Risk Based Maintenance Strategy for Coastal Concrete Structures

Transcription

1 10DBMC Internatonal Conférene On Durablty of Bulng Materals an Components Rsk Base Mantenane Strategy for Coastal Conrete Strutures C.Q. L 1, W. Lawanwsut 1, J.J 2 1 Unversty of Dunee, Department of Cvl Engneerng, Dunee, Dunee, UK 2 Zhejang Unversty of Tehnology, The College of Cvl Engneerng an Arhteture, Hangzhou, Zhejang, , P.R. Chna.q.l@unee.a.uk TT4-88 ABSTRACT Corroson of renforng steel n onrete s the omnant ause of premature falures of renfore onrete strutures loate n hlore-laen envronments, leang to ultmate strutural ollapse. It s also observe that some severely eterorate onrete strutures survve for many years wthout mantenane. Ths rases the queston of why an how to mantan orroson affete onrete strutures, n partular n the lmate of the nreasng sarty of resoures. The present paper attempts to formulate a mantenane strategy base on rsk ost optmzaton of the struture urng ts whole serve lfe. A tme-epenent relablty metho s employe to etermne the rsk of attanng eah phase of the serve lfe. To faltate pratal applaton of the formulate mantenane strategy, an algorthm s evelope an programme n a user-frenly manner wth a worke example. A mert of the propose mantenane strategy s that moels use n rsk assessment for orroson affete onrete strutures are relate to some of esgn rtera use by prattoners. It s foun n the paper that there exst an optmal number of mantenanes for rakng an elamnaton that returns the mnmum total ost for the struture of ts whole lfe. The mantenane strategy presente n the paper an help strutural engneers, operators an asset managers evelop a osteffetve management sheme for orroson affete oastal onrete strutures. KEYWORDS Conrete strutures, Mantenane, Renforement orroson, Rsk, Total ost.

2 1 INTRODUCTION Corroson of renforng steel bars [rebar] n onrete s the omnant ause of premature falures of renfore onrete [RC] strutures loate n hlore-laen envronments [ACI C , Broomfel 1997]. The orroson nue strutural eteroraton s a graual proess, onsstng of a few phases urng the serve lfe of RC strutures. These nlue orroson ntaton; onrete rakng; elamnaton an the fnal rupture of the struture [member] ue to loss of strength. Muh of the mantenane for suh strutures s relate to these phases of serve lfe. Wth the nreasng sarty of resoures, any mantenane of eterorate strutures nees to be evaluate osteffetvely, takng nto aount eonom onstrants. One soluton oul be to prolong the overall serve lfe of orroson affete RC strutures by extenng the tme pero of eah phase through ntermeate mantenanes, prove that ther safety s not ompromse. A rsk-ost optmze approah an aheve ths. The ntenton of ths paper s to formulate a mantenane strategy base on rsk ost optmzaton of the struture urng ts whole serve lfe. A performane-base moel s propose to etermne eah phase of serve lfe of orroson affete RC strutures. A tme-epenent relablty metho s employe to etermne the rsk of attanng the lmt state of eah phase. To faltate pratal applaton of the formulate mantenane strategy, an algorthm s evelope. An example s gven to llustrate the applaton of the propose mantenane strategy to RC seawalls. A mert of the propose mantenane strategy s that moels use n rsk assessment for eah phase of serve lfe are retly relate to esgn rtera use by prattoners. The mantenane strategy presente n the paper an help strutural engneers, operators an asset managers make esons wth regar to repars, strengthenng an/or rehabltaton of orroson affete RC strutures. 2 OPTIMISATION FORMULATION In researh projet onute at the Unversty of Dunee, a quanttatve rsk-base mantenane strategy for oastal onrete struture s aopte. The goal s to mantan the safety margn of the struture above a presrbe aeptable level throughout the serve lfe of the struture, whle ntermeate mantenane s arre out to meet the serveablty requrements of the struture. Types of mantenane wll be etermne by types of strutural performane [response], nlung [] superfal pathng for onrete rakng, [] major repar for onrete elamnaton an [] overall strutural strengthenng for rupture [or en of serve lfe]. The attanment of a lmt state at eah phase,.e., rakng, elamnaton or rupture, s quantfe by a probablty p, p or p r, respetvely. Clearly only when p or p s greater than an aeptable lmt respetvely wll the orresponng mantenane be warrante to aheve an ost effetveness. Smlarly, p r has to be smaller than an aeptable lmt to elmnate unue rsk of ollapse. Wth these onstrants, the tme an number of mantenanes an be etermne through onventonal optmzaton n terms of a total ost, C T. Mathematally ths an be expresse as nm n m = 1 = 1 Mnmzng C ( t ) = C ( t ) p ( t ) + C ( t ) p ( t ) + C ( t ) p ( t ) Subjet to T L p ( t ) p, a, p ( t ) p, a, pr ( tl ) pr, a TT4-88, Rsk base mantenane strategy for oastal onrete strutures, C.Q. L, W. Lawanwsut, J.J. [1] where C an C are mantenane osts of rakng an elamnaton an C r s the ost ue to strutural rupture [ollapse]. All osts are relatve to the ntal onstruton ost of the struture so that the ata on osts are relatvely easy to ollet. The esgn varables n ths optmzaton are t, t, tl, n m an n m. The varables t an t are the tme of mantenanes ue to rakng an elamnaton respetvely; t L s the tme of strengthenng or en of serve lfe; n m an n m are the number of mantenanes ue to rakng an elamnaton respetvely at fferent tmes an loatons of a struture. For smplty, nterepenene between rakng an elamnaton s not nlue n r L r L

