Australan Earthquake Engneerng Socety 21 Conference, Perth, Western Australa MR Damper n Reducng Poundng Effect of Base- Isolated RC Hghway Brdges M. Neaz Shekh 1, Jngya Xong 2, and Wehua L 3 1. Senor Lecturer, School of Cvl, Mnng and Envronmental Engneerng, Unversty of Wollongong, NSW 2522, Australa. Emal: mshekh@uow.edu.au 2. Postgraduate student, School of Cvl, Mnng and Envronmental Engneerng, Unversty of Wollongong, NSW 2522, Australa. 3. Assocate Professor, School of Mechancal, Materals and Mechatronc Engneerng, Unversty of Wollongong, NSW 2522, Australa. Emal: wehual@uow.edu.au Abstract Sgnfcant structural damage due to poundng between adjacent superstructures of multspan renforced concrete (RC) hghway brdges has been observed n past earthquakes. Dfferent methods have been proposed n the lterature to mtgate the adverse poundng effect. Ths paper presents an analytcal nvestgaton on the use of magnetorheologcal (MR) dampers n reducng the poundng effect of base-solated mult-span RC hghway brdges. It has been observed that MR damper can effectvely reduce adverse poundng effect. Three control strateges (passve off, passve on, and bang bang control) of MR damper have been nvestgated. Although all the control strateges are found to be effectve, the bang bang control has been observed to be the most effectve. Keywords: MR damper, poundng, hghway brdges, control strateges, earthquakes
1. INTRODUCTION Brdges are consdered one of the most crtcal components of hghway transportaton networks, as closure of a brdge due to partal damage or collapse can dsrupt the total transportaton system. However, earthquakes n the past few decades around the world have demonstrated the vulnerablty of engneered brdges even n the event of a moderate earthquake. In general, brdges lack structural redundancy and hence suffer severe damage whch leads to falure durng earthquakes. A more robust brdge desgn s not consdered economcal or even effectve, unless earthquake nduced forces n the structure are reduced by means of sesmc solaton. Sesmc solaton devces generally used n the brdge decouple the brdge deck from the brdge substructure and hence reduce sesmc forces transmtted to abutments and pers. However, n the event of a moderate to strong earthquake ground moton, the dsplacement demand at the expanson jont of a base-solated mult-span brdge can be many tmes hgher than the clearance between the decks. The phenomenon s commonly known as sesmc poundng. Poundng has been dentfed as one of the man causes of the ntaton of damage and may change the sesmc response of the entre brdge. A number of studes have been conducted to nvestgate the effectveness of structural control devces n reducng the poundng effect of brdges. Jankowsk et al. (2) nvestgated the use of dampers and stffeners, rubber bumpers, crushable devces, and shock transmsson unts to mtgate the poundng effect. Zhu et al. (24) further nvestgated the effectveness of such control devces by 3D non-lnear modellng of a three span elevated steel brdge and observed 5% reducton n structural response. However, proposed control devces make the brdge decks contnuous and may place hgh force demand at brdge pers. The magnetorheologcal (MR) damper, a sem actve control devce, has recently been found to be effectve, based on both analytcal and expermental nvestgaton, to reduce the vbraton of structures under earthquake nduced ground motons (Sreteanu and Stammers, 2; Spencer et al., 1997). The MR damper s an ntellgent devce whch can adjust ts dampng parameters by alterng the magnetc feld n the MR flud. Guo and L (28) nvestgated the possblty of usng MR dampers to reduce the poundng effect of adjacent segments of hghway brdges n extreme earthquake events. They desgned MR damper to trace the nstantaneous optmal control forces for manpulatng the dampers. Later, Guo et al. (29) carred out both analytcal and expermental nvestgatons (shakng table tests) on a 1:2 scaled base-solated brdge model and proposed an optmzaton approach for MR dampers whch can effectvely reduce sesmc poundng effect. The am of ths paper s to nvestgate whether MR dampers wth smple control strateges can effectvely reduce the poundng effect of base-solated mult-span RC hghway brdge. A three- segment base solated mult-span hghway brdge has been modelled usng MATLAB SIMULINK. Three smple control strateges namely, Passve off, passve on and bang bang control strateges have been nvestgated. It has been observed that even smple control strateges can be effectve n reducng the forces generated due to poundng of adjacent superstructure segments.
