機(jī)械設(shè)計(jì)外文翻譯-橋梁使用系統(tǒng)可靠性評(píng)估【中文3359字】【PDF+中文WORD】,中文3359字,PDF+中文WORD,機(jī)械設(shè)計(jì),外文,翻譯,橋梁,使用,系統(tǒng),可靠性,評(píng)估,中文,3359,PDF,WORD Bridge Rating Using System Reliability Assessment.II:Improvements to Bridge Rating PracticesNaiyu Wang,M.ASCE1;Bruce R.Ellingwood,Dist.M.ASCE2;and Abdul-Hamid Zureick,M.ASCE3Abstract:The current bridge-rating process described in AASHTO Manual for Bridge Evaluation,First Edition permits ratings to bedetermined by allowable stress,load factor,or load and resistance factor methods.These three rating methods may lead to different ratedcapacities and posting limits for the same bridge,a situation that has serious implications with regard to public safety and the economic well-being of communities that may be affected by bridge postings or closures.This paper is the second of two papers that summarize a researchprogram to developimprovements to the bridge-rating process by using structural reliability methods.The first paper provided background onthe research program and summarized a coordinated program of load testing and analysis to support the reliability assessment leading to therecommended improvements.This second paper presents the reliability basis for the recommended load rating,develops methods that closelycouple the rating process to the results of in situ inspection and evaluation,and recommends specific improvements to current bridge-ratingmethods in a format that is consistent with the load and resistance factor rating(LRFR)option in the AASHTO Manual for Bridge Evalu-ation.DOI:10.1061/(ASCE)BE.1943-5592.0000171.2011 American Society of Civil Engineers.CE Database subject headings:Concrete bridges;Reinforced concrete;Prestressed concrete;Load factors;Reliability;Steel;Ratings.Author keywords:Bridges(rating);Concrete(reinforced);Concrete(prestressed);Condition assessment;Loads(forces);Reliability;Steel;structural engineering.IntroductionThe AASHTO Manual for Bridge Evaluation(MBE),First Edition(AASHTO 2008)allows bridge ratings to be determined throughthe traditional allowable stress rating(ASR)or load factor rating(LFR)methods or by the more recent load and resistance factorrating(LRFR)method,which is consistent with the AASHTOLRFD Bridge Design Specifications(2007).These three ratingmethods may lead to different rated capacities and posted limitsfor the same bridge(NCHRP 2001;Wang et al.2009),a situationthat cannot be justified from a professional engineering viewpointand has implications for the safety and economic well-being ofthose affected by bridge postings or closures.To address this issue,the Georgia Institute of Technology has conducted a multiyearresearch program aimed at making improvements to the processby which the condition of existing bridge structures in Georgiaare assessed.The end product of this research program is set ofrecommended guidelines for the evaluation of existing bridges(Ellingwood et al.2009).These guidelines are established by a co-ordinated program of load testing and advanced finite-elementmodeling,which have been integrated within a structural reliabilityframework to determine practical bridge-rating methods that areconsistent with those used to develop the AASHTO LRFD BridgeDesign Specifications(AASHTO 2007).It is believed that bridgeconstruction and rating practices are similar enough in other non-seismic areas to make the inferences,conclusions,and recommen-dations valid for large regions in the central and eastern UnitedStates(CEUS).The recent implementation of LRFD and its companion ratingmethod,LRFR,both of which have been supported by structuralreliability methods,enable bridge design and condition assessmentto be placed on a more rational basis.Notwithstanding these ad-vances,improved techniques for evaluating the bridge in its in situcondition would minimize the likelihood of unnecessary posting.For example,material strengths in situ may be vastly different fromthe standardized or nominal values assumed in design and currentrating practices attributable to strength gain of concrete on onehand and deterioration attributable to aggressive attack from physi-cal or chemical mechanisms on the other.Satisfactory performanceof a well-maintained bridge over a period of years of service pro-vides additional information not available at the design stage thatmight be taken into account in making decisions regarding postingor upgrading.Investigating bridge system reliability rather thansolely relying on component-based rating methods may also beof significant benefit.Proper consideration of these factors is likelyto contribute to a more realistic capacity rating of existing bridges.This paper is the second of two companion papers that providethe technical bases for proposed improvements to the current LRFRpractice.The first paper(Wang et al.2011)summarized the currentbridge-rating process and practices in the United States,andpresented the results of a coordinated bridge testing and analysisprogram conducted to support revisions to the current rating