3 Equaton [1] to aheve effetve pratal applatons as wll be shown n the example, but t an be ealt wth n prnple usng ontonal probablty [Melhers 1999]. In Equaton [1], the probablty terms wth subsrpts a are aeptable lmts. The outputs of the optmzaton wll form the bass of a mantenane strategy for a struture. That s to etermne when [ t or t ] an where [n m or n m ] an what types of mantenane [rakng or elamnaton] are neessary urng the serve lfe of the struture an the assoate onfene of ahevng eah phase of the serve lfe [p, p an p r ]. 3 RISK ASSESSMENT 3.1 Corroson nue onrete rakng Aorng to esgn oes an stanars, e.g., ACI 318 [1999] an BS 8110 [1997], the performane rteron relate to onrete rakng of pratal RC strutures s to lmt the rak wth to an aeptable level. In the theory of strutural relablty, ths rteron s expresse n the form of a lmt state funton as follows G( w, w, = w ( w( [2] r r where w ( s the rak wth [loa effet] at the surfae of onrete over at tme t an w r ( s a rtal lmt for the rak wth. Wth ths lmt state funton, the probablty of strutural falure ue to orroson nue onrete rakng, p (, an be etermne by usng tme-epenent relablty metho [Melhers 1999]. An analytal soluton for uprossng rate problem wth a etermnst threshol has been erve by L an Melhers [1993], therefore p ( an be etermne by t σ w& w( w r µ w( µ w& w( µ w& w( µ w& w( p = + Φ ( φ φ τ σ w( σ w( σ w w t w w t w w t 0 & ( ) σ & ( ) σ & ( ) [3] where φ ( ) an Φ ( ) are the stanar normal ensty funton an the strbuton funton, an enotes the ontonal probablty. When the stohast moel of rak wth s establshe, all the varables n Equaton [3] an be etermne as shown n L an Melhers [1993]. The rak wth w( an be expresse n terms of prmary ontrbutng fators, whh are treate as bas ranom varables. The statsts of w( an be obtane usng the tehnque of Monte Carlo smulaton. By ntroung a ranom varable ξ w n suh a way that ts mean s unty,.e., E( ξ w) = 1, the rak wth w( an be moele as follows w( = w ( ξ [4] w where w ( s treate as a pure tme funton of rak wth. L et al. [2003] evelope an analytal soluton to orroson nue rak wth w, base on frature mehans an the moel of thkwall ylner as shown n Fg. 1 [Bažant 1979; Pantazopoulou an Papoula 2001] 4π ( 2πbf w ( s t = [5] α α (1 υ E )( a / b) + (1 + υ )( b / a) ef where a an b are the nner an outer ra of the thk-wall ylner [Fg. 1], υ s Posson s rato of onrete, E ef s the effetve elast moulus of onrete an f t s the tensle strength. The key varables n Equaton [5] are the thkness of the rng of orroson prouts s, whh s retly TT4-88, Rsk base mantenane strategy for oastal onrete strutures, C.Q. L, W. Lawanwsut, J.J.

