreased by around a factor of 2. As ndcated by Fgure 4, smlar results are predcted by the numercal model. When a wall s retroftted wth a cable, the appearance of the crack cannot be prevented (smlar crackng loads were predcted for walls wth and wthout cables, ndcated by a sudden drop n load around 20 kn). However, the behavour of the walls would be qute dfferent after the

8 formaton of the dagonal cracks. For the URM wall, major cracks developed along the dagonal drecton, the wall faled due to compressve crushng at the supports and rotated as a rgd body. For the wall retroftted wth the cable, the cable could prevent the development of the man dagonal cracks, allowng the cracks to spread more evenly over the entre wall. The wall then could contnue to carry hgher load. Ths also agrees wth the expermental results. 50 Horzontal force (kn) Cable URM Horzontal dsplacement (mm) Fgure 4 - Smulated Behavour of the Wall wth and wthout Cable DEM Model The above dscusson of wall behavour can be demonstrated by the mnmum prncpal stresses dstrbuton shown n Fgure 5. For the URM wall (Fgure 5(a)), when the dagonal cracks are fully open, two dstnct struts are formed, one at each sde of the dagonal crack. The concentraton of the large compressve stress at the supports leads to the collapse of the wall. However, for the retroftted wall (Fgure 5(b)), the full openng of the dagonal cracks was prevented by the exstence of the cable. Two dstnct struts are not formed. A more contnuous stress dstrbuton s observed. JOB TITLE : Masorny w alls; JOB TITLE : Masorny w alls; UDEC (Verson 3.10) UDEC (Verson 3.10) LEGEND LEGEND 31-Jan-05 12:52 cycle major prncpal stress cont contour nterval= 1.000E E+00 to 0.000E Jan-05 12:51 cycle major prncpal stress cont contour nterval= 2.000E E+01 to 0.000E E E E E E E E E E E E E E E E s,mnvzx;klcjhvpasd89f7q-ldosas 1ojaspojfzxcnvxmnbz;kasjhdfqp s,mnvzx;klcjhvpasd89f7q-ldosas 1ojaspojfzxcnvxmnbz;kasjhdfqp (a) URM wall (b) Retroftted wall Fgure 5 - Prncpal Stress Dstrbutons from DEM at a Dsplacement of 2.7 mm The tensle and shear cracks that develop at the same dsplacement of 2.7 mm for walls wth and wthout a cable predcted by the numercal model are llustrated n Fgure 6. For the URM wall (Fgure 6(a)), two stepped dagonal cracks through the head and bed jonts are formed at ths loadng stage. For a wall retroftted wth a cable under the same dsplacement, only horzontal tensle cracks are developed along the top and bottom of the wall; no major dagonal cracks are formed (Fgure 6(b)). Ths proved further that the load transmsson path and the crackng patterns of the wall are changed when cable retrofttng s ntroduced.

9 (a) URM wall (b) Wall retroftted wth cable Fgure 6 - Crack Patterns of the Analyss usng DEM at a Dsplacement of 2.7 mm CONCLUSIONS Numercal modellng of masonry s not an easy task due the nfluence of mortar jonts as planes of weakness. In the past few years, an alternatve and smple way of modellng masonry usng the Dstnct Element Method has been developed and valdated by expermental results. In ths paper, the model s further developed to smulate the behavour of unrenforced masonry walls before and after retrofttng wth a cable system. The model s valdated by comparng the results wth those obtaned from experments, whch nclude the force-dsplacement dagram, ultmate load capacty and the falure pattern of the wall wth and wthout retrofttng. The analyss has confrmed the expermental results that usng a smple cable system to retroft low-rse masonry walls s an effectve technque to ncrease sgnfcantly the n-plane strength, ductlty, and energy dsspaton capacty. The mprovement n the ultmate lateral load resstance of the retroftted walls wth cables s around two tmes the capacty of URM wall. REFERENCES 1. Zhuge, Y. and Hunt, S. An Improved Dstnct Element Model for Masonry Shear Panels. Proceedngs of the Second Internatonal Conference on Advances n Structural Engneerng and Mechancs, Busan, Korea, Zhuge, Y. and Hunt, S. Numercal Smulaton of Masonry Shear Panels wth Dstnct Element Approach. Structural Eng. And Mechancs an Internatonal Journal, Vol. 15, No4, 2003, pp Cundall, P. A. A Computer Model for Smulatng Progressve Large Scale Movements n Blocky Rock Systems. Proceedngs of the Sym. of the Internatonal Socety for Rock mechancs, Nancy, Francs, Vol. 1, II-8, 1971, pp ITASCA Consultng Group. Unversal Dstnct Element Code. ITASCA consultng Group, Inc., Mnneapols, Mnnesota, USA, 2000.

10 5. Chuang, S, Zhuge, Y. and McBean, P. Expermental Testng of Unrenforced Masonry Walls Retroftted by Cable System. Proceedngs of the 7th Australasan Masonry Conference, Newcastle, 2004, pp Lotf, H. and Shng, P. Interface Model Appled to Fracture of Masonry Structure. Journal of Structural Eng. ASCE, 1994, pp Lourenco, P. B. Computatonal Strateges for Masonry Structures. PhD Thess, Delft Unversty of Technology, The Netherlands, Gambarotta, L. and Lagomarsno, S. Damage Models for the Sesmc Response of Brck Masonry Shear Walls. Part II: the contnuum model and ts applcatons. Earthquake Engneerng & Structural Dynamcs, 26, 1997, pp Zhuge, Y. Dstnct Element Modellng of Unrenforced Masonry Walls. Proc. of the 7th East Asa-Pacfc Conference of Structural Eng. and Constructon, Koch, Japan, 1999, pp