pro-cedures.This paper describes the reliability analysis frameworkthat provides the basis for recommended improvements to theMBE and recommends specific improvements to the MBE thataddress the preceding factors.1Senior Structural Engineer,Simpson,Gumpertz,and Heger,Inc.,41Seyon St.,Waltham,MA 02453;formerly,Graduate Research Assistant,School of Civil and Environmental Engineering,Georgia Institute ofTechnology.2Professor,School of Civil and Environmental Engineering,Georgia Institute of Technology,790 Atlantic Dr.,Atlanta,GA 30332-0355(corresponding author).E-mail:ellingwoodgatech.edu3Professor,School of Civil and Environmental Engineering,GeorgiaInstitute of Technology,790 Atlantic Dr.,Atlanta,GA 30332-0355.Note.This manuscript was submitted on March 19,2010;approved onAugust 2,2010;published online on October 14,2011.Discussion periodopen until April 1,2012;separate discussions must be submitted for indi-vidual papers.This paper is part of the Journal of Bridge Engineering,Vol.16,No.6,November 1,2011.ASCE,ISSN 1084-0702/2011/6-863871/$25.00.JOURNAL OF BRIDGE ENGINEERING ASCE/NOVEMBER/DECEMBER 2011/863Downloaded 21 Mar 2012 to 180.95.224.53.Redistribution subject to ASCE license or copyright.Visit http:/www.ascelibrary.orgReliability Bases for Bridge Load RatingBridge design,as codified in the AASHTO-LRFD specifications(2007),is established by modern principles of structural reliabilityanalysis.The process by which existing bridges are rated mustbe consistent with those principles.Uncertainties in the perfor-mance of an existing bridge arise from variations in loads,materialstrength properties,dimensions,natural and artificial hazards,insufficient knowledge,and human errors in design and construc-tion(Ellingwood et al.1982;Galambos et al.1982;Nowak 1999).Probability-based limit states design/evaluation concepts provide arational and powerful theoretical basis for handling these uncertain-ties in bridge evaluation.The limit states for bridge design and evaluation can be definedin the general formGX 01where X X1;X2;X3;Xn=load and resistance randomvariables.On the basis of bridge performance objectives,these limitstates may relate to strength(for public safety)or to excessivedeformation,cracking,wear of the traffic surface,or other sourcesof functional impairment.A state of unsatisfactory performance isdefined,by convention,when GX 0.Thus,the probability offailure can be estimated asPf PGX 0?ZfXxdx2where fXx=joint density function of X;and=failure domain inwhich Gx 0.In modern first-order(FO)reliability analysis(Melchers 1999),Eq.(2)is often approximated byPf?3where =standard normal distribution function;and =reliability index.For well-behaved limit states,Eq.(3)usually isan excellent approximation to Eq.(2),and and Pfcan be usedinterchangeably as reliability measures(Ellingwood 2000).Whenthe failure surface in Eq.(1)is complex or when the reliability of astructural system,in which the structural behavior is modeledthrough finite-element analysis,is of interest,Eq.(2)can be evalu-ated efficiently by Monte Carlo(MC)simulation.The AASHTO LRFD Bridge Design Specifications(2007)areestablished on FO reliability analysis,applied to individual girders(Nowak 1999;Kim and Nowak 1997;Tabsh and Nowak 1991).With the supporting probabilistic modeling of resistance and loadterms(Nowak 1993;Bartlett and McGregor 1996;Moses andVerma 1987),an examination of existing bridge design practicesled to a target reliability index,equal to 3.5 based on a 75-yearservice period(Nowak 1999,Moses 2001).Consistent with suchreliability-based performance objective,the AASHTO-LRFD spec-ifications stipulate that in the design of new bridges1:25D 1:5DA 1:75L I Rn4where D=dead load excluding weight of thewearing surface;DA=weight of the wearing surface(asphalt);(L I)represents live loadincluding impact;Rn=design strength,in which Rn=nominalresistance;and =resistance factor which depends on the particu-lar limit state ofinterest.This equation is familiar to most designers.When the reliability of an existing bridge is considered,allow-ance should be made for the specific knowledge regarding its struc-tural details and past performance.Field inspection data,loadtesting,material tests,or traffic surveys,if available,can be utilizedto modify the probability distributions describing the structuralbehavior and response in Eq.(2).The metric for acceptable perfor-mance is obtained by modifying Eq.(2)to reflect the additionalinformation gatheredPf PGX 0jH?PT5where H represents what is learned from previous successfulperformance,in-service inspection,and supporting in situ testing,if any.The target probability,PT,should depend on the economicsof rehabilitation/repair,consequences of future outages,and thebridge rating sought.In the AASHTO-LRFR method(2007),thetarget for design level checking by using HL-93 load model(at inventory level)is 3.5,which is comparable to the reliabilityfor new bridges,whereas the target for HL-93 operating leveland for legal,and permit loads is reduced to 2.5 owing to thereduced load model and reduced exposure period(5 years)(Moses2001).The presence of H in Eq.