MEASUREMENTS OF THE FREE VIBRATION RESPONSE OF THE ASINELLI TOWER IN BOLOGNA AND ITS INTERPRETATION

Transcription

1 MEASUREMENTS OF THE FREE VIBRATION RESPONSE OF THE ASINELLI TOWER IN BOLOGNA AND ITS INTERPRETATION Michl PALERMO 1, Riccardo M. AZZARA, Simontta BARACCANI 1, Adriano CAVALIERE 3, Andra MORELLI 3, Stfano SILVESTRI 1, Giada GASPARINI 1, Tomaso TROMBETTI 1, Lucia ZACCARELLI 3 ABSTRACT Sinc th arly 0th cntury th two main towrs of Bologna (Northrn Italy), Asinlli and Garisnda, prhaps th main monumntal landmark of th city, hav bn studid by rsarchrs of th Univrsity of Bologna, in ordr to assss thir structural safty (Cavani 191). Following th two mainshocks of th sismic squnc of Emilia Romagna (Northrn Italy) (May 0th and 9th, 013, rspctivly M 5.9 and 5.8, about 50 km far from Bologna), six sismic stations hav bn installd by th Istituto Nazional di Gofisica Vulcanologia (INGV) insid th two Towrs in ordr to valuat thir sismic rspons, with spcial attntion to th idntification of th fundamntal frquncis. Continuous masurmnts wr carrid out from Jun to Sptmbr 01. During th xprimnt th maximum magnitud arthquak rcordd in th surrounding aras of Bologna was not gratr than M 3.. Dspit this magnitud valu, th lvl of sismic nois background in th cntr of th city is too high to rcord sismograms usful for th analyisiys, thrfor addrssd only to th us of ambint nois. Th prsnt papr provids th first rsults of a joint study dvlopd by INGV and th Univrsity of Bologna aimd at providing an intrprtation of th xprimntal data as obtaind from th continuous monitoring (Azzara t al. 013, 014). In dtail, analysing th fr vibration rspons of th Asinlli Towr, th typical rspons of a crtain class of in-plan asymmtric buildings has bn clarly rcognizd. Starting from th dynamics of in-plan asymmtric buildings, a procdur to stimat th quivalnt ccntricity of masonry towrs is prsntd. Th valuation of th quivalnt ccntricity may b of importanc for th sismic assssmnt of masonry towrs. 1 Univrsity of Bologna, Bologna, Dipartimnto DICAM Istituto Nazional di Gofisica Vulcanologia, Ossrvatorio Sismologico di Arzzo 3 Istituto Nazional di Gofisica Vulcanologia, Szion di Bologna 1

2 INTRODUCTION Th Italian monumntal hritag is worldwid rcognizd as on of th richst and various, thanks to th old history of th country. Among th many symbols of th Italian monumntal hritag, th two mdival towrs of Bologna, th Garisnda and th Asinlli Towrs, locatd in th harth of th town, ar among th most known and attractiv ons [Rovrsi 1989]. Th Asinlli Towr, 97 m tall, was built btwn th XII and XIII cntury, an historical priod charactrizd by strong political dbats, spcially btwn th Church and th Empir. It was commissiond by th on of th most influntial family at th tim, th Asinlli Family, as a symbol of thir powr. During its almost millnnial lif, th Towr was subjctd to various accidnts such as firs (th most dstructiv is datd 1398 and damagd most of th intrnal wood structurs and th slnitic basmnt), lightnings (in 1754 a lightning causd damags to all th uppr part of th towr, for about 30 m of lngth) and arthquaks. Th 1399 arthquak causd th failur of th uppr part of th Towr (th littl bll towr) which was rconstructd. It fll down again during th 1505 Appnnino Modns arthquak. Historical documnts rport that also othr portions of masonry fll down during that arthquak. Bsid natural accidnts, in 1943, during World War II, th Towr was hit by a bomb xplosion occurrd not far from it. In mor rcnt yars (nd of 1990s) th Towr has bn subjctd to strngthning intrvntions as a joint projct btwn th Municipality and th Univrsity of Bologna. Bfor th strngthning, in situ and laboratory tsts wr prformd to charactriz th mchanical proprtis of th masonry. From 011, TECNO IN monitoring systm S.p.A. was commissiond by th Municipality of Bologna to prform ral-tim masurmnts to valuat th static rspons of th towrs rlatd to nvironmntal agnts. (A full dscription of th monitoring systm is availabl on Masurmnts includ dformations across th main cracks through short-bas dformomtrs, dformations of critical portion of masonry through short-bas dformomtrs, tilt masurmnts, strains along th stl tis through strain gags, tmpraturs and wind spd through a mtorological station placd at th top of th Towr. In 01, following th sismic squnc of Emilia Romagna, startd on 0th May with an M 6. arthquak, th Istituto Nazional di Gofisica Vulcanologia (INGV) was calld by th local authoritis to dsign an xprimnt for th dynamical monitoring of th Towrs. At th momnt of prparation of this papr, tha rport containing a dscription of th first rsults of th dynamical monitoring is naring publication on th INGV wbsit. Th objctiv of th prsnt papr is to invstigat on a particular dynamic phnomnon that has bn rcognizd by analyzing th data of th dynamic monitoring. Th phnomnon dals with bat wavs and it was alrady rcognizd by som of th authors studying th bhaviour of planar asymmtric systms. THE ASINELLI TOWER Th Asinlli Towr is a 97 m high masonry towr with an inclination of 1.7 (corrsponding to a ovrhanging of.5 m) along th Wst dirction (Figur 1). Th towr cross sction dimnsion (almost squar along th ntir hight) gradually dcras (almost linarly) from 8.5m sid lngth at th bas to 6.0m at th top, xcpting a suddn discontinuity at a hight of 34 m. Th xtrnal walls ar ralizd according to th a sacco tchniqu (Figur 1): two skins of brick masonry with an

