PERFORMANCE ASSESSMENT FOR UNREINFORCED MASONRY BUILDINGS IN LOW SEISMIC HAZARD AREAS

Transcription

1 13 th World Conference on Earthquake Engneerng Vancouver, B.C., Canada August 1-6, 4 Paper No. 49 PERFORMANCE ASSESSMENT FOR UNREINFORCED MASONRY BUILDINGS IN LOW SEISMIC HAZARD AREAS Rcardo BONETT 1, Alex H. BARBAT, Lus G. PUJADES, Sergo LAGOMARSINO 3 and Andrea PENNA 4 SUMMARY The Example dstrct of Barcelona has an mportant hstorcal, archtectural and cultural value, coverng about 75 hectares of the cty. Most of ts housngs are unrenforced masonry buldngs havng an average age of about 1 years. These buldngs are tall and they have been desgned and bult wthout any earthquake resstant consderaton. Furthermore, they show some partcular features, typcal of the constructve technques at that tme, whch have been dentfed as addtonal potental damage sources. In order to evaluate the expected sesmc performance of these buldngs, a typcal sx-story unrenforced masonry buldng was modeled. The buldng was desgned and constructed n 188 and contans detals whch are typcal of that constructve perod of the Example dstrct. The dynamc behavor was studed by means of a structural analyss procedure, whch uses macro elements to model the masonry panels. Ths model descrbes the nonlnear n-plane mechancal behavor of the panels and assesses the expected damage n masonry buldngs due to earthquakes. Monte Carlo smulaton has been used to take nto account the uncertantes n the mechancal propertes of the materals. In ths way, the mean sesmc capacty curves of the buldng and ther correspondng standard devatons have been obtaned. The sesmc demand has been consdered by usng response spectra proposed by the Cartographc Insttute of Catalona (ICC, Irzarry [1]). The results here obtaned for the sesmc performance of ths type of buldngs, make clear ther hgh vulnerablty and, therefore, t s advsable retrofttng them n order to mprove ther sesmc behavor. INTRODUCTION The emblematc zone of the central dstrct of Barcelona, Span, denomnated Example, was desgned n the mddle of the nneteenth century. Ths urban area has an mportant hstorcal, archtectural and cultural value and covers approxmately 75 hectares of the cty. The most representatve typology of ths dstrct corresponds to unrenforced masonry buldngs (URM), whch are ncorporated nto numerous 1 Professor - Natonal Unversty of Colomba, Medelln Colomba Professor - Techncal Unversty of Catalona, Barcelona Span 3 Professor Unversty of Genoa, Genoa Italy 4 Researcher - European Center for Tranng and Research n Earthquake Engneerng, Pava Italy

