DAMAGE IDENTIFICATION IN A BENCHMARK CABLE-STAYED BRIDGE USING

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1 7th European Workshop on Structural Health Montorng July 8-11, La Cté, Nantes, France More Info at Open Access Database DAMAGE IDENTIFICATION IN A BENCHMARK CABLE-STAYED BRIDGE USING THE INTERPOLATION METHOD Marco Domanesch 1, Mara Pna Lmongell 2, Luca Martnell 1 1 Poltecnco d Mlano, DICA, Pazza Leonardo da vnc,32, Mlano 2 Poltecnco d Mlano, ABC, Pazza Leonardo da vnc,32, Mlano maraguseppna.lmongell@polm.t ABSTRACT In ths paper the damage localzaton algorthm based on Operatonal Deformed Shapes (ODS) and known as Interpolaton Damage Detecton Method (IDDM), s appled to the numercal model of a cable stayed brdge. Frequency response functons (FRFs) have been calculated basng on the responses of the brdge to low ntensty sesmc exctaton and used to recover the ODS both n the transversal and n the vertcal drecton. The analyss have been carred n the undamaged confguraton and repeated n several dfferent damaged confguratons Results show that the method s able to provde the correct of damage, provded an accurate estmaton of the ODSs s avalable. KEYWORDS : damage localzaton, cable-stayed brdge, nose, nterpolaton method. INTRODUCTION Long span cable stayed brdges play an mportant role on the socal and economc lfe and are, by all means, strategc structures. Able to span long dstances, they are expected to be able to promse servceablty n dfferent condtons, among the others, after extreme loadng events. In ths lght, damage assessment technques, can gve an mportant contrbuton. One of the major problems n the assessment and calbraton of analytcal methods for damage dentfcaton of large cvl structures and nfrastructures s the scarce avalablty of data recorded on really damaged structures. To overcome ths shortcomng, a detaled fnte element model, able to correctly and relably reproduce the real behavor of the structure under ambent exctaton can be an nvaluable tool enablng the smulaton of several dfferent damage scenaros that can be used to test the performance of any montorng system. Stay cables are the most crtcal load bearng elements for cable-stayed brdges thus the montorng of ther damage state s a very mportant task. In ths paper some prelmnary results on the applcaton of a method of damage localzaton known as Interpolaton Damage Detecton Method (IDDM) are presented wth reference to the numercal model of an exstent cable stayed brdge subject of an nternatonal benchmark. The authors have recently developed a new fnte element model of the benchmark structure addressng new ssues n the smulaton of the brdge dynamc. The numercal model has been used to smulate the structural response of the structure n the undamaged state, and n several dfferent damage states, under a sesmc exctaton havng the ntensty of after-shock events. Earthquake records are the natural accelerograms, as adopted n the orgnal benchmark, appled n a multsupport confguraton of the structure. Basng on responses calculated by the fnte element model, the operatonal deformed shapes of the structure have been calculated and used to check the relablty of the IDDM n detectng damage smulated through a reducton of stffness n a number of stay cables. Several damage scenaros were smulated wth dfferent and severty of damage n order to check the senstvty of the damage dentfcaton method to both the and the severty of damage. Copyrght Inra (2014) 2107