3 intrnal rubbl and mortar fill. Th fill is composd of irrgular matrials including brick fragmnts and irrgular stons bound by arial mortar. Common solid bricks ar usd for th outr skins, whil th basmnt is ralizd with slnitic bricks. Th wall thicknss (th two skins plus th intrnal fill) also gradually dcrass from 3.15 m at th bas to 0.45 m at th top, xcpting for thr main discontinuitis at 11.5 m, 34.0 m and 56.0 m. Th masonry assmblis ar not rgular, with variations in both th width of th bricks and th thicknss of th mortar (from 1.0 cm to 3.0 cm). Limitd in-tsts and laboratory tsts wr prformd in ordr to charactriz th matrial proprtis of th towr. In-situ tsts includd flat jack dformability tsts (on comprssion tst and two shar tsts) according to ASTM 1197C standard and pointing hardnss tsts (six tsts: on on th intrnal wall and 5 on th xtrnal walls) with th hammr pndulum (RILEM TC17MS D.,. Laboratory tsts wr prformd on masonry cors and includd comprssion tsts and masurmnts of dnsity. Th brick showd a comprssion strngth around 10 MPa and a Young s modulus of approximatly 8000 MPa. On avrag, th rsults of th analyss of th cors rval that th intrnal portion of th masonry ( sacco ) is charactrizd by a comprssion strngth of 4 MPa and a Young s modulus of 500 MPa. It has to b notd that th basmnt sms to hav highr mchanical proprtis (a comprssiv strngth of 6 MPa and a Young s moduls of 4000 MPa). Dnsity masurmnts providd th following valus: -4 kn/m 3 for th slnitic bricks at th bas; kn/m 3 for th masonry bricks and m 3 for th intrnal fill. No masurmnts of tnsil strngths and Poisson s cofficints ar availabl and no xprimntal data ar availabl for th slnitic basmnt at all. Valus obtaind from xprimntal tsts (unpublishd rsults of tsts commissiond by th Univrsity of Bologna) on th slnitic basmnt of th nar Garisnda towr (comprssiv strngth qual to 11.9 MPa) may b considrd as rasonabl. (a) Figur 1. (a) Th Asinlli Towr lvation with th indication of th main discontinuitis. (b) A schmatic viw (vrtical cross-sction) of th a sacco masonry. (b)