4 relate to the orroson rate orr as shown n Lu an Weyers [1998], an the stffness reuton fator α, whh s relate to stress ontons an onrete property an geometry as shown n L et al. [2003]. [a] [b] [] Fgure 1. Shemat representaton of rakng proess. In Equaton [5] the mean an auto-ovarane funtons for w ( are [see, e.g., L an Melhers 1993] µ ( = E[ w( ] = w (. E[ ξ ] w ( [6] C w w = ww ( t, t j 2 w ) = λ ρ w ( t ) w ( t ) [7] w j where ρ w s [auto-]orrelaton oeffent for w ( between two ponts n tme t an t j an λ w s oeffent of varaton for ξ w. Both of an be estmate usng the tehnque of Monte Carlo smulaton. Wth µ w an Cww( t, t j ) an the assumpton of Gaussan proess, the other statstal parameters of w ( an be etermne [L an Melhers 1993]. 3.2 Corroson nue onrete elamnaton The ervaton of the probablty of strutural falure ue to orroson nue onrete elamnaton s smlar to that for rakng falure one a moel for elamnaton s establshe. Conrete elamnates from the struture when the orroson nue raks n the onrete propagate an the neghborng raks jon together to form a frature plane that runs through the rebars. One the frature plane s forme, the onrete over separates from the substrate onrete an falls off. When the followng geometr onton for onrete seton s met [Bažant 1979; L et al. 2004], the raks woul propagate between the rebars an form a frature plane parallel to the surfae of onrete over S D < 2C [8] where S s the spang between rebars, D s the ameter of the rebar an C s the epth of onrete over. Otherwse, the nlne frature plane woul be forme. Ths Seton only onerns wth the elamnaton from a frature plane parallel to the surfae of onrete over. For nlne frature plane, formulae n Bažant [1979] wll be use. For the onrete over to separate from the substrate onrete, ertan rak openng,.e., rak wth, at the frature plane s requre. When the rak wth at any pont along the rak w( r, s larger than a rtal lmt w the layer of onrete [.e., over] wll elamnate at the frature plane. Sne the orroson nue rak s tapere from the rebar [see Fg. 1 []] t s suffent that when the rak wth at the pont that two raks jon together,.e., r = b = S/2, s larger than a rtal lmt the onrete over elamnates. The lmt state funton for ths onton s G( w, w, = w ( w( [9] TT4-88, Rsk base mantenane strategy for oastal onrete strutures, C.Q. L, W. Lawanwsut, J.J.