2 1 THE DAMAGE LOCALIZATION METHOD The Interpolaton Damage Detecton Method (IDDM) has been successfully appled for damage localzaton of multstory buldngs [3, 5], supported brdges [4], suspenson brdges [6] and recently extended to the case of two-dmensonal structures [7]. Thanks to ts formulaton based on the detecton of reducton of smoothness n the Operatonal Deformed Shapes (ODS), the IDDM can be appled to any type of structure provded the (ODS) can be estmated accurately n the orgnal and n the damaged confguratons and a proper contnuous functon s used to nterpolate the ODS n order to detect possble reductons of smoothness. The basc dea of the IDDM for beam-lke structures can be descrbed wth reference to Fgure 1. z 1 zl 1 z l z l 1 H, l 1 z H, l z zn z at frequency f z H z splne nterpolaton H z H z profle of recorded FRF s Fgure 1: The nterpolaton error Let z1, zn, be nstrumented of the structure where responses n terms of acceleraton have been recorded. At each frequency value, the set of frequency response functons HR(z) measured at the nstrumented s, gve the operatonal deformed shape (ODS) at that frequency (red dots n Fgure 1). At the l-th zl the FRF can be calculated through the splne nterpolaton usng the followng relatonshp: S zl, f c j, l f z l zl 1 H. (1) 3 j 0 where the coeffcents (c0l, c1l c2l c3l) are calculated from the values of the transfer functons recorded at the other s: c, l g H R zk, l (1) The explct expressons of the coeffcent of the splne functon cj,l n terms of the FRF s are determned mposng contnuty of the splne functon and of ts frst and second dervatve n the knots (that s at the ends of each subnterval). More detals on the splne nterpolaton procedure to calculate acceleraton responses can be found n reference Lmongell (2003). In terms of FRF s the nterpolaton error at z (n the followng the ndex l wll be dropped for clarty of notaton) at the -th frequency value f, s defned as the dfference between the magntudes of recorded and nterpolated frequency response functons: E z, f H z, f H z, f (2) In order to characterze each z wth a sngle error parameter, the norm of the error on the sgnfcant frequency range (that s the frequency range wth a sgnal to nose rato suffcently hgh to allow a correct defnton of the FRF) s calculated: N z z f 1 j 2, (3) The sgnfcant frequency range s selected lmtng the summaton n equaton (3) to the frequency range of the fundamental modes of the structure. Ths frequency range can be tuned basng on vbraton tests carred out on the undamaged structure. 2108

3 If a reducton of stffness (damage) occurs at a certan, the operatonal shapes change n the regon close to that and specfcally ther smoothness decreases due to the dscontnuty of curvature nduced by damage. If the estmaton of the error functon through Eq. (3) s repeated n the baselne (undamaged) and n the nspecton (possbly damaged) confguraton, the dfference z between the two values, denoted respectvely by E0(z) and Ed(z), can provde an ndcaton about the exstence of degradaton at z. An ncrease ( z 0 ) of the nterpolaton error between the reference confguraton and the current confguraton at a staton z,.e., hghlghts a localzed reducton of smoothness and therefore, t s assumed to be a symptom of a local decrease of stffness at z assocated wth the occurrence of damage. Basng on ths assumpton the followng condtons wll be assumed to defne the damage ndex IDI(z): IDI( z) f ( z) 0 (4) IDI z 0 f ( z) 0 In order to remove the effect of random varatons of and assumng a Normal dstrbuton of ths functon, the 98% percentle s assumed as a mnmum value beyond whch no damage s consdered at that. In other words a gven s consdered close to a damaged porton of the structure f the varaton of the nterpolaton error exceeds the calculated n terms of the mean and varance e of the on the populaton of avalable records that s: z E 2 (5) The damage ndex s then defned by the relaton: IDI z E ( z ) 2 (6) 2 THE BILL EMERSON MEMORIAL BRIDGE Ths brdge at the base of ths study s a fan-type cable stayed brdge (Fgure 1) whch crosses the Msssspp Rver near Cape Grardeau (USA) wth a composte concrete-steel deck stffened by two longtudnal steel grders (Fgure 2). Fgure 2: The Bll Emerson Memoral Brdge (Framerotblues, 2007; wth permsson) The brdge s 1206 m long wth a man span length of m. One hundred and twenty eght stays, made of hgh-strength, low-relaxaton steel, are arranged accordng to a fan-type dstrbuton. The smallest cable area s 28.5 cm 2 and the largest cable area s 76.3 cm 2. The deck s supported by two towers n the cable-stayed spans. Twelve addtonal pers support the Illnos approach spans. Each tower has a sold secton below the cap beam, and a hollow secton n the upper porton 2109