4 THE EXPERIMENT CONDUCTED BY THE INGV Four sismic stations wr installd insid th Asinlli Towr. All th stations wr quippd with triaxial sismomtrs (Lnnartz L3d5s, 0. Hz ignfrquncy) coupld to AD 4-bit convrtrs (Rftk 7A/07). Data, sampld at 00 sps, wr continuously rcordd from th Jun 01 to 17h Sptmbr 01. Th location of th thr sits was drivn by considrations about th obsrvd structural changs along th Towr and on th rsults of studis conductd by th Univrsity of Modna about th slop of th Towr (Brtacchini t al. 010). Th sismic stations wr locatd at 35 m, 70 m and on at th top. Th fourth station was installd at th basmnt. Although th sismic squnc in Emilia-Romagna was activ during th monitoring intrval but no arthquak was ffctivly rcordd du to th strong sismic nois background of th city cntr. Thrfor th usd datast consists ssntially of sismic ambint nois: th ground vibration inducd by natural or artificial sourcs that propagat along th towrs. Avrag hourly Fast Fourir Transform (FFT) has bn computd in ordr to stimat th Towr frquncis of vibration (Figur a). Th xprimntal frquncis show a good agrmnt with thos stimatd through FE modls (Cccoli t al. 011). Th first thr flxural frquncis fall within th rang of Hz, Hz and Hz, rspctivly. Looking at th spctra and focusing in th frquncy rang btwn and 3 Hz, it is possibl to idntify a small frquncy pak that, in agrmnt with th rsults of FE modls (Cccoli t al. 011), could b associatd to th first torsional mod. In ordr to bttr discriminat th rotational componnt from th translational componnts two othr sismic stations hav bn installd at th top of Asinlli. Th two stations, gographically orintd, wr placd at opposit cornrs of th summit trrac. Figur b shows th dconvolution of th vrtical componnt (that should not b influncd by torsional motion) from th anti-corrlatd portion of th signal rcordd by th two sismic stations. Th torsional frquncy falls in th rang Hz fitting th rsults obtaind by th thortical modls (Cccoli t al. 011). THE TOWER DYNAMIC RESPONSE IN FREE VIBRATION Sismic continuous monitoring has allowd to rcogniz th occurrnc of frqunt transints propagating along th towrs that can b probably ascribd to th passag of havy vhicls along th strts surrounding th towr. Th oscillation producs a clar ffct of dampd bating (Figur 3) whos duration and amplitud can b rlatd to th amplitud of th triggring signal. Th frquncy of th bat and th damping ratio can b rlatd to th physical and gomtric proprtis of th structur, undrstanding th mchanism and modlling th phnomnon can hlp to bttr invstigat th dynamical bhaviour of th Towr. Figur. (a) Avrag hourly FFT computd on th two horizontal componnts; (b) Spctral ratio btwn th anti-corrlatd horizontal signal rcordd by two sismic station installd at th top of th Asinlli Towr. 4

5 Figur 3. Batings phnomnon inducd by a transint signal as rcordd at th top of th towr. It is worth to not that, in gnral, th ratio btwn th fundamntal torsional and latral priods (rfrrd to as torsional-to-latral frquncy ratio, Ω θ, s Chopra 1995) of a uniform (i.. constant gomtrical and mchanical proprtis along th hight) towr can b stimatd using th following rlationship (Dn Hartog 1947): 1,t l J t 1,f (1 ) J (1) whr J / A is th radius of inrtia of th cross sction of th towr. Typically, /l ratios vary btwn 0.01 (for slndr towrs) and 0.06 (for squat towr) lading to torsional-to-latral frquncy ratios btwn 3.0 to 0.0 (assuming a Poisson s cofficint of 0.). Ths valus ar common for high torsionally-stiff structurs. From a rcordd displacmnt rspons (as th on displayd in Figur 3) th following information can b asily masurd/obtaind (Figur 4): Numbr of fast oscillations includd in a slow oscillation: fast () N slow whr ω fast and ω slow ar th frquncy of th fast and slow oscillations, rspctivly. Th ratio btwn th minimum and th maximum amplituds of th ocsillation within an ntir slow oscillation j: R u / u (3) min, j max, j Figur 4. th graphical rprsntation of th information which can obtaind from th rcordd displacmnt rspons.