2. MODELLING FOR POUNDING OF BASE-ISOLATED RC HIGHWAY BRIDGE 2.1 Modellng assumptons The base-solated hghway brdge analysed n ths study conssts of flexble bearngs wth stff pers (Secton 4.1) whose stffness s sgnfcantly hgher than the stffness of flexble bearngs. The contrbuton of brdge pers to the dynamc response of the brdge s consdered small and hence not consdered. The spatal varaton of earthquake ground moton s not consdered crtcal, as the studed brdge s not very long. Also, mult-support ground moton s not consdered crtcal for ths not very long brdge. Hence, the poundng effect s consdered arsng from the dynamc characterstcs of the brdge segments. The poundng effect between the superstructure and abutment s consdered beyond the scope of the paper. 2.2 Smplfed modellng for poundng between adjacent superstructure segments Poundng between adjacent superstructure segments of brdges s a complex phenomenon whch may nvolve plastc deformaton, frcton, local crushng as well as fracture at contact surfaces. Poundng forces act durng tme lapses that are very small compared to the natural vbraton perods of the structures (Vega et al. 29). Moreover, generated stress waves also propagate nto the mpactng bodes. Accurate modellng consderng the factors descrbed above s complcated and consdered not mportant for the scope of ths study. A smplfed modellng approach for poundng between adjacent segments s consdered suffcent. Smplfed modellng for poundng can be developed adoptng ether stereo mechancal approach or contact-element approach. The analyss conducted n ths study s based on contact-element approach because of ts transparency and smplcty n ts mathematcal formulaton. Fgure 1 shows a schematc dagram of the brdge poundng model, based on the contact-element approach. It s assumed that the adjacent segments are connected by a lnear sprng and a damper. m -1 k d m k -1 c k c -1 c Fgure 1: Brdge poundng model based on contact element approach K, c, d are the lnear stffness of the contact sprng, the lnear dampng coeffcent of the dashpot, and the clearance between the (-1) th and th segments, respectvely. Under longtudnal ground moton, the response of each segment s ndependent of each other, unless the relatve dsplacement between the two adjacent segments becomes larger than the
clearance between them, whch s the condton of poundng. The relatve dsplacement can be calculated as: δ( 1, )() t = x 1 () t x () t d (1) Where δ( 1, )() t s the relatve dsplacement between the (-1) th segment and the th segment; x 1 () t and x () t are the dsplacements of the (-1) th segment and the th segment wth respect to the brdge foundaton. The poundng force between the colldng superstructures can be expressed as: F () t = k () t δ ( 1, ) () t + c(t)δ& ( 1, )( t) for δ( 1, )( t) (2) F () t = for δ( 1, )( t) < (3) Where F () t s the poundng force between the (-1) th and the th segments of the brdge. δ& ( 1, )() t s the relatve velocty between adjacent superstructure segments. The poundng effect s appears only when the adjacent segments are n contact. So the stffness of the lnear mpact sprng k () t and the lnear mpact dampng coeffcent c (t) are tme dependent: k () t = k ; c() t = c for δ( 1, )( t) (4) k () t = ; cp, () t = for δ( 1, )( t) < (5) The contact stffness k n equaton 2 s taken to be proportonal to the axal stffness of the contact superstructures (Mason and Kasa,1992): E 1, A 1, k = (6) l 1, The E -1, s the elastc modulus; A -1, s the cross secton area; l -1, s the length of the deck wth small axal stffness. The dampng coeffcent of the mpact model s obtaned from the formula suggested n Anagnostopoulos, 1988. m 1m c = 2 ξ k (7) m + m ln e 1 2 2 ( ln e ) + π j ξ = (8) j Where, ξ s the dampng rato of the th element, whch s correlated wth the coeffcent of resttuton e j. m -1 and m are the mass of the (-1) th and th segment of the superstructure. The values of e j vary from.5 to.75 (Anagnostopoulos, 1988). However, the poundng pattern s not sgnfcantly affected by mpact element dampng (Jankowsk et al. 1998). A base-solated hghway brdge s consttuted by several superstructure segments. Each segment s assumed as a lnear ndependent sngle-degree of freedom system wth lumped mass. By consderng the equlbrum of forces for each degree of freedom, the governng equatons of moton for each superstructure segment can be obtaned as: m & x 1 1 + c x& 1 1 + k1x1 + c ( x& 1 1 ) + k 1( x1 + d1) + c2( x& 1 x& 2 ) + k 2( x1 x2 d2 ) = m1u & g, 1( t).