(5)is a conceptual departure fromEqs.(2)and(3),which provide the basis for LRFD.For example,traffic demands on bridges located in different places in the high-way system may be different.To take this situation into account,LRFR introduces a set of live-load factors for the legal load rating,which depend on the in situ traffic described by the average dailytruck traffic(ADTT).Furthermore,the component nominal resis-tance in LRFR is factored by a system factor sand a membercondition factor cin addition to the basic resistance factor for a particular component limit state.The system factor dependson the perceived redundancy level of a given bridge in its rating,whereas the condition factor is to account for the bridges site-specific deterioration condition,and purports to include the addi-tional uncertainty because of any deterioration that may be present.The basis for the LRFR tabulated values for cwill be furtherexamined later in this paper.The LRFR option in the AASHTO MBE extends the limit statedesign philosophy to the bridge evaluation process in an attempt toachieve a uniform target level of safety for existing highway bridgesystems.However,the uncertainty models of load and resistanceembedded in the LRFR rating format represent typical values fora large population of bridges involving different materials,con-struction practices,and site-specific traffic conditions.Althoughthe LRFR live-load model has been modified for some of the spe-cific cases as discussed previously,the bridge resistance modelshould also be“customized”for an individual bridge by incorpo-rating available site-specific knowledge to reflect the fact that eachbridge is unique in its as-built condition.A rating procedure thatdoes not incorporate in situ data properly may result in inaccurateratings(and consequent unnecessary rehabilitationor postingcosts)for otherwise well-maintained bridges,as indicated by many loadtests(Nowak and Tharmabala 1988;Bakht and Jaeger 1990;Moseset al.1994;Fu and Tang 1995;Faber et al.2000;Barker 2001;Bhattacharya et al.2005).Improvements in practical guidancewould permit the bridge engineer to include more site-specificknowledge in the bridge-rating process to achieve realistic evalu-ations of the bridge performance.This guidance must have a struc-tural reliability basis.Improvements in Bridge Rating by UsingReliability-Based MethodsIn this section,the bridge ratings in light of the reliability-based updating of in-service strength described in the previoussection are examined.The possibilities of incorporating availablesite-specific data obtained from material tests,load tests,advanced864/JOURNAL OF BRIDGE ENGINEERING ASCE/NOVEMBER/DECEMBER 2011Downloaded 21 Mar 2012 to 180.95.224.53.Redistribution subject to ASCE license or copyright.Visit http:/www.ascelibrary.orgstructural analysis,and successful service performance to make fur-ther recommendations for improving rating analysis are explored.Incorporation of In Situ Material TestingThe companion paper summarized the load test of Bridge ID129-0045,a reinforced concrete T-beam bridge that was designedaccording to the AASHTO 1953 design specification for H-15loading and was constructed in 1957.The specified 28-day com-pression strength of the concrete was 17.2 MPa(2,500 psi),whereas the yield strength of the reinforcement was 276 MPa(40 ksi).The scheduled demolition of this bridge provided an op-portunity to secure drilled cores to determine the statistical proper-ties of the in situ strength of the 51-year old concrete in the bridge.Four-inch diameter drilled cores were taken from the slab of thebridge before its demolition.Seven cores were taken from the slabat seven different locations along both the length and width of thebridge.Cores also were taken from three of the girders that were ingood condition after demolition;these were cut into 203 mm(8-in.)lengths and the jagged ends were smoothed and capped,resultingin a total of 14 girder test cylinders.Tests of these 102 203 mm(4 8 in.)cylinders conformed to ASTM Standard C42(ASTM1995)and the results are presented in Table 1.An analysis of thesedata indicated no statistically significant difference in the concretecompression strength in the girders and slab,and the data weretherefore combined for further analysis.The mean(average)com-pression strength of the concrete is 33 MPa(4,820 psi)and thecoefficient of variation(COV)is 12%,which is representative ofgood-quality concrete(Bartlett and MacGregor 1996).The meanstrength is 1.93 times the specified compressionstrength of the con-crete.This increase in compression strength over a period of morethan 50 years is typical of the increases found for good-quality con-crete by other investigators(Washa and Wendt 1975).If these results are typical of well-maintained older concretebridges,the in situ concrete strength is likely to be substantiallygreater than the 28-day strength that is customarily specified