6 R is clarly btwn 0.0 and 1.0 th quivalnt damping ratio (logarithmic dcrmnt mthod Chopra 1995): 1 u max, j ln n u max, jn (4) THE DYNAMIC BEHAVIOUR OF IN-PLAN ASYMMETRIC SYSTEMS Th dynamic bhaviour of ccntric structurs has bn th objctiv of xtnsiv rsarch sinc th lat 1970s (Kan and Chopra 1977, Hjal and Chopra 1987, Rutnbrg 199, Nagarajaiah t al. 1993, Prus and Fajfar 005). In prvious rsarch works (Trombtti and Cont 005, Trombtti t al. 008), som of th authors idntifid a structural paramtr, calld alpha, rlatd to th attitud of on-story torsionally-stiff systms to dvlop a rotational rspons in fr vibration and proposd a simplifid procdur, calld Alpha-mthod, for th stimation of th maximum torsional rspons. Th mthod has bn xtndd to all classs of on-story asymmtric systms, including both torsionally stiff and torsionally flxibl systms (Palrmo t al. 013). Undr th following assumptions: qual total latral stiffnss k along th x- and th y-dirction (i.. k=k x =k y, whr k x and k y ar th translational stiffnss th x- and th y-dirction, rspctivly); th rotational rspons u θ dvlopd undr dynamic xcitation is small nough to allow th approximation u sinu tanu ; th quations of motion for a 3D on-story systm idalization with rigid diaphragm (assumd as a 3-dof systms) can b writtn as follows (with rfrnc to a systm with th origin locatd at th cntr mass CM, s Figur 5 ): m 0 0 u ( ) ( ) x t ux t y ux( t) px( t) 0 m 0 uy ( t) C uy ( t) m L 0 1 x 1 uy ( t) (5) py ( t) 0 0 m u ( t) u ( t) u ( t) p ( t) y x whr: m is th mass of th systm; x =E x /D and y =E y /D ar th rlativ ccntricitis in th x and y-dirction, rspctivly; is th global ccntricity,; D is th quivalnt diagonal qual to 1 (for a rctangular plan D is qual to th diagonal); E x and E y ar th ccntricitis in th x and y-dirction ; [C] is th damping matrix (classical damping is assumd). Valus of paramtr Ω θ sparat planar asymmtric systms in two catgoris: torsionally-stiff systms charactrizd by Ω θ 1.0; torsionally-flxibl systms charactrizd by Ω θ < 1.0. Th undampd fr vibration rspons (from an initial displacmnt a along th y-dirction) of th studid systm is givn by: x y uy ( t) a A1 cos1t cos t A3 cos3t x ux ( t) a A1 cos1t cost A3 cos3t (6) a x u ( t) A4 cos 1t cos3t whr A 1, A 3 and A 4 ar dfind as follows (Trombtti and Cont 005): 6

7 and: Figur 5. Plan viw of a on-story ccntric systm. 13 A1 A A L 1 1 / 1/ / 1 L 3 3 / 1/ ar th normalizd (squard) natural frquncis of th systm. In th cas of undampd fr vibrations, th paramtr alpha, rlatd to th ratio btwn th maximum rotational and th maximum longitudinal displacmnt rspons, has bn drivd in a closd-form as a function of and Ω θ (Trombtti and Cont 005): u u u,max y,max L Th dampd fr vibration rspons of th systm rprsntd in Figur 5 is givn by (Trombtti and Cont 005): x y uy ( t) a Exp 1t A1 cosd 1t Exp 1 t cos Dt x + A 3Exp 3 1 tcosd3t (10) ux ( t) a Exp 1t A1 cosd 1t Exp 1 t cosdt A Exp t cos t u () t D a A Exp t t Exp t t x 4 1 cos D1 3 1 cos D3 (7) (8) (9)