2 almost square blocks, denomnated slands. The constructon of these buldngs took place between 186 and 194, wth 5 buldngs n average for each block. They were desgned only to vertcal statc loads, wthout any consderaton of sesmc desgn crtera, because they were bult pror to the frst Spansh sesmc code. All of the exstng URM buldngs n ths area already have exceeded ther lfe perod and only a small part of them are new renforced concrete buldngs. The slabs of these buldngs are wooden, or are made of renforced concrete or steel (accordng to the buldng perod) wth ceramc celng vaults. Due to the great heght of the frst floor of these buldngs, almost all of them have soft frst floors. Moreover, due to the need of bgger commercal areas n the frst floors, cast ron columns were used nstead of masonry walls, reducng even more the stffness of the buldngs. Therefore, we expected hgh vulnerablty for ths buldng typology. Recently, researchers at the ICC, have re-evaluated the sesmc hazard of Barcelona, approachng the problem from two ponts of vew: determnstc and probablstc (Irzarry [1]). So, two types of response spectra are avalable: the frst one corresponds to the bggest hstorcal earthquake n the cty (determnst case) and the second s the 475 year return perod earthquake, namely, the earthquake whose ntensty has a 1% probablty to be exceeded n a 5 years perod (probablstc case). Obtanng these two elastc response spectra has been an mportant contrbuton to the defnton of the sesmc hazard, because we are now able to apply capacty-demand based analyses to evaluate the sesmc performance of the buldngs n the cty. The N method proposed by Fajfar [] s used wth ths am. Startng from the obtaned demand of spectral dsplacement and usng the damage states proposed by Calv [3] for URM structures, the expected damage grade and thus the performance of the buldng can be easly determned. For many years n the past, the mechancal propertes of the materals used to buld the structures of the Example, were determned emprcally. Therefore these propertes may show a wde range of varablty and a hgh uncertanty. In order to keep these uncertantes wthn a reasonable range n the case of our buldng class, we have requested expert opnons and we have used Monte Carlo smulatons to evaluate probablstc capacty spectra. As a result, the man parameters defnng the mechancal characterstcs of the model are defned by random varables whch, startng from smple assumptons about ther probablty densty functon, can be characterzed by a mean value and ts covarance. A number of buldng samples are then generated n such a way that the numercal values for the parameters and propertes nvolved n the model ft well the correspondng probablty densty functon. Ths smulaton process allows descrbng the behavor of a wde group of buldngs showng smlar geometrcal and constructve features. Furthermore, the Monte Carlo technques allow studyng the nfluence of the uncertantes n the structural parameters on the evaluaton of the sesmc performance level. STRUCTURAL TYPOLOGY The typcal Example URM buldng, whch has been studed, has sx stores, brck walls of 3 cm for the façade walls and 15 cm n the other walls. The two frst floors have metallc beams and ceramc celng vaults smply supported on metallc man beams and cast ron columns. Rubble s placed on the upper part of the vaults and above t there s a lme mortar layer and the pavement (see Fgure 1). For the other stores, the slab s made of wooden beams, supportng the ceramc celng vaults, as t can be seen n Fgure. At the basement and ground floors, the masonry bearng walls of the upper part of the structure are supported on metallc man beams, whch n turn, are supported on cast ron columns. The columns are supported on a block, whch s supported on the masonry foundaton, beng ths type of connecton very deformable.

3 Fgure 1. Detal of the slab wth steel beam and ceramcs celng vaults (taken from the orgnal archtectonc plans of the buldng). Fgure. Detal of the slab wth wood beam and ceramcs celng vaults (taken from the orgnal archtectonc plans of the buldng). The Example dstrct has about 9 housngs and about 7% of them correspond to the URM typology here descrbed. Therefore, ths sx-story URM buldng constructed n 188, wth detals typcal of that constructve perod n the Example dstrct, has been chosen for a detaled study of ths type of buldngs. The man purpose of ths work has been evaluatng the dynamc behavor and sesmc performance of the buldngs of Barcelona whch are well represented by ths typology. The dstrbuton n plant of the buldng s almost rectangular (18.9 m 4.5 m) and the buldng has a central and two lateral squared patos. In elevaton, the buldng shows certan rregulartes, such as: cast ron columns at the ground floor, masonry bearng walls drectly supported on metallc man beams, whch, n turn, are supported on the mentoned columns. Therefore, there s a consderable varaton of the stffness wth the heght of the structure, reducng ts sesmc capacty n such a way that we may expect the typcal collapse mechansm produced by the presence of a soft floor. SEISMIC DEMAND Barcelona, cty located n the northeast of Span, has a moderate sesmc hazard and low tectonc actvty. Startng from 1998 a detaled analyss of the mcrozonaton of the cty has been undertaken. Ths analyss allowed classfyng the sol of the cty n four types correspondng to 4 homogeneous areas (Cd [4]). The