4 (Fgure 3). For the out-of-plane behavor, the upper porton of the towers above the cap beams remans nearly elastc wth a sgnfcant margn of safety. The lower porton of the towers, however, lkely experences moderate yeldng out of plane durng the desgn earthquake though the safety of the brdge s not a concern. The n-plane behavor of the two towers s always n the elastc range under the desgn earthquake, wth a large margn of safety. For a more detaled descrpton of the structure, as well as of ts members, the reader s referred to [2]. 3 THE NUMERICAL MODEL OF THE BRIDGE Ths brdge was the subject of a well-known benchmark on brdge control [2]. The model of the cable-stayed brdge s set-up [8, 9, 11] n the ANSYS multpurpose fnte element framework, wth some enhancements wth respect to the orgnal model dstrbuted along wth the benchmark fles. Frstly, the rendton of the numercal model adopted n ths study [10, 11] comprses sol-structure nteracton through the use of mpedance functons and lumped masses, sprngs and dampers actng n the vertcal, transversal and longtudnal drecton at each foundaton (bents and pers). Furthermore the modellng of cables has been enhanced movng from a sngle rod type representaton (also called a one-element cable system) to a descrpton wth sx rope elements for each cable enablng an mproved modellng of the stays-deck coupled response. The non-lnearty between deformatons and dsplacements s also accounted for by evaluatng the dynamc equlbrum of the structure at any nstant n the deformed confguraton. The resultng fnte element mesh n ANSYS [1] comprses (Fgure 4) lnear beam elements for towers and the deck frame, lnear shells elements for the concrete deck slab, tenson only elements for the stay cables, for a total number of about 2600 nodes and 2800 elements. The materals are characterzed as lnear elastc. Hgh performance concrete s adopted for the pers (E= 50 GPa); hgh-strength, low-relaxaton steel for the stay cables (E= 210 GPa). The mxed structure of the deck (steel frame wth concrete slab) s modeled by concrete shell elements connected to steel beams. The two materals retan the specfed characterstcs. A structural dampng equal to 3% of the crtcal one s assgned to the brdge model as a Raylegh type dampng computed between the frst (0.28s) and the sxth (0.64s) mode, ensurng reasonable values of the dampng ratos for the modes whch contrbute the most to the sesmc response. (a) (b) c) Fgure 3: a) Deck cross-secton. b) Towers elevaton c) FEM model. 2110

5 The 3-D response and behavor of the cable-stayed brdge model s such that the vbraton modes are characterzed by coupled shapes. The dynamc characterstcs of the brdge also ndcate that the cable-stayed structure s more flexble n the vertcal drecton and less so n the longtudnal drecton. In order to verfy the feasblty of the IDDM for ths type of structure, the Frequency Response Functons must be calculated to obtan the Operatonal Deformed Shapes. To ths am any type of known exctaton could be appled n order to calculate the FRFs. Heren a sesmc type exctaton s appled at the support of the brdge (base of towers and bents) n a mult-support confguraton, accountng for a tme delay due to wave propagaton. The sgnal recorded durng the Gebze earthquake (recorded at the Gebze Tubtak Marmara Arastrma Merkez on Aug. 17, 1999) scaled to a peak accekeraton of 0.02g was used as nput [9]. The scalng of the nput to a low value of the peak acceleraton s meant to smulate the acquston of nformaton from responses nduced by after-shocks not lkely to nduce (addtonal) damage to the structure or to nduce strong non-lnear behavor of the structure and of the dsspatve control devces, thus keepng the structural response n the lnear range. 