8 whr is th damping ratio (constant for all mods); 1 1 and arctan 1 Di i 1 ; i=1,,3. It can b notd that for high torsionally-stiff structurs A 3 is clos to zro (Trombtti and Cont 005) and th displacmnt rsponss uy () t and ux() t givn by Eqs. 6 and 10 can b simplifid as follows: x y uy ( t) a A1 cos1t cos t x (11) ux ( t) a A1 cos1t cost x y uy ( t) a Exp 1t A1 cosd 1t Exp 1 t cos Dt x (1) ux ( t) a Exp 1t A1 cosd 1t Exp 1 tcosdt Eq. 11 is th sum of two undampd SDOF harmonic rspons having frquncis qual to ω 1 and ω whil Eq. 1 is th sum of two dampd SDOF harmonic rspons having (undampd) frquncis qual to ω 1 and ω. Furthrmor for high torsionally-stiff systms A 1 is clos to on, whil 1 is clos (Figur 6). Undr ths two conditions (closly spacd frquncis and similar amplituds): (i) th longitudinal rsponss ux() t and uy () t assum th shap of slow modulatd wavs containing fast modulatd wavs; (ii) whn th nvlop of th longitudinal displacmnt rachs its maximum valu, that of th transvrsal displacmnt is at its minimum and vic vrsa. Th phnomnon is known as bating phnomnon and inducs a mutual nrgy/motion transfr which is maximizd whn x = y (Trombtti and Cont 005). An illustrativ xampl of undampd and dampd bats is shown in Figur 7. A clar similarity btwn th Towr fr vibration rspons and th fr vibration rspons of a 3-dof ccntric systm may b notd by comparing Figur with Figur 7. ; THE EQUIVALENT ECCENTRICTY FROM THE TOWER RESPONSE IN FREE VIBRATION From th analogy btwn th obsrvd dynamic rspons of th Towr and th thortical dynamic rspons of a 3-dof ccntric systm, a simpl procdur for th valuation of th quivalnt ccntricity which mak us of th rcordd data can b dvlopd. From th rlationships btwn N, fast and slow frquncis ω fast and ω slow and ω 1 and ω : (a) (b) Figur 6. (a) A 1 and A 3 vs and Ω θ. (b) Ω 1 vs and Ω θ. 8

9 (a) (b) Figur 7. Fr vibration rspons for a systm charactrizd by 1 =.0 rad/s and 1 =.1 rad/s. (a) undampd fr vibration rspons; (b) dampd fr vibration rspons ( ). N fast slow 1 fast (13) 1 slow and making us of Eq. 8 it is possibl, aftr simpl mathmatical dvlopmnts, to obtain th following clos-form xprssion of N as a function of and Ω θ (Figur 8): / ( 1 1) 1 1 ( 1 1) N (14) / ( 1 1) 1 1 ( 1 1) It can b notd that N rmains quit flat (<10) for larg valus of (>0.3) and limitd torsionally-stiff systms (1.0 < Ω θ <.0). On th contrary, as long as dcrass and/or Ω θ incrass, N grows vry rapidly achiving valus largr than 1000 (maning rally long slow oscillations). For th sak of clarnss, -D curvs rprsntation of N vrsus for slctd Ω θ ar displayd in Figur 9. It can b notd that for N lss than 100 and Ω θ btwn 5 and 15 (typical of masonry towrs) quivalnt ccntricity may bcom quit larg. Onc N is masurd and Ω θ is stimatd (Eq. 1 or similar) Eq. 14 allows to obtain th following clos-form xprssion of th quivalnt ccntricity (Figur 10): ( 1) ( 1) N N N 3 N 1 It can b notd that, for a fixd N, th quivalnt ccntricity incrass almost linarly with Ω θ. On th contrary, for a fixd Ω θ, ccntricity dcrass almost linarly with N. From a thortical point of viw th quivalnt ccntricity may bcom quit larg and vn fall out from th plan of th systm (for a squar plan an quivalnt ccntricity =0.35 lads to E=0.5L ). For th Asinlli Towr, by assuming N around 55 (s Figur 4) and Ω θ around (Eq. 1), Eq. 15 lads to an quivalnt ccntricity qual to Finally, onc th quivalnt ccntricity is valuatd, it is possibl to stimat its two componnts ( x and y ) by comparing th masurd ratio R (Eq. 3) with that obtaind from Eq. 11 (i. from th two componnts of th longitudinal (or transvrsal) displacmnt): A 1 R (16) A 1 (15)

10 (a) (b) Figur 8. N vs and Ω θ. (a) ntir domain; (b) zoom for btwn 0.3 and 0.5 and Ω θ btwn 1.0 and.0. Figur 9. N vs for slctd Ω θ from 5 to 15. (a) (b) Figur 10. vs N and Ω θ : (a) ntir domain; (b) zoom for N btwn 50 and 100 and Ω θ btwn 1.0 and.0. lading to: R 1 x R (1 A ) 1 A 1 1 (17) As an illustrativ xampl Figur 11 displays th intraction btwn x and R for A 1 =