4 sesmc hazard, consderng the sze of the acton n terms of the ntensty and spectral acceleratons for perods of,.3,.6, 1. and. s, has been recently reevaluated. The problem has been analyzed startng both from the determnstc and probablstc ponts of vew. Fnally, the sesmc demand was defned by means of the elastc response spectra for the four zones of the cty (Irzarry [1]). The Acceleraton Dsplacement Response Spectra (ADRS), correspondng to the determnstc and probablstc hazard scenaros, can be seen n Fgure 3..6 S a (g).5 ICC probablstc case -spectrum.4.3. ICC determnstc case - spectrum S d (cm) Fgure 3. Response spectra for determnstc and probablstc scenaros. STRUCTURAL CAPACITY Buldng Structural model TREMURI program has been used for modelng the consdered buldng type. Ths program was developed by Galasco [5]. A non-lnear macro-element model, able to reproduce earthquake damage to masonry buldngs and falure modes observed n expermental testng, s mplemented n the program: t allows 3-dmensonal modellng and several sesmc analyss procedures. The 3-dmensonal modellng of whole URM buldngs starts from some hypotheses on ther structural and sesmc behavour: the bearng structure, both referrng to vertcal and horzontal loads, s dentfed, nsde the constructon, wth walls and floors (or vaults); the walls are the bearng elements, whle the floors, n addton to share vertcal loads to the walls, are consdered as planar stffenng elements (orthotropc 3-4 nodes membrane elements), on whch the horzontal actons dstrbuton between the walls depend; the local flexural behavour of the floors and the walls out-of-plane response are not computed because they are consdered neglgble wth respect to the global buldng response, whch s governed by ther n-plane behavour (a global sesmc response s possble only f vertcal and horzontal elements are properly connected). A frame-type representaton of the n-plane behavour of masonry walls s adopted: each wall of the buldng s subdvded nto pers and lntels ( nodes macro-elements) connected by rgd areas (nodes). Earthquake damage observaton shows, n fact, that only rarely (very rregular geometry or very small openngs) cracks appear n these areas of the wall: for ths reason these regons deformaton s assumed to be neglgble, relatvely to the macro-elements non-lnear deformatons governng the sesmc response. The presence of strngcourses (beam elements), te-rods (noncompressve spar elements), prevous damage, heterogeneous masonry portons, gaps and rregulartes can be easly ncluded n the structural model.

5 The non-lnear macro-element model, representatve of a whole masonry panel, proposed by Gambarotta [7], permts, wth a lmted number of degrees of freedom (8), to represent the two man masonry falure modes, bendng-rockng and shear-sldng (wth frcton) mechansms, on the bass of mechancal assumptons. Ths model consders, by means of nternal varables, the shear-sldng damage evoluton, whch controls the strength deteroraton (softenng) and the stffness degradaton. Fgure 4 shows the three substructures, whch a macro element s dvded: Two layers, nferor1 and superor3, n whch s concentrated the bendng and axal effects. Fnally a central part, ths one suffers shear deformatons and presents no evdence of axal or bendng deformatons. A complete cnematc model should take nto account the three degrees of freedom for each node and j on the extremtes: axal dsplacement w, horzontal dsplacement u and rotaton ϕ. There are two degrees of freedom for the central zone: axal dsplacement δ and rotaton φ (Fgure 4). h 3 ϕ j w j u j j ϕ w δ φ u M N T n m M j 3 N j j T j T M N (a) 1 ϕ 1 1 w b w 1 u 1 u ϕ s 1 T 1 M 1 N 1 (b) M 1 1 T 1 1 N 1 T M N Fgure 4. Cnematc model for the macro element [6]. Thus, cnematc s descrbed by an eght degree freedom vector, a T = {u w ϕ u j w j ϕ j δ φ}, whch s obtaned for each macro element. It s assumed, for ths hypothess, that the extremtes have an nfntesmal wdth ( ). The overturnng mechansm, whch happens because the materal does not resst tracton stress s modeled by a mono lateral elastc contact between 1 and 3 nterfaces. The consttutve equatons between the cnematc varables w, ϕ and the correspondent statc quanttes n and m are uncoupled to the lmt m b condton, when the secton s smaller than the entre compresson zone. n 6 For substructure 1 the followng equatons are obtaned: ( w ) N N = ka δ + (1) 1 M = kab ϕ φ + M 1 ( ) ()