5 Wth ths lmt state funton, the probablty of strutural falure ue to orroson nue onrete elamnaton an be etermne. The rest s the same as that for rakng falure an hene wll not be repeate here. 3.3 Corroson nue strutural rupture Eventually, the rebar orroson n onrete wll reue the strength of RC strutures an leas to the rupture at the rtal ross-seton of a strutural member. The lmt state funton for strutural rupture an be expresse as G( R, R, = R( R ( [10] a a where R ( s the resual strength at tme t an R a s a mnmum aeptable strength. Equaton [10] represents a typal ownrossng problem n relablty alulaton. Mathematally t has approve [Melhers 1999] that the formulaton an soluton of a ownrossng problem are exatly the same as those of uprossng, when the problem s looke at upse-own. Therefore, p r ( an be etermne one the moel of R ( s establshe. In analogy to the moel for rak wth of Equaton [4], the resual strength R ( an be moele as R( = R s ( ξ [11] R where R s ( s the resual strength at the rtal ross-seton of a strutural member, ξ R s a ranom varable wth E( ξr ) = 1 an λ R. The resual setonal strength R s ( an be expresse, n terms of the net area of rebar (, as A net R ( E, =ψ f [ A ( E, ] [12] s net where f [ ] s prove by stanar onrete esgn oes [e.g., ACI 318, BS 8110]. The use of oe formula an faltate the easy an ret applaton of the evelope moel by prattoners. In Equaton [12], ψ s a oeffent to be etermne from albraton of the oe formula f [ ] aganst ata from ret loang test [L 2003]; an E s a vetor of fators affetng ross-setonal area reuton of the rebar. The most sgnfant fator s the orroson rate orr. The statsts of R ( an be etermne n a smlar way as that of rak wth. 4 WORKED EXAMPLE To llustrate the applaton of the propose mantenane strategy an n partular the evelope algorthm to pratal strutures, a RC seawall s use as an example. As an be seen from the moels of strutural response n eah phase of serve, a key parameter n the moels s the orroson urrent ensty orr. In fat, t s an essental parameter for the assessment of orroson nue strutural eteroraton. The measurement of t, however, s very ste or struture spef an ts auray affets the assessment to a great eal. A omprehensve test on a large sale RC seawalls has been unertaken from whh the orr an be use. Ths s the prmary reason to use a RC seawall as an example here although the ata on orr s stll prelmnary [Table 1]. The wall has a menson of 1000 [we] x 2000 [hgh] x 150 [thk] mm. It s subjete to smulate seawater spray uner smultaneous serve loa of 60% nomnal strength. Other varables of the geometry an materal propertes of the wall are also shown n Table 1. Wth these nputs, the optmze tme an number of rakng an elamnaton mantenanes an the serve lfe an be etermne usng the evelope omputer programme [more etals are referre to L et al. 2004]. The results n Fg. 2 emonstrate TT4-88, Rsk base mantenane strategy for oastal onrete strutures, C.Q. L, W. Lawanwsut, J.J.

6 that the total ost s a funton of the number of rakngs an elamnatons an there exsts a mnmum total ost for a gven aepte rsk. Ths an be the vnaton of the formulaton of Equaton [1]. The results are shown n Fg. 3 [wnow mage]. As an be seen, repars for rakng for fferent rebars [loaton] an at fferent tmes are learly marke. Same s for elamnaton. From Fg. 4, t s of nterest to note that the ost of strutural rupture affets the optmal number of rakng an elamnaton mantenanes. Hgher strutural rupture ost leas to hgher mnmum total ost when the number of rakng an elamnaton mantenanes s small. However, when the number of mantenanes s large, the effet of strutural rupture ost on the mnmum total ost mnshes as shown n Fg. 4. Clearly the nformaton n Fg. 3 an well equp oastal engneers an asset managers wth a ratonal an pratal mantenane strategy for oastal nfrastruture subjet to orroson attaks an thereby prove a ost-effetve asset management sheme. Bas varables Symbol Mean COV Conrete over C 30 mm 0.2 Dameter of rebar D 10 mm 0.15 Thkness of pore ban µm - Effetve moulus of onrete E ef GPa 0.12 Elast moulus of steel E s 200 GPa - Compressve strength of onrete f 30 MPa 0.15 Tensle strength of onrete f t 3.0 MPa 0.2 Yel strength of steel f y 543 MPa 0.15 Corroson urrent ensty orr t Rebar spang s 186 mm - Posson s rato of onrete υ Relatve ost for rakng repar C (0) 10% - Relatve ost for elamnaton repar C (0) 20% - Relatve ost ue to rupture C (0) 10 - Table 1. Values of bas varables r 5 4 Total Cost nm=1 nm=2 nm=3 nm= Number of Crakng Mantenane Fgure 2. Total ost vs. number of rakng an elamnaton mantenane. TT4-88, Rsk base mantenane strategy for oastal onrete strutures, C.Q. L, W. Lawanwsut, J.J.