4 SIMULATED DAMAGE SCENARIOS Stay cables are the key components n cable-stayed brdges bearng most of the weght of deck hence the prompt dentfcaton of damage n these structural elements s of paramount mportance for a proper post-event strategy of nterventon and mantenance. Due to the large number of stay cables n one cable stayed brdge, a montorng technque able to gve ndcaton about the of a damaged stay cable wthout requrng the placement of sensors on each cable would allow the optmzaton of the montorng system reducng the costs. Fgure 4: Damage scenaros Damage to cable stays s one of the most dffcult to dentfy due to ts local character that needs the dentfcaton and the analyss of hgher modes, usually the most dffcult to detect relably. In ths paper n order to check the senstvty of the IDDM the method s tested aganst ths very challengng task of damage detecton n stays. Damage has been smulated by reducng the transversal secton of 3 adjacent stays of 10%, 25% and 50% of the orgnal secton. Two dfferent damage s have been consdered (see Fgure 4): poston 1 s located at half span between Bent 1 and Per 2; poston 2 s placed between 1/4 and 1/3 of the central span, close to Per 2. The name of each damage scenaro ndcates the (1 or 2) of the damaged stays and the amount of secton reducton. For example scenaro C1_10 corresponds to a 10% reducton of the transversal secton of three stays at 1. Both sngle (only one damaged ) and multple (two damaged s) damage scenaros have been consdered. 5 DISCUSSION OF RESULTS Responses calculated by the fnte element model have been used to check the relablty of the IDDM n locatng the damaged porton of the brdge. The operatonal deformed shapes of the deck n the transversal and n the vertcal drectons of the brdge are reported respectvely n Fgure 5 lmted to the frequency range 0-2Hz. The ODSs have been obtaned from the Frequency Response 2111

6 Functons calculated from the responses at the nodes of the deck n the transversal and n the vertcal drecton. In order to gve a measure of the severty of damage related to the consdered scenaros, n columns 3 to 11 of Table 1, are reported the percentage varatons f=(f-fo)/fo of the frequences wth respect to ther value fo n the undamaged confguraton, of the frst 10 modes that mostly contrbute to the response n the vertcal or transversal drecton. node f [Hz] node f [Hz] Transversal Vertcal Fgure 5: Operatonal deformed shapes of the brdge deck for frequences n the range 0-2 Hz. The hghest varaton s found for the most severe scenaro (C1_2_50) correspondng to a reducton of 50% of stffness n 6 cables of the brdge. In ths case a varaton of 0.61% of the modal frequency of the 10 th mode s found. These varatons of frequency are very low and would hardly allow the detecton of damage, not to consder that n a real case nose would affect the estmaton of modal parameters thus completely hamperng the dentfcaton of damage through the estmated values of modal frequences. Table 1: Percentage varaton of modal frequences. M fo[hz] C1_10 C1_25 C1_50 C2_10 C2_25 C2_50 C12_10 C12_25 C12_50 dr V T T V V V V T T T On the contrary, under the same assumptons, that s neglectng the effect of nose n recorded data, the IDDM allows both the detecton and the localzaton of damage for the all the consdered damage scenaros. The IDDM has been appled usng responses n both the transversal and the vertcal drecton for all the consdered damage scenaros but due to space lmtaton only a selecton of results s reported heren. Fgure 6 reports the results relevant to the worst cases from a damage detecton pont of vew that s the ones correspondng to the lower severty of damage and specfcally scenaros C1_10, C2_10 and C12_