( x& x& ) + k ( x x + d ) + c ( x& x& ) + k ( x x d ) m u&& ( t) m & x c x& + k x + c = + 1 1 + 1 + 1 + 1 + 1 + 1 3 g,. m & x c x& + k x + c x& x& + k x x + d + c x& + k x d = m u& ( ) ( ) ( ) ( ) ( t) n n + n n n n n n n 1 n n n 1 n n+ 1 n n+ 1 n n+ 1 (9) Where, x, x&, & x, are dsplacement, velocty and acceleraton of the segment relatve to the ground. && x, () t s the nput ground moton acceleraton. g By usng the matrx-vector notaton the governng equaton of moton of the structure n the longtudnal drecton wth the poundng effects can be wrtten as: M X& t + C + C t X& t + K + K t X t + E t d = Mu& t (1) () [ ()] () ( ) P [ ] ( ) ( ) ( ) p M s the mass matrx, C s the dampng matrx, and K s the stffness matrx of the superstructure. In ths study, the dampng and stffness are from the rubber bearng used for base solaton. C P (t) and K P (t) are the contact dampng and stffness matrces due to poundng. X & () t, X & () t, X () t are the acceleraton,velocty and the dsplacement vectors of the segment wth respect to the ground. E P (t) s the of poundng force matrx. Consderng nstallaton of the MR damper, the equaton of the hghway brdge wth MR damper s shown n below: M X& () t + [ C + C P () t ] X& () t + [ K + K p ( t) ] X ( t) + EP ( t) d P+ Fd = Mu& g ( t) (11) Where F d s the control force generated by the MR damper. It depends on the locaton and the type of MR dampers. In ths study MR damper has been nstalled between each superstructure segment and the correspondng cap beam (Fgure 2). The control force provded by the MR damper can act drectly on the superstructure segment to reduce relatve dsplacement and hence the poundng force. Segment P P g n g, n Rubber Bearng MR damper Fgure 2: MR damper between superstructure segment and the cap beam 3. MODELLING OF MR DAMPER 3.1 Behavour of MR damper Magnetorheologcal (MR) dampers, consstng of a fxed orfce damper flled wth a controllable MR flud, are semactve control devces whch offer hghly relable operaton. Even n the case of malfuncton, they become passve dampers. Although the MR damper s
a hghly non-lnear devce, a smple but approprate model for the MR damper can relably predct the behavour of controlled structure. Spencer et al. (1997) proposed a phenomenologcal model based on a Bouc-Wen hysteress model, whch has been adopted heren, that can relably predct the hysteretc behavour over a wde range. In the model, steady-state yeld forces due to the MR damper vary lnearly wth the appled voltage change and have a nonzero ntal value (e. at V). The vscous dampng constant also vares lnearly wth appled voltage. 3.2 Control of MR damper To reduce the poundng between adjacent superstructures, MR dampers are assumed to be nstalled between the decks and the pers of each segment. Three smple control algorthms have been chosen to be tested: Passve off: In passve off, there s no current nput to the MR devce and hence there s no voltage nput. As no magnetc feld acts, the MR flud does not exhbt any magnetorheologcal propertes. Effectvely, MR dampers act as passve dampers. Passve on: In ths control system, the current supply and hence the voltage remans constant. In ths study voltage s kept constant at 2 V. Bang-bang control: Bang-bang control has been used for vbraton control of cable brdges (Jansen and Dyke, 2). The control algorthm swtches between two states wthout any nterval and s related to the dsplacement and velocty of the superstructure segments. When the dsplacement and velocty of the adjacent superstructure segments have the same drecton, the stffness and dampng of the system ncrease and reach the maxmum value (2 V). However, when the dsplacement and velocty of the system have dfferent drectons, the stffness and dampng of the system drop to the mnmum value ( V). The control algorthm can be wrtten as: Vmax x() t x& () t > V() t = (12) Vmn x() t x& () t Where, V() ts the control sgnal. Vmax and Vmn are the maxmum and mnmum value of the nput voltage respectvely. 