11 Figur 11. x vs r for th cas of A 1 =1.0. CONCLUSIONS In this papr th first rsults of a rsarch work aimd at providing an intrprtation of th data obtaind from th dynamic monitoring of th Asinlli Towr ar prsntd. Th work is th rsult of a joint ffort btwn th INGV which was in charg of carrying out th xprimnts and procssing th data and th Univrsity of Bologna which was in charg of providing a structural intrprtation of th rcordd data. In dtail th prsnt work is mainly focusd on th analysis of th fr vibration rspons of th Towr triggrd by th passag of havy vhicls. Th analyss of th displacmnt rspons allowd to clarly rcogniz bat wavs similar to thos alrady obsrvd by som of th authors studying th dynamic rspons of planar ccntric systms. From this analogy, a simpl mthod for th stimation of th quivalnt ccntricity of th Towr starting from th rcordd rspons in fr vibration has bn dvlopd. ACKNOWLEDGEMENTS Bologna Municipality is gratfully acknowldgd for facilitating th xprimntal work. REFERENCES ASTM C (009). Standard Tst Mthod for In Situ Masurmnt of Masonry Dformability Proprtis Using th Flatjack Mthod. Azzara R M., Zaccarlli L., Morlli A., Trombtti T., Dallavall G., Cavalir A., Dansi S. (014). Sismic monitoring of th Asinlli and Garisnda mdival towrs in Bologna (Italy), an instrumntal contribution to th nginring modling dirctd to thir protction. Procdings of th nd Intrnational Confrnc on protction of historical constructions, 7-9 May 014, in prss. Brtacchini, E., Boni E., Capra A., Castagntti C., Dubbini M. (010). Trrstrial Lasr Scannr for Survying and Monitoring Middl Ag T owrs. In: XXIV FIG Congrss. Sydny, Australia, 010, vol. TS 4D - numbr 4445, p. 1-13, Copnaghn:FIG Fdration INtrnational ds Gomtrs, ISBN: Cccoli, C., Bndtti A., Trombtti T., Silvstri S., Gasparini G., Lomtti A. (011). Valutazion dll carattristich dinamich sismich dlla torr dgli asinlli sita in Bologna, unpublishd manuscript. Chopra A.K. (1995) Dynamics of Structurs: Thory and Applications to th Earthquak Enginring, 3rd Edition. Gol R. K., Chopra, A. K. (1991). Inlastic sismic rspons of on story, asymmtric plan systms: Effcts of systm paramtrs and yilding. Earthquak nginring & structural dynamics, 0(3), 01-. Hjal R., Chopra A.K. (1987) Earthquak rspons of torsionally coupld buildings. Rport UCB/EERC 87/0, Earthquak Enginring Rsarch Cntr, Univrsity of California, Brkly, CA. Kan, C.L., Chopra, A.K. (1987). Linar and non linar arthquak rsponss of simply torsionally coupld systms, Earthquak Enginring Rsarch cntr, Univrsity of California, Brkly, CA, Nagarajaiah S., Rinhorn AM, Constantinou MC. (1993) Torsion in bas isolatd structurs with lastomric

12 isolation systms, Journal of Structural Enginring ASCE 119, Palrmo, M., Silvstri, S., Gasparini, G., & Trombtti, T. (013). Physically-basd prdiction of th maximum cornr displacmnt magnification of on-story ccntric systms. Bulltin of Earthquak Enginring, 11(5), Prus I., Fajfar P (005) On th inlastic torsional rspons of singl-story structurs undr bi-axial xcitation. Earthquak Enginring and Structural Dynamics. 34, RILEM TC 17-MS (001). Non dstructiv tsts for masonry matrials and structurs. Matrials and Structurs, Vol. 34, pp Rovrsi G. L torri di Bologna. Quando prché sorsro, com vnnro costruit, chi l innalzò, com scomparvro, quali sistono ancora, 1989, Edizioni Grafis, Bologna. Rutnbrg, A. (199). Nonlinar rspons of asymmtric building structurs and sismic cods: A stat of th Art. Europan Earthquak Enginring, VI (), Trombtti T., Cont J.P. (005) Nw insight into and simplifid approach to sismic analysis of torsionally coupld on-story, lastic systms. Journal of Sound and Vibration 86,