6 Where A = s b, corresponds to the transversal secton of the panel. The nelastc contrbuton N and M are obtaned from the unlateral condton of perfect elastc contact: N 1 [ ϕ φ b + ( δ w )] H e, k A = b 8ϕ φ 6 (3) 1 [ ] H e k A (4) M = [( ϕ φ) b ( δ w )] ϕ φ b + ( δ w ) b 4( ϕ φ) ϕ φ 6 Where H () s the Heavsde s functon. The panel s shear response s expressed consderng a unform shear deformaton dstrbuton u u j γ = + φ n the central part and mposng a relatonshp between the cnematc quanttes u, h u j andφ, and the shear stress T = Tj. The crackng damage s usually located on the dagonals, where the dsplacement take place along the jonts and s represented by an nelastc deformaton component, whch s actvated when the Coulomb s lmt frcton condton s reached. From the effectve shear deformaton correspondng to module and ndcatng the elastc shear module as G, the consttutve equatons can be expressed as: ( u u + h) T GA T = j φ + h (5) GA cα h (6) T = u u j + φh + f h 1+ cα GA Where the nelastc component T ncludes the frcton stress f effect, opposed to the sldng mechansm, and nvolves a damage parameter α and an un-dmensonal coeffcent whch controls the nelastc deformaton c. In ths model, the frcton plays the role of an ntern varable defned by the followng lmt condton [6]: Φ S = f µ N (7) Where µ corresponds to the frcton coeffcent. These consttutve equatons can represent the panel s resstance varaton due to changes on axal stresses N j = N. The damage and ts effects upon panel s mechancal characterstcs are descrbed by the damage varable α whch grows accordng to falure crtera [5]: Φ d = Y ( S ) R( α ), (8) Where Y = 1 cq s the rate of energy lberaton by damage; R s the resstance functon and T S = { t n m } s the nternal stress vector. Assumng R as a growng functon of α to the crtcal value α = 1and decreasng for hgher values; the model can represent the stffness degradaton, the resstance C degradaton and pnchng effect.

7 The complete consttutve model, for the macro element, can be expressed n the followng fnte form: { T N M T N M N M } = Ka Q (9) Q + Q = j j j contans the nonlnear terms evaluated by the evoluton equatons for the damage varable α and the frcton, f. Fnally K s the elastc stffness matrx: GA / h GA / h K = GA ka ka kab kab /1 /1 GA / h GA / h GA ka ka kab kab /1 /1 ka ka ka GA kab /1 GA kab /1 GAh + kab / 6 (1) The nonlnear terms N and M are defned though the followng equaton: N = N N ; M = M M + T h (11) j The macro element shear model s a smplfcaton of a more complex contnuous model (see Gambarotta [7]) whose parameters are drectly correlated wth the masonry elements mechancals propertes. The macro model parameters should be consdered as a representatve of an average behavor. In addton to ts geometrcal characterstcs, the macro element s defned from sx parameters: The shear module G, the axal stffness K, the shear resstance of the masonry f vq, the un-dmensonal coeffcent that controls the nelastc deformaton c, the global frcton coeffcent f and β factor whch controls the softenng. The last factor s defned by pllar, as well as lntels. The macro-element used n the program to assemble the wall model keeps also nto account the effect (especally n bendng-rockng mechansms) of the lmted compressve strength of masonry (Penna [13]). Toe crushng effect s modelled by means of phenomenologcal non-lnear consttutve law wth stffness degrade n compresson: the effect of ths modellzaton on the cyclc vertcal dsplacement-rotaton nteracton s represented n Fgure 5. In order to perform non-lnear sesmc analyses of URM buldngs a set of analyss procedures has been mplemented: ncremental statc (Newton-Raphson) wth force or dsplacement control, 3D pushover analyss wth fxed load pattern and 3D tme-hstory dynamc analyss (Newmark ntegraton method; Raylegh vscous dampng). The pushover procedure, wth an effectve algorthm, transforms the problem of pushng a structure mantanng constant ratos between the appled forces nto an equvalent ncremental statc analyss wth one d.o.f. dsplacement control. Addtonal nformaton and further descrptons of the non-lnear macro-element modellng and analyss of URM buldngs can be found n Galasco [14] j