4. EFFECTIVENESS OF MR DAMPER IN REDUCING POUNDING EFFECT 4.1 Parameter of mult-span RC hghway brdge The brdge model adopted n ths study was developed based on the model orgnally presented by Jankowsk et al. (2). A three-span brdge model has been developed for ths study. Each segment conssts of three equal spans of 4 m long and 14 m wde pre-stressed concrete deck wth a mass of 2x1 4 kg/m. The brdge substructure conssts of RC pers of equal heght of 11.5 m. The brdge deck s supported by two hgh-dampng rubber bearngs. The dampng rato of the bearngs s.14. The expanson jonts between segments are taken as.5 m. As the contrbuton of the brdge per to the total stffness s small, for the
smplcty of the analyses, the stffness contrbuton by the pers s gnored. The stffness of end segments and md segment are consdered as 8.15 x1 7 and 7.19x1 7 N/m, respectvely. Hence, the fundamental vbraton perods of end segments and the md segment are 1.78 s and 1.148 s, respectvely. The contact stffness and dampng coeffcents are calculated as 3.475x1 9 N/m and 1.88 x1 7 N.s/m, calculated based on the structural propertes of the brdge (Equatons 6-7). 4.2 Input Ground Moton records The 194 El Centro (north-south components) are used to demonstrate the effectveness of the MR damper n reducng the poundng effect. The earthquake records have been scaled to obtan the peak ground acceleraton of 8 gal to represent the ground moton of a strong earthquake. 4.3 Response of the brdge wthout control The base solated three-segment RC brdge model wthout the ncluson of the poundng effect (wthout the ncluson of contact element) s frst analysed to evaluate the response of the uncontrolled model n the event of an earthquake ground moton. Fgure 3 shows the tme hstores of the structural responses of the brdge (segment 2) under scaled El Centro earthquake ground moton when poundng has not been consdered n the analyss. It can be seen that the maxmum dsplacement and acceleraton response of the segment are.143 m and 9.6 m/sec 2. The relatve dsplacement between adjacent segments s well above the spacng between them. Dsplacement (m).3.2.1 -.1 -.2 No Poundng Poundng Acceleraton (m/s/s) 4 2-2 No Poundng Poundng -.3 2 4 6 8 1 Poundng Force (MN) 8 6 4 2-4 2 4 6 8 1 Segment 2 (Left) Segment 2 (Rght) 2 4 6 8 1 Fgure 3: Structural response of segment 2 under El Centro earthquake ground moton
The dynamc responses of the uncontrolled brdge model wth poundng effects by applyng the contact pont under El Centro earthquake are also shown n Fgure 3. It can be observed that several sharp peaks appear n the tme hstory responses due to poundng wth the applcaton of contact pont. The segment has been subjected to several collsons on the leftand rght sde of the segment, as evdent n Fgure 3. The peak dsplacement of the response has been reduced from.143 m to.126 m. However, maxmum acceleraton of the segment has been ncreased nearly four tmes from 8.56 m/s 2 to 33.87 m/s 2. The maxmum poundng forces on the left and rght sde of the segment have been observed to be 68.29 and 65.59 MN. Such poundng forces are capable of causng sgnfcant damage to the brdge model consdered heren. 