7 EWSHM Nantes, France C1_10 damage 1.4E-02 C1_10 damage a) (d) C2_10 damage 4.5E E-03 C2_10 damage 3.0E E E E E E E+00 (b) (e) C1_2_10 damage 1.4E-02 C1_2_10 damage (c) Fgure 6. Damage parameter and for the three damage scenaros C1_10, C2_10, C12_10. a) b) c) FRF n the transversal drecton d) e) f) TF n the vertcal drecton. The values of the s, calculated basng on FRF recovered from transversal (T) are reported n Fgure 6 a,b,c. The IDDM has been appled also usng the transmssblty functons of the vertcal responses at the nodes wth respect to the vertcal response measured at a reference node. As reference has been assumed the node located on the secton of the deck correspondng to Per2. Results are reported n Fgure 6a to 6f for scenaros C1_10, C2_10 and C1_2_10. In the fgures a blue vertcal bar ndcates the actual of damage assumed at the node jonng the deck wth the damaged stay. The red dotted bar represents the correspondng to the 98% percentle of the dstrbuton. Ths defnes the mnmum value that the (z) has to reach n order to tag z as close (f) 2113

8 to a damaged porton of the structure. In all cases, even f damage s very low (10% reducton of transversal secton) the damaged secton s correctly dentfed. Of course the method s not able to ndcate f the damage s located n the deck or n the cables, snce only responses on the deck were consdered n the procedure, but the damaged porton of the structure s correctly dentfed. The procedure shows a good accuracy and relablty beng able to correctly locate damage n all the consdered cases. Results obtaned usng FRFs calculated wth respect to the base nput shown a hgher degree of relablty wth respect to those calculated basng on transmssblty functons. In the second case functon presents values greater than zero at several non-damaged nodes and ths, for the case C12_10 hampers damage detecton at 2 f the percentle of 98% s consdered. 6. CONCLUSIONS The Interpolaton Damage Detecton Method was appled to detect damage n stays usng the numercal model of the Bll Emerson Memoral cable stayed brdge. Results show that, f the Frequency Response functons can be accurately estmated, the method s successful n detectng small and localzed damages. Ths result can be accomplshed usng both Frequency Response Functons of the responses calculated wth respect to the base nput, both usng Transmssblty Functons calculated wth respect to the response at a reference node. In the frst case a hgher relablty of results s obtaned: the actual of damage s correctly dentfed n all cases and also for multple damaged s. REFERENCES [1] ANSYS. (2011). Academc release 12 user manual, ANSYS, Canonsburg, PA. [2] Cacedo, J. M., Dyke, S. J., Moon, S. J., Bergman, L. A., Turan, G., and Hague, S. (2003). Phase II benchmark control problem for sesmc response of cable-stayed brdges. J. Struct. Control, 10(3 4), [3] Lmongell, M.P., (2014). Sesmc health montorng of an nstrumented multstorey buldng usng the Interpolaton Method. Earthquake Engng. Struct. Dyn. do: /eqe [4] Lmongell M.P. (2010). Frequency response functon nterpolaton for damage detecton under changng envronment. MSSP do: /j.ymssp [5] Lmongell, M.P., (2011). The nterpolaton damage detecton method for frames under sesmc exctaton. Journal of Sound and Vbraton, [6] Domanesch M., Lmongell M.P., Martnell L., (2012). Damage detecton n a suspenson brdge model usng the Interpolaton Damage Detecton Method Brdge Mantenance, Safety, Management, Reslence and Sustanablty Bondn & Frangopol (Eds) 2012 Taylor & Francs Group, London, ISBN [7] Lmongell M.P. (2014). Two dmensonal damage localzaton usng the nterpolaton method. Submtted to Journal of Sound and Vbratons. [8] M. Domanesch, L. Martnell (2012), Performance Comparson of Passve Control Schemes for the Numercally Improved ASCE Cable-Stayed Brdge Model, Earthquakes and Structures, 3(2): Techno Press. ISSN: (Prnt), ISSN: (Onlne). [9] M. Domanesch, L. Martnell (2014), Deepenng the ASCE brdge benchmark: transversal response under sesmc loadng, Journal of Brdge Engneerng ASCE, 19 (3), art. no DOI: /(ASCE)BE [10] M. Domanesch, M.P. Lmongell, L. Martnell (2013), Vbraton Based Damage Localzaton Usng MEMS on a Suspenson Brdge Mod2012el, Smart Structures and Systems, 12(6), [11] M. Ismal, J. Rodellar, G. Carusone, M. Domanesch, L. Martnell (2013), Characterzaton, modelng and assessment of Roll-N-Cage solator usng the cable-stayed brdge benchmark, Acta Mechanca, 224,