8 w ϕ Fgure 5. Cyclc vertcal dsplacement-rotaton nteracton wth (red lne) and w/o toe crushng (blue dots) [13] Macro element model for the studed buldng of the Example Fgure 6 shows a three-dmensonal vew and n plant of the model used for the representatve buldng of the Example. The model s defned by 8 walls n the x drecton (walls M1 to M8) and 6 walls n the y drecton (walls M9 to M14). Each wall has been modeled as an assemblage of pers, lntels and frame elements (n some cases) connected to the nodes of the model by means of rgd jonts. All the nodes have 5 degrees of freedom (3 dsplacement components and rotaton components correspondng to the axes x and y) except the base nodes of the model. The slabs have been modeled as an orthotropc fnte element daphragm, defned by 3 or 4 nodes connected to the three-dmensonal nodes of each level. A man analyss drecton s dentfed, whch s characterzed by a Young s modulus E 1 and the drecton perpendcular to ths one s characterzed by a Young s modulus E. Fgure 7 shows the macro element model correspondng to walls 1 and. M8 M7 M6 M14 M1 3 M1 M5 M4 M11 M1 M9 M3 M M1 Fgure 6. Three-dmensonal model of the analyzed typcal buldng of the Example. In order to analyze the constructve system of the URM buldngs of the Example, t s necessary to have a good knowledge on the materals used for ther man elements. Brcks are the basc materal of these buldngs, beng used wdely n walls, stars and slabs. The typcal dmensons of the used brcks are 3 15 cm and ther thckness vares between 3 and 11 cm. Ths knd of man-made brcks were used untl the begnnng of the XX th century. Later, mechancal systems were used, consderably mprovng ther qualty and compactness. Lme mortar was used n the constructve process of the buldngs of the

9 Example. The wde use of ths materal s assocated to constructve tradton, to consumpton habts and, apparently, to ts strength whch was consdered to be adequate at that perod. N n5 417 n6 418 n7 419 n8 4 N N n1 41 n 413 n3 414 n4 415 N N67 46 n17 47 n18 48 n19 49 n 41 N N41 41 n13 4 n14 43 n15 44 n16 45 N N15 n9 n1 n11 n1 N N n5 39 n6 393 n7 394 n8 395 N19 N n N3 438 N n48 44 N N n45 43 N N n N N69 46 n43 47 N7 N n44 43 N N43 41 n41 4 N44 N n4 45 N N17 n37 n38 N18 N19 n39 n 4 N N191 n33 n34 N19 N193 n35 n 36 N N163 n1 n n3 n4 N N165 n9 n3 N166 N167 n31 n 3 N168 Fgure 7. Macro-element model. Walls 1 and. As sad before, n ths work, probablty densty functons, pdf, are used to defne the most mportant parameters of the model. These functons are characterzed by a mean value and a covarance. The defnton of the mean value of each parameter has been defned usng the opnon of experts, who provded suffcent nformaton for defnng a model. Nevertheless, due to the subjectve character of ths nformaton, the man parameters have been consdered as random varables wth ther uncertantes. The most mportant mechancal propertes of the materals used n the analyss of the buldng of the Example are descrbed below. Masonry Young s modulus of the wall E = N/m Shear modulus G = N/m Shear strength τ = N/m Softenng factor for the pers β p =.5 Softenng factor for the lntels β d =.5 Cast ron columns Young s modulus E s = N/m Specfc weght γ s = 785 kg/m 3 Concrete columns Young s modulus E h = N/m Specfc weght γ h = 5 kg/m 3 Slabs Young s modulus n the man drecton E 1 = N/m Young s modulus n the orthogonal drecton E = N/m Shear modulus G = N/m Among all these characterstcs, those shown n Table 1 have been defned as random varables because they have an mportant nfluence on the structural response of ths type of buldngs. The normal probablty dstrbuton functon has been used for the three varables, where the mean value of each