4.4 Response of the brdge wth control by MR damper The advantages of the applcaton of MR dampers n reducng the poundng effect have been nvestgated. The brdge has been analysed for three control strateges: passve off, passve on, and bang-bang control. As mentoned n Secton 3.2, the current s held at the constant values of and 2 V for passve off and passve on MR dampers, respectvely. Fgures 4-6 represent the tme hstores of the structural responses of the brdge under scaled El Centro earthquake ground moton for the three control strateges adopted heren. The dynamc responses of the brdge n the form of peak values have been reported n Table 1. It can be observed from Fgure 4 that peak dsplacement of the brde segment has been reduced from.126 m to.11 m, provdng a 2% reducton wth the nstallaton of passve off MR damper when compared wth uncontrolled response of the brdge segment. Smlarly peak acceleraton of the brdge segment has been reduced from 33.87 m/s 2 to 27.87 m/s 2. The reducton s about 18% (Table 1). Left sde poundng and rght sde poundng forces of the segment have been reduced from 68.29 MN to 53.1 MN and 65.59 MN to 5.22 MN. The acheved reductons are well above 2%. Fgure 5 reveals that structural response of the brdge segment can be sgnfcantly suppressed by the nstallaton of passve on MR dampers. The peak dsplacement and acceleraton of the brdge segment have been reduced from.126 m to.77 m and 33.87 m/s 2 to 18.25 m/se2, provdng reductons of 39% and 46% respectvely (Table 1). Also, left sde and rght sde poundng forces have been reduced from 68.29 MN to 42.66 MN and 65.59 MN to 52.23 MN. The reductons are 38% and 2%, respectvely. Fgure 6 represents the structural response of the brdge wth the nstallaton of MR damper actng on a smple control strategy termed as bang-bang control. It s mportant to note that the maxmum nput current has been consdered as 2 V, smlar to passve on MR damper. Slghtly mproved performance n the reducton of the poundng force has been observed wth the adopted smple control strategy. The peak dsplacement and acceleraton of the brdge segment have been reduced from.126 m to.77 m and 33.87 m/s 2 to 2.25 m/s 2, provdng reductons of 39% and 4% respectvely (Table 1). Left sde and rght sde
poundng forces have been reduced from 68.29 MN to 37.1 MN and 65.59 MN to 44.5 MN. The reductons are 46% and 33%, respectvely. It can be observed from the analyss (Fgures 4-6 and Table 1) that peak dsplacement, acceleraton, and poundng forces can be sgnfcantly reduced by the nstallaton of MR dampers, although poundng forces have not been mtgated fully. It s mportant to note that the scaled El Centro ground moton s representatve of very strong earthquake ground moton. The poundng effect could be completely mtgated f the analyss were conducted for moderate earthquake ground shakng levels. All three control strateges have been found to be effectve n reducng poundng forces generated due to collson between adjacent segments as a result of velocty exchange. Poundng of the brdge model has been observed to be reduced to some extent wth the nstallaton of passve off MR dampers, whch manly provdes addtonal dampng to the model. However, due to low energy dsspaton ablty, consderable poundng forces have been observed for the analysed brdge. Passve on MR dampers have been observed to be effectve n reducng peak dsplacement and acceleraton response of the brdge. Also, sgnfcant reducton of poundng forces has been acheved wth the nstallaton of passve on MR damper. Improved performance has been observed wth the nstallaton of MR dampers adoptng the bang-bang control strategy. It s recommended to extend the study to nvestgate other control strateges whch mght be able to reduce or mtgate the poundng force more effcently. Dsplacement (m).2.1 -.1 Uncontrolled Passve Off Acceleraton (m/s/s) 4 2-2 uncontrolled passve off -.2 2 4 6 8 1-4 2 4 6 8 1 Poundng Force (MN) 1 8 6 4 2 Uncontrolled ( Left) Passve off (Left) Poundng Force (MN) 1 8 6 4 2 Uncontrolled (Rght) Passve Off (Rght) 2 4 6 8 1 2 4 6 8 1 Fgure 4: Structural response of brdge (segment 2) wth MR damper (passve off) under El Centro earthquake ground moton