7 Fgure 3. Outputs of optmzaton wth optmal tme an loaton of rakng an elamnaton [wnow mage]. Total Cost Cr = 10 Cr = 50 Cr = Number of Mantenane Fgure 4. Effet of ost ue to strutural rupture to mnmum total ost. TT4-88, Rsk base mantenane strategy for oastal onrete strutures, C.Q. L, W. Lawanwsut, J.J.

8 5 CONCLUSIONS A rsk ost optmze mantenane strategy for orroson affete onrete strutures has been formulate base on whole lfe behavor of the struture. A performane-base moel for serve lfe preton has also been propose. A tme-epenent relablty metho s employe n the paper to etermne the rsk of attanng the lmt state of eah phase of serve lfe. To faltate pratal applaton of the formulate mantenane strategy, an algorthm has been evelope an programme n a user-frenly manner an on wnow base. The propose mantenane strategy has the avantage that moels use n rsk assessment for eah phase of serve lfe are relate to some of esgn rtera use by prattoners an that multple lmt states for the struture have been onsere n the rskost optmzaton. It has been foun n the paper that there exst an optmal number of mantenanes for rakng an elamnaton that returns the mnmum total ost for the struture of ts whole lfe. It has also been foun that the ost of strutural rupture affets the optmal number of rakng an elamnaton mantenanes. It an be onlue that the propose mantenane strategy an help strutural engneers, operators an asset managers make esons wth regar to repars, strengthenng an/or rehabltaton of orroson affete onrete strutures. 6 ACKNOWLEDGEMENTS Fnanal support from the Royal Aaemy of Engneerng, UK wth Awar No /93 an Australan Researh Counl wth Grant No. LX s gratefully aknowlege. 7 REFERENCES ACI Commttee , Corroson of metals n onrete, ACI Journal, 82[1], ACI , Bulng Coe Requrements for Strutural Conrete wth Commentary, Ameran Conrete Insttute. Bažant, Z.P. 1979, Physal moel for steel orroson n onrete sea strutures applaton, Journal of Strutural Dvson, ASCE, 105[ST6], Broomfel, J. 1997, Corroson of Steel n Conrete, Unerstanng, Investgatng & Repar, E & FN Spon, Lonon. BS , Strutural Use of Conrete Part 1: Coe of Prate for Desgn an Construton, Brtsh Stanars Insttuton. L, C.Q. 2003, Lfe yle moelng of orroson affete onrete strutures propagaton, Journal of Strutural Engneerng, ASCE, 129[6], L, C.Q. & Melhers, R.E. 1993, Outrossngs from onvex polyherons for nonstatonary gaussan proesses, J. Engrg. Meh., ASCE, 119[11], L, C.Q.,, J.J. & Lawanwsut, W. 2004, Conrete elamnaton ause by steel renforement orroson, ACI Strutural Journal (submtte). L, C.Q.,, J.J., Lawanwsut, W. & Chen, Z.J. 2003, An analytal moel for orroson nue rak wth n renfore onrete strutures, ACI Strutural Journal (submtte). L, C.Q., Lawanwsut, W. & Make R.I. 2004, A rsk ost optmze mantenane strategy for orroson affete onrete strutures, Journal of Computer-Ae Cvl an Infrastruture Engneerng (CACAIE), (submtte). Lu, Y. & Weyers, R.E. 1998, Moelng the tme-to-orroson rakng n hlore ontamnate renfore onrete strutures, ACI Materals Journal, 95[6], Melhers, R.E. 1999, Strutural Relablty Analyss an Preton, John Wley an Sons, Chhester. Pantazopoulou, S.J. & Papoula, K.D. 2001, Moelng over-rakng ue to renforement orroson n r strutures, Journal of Engneerng Mehans, ASCE, 127[4], TT4-88, Rsk base mantenane strategy for oastal onrete strutures, C.Q. L, W. Lawanwsut, J.J.