10 parameter corresponds to the values proposed by experts. The covarance has been defned n such a way to cover a reasonable varaton range for each parameter. Table 1. Probablty dstrbuton functons for random varables. Mean value and covarance. Parameter fdp Mean Covarance Young s modulus E Normal.11 9 N/m.3 Shear strength τ Normal N/m.3 Softenng factor β p Normal.5.3 Capacty curve The capacty curve generally corresponds to the frst mode of vbraton of the structure, based on the assumpton that the fundamental mode of vbraton contans the predomnant response of the structure. In the case of the analyzed buldng, a force dstrbuton was establshed correspondng to the bendng modal shape orented along the y axs. Therefore, the walls 9, 1, 11, 1, 13 and 14 are nvolved n the analyss (see Fgure 7). However, for the sake of smplcty, the loads only wll be appled to the walls 9 and 14, whch really provde the greater stffness n that drecton. Fgure 8. Mean, mean + 1σ and mean 1σ capacty spectra. The capacty curve s obtaned by performng a pushover analyss wth ths load pattern. Ths curve descrbes the relatonshp between base shear and the roof dsplacement of an equvalent sngle degree of freedom model, characterzed by the perod and the modal mass of the thrd mode of vbraton. The response of the model of the typcal URM buldng s defned by means of the capacty curves obtaned by means of the Monte Carlo smulaton technque. Thus, 1 samples for each varable were generated and a structural model was defned for each sample group. One hundred capacty curves were thus obtaned. The advanced computatonal tool STAC [8] has been used n the smulaton process. Fgure 8 shows the mean capacty spectra together wth ther standard devatons. Ths type of the representaton shows the senstvty of these methods to the uncertantes n the structural parameters. The blnear representaton s obtaned for these three spectra usng the values of the spectral dsplacement and acceleraton for the yeldng pont ( D y, S ) ay and for the pont of the ultmate capacty ( D u ), Sau. Table shows these values for the mean capacty spectrum.

11 Table. Blnear representaton parameters of the capacty spectrum. Capacty Spectrum D y ( cm) ( g) D ( cm ) u ( g) S ay S au x DAMAGE STATE LIMITS In order to obtan the damage state lmts or the performance levels of the URM buldng of the Example, there are nether laboratory tests nor avalable values calbrated from observed damage durng earthquakes. Addtonally, the values of the mechancal propertes of the materals used n ths structural typology are not completely known. Takng nto account all these aspects, the thresholds of the spectral dsplacement for the dscrete damage states are defned based on the blnear representaton of the capacty spectrum. Table 3 shows the expressons proposed by Lagomarsno [9] to defne the varaton ntervals of the spectral dsplacement for the fve damage states here consdered: no damage, slght, moderate, severe and complete. Table 3. Spectral dsplacement for the damage states [9, 1]. Damage state Spectral dsplacement, S d No damage d <.7D Slght.7D y Moderate Dy Extensve D.5( D D ) y u y S y < d S D y S D +.5( D D ) < d + < S d Complete S d > y u y Startng from the expressons of Table 3 and usng the values of D y and D u obtaned for the sx-story buldng (see Table 4), the thresholds of the spectral dsplacement are obtaned for the fve damage states. D u D u Table 4. Thresholds for the spectral dsplacement. Damage state Threshold, S d (cm) No damage Sd <.48 Slght.48 < S d.69 Moderate.69 < S d 1.17 Extensve 1.17 < S d.61 Complete Sd >.61 SEISMIC PERFORMANCE In order to evaluate the sesmc performance of the typcal URM buldng of the Example, the N method proposed by Fajfar [] was used. Startng from a frst verson, publshed n 1987, the method has been