Dsplacement (m).2.1 -.1 Uncontrolled passve on Acceleraton (m/s/s) 4 2-2 Uncontrolled passve on -.2 2 4 6 8 1-4 2 4 6 8 1 Poundng Force (MN) 1 8 6 4 2 Uncontrolled (Left) Passve on (Left) 2 4 6 8 1 Poundng Force (MN) 1 8 6 4 2 Uncontrolled (Rght) Passve on (Rght) 2 4 6 8 1 Fgure 5: Structural response of brdge (segment 2) wth MR damper (passve on) under El Centro earthquake ground moton Dsplacement (m).2.1 -.1 Uncontrolled Bang bang control Acceleraton (m/s/s) 4 2-2 Uncontrolled Bang bang control -.2 2 4 6 8 1-4 2 4 6 8 1 Poundng Force (MN) 1 8 6 4 2 Uncontrolled (Left) Bang bang control (Left) Poundng Force (MN) 1 8 6 4 2 Uncontrolled (Rght) Bang bang control (Rght) 2 4 6 8 1 2 4 6 8 1 Fgure 6: Structural response of brdge (segment 2) wth MR damper (bang bang control) under El Centro earthquake ground moton
Table 1 Response of the brdge (segment 2) wth MR damper under El Centro earthquake ground moton Earthquake Record The El Centro Earthquake Response Control of MR damper Quantty Wthout Bang-bang Passve off Passve on control control Dsplacement.15.88 ( 17%).75 (29%).64 (39%) (m) -.126 -.11(2%) -.77 (39%) -.77 (39%) Acceleraton 33.87 27.87 (18%) 18.25 (46%) 2.25 (4%) (m/s 2 ) -29.78-22.37 (25%) -21.76 (27%) -18.83 (37%) Left sde of poundng 68.29 53.1 (22%) 42.66 (38%) 37.1 (46%) force(mn) -14.9-1.85 (27%) -5.57 (63%) -6.28 (58%) Rght sde of poundng 65.59 5.22 (23%) 52.32 (2%) 44.5 (33%) force(mn) -14.3-1.6 (24%) -1.74 (23%) -8.79 (37%) N.B. Bold fonts represent absolute maxmum response quanttes. Values wthn bracket represent percentage of reductons. Postve values ndcate response n the drecton of ground moton and negatve values represent response opposte to the drecton of ground moton. 5. CONCLUSIONS Brdges are consdered crtcal components of hghway transportaton systems; however, recent earthquakes have demonstrated ther vulnerablty even n the event of moderate levels of earthquake ground motons. Poundng between superstructure segments s consdered one of the man reasons for damage and collapse of base-solated mult-span RC hghway brdges. A smplfed analytcal model n conjuncton wth MR dampers for poundng between adjacent superstructure segments has been developed. Lnear vsco-elastc contact element approach has been chosen to model the sesmc poundng effect, as the parameter selecton and numercal soluton s easer and transparent n such approach. Analyss of a three-segment brdge shows that poundng can generate sgnfcant force whch may cause damage at the pont of collson. Acceleraton of superstructure segment due to poundng has been observed to be amplfed by several tmes. It has been observed that the sesmc poundng effect can be effectvely reduced by MR dampers. Three control strateges namely, passve off, passve on, and bang-bang control have been nvestgated. The poundng of the superstructure segments can be reduced by passve-off control strategy to some extent due to ther low energy dsspaton ablty. In the case of passve on control strategy, the poundng between adjacent superstructure segments has been reduced effectvely. However, wth ts smple control algorthm, the bang bang control has been found to be the most effectve.
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