forbridge design or condition evaluation.Accordingly,the bridge en-gineer should be provided incentives in the rating criteria to rate abridge by using the best possible information from in situ materialstrength testing whenever feasible(Ellingwood et al.2009).It iscustomary to base the specified compression strength of concreteon the 10th percentile of a normal distribution of cylinder strengths(Standard 318-05;ACI 2005).A suitable estimate for this 10th per-centile based on a small sample of data is provided byfc?X1?kV6where?X=sample mean;V=sample coefficient of variation;andk p%lower confidence interval on the 10th percentile compres-sion strength.By using the 21 tests from Bridge ID 129-0045 withp%75%as an example,k=1.520(Montgomery 1996)and fccan be expressed as fc 11:520 0:12 4;820 3;941 psi(27.17 MPa),a value that is 58%higher than the 17.2 MPa(2,500 psi)that otherwise would be used in the rating calculations.In the FE modeling of this bridge that preceded these strengthtests,the concrete compression strength was set at 17.2 MPa(2,500 psi),which was the only information available before thematerial test.To determine the impact of using the actual concretestrength in an older bridge on the rating process,the finite-elementmodel was revised to account for the increased concrete compres-sion strength(and the corresponding increase in stiffness)into theanalysis of the bridge.Only a modest enhancement in the estimatedbridge capacity in flexure was obtained,but a 34%increase wasachieved in the shear capacity ratings for the girders by using theresults of Table 1.Bridge System Reliability Assessment on the Basisof Static Push-Down AnalysisAlthough component-based design of a new bridge provides ad-equate safety at reasonable cost,component-based evaluation ofan existing bridge for rating purposes may be overly conservativeand result in unnecessary repair or posting costs.It is preferable toperform load rating regarding bridge posting or road closurethrough a system-level analysis.A properly conducted proof loadtest can be an effective way to learn the bridges structural perfor-mance as a system and to update the bridge load capacity assess-ment in situations in which the analytical approach produces lowratings,or structural analysis is difficult to perform because ofdeterioration or lack of documentation(Saraf and Nowak 1998).However,a proof load test represents a significant investment incapital,time,and personnel,and the trade-off between the informa-tion gain and the riskof damaging the bridge during the test mustbeconsidered.Proof tests are rarely conducted by the state DOTs(Wang et al.2009)for rating purposes.One of the key conclusions from the companion paper(Wanget al.2011),in which bridge response measurements obtained fromthe load tests of the four bridges were compared with the results offinite-element analyses of those bridges with ABAQUS(2006),was that the finite-element modeling procedure was sufficientfor conducting virtual load tests of similar bridges.These virtualload tests can provide the basis for developing recommendationsfor improving guidelines for bridge ratings by using structural reli-ability principles.As noted in the introductory section,such guide-lines require the bridge to be modeled as a structural system toproperly identify the performance limit states on which such guide-lines are to be based.To identify such performance limit states and to gain a realisticappraisal of the conservatism inherent in current bridge design andcondition rating procedures,a series of static push-down analysesof the four bridges was performed.These analyses are aimed atdetermining the actual structural behavior of typical bridges whenloaded well beyond their design limit;as a sidelight,they provideadditional information to support rational evaluation of permit loadapplications(section 6A.4.5 in the Manual of Bridge Evaluation).In a push-down analysis,two rating vehicles are placed side-by-side on the bridge in a position that maximizes the response quan-tity of interest in the evaluation(e.g.,maximum moment,shear,anddeflection).The loads are then scaled upward statically and the per-formance of the bridge system is monitored.The dead weight of thebridge structure is included in the analysis.The response is initiallyelastic.As the static load increases,however,elements of the bridgestructure begin to yield,crack,or buckle,and the generalized load-deflection behavior becomes nonlinear.If the bridge structure isredundant and the structural element behaviors are ductile,substan-tial load redistribution may occur.At some point,however,a smallincrement in static load leads to a large increment in displacement.At that point,the bridge has reached its practical load-carryinglimit,and is at a state of incipient collapse.Table 1.Compression Tests of 4 8 in:Cores Drilled from RC ConcreteBridge(ID 129-0045)SourceNumberAverage(psi)Standarddeviation(psi)Coefficient ofvariationGirder144,8806030.12Slab74,6985730.12Overall214,8205860.12Note:1 psi 6:9 Pa.JOU