12 revsed and updated to the present verson, n whch the Acceleraton-Dsplacement format s used. Nowadays, the method combnes the vsual representaton advantages of the capacty spectrum method [1] wth the physcal bass of the nelastc demand spectrum [11]. The basc characterstcs of the method are: use of two dfferent mathematcal models, applcaton of the response spectrum, nonlnear statc analyss (pushover analyss) and the selecton of a model, whch takes nto account the cumulatve damage. Ths last aspect s very mportant for exstng buldngs, whch frequently have not been desgned to resst many hysteretc cycles wthn nelastc ranges []. In ths case, two response spectra (one determnstc and one probablstc) have been used to descrbe the sesmc demand. For each of them, the spectral dsplacement demand s obtaned and the performance pont s evaluated (see Table 5). Fgures 9 and 1 show the graphcal representatons of the performance pont correspondng to the determnstc and probablstc cases of the sesmc demand, respectvely. Table 5. Damage state and performance levels. Demand spectrum S d (cm) Damage state Performance levels Determnstc.67 Slght Operatonal Probablstc 1.13 Moderate Lfe-safe.4 S a (g).3 ICC determnstc case spectrum - PGA =.141 g Blnear representaton. Perfomance pont S dp =.67 cm S ap =.1 g S d (cm) Fgure 9. Sesmc performance pont (determnstc case). FRAGILITY CURVES Fraglty curves have been generated startng from the assumpton that the cumulatve probablty of reachng or exceedng a partcular damage state follows a lognormal dstrbuton. Therefore, for a gven spectral dsplacement and damage state, ths probablty can be obtaned by means of the followng equaton:

13 (1) 1 [ ] S d P DS DS / Sd = Φ ln β DS Sd, DS S d, DS s the mean value of the spectral dsplacement at whch the buldng reaches the damage state threshold DS, β ED s the standard devaton of the natural logarthm of ths spectral dsplacement and Φ s the cumulatve standard normal dstrbuton functon. The subscrpt stays for the damage state: slght ( = 1), moderate ( = ), extensve ( = 3) and complete ( = 4). In order to calculate the probabltes startng from the dstrbuton functon Φ[ ] (equaton 1), t s necessary to defne S, and for each damage state. Table 6 and Fgure 11 show the parameters and the fraglty curves obtaned for the studed URM buldng. d ED β ED.5 S a (g).4.3. ICC probablstc case spectrum - PGA =.194 g Blneal representaton Demand spectrum - Ductlty = 1.7 Performance pont S dp = 1.13 cm S ap =.14 g S d (m) Fgure 1. Sesmc performance pont (probablstc case). In order to estmate the expected damage for each sesmc hazard scenaro (determnstc and probablstc), we use the spectral dsplacements n Table 5 and the fraglty curves n Fgure 11 to obtan the probabltes of each damage state. We can see n Fgure 1 how the Slght damage state s the most probable damage state n the determnstc case, whle t s the Severe damage state n the probablstc case. Table 6. Parameters of the lognormal dstrbuton functon. Damage S d, DS β DS state Slght Moderate Extensve Complete.61.65

14 FD = Prob (DS > ds / Sd = Sd ) NO DAMAGE SLIGHT MODERATE EXTENSIVE COMPLETE S d (cm) Fgure 11. Fraglty curves for sx-story URM buldng of the Example. Fgure 1. Damage probabltes for the determnstc and probablstc sesmc scenaros. DISCUSSION AND CONCLUSIONS The sesmc performance of a typcal unrenforced masonry buldng of the Example dstrct n Barcelona, Span, has been analyzed. The capacty of the buldng was studed by usng a structural model, whch uses macro elements for the masonry panels. The expected demand has been defned by two response spectra proposed by the Cartographc Insttute of Catalona. The frst one corresponds to the bggest hstorcal earthquake n the cty (determnstc case) whle the second corresponds to a 475 years return perod earthquake (probablstc case). The mechancal propertes of the materals used for the constructon of the URM buldngs n Barcelona, show a hgh varablty and Monte Carlo smulaton has been performed to take nto account the uncertantes. In ths way we have obtaned mean sesmc capacty curves together wth ther correspondng standard devatons. The results show an mportant dsperson, whch can also be observed n the expected damage. The performance pont of the URM buldng of the Example for the determnstc case remans wthn the elastc range and the most probable damage state s the slght. Nevertheless, when the probablstc case s analyzed, the most probable damage state s the

15 severe or pre-collapse state. Ths stuaton s typcal of areas wth low to moderate sesmc hazard. Any way, n both cases, probablstc and determnstc, we found sgnfcant probabltes for the severe and collapse damage states, ndcatng the hgh vulnerablty of most of the buldngs n the Example dstrct. Ths hgh vulnerablty and expected damage s due to the neglect of any sesmc consderaton n the cty. Ths fact s ncreased because the low sesmc requrements planned n the Spansh sesmc codes for the cty and would result n consderable damage n the case of a relatvely low earthquake. Therefore, an mportant concluson of ths work s that t s very convenent to serously consder retrofttng and upgradng the sesmc performance of the buldngs of the cty, partcularly those whose functon s mportant n the post-earthquake emergency, as for example, hosptals. ACKNOWLEDGMENTS Ths work has been partally sponsored by the Spansh Mnstry of Scence and Technology and wth FEDER funds (projects: REN--174-C5-1/RIES, REN C4-1 y REN-3365/- RIES), by the European Commsson (RISK-UE Project, contract EVK4-CT--14) and by the Cvl Engneerng School of Barcelona (UPC). REFERENCES 1. Irzarry J., Goula X., Roca A. and T. Susagna. Earthquake rsk scenaros for monuments of Barcelona. 13 th World Conference on Earthquake Engneerng. Vancouver B.C. 4. Paper N pp.. Fajfar, P. and Gaspersc, P. The N method for the sesmc damage analyss of RC buldngs. Earthquake Engneerng and Structural Dynamcs 1996, 5: Calv, M. C. A dsplacement-based approach for vulnerablty evaluaton of classes of buldngs, Journal of Earthquake Engneerng 1999, 3 (3): Cd, J. Zonfcacón sísmca de la cudad de Barcelona basada en métodos de smulacón numérca de efectos locales. Tess Doctoral, Unversdad Poltécnca de Cataluña, Barcelona, Galasco, M., Lagomarsno, S. y Penna, A. TREMURI Program: Sesmc Analyser of 3D Masonry Buldngs, Unversdad de Genoa,. 6. Brencch, A. and Lagomarsno, S. A macroelement dynamc model for masonry shear walls, Computer Methods n Structural Masonry-4, edted by G.N.Pande, J. Mddleton and B. Kralj, Gambarotta, L. and Lagomarsno, S. A mcrocrack damage model for brttle materals. Internatonal Journal Solds and Structures 1993, 3: STAC program. Stochastc análss computatonal, Internatonal Center for Numercal Methods n Engneerng (CIMNE), Barcelona,. 9. Lagomarsno, S. and Penna, A. Gudelnes for the mplementaton of the II level vulnerablty methodology. WP4: Vulnerablty assessment of current buldngs. RISK-UE project: An advanced approach to earthquake rsk scenaros wth applcaton to dfferent European towns, Freeman, S. A. Development and use of capacty spectrum method. Proceedngs of the 6 th U. S. Natonal Conference on Earthquake Engneerng, Seattle, EERI. Oakland. 11. Fajfar, P. Capacty spectrum method based on nelastc demand spectra. Earthquake Engneerng and Structural Dynamcs 1999, 8: RISK-UE project. An advanced approach to earthquake rsk scenaros wth applcaton to dfferent European towns, European Commsson, contract EVK4-CT--14, Penna, A A macro-element procedure for the dynamc non-lnear analyss of masonry buldngs, Ph.D. Dssertaton,, Poltecnco d Mlano (n talan). 14. Galasco, A., Lagomarsno S., Penna, A., Resemn, S. Non-lnear sesmc analyss of masonry structures, Proc. 13th WCEE, 4, Vancouver, paper Nº. 843.